Finite Group Databasebeta

← #8095602

Subgroups — #8095602

Order 512.

5933 conjugacy classes of subgroups.

The subgroup lattice has 2039 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53129C212yesmaximal, complemented
2#53103C212yesmaximal, complemented
3#53103C212yesmaximal, complemented
4#53102C212yesmaximal, complemented
5#53098C212yesmaximal, complemented
6#53078C212yesmaximal, complemented
7#53060C212yesmaximal, complemented
8#53051C212yesmaximal, complemented
9#52345C214yesmaximal, complemented
10#52315C214yesmaximal, complemented
11#46339C212yesmaximal, complemented
12#46338C212yesmaximal, complemented
13#46338C212yesmaximal, complemented
14#46333C212yesmaximal, complemented
15#45732C214yesmaximal, complemented
16#45721C212yesmaximal, complemented
17#45655C212yesmaximal, complemented
18#45642C212yesmaximal, complemented
19#45588C214yesmaximal, complemented
20#45518C212yesmaximal, 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#35157C211yesmaximal, characteristic, complemented
32#35150C211yesmaximal, characteristic, complemented
33#34936C211yesmaximal, characteristic, complemented
34#34737C211yesmaximal, characteristic, complemented
35C2×#2414C211yesmaximal, characteristic, complemented
36C22×H(5,𝔽2)C2211yescharacteristic
37C2×#537C2211yescharacteristic
38C2×#535C2211yescharacteristic
39C2×#532C2211yescharacteristic
40C2×#525C2211yescharacteristic
41C2×#525C2211yescharacteristic
42C2×#525C2211yescharacteristic
43C2×#525C2211yescharacteristic
44C2×#525C2211yescharacteristic, complemented
45C2×#525C2211yescharacteristic, complemented
46C22×#121C2211yescharacteristic
47C22×#121C2211yescharacteristic
48C2×#520C2211yescharacteristic, complemented
49C22×C4×D4C2211yescharacteristic, complemented
50C22×#117C2211yescharacteristic, complemented
51C22×#117C2211yescharacteristic, complemented
52#2863C2212yescomplemented
53#2860C2212yescomplemented
54#2860C2212yescomplemented
55#2860C2212yescomplemented
56#2856C2212yescomplemented
57#2855C2212yescomplemented
58#2854C2214yescomplemented
59#2854C2212yescomplemented
60#2853C2214yescomplemented
61#2850C2212yescomplemented
62#2837C2214yescomplemented
63#2829C2214yescomplemented
64#2829C2214yescomplemented
65#2829C2214yescomplemented
66#2829C2214yescomplemented
67#2829C2214yescomplemented
68#2828C2214yescomplemented
69#2828C2214yescomplemented
70#2828C2214yescomplemented
71#2828C2214yescomplemented
72#2828C2214yescomplemented
73#2827C2214yescomplemented
74#2825C2214yescomplemented
75#2825C2214yescomplemented
76#2818C2214yescomplemented
77#2815C2214yescomplemented
78#2815C2214yescomplemented
79#2813C2214yescomplemented
80#2812C2214yescomplemented
81#2812C2214yescomplemented
82#2803C2214yescomplemented
83#2803C2214yescomplemented
84#2803C2214yescomplemented
85#2801C2214yescomplemented
86#2797C2214yescomplemented
87#2797C2214yescomplemented
88#2797C2214yescomplemented
89#2796C2214yescomplemented
90#2796C2214yescomplemented
91#2796C2214yescomplemented
92#2795C2214yescomplemented
93#2795C2214yescomplemented
94#2790C2214yescomplemented
95#2780C2214yescomplemented
96#2756C2214yescomplemented
97#2752C2214yescomplemented
98#2752C2214yescomplemented
99#2749C2214yescomplemented
100#2746C2214yescomplemented
101#2735C2214yescomplemented
102#2735C2214yescomplemented
103#2714C2214yescomplemented
104#2714C2214yescomplemented
105#2714C2214yescomplemented
106#2714C2214yescomplemented
107#2705C2214yescomplemented
108#2703C2214yescomplemented
109#2691C2214yescomplemented
110#2688C2214yescomplemented
111#2685C2214yescomplemented
112#2685C2214yescomplemented
113#2685C2214yescomplemented
114#2685C2214yescomplemented
115#2678C2214yescomplemented
116#2678C2214yescomplemented
117#2678C2214yescomplemented
118#2678C2214yescomplemented
119#2673C2214yescomplemented
120#2669C2214yescomplemented
121#2669C2214yescomplemented
122#2645C2212yescomplemented
123#2644C2212yescomplemented
124#2644C2212yescomplemented
125#2644C2212yescomplemented
126#2625C2212yescomplemented
127#2624C2212yescomplemented
128#2622C2214yescomplemented
129#2620C2212yescomplemented
130#2619C2212yescomplemented
131#2617C2214yescomplemented
132#2542C2211yescharacteristic, complemented
133#2542C2211yescharacteristic, complemented
134#2541C2211yescharacteristic, complemented
135#2541C2211yescharacteristic, complemented
136#2540C2211yescharacteristic, complemented
137#2540C2211yescharacteristic, complemented
138#2540C2211yescharacteristic, complemented
139#2540C2211yescharacteristic, complemented
140#2539C2212yescomplemented
141#2539C2212yescomplemented
142#2538C2212yescomplemented
143#2537C2212yescomplemented
144#2536C2212yescomplemented
145#2535C2212yescomplemented
146#2534C2214yescomplemented
147#2513C2212yescomplemented
148#2513C2212yescomplemented
149#2512C2212yescomplemented
150#2512C2212yescomplemented
151#2510C2214yescomplemented
152#2501C2212yescomplemented
153#2500C2212yescomplemented
154#2500C2212yescomplemented
155#2499C2212yescomplemented
156#2499C2212yescomplemented
157#2498C2214yescomplemented
158#2497C2212yescomplemented
159#2496C2212yescomplemented
160#2495C2212yescomplemented
161#2494C2212yescomplemented
162#2487C2212yescomplemented
163#2487C2212yescomplemented
164#2486C2212yescomplemented
165#2486C2212yescomplemented
166#2485C2212yescomplemented
167#2485C2212yescomplemented
168#2485C2212yescomplemented
169#2485C2212yescomplemented
170#2485C2212yescomplemented
171#2485C2212yescomplemented
172#2485C2212yescomplemented
173#2485C2212yescomplemented
174#2481C2214yescomplemented
175#2480C2214yescomplemented
176#2480C2214yescomplemented
177#2448C2212yescomplemented
178#2447C2212yescomplemented
179#2446C2212yescomplemented
180#2445C2212yescomplemented
181#2444C2214yescomplemented
182#2443C2214yescomplemented
183#2435C2212yescomplemented
184#2433C2212yescomplemented
185#2433C2212yescomplemented
186#2432C2212yescomplemented
187#2431C2212yescomplemented
