Finite Group Databasebeta

← #8094779

Subgroups — #8094779

Order 512.

6197 conjugacy classes of subgroups.

The subgroup lattice has 2058 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53128C212yesmaximal, complemented
2#53103C212yesmaximal, complemented
3#53098C212yesmaximal, complemented
4#53098C212yesmaximal, complemented
5#53095C212yesmaximal, complemented
6#52988C212yesmaximal, complemented
7#52981C212yesmaximal, complemented
8#52971C212yesmaximal, complemented
9#52347C214yesmaximal, complemented
10#52320C214yesmaximal, complemented
11#46339C212yesmaximal, complemented
12#46339C212yesmaximal, complemented
13#46338C212yesmaximal, complemented
14#46328C212yesmaximal, complemented
15#45701C212yesmaximal, complemented
16#45616C212yesmaximal, complemented
17#45608C212yesmaximal, complemented
18#45563C214yesmaximal, complemented
19#45483C212yesmaximal, complemented
20#45444C214yesmaximal, complemented
21#35563C211yesmaximal, characteristic, complemented
22#35518C211yesmaximal, characteristic, complemented
23#35517C211yesmaximal, characteristic, complemented
24#35513C211yesmaximal, characteristic, complemented
25#35512C211yesmaximal, characteristic, complemented
26#35512C211yesmaximal, characteristic, complemented
27#35267C211yesmaximal, characteristic, complemented
28#35266C211yesmaximal, characteristic, complemented
29#35263C211yesmaximal, characteristic, complemented
30#35252C211yesmaximal, characteristic, complemented
31#35227C211yesmaximal, characteristic, complemented
32#35223C211yesmaximal, characteristic, complemented
33#34936C211yesmaximal, characteristic, complemented
34#34737C211yesmaximal, characteristic, complemented
35C2×#2416C211yesmaximal, characteristic, complemented
36C22×H(5,𝔽2)C2211yescharacteristic
37C2×#560C2214yescomplemented
38C2×#537C2211yescharacteristic
39C2×#535C2211yescharacteristic
40C2×#532C2211yescharacteristic
41C2×#525C2211yescharacteristic
42C2×#525C2211yescharacteristic
43C2×#525C2211yescharacteristic
44C2×#525C2211yescharacteristic
45C2×#525C2211yescharacteristic, complemented
46C2×#525C2211yescharacteristic, complemented
47C22×#121C2211yescharacteristic
48C22×#121C2211yescharacteristic
49C22×#121C2212yescomplemented
50C2×#520C2211yescharacteristic, complemented
51C22×C4×D4C2211yescharacteristic, complemented
52C22×#117C2211yescharacteristic, complemented
53C23×C4⋊C4C2211yescharacteristic, complemented
54#2863C2212yescomplemented
55#2860C2212yescomplemented
56#2860C2212yescomplemented
57#2860C2212yescomplemented
58#2856C2212yescomplemented
59#2855C2212yescomplemented
60#2854C2212yescomplemented
61#2850C2212yescomplemented
62#2849C2214yescomplemented
63#2847C2214yescomplemented
64#2842C2214yescomplemented
65#2837C2214yescomplemented
66#2837C2214yescomplemented
67#2829C2214yescomplemented
68#2829C2214yescomplemented
69#2829C2214yescomplemented
70#2829C2214yescomplemented
71#2828C2214yescomplemented
72#2827C2214yescomplemented
73#2827C2214yescomplemented
74#2826C2214yescomplemented
75#2826C2214yescomplemented
76#2826C2214yescomplemented
77#2825C2214yescomplemented
78#2825C2214yescomplemented
79#2823C2214yescomplemented
80#2815C2214yescomplemented
81#2813C2214yescomplemented
82#2813C2214yescomplemented
83#2812C2214yescomplemented
84#2795C2214yescomplemented
85#2790C2214yescomplemented
86#2790C2214yescomplemented
87#2780C2214yescomplemented
88#2780C2214yescomplemented
89#2756C2214yescomplemented
90#2756C2214yescomplemented
91#2752C2214yescomplemented
92#2749C2214yescomplemented
93#2749C2214yescomplemented
94#2746C2214yescomplemented
95#2746C2214yescomplemented
96#2735C2214yescomplemented
97#2714C2214yescomplemented
98#2714C2214yescomplemented
99#2705C2214yescomplemented
100#2705C2214yescomplemented
101#2703C2214yescomplemented
102#2703C2214yescomplemented
103#2699C2214yescomplemented
104#2699C2214yescomplemented
105#2699C2214yescomplemented
106#2697C2214yescomplemented
107#2697C2214yescomplemented
108#2697C2214yescomplemented
109#2691C2214yescomplemented
110#2691C2214yescomplemented
111#2688C2214yescomplemented
112#2688C2214yescomplemented
113#2685C2214yescomplemented
114#2685C2214yescomplemented
115#2678C2214yescomplemented
116#2678C2214yescomplemented
117#2675C2214yescomplemented
118#2673C2214yescomplemented
119#2673C2214yescomplemented
120#2669C2214yescomplemented
121#2668C2214yescomplemented
122#2668C2214yescomplemented
123#2668C2214yescomplemented
124#2645C2212yescomplemented
125#2644C2212yescomplemented
126#2644C2212yescomplemented
127#2644C2212yescomplemented
128#2625C2212yescomplemented
129#2624C2212yescomplemented
130#2623C2214yescomplemented
131#2620C2212yescomplemented
132#2619C2212yescomplemented
133#2618C2214yescomplemented
134#2542C2211yescharacteristic, complemented
135#2542C2211yescharacteristic, complemented
136#2541C2211yescharacteristic, complemented
137#2541C2211yescharacteristic, complemented
138#2540C2211yescharacteristic, complemented
139#2540C2211yescharacteristic, complemented
140#2540C2211yescharacteristic, complemented
141#2540C2211yescharacteristic, complemented
142#2539C2212yescomplemented
143#2539C2212yescomplemented
144#2538C2212yescomplemented
145#2537C2212yescomplemented
146#2536C2212yescomplemented
147#2535C2212yescomplemented
148#2534C2214yescomplemented
149#2513C2212yescomplemented
150#2513C2212yescomplemented
151#2512C2212yescomplemented
152#2512C2212yescomplemented
153#2510C2214yescomplemented
154#2504C2212yescomplemented
155#2503C2212yescomplemented
156#2502C2212yescomplemented
157#2501C2212yescomplemented
158#2501C2212yescomplemented
159#2498C2214yescomplemented
160#2497C2212yescomplemented
161#2496C2212yescomplemented
162#2495C2212yescomplemented
163#2494C2212yescomplemented
164#2487C2212yescomplemented
165#2487C2212yescomplemented
166#2487C2212yescomplemented
167#2487C2212yescomplemented
168#2486C2212yescomplemented
169#2486C2212yescomplemented
170#2486C2212yescomplemented
171#2486C2212yescomplemented
172#2485C2212yescomplemented
173#2485C2212yescomplemented
174#2485C2212yescomplemented
175#2485C2212yescomplemented
176#2481C2214yescomplemented
177#2480C2214yescomplemented
178#2480C2214yescomplemented
179#2448C2212yescomplemented
180#2447C2212yescomplemented
