Finite Group Databasebeta

← #8094905

Subgroups — #8094905

Order 512.

6414 conjugacy classes of subgroups.

The subgroup lattice has 1290 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53059C214yesmaximal, complemented
2#53055C214yesmaximal, complemented
3#52969C212yesmaximal, complemented
4#52966C212yesmaximal, complemented
5#52960C212yesmaximal, complemented
6#52957C212yesmaximal, complemented
7#52398C214yesmaximal, complemented
8#52397C214yesmaximal, complemented
9#46335C214yesmaximal, complemented
10#46324C214yesmaximal, complemented
11#45683C212yesmaximal, complemented
12#45604C214yesmaximal, complemented
13#45600C214yesmaximal, complemented
14#45599C212yesmaximal, complemented
15#45487C212yesmaximal, complemented
16#45478C212yesmaximal, complemented
17#35540C212yesmaximal, complemented
18#35528C212yesmaximal, complemented
19#35514C212yesmaximal, complemented
20#35252C212yesmaximal, complemented
21#35250C212yesmaximal, complemented
22#35160C212yesmaximal, complemented
23C2×#2541C211yesmaximal, characteristic, complemented
24#34809C211yesmaximal, characteristic, complemented
25#34736C211yesmaximal, characteristic, complemented
26C23×#41C2211yescharacteristic
27C2×#560C2214yescomplemented
28C2×#535C2212yes—
29C2×#535C2212yes—
30C22×#127C2212yes—
31C22×#127C2211yescharacteristic, complemented
32C2×#525C2212yes—
33C22×#121C2212yes—
34C22×#121C2212yescomplemented
35C2×#518C2212yescomplemented
36C22×C4×D4C2211yescharacteristic
37C22×#117C2211yescharacteristic, complemented
38#2856C2214yescomplemented
39#2852C2218yescomplemented
40#2850C2214yescomplemented
41#2847C2214yescomplemented
42#2847C2214yescomplemented
43#2830C2214yescomplemented
44#2828C2218yescomplemented
45#2828C2214yescomplemented
46#2826C2214yescomplemented
47#2825C2218yescomplemented
48#2825C2218yescomplemented
49#2824C2218yescomplemented
50#2824C2214yescomplemented
51#2818C2218yescomplemented
52#2815C2218yescomplemented
53#2815C2214yescomplemented
54#2813C2218yescomplemented
55#2812C2214yescomplemented
56#2797C2218yescomplemented
57#2784C2214yescomplemented
58#2778C2218yescomplemented
59#2760C2214yescomplemented
60#2749C2218yescomplemented
61#2737C2218yescomplemented
62#2714C2218yescomplemented
63#2709C2218yescomplemented
64#2709C2214yescomplemented
65#2703C2218yescomplemented
66#2699C2214yescomplemented
67#2693C2214yescomplemented
68#2691C2218yescomplemented
69#2688C2218yescomplemented
70#2688C2218yescomplemented
71#2688C2218yescomplemented
72#2678C2218yescomplemented
73#2675C2214yescomplemented
74#2673C2218yescomplemented
75#2673C2218yescomplemented
76#2673C2218yescomplemented
77#2669C2214yescomplemented
78#2669C2218yescomplemented
79#2668C2214yescomplemented
80#2643C2218yescomplemented
81#2620C2214yescomplemented
82#2619C2214yescomplemented
83#2615C2214yescomplemented
84#2615C2214yescomplemented
85#2544C2214yescomplemented
86#2544C2214yescomplemented
87#2541C2212yes—
88#2541C2212yes—
89#2541C2212yes—
90#2541C2212yes—
91#2541C2212yescomplemented
92#2541C2214yescomplemented
93#2541C2212yescomplemented
94#2541C2212yescomplemented
95#2541C2214yescomplemented
96#2541C2212yescomplemented
97#2537C2214yescomplemented
98#2537C2214yescomplemented
99#2535C2214yescomplemented
100#2535C2214yescomplemented
101#2514C2214yescomplemented
102#2513C2214yescomplemented
103#2512C2214yescomplemented
104#2511C2214yescomplemented
105#2497C2214yescomplemented
106#2496C2214yescomplemented
107#2495C2214yescomplemented
108#2494C2214yescomplemented
109#2487C2211yescharacteristic, complemented
110#2487C2211yescharacteristic, complemented
111#2486C2211yescharacteristic, complemented
112#2486C2211yescharacteristic, complemented
113#2485C2212yescomplemented
114#2485C2212yescomplemented