188#2428C2212yescomplemented
189#2428C2212yescomplemented
190#2426C2212yescomplemented
191#2426C2212yescomplemented
192#2425C2214yescomplemented
193#2424C2214yescomplemented
194#2417C2211yescharacteristic, complemented
195#2417C2212yescomplemented
196#2417C2211yescharacteristic, complemented
197#2416C2211yescharacteristic, complemented
198#2416C2212yescomplemented
199#2416C2212yescomplemented
200#2416C2212yescomplemented
201#2416C2212yescomplemented
202#2416C2212yescomplemented
203#2416C2211yescharacteristic, complemented
204#2415C2212yescomplemented
205#2415C2212yescomplemented
206#2415C2212yescomplemented
207#2415C2212yescomplemented
208#2415C2211yescharacteristic, complemented
209#2415C2212yescomplemented
210#2415C2211yescharacteristic, complemented
211#2414C2211yescharacteristic, complemented
212#2414C2212yescomplemented
213#2414C2212yescomplemented
214#2414C2212yescomplemented
215#2414C2212yescomplemented
216#2414C2212yescomplemented
217#2414C2212yescomplemented
218#2414C2212yescomplemented
219#2414C2212yescomplemented
220#2414C2212yescomplemented
221#2414C2212yescomplemented
222#2414C2212yescomplemented
223#2414C2212yescomplemented
224#2414C2212yescomplemented
225#2414C2212yescomplemented
226#2414C2212yescomplemented
227#2414C2211yescharacteristic, complemented
228#2414C2212yescomplemented
229#2414C2212yescomplemented
230#2413C2212yescomplemented
231#2412C2214yescomplemented
232#2412C2212yescomplemented
233#2411C2214yescomplemented
234#2411C2212yescomplemented
235#2410C2214yes—
236#2410C2214yes—
237#2410C2212yescomplemented
238#2410C2214yescomplemented
239#2408C2212yescomplemented
240#2408C2212yescomplemented
241#2408C2212yescomplemented
242#2408C2212yescomplemented
243#2408C2212yescomplemented
244#2408C2212yescomplemented
245#2408C2212yescomplemented
246#2408C2212yescomplemented
247#2408C2214yescomplemented
248#2408C2212yescomplemented
249#2408C2212yescomplemented
250#2407C2212yescomplemented
251#2407C2212yescomplemented
252#2407C2212yescomplemented
253#2407C2212yescomplemented
254#2407C2212yescomplemented
255#2407C2212yescomplemented
256#2407C2212yescomplemented
257#2407C2212yescomplemented
258#2407C2212yescomplemented
259#2407C2212yescomplemented
260#2405C2214yes—
261#2405C2214yes—
262#2403C2214yes—
263#2403C2214yes—
264#2397C2212yescomplemented
265#2397C2212yescomplemented
266#2392C2212yescomplemented
267#2392C2212yescomplemented
268C2×#394C2212yescomplemented
269C2×#392C2212yescomplemented
270#2383C2214yescomplemented
271#2377C2214yescomplemented
272#2375C2214yescomplemented
273#2375C2214yescomplemented
274#2317C2211yescharacteristic, complemented
275#2317C2211yescharacteristic, complemented
276#2316C2211yescharacteristic, complemented
277#2316C2211yescharacteristic, complemented
278#2311C2211yescharacteristic
279#2311C2211yescharacteristic
280#2311C2211yescharacteristic
281#2311C2211yescharacteristic
282#2311C2211yescharacteristic
283#2311C2211yescharacteristic, complemented
284#2309C2211yescharacteristic
285#2309C2211yescharacteristic
286C4×#127C2212yescomplemented
287C4×#127C2212yescomplemented
288C4×#121C2212yescomplemented
289C4×#121C2212yescomplemented
290#2297C2211yescharacteristic
291#2296C2211yescharacteristic, complemented
292C2×#390C2211yescharacteristic
293C2×#390C2212yescomplemented
294C2×#389C2211yescharacteristic, complemented
295C2×#388C2212yescomplemented
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×D4C2314yes—
309C23×D4C2312yes—
310C23×D4C2312yes—
311C23×D4C2311yescharacteristic
312C23×D4C2312yes—
313C23×D4C2312yes—
314C24×C4C2311yescharacteristic
315C24×C4C2311yescharacteristic
316#537—44no—
317#535—44no—
318#532—44no—
319C2×C4⋊Q8C2311yescharacteristic
320C2×#127C2312yes—
321C2×#127C2312yes—
322C2×#127C2312yes—
323C2×#127C2311yescharacteristic
324C2×#126C2314yes—
325C2×#126C2314yes—
326C2×#126C2314yes—
327C2×#124C2312yes—
328C2×#124C2311yescharacteristic
329C2×#124C2311yescharacteristic
330#525—44no—
331#525—44no—
332#525—44no—
333#525—44no—
334#525—44no—
335#525—44no—
336C2×#123C2312yes—
337C2×#123C2312yes—
338C2×#123C2312yes—
339C2×#123C2312yes—
340C2×#123C2312yes—
341C2×#123C2312yes—
342C2×#123C2314yes—
343C2×#123C2314yes—
344C2×C22⋊Q8C2311yescharacteristic
345C2×C22⋊Q8C2311yescharacteristic
346C2×C22⋊Q8C2311yescharacteristic
347C2×C22⋊Q8C2311yescharacteristic
348C2×C22⋊Q8C2311yescharacteristic
349C2×C22⋊Q8C2311yescharacteristic
350C2×C22⋊Q8C2311yescharacteristic
351C2×C22⋊Q8C2311yescharacteristic
352C2×C22⋊Q8C2311yescharacteristic
353C2×C22⋊Q8C2311yescharacteristic
354C2×C22⋊Q8C2312yes—
355C2×C22⋊Q8C2311yescharacteristic
356C2×C22⋊Q8C2311yescharacteristic
357C2×C22⋊Q8C2312yes—
358C2×#121—44no—
359C2×#121—44no—
360C2×#121C2312yes—
361C2×#121C2311yescharacteristic
362C2×#121C2314yes—
363C2×#121C2311yescharacteristic
364C2×#121C2314yes—
365C2×#121C2311yescharacteristic
366C2×#121C2312yes—
367C2×#121C2311yescharacteristic
368C2×#121C2312yes—
369C2×#121C2312yes—
370C2×#121C2312yes—
371C2×#121C2312yes—
372C2×#121C2312yes—
373C2×#121C2312yes—
374C2×#121C2312yes—
375C2×#121C2312yes—
376C2×#121C2311yescharacteristic
377C2×#121C2311yescharacteristic
378C2×#121C2311yescharacteristic
379C2×#121C2311yescharacteristic
380C2×#121C2311yescharacteristic
381C2×#121C2311yescharacteristic
382C2×#121C2312yes—
383C2×#121C2312yes—
384C2×#121C2312yes—
385C2×#121C2312yes—
386C2×#121C2312yes—
387C2×#121C2311yescharacteristic
388C2×#121C2311yescharacteristic
389C2×#121C2312yes—
390C2×#121C2314yes—
391C2×#121C2314yes—
392C2×#121C2314yes—
393C2×#121C2314yes—
394C2×#120C2312yes—
395C2×#120C2312yes—
396C2×#120C2312yes—
397C2×#120C2314yes—
398C2×#120C2314yes—
399C2×#120C2312yes—
400C2×#120C2312yes—
401C2×#120C2314yes—
402C2×#120C2312yes—
403C2×#120C2314yes—
404C2×#120C2314yes—
405C2×#120C2314yes—
406C2×#120C2314yes—
407#520—44no—
408C2×C4×Q8C2312yes—
409C2×C4×D4—44no—
410C2×C4×D4C2311yescharacteristic
411C2×C4×D4C2311yescharacteristic
