Finite Group Databasebeta

← #7732361

Subgroups — #7732361

Order 512.

8178 conjugacy classes of subgroups.

The subgroup lattice has 1950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3558C211yesmaximal, characteristic, complemented
2C2×#3459C211yesmaximal, characteristic, complemented
3#50656C214yesmaximal, complemented
4#50655C214yesmaximal, complemented
5#47685C214yesmaximal, complemented
6#47683C214yesmaximal, complemented
7#44022C214yesmaximal, complemented
8#43886C214yesmaximal, complemented
9#39420C212yesmaximal, complemented
10#39412C212yesmaximal, complemented
11#39383C212yesmaximal, complemented
12#39358C212yesmaximal, complemented
13#39137C212yesmaximal, complemented
14#39130C212yesmaximal, complemented
15#37658C212yesmaximal, complemented
16#37650C212yesmaximal, complemented
17#37649C212yesmaximal, complemented
18#37648C212yesmaximal, complemented
19#37546C211yesmaximal, characteristic, complemented
20#37278C212yesmaximal, complemented
21#37271C212yesmaximal, complemented
22#36097C212yesmaximal, complemented
23D4×#121C212yesmaximal, complemented
24#35569C212yesmaximal, complemented
25#35565C212yesmaximal, complemented
26#35238C211yesmaximal, characteristic, complemented
27#35165C211yesmaximal, characteristic, complemented
28C2×#2540C211yesmaximal, characteristic, complemented
29#34243C211yesmaximal, characteristic, complemented
30#3558—216no—
31C2×#562C2212yescomplemented
32C2×H(3,𝔽4)C2212yescomplemented
33C2×#559C2212yescomplemented
34C2×#548C2212yescomplemented
35C2×#546C2212yescomplemented
36C2×#546C2214yescomplemented
37C2×D42C2212yescomplemented
38C2×D42C2214yescomplemented
39#3459—216no—
40C2×#543C2211yescharacteristic, complemented
41C2×#542C2212yescomplemented
42C2×#539C2212yescomplemented
43C2×#539C2212yescomplemented
44C2×#539C2212yescomplemented
45C2×#538C2211yescharacteristic
46C2×#538C2214yescomplemented
47C2×#538C2212yescomplemented
48C2×#538C2212yescomplemented
49C2×#538C2211yescharacteristic, complemented
50C2×#538C2212yescomplemented
51C2×#537C2212yescomplemented
52C2×#535C2212yescomplemented
53C2×#535C2212yescomplemented
54C2×#535C2212yescomplemented
55C2×#534C2212yes—
56C2×#534C2211yescharacteristic
57C2×#534C2212yescomplemented
58C2×#532C2211yescharacteristic, complemented
59C2×#529C2211yescharacteristic
60C2×#529C2212yescomplemented
61C2×#529C2211yescharacteristic, complemented
62C2×#529C2212yescomplemented
63C22×#124C2211yescharacteristic, complemented
64C2×#525C2212yescomplemented
65C2×#525C2212yescomplemented
66C2×#525C2212yescomplemented
67C2×#525C2212yescomplemented
68C22×C22⋊Q8C2211yescharacteristic, complemented
69C22×C22⋊Q8C2211yescharacteristic, complemented
70C22×#121C2211yescharacteristic
71C22×#121C2212yescomplemented
72C22×#121C2211yescharacteristic, complemented
73C22×C4×D4C2212yescomplemented
74C22×C4×D4C2211yescharacteristic, complemented
75#2856C2212yescomplemented
76#2856C2212yescomplemented
77#2850C2212yescomplemented
78#2850C2212yescomplemented
79#2848C2212yescomplemented
80#2847C2212yescomplemented
81#2847C2212yescomplemented
82#2847C2212yescomplemented
83#2820C2212yescomplemented
84#2819C2212yescomplemented
85#2733C2214yescomplemented
86#2730C2214yescomplemented
87#2723C2214yescomplemented
88#2714C2214yescomplemented
89#2714C2214yescomplemented
90#2711C2214yescomplemented
91#2710C2214yescomplemented
92#2706C2214yescomplemented
93#2705C2214yescomplemented
94#2705C2214yescomplemented
95#2694C2214yescomplemented
96#2692C2214yescomplemented
97#2685C2214yescomplemented
98#2683C2214yescomplemented
99#2682C2214yescomplemented
100#2682C2214yescomplemented
101#2682C2214yescomplemented
102#2681C2214yescomplemented
103#2681C2214yescomplemented
104#2679C2214yescomplemented
105#2678C2214yescomplemented
106#2678C2214yescomplemented
107#2678C2214yescomplemented
108#2678C2214yescomplemented
109#2676C2214yescomplemented
110#2676C2214yescomplemented
111#2676C2214yescomplemented
112#2676C2214yescomplemented
113#2675C2214yescomplemented
114#2673C2214yescomplemented
115#2673C2214yescomplemented
116#2673C2214yescomplemented
117#2672C2214yescomplemented
118#2672C2214yescomplemented
119#2671C2214yescomplemented
120#2670C2214yescomplemented
121#2670C2214yescomplemented
122#2669C2214yescomplemented
123#2669C2214yescomplemented
124#2669C2214yescomplemented
125#2662C2214yescomplemented
126#2662C2214yescomplemented
127#2626C2212yescomplemented
128#2620C2212yescomplemented
129#2620C2212yescomplemented
130#2620C2212yescomplemented
131#2619C2212yescomplemented
132#2617C2212yescomplemented
133#2617C2212yescomplemented
134#2617C2212yescomplemented
135#2616C2212yescomplemented
136#2615C2212yescomplemented
137#2592C2212yescomplemented
138#2567C2211yescharacteristic, complemented
139#2566C2212yescomplemented
140#2563C2211yescharacteristic, complemented
141#2560C2214yescomplemented
142#2557C2214yescomplemented
143#2556C2214yescomplemented
144#2555C2214yescomplemented
145#2554C2214yescomplemented
146#2548C2211yescharacteristic, complemented
147#2548C2214yescomplemented
148#2547C2212yescomplemented
149#2544C2212yescomplemented
150#2544C2214yescomplemented
151#2541C2212yescomplemented
152#2541C2214yescomplemented
153#2541C2212yescomplemented
154#2541C2214yescomplemented
155#2541C2211yescharacteristic, complemented
156#2541C2212yescomplemented
157#2540C2212yescomplemented
158#2540C2212yescomplemented
159#2540C2212yescomplemented
160#2540C2212yescomplemented
161#2540C2214yescomplemented
162#2540C2214yescomplemented
163#2540C2212yescomplemented
164#2540C2214yescomplemented
165#2540C2212yescomplemented
166#2540C2212yescomplemented
167#2540C2214yescomplemented