115#2484C2212yescomplemented
116#2483C2212yescomplemented
117#2483C2218yescomplemented
118#2482C2212yes—
119#2436C2214yescomplemented
120#2433C2214yescomplemented
121#2431C2214yescomplemented
122#2431C2214yescomplemented
123#2428C2214yescomplemented
124#2428C2214yescomplemented
125#2428C2214yescomplemented
126#2428C2214yescomplemented
127#2428C2214yescomplemented
128#2428C2214yescomplemented
129#2427C2214yescomplemented
130#2427C2214yescomplemented
131#2422C2214yescomplemented
132#2422C2214yescomplemented
133#2422C2214yescomplemented
134#2422C2214yescomplemented
135#2420C2214yescomplemented
136#2420C2214yescomplemented
137#2420C2214yescomplemented
138#2420C2214yescomplemented
139#2416C2214yescomplemented
140#2416C2214yescomplemented
141#2414C2214yescomplemented
142#2414C2214yescomplemented
143#2412C2218yescomplemented
144#2411C2218yescomplemented
145#2410C2218yescomplemented
146#2410C2218yescomplemented
147#2410C2218yescomplemented
148#2410C2218yescomplemented
149#2409C2211yescharacteristic, complemented
150#2409C2211yescharacteristic, complemented
151#2408C2211yescharacteristic, complemented
152#2408C2211yescharacteristic, complemented
153#2407C2212yescomplemented
154#2407C2212yescomplemented
155#2406C2212yes—
156#2405C2212yes—
157#2405C2218yes—
158#2405C2212yes—
159#2404C2212yes—
160#2404C2218yes—
161#2403C2218yes—
162#2403C2212yes—
163#2395C2212yescomplemented
164#2395C2212yescomplemented
165#2388C2212yescomplemented
166#2388C2212yescomplemented
167C2×#392C2212yes—
168C2×#392C2212yescomplemented
169#2380C2214yescomplemented
170#2377C2218yescomplemented
171#2317C2212yescomplemented
172#2317C2212yescomplemented
173#2311C2212yes—
174#2311C2212yes—
175#2309C2212yescomplemented
176C4×#123C2212yescomplemented
177C4×#123C2212yescomplemented
178C4×#120C2212yescomplemented
179C4×#120C2212yescomplemented
180#2297C2212yes—
181#2296C2212yescomplemented
182C2×#390C2212yescomplemented
183#2280C2211yescharacteristic
184#2280C2212yes—
185#2280C2211yescharacteristic, complemented
186C2×C4×C4⋊C4C2211yescharacteristic, complemented
187C22×#41—44no—
188C22×#41—48no—
189C22×#41C2312yes—
190C22×#41C2312yes—
191C22×#41C2312yes—
192C22×#41C2312yes—
193C23×Q8C2311yescharacteristic
194C23×D4C2312yes—
195C23×D4C2311yescharacteristic
196C23×D4C2312yes—
197C23×D4C2311yescharacteristic
198C23×D4C2312yes—
199C23×D4C2314yes—
200C23×D4C2314yes—
201C23×D4C2312yes—
202C24×C4C2311yescharacteristic
203C24×C4C2311yescharacteristic
204C24×C4C2312yes—
205#560—416no—
206#535—48no—
207#535—48no—
208C2×#127—44no—
209C2×#127—48no—
210C2×#127C2314yes—
211C2×#127C2314yes—
212C2×#127C2314yes—
213C2×#127C2314yes—
214C2×#127C2314yes—
215C2×#127C2312yes—
216C2×#127C2312yes—
217C2×#127C2312yes—
218C2×#127C2312yes—
219C2×#127C2314yes—
220C2×#126C2318yes—
221C2×#124C2314yes—
222C2×#124C2314yes—
223#525—48no—
224C2×#123C2312yes—
225C2×#123C2314yes—
226C2×#123C2312yes—
227C2×#123C2318yes—
228C2×#123C2318yes—
229C2×C22⋊Q8C2312yes—
230C2×C22⋊Q8C2312yes—
231C2×#121—48no—
232C2×#121—48no—
233C2×#121C2314yes—
234C2×#121C2314yes—
235C2×#121C2314yes—
236C2×#121C2314yes—
237C2×#121C2314yes—
238C2×#121C2314yes—
239C2×#121C2312yes—
240C2×#121C2318yes—
241C2×#121C2314yes—
242C2×#121C2312yes—
243C2×#121C2314yes—
244C2×#121C2318yes—
245C2×#121C2314yes—
246C2×#121C2314yes—
247C2×#121C2314yes—
248C2×#121C2314yes—
249C2×#121C2318yes—
250C2×#121C2318yes—
251C2×#121C2318yes—
252C2×#121C2318yes—
253C2×#121C2318yes—
254C2×#121C2318yes—
255C2×#120C2312yes—
256C2×#120C2318yes—
257C2×#120C2314yes—
258C2×#120C2318yes—
259C2×#120C2318yes—
260C2×#120C2312yes—
261C2×#120C2318yes—
262#518—48no—
263C2×C4×D4—44no—
264C2×C4×D4C2311yescharacteristic
265C2×C4×D4C2311yescharacteristic
266C2×C4×D4C2314yes—