412C2×C4×D4C2312yes—
413C2×C4×D4C2312yes—
414C2×C4×D4C2312yes—
415C2×C4×D4C2312yes—
416C2×C4×D4C2312yes—
417C2×C4×D4C2312yes—
418C2×C4×D4C2312yes—
419C2×C4×D4C2312yes—
420C2×C4×D4C2312yes—
421C2×C4×D4C2311yescharacteristic
422C2×C4×D4C2311yescharacteristic
423C2×C4×D4C2312yes—
424C2×C4×D4C2312yes—
425C2×C4×D4C2312yes—
426C2×C4×D4C2311yescharacteristic
427C2×C4×D4C2311yescharacteristic
428C2×C4×D4C2312yes—
429C2×C4×D4C2311yescharacteristic
430C2×C4×D4C2311yescharacteristic
431C2×C4×D4C2314yes—
432C2×C4×D4C2312yes—
433C2×C4×D4C2312yes—
434C2×#117—44no—
435C2×#117—44no—
436C2×#117C2311yescharacteristic
437C2×#117C2311yescharacteristic
438C2×#117C2311yescharacteristic
439C2×#117C2311yescharacteristic
440C2×#117C2311yescharacteristic
441C2×#117C2312yes—
442C2×#117C2312yes—
443C2×#117C2312yes—
444C2×#117C2312yes—
445C2×#117C2311yescharacteristic
446C2×#117C2311yescharacteristic
447C2×#117C2312yes—
448C2×#117C2312yes—
449C2×#117C2312yes—
450C22×C4⋊C4C2311yescharacteristic
451C22×C4⋊C4C2311yescharacteristic
452C22×C4⋊C4C2311yescharacteristic
453C22×C4⋊C4C2311yescharacteristic
454C22×C4⋊C4C2311yescharacteristic
455C22×C4⋊C4C2311yescharacteristic
456C22×C4⋊C4C2312yes—
457C22×C4⋊C4C2312yes—
458C22×C22⋊C4C2312yes—
459C22×C22⋊C4C2312yes—
460C22×C22⋊C4C2311yescharacteristic
461C22×C22⋊C4C2312yes—
462C22×C22⋊C4C2312yes—
463C22×C22⋊C4C2311yescharacteristic
464C22×C22⋊C4C2312yes—
465C22×C22⋊C4C2312yes—
466C22×C22⋊C4C2312yes—
467C22×C42C2311yescharacteristic
468C22×C42C2312yes—
469C22×C42C2312yes—
470#401C2314yes—
471#400C2314yes—
472#400C2314yes—
473#400C2314yes—
474#400C2314yes—
475#400C2314yes—
476#399C2312yes—
477#399C2312yes—
478#399C2312yes—
479#399C2312yes—
480#399C2314yes—
481#399C2312yes—
482#399C2314yes—
483#399C2312yes—
484#399C2312yes—
485#399C2312yes—
486#398C2314yes—
487#398C2314yes—
488#398C2314yes—
489#398C2312yes—
490#398C2312yes—
491#397C2314yes—
492#397C2314yes—
493#397C2314yes—
494#397C2314yes—
495#397C2314yes—
496#397C2314yes—
497#397C2314yes—
498#397C2314yes—
499#397C2312yes—
500#397C2314yes—
501#397C2314yes—
502#397C2314yes—
503#397C2314yes—
504#397C2314yes—
505#397C2314yes—
506#397C2314yes—
507#397C2314yes—
508#397C2314yes—
509#397C2314yes—
510#397C2314yes—
511#397C2314yes—
512#397C2314yes—
513#397C2314yes—
514#397C2312yes—
515#396C2314yes—
516#396C2314yes—
517#396C2312yes—
518#396C2314yes—
519#396C2314yes—
520#396C2314yes—
521#396C2312yes—
522#396C2312yes—
523#396C2314yes—
524#396C2314yes—
525#396C2314yes—
526#396C2314yes—
527#396C2312yes—
528#394C2312yes—
529#394C2314yes—
530#394C2314yes—
531#394C2314yes—
532#394C2314yes—
533#394C2314yes—
534#394C2312yes—
535#394C2314yes—
536#394C2314yes—
537#394C2314yes—
538#394C2314yes—
539#394C2314yes—
540#394C2314yes—
541#394C2314yes—
542#394C2314yes—
543#394C2312yes—
544#394C2314yes—
545#394C2314yes—
546#394C2314yes—
547#394C2314yes—
548#394C2314yes—
549#394C2314yes—
550#394C2314yes—
551#394C2314yes—
552#394C2314yes—
553#394C2314yes—
554#394C2314yes—
555#394C2314yes—
556#394C2314yes—
557#394C2312yes—
558#394C2312yes—
559#394C2314yes—
560#394C2314yes—
561#394C2314yes—
562#394C2314yes—
563#394C2314yes—
564#394C2314yes—
565#394C2314yes—
566#394C2314yes—
567#394C2314yes—
568#394C2314yes—
569#394C2314yes—
570#394C2314yes—
571#394C2314yes—
572#394C2312yes—
573#392C2314yes—
574#392C2314yes—
575#392C2314yes—
576#392C2314yes—
577#392C2314yes—
578#392C2314yes—
579#392C2312yes—
580#392C2312yes—
581#392C2314yes—
582#392C2314yes—
583#392C2314yes—
584#392C2314yes—
585#392C2314yes—
586#392C2314yes—
587#392C2312yes—
588#392C2312yes—
589#392C2312yes—
590#392C2312yes—
591#392C2314yes—
592#392C2314yes—
593#392C2314yes—
594#392C2314yes—
595#392C2314yes—
596#392C2314yes—
597#392C2314yes—
598#392C2314yes—
599#392C2314yes—
600#392C2312yes—
601#392C2312yes—
602#392C2312yes—
603#392C2312yes—
604#392C2314yes—
605#392C2314yes—
606#391C2312yes—
607#391C2312yes—
608#391C2312yes—
609#391C2312yes—
610#391C2312yes—
611#391C2312yes—
612#391C2311yescharacteristic
613#391C2311yescharacteristic
614#390C2312yes—
615#390C2312yes—
616#390C2312yes—
617#390C2312yes—
618#390C2312yes—
619#390C2312yes—
620#390C2312yes—
621#390C2312yes—
622#390C2312yes—
623#390C2312yes—
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#390C2314yes—
641#390C2314yes—
642#390C2314yes—
643#390C2312yes—
644#390C2314yes—
645#390C2314yes—
646#390C2314yes—
647#390C2314yes—
648#390C2312yes—
649#390C2311yescharacteristic
650#390C2314yes—
651#390C2314yes—
652#390C2312yes—
653#390C2311yescharacteristic
654#390C2312yes—
655#390C2314yes—
656#390C2314yes—
657#390C2312yes—
658#390C2312yes—
659#389C2312yes—
660#389C2312yes—
661#389C2312yes—
662#389C2312yes—
663#389C2312yes—
664#389C2312yes—
665#389C2312yes—
666#389C2312yes—
667#389C2312yes—
668#389C2312yes—
669#389C2312yes—
670#389C2312yes—
671#389C2314yes—
672#389C2314yes—
673#389C2311yescharacteristic
674#389C2311yescharacteristic
675#389C2312yes—
676#389C2312yes—
677#389C2314yes—
678#389C2311yescharacteristic
679#389C2311yescharacteristic
680#389C2312yes—
681#389C2312yes—
682#389C2312yes—
683#389C2312yes—
684#388C2312yes—
685#388C2314yes—
686#388C2314yes—
687#388C2314yes—
688#388C2314yes—
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#388C2314yes—
706#388C2314yes—
707#388C2314yes—
708#388C2314yes—
709#388C2314yes—
710#388C2312yes—
711#388C2314yes—
712#388C2314yes—
713#388C2314yes—
714#388C2314yes—
715#388C2312yes—
716#388C2312yes—
717#388C2314yes—
718#388C2314yes—
719#387C2314yes—
720#387C2314yes—
721#387C2314yes—
722#387C2314yes—
723#387C2314yes—
724#387C2314yes—
725#387C2314yes—
726#387C2314yes—
727#387C2314yes—
728#387C2314yes—
729#387C2314yes—
730#386C2314yes—
731#386C2314yes—
732#386C2314yes—
733#386C2314yes—
734#386C2314yes—
735#386C2314yes—
736#386C2312yes—
737#386C2314yes—
738#386C2314yes—
739#386C2314yes—
740#386C2314yes—
741#386C2314yes—
742#386C2314yes—
743#386C2314yes—
744#386C2312yes—
745#386C2314yes—