168#2539C2214yescomplemented
169#2539C2214yescomplemented
170#2538C2212yescomplemented
171#2537C2212yescomplemented
172#2537C2212yescomplemented
173#2537C2212yescomplemented
174#2536C2212yescomplemented
175#2535C2212yescomplemented
176#2535C2214yescomplemented
177#2521C2214yescomplemented
178#2512C2214yescomplemented
179#2472C2214yescomplemented
180#2472C2214yescomplemented
181#2467C2214yescomplemented
182#2463C2214yescomplemented
183#2461C2214yescomplemented
184#2461C2214yescomplemented
185#2461C2214yescomplemented
186#2456C2214yescomplemented
187#2454C2214yescomplemented
188#2449C2214yescomplemented
189#2449C2214yescomplemented
190#2445C2214yescomplemented
191#2445C2214yescomplemented
192#2443C2214yescomplemented
193#2437C2214yescomplemented
194#2433C2214yescomplemented
195#2433C2214yescomplemented
196#2433C2214yescomplemented
197#2430C2214yescomplemented
198#2428C2214yescomplemented
199#2428C2214yescomplemented
200#2426C2214yescomplemented
201#2424C2214yescomplemented
202#2424C2214yescomplemented
203#2424C2214yescomplemented
204#2424C2214yescomplemented
205#2424C2214yescomplemented
206#2424C2214yescomplemented
207#2422C2214yescomplemented
208#2418C2214yescomplemented
209#2417C2212yescomplemented
210#2416C2212yescomplemented
211#2416C2212yescomplemented
212#2416C2212yescomplemented
213#2416C2214yescomplemented
214#2416C2214yescomplemented
215#2415C2212yescomplemented
216#2414C2212yescomplemented
217#2411C2214yescomplemented
218#2410C2214yescomplemented
219#2410C2214yescomplemented
220#2410C2214yescomplemented
221#2410C2214yescomplemented
222#2410C2214yescomplemented
223#2409C2212yescomplemented
224#2408C2212yescomplemented
225#2408C2214yescomplemented
226#2408C2212yescomplemented
227#2408C2212yescomplemented
228#2407C2212yescomplemented
229#2407C2212yescomplemented
230#2403C2214yescomplemented
231C2×#399C2212yescomplemented
232C2×#392C2212yescomplemented
233#2370C2212yescomplemented
234#2367C2212yescomplemented
235#2361C2214yescomplemented
236#2359C2214yescomplemented
237#2358C2214yescomplemented
238#2355C2211yescharacteristic, complemented
239#2354C2211yescharacteristic, complemented
240#2352C2212yescomplemented
241Q8×C4⋊C4C2211yescharacteristic, complemented
242D4×C4⋊C4C2211yescharacteristic, complemented
243D4×C4⋊C4C2212yescomplemented
244D4×C22⋊C4C2214yescomplemented
245#2334C2214yescomplemented
246#2324C2212yescomplemented
247#2324C2212yescomplemented
248#2324C2212yescomplemented
249#2323C2212yescomplemented
250#2314C2212yescomplemented
251#2311C2212yescomplemented
252C4×C22⋊Q8C2212yescomplemented
253C4×C22⋊Q8C2212yescomplemented
254C4×#121C2212yes—
255C4×#121C2212yescomplemented
256C2×#390C2212yescomplemented
257C2×#390C2212yescomplemented
258#2285C2211yescharacteristic, complemented
259#2274C2212yescomplemented
260C2×C4×C4⋊C4C2211yescharacteristic, complemented
261C22×#41C2312yes—
262C22×#41C2312yes—
263C22×#41C2312yes—
264C23×Q8C2311yescharacteristic
265C23×D4C2311yescharacteristic
266C23×D4C2312yes—
267C23×D4C2314yes—
268C23×D4C2311yescharacteristic
269C23×D4C2312yes—
270C23×D4C2312yes—
271C23×D4C2312yes—
272C23×D4C2314yes—
273C24×C4C2311yescharacteristic
274C24×C4C2311yescharacteristic
275C24×C4C2312yes—
276#562—216no—
277H(3,𝔽4)—216no—
278#559—216no—
279#548—216no—
280#546—232no—
281#546—216no—
282D42—216no—
283D42—416no—
284#543—28no—
285#542—216no—
286#539—216no—
287#539—216no—
288#539—216no—
289#538—216no—
290#538—232no—
291#538—216no—
292#538—28no—
293#538—216no—
294#538—28no—
295#537—48no—
296#535—216no—
297#535—48no—
298#535—48no—
299#534—216no—
300#534—28no—
301#534—216no—
302#532—28no—
303C2×C4⋊Q8C2311yescharacteristic
304C2×#127C2312yes—
305C2×#127C2311yescharacteristic
306C2×#127C2314yes—
307C2×#127C2314yes—
308C2×#127C2314yes—
309C2×#127C2312yes—
310C2×#127C2314yes—
311#529—216no—
312#529—216no—
313#529—28no—
314#529D4116yescomplemented
315C2×#126C2314yes—
316C2×#126C2312yes—
317C2×#126C2312yes—
318C2×#126C2312yes—
319C2×#126C2312yes—
320C2×#126C2312yes—
321C2×#126C2312yes—
322C2×#125C2311yescharacteristic
323C2×#125C2312yes—
324C2×#125C2312yes—
325C2×#125C2311yescharacteristic
326C2×#124—28no—
327C2×#124C2311yescharacteristic
328C2×#124C2312yes—
329C2×#124C2312yes—
330C2×#124C2312yes—
331C2×#124C2312yes—
332C2×#124C2312yes—
333C2×#124C2312yes—
334C2×#124C2312yes—
335C2×#124C2314yes—
336C2×#124C2312yes—
337C2×#124C2314yes—
338C2×#124C2314yes—
339C2×#124C2314yes—
340C2×#124C2314yes—
341C2×#124C2312yes—
342C2×#124C2311yescharacteristic
343#525—216no—
344#525—216no—
345#525—216no—
346#525—48no—
347C2×#123C2312yes—
348C2×#123C2312yes—
349C2×#123C2312yes—
350C2×#123C2312yes—
351C2×#123C2312yes—
352C2×#123C2312yes—
353C2×#123C2312yes—
354C2×#123C2312yes—
355C2×#123C2312yes—
356C2×#123C2312yes—
357C2×#123C2312yes—
358C2×#123C2314yes—
359C2×#123C2314yes—
360C2×#123C2314yes—
361C2×#123C2314yes—
362C2×#123C2314yes—
363C2×#123C2312yes—
364C2×C22⋊Q8—44no—
365C2×C22⋊Q8—44no—
366C2×C22⋊Q8C2312yes—
367C2×C22⋊Q8C2312yes—
368C2×C22⋊Q8C2312yes—
369C2×C22⋊Q8C2311yescharacteristic
370C2×C22⋊Q8C2312yes—
371C2×C22⋊Q8C2312yes—
372C2×C22⋊Q8C2312yes—
373C2×C22⋊Q8C2312yes—
374C2×C22⋊Q8C2312yes—
375C2×C22⋊Q8C2312yes—
376C2×C22⋊Q8C2312yes—
377C2×C22⋊Q8C2312yes—
378C2×C22⋊Q8C2314yes—
379C2×C22⋊Q8C2314yes—
380C2×C22⋊Q8C2312yes—
381C2×C22⋊Q8C2312yes—
382C2×C22⋊Q8C2312yes—
383C2×C22⋊Q8C2312yes—
384C2×C22⋊Q8C2314yes—
385C2×C22⋊Q8C2314yes—
386C2×C22⋊Q8C2314yes—
387C2×C22⋊Q8C2311yescharacteristic
388C2×#121—44no—
389C2×#121—44no—
390C2×#121—48no—
391C2×#121C2312yes—
392C2×#121C2312yes—
393C2×#121C2312yes—
394C2×#121C2312yes—
395C2×#121C2312yes—
396C2×#121C2312yes—
397C2×#121C2311yescharacteristic