181#2446C2212yescomplemented
182#2445C2212yescomplemented
183#2444C2214yescomplemented
184#2443C2214yescomplemented
185#2435C2212yescomplemented
186#2433C2212yescomplemented
187#2433C2212yescomplemented
188#2432C2212yescomplemented
189#2431C2212yescomplemented
190#2428C2212yescomplemented
191#2428C2212yescomplemented
192#2426C2212yescomplemented
193#2426C2212yescomplemented
194#2425C2214yescomplemented
195#2424C2214yescomplemented
196#2417C2211yescharacteristic, complemented
197#2417C2212yescomplemented
198#2417C2212yescomplemented
199#2417C2212yescomplemented
200#2417C2212yescomplemented
201#2417C2212yescomplemented
202#2417C2211yescharacteristic, complemented
203#2416C2212yescomplemented
204#2416C2212yescomplemented
205#2416C2212yescomplemented
206#2416C2212yescomplemented
207#2416C2212yescomplemented
208#2416C2212yescomplemented
209#2416C2212yescomplemented
210#2416C2212yescomplemented
211#2416C2212yescomplemented
212#2416C2212yescomplemented
213#2416C2212yescomplemented
214#2416C2212yescomplemented
215#2416C2212yescomplemented
216#2416C2212yescomplemented
217#2416C2212yescomplemented
218#2416C2212yescomplemented
219#2416C2211yescharacteristic, complemented
220#2416C2211yescharacteristic, complemented
221#2416C2212yescomplemented
222#2415C2211yescharacteristic, complemented
223#2415C2212yescomplemented
224#2415C2211yescharacteristic, complemented
225#2414C2211yescharacteristic, complemented
226#2414C2212yescomplemented
227#2414C2212yescomplemented
228#2414C2212yescomplemented
229#2414C2212yescomplemented
230#2414C2212yescomplemented
231#2414C2211yescharacteristic, complemented
232#2413C2212yescomplemented
233#2412C2212yescomplemented
234#2412C2214yescomplemented
235#2411C2214yescomplemented
236#2411C2212yescomplemented
237#2410C2214yes—
238#2410C2214yes—
239#2410C2214yescomplemented
240#2410C2212yescomplemented
241#2408C2212yescomplemented
242#2408C2212yescomplemented
243#2408C2212yescomplemented
244#2408C2212yescomplemented
245#2408C2212yescomplemented
246#2408C2214yescomplemented
247#2408C2212yescomplemented
248#2408C2212yescomplemented
249#2408C2212yescomplemented
250#2408C2212yescomplemented
251#2408C2212yescomplemented
252#2407C2212yescomplemented
253#2407C2212yescomplemented
254#2407C2212yescomplemented
255#2407C2212yescomplemented
256#2407C2212yescomplemented
257#2407C2212yescomplemented
258#2407C2212yescomplemented
259#2407C2212yescomplemented
260#2407C2212yescomplemented
261#2407C2212yescomplemented
262#2405C2214yes—
263#2405C2214yes—
264#2403C2214yes—
265#2403C2214yes—
266#2397C2212yescomplemented
267#2397C2212yescomplemented
268#2392C2212yescomplemented
269#2392C2212yescomplemented
270C2×#396C2212yescomplemented
271C2×#394C2212yescomplemented
272#2377C2214yescomplemented
273#2377C2214yescomplemented
274#2375C2214yescomplemented
275#2317C2211yescharacteristic, complemented
276#2317C2211yescharacteristic, complemented
277#2316C2211yescharacteristic, complemented
278#2316C2211yescharacteristic, complemented
279#2311C2211yescharacteristic
280#2311C2211yescharacteristic
281#2311C2211yescharacteristic
282#2311C2211yescharacteristic
283#2311C2211yescharacteristic
284#2311C2211yescharacteristic, complemented
285#2309C2211yescharacteristic
286#2309C2211yescharacteristic
287C4×#127C2212yescomplemented
288C4×#127C2212yescomplemented
289C4×#121C2212yescomplemented
290C4×#121C2212yescomplemented
291#2297C2211yescharacteristic
292#2296C2211yescharacteristic, complemented
293C2×#390C2211yescharacteristic
294C2×#389C2211yescharacteristic, complemented
295C2×#386C2212yescomplemented
296#2280C2211yescharacteristic, complemented
297C2×#380C2211yescharacteristic, complemented
298C4×#117C2211yescharacteristic, complemented
299C2×H(5,𝔽2)—44no—
300C2×H(5,𝔽2)—44no—
301C2×H(5,𝔽2)—44no—
302C22×#41C2311yescharacteristic
303C22×#41C2311yescharacteristic
304C22×#41C2311yescharacteristic
305C22×#41C2312yes—
306C22×#41C2312yes—
307C23×D4C2311yescharacteristic
308C23×D4C2311yescharacteristic
309C23×D4C2314yes—
310C23×D4C2312yes—
311C23×D4C2312yes—
312C23×D4C2312yes—
313C23×D4C2312yes—
314C24×C4C2311yescharacteristic
315C24×C4C2311yescharacteristic
316C24×C4C2312yes—
317#560—416no—
318#537—44no—
319#535—44no—
320#532—44no—
321C2×C4⋊Q8C2311yescharacteristic
322C2×#127C2312yes—
323C2×#127C2312yes—
324C2×#127C2312yes—
325C2×#127C2311yescharacteristic
326C2×#126C2314yes—
327C2×#126C2314yes—
328C2×#126C2314yes—
329C2×#124C2312yes—
330C2×#124C2311yescharacteristic
331C2×#124C2311yescharacteristic
332#525—44no—
333#525—44no—
334#525—44no—
335#525—44no—
336#525—44no—
337#525—44no—
338C2×#123C2314yes—
339C2×#123C2314yes—
340C2×#123C2312yes—
341C2×#123C2312yes—
342C2×#123C2312yes—
343C2×#123C2312yes—
344C2×#123C2312yes—
345C2×#123C2312yes—
346C2×#123C2314yes—
347C2×#123C2314yes—
348C2×C22⋊Q8C2311yescharacteristic
349C2×C22⋊Q8C2311yescharacteristic
350C2×C22⋊Q8C2311yescharacteristic
351C2×C22⋊Q8C2311yescharacteristic
352C2×C22⋊Q8C2311yescharacteristic
353C2×C22⋊Q8C2311yescharacteristic
354C2×C22⋊Q8C2311yescharacteristic
355C2×C22⋊Q8C2311yescharacteristic
356C2×C22⋊Q8C2311yescharacteristic
357C2×C22⋊Q8C2311yescharacteristic
358C2×C22⋊Q8C2312yes—
359C2×C22⋊Q8C2311yescharacteristic
360C2×C22⋊Q8C2311yescharacteristic
361C2×C22⋊Q8C2312yes—
362C2×#121—44no—
363C2×#121—44no—
364C2×#121—48no—
365C2×#121C2314yes—
366C2×#121C2312yes—
367C2×#121C2314yes—
368C2×#121C2314yes—
369C2×#121C2312yes—
370C2×#121C2311yescharacteristic
371C2×#121C2311yescharacteristic
372C2×#121C2314yes—
373C2×#121C2311yescharacteristic
374C2×#121C2312yes—
375C2×#121C2311yescharacteristic
376C2×#121C2314yes—
377C2×#121C2312yes—
378C2×#121C2312yes—
379C2×#121C2312yes—
380C2×#121C2312yes—
381C2×#121C2312yes—
382C2×#121C2312yes—
383C2×#121C2312yes—
384C2×#121C2312yes—
385C2×#121C2311yescharacteristic
386C2×#121C2311yescharacteristic
387C2×#121C2311yescharacteristic
388C2×#121C2311yescharacteristic
389C2×#121C2311yescharacteristic
390C2×#121C2311yescharacteristic
391C2×#121C2312yes—
392C2×#121C2314yes—
393C2×#121C2314yes—
394C2×#121C2314yes—
395C2×#121C2314yes—
396C2×#121C2312yes—
397C2×#121C2312yes—
398C2×#121C2312yes—
399C2×#121C2311yescharacteristic
400C2×#121C2311yescharacteristic