746#386C2314yes—
747#386C2314yes—
748#386C2314yes—
749#386C2314yes—
750#386C2314yes—
751#386C2314yes—
752#386C2312yes—
753#386C2312yes—
754#386C2312yes—
755#386C2312yes—
756#385C2314yes—
757#385C2314yes—
758#385C2314yes—
759#385C2314yes—
760#385C2314yes—
761#385C2314yes—
762#385C2314yes—
763#385C2314yes—
764#385C2314yes—
765#385C2314yes—
766#385C2312yes—
767#385C2312yes—
768#384C2312yes—
769#384C2312yes—
770#384C2312yes—
771#384C2312yes—
772#383C2314yes—
773#382C2312yes—
774#382C2312yes—
775#381C2312yes—
776#381C2314yes—
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#380C2312yes—
793#380C2312yes—
794#380C2312yes—
795#380C2312yes—
796#380C2312yes—
797#380C2312yes—
798#380C2311yescharacteristic
799#380C2311yescharacteristic
800#380C2311yescharacteristic
801#380C2311yescharacteristic
802#380C2314yes—
803#379C2314yes—
804#379C2314yes—
805#379C2312yes—
806#379C2314yes—
807#379C2314yes—
808#379C2314yes—
809#379C2314yes—
810#379C2314yes—
811#379C2314yes—
812C4×C4⋊C4C2312yes—
813C4×C4⋊C4C2312yes—
814C4×C4⋊C4C2311yescharacteristic
815C4×C4⋊C4C2311yescharacteristic
816C4×C4⋊C4C2311yescharacteristic
817C4×C4⋊C4C2311yescharacteristic
818C4×C22⋊C4C2312yes—
819C4×C22⋊C4C2312yes—
820C4×C22⋊C4C2312yes—
821C4×C22⋊C4C2312yes—
822C4×C22⋊C4C2312yes—
823C4×C22⋊C4C2312yes—
824#376C2312yes—
825C2×#95C2312yes—
826C2×#95C2312yes—
827C43C2312yes—
828C25C2411yescharacteristic
829C25C2412yes—
830C25C2411yescharacteristic
831C25C2414yes—
832H(5,𝔽2)—464no—
833C2×#41—24no—
834C2×#41—24no—
835C2×#41—24no—
836C2×#41—24no—
837C2×#41—24no—
838C2×#41—24no—
839C2×#41—24no—
840C2×#41—24no—
841C2×#41—24no—
842C2×#41—44no—
843C2×#41—44no—
844C2×#41—44no—
845C2×#41—44no—
846C2×#41—44no—
847C2×#41—44no—
848C22×Q8C2411yescharacteristic
849C22×Q8C2411yescharacteristic
850C22×Q8C2411yescharacteristic
851C22×D4—24no—
852C22×D4—24no—
853C22×D4—24no—
854C22×D4—42no—
855C22×D4—44no—
856C22×D4—44no—
857C22×D4—44no—
858C22×D4—44no—
859C22×D4—44no—
860C22×D4—44no—
861C22×D4—42no—
862C22×D4—44no—
863C22×D4—44no—
864C22×D4—42no—
865C22×D4—48no—
866C22×D4—48no—
867C22×D4—48no—
868C22×D4—44no—
869C22×D4—82no—
870C22×D4—82no—
871C22×D4—82no—
872C22×D4C2412yes—
873C22×D4C2411yescharacteristic
874C22×D4C2412yes—
875C22×D4C2412yes—
876C22×D4C2412yes—
877C22×D4C2411yescharacteristic
878C22×D4C2412yes—
879C22×D4C2411yescharacteristic
880C22×D4C2411yescharacteristic
881C22×D4C2411yescharacteristic
882C22×D4C2411yescharacteristic
883C22×D4C2412yes—
884C22×D4C2412yes—
885C22×D4C2412yes—
886C22×D4C2412yes—
887C22×D4C2414yes—
888C22×D4C2411yescharacteristic
889C22×D4C2412yes—
890C22×D4C2412yes—
891C22×D4C2412yes—
892C22×D4C2412yes—
893C22×D4C2412yes—
894C22×D4C2412yes—
895C22×D4C2412yes—
896C22×D4C2412yes—
897C22×D4C2412yes—
898C22×D4C2412yes—
899C22×D4C2414yes—
900C22×D4C2414yes—
901C22×D4C2414yes—
902C22×D4C2414yes—
903C22×D4C2414yes—
904C22×D4C2414yes—
905C22×D4C2414yes—
906C22×D4C2414yes—
907C23×C4—24no—
908C23×C4—24no—
909C23×C4—24no—
910C23×C4—24no—
911C23×C4—24no—
912C23×C4—24no—
913C23×C4C2411yescharacteristic
914C23×C4C2411yescharacteristic
915C23×C4C2411yescharacteristic
916C23×C4C2412yes—
917C23×C4C2411yescharacteristic
918C23×C4C2411yescharacteristic
919C23×C4C2411yescharacteristic
920C23×C4C2411yescharacteristic
921C23×C4C2411yescharacteristic
922C23×C4C2411yescharacteristic
923C23×C4C2412yes—
924C23×C4C2411yescharacteristic
925C23×C4C2412yes—
926C23×C4C2411yescharacteristic
927C23×C4C2411yescharacteristic
928C23×C4C2412yes—
929C23×C4C2412yes—
930C23×C4C2412yes—
931C23×C4C2412yes—
932C23×C4C2412yes—
933C23×C4C2414yes—
934C23×C4C2414yes—
935C23×C4C2411yescharacteristic
936C4⋊Q8—42no—
937#127—44no—
938#127—42no—
939#127—44no—
940#127—44no—
941#126—48no—
942#126—84no—
943#126—84no—
944#124—42no—
945#124—42no—
946#124—44no—
947#123—44no—
948#123—44no—
949#123—44no—
950#123—44no—
951#123—44no—
952#123—44no—
953#123—84no—
954#123—84no—
955C22⋊Q8—42no—
956C22⋊Q8—42no—
957C22⋊Q8—42no—
958C22⋊Q8—42no—
959C22⋊Q8—42no—
960C22⋊Q8—42no—
961C22⋊Q8—42no—
962C22⋊Q8—42no—
963C22⋊Q8—42no—
964C22⋊Q8—42no—
965C22⋊Q8—42no—
966C22⋊Q8—42no—
967C22⋊Q8—44no—
968C22⋊Q8—44no—
969#121—44no—
970#121—44no—
971#121—44no—
972#121—44no—
973#121—44no—
974#121—44no—
975#121—44no—
976#121—44no—
977#121—44no—
978#121—42no—
979#121—42no—
980#121—42no—
981#121—42no—
982#121—42no—
983#121—42no—
984#121—42no—
985#121—42no—
986#121—42no—
987#121—42no—
988#121—42no—
989#121—42no—
990#121—44no—
991#121—44no—
992#121—44no—
993#121—44no—
994#121—44no—
995#121—48no—
996#121—44no—
997#121—44no—
998#121—48no—
999#121—84no—
1000#121—84no—
1001#121—84no—
1002#121—84no—
1003#120—48no—
1004#120—44no—
1005#120—44no—
1006#120—44no—
1007#120—44no—
1008#120—44no—
1009#120—44no—
1010#120—48no—
1011#120—48no—
1012#120—84no—
1013#120—84no—
1014#120—84no—
1015#120—84no—
1016C4×Q8—44no—
1017C4×D4—44no—
1018C4×D4—42no—
1019C4×D4—42no—
1020C4×D4—42no—
1021C4×D4—42no—
1022C4×D4—42no—
1023C4×D4—42no—
1024C4×D4—42no—
1025C4×D4—42no—
1026C4×D4—44no—
1027C4×D4—44no—
1028C4×D4—44no—
1029C4×D4—44no—
1030C4×D4—44no—
1031C4×D4—44no—
1032C4×D4—44no—
1033C4×D4—44no—
1034C4×D4—44no—
1035C4×D4—44no—
1036C4×D4—44no—
1037C4×D4—44no—
1038C4×D4—44no—
1039C4×D4—44no—
1040C4×D4—48no—
1041#117—24no—
1042#117—24no—
1043#117—24no—
1044#117—24no—
1045#117—24no—
1046#117—44no—
1047#117—44no—
1048#117—44no—
1049#117—44no—
1050#117—44no—
1051#117—44no—
1052#117—42no—
1053#117—42no—
1054#117—44no—
1055C2×C4⋊C4—24no—
1056C2×C4⋊C4—24no—
1057C2×C4⋊C4—24no—
1058C2×C4⋊C4—42no—
1059C2×C4⋊C4—42no—
1060C2×C4⋊C4—44no—
1061C2×C4⋊C4—42no—
1062C2×C4⋊C4—82no—
1063C2×C4⋊C4C2412yes—
1064C2×C4⋊C4C2411yescharacteristic
1065C2×C4⋊C4C2412yes—
1066C2×C4⋊C4C2411yescharacteristic
1067C2×C4⋊C4C2411yescharacteristic
1068C2×C4⋊C4C2412yes—
1069C2×C4⋊C4C2412yes—
1070C2×C4⋊C4C2411yescharacteristic
1071C2×C4⋊C4C2411yescharacteristic
1072C2×C4⋊C4C2412yes—
1073C2×C4⋊C4C2412yes—
1074C2×C4⋊C4C2411yescharacteristic