398C2×#121C2312yes—
399C2×#121C2312yes—
400C2×#121C2314yes—
401C2×#121C2312yes—
402C2×#121C2312yes—
403C2×#121C2312yes—
404C2×#121C2312yes—
405C2×#121C2312yes—
406C2×#121C2312yes—
407C2×#121C2314yes—
408C2×#121C2312yes—
409C2×#121C2314yes—
410C2×#121C2314yes—
411C2×#121C2314yes—
412C2×#121C2312yes—
413C2×#121C2312yes—
414C2×#121C2312yes—
415C2×#121C2312yes—
416C2×#121C2312yes—
417C2×#121C2312yes—
418C2×#121C2314yes—
419C2×#121C2314yes—
420C2×#121C2314yes—
421C2×#121C2312yes—
422C2×#121C2312yes—
423C2×#121C2314yes—
424C2×#121C2314yes—
425C2×#121C2314yes—
426C2×#121C2314yes—
427C2×#121C2314yes—
428C2×#121C2314yes—
429C2×#121C2314yes—
430C2×#121C2314yes—
431C2×#121C2314yes—
432C2×#121C2314yes—
433C2×#121C2314yes—
434C2×#121C2314yes—
435C2×#121C2311yescharacteristic
436C2×#120C2314yes—
437C2×#120C2312yes—
438C2×#120C2312yes—
439C2×#120C2314yes—
440C2×#120C2312yes—
441C2×#120C2314yes—
442C2×#120C2314yes—
443C2×#120C2312yes—
444C2×#120C2312yes—
445C2×#120C2312yes—
446C2×#120C2314yes—
447C2×#120C2314yes—
448C2×#120C2314yes—
449C2×#120C2314yes—
450C2×#120C2314yes—
451C2×#120C2314yes—
452C2×#120C2314yes—
453C2×#120C2314yes—
454C2×#120C2314yes—
455C2×#120C2314yes—
456C2×C4×Q8C2311yescharacteristic
457C2×C4×Q8C2312yes—
458C2×C4×Q8C2312yes—
459C2×C4×Q8C2311yescharacteristic
460C2×C4×D4—216no—
461C2×C4×D4—28no—
462C2×C4×D4C2311yescharacteristic
463C2×C4×D4C2312yes—
464C2×C4×D4C2312yes—
465C2×C4×D4C2312yes—
466C2×C4×D4C2312yes—
467C2×C4×D4C2314yes—
468C2×C4×D4C2312yes—
469C2×C4×D4C2312yes—
470C2×C4×D4C2312yes—
471C2×C4×D4C2312yes—
472C2×C4×D4C2312yes—
473C2×C4×D4C2312yes—
474C2×C4×D4C2312yes—
475C2×C4×D4C2312yes—
476C2×C4×D4C2312yes—
477C2×C4×D4C2312yes—
478C2×C4×D4C2312yes—
479C2×C4×D4C2312yes—
480C2×C4×D4C2314yes—
481C2×C4×D4C2314yes—
482C2×C4×D4C2314yes—
483C2×C4×D4C2314yes—
484C2×C4×D4C2314yes—
485C2×C4×D4C2312yes—
486C2×C4×D4C2312yes—
487C2×C4×D4C2311yescharacteristic
488C2×#117C2312yes—
489C2×#117C2312yes—
490C2×#117C2312yes—
491C2×#117C2312yes—
492C2×#117C2312yes—
493C22×C4⋊C4C2311yescharacteristic
494C22×C4⋊C4C2311yescharacteristic
495C22×C4⋊C4C2312yes—
496C22×C4⋊C4C2311yescharacteristic
497C22×C4⋊C4C2312yes—
498C22×C4⋊C4C2312yes—
499C22×C4⋊C4C2312yes—
500C22×C22⋊C4C2312yes—
501C22×C22⋊C4C2311yescharacteristic
502C22×C22⋊C4C2311yescharacteristic
503C22×C22⋊C4C2312yes—
504C22×C22⋊C4C2312yes—
505C22×C22⋊C4C2312yes—
506C22×C22⋊C4C2314yes—
507C22×C22⋊C4C2312yes—
508C22×C22⋊C4C2314yes—
509C22×C22⋊C4C2312yes—
510C22×C22⋊C4C2312yes—
511C22×C22⋊C4C2312yes—
512C22×C42C2312yes—
513C22×C42C2312yes—
514C22×C42C2311yescharacteristic
515#399C2314yes—
516#399C2314yes—
517#399C2314yes—
518#399C2314yes—
519#399C2314yes—
520#399C2314yes—
521#399C2314yes—
522#398C2314yes—
523#398C2314yes—
524#397C2314yes—
525#397C2314yes—
526#397C2314yes—
527#397C2314yes—
528#397C2314yes—
529#396C2314yes—
530#396C2314yes—
531#396C2314yes—
532#396C2314yes—
533#396C2314yes—
534#396C2314yes—
535#396C2314yes—
536#396C2314yes—
537#396C2314yes—
538#396C2314yes—
539#396C2314yes—
540#396C2314yes—
541#395C2314yes—
542#395C2314yes—
543#395C2314yes—
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#394C2314yes—
558#394C2314yes—
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#394C2314yes—
573#393C2314yes—
574#393C2314yes—
575#393C2314yes—
576#393C2314yes—
577#392C2314yes—
578#392C2314yes—
579#392C2314yes—
580#392C2314yes—
581#392C2314yes—
582#392C2314yes—
583#392C2314yes—
584#392C2314yes—
585#392C2314yes—
586#392C2314yes—
587#392C2314yes—
588#392C2314yes—
589#392C2314yes—
590#392C2314yes—
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#391C2312yes—
604#391C2314yes—
605#391C2312yes—
606#391C2312yes—
607#391C2312yes—
608#390C2314yes—
609#390C2312yes—
610#390C2312yes—
611#390C2312yes—
612#390C2314yes—
613#390C2312yes—
614#390C2312yes—
615#390C2312yes—
616#390C2314yes—
617#390C2314yes—
618#390C2314yes—
619#390C2312yes—
620#390C2314yes—
621#390C2314yes—
622#390C2314yes—
623#390C2312yes—
624#390C2314yes—
625#390C2314yes—
626#390C2314yes—
627#390C2314yes—
628#390C2314yes—
629#390C2314yes—
630#390C2314yes—
631#390C2314yes—
632#390C2314yes—
633#390C2314yes—
634#390C2314yes—
635#390C2314yes—
636#390C2314yes—
637#390C2314yes—
638#390C2314yes—
639#390C2314yes—
640#389C2312yes—
641#389C2312yes—
642#389C2314yes—
643#389C2314yes—
644#389C2314yes—
645#389C2312yes—
646#389C2312yes—
647#389C2314yes—
648#389C2314yes—
649#388C2314yes—
650#388C2314yes—
651#388C2314yes—
652#388C2314yes—
653#388C2314yes—
654#388C2314yes—
655#388C2314yes—
656#388C2314yes—
657#388C2314yes—
658#388C2314yes—
659#388C2314yes—
660#388C2314yes—
661#388C2314yes—
662#388C2314yes—
663#388C2314yes—
664#388C2314yes—
665#388C2314yes—
666#388C2314yes—
667#387C2314yes—
668#387C2314yes—
669#387C2314yes—
670#387C2314yes—
671#387C2314yes—
672#387C2314yes—
673#386C2314yes—
674#386C2314yes—
675#386C2314yes—
676#386C2314yes—
677#386C2314yes—
678#386C2314yes—
679#386C2314yes—
680#386C2314yes—
681#386C2314yes—
682#386C2314yes—
683#386C2314yes—
684#386C2314yes—
685#386C2314yes—
686#386C2314yes—
687#386C2314yes—
688#386C2314yes—
689#386C2314yes—
690#386C2314yes—
691#386C2314yes—
692#386C2314yes—
693#386C2314yes—
694#386C2314yes—
695#386C2314yes—
696#386C2314yes—
697#386C2314yes—
698#385C2314yes—
699#385C2314yes—
700#385C2314yes—
701#385C2314yes—
702#385C2314yes—
703#385C2314yes—
704#385C2314yes—
705#385C2314yes—
706#385C2314yes—
707#385C2314yes—
708#385C2314yes—
709#385C2314yes—
710#385C2314yes—
711#384C2312yes—
712#384C2312yes—
713#384C2311yescharacteristic
714#384C2311yescharacteristic
715#382C2312yes—
716#382C2312yes—
717#382C2312yes—
718#380C2312yes—
719#380C2312yes—
720#380C2314yes—