267C2×C4×D4C2314yes—
268C2×C4×D4C2311yescharacteristic
269C2×C4×D4C2311yescharacteristic
270C2×C4×D4C2311yescharacteristic
271C2×C4×D4C2311yescharacteristic
272C2×C4×D4C2311yescharacteristic
273C2×C4×D4C2311yescharacteristic
274C2×C4×D4C2314yes—
275C2×C4×D4C2314yes—
276C2×C4×D4C2314yes—
277C2×C4×D4C2314yes—
278C2×#117—44no—
279C2×#117C2312yes—
280C2×#117C2312yes—
281C2×#117C2312yes—
282C2×#117C2312yes—
283C2×#117C2312yes—
284C2×#117C2312yes—
285C22×C4⋊C4C2312yes—
286C22×C4⋊C4C2311yescharacteristic
287C22×C4⋊C4C2311yescharacteristic
288C22×C4⋊C4C2311yescharacteristic
289C22×C22⋊C4C2311yescharacteristic
290C22×C22⋊C4C2314yes—
291C22×C22⋊C4C2311yescharacteristic
292C22×C22⋊C4C2314yes—
293C22×C22⋊C4C2312yes—
294C22×C22⋊C4C2318yes—
295C22×C42C2311yescharacteristic
296C22×C42C2312yes—
297C22×C42C2312yes—
298#401C2318yes—
299#400C2318yes—
300#400C2318yes—
301#400C2318yes—
302#400C2312yes—
303#400C2312yes—
304#399C2312yes—
305#399C2312yes—
306#398C2312yes—
307#398C2312yes—
308#397C2314yes—
309#397C2318yes—
310#397C2318yes—
311#397C2312yes—
312#397C2314yes—
313#397C2318yes—
314#397C2318yes—
315#397C2318yes—
316#397C2318yes—
317#397C2318yes—
318#397C2318yes—
319#397C2318yes—
320#397C2312yes—
321#396C2318yes—
322#396C2318yes—
323#396C2318yes—
324#395C2312yes—
325#395C2312yes—
326#394C2314yes—
327#394C2318yes—
328#394C2318yes—
329#394C2318yes—
330#394C2318yes—
331#394C2318yes—
332#394C2318yes—
333#394C2318yes—
334#394C2318yes—
335#394C2318yes—
336#394C2314yes—
337#394C2318yes—
338#394C2318yes—
339#394C2314yes—
340#394C2312yes—
341#394C2318yes—
342#394C2318yes—
343#394C2318yes—
344#394C2318yes—
345#394C2312yes—
346#394C2314yes—
347#394C2318yes—
348#393C2312yes—
349#393C2318yes—
350#393C2312yes—
351#393C2318yes—
352#392C2314yes—
353#392C2318yes—
354#392C2318yes—
355#392C2318yes—
356#392C2318yes—
357#392C2318yes—
358#392C2314yes—
359#392C2314yes—
360#392C2314yes—
361#392C2314yes—
362#392C2318yes—
363#392C2318yes—
364#392C2318yes—
365#392C2314yes—
366#392C2314yes—
367#392C2318yes—
368#392C2318yes—
369#392C2318yes—
370#392C2318yes—
371#392C2318yes—
372#392C2314yes—
373#392C2314yes—
374#392C2314yes—
375#392C2312yes—
376#392C2312yes—
377#392C2318yes—
378#391C2314yes—
379#391C2314yes—
380#391C2312yes—
381#391C2312yes—
382#390C2314yes—
383#390C2314yes—
384#390C2314yes—
385#390C2314yes—
386#390C2314yes—
387#390C2314yes—
388#390C2314yes—
389#390C2318yes—
390#390C2318yes—
391#390C2314yes—
392#390C2312yes—
393#390C2312yes—
394#390C2314yes—
395#390C2314yes—
396#389C2314yes—
397#389C2314yes—
398#389C2314yes—
399#389C2314yes—
400#389C2312yes—
401#389C2312yes—
402#389C2312yes—
403#389C2312yes—
404#388C2314yes—
405#388C2318yes—
406#388C2318yes—
407#388C2318yes—
408#388C2318yes—
409#388C2318yes—
410#388C2314yes—
411#387C2318yes—
412#387C2318yes—
413#387C2318yes—
414#387C2314yes—
415#387C2314yes—
416#386C2318yes—
417#386C2318yes—
418#386C2318yes—
419#386C2318yes—
420#386C2318yes—
421#386C2314yes—
422#386C2318yes—
423#386C2318yes—
424#386C2318yes—
425#386C2318yes—
426#386C2318yes—
427#386C2318yes—
428#386C2318yes—
429#386C2318yes—
430#386C2318yes—
431#386C2318yes—
432#386C2314yes—
433#386C2318yes—
434#386C2318yes—
435#386C2312yes—
436#386C2312yes—
437#386C2318yes—
438#386C2318yes—
439#386C2318yes—
440#386C2314yes—
441#386C2312yes—
442#386C2314yes—
443#386C2312yes—
444#385C2312yes—
445#385C2318yes—
446#385C2312yes—
447#385C2318yes—
448#385C2318yes—
449#385C2314yes—
450#385C2314yes—
451#385C2318yes—
452#385C2314yes—
453#385C2312yes—
454#385C2314yes—
455#385C2312yes—
456#384C2314yes—
457#384C2314yes—
458#383C2318yes—
459#382C2314yes—
460#382C2314yes—
461#381C2318yes—
462#381C2314yes—
463#381C2312yes—
464#381C2312yes—
465#381C2318yes—
466#381C2312yes—