401C2×#121C2314yes—
402C2×#121C2312yes—
403C2×#121C2314yes—
404C2×#121C2314yes—
405C2×#120C2312yes—
406C2×#120C2312yes—
407C2×#120C2312yes—
408C2×#120C2314yes—
409C2×#120C2312yes—
410C2×#120C2312yes—
411C2×#120C2314yes—
412C2×#120C2314yes—
413C2×#120C2314yes—
414C2×#120C2314yes—
415C2×#120C2312yes—
416C2×#120C2314yes—
417C2×#120C2314yes—
418#520—44no—
419C2×C4×Q8C2312yes—
420C2×C4×D4—44no—
421C2×C4×D4C2311yescharacteristic
422C2×C4×D4C2311yescharacteristic
423C2×C4×D4C2312yes—
424C2×C4×D4C2312yes—
425C2×C4×D4C2312yes—
426C2×C4×D4C2312yes—
427C2×C4×D4C2312yes—
428C2×C4×D4C2312yes—
429C2×C4×D4C2312yes—
430C2×C4×D4C2312yes—
431C2×C4×D4C2312yes—
432C2×C4×D4C2311yescharacteristic
433C2×C4×D4C2311yescharacteristic
434C2×C4×D4C2312yes—
435C2×C4×D4C2312yes—
436C2×C4×D4C2312yes—
437C2×C4×D4C2311yescharacteristic
438C2×C4×D4C2311yescharacteristic
439C2×C4×D4C2312yes—
440C2×C4×D4C2311yescharacteristic
441C2×C4×D4C2311yescharacteristic
442C2×C4×D4C2314yes—
443C2×C4×D4C2312yes—
444C2×C4×D4C2312yes—
445C2×#117—44no—
446C2×#117C2311yescharacteristic
447C2×#117C2311yescharacteristic
448C2×#117C2311yescharacteristic
449C2×#117C2311yescharacteristic
450C2×#117C2311yescharacteristic
451C2×#117C2312yes—
452C2×#117C2312yes—
453C2×#117C2311yescharacteristic
454C2×#117C2311yescharacteristic
455C2×#117C2312yes—
456C22×C4⋊C4—44no—
457C22×C4⋊C4C2311yescharacteristic
458C22×C4⋊C4C2311yescharacteristic
459C22×C4⋊C4C2311yescharacteristic
460C22×C4⋊C4C2312yes—
461C22×C4⋊C4C2311yescharacteristic
462C22×C4⋊C4C2312yes—
463C22×C4⋊C4C2312yes—
464C22×C4⋊C4C2312yes—
465C22×C4⋊C4C2312yes—
466C22×C4⋊C4C2312yes—
467C22×C4⋊C4C2311yescharacteristic
468C22×C4⋊C4C2311yescharacteristic
469C22×C4⋊C4C2312yes—
470C22×C22⋊C4C2311yescharacteristic
471C22×C22⋊C4C2312yes—
472C22×C22⋊C4C2312yes—
473C22×C22⋊C4C2312yes—
474C22×C22⋊C4C2312yes—
475C22×C22⋊C4C2312yes—
476C22×C22⋊C4C2311yescharacteristic
477C22×C22⋊C4C2312yes—
478C22×C42C2311yescharacteristic
479C22×C42C2312yes—
480#401C2314yes—
481#400C2314yes—
482#400C2314yes—
483#400C2314yes—
484#400C2314yes—
485#400C2314yes—
486#400C2314yes—
487#400C2314yes—
488#399C2312yes—
489#399C2312yes—
490#399C2312yes—
491#399C2312yes—
492#399C2312yes—
493#399C2314yes—
494#399C2314yes—
495#399C2312yes—
496#399C2312yes—
497#399C2314yes—
498#399C2314yes—
499#399C2312yes—
500#398C2314yes—
501#398C2314yes—
502#398C2314yes—
503#398C2312yes—
504#398C2314yes—
505#398C2314yes—
506#398C2312yes—
507#398C2314yes—
508#398C2314yes—
509#397C2312yes—
510#397C2314yes—
511#397C2314yes—
512#397C2314yes—
513#397C2314yes—
514#397C2314yes—
515#397C2314yes—
516#397C2314yes—
517#397C2314yes—
518#397C2314yes—
519#397C2314yes—
520#397C2314yes—
521#397C2314yes—
522#397C2314yes—
523#397C2314yes—
524#397C2312yes—
525#397C2314yes—
526#397C2314yes—
527#397C2314yes—
528#397C2314yes—
529#396C2312yes—
530#396C2314yes—
531#396C2314yes—
532#396C2314yes—
533#396C2314yes—
534#396C2314yes—
535#396C2312yes—
536#396C2314yes—
537#396C2312yes—
538#396C2314yes—
539#396C2314yes—
540#396C2314yes—
541#396C2314yes—
542#396C2314yes—
543#396C2314yes—
544#396C2314yes—
545#396C2314yes—
546#396C2314yes—
547#396C2314yes—
548#396C2314yes—
549#396C2312yes—
550#394C2314yes—
551#394C2314yes—
552#394C2314yes—
553#394C2314yes—
554#394C2314yes—
555#394C2314yes—
556#394C2314yes—
557#394C2314yes—
558#394C2314yes—
559#394C2314yes—
560#394C2314yes—
561#394C2312yes—
562#394C2314yes—
563#394C2314yes—
564#394C2314yes—
565#394C2314yes—
566#394C2314yes—
567#394C2314yes—
568#394C2314yes—
569#394C2312yes—
570#394C2314yes—
571#394C2314yes—
572#394C2312yes—
573#394C2314yes—
574#394C2314yes—
575#394C2314yes—
576#394C2314yes—
577#394C2314yes—
578#394C2314yes—
579#394C2314yes—
580#394C2314yes—
581#394C2314yes—
582#394C2314yes—
583#394C2314yes—
584#394C2312yes—
585#394C2312yes—
586#394C2312yes—
587#394C2314yes—
588#394C2314yes—
589#392C2312yes—
590#392C2312yes—
591#392C2314yes—
592#392C2314yes—
593#392C2314yes—
594#392C2314yes—
595#392C2314yes—
596#392C2314yes—
597#392C2314yes—
598#392C2314yes—
599#392C2314yes—
600#392C2314yes—
601#392C2314yes—
602#392C2314yes—
603#392C2314yes—
604#392C2312yes—
605#392C2312yes—
606#392C2312yes—
607#392C2312yes—
608#392C2312yes—
609#392C2312yes—
610#392C2312yes—
611#392C2312yes—
612#392C2314yes—
613#392C2314yes—
614#392C2314yes—
615#392C2314yes—
616#391C2312yes—
617#391C2312yes—
618#391C2312yes—
619#391C2312yes—
620#391C2312yes—
621#391C2312yes—
622#391C2311yescharacteristic
623#391C2311yescharacteristic
624#390C2312yes—
625#390C2312yes—
626#390C2312yes—
627#390C2312yes—
628#390C2312yes—
629#390C2312yes—
630#390C2312yes—
631#390C2312yes—
632#390C2312yes—
633#390C2312yes—
634#390C2312yes—
635#390C2312yes—
636#390C2312yes—
637#390C2312yes—
638#390C2312yes—
639#390C2312yes—
640#390C2312yes—
641#390C2312yes—
642#390C2312yes—
643#390C2312yes—
644#390C2312yes—
645#390C2312yes—
646#390C2312yes—
647#390C2312yes—
648#390C2312yes—
649#390C2312yes—
650#390C2314yes—
651#390C2314yes—
652#390C2314yes—
653#390C2312yes—
654#390C2311yescharacteristic
655#390C2312yes—
656#390C2314yes—
657#390C2314yes—
658#390C2312yes—
659#390C2311yescharacteristic
660#390C2312yes—
661#390C2312yes—
662#390C2312yes—
663#389C2312yes—
664#389C2312yes—
665#389C2312yes—
666#389C2312yes—
667#389C2312yes—
668#389C2312yes—
669#389C2312yes—
670#389C2312yes—
671#389C2312yes—
672#389C2312yes—
673#389C2312yes—
674#389C2312yes—
675#389C2312yes—
676#389C2314yes—
677#389C2311yescharacteristic
678#389C2311yescharacteristic
679#389C2312yes—
680#389C2311yescharacteristic
681#389C2311yescharacteristic
682#389C2312yes—
683#389C2312yes—
684#389C2312yes—
685#389C2312yes—
686#388C2314yes—
687#388C2314yes—
688#388C2312yes—
689#388C2314yes—
690#388C2314yes—
691#388C2314yes—
692#388C2314yes—
693#388C2314yes—
694#388C2314yes—
695#388C2314yes—
696#388C2314yes—
697#388C2314yes—
698#388C2314yes—
699#388C2314yes—
700#388C2314yes—
701#388C2314yes—
702#388C2314yes—
703#388C2314yes—
704#388C2314yes—
705#388C2312yes—
706#388C2314yes—
707#388C2312yes—
708#388C2312yes—
709#387C2314yes—
710#387C2314yes—
711#387C2314yes—
712#387C2314yes—
713#387C2314yes—
714#387C2314yes—
715#387C2314yes—
716#386C2314yes—
717#386C2314yes—
718#386C2314yes—
719#386C2314yes—