721#380C2314yes—
722#380C2312yes—
723#380C2312yes—
724#380C2312yes—
725#380C2312yes—
726#380C2312yes—
727#380C2312yes—
728#380C2312yes—
729#380C2314yes—
730#380C2312yes—
731#380C2314yes—
732#379C2314yes—
733#379C2314yes—
734#379C2314yes—
735#379C2314yes—
736C4×C4⋊C4C2314yes—
737C4×C4⋊C4C2311yescharacteristic
738C4×C4⋊C4C2312yes—
739C4×C4⋊C4C2311yescharacteristic
740C4×C4⋊C4C2312yes—
741C4×C4⋊C4C2312yes—
742C4×C4⋊C4C2311yescharacteristic
743C4×C4⋊C4C2311yescharacteristic
744C4×C4⋊C4C2312yes—
745C4×C4⋊C4C2312yes—
746C4×C4⋊C4C2312yes—
747C4×C4⋊C4C2314yes—
748C4×C4⋊C4C2314yes—
749C4×C4⋊C4C2312yes—
750C4×C4⋊C4C2312yes—
751C4×C22⋊C4C2314yes—
752C4×C22⋊C4C2314yes—
753C4×C22⋊C4C2314yes—
754C4×C22⋊C4C2314yes—
755C4×C22⋊C4C2314yes—
756C2×#95C2312yes—
757C25C2412yes—
758C25C2411yescharacteristic
759C25C2412yes—
760C25C2411yescharacteristic
761C25C2414yes—
762C2×#41—28no—
763C2×#41—28no—
764C2×#41—28no—
765C2×#41—44no—
766C2×#41—44no—
767C2×#41—44no—
768C2×#41—44no—
769C2×#41—44no—
770C2×#41—44no—
771C22×Q8—24no—
772C22×Q8—42no—
773C22×Q8—42no—
774C22×Q8C2412yes—
775C22×Q8C2411yescharacteristic
776C22×Q8C2412yes—
777C22×Q8C2412yes—
778C22×Q8C2412yes—
779C22×Q8C2411yescharacteristic
780C22×D4—24no—
781C22×D4—28no—
782C22×D4—28no—
783C22×D4—28no—
784C22×D4—216no—
785C22×D4—24no—
786C22×D4—24no—
787C22×D4—28no—
788C22×D4—42no—
789C22×D4—42no—
790C22×D4—44no—
791C22×D4—44no—
792C22×D4—44no—
793C22×D4—48no—
794C22×D4—44no—
795C22×D4—42no—
796C22×D4—44no—
797C22×D4—44no—
798C22×D4—48no—
799C22×D4—48no—
800C22×D4—48no—
801C22×D4—82no—
802C22×D4—82no—
803C22×D4—84no—
804C22×D4C2412yes—
805C22×D4C2414yes—
806C22×D4C2412yes—
807C22×D4C2412yes—
808C22×D4C2412yes—
809C22×D4C2412yes—
810C22×D4C2412yes—
811C22×D4C2412yes—
812C22×D4C2414yes—
813C22×D4C2412yes—
814C22×D4C2412yes—
815C22×D4C2414yes—
816C22×D4C2414yes—
817C22×D4C2411yescharacteristic
818C22×D4C2412yes—
819C22×D4C2412yes—
820C22×D4C2414yes—
821C22×D4C2412yes—
822C22×D4C2412yes—
823C22×D4C2414yes—
824C22×D4C2414yes—
825C22×D4C2412yes—
826C22×D4C2414yes—
827C22×D4C2412yes—
828C22×D4C2412yes—
829C22×D4C2414yes—
830C22×D4C2414yes—
831C22×D4C2414yes—
832C22×D4C2414yes—
833C22×D4C2414yes—
834C22×D4C2414yes—
835C22×D4C2414yes—
836C22×D4C2414yes—
837C22×D4C2414yes—
838C22×D4C2414yes—
839C22×D4C2411yescharacteristic
840C23×C4—24no—
841C23×C4—24no—
842C23×C4—28no—
843C23×C4—42no—
844C23×C4—42no—
845C23×C4—44no—
846C23×C4—42no—
847C23×C4—42no—
848C23×C4—44no—
849C23×C4C2412yes—
850C23×C4C2412yes—
851C23×C4C2412yes—
852C23×C4C2412yes—
853C23×C4C2412yes—
854C23×C4C2412yes—
855C23×C4C2411yescharacteristic
856C23×C4C2411yescharacteristic
857C23×C4C2412yes—
858C23×C4C2412yes—
859C23×C4C2411yescharacteristic
860C23×C4C2411yescharacteristic
861C23×C4C2412yes—
862C23×C4C2412yes—
863C23×C4C2412yes—
864C23×C4C2412yes—
865C23×C4C2414yes—
866C23×C4C2414yes—
867C23×C4C2414yes—
868C23×C4C2412yes—
869C23×C4C2414yes—
870C23×C4C2412yes—
871C23×C4C2411yescharacteristic
872C4⋊Q8—24no—
873#127—24no—
874#127—28no—
875#127—48no—
876#127—48no—
877#127—48no—
878#127—82no—
879#127—84no—
880#126—28no—
881#126—28no—
882#126—28no—
883#126—216no—
884#126—28no—
885#126—28no—
886#126C2×D4116yescomplemented
887#125—28no—
888#125—28no—
889#125—24no—
890#125C2×D418yescomplemented
891#124—28no—
892#124—216no—
893#124—28no—
894#124—216no—
895#124—216no—
896#124—28no—
897#124—28no—
898#124—28no—
899#124—28no—
900#124—24no—
901#124—28no—
902#124—28no—
903#124—48no—
904#124—48no—
905#124—82no—
906#124C2×D418yescomplemented
907#123—28no—
908#123—28no—
909#123—28no—
910#123—28no—
911#123—28no—
912#123—28no—
913#123—216no—
914#123—216no—
915#123—216no—
916#123—28no—
917#123—28no—
918#123—28no—
919#123—28no—
920#123—28no—
921#123—216no—
922#123—48no—
923#123C2×D4116yescomplemented
924C22⋊Q8—28no—
925C22⋊Q8—24no—
926C22⋊Q8—28no—
927C22⋊Q8—28no—
928C22⋊Q8—28no—
929C22⋊Q8—28no—
930C22⋊Q8—28no—
931C22⋊Q8—28no—
932C22⋊Q8—216no—
933C22⋊Q8—216no—
934C22⋊Q8—28no—
935C22⋊Q8—28no—
936C22⋊Q8—28no—
937C22⋊Q8—28no—
938C22⋊Q8—48no—
939C22⋊Q8—48no—
940C22⋊Q8—48no—
941C22⋊Q8—44no—
942C22⋊Q8—44no—
943C22⋊Q8—44no—
944C22⋊Q8—44no—
945C22⋊Q8C2×D418yescomplemented
946#121—28no—
947#121—28no—
948#121—216no—
949#121—24no—
950#121—28no—
951#121—28no—
952#121—28no—
953#121—28no—
954#121—28no—
955#121—28no—
956#121—216no—
957#121—216no—
958#121—216no—
959#121—28no—
960#121—28no—
961#121—28no—
962#121—28no—
963#121—28no—
964#121—28no—
965#121—28no—
966#121—216no—
967#121—48no—
968#121—48no—
969#121—48no—
970#121—48no—
971#121—48no—
972#121—48no—
973#121—48no—
974#121—48no—
975#121—48no—
976#121—48no—
977#121—44no—
978#121—44no—
979#121—44no—
980#121—44no—
981#121—44no—
982#121—44no—
983#121—44no—
984#121—44no—
985#121—48no—
986#121—48no—
987#121—48no—
988#121—48no—
989#121—84no—
990#121C2×D418yes—
991#120—216no—
992#120—28no—
993#120—28no—
994#120—216no—
995#120—28no—
996#120—28no—
997#120—28no—
998#120—28no—
999#120—216no—
1000#120—216no—
1001#120—216no—
1002#120—216no—
1003#120—48no—
1004#120—48no—
1005#120—48no—
1006#120—48no—
1007#120—48no—
1008#120—48no—
1009#120—48no—
1010#120—84no—
1011C4×Q8—24no—
1012C4×Q8—28no—
1013C4×Q8—82no—
1014C4×Q8C2×D418yescomplemented
1015C4×D4—28no—
1016C4×D4—28no—
1017C4×D4—28no—
1018C4×D4—28no—
1019C4×D4—28no—
1020C4×D4—216no—
1021C4×D4—28no—
1022C4×D4—28no—
1023C4×D4—216no—
1024C4×D4—28no—
1025C4×D4—28no—
1026C4×D4—28no—
1027C4×D4—28no—
1028C4×D4—28no—
1029C4×D4—28no—
1030C4×D4—24no—
1031C4×D4—28no—
1032C4×D4—28no—
1033C4×D4—28no—
1034C4×D4—48no—
1035C4×D4—48no—
1036C4×D4—48no—
1037C4×D4—48no—
1038C4×D4—82no—
1039C4×D4C2×D4116yescomplemented
1040C4×D4C2×D418yescomplemented
1041#117—28no—
1042#117—28no—