467#381C2312yes—
468#380C2314yes—
469#380C2314yes—
470#380C2314yes—
471#380C2314yes—
472#380C2312yes—
473#380C2312yes—
474#380C2312yes—
475#380C2312yes—
476#380C2318yes—
477#380C2312yes—
478#380C2311yescharacteristic
479#380C2311yescharacteristic
480#380C2318yes—
481#380C2312yes—
482#380C2311yescharacteristic
483#380C2311yescharacteristic
484#379C2318yes—
485#379C2314yes—
486#379C2312yes—
487#379C2312yes—
488#379C2312yes—
489#379C2312yes—
490C4×C4⋊C4C2314yes—
491C4×C4⋊C4C2314yes—
492C4×C4⋊C4C2312yes—
493C4×C4⋊C4C2312yes—
494C4×C4⋊C4C2312yes—
495C4×C4⋊C4C2312yes—
496C4×C22⋊C4C2312yes—
497C4×C22⋊C4C2314yes—
498C4×C22⋊C4C2314yes—
499C4×C22⋊C4C2312yes—
500C4×C22⋊C4C2314yes—
501C4×C22⋊C4C2314yes—
502C4×C22⋊C4C2312yes—
503C4×C22⋊C4C2312yes—
504C2×#95C2312yes—
505C25C2411yescharacteristic
506C25C2411yescharacteristic
507C25C2414yes—
508C25C2412yes—
509C2×#41—28no—
510C2×#41—28no—
511C2×#41—28no—
512C2×#41—44no—
513C2×#41—48no—
514C2×#41—48no—
515C2×#41—44no—
516C2×#41—44no—
517C2×#41—44no—
518C2×#41—44no—
519C2×#41—464no—
520C22×Q8—42no—
521C22×Q8—44no—
522C22×Q8C2412yes—
523C22×Q8C2412yes—
524C22×D4—24no—
525C22×D4—28no—
526C22×D4—28no—
527C22×D4—28no—
528C22×D4—42no—
529C22×D4—42no—
530C22×D4—44no—
531C22×D4—44no—
532C22×D4—44no—
533C22×D4—42no—
534C22×D4—48no—
535C22×D4—48no—
536C22×D4—44no—
537C22×D4—44no—
538C22×D4—44no—
539C22×D4—48no—
540C22×D4—48no—
541C22×D4—48no—
542C22×D4—84no—
543C22×D4—84no—
544C22×D4—84no—
545C22×D4C2414yes—
546C22×D4C2414yes—
547C22×D4C2414yes—
548C22×D4C2412yes—
549C22×D4C2411yescharacteristic
550C22×D4C2411yescharacteristic
551C22×D4C2411yescharacteristic
552C22×D4C2414yes—
553C22×D4C2418yes—
554C22×D4C2418yes—
555C22×D4C2414yes—
556C22×D4C2414yes—
557C22×D4C2414yes—
558C22×D4C2418yes—
559C22×D4C2418yes—
560C22×D4C2418yes—
561C22×D4C2418yes—
562C22×D4C2418yes—
563C22×D4C2418yes—
564C22×D4C2414yes—
565C22×D4C2414yes—
566C22×D4C2414yes—
567C22×D4C2412yes—
568C22×D4C2411yescharacteristic
569C23×C4—24no—
570C23×C4—24no—
571C23×C4—28no—
572C23×C4—28no—
573C23×C4—44no—
574C23×C4—48no—
575C23×C4C2411yescharacteristic
576C23×C4C2411yescharacteristic
577C23×C4C2411yescharacteristic
578C23×C4C2411yescharacteristic
579C23×C4C2411yescharacteristic
580C23×C4C2411yescharacteristic
581C23×C4C2411yescharacteristic
582C23×C4C2411yescharacteristic
583C23×C4C2411yescharacteristic
584C23×C4C2411yescharacteristic
585C23×C4C2411yescharacteristic
586C23×C4C2414yes—
587C23×C4C2414yes—
588C23×C4C2411yescharacteristic
589C23×C4C2412yes—
590C23×C4C2412yes—
591C23×C4C2418yes—
592C23×C4C2418yes—
593C23×C4C2412yes—
594C23×C4C2414yes—
595C23×C4C2411yescharacteristic
596#127—216no—
597#127—44no—
598#127—44no—
599#127—44no—
600#127—44no—
601#127—48no—
602#127—48no—
603#127—48no—
604#127—48no—
605#127—48no—
606#126—416no—
607#124—48no—
608#124—48no—
609#123—28no—
610#123—416no—
611#123—48no—
612#123—44no—
613#123—88no—
614C22⋊Q8—44no—
615C22⋊Q8—44no—
616#121—416no—
617#121—416no—
618#121—416no—
619#121—48no—
620#121—48no—
621#121—48no—
622#121—48no—
623#121—48no—
624#121—48no—
625#121—48no—
626#121—48no—
627#121—44no—
628#121—44no—
629#121—48no—
630#121—48no—
631#121—48no—
632#121—48no—
633#121—416no—
634#121—88no—
635#121—88no—
636#121—88no—
637#121—88no—
638#120—28no—
639#120—44no—
640#120—48no—
641#120—416no—
642#120—416no—
643#120—416no—
644#120—88no—
645C4×D4—48no—
646C4×D4—48no—
647C4×D4—48no—
648C4×D4—48no—
649C4×D4—42no—
650C4×D4—42no—
651C4×D4—42no—
652C4×D4—42no—
653C4×D4—42no—
654C4×D4—42no—
655C4×D4—42no—
656C4×D4—42no—
657C4×D4—48no—
658C4×D4—48no—
659#117—28no—
660#117—28no—
661#117—28no—
662#117—44no—
663#117—44no—
664#117—44no—
665C2×C4⋊C4—28no—
666C2×C4⋊C4—42no—
667C2×C4⋊C4—42no—
668C2×C4⋊C4—42no—