720#386C2314yes—
721#386C2314yes—
722#386C2314yes—
723#386C2314yes—
724#386C2314yes—
725#386C2314yes—
726#386C2314yes—
727#386C2314yes—
728#386C2312yes—
729#386C2314yes—
730#386C2314yes—
731#386C2314yes—
732#386C2314yes—
733#386C2314yes—
734#386C2314yes—
735#386C2314yes—
736#386C2314yes—
737#386C2314yes—
738#386C2314yes—
739#386C2314yes—
740#386C2314yes—
741#386C2312yes—
742#386C2314yes—
743#386C2314yes—
744#386C2314yes—
745#386C2314yes—
746#386C2312yes—
747#386C2312yes—
748#386C2312yes—
749#386C2312yes—
750#386C2314yes—
751#386C2314yes—
752#385C2314yes—
753#385C2314yes—
754#385C2314yes—
755#385C2314yes—
756#385C2314yes—
757#385C2314yes—
758#385C2314yes—
759#385C2314yes—
760#385C2314yes—
761#385C2314yes—
762#385C2314yes—
763#385C2314yes—
764#385C2312yes—
765#385C2312yes—
766#384C2312yes—
767#384C2312yes—
768#384C2312yes—
769#384C2312yes—
770#383C2314yes—
771#382C2312yes—
772#382C2312yes—
773#381C2314yes—
774#381C2314yes—
775#381C2314yes—
776#381C2312yes—
777#381C2314yes—
778#380C2312yes—
779#380C2312yes—
780#380C2312yes—
781#380C2312yes—
782#380C2312yes—
783#380C2312yes—
784#380C2312yes—
785#380C2312yes—
786#380C2312yes—
787#380C2312yes—
788#380C2312yes—
789#380C2312yes—
790#380C2314yes—
791#380C2314yes—
792#380C2314yes—
793#380C2314yes—
794#380C2312yes—
795#380C2312yes—
796#380C2314yes—
797#380C2312yes—
798#380C2312yes—
799#380C2311yescharacteristic
800#380C2311yescharacteristic
801#380C2312yes—
802#380C2311yescharacteristic
803#380C2312yes—
804#380C2311yescharacteristic
805#379C2314yes—
806#379C2314yes—
807#379C2314yes—
808#379C2314yes—
809#379C2314yes—
810#379C2312yes—
811#379C2314yes—
812#379C2314yes—
813#379C2314yes—
814C4×C4⋊C4C2312yes—
815C4×C4⋊C4C2312yes—
816C4×C4⋊C4C2311yescharacteristic
817C4×C4⋊C4C2311yescharacteristic
818C4×C4⋊C4C2311yescharacteristic
819C4×C4⋊C4C2311yescharacteristic
820C4×C22⋊C4C2312yes—
821C4×C22⋊C4C2312yes—
822C4×C22⋊C4C2312yes—
823C4×C22⋊C4C2312yes—
824C4×C22⋊C4C2312yes—
825C4×C22⋊C4C2312yes—
826#376C2312yes—
827C2×#95C2312yes—
828C2×#95C2312yes—
829C43C2312yes—
830C25C2411yescharacteristic
831C25C2411yescharacteristic
832C25C2412yes—
833C25C2414yes—
834H(5,𝔽2)—464no—
835C2×#41—24no—
836C2×#41—24no—
837C2×#41—24no—
838C2×#41—24no—
839C2×#41—24no—
840C2×#41—24no—
841C2×#41—24no—
842C2×#41—24no—
843C2×#41—24no—
844C2×#41—44no—
845C2×#41—44no—
846C2×#41—44no—
847C2×#41—44no—
848C2×#41—44no—
849C2×#41—44no—
850C22×Q8C2411yescharacteristic
851C22×Q8C2411yescharacteristic
852C22×Q8C2411yescharacteristic
853C22×D4—24no—
854C22×D4—24no—
855C22×D4—24no—
856C22×D4—24no—
857C22×D4—44no—
858C22×D4—44no—
859C22×D4—44no—
860C22×D4—44no—
861C22×D4—44no—
862C22×D4—44no—
863C22×D4—42no—
864C22×D4—44no—
865C22×D4—44no—
866C22×D4—42no—
867C22×D4—48no—
868C22×D4—48no—
869C22×D4—48no—
870C22×D4—44no—
871C22×D4—44no—
872C22×D4—44no—
873C22×D4—82no—
874C22×D4C2412yes—
875C22×D4C2411yescharacteristic
876C22×D4C2412yes—
877C22×D4C2412yes—
878C22×D4C2412yes—
879C22×D4C2411yescharacteristic
880C22×D4C2412yes—
881C22×D4C2411yescharacteristic
882C22×D4C2411yescharacteristic
883C22×D4C2411yescharacteristic
884C22×D4C2411yescharacteristic
885C22×D4C2412yes—
886C22×D4C2412yes—
887C22×D4C2412yes—
888C22×D4C2412yes—
889C22×D4C2412yes—
890C22×D4C2412yes—
891C22×D4C2412yes—
892C22×D4C2412yes—
893C22×D4C2412yes—
894C22×D4C2412yes—
895C22×D4C2414yes—
896C22×D4C2414yes—
897C22×D4C2414yes—
898C22×D4C2412yes—
899C22×D4C2412yes—
900C22×D4C2412yes—
901C22×D4C2412yes—
902C22×D4C2414yes—
903C22×D4C2414yes—
904C22×D4C2414yes—
905C22×D4C2414yes—
906C22×D4C2414yes—
907C22×D4C2414yes—
908C22×D4C2411yescharacteristic
909C23×C4—24no—
910C23×C4—24no—
911C23×C4—24no—
912C23×C4—24no—
913C23×C4—24no—
914C23×C4—24no—
915C23×C4—44no—
916C23×C4—44no—
917C23×C4—82no—
918C23×C4C2411yescharacteristic
919C23×C4C2411yescharacteristic
920C23×C4C2411yescharacteristic
921C23×C4C2411yescharacteristic
922C23×C4C2411yescharacteristic
923C23×C4C2411yescharacteristic
924C23×C4C2411yescharacteristic
925C23×C4C2412yes—
926C23×C4C2411yescharacteristic
927C23×C4C2411yescharacteristic
928C23×C4C2412yes—
929C23×C4C2411yescharacteristic
930C23×C4C2412yes—
931C23×C4C2411yescharacteristic
932C23×C4C2411yescharacteristic
933C23×C4C2412yes—
934C23×C4C2412yes—
935C23×C4C2412yes—
936C23×C4C2412yes—
937C23×C4C2414yes—
938C23×C4C2412yes—
939C23×C4C2414yes—
940C23×C4C2414yes—
941C23×C4C2414yes—
942C23×C4C2411yescharacteristic
943C4⋊Q8—42no—
944#127—28no—
945#127—42no—
946#127—44no—
947#127—44no—
948#126—48no—
949#126—48no—
950#126—84no—
951#124—42no—
952#124—42no—
953#124—44no—
954#123—44no—
955#123—44no—
956#123—44no—
957#123—44no—
958#123—44no—
959#123—44no—
960#123—48no—
961#123—48no—
962#123—48no—
963#123—84no—
964C22⋊Q8—42no—
965C22⋊Q8—42no—
966C22⋊Q8—42no—
967C22⋊Q8—42no—
968C22⋊Q8—42no—
969C22⋊Q8—42no—
970C22⋊Q8—42no—
971C22⋊Q8—42no—
972C22⋊Q8—42no—
973C22⋊Q8—42no—
974C22⋊Q8—42no—
975C22⋊Q8—42no—
976C22⋊Q8—44no—
977C22⋊Q8—44no—
978#121—216no—
979#121—28no—
980#121—48no—
981#121—48no—
982#121—44no—
983#121—48no—
984#121—48no—
985#121—48no—
986#121—44no—
987#121—44no—
988#121—44no—
989#121—44no—
990#121—44no—
991#121—44no—
992#121—44no—
993#121—44no—
994#121—42no—
995#121—42no—
996#121—42no—
997#121—42no—
998#121—42no—
999#121—42no—
1000#121—42no—
1001#121—42no—
1002#121—42no—
1003#121—42no—
1004#121—42no—
1005#121—42no—
1006#121—44no—
1007#121—44no—
1008#121—44no—
1009#121—44no—
1010#121—48no—
1011#121—44no—
1012#121—44no—
1013#121—48no—
1014#121—48no—
1015#121—48no—
1016#121—84no—
1017#121—84no—
1018#120—48no—
1019#120—44no—
1020#120—44no—
1021#120—44no—
1022#120—44no—
1023#120—44no—
1024#120—44no—
1025#120—48no—
1026#120—48no—
1027#120—48no—
1028#120—48no—
1029#120—84no—
1030#120—84no—
1031C4×Q8—44no—
1032C4×D4—44no—
1033C4×D4—42no—
1034C4×D4—42no—
1035C4×D4—42no—
1036C4×D4—42no—
1037C4×D4—42no—
1038C4×D4—42no—
1039C4×D4—42no—
1040C4×D4—42no—
1041C4×D4—44no—
1042C4×D4—44no—
1043C4×D4—44no—
1044C4×D4—44no—
1045C4×D4—44no—
1046C4×D4—44no—
1047C4×D4—44no—
1048C4×D4—44no—
1049C4×D4—44no—
1050C4×D4—44no—
1051C4×D4—44no—
1052C4×D4—44no—
1053C4×D4—44no—
1054C4×D4—44no—
1055C4×D4—48no—
1056#117—24no—
1057#117—24no—
1058#117—24no—
1059#117—24no—
1060#117—24no—
1061#117—44no—
1062#117—44no—