1043#117—28no—
1044#117—44no—
1045#117C2×D4116yescomplemented
1046C2×C4⋊C4—24no—
1047C2×C4⋊C4—28no—
1048C2×C4⋊C4—24no—
1049C2×C4⋊C4—24no—
1050C2×C4⋊C4—28no—
1051C2×C4⋊C4—44no—
1052C2×C4⋊C4—44no—
1053C2×C4⋊C4C2412yes—
1054C2×C4⋊C4C2412yes—
1055C2×C4⋊C4C2412yes—
1056C2×C4⋊C4C2412yes—
1057C2×C4⋊C4C2412yes—
1058C2×C4⋊C4C2414yes—
1059C2×C4⋊C4C2412yes—
1060C2×C4⋊C4C2414yes—
1061C2×C4⋊C4C2411yescharacteristic
1062C2×C4⋊C4C2411yescharacteristic
1063C2×C4⋊C4C2412yes—
1064C2×C4⋊C4C2412yes—
1065C2×C4⋊C4C2414yes—
1066C2×C4⋊C4C2412yes—
1067C2×C4⋊C4C2412yes—
1068C2×C4⋊C4C2412yes—
1069C2×C4⋊C4C2412yes—
1070C2×C4⋊C4C2412yes—
1071C2×C4⋊C4C2412yes—
1072C2×C4⋊C4C2414yes—
1073C2×C4⋊C4C2412yes—
1074C2×C4⋊C4C2411yescharacteristic
1075C2×C4⋊C4C2412yes—
1076C2×C4⋊C4C2412yes—
1077C2×C4⋊C4C2414yes—
1078C2×C4⋊C4C2411yescharacteristic
1079C2×C4⋊C4C2412yes—
1080C2×C4⋊C4C2414yes—
1081C2×C4⋊C4C2414yes—
1082C2×C4⋊C4C2412yes—
1083C2×C4⋊C4C2412yes—
1084C2×C4⋊C4C2412yes—
1085C2×C4⋊C4C2414yes—
1086C2×C4⋊C4C2414yes—
1087C2×C4⋊C4C2414yes—
1088C2×C4⋊C4C2414yes—
1089C2×C4⋊C4C2414yes—
1090C2×C4⋊C4C2414yes—
1091C2×C4⋊C4C2412yes—
1092C2×C4⋊C4C2412yes—
1093C2×C4⋊C4C2412yes—
1094C2×C4⋊C4C2412yes—
1095C2×C4⋊C4C2412yes—
1096C2×C4⋊C4C2411yescharacteristic
1097C2×C4⋊C4C2411yescharacteristic
1098C2×C4⋊C4C2411yescharacteristic
1099C2×C4⋊C4C2411yescharacteristic
1100C2×C22⋊C4—24no—
1101C2×C22⋊C4—24no—
1102C2×C22⋊C4—28no—
1103C2×C22⋊C4—28no—
1104C2×C22⋊C4—28no—
1105C2×C22⋊C4—28no—
1106C2×C22⋊C4—216no—
1107C2×C22⋊C4—44no—
1108C2×C22⋊C4—48no—
1109C2×C22⋊C4—44no—
1110C2×C22⋊C4—44no—
1111C2×C22⋊C4—44no—
1112C2×C22⋊C4C2414yes—
1113C2×C22⋊C4C2414yes—
1114C2×C22⋊C4C2412yes—
1115C2×C22⋊C4C2412yes—
1116C2×C22⋊C4C2412yes—
1117C2×C22⋊C4C2412yes—
1118C2×C22⋊C4C2412yes—
1119C2×C22⋊C4C2412yes—
1120C2×C22⋊C4C2412yes—
1121C2×C22⋊C4C2412yes—
1122C2×C22⋊C4C2412yes—
1123C2×C22⋊C4C2412yes—
1124C2×C22⋊C4C2414yes—
1125C2×C22⋊C4C2414yes—
1126C2×C22⋊C4C2414yes—
1127C2×C22⋊C4C2414yes—
1128C2×C22⋊C4C2414yes—
1129C2×C22⋊C4C2414yes—
1130C2×C22⋊C4C2414yes—
1131C2×C22⋊C4C2414yes—
1132C2×C22⋊C4C2414yes—
1133C2×C22⋊C4C2414yes—
1134C2×C22⋊C4C2414yes—
1135C2×C22⋊C4C2412yes—
1136C2×C22⋊C4C2412yes—
1137C2×C22⋊C4C2412yes—
1138C2×C22⋊C4C2412yes—
1139C2×C22⋊C4C2414yes—
1140C2×C22⋊C4C2414yes—
1141C2×C22⋊C4C2414yes—
1142C2×C22⋊C4C2414yes—
1143C2×C22⋊C4C2412yes—
1144C2×C22⋊C4C2412yes—
1145C2×C22⋊C4C2412yes—
1146C2×C22⋊C4C2412yes—
1147C2×C22⋊C4C2412yes—
1148C2×C22⋊C4C2414yes—
1149C2×C22⋊C4C2414yes—
1150C2×C22⋊C4C2414yes—
1151C2×C22⋊C4C2414yes—
1152C2×C22⋊C4C2414yes—
1153C2×C22⋊C4C2414yes—
1154C2×C22⋊C4C2414yes—
1155C2×C22⋊C4C2414yes—
1156C2×C22⋊C4C2414yes—
1157C2×C22⋊C4C2414yes—
1158C2×C22⋊C4C2414yes—
1159C2×C22⋊C4C2414yes—
1160C2×C22⋊C4C2414yes—
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⋊C4C2414yes—
1171C2×C22⋊C4C2414yes—
1172C2×C22⋊C4C2414yes—
1173C2×C22⋊C4C2414yes—
1174C2×C22⋊C4C2414yes—
1175C2×C22⋊C4C2414yes—
1176C2×C22⋊C4C2414yes—
1177C2×C22⋊C4C2414yes—
1178C2×C22⋊C4C2412yes—
1179C2×C22⋊C4C2412yes—
1180C2×C22⋊C4C2412yes—
1181C2×C22⋊C4C2412yes—
1182C2×C22⋊C4C2412yes—
1183C2×C42—28no—
1184C2×C42—82no—
1185C2×C42C2×D418yescomplemented
1186C2×C42C2412yes—
1187C2×C42C2414yes—
1188C2×C42C2414yes—
1189C2×C42C2412yes—
1190C2×C42C2412yes—
1191C2×C42C2414yes—
1192C2×C42C2414yes—
1193C2×C42C2412yes—
1194C2×C42C2414yes—
1195C2×C42C2412yes—
1196C2×C42C2412yes—
1197C2×C42C2412yes—
1198C2×C42C2411yescharacteristic
1199C2×C42C2412yes—
1200C2×C42C2411yescharacteristic
1201C2×C42C2411yescharacteristic
1202C2×C42C2411yescharacteristic
1203#95C2412yes—
1204#95C2412yes—
1205#95C2412yes—
1206#95C2412yes—
1207#95C2414yes—
1208#95C2414yes—
1209#95C2414yes—
1210#95C2414yes—
1211#95C2414yes—
1212#95C2414yes—
1213#95C2414yes—
1214#95C2414yes—
1215#95C2414yes—
1216#95C2414yes—
1217#95C2414yes—
1218#95C2414yes—
1219#95C2414yes—
1220#95C2414yes—
1221#95C2414yes—
1222#95C2414yes—
1223#95C2414yes—
1224#95C2414yes—
1225#95C2414yes—
1226#95C2414yes—
1227C24—22no—
1228C24—22no—
1229C24—22no—
1230C24—24no—
1231C24—24no—
1232C24—24no—
1233C24—22no—
1234C24—22no—
1235C24—24no—
1236C24—24no—
1237C24—28no—
1238C24—41no—
1239C24—41no—
1240C24—41no—
1241C24—41no—
1242C24—42no—
1243C24—42no—
1244C24—41no—
1245C24—41no—
1246C24—42no—
1247C24—41no—
1248C24—41no—
1249C24—42no—
1250C24—42no—
1251C24—44no—
1252C24—42no—
1253C24—42no—
1254C24—42no—
1255C24—42no—
1256C24—44no—
1257C24—44no—
1258C24—44no—
1259C24—44no—
1260C24—44no—
1261C24H(5,𝔽2)14yes—
1262C24C2514yes—
1263C24C2512yes—
1264C24C2512yes—
1265C24C2514yes—
1266C24C2512yes—
1267C24C2512yes—
1268C24C2511yescharacteristic
1269#41—816no—
1270#41—816no—
1271#41—816no—
1272C2×Q8—24no—
1273C2×Q8—22no—
1274C2×Q8—24no—
1275C2×Q8—24no—
1276C2×Q8—24no—
1277C2×Q8—24no—
1278C2×Q8—24no—
1279C2×Q8—41no—
1280C2×Q8—41no—
1281C2×Q8—42no—
1282C2×Q8—42no—
1283C2×Q8—42no—
1284C2×Q8—42no—
1285C2×Q8—42no—
1286C2×Q8—41no—
1287C2×Q8—41no—
1288C2×Q8—42no—
1289C2×Q8—88no—
1290C2×Q8C22×D414yes—
1291C2×D4—24no—
1292C2×D4—24no—
1293C2×D4—24no—
1294C2×D4—24no—
1295C2×D4—28no—
1296C2×D4—28no—
1297C2×D4—28no—
1298C2×D4—24no—
1299C2×D4—24no—
1300C2×D4—24no—
1301C2×D4—24no—
1302C2×D4—24no—
1303C2×D4—24no—
1304C2×D4—28no—
1305C2×D4—24no—
1306C2×D4—28no—
1307C2×D4—24no—
1308C2×D4—24no—
1309C2×D4—28no—
1310C2×D4—28no—
1311C2×D4—28no—
1312C2×D4—28no—
1313C2×D4—24no—
1314C2×D4—24no—
1315C2×D4—24no—
1316C2×D4—24no—
1317C2×D4—24no—
1318C2×D4—28no—
1319C2×D4—24no—
1320C2×D4—22no—
1321C2×D4—24no—
1322C2×D4—24no—
1323C2×D4—24no—
1324C2×D4—24no—
1325C2×D4—28no—
1326C2×D4—28no—
1327C2×D4—28no—
1328C2×D4—24no—
1329C2×D4—24no—
1330C2×D4—24no—
1331C2×D4—24no—
1332C2×D4—28no—
1333C2×D4—28no—
1334C2×D4—28no—