669C2×C4⋊C4C2412yes—
670C2×C4⋊C4C2412yes—
671C2×C4⋊C4C2414yes—
672C2×C4⋊C4C2414yes—
673C2×C4⋊C4C2412yes—
674C2×C4⋊C4C2412yes—
675C2×C4⋊C4C2412yes—
676C2×C4⋊C4C2412yes—
677C2×C4⋊C4C2414yes—
678C2×C4⋊C4C2414yes—
679C2×C4⋊C4C2412yes—
680C2×C4⋊C4C2412yes—
681C2×C4⋊C4C2411yescharacteristic
682C2×C4⋊C4C2411yescharacteristic
683C2×C4⋊C4C2411yescharacteristic
684C2×C4⋊C4C2411yescharacteristic
685C2×C4⋊C4C2414yes—
686C2×C4⋊C4C2414yes—
687C2×C4⋊C4C2414yes—
688C2×C4⋊C4C2414yes—
689C2×C4⋊C4C2418yes—
690C2×C4⋊C4C2418yes—
691C2×C4⋊C4C2418yes—
692C2×C4⋊C4C2418yes—
693C2×C22⋊C4—44no—
694C2×C22⋊C4—416no—
695C2×C22⋊C4—42no—
696C2×C22⋊C4—42no—
697C2×C22⋊C4—48no—
698C2×C22⋊C4—48no—
699C2×C22⋊C4C2414yes—
700C2×C22⋊C4C2414yes—
701C2×C22⋊C4C2414yes—
702C2×C22⋊C4C2414yes—
703C2×C22⋊C4C2414yes—
704C2×C22⋊C4C2414yes—
705C2×C22⋊C4C2412yes—
706C2×C22⋊C4C2412yes—
707C2×C22⋊C4C2414yes—
708C2×C22⋊C4C2411yescharacteristic
709C2×C22⋊C4C2411yescharacteristic
710C2×C22⋊C4C2411yescharacteristic
711C2×C22⋊C4C2411yescharacteristic
712C2×C22⋊C4C2411yescharacteristic
713C2×C22⋊C4C2411yescharacteristic
714C2×C22⋊C4C2411yescharacteristic
715C2×C22⋊C4C2411yescharacteristic
716C2×C22⋊C4C2418yes—
717C2×C22⋊C4C2418yes—
718C2×C22⋊C4C2418yes—
719C2×C22⋊C4C2418yes—
720C2×C22⋊C4C2418yes—
721C2×C22⋊C4C2418yes—
722C2×C22⋊C4C2414yes—
723C2×C22⋊C4C2414yes—
724C2×C22⋊C4C2414yes—
725C2×C22⋊C4C2414yes—
726C2×C22⋊C4C2414yes—
727C2×C22⋊C4C2418yes—
728C2×C22⋊C4C2418yes—
729C2×C22⋊C4C2418yes—
730C2×C22⋊C4C2418yes—
731C2×C22⋊C4C2418yes—
732C2×C22⋊C4C2418yes—
733C2×C22⋊C4C2418yes—
734C2×C22⋊C4C2418yes—
735C2×C22⋊C4C2412yes—
736C2×C22⋊C4C2418yes—
737C2×C22⋊C4C2414yes—
738C2×C22⋊C4C2414yes—
739C2×C22⋊C4C2414yes—
740C2×C22⋊C4C2418yes—
741C2×C22⋊C4C2418yes—
742C2×C22⋊C4C2418yes—
743C2×C22⋊C4C2414yes—
744C2×C22⋊C4C2414yes—
745C2×C22⋊C4C2412yes—
746C2×C22⋊C4C2414yes—
747C2×C42—24no—
748C2×C42—44no—
749C2×C42—44no—
750C2×C42C2414yes—
751C2×C42C2414yes—
752C2×C42C2414yes—
753C2×C42C2411yescharacteristic
754C2×C42C2411yescharacteristic
755C2×C42C2411yescharacteristic
756C2×C42C2411yescharacteristic
757C2×C42C2414yes—
758C2×C42C2414yes—
759C2×C42C2414yes—
760#95C2414yes—
761#95C2414yes—
762#95C2412yes—
763#95C2414yes—
764#95C2412yes—
765#95C2414yes—
766#95C2414yes—
767#95C2414yes—
768#95C2414yes—
769#95C2412yes—
770#95C2414yes—
771#95C2412yes—
772#95C2414yes—
773#95C2414yes—
774#95C2414yes—
775#95C2414yes—
776#95C2414yes—
777#95C2414yes—
778#95C2414yes—
779#95C2414yes—
780#95C2418yes—
781#95C2418yes—
782#95C2418yes—
783#95C2418yes—
784#95C2418yes—
785#95C2418yes—
786#95C2418yes—
787#95C2418yes—
788C24—22no—
789C24—22no—
790C24—22no—
791C24—22no—
792C24—24no—
793C24—24no—
794C24—28no—
795C24—28no—
796C24—28no—
797C24—24no—
798C24—42no—
799C24—44no—
800C24—41no—
801C24—41no—
802C24—42no—
803C24—42no—
804C24—42no—
805C24—44no—
806C24—44no—
807C24—44no—
808C24—44no—
809C24—44no—
810C24C2514yes—
811C24C2511yescharacteristic
812C24C2518yes—
813C24C2511yescharacteristic
814C24C2511yescharacteristic
815C24C2511yescharacteristic
816C24C2511yescharacteristic
817#41—432no—
818#41—432no—
819#41—432no—
820#41—432no—
821C2×Q8—24no—
822C2×Q8—24no—
823C2×Q8—24no—
824C2×Q8—44no—
825C2×Q8—42no—
826C2×Q8—416no—
827C2×D4—28no—
828C2×D4—28no—
829C2×D4—28no—
830C2×D4—22no—
831C2×D4—22no—
832C2×D4—28no—
833C2×D4—216no—
834C2×D4—216no—
835C2×D4—28no—
836C2×D4—28no—
837C2×D4—28no—
838C2×D4—28no—
839C2×D4—28no—
840C2×D4—24no—
841C2×D4—28no—
842C2×D4—22no—
843C2×D4—24no—
844C2×D4—24no—
845C2×D4—28no—
846C2×D4—22no—
847C2×D4—22no—
848C2×D4—28no—
849C2×D4—41no—
850C2×D4—41no—
851C2×D4—41no—
852C2×D4—41no—
853C2×D4—41no—
854C2×D4—41no—
855C2×D4—44no—
856C2×D4—44no—
857C2×D4—44no—
858C2×D4—42no—
859C2×D4—44no—
860C2×D4—416no—