1063#117—42no—
1064#117—42no—
1065#117—44no—
1066C2×C4⋊C4—24no—
1067C2×C4⋊C4—24no—
1068C2×C4⋊C4—24no—
1069C2×C4⋊C4—44no—
1070C2×C4⋊C4—44no—
1071C2×C4⋊C4—44no—
1072C2×C4⋊C4—44no—
1073C2×C4⋊C4—42no—
1074C2×C4⋊C4—42no—
1075C2×C4⋊C4—44no—
1076C2×C4⋊C4—44no—
1077C2×C4⋊C4—44no—
1078C2×C4⋊C4—42no—
1079C2×C4⋊C4C2412yes—
1080C2×C4⋊C4C2412yes—
1081C2×C4⋊C4C2412yes—
1082C2×C4⋊C4C2412yes—
1083C2×C4⋊C4C2412yes—
1084C2×C4⋊C4C2411yescharacteristic
1085C2×C4⋊C4C2411yescharacteristic
1086C2×C4⋊C4C2411yescharacteristic
1087C2×C4⋊C4C2411yescharacteristic
1088C2×C4⋊C4C2411yescharacteristic
1089C2×C4⋊C4C2412yes—
1090C2×C4⋊C4C2414yes—
1091C2×C4⋊C4C2411yescharacteristic
1092C2×C4⋊C4C2411yescharacteristic
1093C2×C4⋊C4C2411yescharacteristic
1094C2×C4⋊C4C2411yescharacteristic
1095C2×C4⋊C4C2411yescharacteristic
1096C2×C4⋊C4C2412yes—
1097C2×C4⋊C4C2414yes—
1098C2×C4⋊C4C2414yes—
1099C2×C4⋊C4C2412yes—
1100C2×C4⋊C4C2412yes—
1101C2×C4⋊C4C2411yescharacteristic
1102C2×C4⋊C4C2411yescharacteristic
1103C2×C4⋊C4C2411yescharacteristic
1104C2×C4⋊C4C2411yescharacteristic
1105C2×C4⋊C4C2414yes—
1106C2×C4⋊C4C2414yes—
1107C2×C4⋊C4C2412yes—
1108C2×C4⋊C4C2412yes—
1109C2×C4⋊C4C2412yes—
1110C2×C4⋊C4C2412yes—
1111C2×C4⋊C4C2412yes—
1112C2×C4⋊C4C2412yes—
1113C2×C4⋊C4C2412yes—
1114C2×C4⋊C4C2412yes—
1115C2×C4⋊C4C2412yes—
1116C2×C4⋊C4C2412yes—
1117C2×C4⋊C4C2412yes—
1118C2×C4⋊C4C2412yes—
1119C2×C4⋊C4C2412yes—
1120C2×C4⋊C4C2412yes—
1121C2×C4⋊C4C2414yes—
1122C2×C4⋊C4C2414yes—
1123C2×C4⋊C4C2414yes—
1124C2×C4⋊C4C2414yes—
1125C2×C4⋊C4C2414yes—
1126C2×C4⋊C4C2414yes—
1127C2×C4⋊C4C2414yes—
1128C2×C4⋊C4C2412yes—
1129C2×C4⋊C4C2414yes—
1130C2×C4⋊C4C2414yes—
1131C2×C4⋊C4C2412yes—
1132C2×C4⋊C4C2412yes—
1133C2×C22⋊C4—44no—
1134C2×C22⋊C4—44no—
1135C2×C22⋊C4—44no—
1136C2×C22⋊C4—42no—
1137C2×C22⋊C4—42no—
1138C2×C22⋊C4—44no—
1139C2×C22⋊C4—44no—
1140C2×C22⋊C4—82no—
1141C2×C22⋊C4C2412yes—
1142C2×C22⋊C4C2412yes—
1143C2×C22⋊C4C2414yes—
1144C2×C22⋊C4C2414yes—
1145C2×C22⋊C4C2412yes—
1146C2×C22⋊C4C2412yes—
1147C2×C22⋊C4C2412yes—
1148C2×C22⋊C4C2412yes—
1149C2×C22⋊C4C2412yes—
1150C2×C22⋊C4C2412yes—
1151C2×C22⋊C4C2412yes—
1152C2×C22⋊C4C2412yes—
1153C2×C22⋊C4C2411yescharacteristic
1154C2×C22⋊C4C2411yescharacteristic
1155C2×C22⋊C4C2411yescharacteristic
1156C2×C22⋊C4C2411yescharacteristic
1157C2×C22⋊C4C2411yescharacteristic
1158C2×C22⋊C4C2411yescharacteristic
1159C2×C22⋊C4C2411yescharacteristic
1160C2×C22⋊C4C2411yescharacteristic
1161C2×C22⋊C4C2414yes—
1162C2×C22⋊C4C2414yes—
1163C2×C22⋊C4C2414yes—
1164C2×C22⋊C4C2414yes—
1165C2×C22⋊C4C2414yes—
1166C2×C22⋊C4C2414yes—
1167C2×C22⋊C4C2414yes—
1168C2×C22⋊C4C2414yes—
1169C2×C22⋊C4C2414yes—
1170C2×C22⋊C4C2412yes—
1171C2×C22⋊C4C2412yes—
1172C2×C22⋊C4C2412yes—
1173C2×C22⋊C4C2412yes—
1174C2×C22⋊C4C2412yes—
1175C2×C22⋊C4C2412yes—
1176C2×C22⋊C4C2412yes—
1177C2×C22⋊C4C2412yes—
1178C2×C22⋊C4C2412yes—
1179C2×C22⋊C4C2412yes—
1180C2×C22⋊C4C2412yes—
1181C2×C22⋊C4C2412yes—
1182C2×C22⋊C4C2412yes—
1183C2×C22⋊C4C2412yes—
1184C2×C22⋊C4C2412yes—
1185C2×C22⋊C4C2412yes—
1186C2×C22⋊C4C2412yes—
1187C2×C22⋊C4C2412yes—
1188C2×C22⋊C4C2412yes—
1189C2×C22⋊C4C2412yes—
1190C2×C22⋊C4C2412yes—
1191C2×C22⋊C4C2412yes—
1192C2×C22⋊C4C2412yes—
1193C2×C22⋊C4C2412yes—
1194C2×C22⋊C4C2412yes—
1195C2×C22⋊C4C2412yes—
1196C2×C22⋊C4C2412yes—
1197C2×C22⋊C4C2412yes—
1198C2×C22⋊C4C2412yes—
1199C2×C22⋊C4C2414yes—
1200C2×C22⋊C4C2414yes—
1201C2×C22⋊C4C2414yes—
1202C2×C22⋊C4C2414yes—
1203C2×C22⋊C4C2414yes—
1204C2×C22⋊C4C2414yes—
1205C2×C22⋊C4C2414yes—
1206C2×C22⋊C4C2414yes—
1207C2×C22⋊C4C2414yes—
1208C2×C22⋊C4C2414yes—
1209C2×C22⋊C4C2414yes—
1210C2×C22⋊C4C2414yes—
1211C2×C22⋊C4C2414yes—
1212C2×C22⋊C4C2414yes—
1213C2×C22⋊C4C2414yes—
1214C2×C22⋊C4C2414yes—
1215C2×C22⋊C4C2414yes—
1216C2×C22⋊C4C2414yes—
1217C2×C22⋊C4C2414yes—
1218C2×C22⋊C4C2414yes—
1219C2×C22⋊C4C2414yes—
1220C2×C22⋊C4C2412yes—
1221C2×C22⋊C4C2414yes—
1222C2×C22⋊C4C2412yes—
1223C2×C22⋊C4C2412yes—
1224C2×C22⋊C4C2412yes—
1225C2×C22⋊C4C2414yes—
1226C2×C22⋊C4C2414yes—
1227C2×C42—24no—
1228C2×C42—44no—
1229C2×C42C2412yes—
1230C2×C42C2412yes—
1231C2×C42C2412yes—
1232C2×C42C2412yes—
1233C2×C42C2412yes—
1234C2×C42C2411yescharacteristic
1235C2×C42C2411yescharacteristic
1236C2×C42C2411yescharacteristic
1237C2×C42C2411yescharacteristic
1238C2×C42C2412yes—
1239C2×C42C2412yes—
1240C2×C42C2412yes—
1241C2×C42C2414yes—
1242C2×C42C2412yes—
1243C2×C42C2412yes—
1244C2×C42C2412yes—
1245#95C2414yes—
1246#95C2414yes—
1247#95C2414yes—
1248#95C2414yes—
1249#95C2412yes—
1250#95C2412yes—
1251#95C2412yes—
1252#95C2412yes—
1253#95C2412yes—
1254#95C2412yes—
1255#95C2412yes—
1256#95C2412yes—
1257#95C2412yes—
1258#95C2412yes—
1259#95C2412yes—
1260#95C2412yes—
1261#95C2412yes—
1262#95C2412yes—
1263#95C2412yes—
1264#95C2412yes—
1265#95C2414yes—
1266#95C2414yes—
1267#95C2414yes—
1268#95C2414yes—
1269#95C2414yes—
1270#95C2414yes—
1271#95C2414yes—
1272#95C2414yes—
1273#95C2414yes—
1274#95C2414yes—
1275#95C2414yes—
1276#95C2414yes—
1277#95C2414yes—
1278#95C2414yes—
1279#95C2414yes—
1280#95C2414yes—
1281#95C2414yes—
1282#95C2414yes—
1283#95C2414yes—
1284#95C2414yes—
1285C24—22no—
1286C24—22no—
1287C24—22no—
1288C24—22no—
1289C24—22no—
1290C24—22no—
1291C24—22no—
1292C24—22no—
1293C24—22no—
1294C24—24no—
1295C24—24no—
1296C24—24no—
1297C24—41no—
1298C24—41no—
1299C24—41no—
1300C24—41no—
1301C24—41no—
1302C24—44no—
1303C24—44no—
1304C24—44no—
1305C24—42no—
1306C24—42no—
1307C24—42no—
1308C24—42no—
1309C24—44no—
1310C24—44no—
1311C24—44no—
1312C24—44no—
1313C24C2512yes—
1314C24C2514yes—
1315C24C2512yes—
1316C24C2511yescharacteristic
1317C24C2512yes—
1318C24C2511yescharacteristic
1319C24C2511yescharacteristic
1320C24C2511yescharacteristic
1321C24C2511yescharacteristic
1322#41—432no—
1323#41—432no—
1324#41—416no—
1325#41—416no—
1326#41—416no—
1327C2×Q8—22no—
1328C2×Q8—22no—
1329C2×Q8—22no—
1330C2×Q8—22no—
1331C2×Q8—22no—
1332C2×Q8—22no—
1333C2×Q8—22no—
1334C2×Q8—22no—
1335C2×Q8—22no—
1336C2×D4—24no—
1337C2×D4—24no—
1338C2×D4—24no—
1339C2×D4—24no—
1340C2×D4—24no—
1341C2×D4—24no—
1342C2×D4—24no—
1343C2×D4—22no—
1344C2×D4—22no—
1345C2×D4—24no—
1346C2×D4—24no—
1347C2×D4—22no—
1348C2×D4—22no—
1349C2×D4—24no—
1350C2×D4—24no—
1351C2×D4—24no—
1352C2×D4—24no—
1353C2×D4—28no—
1354C2×D4—28no—
1355C2×D4—24no—