1075C2×C4⋊C4C2411yescharacteristic
1076C2×C4⋊C4C2411yescharacteristic
1077C2×C4⋊C4C2411yescharacteristic
1078C2×C4⋊C4C2411yescharacteristic
1079C2×C4⋊C4C2412yes—
1080C2×C4⋊C4C2412yes—
1081C2×C4⋊C4C2412yes—
1082C2×C4⋊C4C2411yescharacteristic
1083C2×C4⋊C4C2411yescharacteristic
1084C2×C4⋊C4C2411yescharacteristic
1085C2×C4⋊C4C2411yescharacteristic
1086C2×C4⋊C4C2414yes—
1087C2×C4⋊C4C2414yes—
1088C2×C4⋊C4C2414yes—
1089C2×C4⋊C4C2412yes—
1090C2×C4⋊C4C2412yes—
1091C2×C4⋊C4C2412yes—
1092C2×C4⋊C4C2412yes—
1093C2×C4⋊C4C2412yes—
1094C2×C4⋊C4C2412yes—
1095C2×C4⋊C4C2412yes—
1096C2×C4⋊C4C2412yes—
1097C2×C4⋊C4C2412yes—
1098C2×C4⋊C4C2412yes—
1099C2×C4⋊C4C2412yes—
1100C2×C4⋊C4C2412yes—
1101C2×C4⋊C4C2412yes—
1102C2×C4⋊C4C2412yes—
1103C2×C4⋊C4C2414yes—
1104C2×C4⋊C4C2414yes—
1105C2×C4⋊C4C2414yes—
1106C2×C4⋊C4C2414yes—
1107C2×C4⋊C4C2414yes—
1108C2×C4⋊C4C2412yes—
1109C2×C4⋊C4C2414yes—
1110C2×C4⋊C4C2412yes—
1111C2×C4⋊C4C2414yes—
1112C2×C4⋊C4C2412yes—
1113C2×C4⋊C4C2414yes—
1114C2×C4⋊C4C2414yes—
1115C2×C22⋊C4—44no—
1116C2×C22⋊C4—44no—
1117C2×C22⋊C4—44no—
1118C2×C22⋊C4—42no—
1119C2×C22⋊C4—42no—
1120C2×C22⋊C4—44no—
1121C2×C22⋊C4—44no—
1122C2×C22⋊C4—82no—
1123C2×C22⋊C4—82no—
1124C2×C22⋊C4C2412yes—
1125C2×C22⋊C4C2412yes—
1126C2×C22⋊C4C2414yes—
1127C2×C22⋊C4C2412yes—
1128C2×C22⋊C4C2412yes—
1129C2×C22⋊C4C2412yes—
1130C2×C22⋊C4C2412yes—
1131C2×C22⋊C4C2414yes—
1132C2×C22⋊C4C2414yes—
1133C2×C22⋊C4C2412yes—
1134C2×C22⋊C4C2412yes—
1135C2×C22⋊C4C2411yescharacteristic
1136C2×C22⋊C4C2411yescharacteristic
1137C2×C22⋊C4C2411yescharacteristic
1138C2×C22⋊C4C2411yescharacteristic
1139C2×C22⋊C4C2411yescharacteristic
1140C2×C22⋊C4C2411yescharacteristic
1141C2×C22⋊C4C2411yescharacteristic
1142C2×C22⋊C4C2411yescharacteristic
1143C2×C22⋊C4C2414yes—
1144C2×C22⋊C4C2414yes—
1145C2×C22⋊C4C2414yes—
1146C2×C22⋊C4C2414yes—
1147C2×C22⋊C4C2414yes—
1148C2×C22⋊C4C2414yes—
1149C2×C22⋊C4C2414yes—
1150C2×C22⋊C4C2414yes—
1151C2×C22⋊C4C2414yes—
1152C2×C22⋊C4C2414yes—
1153C2×C22⋊C4C2412yes—
1154C2×C22⋊C4C2412yes—
1155C2×C22⋊C4C2412yes—
1156C2×C22⋊C4C2412yes—
1157C2×C22⋊C4C2412yes—
1158C2×C22⋊C4C2412yes—
1159C2×C22⋊C4C2412yes—
1160C2×C22⋊C4C2412yes—
1161C2×C22⋊C4C2412yes—
1162C2×C22⋊C4C2412yes—
1163C2×C22⋊C4C2412yes—
1164C2×C22⋊C4C2412yes—
1165C2×C22⋊C4C2412yes—
1166C2×C22⋊C4C2412yes—
1167C2×C22⋊C4C2412yes—
1168C2×C22⋊C4C2412yes—
1169C2×C22⋊C4C2412yes—
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⋊C4C2414yes—
1183C2×C22⋊C4C2414yes—
1184C2×C22⋊C4C2414yes—
1185C2×C22⋊C4C2414yes—
1186C2×C22⋊C4C2414yes—
1187C2×C22⋊C4C2414yes—
1188C2×C22⋊C4C2414yes—
1189C2×C22⋊C4C2414yes—
1190C2×C22⋊C4C2414yes—
1191C2×C22⋊C4C2414yes—
1192C2×C22⋊C4C2414yes—
1193C2×C22⋊C4C2414yes—
1194C2×C22⋊C4C2414yes—
1195C2×C22⋊C4C2414yes—
1196C2×C22⋊C4C2414yes—
1197C2×C22⋊C4C2414yes—
1198C2×C22⋊C4C2414yes—
1199C2×C22⋊C4C2414yes—
1200C2×C22⋊C4C2412yes—
1201C2×C22⋊C4C2412yes—
1202C2×C22⋊C4C2414yes—
1203C2×C22⋊C4C2414yes—
1204C2×C22⋊C4C2412yes—
1205C2×C22⋊C4C2412yes—
1206C2×C22⋊C4C2412yes—
1207C2×C22⋊C4C2414yes—
1208C2×C22⋊C4C2414yes—
1209C2×C22⋊C4C2412yes—
1210C2×C22⋊C4C2414yes—
1211C2×C22⋊C4C2414yes—
1212C2×C42—24no—
1213C2×C42—44no—
1214C2×C42—44no—
1215C2×C42C2412yes—
1216C2×C42C2412yes—
1217C2×C42C2412yes—
1218C2×C42C2412yes—
1219C2×C42C2412yes—
1220C2×C42C2411yescharacteristic
1221C2×C42C2411yescharacteristic
1222C2×C42C2411yescharacteristic
1223C2×C42C2411yescharacteristic
1224C2×C42C2412yes—
1225C2×C42C2412yes—
1226C2×C42C2412yes—
1227C2×C42C2414yes—
1228C2×C42C2414yes—
1229C2×C42C2414yes—
1230C2×C42C2412yes—
1231C2×C42C2412yes—
1232C2×C42C2412yes—
1233#95C2414yes—
1234#95C2414yes—
1235#95C2414yes—
1236#95C2414yes—
1237#95C2412yes—
1238#95C2412yes—
1239#95C2412yes—
1240#95C2412yes—
1241#95C2412yes—
1242#95C2412yes—
1243#95C2412yes—
1244#95C2412yes—
1245#95C2412yes—
1246#95C2412yes—
1247#95C2412yes—
1248#95C2412yes—
1249#95C2412yes—
1250#95C2412yes—
1251#95C2412yes—
1252#95C2412yes—
1253#95C2414yes—
1254#95C2414yes—
1255#95C2414yes—
1256#95C2414yes—
1257#95C2414yes—
1258#95C2414yes—
1259#95C2414yes—
1260#95C2414yes—
1261#95C2414yes—
1262#95C2414yes—
1263#95C2414yes—
1264#95C2414yes—
1265#95C2414yes—
1266#95C2414yes—
1267#95C2414yes—
1268#95C2414yes—
1269#95C2414yes—
1270#95C2414yes—
1271#95C2414yes—
1272#95C2414yes—
1273C24—22no—
1274C24—22no—
1275C24—22no—
1276C24—22no—
1277C24—22no—
1278C24—22no—
1279C24—24no—
1280C24—24no—
1281C24—22no—
1282C24—24no—
1283C24—41no—
1284C24—41no—
1285C24—41no—
1286C24—41no—
1287C24—41no—
1288C24—41no—
1289C24—41no—
1290C24—44no—
1291C24—44no—
1292C24—44no—
1293C24—42no—
1294C24—42no—
1295C24—42no—
1296C24—42no—
1297C24—44no—
1298C24—44no—
1299C24—44no—
1300C24—44no—
1301C24C2512yes—
1302C24C2512yes—
1303C24C2514yes—
1304C24C2511yescharacteristic
1305C24C2511yescharacteristic
1306C24C2511yescharacteristic
1307C24C2512yes—
1308C24C2511yescharacteristic
1309C24C2511yescharacteristic
1310#41—432no—
1311#41—432no—
1312#41—416no—
1313#41—416no—
1314#41—416no—
1315C2×Q8—22no—
1316C2×Q8—22no—
1317C2×Q8—22no—
1318C2×Q8—22no—
1319C2×Q8—22no—
1320C2×Q8—22no—
1321C2×Q8—22no—
1322C2×Q8—22no—
1323C2×Q8—22no—
1324C2×D4—24no—
1325C2×D4—24no—
1326C2×D4—24no—
1327C2×D4—24no—
1328C2×D4—24no—
1329C2×D4—24no—
1330C2×D4—24no—
1331C2×D4—24no—
1332C2×D4—24no—
1333C2×D4—22no—
1334C2×D4—22no—
1335C2×D4—24no—
1336C2×D4—24no—
1337C2×D4—28no—
1338C2×D4—24no—
1339C2×D4—22no—
1340C2×D4—22no—
1341C2×D4—22no—
1342C2×D4—24no—
1343C2×D4—24no—
1344C2×D4—24no—
1345C2×D4—24no—
1346C2×D4—24no—
1347C2×D4—22no—
1348C2×D4—22no—
1349C2×D4—22no—
1350C2×D4—22no—
1351C2×D4—22no—
1352C2×D4—24no—
1353C2×D4—22no—
1354C2×D4—22no—
1355C2×D4—22no—
1356C2×D4—24no—
1357C2×D4—41no—
1358C2×D4—41no—
1359C2×D4—41no—
1360C2×D4—41no—
1361C2×D4—44no—
1362C2×D4—44no—
1363C2×D4—44no—
1364C2×D4—44no—
1365C2×D4—44no—
1366C2×D4—44no—
1367C2×D4—41no—
1368C2×D4—41no—
1369C2×D4—41no—
1370C2×D4—41no—
1371C2×D4—42no—
1372C2×D4—42no—
1373C2×D4—42no—
1374C2×D4—42no—
1375C2×D4—42no—