861C2×D4—44no—
862C2×D4—44no—
863C2×D4—44no—
864C2×D4—48no—
865C2×D4—48no—
866C2×D4—48no—
867C2×D4—48no—
868C2×D4—48no—
869C2×D4—44no—
870C2×D4—44no—
871C2×D4—48no—
872C2×D4—48no—
873C2×D4—48no—
874C2×D4—48no—
875C2×D4—48no—
876C2×D4—44no—
877C2×D4—44no—
878C2×D4—44no—
879C2×D4—44no—
880C2×D4—44no—
881C2×D4—48no—
882C2×D4—48no—
883C2×D4—44no—
884C2×D4—48no—
885C2×D4—48no—
886C2×D4—48no—
887C2×D4—48no—
888C2×D4—48no—
889C2×D4—48no—
890C2×D4—48no—
891C2×D4—48no—
892C2×D4—48no—
893C2×D4—48no—
894C2×D4—48no—
895C2×D4—48no—
896C2×D4—432no—
897C2×D4—416no—
898C2×D4—432no—
899C2×D4—816no—
900C2×D4—832no—
901C2×D4—832no—
902C2×D4—816no—
903C2×D4H(5,𝔽2)14yes—
904C22×C4—22no—
905C22×C4—22no—
906C22×C4—22no—
907C22×C4—22no—
908C22×C4—28no—
909C22×C4—24no—
910C22×C4—24no—
911C22×C4—22no—
912C22×C4—22no—
913C22×C4—24no—
914C22×C4—22no—
915C22×C4—22no—
916C22×C4—22no—
917C22×C4—22no—
918C22×C4—24no—
919C22×C4—24no—
920C22×C4—22no—
921C22×C4—22no—
922C22×C4—22no—
923C22×C4—22no—
924C22×C4—28no—
925C22×C4—24no—
926C22×C4—24no—
927C22×C4—24no—
928C22×C4—24no—
929C22×C4—24no—
930C22×C4—24no—
931C22×C4—28no—
932C22×C4—28no—
933C22×C4—44no—
934C22×C4—42no—
935C22×C4—44no—
936C22×C4—44no—
937C22×C4—44no—
938C22×C4—44no—
939C22×C4—44no—
940C22×C4—42no—
941C22×C4—42no—
942C22×C4—42no—
943C22×C4—44no—
944C22×C4—42no—
945C22×C4—48no—
946C22×C4—48no—
947C22×C4—48no—
948C22×C4—48no—
949C22×C4—48no—
950C22×C4—48no—
951C22×C4—432no—
952C22×C4—416no—
953C22×C4—416no—
954C22×C4H(5,𝔽2)14yes—
955C22×C4H(5,𝔽2)18yes—
956C22×C4C2511yescharacteristic
957C22×C4C2511yescharacteristic
958C22×C4C2514yes—
959C22×C4C2511yescharacteristic
960C22×C4C2511yescharacteristic
961C22×C4C2514yes—
962C22×C4C2518yes—
963C22×C4C2514yes—
964C22×C4C2514yes—
965C22×C4C2514yes—
966C22×C4C2514yes—
967C22×C4C2514yes—
968C22×C4C2511yescharacteristic
969C22×C4C2511yescharacteristic
970C22×C4C2511yescharacteristic
971C22×C4C2511yescharacteristic
972C22×C4C2511yescharacteristic
973C22×C4C2511yescharacteristic
974C4⋊C4—28no—
975C4⋊C4—28no—
976C4⋊C4—24no—
977C4⋊C4—24no—
978C4⋊C4—24no—
979C4⋊C4—24no—
980C4⋊C4—24no—
981C4⋊C4—24no—
982C4⋊C4—28no—
983C4⋊C4—28no—
984C4⋊C4—42no—
985C4⋊C4—42no—
986C4⋊C4—41no—
987C4⋊C4—41no—
988C4⋊C4—41no—
989C4⋊C4—41no—
990C4⋊C4—44no—
991C4⋊C4—44no—
992C4⋊C4—48no—
993C4⋊C4—48no—
994C4⋊C4—44no—
995C4⋊C4—44no—
996C4⋊C4—48no—
997C4⋊C4—48no—
998C22⋊C4—28no—
999C22⋊C4—28no—
1000C22⋊C4—28no—
1001C22⋊C4—24no—
1002C22⋊C4—28no—
1003C22⋊C4—24no—
1004C22⋊C4—28no—
1005C22⋊C4—28no—
1006C22⋊C4—44no—
1007C22⋊C4—41no—
1008C22⋊C4—41no—
1009C22⋊C4—41no—
1010C22⋊C4—41no—
1011C22⋊C4—41no—
1012C22⋊C4—41no—
1013C22⋊C4—41no—
1014C22⋊C4—41no—
1015C22⋊C4—48no—
1016C22⋊C4—48no—
1017C22⋊C4—48no—
1018C22⋊C4—48no—
1019C22⋊C4—48no—
1020C22⋊C4—48no—
1021C22⋊C4—44no—
1022C22⋊C4—44no—
1023C22⋊C4—44no—
1024C22⋊C4—44no—
1025C22⋊C4—42no—
1026C22⋊C4—48no—
1027C22⋊C4—48no—
1028C22⋊C4—48no—
1029C22⋊C4—48no—
1030C22⋊C4—48no—
1031C22⋊C4—48no—
1032C22⋊C4—44no—
1033C22⋊C4—48no—
1034C22⋊C4—48no—
1035C22⋊C4—48no—
1036C22⋊C4—48no—
1037C22⋊C4—48no—
1038C22⋊C4—44no—
1039C22⋊C4—44no—
1040C22⋊C4—44no—
1041C22⋊C4—48no—
1042C22⋊C4—44no—
1043C22⋊C4—42no—
1044C22⋊C4—44no—
1045C22⋊C4—44no—
1046C42—22no—
1047C42—22no—
1048C42—22no—
1049C42—22no—
1050C42—28no—
1051C42—28no—
1052C42—28no—
1053C42—28no—
1054C42—44no—
1055C42—44no—
1056C23—21no—
1057C23—21no—
1058C23—22no—
1059C23—21no—
1060C23—21no—
1061C23—22no—
1062C23—22no—
1063C23—21no—
1064C23—21no—
1065C23—22no—
1066C23—22no—
1067C23—24no—
1068C23—21no—
1069C23—28no—
1070C23—28no—
1071C23—21no—
1072C23—22no—
1073C23—24no—
1074C23—28no—
1075C23—28no—
1076C23—22no—
1077C23—24no—
1078C23—24no—
1079C23—21no—
1080C23—21no—
1081C23—24no—
1082C23—21no—
1083C23—28no—
1084C23—21no—