1356C2×D4—24no—
1357C2×D4—24no—
1358C2×D4—24no—
1359C2×D4—28no—
1360C2×D4—24no—
1361C2×D4—22no—
1362C2×D4—22no—
1363C2×D4—22no—
1364C2×D4—22no—
1365C2×D4—24no—
1366C2×D4—24no—
1367C2×D4—24no—
1368C2×D4—24no—
1369C2×D4—24no—
1370C2×D4—22no—
1371C2×D4—22no—
1372C2×D4—22no—
1373C2×D4—22no—
1374C2×D4—22no—
1375C2×D4—24no—
1376C2×D4—22no—
1377C2×D4—24no—
1378C2×D4—41no—
1379C2×D4—41no—
1380C2×D4—41no—
1381C2×D4—41no—
1382C2×D4—44no—
1383C2×D4—44no—
1384C2×D4—44no—
1385C2×D4—44no—
1386C2×D4—44no—
1387C2×D4—44no—
1388C2×D4—41no—
1389C2×D4—41no—
1390C2×D4—42no—
1391C2×D4—42no—
1392C2×D4—42no—
1393C2×D4—42no—
1394C2×D4—42no—
1395C2×D4—42no—
1396C2×D4—42no—
1397C2×D4—42no—
1398C2×D4—42no—
1399C2×D4—42no—
1400C2×D4—42no—
1401C2×D4—42no—
1402C2×D4—42no—
1403C2×D4—42no—
1404C2×D4—42no—
1405C2×D4—42no—
1406C2×D4—42no—
1407C2×D4—44no—
1408C2×D4—44no—
1409C2×D4—44no—
1410C2×D4—44no—
1411C2×D4—44no—
1412C2×D4—44no—
1413C2×D4—44no—
1414C2×D4—42no—
1415C2×D4—42no—
1416C2×D4—42no—
1417C2×D4—42no—
1418C2×D4—44no—
1419C2×D4—42no—
1420C2×D4—42no—
1421C2×D4—42no—
1422C2×D4—42no—
1423C2×D4—44no—
1424C2×D4—42no—
1425C2×D4—42no—
1426C2×D4—42no—
1427C2×D4—42no—
1428C2×D4—42no—
1429C2×D4—42no—
1430C2×D4—42no—
1431C2×D4—44no—
1432C2×D4—44no—
1433C2×D4—44no—
1434C2×D4—44no—
1435C2×D4—44no—
1436C2×D4—44no—
1437C2×D4—44no—
1438C2×D4—44no—
1439C2×D4—44no—
1440C2×D4—416no—
1441C2×D4—464no—
1442C2×D4—432no—
1443C2×D4—432no—
1444C2×D4—416no—
1445C2×D4—816no—
1446C2×D4—816no—
1447C2×D4H(5,𝔽2)14yescomplemented
1448C22×C4—22no—
1449C22×C4—22no—
1450C22×C4—22no—
1451C22×C4—24no—
1452C22×C4—22no—
1453C22×C4—22no—
1454C22×C4—22no—
1455C22×C4—22no—
1456C22×C4—22no—
1457C22×C4—24no—
1458C22×C4—24no—
1459C22×C4—24no—
1460C22×C4—28no—
1461C22×C4—22no—
1462C22×C4—22no—
1463C22×C4—22no—
1464C22×C4—22no—
1465C22×C4—22no—
1466C22×C4—22no—
1467C22×C4—22no—
1468C22×C4—24no—
1469C22×C4—22no—
1470C22×C4—22no—
1471C22×C4—22no—
1472C22×C4—22no—
1473C22×C4—22no—
1474C22×C4—22no—
1475C22×C4—22no—
1476C22×C4—22no—
1477C22×C4—22no—
1478C22×C4—22no—
1479C22×C4—24no—
1480C22×C4—22no—
1481C22×C4—22no—
1482C22×C4—22no—
1483C22×C4—22no—
1484C22×C4—22no—
1485C22×C4—22no—
1486C22×C4—24no—
1487C22×C4—24no—
1488C22×C4—24no—
1489C22×C4—24no—
1490C22×C4—24no—
1491C22×C4—24no—
1492C22×C4—22no—
1493C22×C4—22no—
1494C22×C4—24no—
1495C22×C4—42no—
1496C22×C4—42no—
1497C22×C4—41no—
1498C22×C4—44no—
1499C22×C4—44no—
1500C22×C4—44no—
1501C22×C4—42no—
1502C22×C4—42no—
1503C22×C4—42no—
1504C22×C4—42no—
1505C22×C4—41no—
1506C22×C4—42no—
1507C22×C4—44no—
1508C22×C4—44no—
1509C22×C4—44no—
1510C22×C4—42no—
1511C22×C4—42no—
1512C22×C4—44no—
1513C22×C4—44no—
1514C22×C4—41no—
1515C22×C4—42no—
1516C22×C4—42no—
1517C22×C4—44no—
1518C22×C4—44no—
1519C22×C4—44no—
1520C22×C4—416no—
1521C22×C4—416no—
1522C22×C4—816no—
1523C22×C4H(5,𝔽2)14yes—
1524C22×C4H(5,𝔽2)14yes—
1525C22×C4H(5,𝔽2)14yes—
1526C22×C4C2512yes—
1527C22×C4C2511yescharacteristic
1528C22×C4C2512yes—
1529C22×C4C2512yes—
1530C22×C4C2512yes—
1531C22×C4C2512yes—
1532C22×C4C2514yes—
1533C22×C4C2514yes—
1534C22×C4C2511yescharacteristic
1535C22×C4C2512yes—
1536C22×C4C2512yes—
1537C22×C4C2512yes—
1538C22×C4C2512yes—
1539C22×C4C2512yes—
1540C22×C4C2511yescharacteristic
1541C22×C4C2512yes—
1542C22×C4C2514yes—
1543C22×C4C2511yescharacteristic
1544C22×C4C2512yes—
1545C22×C4C2512yes—
1546C22×C4C2511yescharacteristic
1547C22×C4C2511yescharacteristic
1548C22×C4C2511yescharacteristic
1549C22×C4C2511yescharacteristic
1550C22×C4C2511yescharacteristic
1551C22×C4C2511yescharacteristic
1552C4⋊C4—24no—
1553C4⋊C4—24no—
1554C4⋊C4—24no—
1555C4⋊C4—24no—
1556C4⋊C4—24no—
1557C4⋊C4—24no—
1558C4⋊C4—22no—
1559C4⋊C4—22no—
1560C4⋊C4—22no—
1561C4⋊C4—22no—
1562C4⋊C4—22no—
1563C4⋊C4—28no—
1564C4⋊C4—22no—
1565C4⋊C4—22no—
1566C4⋊C4—22no—
1567C4⋊C4—22no—
1568C4⋊C4—22no—
1569C4⋊C4—24no—
1570C4⋊C4—44no—
1571C4⋊C4—44no—
1572C4⋊C4—42no—
1573C4⋊C4—42no—
1574C4⋊C4—41no—
1575C4⋊C4—41no—
1576C4⋊C4—41no—
1577C4⋊C4—41no—
1578C4⋊C4—44no—
1579C4⋊C4—44no—
1580C4⋊C4—42no—
1581C4⋊C4—42no—
1582C4⋊C4—42no—
1583C4⋊C4—42no—
1584C4⋊C4—42no—
1585C4⋊C4—42no—
1586C4⋊C4—42no—
1587C4⋊C4—42no—
1588C4⋊C4—42no—
1589C4⋊C4—42no—
1590C4⋊C4—42no—
1591C4⋊C4—42no—
1592C4⋊C4—42no—
1593C4⋊C4—42no—
1594C4⋊C4—42no—
1595C4⋊C4—44no—
1596C4⋊C4—42no—
1597C4⋊C4—44no—
1598C4⋊C4—44no—
1599C4⋊C4—44no—
1600C4⋊C4—44no—
1601C4⋊C4—44no—
1602C4⋊C4—44no—
1603C4⋊C4—44no—
1604C4⋊C4—44no—
1605C4⋊C4—42no—
1606C22⋊C4—24no—
1607C22⋊C4—24no—
1608C22⋊C4—28no—
1609C22⋊C4—24no—
1610C22⋊C4—24no—
1611C22⋊C4—24no—
1612C22⋊C4—24no—
1613C22⋊C4—24no—
1614C22⋊C4—28no—
1615C22⋊C4—24no—
1616C22⋊C4—42no—
1617C22⋊C4—42no—
1618C22⋊C4—41no—
1619C22⋊C4—41no—
1620C22⋊C4—41no—
1621C22⋊C4—41no—
1622C22⋊C4—41no—
1623C22⋊C4—41no—
1624C22⋊C4—41no—
1625C22⋊C4—41no—
1626C22⋊C4—44no—
1627C22⋊C4—44no—
1628C22⋊C4—44no—
1629C22⋊C4—44no—
1630C22⋊C4—44no—
1631C22⋊C4—44no—
1632C22⋊C4—44no—
1633C22⋊C4—44no—
1634C22⋊C4—42no—
1635C22⋊C4—44no—
1636C22⋊C4—44no—
1637C22⋊C4—42no—
1638C22⋊C4—44no—
1639C22⋊C4—42no—
1640C22⋊C4—42no—
1641C22⋊C4—42no—
1642C22⋊C4—42no—
1643C22⋊C4—42no—
1644C22⋊C4—42no—
1645C22⋊C4—42no—
1646C22⋊C4—42no—
1647C22⋊C4—42no—
1648C22⋊C4—42no—
1649C22⋊C4—42no—
1650C22⋊C4—42no—
1651C22⋊C4—42no—
1652C22⋊C4—42no—
1653C22⋊C4—42no—
1654C22⋊C4—42no—
1655C22⋊C4—42no—
1656C22⋊C4—42no—
1657C22⋊C4—42no—
1658C22⋊C4—42no—
1659C22⋊C4—42no—
1660C22⋊C4—42no—
1661C22⋊C4—42no—
1662C22⋊C4—42no—
1663C22⋊C4—42no—
1664C22⋊C4—42no—
1665C22⋊C4—42no—
1666C22⋊C4—42no—
1667C22⋊C4—44no—
1668C22⋊C4—44no—
1669C22⋊C4—44no—
1670C22⋊C4—44no—
1671C22⋊C4—44no—
1672C22⋊C4—44no—
1673C22⋊C4—44no—
1674C22⋊C4—44no—
1675C22⋊C4—44no—
1676C22⋊C4—44no—
1677C22⋊C4—44no—
1678C22⋊C4—44no—
1679C22⋊C4—42no—
1680C22⋊C4—44no—
1681C22⋊C4—44no—
1682C22⋊C4—44no—
1683C22⋊C4—44no—
1684C22⋊C4—44no—
1685C22⋊C4—42no—
1686C22⋊C4—44no—
1687C22⋊C4—44no—
1688C22⋊C4—44no—
1689C22⋊C4—44no—
1690C22⋊C4—44no—
1691C22⋊C4—42no—
1692C42—22no—
1693C42—22no—
1694C42—22no—
1695C42—22no—
1696C42—24no—
1697C42—24no—
1698C42—24no—
1699C42—24no—
1700C42—24no—
1701C42—24no—
1702C42—42no—
1703C42—42no—
1704C42—42no—
1705C42—44no—
1706C42—42no—
1707C42—42no—
1708C23—21no—
1709C23—21no—
1710C23—21no—
1711C23—21no—
1712C23—28no—
1713C23—21no—
1714C23—21no—