1376C2×D4—42no—
1377C2×D4—42no—
1378C2×D4—42no—
1379C2×D4—42no—
1380C2×D4—42no—
1381C2×D4—42no—
1382C2×D4—42no—
1383C2×D4—42no—
1384C2×D4—42no—
1385C2×D4—42no—
1386C2×D4—42no—
1387C2×D4—42no—
1388C2×D4—42no—
1389C2×D4—42no—
1390C2×D4—42no—
1391C2×D4—42no—
1392C2×D4—44no—
1393C2×D4—44no—
1394C2×D4—44no—
1395C2×D4—44no—
1396C2×D4—44no—
1397C2×D4—44no—
1398C2×D4—44no—
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—42no—
1411C2×D4—42no—
1412C2×D4—42no—
1413C2×D4—42no—
1414C2×D4—42no—
1415C2×D4—42no—
1416C2×D4—42no—
1417C2×D4—42no—
1418C2×D4—42no—
1419C2×D4—44no—
1420C2×D4—44no—
1421C2×D4—44no—
1422C2×D4—44no—
1423C2×D4—44no—
1424C2×D4—44no—
1425C2×D4—44no—
1426C2×D4—44no—
1427C2×D4—44no—
1428C2×D4—44no—
1429C2×D4—416no—
1430C2×D4—464no—
1431C2×D4—432no—
1432C2×D4—432no—
1433C2×D4—416no—
1434C2×D4—816no—
1435C2×D4—816no—
1436C22×C4—22no—
1437C22×C4—22no—
1438C22×C4—24no—
1439C22×C4—22no—
1440C22×C4—22no—
1441C22×C4—22no—
1442C22×C4—22no—
1443C22×C4—22no—
1444C22×C4—22no—
1445C22×C4—24no—
1446C22×C4—24no—
1447C22×C4—24no—
1448C22×C4—22no—
1449C22×C4—22no—
1450C22×C4—24no—
1451C22×C4—22no—
1452C22×C4—22no—
1453C22×C4—22no—
1454C22×C4—22no—
1455C22×C4—22no—
1456C22×C4—22no—
1457C22×C4—22no—
1458C22×C4—22no—
1459C22×C4—22no—
1460C22×C4—22no—
1461C22×C4—22no—
1462C22×C4—22no—
1463C22×C4—22no—
1464C22×C4—22no—
1465C22×C4—24no—
1466C22×C4—22no—
1467C22×C4—22no—
1468C22×C4—22no—
1469C22×C4—22no—
1470C22×C4—22no—
1471C22×C4—22no—
1472C22×C4—24no—
1473C22×C4—24no—
1474C22×C4—24no—
1475C22×C4—24no—
1476C22×C4—24no—
1477C22×C4—24no—
1478C22×C4—22no—
1479C22×C4—22no—
1480C22×C4—24no—
1481C22×C4—22no—
1482C22×C4—42no—
1483C22×C4—41no—
1484C22×C4—42no—
1485C22×C4—44no—
1486C22×C4—44no—
1487C22×C4—44no—
1488C22×C4—42no—
1489C22×C4—42no—
1490C22×C4—42no—
1491C22×C4—41no—
1492C22×C4—42no—
1493C22×C4—42no—
1494C22×C4—41no—
1495C22×C4—42no—
1496C22×C4—42no—
1497C22×C4—42no—
1498C22×C4—42no—
1499C22×C4—44no—
1500C22×C4—44no—
1501C22×C4—44no—
1502C22×C4—416no—
1503C22×C4—416no—
1504C22×C4H(5,𝔽2)14yes—
1505C22×C4H(5,𝔽2)14yes—
1506C22×C4H(5,𝔽2)14yes—
1507C22×C4C2511yescharacteristic
1508C22×C4C2512yes—
1509C22×C4C2512yes—
1510C22×C4C2512yes—
1511C22×C4C2512yes—
1512C22×C4C2514yes—
1513C22×C4C2514yes—
1514C22×C4C2512yes—
1515C22×C4C2512yes—
1516C22×C4C2512yes—
1517C22×C4C2512yes—
1518C22×C4C2512yes—
1519C22×C4C2512yes—
1520C22×C4C2512yes—
1521C22×C4C2514yes—
1522C22×C4C2511yescharacteristic
1523C22×C4C2512yes—
1524C22×C4C2511yescharacteristic
1525C22×C4C2511yescharacteristic
1526C22×C4C2511yescharacteristic
1527C22×C4C2511yescharacteristic
1528C22×C4C2512yes—
1529C22×C4C2511yescharacteristic
1530C22×C4C2511yescharacteristic
1531C22×C4C2511yescharacteristic
1532C22×C4C2511yescharacteristic
1533C4⋊C4—24no—
1534C4⋊C4—24no—
1535C4⋊C4—24no—
1536C4⋊C4—24no—
1537C4⋊C4—24no—
1538C4⋊C4—24no—
1539C4⋊C4—22no—
1540C4⋊C4—22no—
1541C4⋊C4—22no—
1542C4⋊C4—22no—
1543C4⋊C4—22no—
1544C4⋊C4—22no—
1545C4⋊C4—22no—
1546C4⋊C4—22no—
1547C4⋊C4—22no—
1548C4⋊C4—22no—
1549C4⋊C4—24no—
1550C4⋊C4—42no—
1551C4⋊C4—42no—
1552C4⋊C4—41no—
1553C4⋊C4—41no—
1554C4⋊C4—41no—
1555C4⋊C4—41no—
1556C4⋊C4—44no—
1557C4⋊C4—44no—
1558C4⋊C4—44no—
1559C4⋊C4—42no—
1560C4⋊C4—42no—
1561C4⋊C4—42no—
1562C4⋊C4—42no—
1563C4⋊C4—42no—
1564C4⋊C4—42no—
1565C4⋊C4—42no—
1566C4⋊C4—42no—
1567C4⋊C4—42no—
1568C4⋊C4—42no—
1569C4⋊C4—42no—
1570C4⋊C4—42no—
1571C4⋊C4—42no—
1572C4⋊C4—42no—
1573C4⋊C4—44no—
1574C4⋊C4—42no—
1575C4⋊C4—44no—
1576C4⋊C4—44no—
1577C4⋊C4—44no—
1578C4⋊C4—44no—
1579C4⋊C4—44no—
1580C4⋊C4—42no—
1581C4⋊C4—44no—
1582C4⋊C4—44no—
1583C4⋊C4—44no—
1584C4⋊C4—42no—
1585C22⋊C4—24no—
1586C22⋊C4—24no—
1587C22⋊C4—24no—
1588C22⋊C4—24no—
1589C22⋊C4—24no—
1590C22⋊C4—28no—
1591C22⋊C4—24no—
1592C22⋊C4—44no—
1593C22⋊C4—42no—
1594C22⋊C4—42no—
1595C22⋊C4—44no—
1596C22⋊C4—44no—
1597C22⋊C4—41no—
1598C22⋊C4—41no—
1599C22⋊C4—41no—
1600C22⋊C4—41no—
1601C22⋊C4—41no—
1602C22⋊C4—41no—
1603C22⋊C4—41no—
1604C22⋊C4—41no—
1605C22⋊C4—44no—
1606C22⋊C4—44no—
1607C22⋊C4—44no—
1608C22⋊C4—44no—
1609C22⋊C4—44no—
1610C22⋊C4—44no—
1611C22⋊C4—44no—
1612C22⋊C4—44no—
1613C22⋊C4—44no—
1614C22⋊C4—42no—
1615C22⋊C4—42no—
1616C22⋊C4—42no—
1617C22⋊C4—42no—
1618C22⋊C4—42no—
1619C22⋊C4—42no—
1620C22⋊C4—42no—
1621C22⋊C4—42no—
1622C22⋊C4—42no—
1623C22⋊C4—42no—
1624C22⋊C4—42no—
1625C22⋊C4—42no—
1626C22⋊C4—42no—
1627C22⋊C4—42no—
1628C22⋊C4—42no—
1629C22⋊C4—42no—
1630C22⋊C4—42no—
1631C22⋊C4—42no—
1632C22⋊C4—42no—
1633C22⋊C4—42no—
1634C22⋊C4—42no—
1635C22⋊C4—42no—
1636C22⋊C4—42no—
1637C22⋊C4—42no—
1638C22⋊C4—42no—
1639C22⋊C4—42no—
1640C22⋊C4—42no—
1641C22⋊C4—42no—
1642C22⋊C4—44no—
1643C22⋊C4—44no—
1644C22⋊C4—44no—
1645C22⋊C4—44no—
1646C22⋊C4—44no—
1647C22⋊C4—44no—
1648C22⋊C4—42no—
1649C22⋊C4—44no—
1650C22⋊C4—44no—
1651C22⋊C4—44no—
1652C22⋊C4—44no—
1653C22⋊C4—44no—
1654C22⋊C4—44no—
1655C22⋊C4—44no—
1656C22⋊C4—44no—
1657C22⋊C4—44no—
1658C22⋊C4—44no—
1659C22⋊C4—44no—
1660C22⋊C4—42no—
1661C22⋊C4—42no—
1662C22⋊C4—44no—
1663C22⋊C4—42no—
1664C22⋊C4—44no—
1665C22⋊C4—44no—
1666C22⋊C4—42no—
1667C22⋊C4—42no—
1668C22⋊C4—44no—
1669C22⋊C4—44no—
1670C22⋊C4—44no—
1671C22⋊C4—44no—
1672C22⋊C4—42no—
1673C42—22no—
1674C42—22no—
1675C42—22no—
1676C42—22no—
1677C42—24no—
1678C42—24no—
1679C42—24no—
1680C42—24no—
1681C42—24no—
1682C42—24no—
1683C42—42no—
1684C42—42no—
1685C42—44no—
1686C42—44no—
1687C42—44no—
1688C42—42no—
1689C42—42no—
1690C42—42no—
1691C23—21no—
1692C23—21no—
1693C23—21no—
1694C23—21no—
1695C23—21no—
1696C23—21no—
1697C23—21no—
1698C23—21no—
1699C23—21no—
1700C23—21no—
1701C23—21no—
1702C23—21no—
1703C23—21no—
1704C23—21no—
1705C23—21no—
1706C23—21no—
1707C23—22no—
1708C23—22no—
1709C23—21no—
1710C23—21no—
1711C23—21no—
1712C23—22no—
1713C23—22no—
1714C23—22no—
1715C23—22no—
1716C23—22no—
1717C23—22no—
1718C23—22no—
1719C23—24no—
1720C23—24no—
1721C23—24no—
1722C23—24no—
1723C23—22no—
1724C23—22no—
1725C23—22no—
1726C23—21no—
1727C23—21no—
1728C23—22no—
1729C23—22no—
1730C23—24no—
1731C23—22no—