1335C2×D4—41no—
1336C2×D4—42no—
1337C2×D4—42no—
1338C2×D4—42no—
1339C2×D4—42no—
1340C2×D4—44no—
1341C2×D4—41no—
1342C2×D4—416no—
1343C2×D4—44no—
1344C2×D4—42no—
1345C2×D4—42no—
1346C2×D4—44no—
1347C2×D4—44no—
1348C2×D4—44no—
1349C2×D4—42no—
1350C2×D4—44no—
1351C2×D4—44no—
1352C2×D4—42no—
1353C2×D4—42no—
1354C2×D4—44no—
1355C2×D4—44no—
1356C2×D4—44no—
1357C2×D4—44no—
1358C2×D4—42no—
1359C2×D4—42no—
1360C2×D4—44no—
1361C2×D4—42no—
1362C2×D4—44no—
1363C2×D4—44no—
1364C2×D4—44no—
1365C2×D4—44no—
1366C2×D4—44no—
1367C2×D4—44no—
1368C2×D4—44no—
1369C2×D4—42no—
1370C2×D4—42no—
1371C2×D4—42no—
1372C2×D4—44no—
1373C2×D4—41no—
1374C2×D4—42no—
1375C2×D4—44no—
1376C2×D4—44no—
1377C2×D4—44no—
1378C2×D4—44no—
1379C2×D4—44no—
1380C2×D4—44no—
1381C2×D4—44no—
1382C2×D4—44no—
1383C2×D4—41no—
1384C2×D4—42no—
1385C2×D4—42no—
1386C2×D4—42no—
1387C2×D4—44no—
1388C2×D4—42no—
1389C2×D4—44no—
1390C2×D4—44no—
1391C2×D4—44no—
1392C2×D4—44no—
1393C2×D4—44no—
1394C2×D4—44no—
1395C2×D4—44no—
1396C2×D4—44no—
1397C2×D4—44no—
1398C2×D4—432no—
1399C2×D4—88no—
1400C2×D4—816no—
1401C2×D4—816no—
1402C2×D4—816no—
1403C2×D4—832no—
1404C2×D4—832no—
1405C2×D4C22×D418yes—
1406C2×D4C22×D414yes—
1407C22×C4—22no—
1408C22×C4—22no—
1409C22×C4—22no—
1410C22×C4—22no—
1411C22×C4—24no—
1412C22×C4—24no—
1413C22×C4—24no—
1414C22×C4—24no—
1415C22×C4—24no—
1416C22×C4—24no—
1417C22×C4—22no—
1418C22×C4—22no—
1419C22×C4—24no—
1420C22×C4—24no—
1421C22×C4—24no—
1422C22×C4—24no—
1423C22×C4—24no—
1424C22×C4—24no—
1425C22×C4—24no—
1426C22×C4—24no—
1427C22×C4—24no—
1428C22×C4—24no—
1429C22×C4—24no—
1430C22×C4—24no—
1431C22×C4—24no—
1432C22×C4—24no—
1433C22×C4—24no—
1434C22×C4—24no—
1435C22×C4—28no—
1436C22×C4—28no—
1437C22×C4—24no—
1438C22×C4—24no—
1439C22×C4—28no—
1440C22×C4—28no—
1441C22×C4—41no—
1442C22×C4—42no—
1443C22×C4—42no—
1444C22×C4—41no—
1445C22×C4—42no—
1446C22×C4—41no—
1447C22×C4—42no—
1448C22×C4—41no—
1449C22×C4—42no—
1450C22×C4—42no—
1451C22×C4—41no—
1452C22×C4—41no—
1453C22×C4—42no—
1454C22×C4—42no—
1455C22×C4—44no—
1456C22×C4—44no—
1457C22×C4—44no—
1458C22×C4—44no—
1459C22×C4—42no—
1460C22×C4—42no—
1461C22×C4—42no—
1462C22×C4—42no—
1463C22×C4—44no—
1464C22×C4—44no—
1465C22×C4—42no—
1466C22×C4—42no—
1467C22×C4—42no—
1468C22×C4—42no—
1469C22×C4—42no—
1470C22×C4—44no—
1471C22×C4—44no—
1472C22×C4—88no—
1473C22×C4—88no—
1474C22×C4—816no—
1475C22×C4C22×D414yes—
1476C22×C4C22×D414yes—
1477C22×C4C22×D418yes—
1478C22×C4C22×D414yes—
1479C22×C4C2514yes—
1480C22×C4C2512yes—
1481C22×C4C2512yes—
1482C22×C4C2514yes—
1483C22×C4C2514yes—
1484C22×C4C2512yes—
1485C22×C4C2512yes—
1486C22×C4C2512yes—
1487C22×C4C2514yes—
1488C22×C4C2512yes—
1489C22×C4C2512yes—
1490C22×C4C2511yescharacteristic
1491C22×C4C2512yes—
1492C22×C4C2511yescharacteristic
1493C22×C4C2512yes—
1494C22×C4C2511yescharacteristic
1495C22×C4C2511yescharacteristic
1496C22×C4C2512yes—
1497C22×C4C2511yescharacteristic
1498C22×C4C2512yes—
1499C22×C4C2512yes—
1500C22×C4C2511yescharacteristic
1501C4⋊C4—24no—
1502C4⋊C4—24no—
1503C4⋊C4—24no—
1504C4⋊C4—24no—
1505C4⋊C4—24no—
1506C4⋊C4—24no—
1507C4⋊C4—24no—
1508C4⋊C4—24no—
1509C4⋊C4—24no—
1510C4⋊C4—24no—
1511C4⋊C4—28no—
1512C4⋊C4—24no—
1513C4⋊C4—24no—
1514C4⋊C4—24no—
1515C4⋊C4—22no—
1516C4⋊C4—28no—
1517C4⋊C4—24no—
1518C4⋊C4—22no—
1519C4⋊C4—28no—
1520C4⋊C4—24no—
1521C4⋊C4—24no—
1522C4⋊C4—24no—
1523C4⋊C4—22no—
1524C4⋊C4—22no—
1525C4⋊C4—28no—
1526C4⋊C4—28no—
1527C4⋊C4—24no—
1528C4⋊C4—44no—
1529C4⋊C4—44no—
1530C4⋊C4—42no—
1531C4⋊C4—42no—
1532C4⋊C4—42no—
1533C4⋊C4—44no—
1534C4⋊C4—44no—
1535C4⋊C4—44no—
1536C4⋊C4—42no—
1537C4⋊C4—44no—
1538C4⋊C4—44no—
1539C4⋊C4—44no—
1540C4⋊C4C22×D418yes—
1541C4⋊C4C22×D418yes—
1542C4⋊C4C22×D418yes—
1543C4⋊C4C22×D418yes—
1544C4⋊C4C22×D414yes—
1545C4⋊C4C22×D414yes—
1546C4⋊C4H(5,𝔽2)14yes—
1547C4⋊C4H(5,𝔽2)14yes—
1548C22⋊C4—24no—
1549C22⋊C4—24no—
1550C22⋊C4—28no—
1551C22⋊C4—24no—
1552C22⋊C4—28no—
1553C22⋊C4—28no—
1554C22⋊C4—28no—
1555C22⋊C4—28no—
1556C22⋊C4—24no—
1557C22⋊C4—24no—
1558C22⋊C4—24no—
1559C22⋊C4—24no—
1560C22⋊C4—24no—
1561C22⋊C4—24no—
1562C22⋊C4—24no—
1563C22⋊C4—24no—
1564C22⋊C4—28no—
1565C22⋊C4—28no—
1566C22⋊C4—28no—
1567C22⋊C4—28no—
1568C22⋊C4—24no—
1569C22⋊C4—24no—
1570C22⋊C4—24no—
1571C22⋊C4—24no—
1572C22⋊C4—28no—
1573C22⋊C4—28no—
1574C22⋊C4—28no—
1575C22⋊C4—24no—
1576C22⋊C4—24no—
1577C22⋊C4—24no—
1578C22⋊C4—24no—
1579C22⋊C4—28no—
1580C22⋊C4—28no—
1581C22⋊C4—28no—
1582C22⋊C4—28no—
1583C22⋊C4—28no—
1584C22⋊C4—28no—
1585C22⋊C4—28no—
1586C22⋊C4—28no—
1587C22⋊C4—28no—
1588C22⋊C4—44no—
1589C22⋊C4—44no—
1590C22⋊C4—44no—
1591C22⋊C4—44no—
1592C22⋊C4—44no—
1593C22⋊C4—44no—
1594C22⋊C4—44no—
1595C22⋊C4—44no—
1596C22⋊C4—44no—
1597C22⋊C4—44no—
1598C22⋊C4—44no—
1599C22⋊C4—44no—
1600C22⋊C4—44no—
1601C22⋊C4—44no—
1602C22⋊C4—44no—
1603C22⋊C4—44no—
1604C22⋊C4—44no—
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⋊C4C22×D418yes—
1615C22⋊C4C22×D418yes—
1616C22⋊C4C22×D418yes—
1617C22⋊C4C22×D418yes—
1618C22⋊C4C22×D418yes—
1619C42—24no—
1620C42—24no—
1621C42—24no—
1622C42—28no—
1623C42—28no—
1624C42—42no—
1625C42—42no—
1626C42—42no—
1627C42—42no—
1628C42—44no—
1629C42—44no—
1630C42—44no—
1631C42C22×D418yes—
1632C42C22×D414yes—
1633C42C22×D414yes—
1634C42C22×D414yes—
1635C42C22×D414yes—
1636C23—21no—
1637C23—21no—
1638C23—21no—
1639C23—21no—
1640C23—22no—
1641C23—22no—
1642C23—22no—
1643C23—22no—
1644C23—22no—
1645C23—22no—
1646C23—22no—
1647C23—22no—
1648C23—22no—
1649C23—22no—
1650C23—22no—
1651C23—22no—
1652C23—28no—
1653C23—22no—
1654C23—22no—
1655C23—24no—
1656C23—24no—
1657C23—22no—
1658C23—24no—
1659C23—24no—
1660C23—24no—
1661C23—24no—
1662C23—22no—
1663C23—22no—
1664C23—22no—
1665C23—24no—
1666C23—22no—
1667C23—24no—