1715C23—21no—
1716C23—21no—
1717C23—21no—
1718C23—21no—
1719C23—21no—
1720C23—21no—
1721C23—21no—
1722C23—21no—
1723C23—21no—
1724C23—21no—
1725C23—21no—
1726C23—21no—
1727C23—21no—
1728C23—21no—
1729C23—21no—
1730C23—21no—
1731C23—22no—
1732C23—24no—
1733C23—21no—
1734C23—22no—
1735C23—21no—
1736C23—22no—
1737C23—22no—
1738C23—21no—
1739C23—21no—
1740C23—22no—
1741C23—22no—
1742C23—22no—
1743C23—22no—
1744C23—22no—
1745C23—22no—
1746C23—22no—
1747C23—22no—
1748C23—24no—
1749C23—24no—
1750C23—24no—
1751C23—22no—
1752C23—24no—
1753C23—22no—
1754C23—22no—
1755C23—21no—
1756C23—22no—
1757C23—24no—
1758C23—22no—
1759C23—22no—
1760C23—21no—
1761C23—24no—
1762C23—22no—
1763C23—22no—
1764C23—21no—
1765C23—22no—
1766C23—44no—
1767C23—44no—
1768C23—44no—
1769C23—44no—
1770C23—44no—
1771C23—44no—
1772C23—44no—
1773C23—44no—
1774C23—44no—
1775C23—416no—
1776C23—44no—
1777C23—48no—
1778C23—82no—
1779C23—82no—
1780C23—82no—
1781C23—84no—
1782C23—84no—
1783C23—84no—
1784C23—84no—
1785C23—84no—
1786C23—84no—
1787C23—164no—
1788C23—164no—
1789C23—164no—
1790C23—164no—
1791C23—164no—
1792C23—164no—
1793C23C2×H(5,𝔽2)12yes—
1794C23C2×H(5,𝔽2)12yes—
1795C23C2×H(5,𝔽2)12yes—
1796C23C2×H(5,𝔽2)12yes—
1797C23C2×H(5,𝔽2)12yes—
1798C23#58512yes—
1799C23C2611yescharacteristic
1800Q8—44no—
1801Q8—44no—
1802Q8—44no—
1803D4—44no—
1804D4—44no—
1805D4—44no—
1806D4—44no—
1807D4—416no—
1808D4—416no—
1809D4—48no—
1810D4—48no—
1811D4—48no—
1812D4—48no—
1813D4—44no—
1814D4—48no—
1815D4—44no—
1816D4—44no—
1817D4—84no—
1818D4—84no—
1819D4—84no—
1820D4—84no—
1821D4—84no—
1822D4—84no—
1823D4—84no—
1824D4—84no—
1825D4—84no—
1826D4—84no—
1827D4—88no—
1828D4—88no—
1829D4—88no—
1830D4—84no—
1831D4—84no—
1832D4—84no—
1833D4—84no—
1834D4—88no—
1835D4—164no—
1836D4—164no—
1837D4—164no—
1838C2×C4—21no—
1839C2×C4—21no—
1840C2×C4—21no—
1841C2×C4—21no—
1842C2×C4—21no—
1843C2×C4—22no—
1844C2×C4—22no—
1845C2×C4—22no—
1846C2×C4—22no—
1847C2×C4—22no—
1848C2×C4—22no—
1849C2×C4—22no—
1850C2×C4—22no—
1851C2×C4—22no—
1852C2×C4—22no—
1853C2×C4—22no—
1854C2×C4—22no—
1855C2×C4—21no—
1856C2×C4—22no—
1857C2×C4—24no—
1858C2×C4—24no—
1859C2×C4—22no—
1860C2×C4—22no—
1861C2×C4—24no—
1862C2×C4—22no—
1863C2×C4—21no—
1864C2×C4—21no—
1865C2×C4—21no—
1866C2×C4—21no—
1867C2×C4—22no—
1868C2×C4—21no—
1869C2×C4—21no—
1870C2×C4—21no—
1871C2×C4—21no—
1872C2×C4—21no—
1873C2×C4—22no—
1874C2×C4—24no—
1875C2×C4—24no—
1876C2×C4—24no—
1877C2×C4—21no—
1878C2×C4—21no—
1879C2×C4—21no—
1880C2×C4—22no—
1881C2×C4—22no—
1882C2×C4—22no—
1883C2×C4—22no—
1884C2×C4—22no—
1885C2×C4—22no—
1886C2×C4—22no—
1887C2×C4—22no—
1888C2×C4—22no—
1889C2×C4—22no—
1890C2×C4—22no—
1891C2×C4—21no—
1892C2×C4—24no—
1893C2×C4—21no—
1894C2×C4—22no—
1895C2×C4—22no—
1896C2×C4—21no—
1897C2×C4—22no—
1898C2×C4—22no—
1899C2×C4—22no—
1900C2×C4—24no—
1901C2×C4—24no—
1902C2×C4—21no—
1903C2×C4—22no—
1904C2×C4—22no—
1905C2×C4—22no—
1906C2×C4—22no—
1907C2×C4—22no—
1908C2×C4—21no—
1909C2×C4—44no—
1910C2×C4—48no—
1911C2×C4—416no—
1912C2×C4—44no—
1913C2×C4—44no—
1914C2×C4—44no—
1915C2×C4—44no—
1916C2×C4—44no—
1917C2×C4—44no—
1918C2×C4—44no—
1919C2×C4—44no—
1920C2×C4—44no—
1921C2×C4—44no—
1922C2×C4—48no—
1923C2×C4—48no—
1924C2×C4—48no—
1925C2×C4—82no—
1926C2×C4—84no—
1927C2×C4—88no—
1928C2×C4—84no—
1929C2×C4—84no—
1930C2×C4—84no—
1931C2×C4—88no—
1932C2×C4—164no—
1933C2×C4#560116yescomplemented
1934C2×C4C2×H(5,𝔽2)12yes—
1935C2×C4C2×H(5,𝔽2)12yes—
1936C2×C4C2×H(5,𝔽2)12yes—
1937C2×C4C2×H(5,𝔽2)12yes—
1938C2×C4C2×H(5,𝔽2)12yes—
1939C2×C4C2×H(5,𝔽2)12yes—
1940C2×C4C2×H(5,𝔽2)12yes—
1941C22—22no—
1942C22—22no—
1943C22—22no—
1944C22—22no—
1945C22—22no—
1946C22—22no—
1947C22—22no—
1948C22—22no—
1949C22—22no—
1950C22—22no—
1951C22—22no—
1952C22—22no—
1953C22—22no—
1954C22—22no—
1955C22—22no—
1956C22—416no—
1957C22—41no—
1958C22—41no—
1959C22—41no—
1960C22—41no—
1961C22—41no—
1962C22—41no—
1963C22—41no—
1964C22—41no—
1965C22—41no—
1966C22—41no—
1967C22—41no—
1968C22—41no—
1969C22—42no—
1970C22—41no—
1971C22—44no—
1972C22—42no—
1973C22—42no—
1974C22—41no—
1975C22—42no—
1976C22—42no—
1977C22—42no—
1978C22—44no—
1979C22—41no—
1980C22—44no—
1981C22—42no—
1982C22—42no—
1983C22—42no—
1984C22—42no—
1985C22—42no—
1986C22—42no—
1987C22—44no—
1988C22—41no—
1989C22—41no—
1990C22—44no—
1991C22—42no—
1992C22—42no—
1993C22—42no—
1994C22—41no—
1995C22—42no—
1996C22—42no—
1997C22—44no—
1998C22—42no—
1999C22—41no—
2000C22—42no—
2001C22—42no—
2002C22—42no—
2003C22—44no—
2004C22—88no—
2005C22—168no—
2006C22—1616no—
2007C22C2×#56014yes—
2008C22C22×H(5,𝔽2)11yescharacteristic
2009C22C22×H(5,𝔽2)11yescharacteristic
2010C22C22×H(5,𝔽2)11yescharacteristic
2011C22C22×H(5,𝔽2)11yescharacteristic
2012C22C2×#58511yescharacteristic
2013C22H(7,𝔽2)11yescharacteristic
2014C222−1+611yescharacteristic
2015C4—22no—
2016C4—41no—
2017C4—44no—
2018C4—42no—
2019C4—41no—
2020C4—41no—
2021C4—42no—
2022C4—44no—
2023C4—44no—
2024C4—42no—
2025C4—42no—
2026C4—42no—
2027C4—42no—
2028C4—41no—
2029C4—41no—
2030C4—41no—
2031C4—41no—
2032C4—42no—
2033C4—42no—
2034C4—42no—
2035C4—42no—
2036C4—42no—
2037C4—42no—
2038C4—42no—
2039C4C2×#56014yes—
2040C4C2×#56014yes—
2041C2—24no—
2042C2—42no—
2043C2—42no—
2044C2—42no—
2045C2—82no—
2046C2—81no—
2047C2—84no—
2048C2—82no—
2049C2—82no—
2050C2C22×#56011yescharacteristic
2051C2#6281811yescharacteristic
2052C2#6287511yescharacteristic
2053C2#6291211yescharacteristic
2054C2#6291411yescharacteristic
2055C2#6295411yescharacteristic
2056C2#6295711yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #53128C2semidirect
2. #53103C2semidirect
3. #53098C2semidirect
4. #53098C2semidirect
5. #53095C2semidirect
6. #52988C2semidirect
7. #52981C2semidirect
8. #52971C2semidirect
9. #52347C2semidirect
10. #52320C2semidirect
11. #46339C2semidirect
12. #46339C2semidirect
13. #46338C2semidirect
14. #46328C2semidirect
15. #45701C2semidirect
16. #45616C2semidirect
17. #45608C2semidirect
18. #45563C2semidirect
19. #45483C2semidirect
20. #45444C2semidirect
21. #35563C2semidirect
22. #35518C2semidirect
23. #35517C2semidirect
24. #35513C2semidirect
25. #35512C2semidirect
26. #35512C2semidirect
27. #35267C2semidirect
28. #35266C2semidirect
29. #35263C2semidirect
30. #35252C2semidirect
31. #35227C2semidirect