1732C23—21no—
1733C23—21no—
1734C23—21no—
1735C23—21no—
1736C23—22no—
1737C23—21no—
1738C23—24no—
1739C23—22no—
1740C23—22no—
1741C23—22no—
1742C23—22no—
1743C23—21no—
1744C23—21no—
1745C23—24no—
1746C23—22no—
1747C23—21no—
1748C23—21no—
1749C23—21no—
1750C23—44no—
1751C23—44no—
1752C23—44no—
1753C23—44no—
1754C23—44no—
1755C23—416no—
1756C23—44no—
1757C23—44no—
1758C23—48no—
1759C23—82no—
1760C23—82no—
1761C23—82no—
1762C23—82no—
1763C23—82no—
1764C23—82no—
1765C23—82no—
1766C23—84no—
1767C23—84no—
1768C23—84no—
1769C23—84no—
1770C23—84no—
1771C23—84no—
1772C23—164no—
1773C23—164no—
1774C23—164no—
1775C23—164no—
1776C23—164no—
1777C23—164no—
1778C23C2×H(5,𝔽2)12yes—
1779C23C2×H(5,𝔽2)12yes—
1780C23C2×H(5,𝔽2)12yes—
1781C23#58512yes—
1782C23C2611yescharacteristic
1783Q8—44no—
1784Q8—44no—
1785Q8—44no—
1786D4—44no—
1787D4—44no—
1788D4—44no—
1789D4—44no—
1790D4—416no—
1791D4—416no—
1792D4—48no—
1793D4—48no—
1794D4—48no—
1795D4—48no—
1796D4—44no—
1797D4—48no—
1798D4—44no—
1799D4—44no—
1800D4—84no—
1801D4—84no—
1802D4—84no—
1803D4—84no—
1804D4—88no—
1805D4—84no—
1806D4—84no—
1807D4—84no—
1808D4—84no—
1809D4—84no—
1810D4—84no—
1811D4—84no—
1812D4—84no—
1813D4—84no—
1814D4—84no—
1815D4—88no—
1816D4—88no—
1817D4—88no—
1818D4—164no—
1819D4—164no—
1820D4—164no—
1821C2×C4—21no—
1822C2×C4—21no—
1823C2×C4—21no—
1824C2×C4—21no—
1825C2×C4—21no—
1826C2×C4—22no—
1827C2×C4—22no—
1828C2×C4—22no—
1829C2×C4—22no—
1830C2×C4—22no—
1831C2×C4—22no—
1832C2×C4—22no—
1833C2×C4—22no—
1834C2×C4—22no—
1835C2×C4—22no—
1836C2×C4—21no—
1837C2×C4—21no—
1838C2×C4—21no—
1839C2×C4—24no—
1840C2×C4—24no—
1841C2×C4—22no—
1842C2×C4—24no—
1843C2×C4—21no—
1844C2×C4—21no—
1845C2×C4—21no—
1846C2×C4—21no—
1847C2×C4—22no—
1848C2×C4—21no—
1849C2×C4—21no—
1850C2×C4—21no—
1851C2×C4—21no—
1852C2×C4—22no—
1853C2×C4—21no—
1854C2×C4—22no—
1855C2×C4—22no—
1856C2×C4—22no—
1857C2×C4—22no—
1858C2×C4—22no—
1859C2×C4—22no—
1860C2×C4—22no—
1861C2×C4—22no—
1862C2×C4—22no—
1863C2×C4—22no—
1864C2×C4—22no—
1865C2×C4—24no—
1866C2×C4—22no—
1867C2×C4—22no—
1868C2×C4—21no—
1869C2×C4—22no—
1870C2×C4—24no—
1871C2×C4—22no—
1872C2×C4—22no—
1873C2×C4—21no—
1874C2×C4—21no—
1875C2×C4—21no—
1876C2×C4—22no—
1877C2×C4—22no—
1878C2×C4—22no—
1879C2×C4—22no—
1880C2×C4—22no—
1881C2×C4—21no—
1882C2×C4—24no—
1883C2×C4—22no—
1884C2×C4—22no—
1885C2×C4—22no—
1886C2×C4—24no—
1887C2×C4—22no—
1888C2×C4—24no—
1889C2×C4—22no—
1890C2×C4—24no—
1891C2×C4—21no—
1892C2×C4—44no—
1893C2×C4—48no—
1894C2×C4—416no—
1895C2×C4—44no—
1896C2×C4—44no—
1897C2×C4—44no—
1898C2×C4—44no—
1899C2×C4—44no—
1900C2×C4—44no—
1901C2×C4—44no—
1902C2×C4—44no—
1903C2×C4—44no—
1904C2×C4—44no—
1905C2×C4—48no—
1906C2×C4—48no—
1907C2×C4—48no—
1908C2×C4—82no—
1909C2×C4—84no—
1910C2×C4—84no—
1911C2×C4—84no—
1912C2×C4—84no—
1913C2×C4—164no—
1914C2×C4#560116yes—
1915C2×C4C2×H(5,𝔽2)12yes—
1916C2×C4C2×H(5,𝔽2)12yes—
1917C2×C4C2×H(5,𝔽2)12yes—
1918C2×C4C2×H(5,𝔽2)12yes—
1919C2×C4C2×H(5,𝔽2)12yes—
1920C2×C4C2×H(5,𝔽2)12yes—
1921C2×C4#58512yes—
1922C22—22no—
1923C22—22no—
1924C22—22no—
1925C22—22no—
1926C22—22no—
1927C22—22no—
1928C22—22no—
1929C22—22no—
1930C22—22no—
1931C22—41no—
1932C22—41no—
1933C22—41no—
1934C22—41no—
1935C22—41no—
1936C22—41no—
1937C22—41no—
1938C22—42no—
1939C22—42no—
1940C22—42no—
1941C22—44no—
1942C22—42no—
1943C22—41no—
1944C22—41no—
1945C22—41no—
1946C22—44no—
1947C22—42no—
1948C22—42no—
1949C22—41no—
1950C22—41no—
1951C22—44no—
1952C22—42no—
1953C22—42no—
1954C22—41no—
1955C22—42no—
1956C22—41no—
1957C22—41no—
1958C22—41no—
1959C22—42no—
1960C22—42no—
1961C22—42no—
1962C22—44no—
1963C22—41no—
1964C22—41no—
1965C22—41no—
1966C22—44no—
1967C22—42no—
1968C22—42no—
1969C22—42no—
1970C22—41no—
1971C22—41no—
1972C22—42no—
1973C22—42no—
1974C22—42no—
1975C22—41no—
1976C22—44no—
1977C22—41no—
1978C22—41no—
1979C22—42no—
1980C22—42no—
1981C22—42no—
1982C22—44no—
1983C22—41no—
1984C22—88no—
1985C22—88no—
1986C22—168no—
1987C22—1616no—
1988C22C2×#56014yes—
1989C22C22×H(5,𝔽2)11yescharacteristic
1990C22C22×H(5,𝔽2)11yescharacteristic
1991C22C22×H(5,𝔽2)11yescharacteristic
1992C22C2×#58511yescharacteristic
1993C22C2×#58511yescharacteristic
1994C22H(7,𝔽2)11yescharacteristic
1995C22H(7,𝔽2)11yescharacteristic
1996C4—22no—
1997C4—41no—
1998C4—42no—
1999C4—41no—
2000C4—44no—
2001C4—41no—
2002C4—42no—
2003C4—44no—
2004C4—42no—
2005C4—42no—
2006C4—42no—
2007C4—42no—
2008C4—41no—
2009C4—41no—
2010C4—41no—
2011C4—41no—
2012C4—42no—
2013C4—42no—
2014C4—42no—
2015C4—44no—
2016C4—42no—
2017C4—42no—
2018C4—42no—
2019C4—42no—
2020C4C2×#56014yes—
2021C4C2×#56014yes—
2022C2—24no—
2023C2—42no—
2024C2—82no—
2025C2—81no—
2026C2—81no—
2027C2—81no—
2028C2—82no—
2029C2—82no—
2030C2—84no—
2031C2C22×#56011yescharacteristic
2032C2#6282111yescharacteristic
2033C2#6287411yescharacteristic
2034C2#6292411yescharacteristic
2035C2#6293011yescharacteristic
2036C2#6295511yescharacteristic
2037C2#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. #53129C2semidirect
2. #53103C2semidirect
3. #53103C2semidirect
4. #53102C2semidirect
5. #53098C2semidirect
6. #53078C2semidirect
7. #53060C2semidirect
8. #53051C2semidirect
9. #52345C2semidirect
10. #52315C2semidirect
11. #46339C2semidirect
12. #46338C2semidirect
13. #46338C2semidirect
14. #46333C2semidirect
15. #45732C2semidirect
16. #45721C2semidirect
17. #45655C2semidirect
18. #45642C2semidirect
19. #45588C2semidirect
20. #45518C2semidirect
21. #35563C2semidirect
22. #35518C2semidirect
23. #35517C2semidirect
24. #35513C2semidirect
25. #35512C2semidirect
26. #35512C2semidirect
27. #35267C2semidirect
28. #35266C2semidirect
29. #35263C2semidirect
30. #35252C2semidirect
31. #35157C2semidirect
32. #35150C2semidirect
33. #34936C2semidirect
34. #34737C2semidirect
35. C2×#2414C2semidirect
44. C2×#525C22semidirect
45. C2×#525C22semidirect
48. C2×#520C22semidirect
49. C22×C4×D4C22semidirect
50. C22×#117C22semidirect
51. C22×#117C22semidirect
52. #2863C22semidirect