1668C23—22no—
1669C23—22no—
1670C23—24no—
1671C23—24no—
1672C23—22no—
1673C23—24no—
1674C23—24no—
1675C23—22no—
1676C23—22no—
1677C23—24no—
1678C23—24no—
1679C23—22no—
1680C23—22no—
1681C23—44no—
1682C23—44no—
1683C23—48no—
1684C23—44no—
1685C23—48no—
1686C23—44no—
1687C23—44no—
1688C23—48no—
1689C23—82no—
1690C23—82no—
1691C23—84no—
1692C23—82no—
1693C23—82no—
1694C23—82no—
1695C23—82no—
1696C23—82no—
1697C23—82no—
1698C23—84no—
1699C23—84no—
1700C23—84no—
1701C23—84no—
1702C23—84no—
1703C23—88no—
1704C23—88no—
1705C23—84no—
1706C23—84no—
1707C23—84no—
1708C23—88no—
1709C23—84no—
1710C23—84no—
1711C23—88no—
1712C23—88no—
1713C23—164no—
1714C23—164no—
1715C23C23×D414yes—
1716C23C23×D412yes—
1717C23C2×H(5,𝔽2)14yes—
1718C23C2×H(5,𝔽2)12yes—
1719C23#58512yes—
1720C23C2611yescharacteristic
1721Q8—44no—
1722Q8—48no—
1723Q8—82no—
1724Q8—84no—
1725Q8—84no—
1726Q8—84no—
1727D4—216no—
1728D4—44no—
1729D4—48no—
1730D4—48no—
1731D4—48no—
1732D4—416no—
1733D4—48no—
1734D4—48no—
1735D4—416no—
1736D4—48no—
1737D4—48no—
1738D4—82no—
1739D4—84no—
1740D4—84no—
1741D4—88no—
1742D4—88no—
1743D4—88no—
1744D4—88no—
1745D4—84no—
1746D4—88no—
1747D4—88no—
1748D4—84no—
1749D4—84no—
1750D4—84no—
1751D4—88no—
1752D4—88no—
1753D4—88no—
1754D4—88no—
1755D4—84no—
1756D4—84no—
1757D4—88no—
1758D4—88no—
1759D4—88no—
1760D4—164no—
1761D4—164no—
1762D4—164no—
1763C2×C4—22no—
1764C2×C4—21no—
1765C2×C4—22no—
1766C2×C4—22no—
1767C2×C4—22no—
1768C2×C4—21no—
1769C2×C4—21no—
1770C2×C4—21no—
1771C2×C4—22no—
1772C2×C4—21no—
1773C2×C4—21no—
1774C2×C4—22no—
1775C2×C4—21no—
1776C2×C4—22no—
1777C2×C4—21no—
1778C2×C4—22no—
1779C2×C4—22no—
1780C2×C4—21no—
1781C2×C4—21no—
1782C2×C4—22no—
1783C2×C4—28no—
1784C2×C4—28no—
1785C2×C4—216no—
1786C2×C4—22no—
1787C2×C4—22no—
1788C2×C4—22no—
1789C2×C4—24no—
1790C2×C4—24no—
1791C2×C4—22no—
1792C2×C4—22no—
1793C2×C4—24no—
1794C2×C4—24no—
1795C2×C4—24no—
1796C2×C4—22no—
1797C2×C4—22no—
1798C2×C4—24no—
1799C2×C4—22no—
1800C2×C4—22no—
1801C2×C4—24no—
1802C2×C4—24no—
1803C2×C4—22no—
1804C2×C4—22no—
1805C2×C4—22no—
1806C2×C4—22no—
1807C2×C4—24no—
1808C2×C4—22no—
1809C2×C4—22no—
1810C2×C4—22no—
1811C2×C4—22no—
1812C2×C4—24no—
1813C2×C4—22no—
1814C2×C4—22no—
1815C2×C4—24no—
1816C2×C4—22no—
1817C2×C4—22no—
1818C2×C4—24no—
1819C2×C4—44no—
1820C2×C4—48no—
1821C2×C4—48no—
1822C2×C4—48no—
1823C2×C4—48no—
1824C2×C4—48no—
1825C2×C4—48no—
1826C2×C4—84no—
1827C2×C4—84no—
1828C2×C4—84no—
1829C2×C4—84no—
1830C2×C4—84no—
1831C2×C4—88no—
1832C2×C4—88no—
1833C2×C4—88no—
1834C2×C4—88no—
1835C2×C4—82no—
1836C2×C4—84no—
1837C2×C4—82no—
1838C2×C4—84no—
1839C2×C4C23×D414yes—
1840C2×C4C23×D414yes—
1841C2×C4C23×D412yes—
1842C2×C4C23×D412yes—
1843C2×C4C23×D412yes—
1844C2×C4C23×D412yes—
1845C2×C4C23×D412yes—
1846C2×C4C23×D414yes—
1847C2×C4C23×D412yes—
1848C2×C4C2×H(5,𝔽2)14yes—
1849C2×C4C2×H(5,𝔽2)14yes—
1850C2×C4C2×H(5,𝔽2)12yes—
1851C2×C4C2×H(5,𝔽2)12yes—
1852C22—22no—
1853C22—22no—
1854C22—22no—
1855C22—22no—
1856C22—22no—
1857C22—22no—
1858C22—24no—
1859C22—24no—
1860C22—24no—
1861C22—24no—
1862C22—24no—
1863C22—24no—
1864C22—42no—
1865C22—42no—
1866C22—42no—
1867C22—42no—
1868C22—42no—
1869C22—42no—
1870C22—42no—
1871C22—42no—
1872C22—44no—
1873C22—44no—
1874C22—42no—
1875C22—42no—
1876C22—42no—
1877C22—42no—
1878C22—44no—
1879C22—44no—
1880C22—42no—
1881C22—42no—
1882C22—44no—
1883C22—44no—
1884C22—44no—
1885C22—42no—
1886C22—44no—
1887C22—42no—
1888C22—44no—
1889C22—42no—
1890C22—42no—
1891C22—44no—
1892C22—42no—
1893C22—42no—
1894C22—44no—
1895C22—44no—
1896C22—42no—
1897C22—42no—
1898C22—44no—
1899C22—44no—
1900C22—88no—
1901C22—88no—
1902C22—816no—
1903C22—168no—
1904C22—1616no—
1905C22#348814yes—
1906C22C24×D411yescharacteristic
1907C22C22×H(5,𝔽2)11yescharacteristic
1908C22C22×H(5,𝔽2)11yescharacteristic
1909C22C22×H(5,𝔽2)11yescharacteristic
1910C22C2×#58511yescharacteristic
1911C22H(7,𝔽2)11yescharacteristic
1912C222−1+611yescharacteristic
1913C4—22no—
1914C4—22no—
1915C4—24no—
1916C4—24no—
1917C4—22no—
1918C4—22no—
1919C4—22no—
1920C4—24no—
1921C4—24no—
1922C4—24no—
1923C4—42no—
1924C4—44no—
1925C4—42no—
1926C4—42no—
1927C4—42no—
1928C4—44no—
1929C4—42no—
1930C4—42no—
1931C4—44no—
1932C4—44no—
1933C4—42no—
1934C4#349814yes—
1935C2—24no—
1936C2—44no—
1937C2—44no—
1938C2—82no—
1939C2—82no—
1940C2—84no—
1941C2—84no—
1942C2C2×#348811yescharacteristic
1943C2C2×#349811yescharacteristic
1944C2#6285311yescharacteristic
1945C2#6289211yescharacteristic
1946C2#6289511yescharacteristic
1947C2#6289611yescharacteristic
1948C2#6289711yescharacteristic
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. C2×#3558C2semidirect
2. C2×#3459C2semidirect
3. #50656C2semidirect
4. #50655C2semidirect
5. #47685C2semidirect
6. #47683C2semidirect
7. #44022C2semidirect
8. #43886C2semidirect
9. #39420C2semidirect
10. #39412C2semidirect
11. #39383C2semidirect
12. #39358C2semidirect
13. #39137C2semidirect
14. #39130C2semidirect
15. #37658C2semidirect
16. #37650C2semidirect
17. #37649C2semidirect
18. #37648C2semidirect
19. #37546C2semidirect
20. #37278C2semidirect
21. #37271C2semidirect
22. #36097C2semidirect
23. D4×#121C2semidirect
24. #35569C2semidirect
25. #35565C2semidirect
26. #35238C2semidirect
27. #35165C2semidirect
28. C2×#2540C2semidirect
29. #34243C2semidirect
31. C2×#562C22semidirect
32. C2×H(3,𝔽4)C22semidirect
33. C2×#559C22semidirect
34. C2×#548C22semidirect
35. C2×#546C22semidirect
36. C2×#546C22semidirect
37. C2×D42C22semidirect
38. C2×D42C22semidirect
40. C2×#543C22semidirect
41. C2×#542C22semidirect
42. C2×#539C22semidirect
43. C2×#539C22semidirect
44. C2×#539C22semidirect
46. C2×#538C22semidirect
47. C2×#538C22semidirect