32. #35223C2semidirect
33. #34936C2semidirect
34. #34737C2semidirect
35. C2×#2416C2semidirect
37. C2×#560C22semidirect
45. C2×#525C22semidirect
46. C2×#525C22semidirect
49. C22×#121C22semidirect
50. C2×#520C22semidirect
51. C22×C4×D4C22semidirect
52. C22×#117C22semidirect
53. C23×C4⋊C4C22semidirect
54. #2863C22semidirect
55. #2860C22semidirect
56. #2860C22semidirect
57. #2860C22semidirect
58. #2856C22semidirect
59. #2855C22semidirect
60. #2854C22semidirect
61. #2850C22semidirect
62. #2849C22semidirect
63. #2847C22semidirect
64. #2842C22semidirect
65. #2837C22semidirect
66. #2837C22semidirect
67. #2829C22semidirect
68. #2829C22semidirect
69. #2829C22semidirect
70. #2829C22semidirect
71. #2828C22semidirect
72. #2827C22semidirect
73. #2827C22semidirect
74. #2826C22semidirect
75. #2826C22semidirect
76. #2826C22semidirect
77. #2825C22semidirect
78. #2825C22semidirect
79. #2823C22semidirect
80. #2815C22semidirect
81. #2813C22semidirect
82. #2813C22semidirect
83. #2812C22semidirect
84. #2795C22semidirect
85. #2790C22semidirect
86. #2790C22semidirect
87. #2780C22semidirect
88. #2780C22semidirect
89. #2756C22semidirect
90. #2756C22semidirect
91. #2752C22semidirect
92. #2749C22semidirect
93. #2749C22semidirect
94. #2746C22semidirect
95. #2746C22semidirect
96. #2735C22semidirect
97. #2714C22semidirect
98. #2714C22semidirect
99. #2705C22semidirect
100. #2705C22semidirect
101. #2703C22semidirect
102. #2703C22semidirect
103. #2699C22semidirect
104. #2699C22semidirect
105. #2699C22semidirect
106. #2697C22semidirect
107. #2697C22semidirect
108. #2697C22semidirect
109. #2691C22semidirect
110. #2691C22semidirect
111. #2688C22semidirect
112. #2688C22semidirect
113. #2685C22semidirect
114. #2685C22semidirect
115. #2678C22semidirect
116. #2678C22semidirect
117. #2675C22semidirect
118. #2673C22semidirect
119. #2673C22semidirect
120. #2669C22semidirect
121. #2668C22semidirect
122. #2668C22semidirect
123. #2668C22semidirect
124. #2645C22semidirect
125. #2644C22semidirect
126. #2644C22semidirect
127. #2644C22semidirect
128. #2625C22semidirect
129. #2624C22semidirect
130. #2623C22semidirect
131. #2620C22semidirect
132. #2619C22semidirect
133. #2618C22semidirect
134. #2542C22semidirect
135. #2542C22semidirect
136. #2541C22semidirect
137. #2541C22semidirect
138. #2540C22semidirect
139. #2540C22semidirect
140. #2540C22semidirect
141. #2540C22semidirect
142. #2539C22semidirect
143. #2539C22semidirect
144. #2538C22semidirect
145. #2537C22semidirect
146. #2536C22semidirect
147. #2535C22semidirect
148. #2534C22semidirect
149. #2513C22semidirect
150. #2513C22semidirect
151. #2512C22semidirect
152. #2512C22semidirect
153. #2510C22semidirect
154. #2504C22semidirect
155. #2503C22semidirect
156. #2502C22semidirect
157. #2501C22semidirect
158. #2501C22semidirect
159. #2498C22semidirect
160. #2497C22semidirect
161. #2496C22semidirect
162. #2495C22semidirect
163. #2494C22semidirect
164. #2487C22semidirect
165. #2487C22semidirect
166. #2487C22semidirect
167. #2487C22semidirect
168. #2486C22semidirect
169. #2486C22semidirect
170. #2486C22semidirect
171. #2486C22semidirect
172. #2485C22semidirect
173. #2485C22semidirect
174. #2485C22semidirect
175. #2485C22semidirect
176. #2481C22semidirect
177. #2480C22semidirect
178. #2480C22semidirect
179. #2448C22semidirect
180. #2447C22semidirect
181. #2446C22semidirect
182. #2445C22semidirect
183. #2444C22semidirect
184. #2443C22semidirect
185. #2435C22semidirect
186. #2433C22semidirect
187. #2433C22semidirect
188. #2432C22semidirect
189. #2431C22semidirect
190. #2428C22semidirect
191. #2428C22semidirect
192. #2426C22semidirect
193. #2426C22semidirect
194. #2425C22semidirect
195. #2424C22semidirect
196. #2417C22semidirect
197. #2417C22semidirect
198. #2417C22semidirect
199. #2417C22semidirect
200. #2417C22semidirect
201. #2417C22semidirect
202. #2417C22semidirect
203. #2416C22semidirect
204. #2416C22semidirect
205. #2416C22semidirect
206. #2416C22semidirect
207. #2416C22semidirect
208. #2416C22semidirect
209. #2416C22semidirect
210. #2416C22semidirect
211. #2416C22semidirect
212. #2416C22semidirect
213. #2416C22semidirect
214. #2416C22semidirect
215. #2416C22semidirect
216. #2416C22semidirect
217. #2416C22semidirect
218. #2416C22semidirect
219. #2416C22semidirect
220. #2416C22semidirect
221. #2416C22semidirect
222. #2415C22semidirect
223. #2415C22semidirect
224. #2415C22semidirect
225. #2414C22semidirect
226. #2414C22semidirect
227. #2414C22semidirect
228. #2414C22semidirect
229. #2414C22semidirect
230. #2414C22semidirect
231. #2414C22semidirect
232. #2413C22semidirect
233. #2412C22semidirect
234. #2412C22semidirect
235. #2411C22semidirect
236. #2411C22semidirect
239. #2410C22semidirect
240. #2410C22semidirect
241. #2408C22semidirect
242. #2408C22semidirect
243. #2408C22semidirect
244. #2408C22semidirect
245. #2408C22semidirect
246. #2408C22semidirect
247. #2408C22semidirect
248. #2408C22semidirect
249. #2408C22semidirect
250. #2408C22semidirect
251. #2408C22semidirect
252. #2407C22semidirect
253. #2407C22semidirect
254. #2407C22semidirect
255. #2407C22semidirect
256. #2407C22semidirect
257. #2407C22semidirect
258. #2407C22semidirect
259. #2407C22semidirect
260. #2407C22semidirect
261. #2407C22semidirect
266. #2397C22semidirect
267. #2397C22semidirect
268. #2392C22semidirect
269. #2392C22semidirect
270. C2×#396C22semidirect
271. C2×#394C22semidirect
272. #2377C22semidirect
273. #2377C22semidirect
274. #2375C22semidirect
275. #2317C22semidirect
276. #2317C22semidirect
277. #2316C22semidirect
278. #2316C22semidirect
284. #2311C22semidirect
287. C4×#127C22semidirect
288. C4×#127C22semidirect
289. C4×#121C22semidirect
290. C4×#121C22semidirect
292. #2296C22semidirect
294. C2×#389C22semidirect
295. C2×#386C22semidirect
296. #2280C22semidirect
297. C2×#380C22semidirect
298. C4×#117C22semidirect
1447. C2×D4H(5,𝔽2)semidirect
1933. C2×C4#560semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#531282
#531032
#530982
#530952
#529882
#529812
#529712
#523472
#523202
#463392
#463382
#463282
#457012
#456162
#456082
#455632
#454832
#454442
#355632
#355182
#355172
#355132
#355122
#352672
#352662
#352632
#352522
#352272
#352232
#349362
#347372
C2×#24162