53. #2860C22semidirect
54. #2860C22semidirect
55. #2860C22semidirect
56. #2856C22semidirect
57. #2855C22semidirect
58. #2854C22semidirect
59. #2854C22semidirect
60. #2853C22semidirect
61. #2850C22semidirect
62. #2837C22semidirect
63. #2829C22semidirect
64. #2829C22semidirect
65. #2829C22semidirect
66. #2829C22semidirect
67. #2829C22semidirect
68. #2828C22semidirect
69. #2828C22semidirect
70. #2828C22semidirect
71. #2828C22semidirect
72. #2828C22semidirect
73. #2827C22semidirect
74. #2825C22semidirect
75. #2825C22semidirect
76. #2818C22semidirect
77. #2815C22semidirect
78. #2815C22semidirect
79. #2813C22semidirect
80. #2812C22semidirect
81. #2812C22semidirect
82. #2803C22semidirect
83. #2803C22semidirect
84. #2803C22semidirect
85. #2801C22semidirect
86. #2797C22semidirect
87. #2797C22semidirect
88. #2797C22semidirect
89. #2796C22semidirect
90. #2796C22semidirect
91. #2796C22semidirect
92. #2795C22semidirect
93. #2795C22semidirect
94. #2790C22semidirect
95. #2780C22semidirect
96. #2756C22semidirect
97. #2752C22semidirect
98. #2752C22semidirect
99. #2749C22semidirect
100. #2746C22semidirect
101. #2735C22semidirect
102. #2735C22semidirect
103. #2714C22semidirect
104. #2714C22semidirect
105. #2714C22semidirect
106. #2714C22semidirect
107. #2705C22semidirect
108. #2703C22semidirect
109. #2691C22semidirect
110. #2688C22semidirect
111. #2685C22semidirect
112. #2685C22semidirect
113. #2685C22semidirect
114. #2685C22semidirect
115. #2678C22semidirect
116. #2678C22semidirect
117. #2678C22semidirect
118. #2678C22semidirect
119. #2673C22semidirect
120. #2669C22semidirect
121. #2669C22semidirect
122. #2645C22semidirect
123. #2644C22semidirect
124. #2644C22semidirect
125. #2644C22semidirect
126. #2625C22semidirect
127. #2624C22semidirect
128. #2622C22semidirect
129. #2620C22semidirect
130. #2619C22semidirect
131. #2617C22semidirect
132. #2542C22semidirect
133. #2542C22semidirect
134. #2541C22semidirect
135. #2541C22semidirect
136. #2540C22semidirect
137. #2540C22semidirect
138. #2540C22semidirect
139. #2540C22semidirect
140. #2539C22semidirect
141. #2539C22semidirect
142. #2538C22semidirect
143. #2537C22semidirect
144. #2536C22semidirect
145. #2535C22semidirect
146. #2534C22semidirect
147. #2513C22semidirect
148. #2513C22semidirect
149. #2512C22semidirect
150. #2512C22semidirect
151. #2510C22semidirect
152. #2501C22semidirect
153. #2500C22semidirect
154. #2500C22semidirect
155. #2499C22semidirect
156. #2499C22semidirect
157. #2498C22semidirect
158. #2497C22semidirect
159. #2496C22semidirect
160. #2495C22semidirect
161. #2494C22semidirect
162. #2487C22semidirect
163. #2487C22semidirect
164. #2486C22semidirect
165. #2486C22semidirect
166. #2485C22semidirect
167. #2485C22semidirect
168. #2485C22semidirect
169. #2485C22semidirect
170. #2485C22semidirect
171. #2485C22semidirect
172. #2485C22semidirect
173. #2485C22semidirect
174. #2481C22semidirect
175. #2480C22semidirect
176. #2480C22semidirect
177. #2448C22semidirect
178. #2447C22semidirect
179. #2446C22semidirect
180. #2445C22semidirect
181. #2444C22semidirect
182. #2443C22semidirect
183. #2435C22semidirect
184. #2433C22semidirect
185. #2433C22semidirect
186. #2432C22semidirect
187. #2431C22semidirect
188. #2428C22semidirect
189. #2428C22semidirect
190. #2426C22semidirect
191. #2426C22semidirect
192. #2425C22semidirect
193. #2424C22semidirect
194. #2417C22semidirect
195. #2417C22semidirect
196. #2417C22semidirect
197. #2416C22semidirect
198. #2416C22semidirect
199. #2416C22semidirect
200. #2416C22semidirect
201. #2416C22semidirect
202. #2416C22semidirect
203. #2416C22semidirect
204. #2415C22semidirect
205. #2415C22semidirect
206. #2415C22semidirect
207. #2415C22semidirect
208. #2415C22semidirect
209. #2415C22semidirect
210. #2415C22semidirect
211. #2414C22semidirect
212. #2414C22semidirect
213. #2414C22semidirect
214. #2414C22semidirect
215. #2414C22semidirect
216. #2414C22semidirect
217. #2414C22semidirect
218. #2414C22semidirect
219. #2414C22semidirect
220. #2414C22semidirect
221. #2414C22semidirect
222. #2414C22semidirect
223. #2414C22semidirect
224. #2414C22semidirect
225. #2414C22semidirect
226. #2414C22semidirect
227. #2414C22semidirect
228. #2414C22semidirect
229. #2414C22semidirect
230. #2413C22semidirect
231. #2412C22semidirect
232. #2412C22semidirect
233. #2411C22semidirect
234. #2411C22semidirect
237. #2410C22semidirect
238. #2410C22semidirect
239. #2408C22semidirect
240. #2408C22semidirect
241. #2408C22semidirect
242. #2408C22semidirect
243. #2408C22semidirect
244. #2408C22semidirect
245. #2408C22semidirect
246. #2408C22semidirect
247. #2408C22semidirect
248. #2408C22semidirect
249. #2408C22semidirect
250. #2407C22semidirect
251. #2407C22semidirect
252. #2407C22semidirect
253. #2407C22semidirect
254. #2407C22semidirect
255. #2407C22semidirect
256. #2407C22semidirect
257. #2407C22semidirect
258. #2407C22semidirect
259. #2407C22semidirect
264. #2397C22semidirect
265. #2397C22semidirect
266. #2392C22semidirect
267. #2392C22semidirect
268. C2×#394C22semidirect
269. C2×#392C22semidirect
270. #2383C22semidirect
271. #2377C22semidirect
272. #2375C22semidirect
273. #2375C22semidirect
274. #2317C22semidirect
275. #2317C22semidirect
276. #2316C22semidirect
277. #2316C22semidirect
283. #2311C22semidirect
286. C4×#127C22semidirect
287. C4×#127C22semidirect
288. C4×#121C22semidirect
289. C4×#121C22semidirect
291. #2296C22semidirect
293. C2×#390C22semidirect
294. C2×#389C22semidirect
295. C2×#388C22semidirect
296. #2280C22semidirect
297. C2×#380C22semidirect
298. C4×#117C22semidirect

Maximal subgroups

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

subgroupindex
#531292
#531032
#531022
#530982
#530782
#530602
#530512
#523452
#523152
#463392
#463382
#463332
#457322
#457212
#456552
#456422
#455882
#455182
#355632
#355182
#355172
#355132
#355122
#352672
#352662
#352632
#352522
#351572
#351502
#349362
#347372
C2×#24142