1085C23—22no—
1086C23—24no—
1087C23—24no—
1088C23—22no—
1089C23—28no—
1090C23—28no—
1091C23—44no—
1092C23—44no—
1093C23—48no—
1094C23—48no—
1095C23—48no—
1096C23—44no—
1097C23—44no—
1098C23—416no—
1099C23—82no—
1100C23—82no—
1101C23—84no—
1102C23—84no—
1103C23—84no—
1104C23—88no—
1105C23—88no—
1106C23—88no—
1107C23—88no—
1108C23—88no—
1109C23—88no—
1110C23—88no—
1111C23—84no—
1112C23—88no—
1113C23C2×H(5,𝔽2)12yes—
1114C23C2×H(5,𝔽2)12yes—
1115C23C2×H(5,𝔽2)12yes—
1116C23C2×H(5,𝔽2)14yes—
1117C23C2611yescharacteristic
1118Q8—48no—
1119Q8—48no—
1120D4—44no—
1121D4—44no—
1122D4—44no—
1123D4—44no—
1124D4—48no—
1125D4—416no—
1126D4—416no—
1127D4—416no—
1128D4—416no—
1129D4—48no—
1130D4—88no—
1131D4—88no—
1132D4—88no—
1133D4—816no—
1134D4—816no—
1135D4—88no—
1136D4—88no—
1137D4—88no—
1138D4—816no—
1139D4—816no—
1140D4—168no—
1141D4—168no—
1142D4—168no—
1143D4—168no—
1144C2×C4—28no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—24no—
1152C2×C4—24no—
1153C2×C4—28no—
1154C2×C4—24no—
1155C2×C4—24no—
1156C2×C4—24no—
1157C2×C4—24no—
1158C2×C4—21no—
1159C2×C4—24no—
1160C2×C4—24no—
1161C2×C4—24no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—28no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—24no—
1168C2×C4—24no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—24no—
1173C2×C4—24no—
1174C2×C4—24no—
1175C2×C4—24no—
1176C2×C4—24no—
1177C2×C4—24no—
1178C2×C4—24no—
1179C2×C4—24no—
1180C2×C4—24no—
1181C2×C4—24no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—28no—
1185C2×C4—44no—
1186C2×C4—416no—
1187C2×C4—48no—
1188C2×C4—416no—
1189C2×C4—44no—
1190C2×C4—44no—
1191C2×C4—44no—
1192C2×C4—44no—
1193C2×C4—44no—
1194C2×C4—44no—
1195C2×C4—44no—
1196C2×C4—44no—
1197C2×C4—44no—
1198C2×C4—44no—
1199C2×C4—416no—
1200C2×C4—84no—
1201C2×C4—84no—
1202C2×C4—168no—
1203C2×C4—168no—
1204C2×C4#560116yescomplemented
1205C2×C4C2×H(5,𝔽2)12yes—
1206C2×C4C2×H(5,𝔽2)12yes—
1207C2×C4C2×H(5,𝔽2)12yes—
1208C2×C4C2×H(5,𝔽2)14yes—
1209C2×C4C2×H(5,𝔽2)14yes—
1210C2×C4#58512yes—
1211C22—22no—
1212C22—22no—
1213C22—24no—
1214C22—24no—
1215C22—22no—
1216C22—22no—
1217C22—24no—
1218C22—24no—
1219C22—41no—
1220C22—41no—
1221C22—41no—
1222C22—41no—
1223C22—42no—
1224C22—42no—
1225C22—41no—
1226C22—41no—
1227C22—48no—
1228C22—44no—
1229C22—48no—
1230C22—44no—
1231C22—41no—
1232C22—41no—
1233C22—48no—
1234C22—42no—
1235C22—42no—
1236C22—48no—
1237C22—44no—
1238C22—44no—
1239C22—44no—
1240C22—41no—
1241C22—41no—
1242C22—48no—
1243C22—48no—
1244C22—42no—
1245C22—44no—
1246C22—44no—
1247C22—48no—
1248C22—42no—
1249C22—88no—
1250C22—88no—
1251C22—816no—
1252C22—1616no—
1253C22C2×#56014yes—
1254C22C22×H(5,𝔽2)11yescharacteristic
1255C22C22×H(5,𝔽2)11yescharacteristic
1256C22C22×H(5,𝔽2)12yes—
1257C22C2×#58511yescharacteristic
1258C22H(7,𝔽2)12yes—
1259C4—22no—
1260C4—22no—
1261C4—44no—
1262C4—41no—
1263C4—41no—
1264C4—44no—
1265C4—48no—
1266C4—44no—
1267C4—44no—
1268C4—41no—
1269C4—41no—
1270C4—41no—
1271C4—41no—
1272C4—44no—
1273C4—44no—
1274C4—44no—
1275C4C2×#56014yes—
1276C4C2×#56014yes—
1277C2—24no—
1278C2—42no—
1279C2—42no—
1280C2—81no—
1281C2—81no—
1282C2—84no—
1283C2—88no—
1284C2C22×#56011yescharacteristic
1285C2#6281811yescharacteristic
1286C2#6287411yescharacteristic
1287C2#6291212yes—
1288C2#6295512yes—
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. #53059C2semidirect
2. #53055C2semidirect
3. #52969C2semidirect
4. #52966C2semidirect
5. #52960C2semidirect
6. #52957C2semidirect
7. #52398C2semidirect
8. #52397C2semidirect
9. #46335C2semidirect
10. #46324C2semidirect
11. #45683C2semidirect
12. #45604C2semidirect
13. #45600C2semidirect
14. #45599C2semidirect
15. #45487C2semidirect
16. #45478C2semidirect
17. #35540C2semidirect
18. #35528C2semidirect