48. C2×#538C22semidirect
49. C2×#538C22semidirect
50. C2×#538C22semidirect
51. C2×#537C22semidirect
52. C2×#535C22semidirect
53. C2×#535C22semidirect
54. C2×#535C22semidirect
57. C2×#534C22semidirect
58. C2×#532C22semidirect
60. C2×#529C22semidirect
61. C2×#529C22semidirect
62. C2×#529C22semidirect
63. C22×#124C22semidirect
64. C2×#525C22semidirect
65. C2×#525C22semidirect
66. C2×#525C22semidirect
67. C2×#525C22semidirect
68. C22×C22⋊Q8C22semidirect
69. C22×C22⋊Q8C22semidirect
71. C22×#121C22semidirect
72. C22×#121C22semidirect
73. C22×C4×D4C22semidirect
74. C22×C4×D4C22semidirect
75. #2856C22semidirect
76. #2856C22semidirect
77. #2850C22semidirect
78. #2850C22semidirect
79. #2848C22semidirect
80. #2847C22semidirect
81. #2847C22semidirect
82. #2847C22semidirect
83. #2820C22semidirect
84. #2819C22semidirect
85. #2733C22semidirect
86. #2730C22semidirect
87. #2723C22semidirect
88. #2714C22semidirect
89. #2714C22semidirect
90. #2711C22semidirect
91. #2710C22semidirect
92. #2706C22semidirect
93. #2705C22semidirect
94. #2705C22semidirect
95. #2694C22semidirect
96. #2692C22semidirect
97. #2685C22semidirect
98. #2683C22semidirect
99. #2682C22semidirect
100. #2682C22semidirect
101. #2682C22semidirect
102. #2681C22semidirect
103. #2681C22semidirect
104. #2679C22semidirect
105. #2678C22semidirect
106. #2678C22semidirect
107. #2678C22semidirect
108. #2678C22semidirect
109. #2676C22semidirect
110. #2676C22semidirect
111. #2676C22semidirect
112. #2676C22semidirect
113. #2675C22semidirect
114. #2673C22semidirect
115. #2673C22semidirect
116. #2673C22semidirect
117. #2672C22semidirect
118. #2672C22semidirect
119. #2671C22semidirect
120. #2670C22semidirect
121. #2670C22semidirect
122. #2669C22semidirect
123. #2669C22semidirect
124. #2669C22semidirect
125. #2662C22semidirect
126. #2662C22semidirect
127. #2626C22semidirect
128. #2620C22semidirect
129. #2620C22semidirect
130. #2620C22semidirect
131. #2619C22semidirect
132. #2617C22semidirect
133. #2617C22semidirect
134. #2617C22semidirect
135. #2616C22semidirect
136. #2615C22semidirect
137. #2592C22semidirect
138. #2567C22semidirect
139. #2566C22semidirect
140. #2563C22semidirect
141. #2560C22semidirect
142. #2557C22semidirect
143. #2556C22semidirect
144. #2555C22semidirect
145. #2554C22semidirect
146. #2548C22semidirect
147. #2548C22semidirect
148. #2547C22semidirect
149. #2544C22semidirect
150. #2544C22semidirect
151. #2541C22semidirect
152. #2541C22semidirect
153. #2541C22semidirect
154. #2541C22semidirect
155. #2541C22semidirect
156. #2541C22semidirect
157. #2540C22semidirect
158. #2540C22semidirect
159. #2540C22semidirect
160. #2540C22semidirect
161. #2540C22semidirect
162. #2540C22semidirect
163. #2540C22semidirect
164. #2540C22semidirect
165. #2540C22semidirect
166. #2540C22semidirect
167. #2540C22semidirect
168. #2539C22semidirect
169. #2539C22semidirect
170. #2538C22semidirect
171. #2537C22semidirect
172. #2537C22semidirect
173. #2537C22semidirect
174. #2536C22semidirect
175. #2535C22semidirect
176. #2535C22semidirect
177. #2521C22semidirect
178. #2512C22semidirect
179. #2472C22semidirect
180. #2472C22semidirect
181. #2467C22semidirect
182. #2463C22semidirect
183. #2461C22semidirect
184. #2461C22semidirect
185. #2461C22semidirect
186. #2456C22semidirect
187. #2454C22semidirect
188. #2449C22semidirect
189. #2449C22semidirect
190. #2445C22semidirect
191. #2445C22semidirect
192. #2443C22semidirect
193. #2437C22semidirect
194. #2433C22semidirect
195. #2433C22semidirect
196. #2433C22semidirect
197. #2430C22semidirect
198. #2428C22semidirect
199. #2428C22semidirect
200. #2426C22semidirect
201. #2424C22semidirect
202. #2424C22semidirect
203. #2424C22semidirect
204. #2424C22semidirect
205. #2424C22semidirect
206. #2424C22semidirect
207. #2422C22semidirect
208. #2418C22semidirect
209. #2417C22semidirect
210. #2416C22semidirect
211. #2416C22semidirect
212. #2416C22semidirect
213. #2416C22semidirect
214. #2416C22semidirect
215. #2415C22semidirect
216. #2414C22semidirect
217. #2411C22semidirect
218. #2410C22semidirect
219. #2410C22semidirect
220. #2410C22semidirect
221. #2410C22semidirect
222. #2410C22semidirect
223. #2409C22semidirect
224. #2408C22semidirect
225. #2408C22semidirect
226. #2408C22semidirect
227. #2408C22semidirect
228. #2407C22semidirect
229. #2407C22semidirect
230. #2403C22semidirect
231. C2×#399C22semidirect
232. C2×#392C22semidirect
233. #2370C22semidirect
234. #2367C22semidirect
235. #2361C22semidirect
236. #2359C22semidirect
237. #2358C22semidirect
238. #2355C22semidirect
239. #2354C22semidirect
240. #2352C22semidirect
241. Q8×C4⋊C4C22semidirect
242. D4×C4⋊C4C22semidirect
243. D4×C4⋊C4C22semidirect
244. D4×C22⋊C4C22semidirect
245. #2334C22semidirect
246. #2324C22semidirect
247. #2324C22semidirect
248. #2324C22semidirect
249. #2323C22semidirect
250. #2314C22semidirect
251. #2311C22semidirect
252. C4×C22⋊Q8C22semidirect
253. C4×C22⋊Q8C22semidirect
255. C4×#121C22semidirect
256. C2×#390C22semidirect
257. C2×#390C22semidirect
258. #2285C22semidirect
259. #2274C22semidirect
260. C2×C4×C4⋊C4C22semidirect
314. #529D4semidirect
886. #126C2×D4semidirect
890. #125C2×D4semidirect
906. #124C2×D4semidirect
923. #123C2×D4semidirect
945. C22⋊Q8C2×D4semidirect
1014. C4×Q8C2×D4semidirect
1039. C4×D4C2×D4semidirect
1040. C4×D4C2×D4semidirect
1045. #117C2×D4semidirect
1185. C2×C42C2×D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35582
C2×#34592
#506562
#506552
#476852
#476832
#440222
#438862
#394202
#394122
#393832
#393582
#391372
#391302
#376582
#376502
#376492
#376482
#375462
#372782
#372712
#360972
D4×#1212
#355692
#355652
#352382
#351652
C2×#25402
#342432