19. #35514C2semidirect
20. #35252C2semidirect
21. #35250C2semidirect
22. #35160C2semidirect
23. C2×#2541C2semidirect
24. #34809C2semidirect
25. #34736C2semidirect
27. C2×#560C22semidirect
31. C22×#127C22semidirect
34. C22×#121C22semidirect
35. C2×#518C22semidirect
37. C22×#117C22semidirect
38. #2856C22semidirect
39. #2852C22semidirect
40. #2850C22semidirect
41. #2847C22semidirect
42. #2847C22semidirect
43. #2830C22semidirect
44. #2828C22semidirect
45. #2828C22semidirect
46. #2826C22semidirect
47. #2825C22semidirect
48. #2825C22semidirect
49. #2824C22semidirect
50. #2824C22semidirect
51. #2818C22semidirect
52. #2815C22semidirect
53. #2815C22semidirect
54. #2813C22semidirect
55. #2812C22semidirect
56. #2797C22semidirect
57. #2784C22semidirect
58. #2778C22semidirect
59. #2760C22semidirect
60. #2749C22semidirect
61. #2737C22semidirect
62. #2714C22semidirect
63. #2709C22semidirect
64. #2709C22semidirect
65. #2703C22semidirect
66. #2699C22semidirect
67. #2693C22semidirect
68. #2691C22semidirect
69. #2688C22semidirect
70. #2688C22semidirect
71. #2688C22semidirect
72. #2678C22semidirect
73. #2675C22semidirect
74. #2673C22semidirect
75. #2673C22semidirect
76. #2673C22semidirect
77. #2669C22semidirect
78. #2669C22semidirect
79. #2668C22semidirect
80. #2643C22semidirect
81. #2620C22semidirect
82. #2619C22semidirect
83. #2615C22semidirect
84. #2615C22semidirect
85. #2544C22semidirect
86. #2544C22semidirect
91. #2541C22semidirect
92. #2541C22semidirect
93. #2541C22semidirect
94. #2541C22semidirect
95. #2541C22semidirect
96. #2541C22semidirect
97. #2537C22semidirect
98. #2537C22semidirect
99. #2535C22semidirect
100. #2535C22semidirect
101. #2514C22semidirect
102. #2513C22semidirect
103. #2512C22semidirect
104. #2511C22semidirect
105. #2497C22semidirect
106. #2496C22semidirect
107. #2495C22semidirect
108. #2494C22semidirect
109. #2487C22semidirect
110. #2487C22semidirect
111. #2486C22semidirect
112. #2486C22semidirect
113. #2485C22semidirect
114. #2485C22semidirect
115. #2484C22semidirect
116. #2483C22semidirect
117. #2483C22semidirect
119. #2436C22semidirect
120. #2433C22semidirect
121. #2431C22semidirect
122. #2431C22semidirect
123. #2428C22semidirect
124. #2428C22semidirect
125. #2428C22semidirect
126. #2428C22semidirect
127. #2428C22semidirect
128. #2428C22semidirect
129. #2427C22semidirect
130. #2427C22semidirect
131. #2422C22semidirect
132. #2422C22semidirect
133. #2422C22semidirect
134. #2422C22semidirect
135. #2420C22semidirect
136. #2420C22semidirect
137. #2420C22semidirect
138. #2420C22semidirect
139. #2416C22semidirect
140. #2416C22semidirect
141. #2414C22semidirect
142. #2414C22semidirect
143. #2412C22semidirect
144. #2411C22semidirect
145. #2410C22semidirect
146. #2410C22semidirect
147. #2410C22semidirect
148. #2410C22semidirect
149. #2409C22semidirect
150. #2409C22semidirect
151. #2408C22semidirect
152. #2408C22semidirect
153. #2407C22semidirect
154. #2407C22semidirect
163. #2395C22semidirect
164. #2395C22semidirect
165. #2388C22semidirect
166. #2388C22semidirect
168. C2×#392C22semidirect
169. #2380C22semidirect
170. #2377C22semidirect
171. #2317C22semidirect
172. #2317C22semidirect
175. #2309C22semidirect
176. C4×#123C22semidirect
177. C4×#123C22semidirect
178. C4×#120C22semidirect
179. C4×#120C22semidirect
181. #2296C22semidirect
182. C2×#390C22semidirect
185. #2280C22semidirect
186. C2×C4×C4⋊C4C22semidirect
1204. C2×C4#560semidirect

Maximal subgroups

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

subgroupindex
#530592
#530552
#529692
#529662
#529602
#529572
#523982
#523972
#463352
#463242
#456832
#456042
#456002
#455992
#454872
#454782
#355402
#355282
#355142
#352522
#352502
#351602
C2×#25412
#348092
#347362