Finite Group Databasebeta

← #7643465

Subgroups — #7643465

Order 512.

5682 conjugacy classes of subgroups.

The subgroup lattice has 1198 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#40200C214yesmaximal, complemented
2#40153C214yesmaximal, complemented
3#39248C214yesmaximal, complemented
4#39009C214yesmaximal, complemented
5#38512C218yesmaximal, complemented
6#38132C218yesmaximal, complemented
7#37411C214yesmaximal, complemented
8#37356C214yesmaximal, complemented
9#36641C211yesmaximal, characteristic, complemented
10C2×#2861C211yesmaximal, characteristic, complemented
11#35676C211yesmaximal, characteristic, complemented
12#35660C211yesmaximal, characteristic, complemented
13#35649C211yesmaximal, characteristic, complemented
14#35639C211yesmaximal, characteristic, complemented
15#35630C211yesmaximal, characteristic, complemented
16#35617C211yesmaximal, characteristic, complemented
17#35541C211yesmaximal, characteristic, complemented
18#35533C211yesmaximal, characteristic, complemented
19#35307C211yesmaximal, characteristic, complemented
20#35256C211yesmaximal, characteristic, complemented
21#35038C214yesmaximal, complemented
22#35030C214yesmaximal, complemented
23#34269C211yesmaximal, characteristic, complemented
24#34259C211yesmaximal, characteristic, complemented
25C4×#532C211yesmaximal, characteristic, complemented
26C22×2−1+4C2211yescharacteristic
27C2×#537C2211yescharacteristic
28C2×#536C2211yescharacteristic
29C2×#535C2211yescharacteristic
30C2×#535C2211yescharacteristic
31C2×#535C2211yescharacteristic
32C2×#532C2211yescharacteristic
33C22×#125C2211yescharacteristic
34C22×#124C2211yescharacteristic
35C2×#520C2211yescharacteristic
36C2×#518C2211yescharacteristic
37C2×C4×#41C2211yescharacteristic
38C2×C4×#41C2211yescharacteristic
39#2863C2212yescomplemented
40#2863C2212yescomplemented
41#2861C2214yes—
42#2861C2214yes—
43#2861C2214yes—
44#2861C2214yes—
45#2860C2212yescomplemented
46#2860C2212yescomplemented
47#2856C2212yes—
48#2855C2214yescomplemented
49#2852C2214yes—
50#2852C2214yes—
51#2850C2212yes—
52#2808C2218yescomplemented
53#2788C2218yescomplemented
54#2779C2218yescomplemented
55#2778C2218yescomplemented
56#2778C2218yescomplemented
57#2775C2218yescomplemented
58#2761C2218yescomplemented
59#2756C2218yescomplemented
60#2756C2218yescomplemented
61#2752C2218yescomplemented
62#2751C2218yescomplemented
63#2749C2218yescomplemented
64#2743C2218yescomplemented
65#2714C2218yescomplemented
66#2703C2218yescomplemented
67#2695C2218yescomplemented
68#2653C2218yescomplemented
69#2650C2218yescomplemented
70#2648C2218yescomplemented
71#2635C2218yescomplemented
72#2625C2214yescomplemented
73#2620C2212yes—
74#2619C2212yes—
75#2595C2218yescomplemented
76#2591C2214yes—
77#2579C2214yes—
78#2574C2218yescomplemented
79#2572C2218yescomplemented
80#2559C2218yescomplemented
81#2548C2212yes—
82#2547C2214yes—
83#2545C2212yes—
84#2544C2214yes—
85#2544C2212yes—
86#2541C2212yes—
87#2514C2214yescomplemented
88#2514C2214yescomplemented
89#2511C2214yescomplemented
90#2511C2214yescomplemented
91#2510C2218yescomplemented
92#2504C2214yes—
93#2493C2218yes—
94#2490C2214yescomplemented
95#2490C2214yescomplemented
96#2489C2214yescomplemented
97#2489C2214yescomplemented
98#2487C2214yes—
99#2467C2218yescomplemented
100#2456C2218yescomplemented
101#2454C2214yescomplemented
102#2453C2214yescomplemented
103#2447C2214yes—
104#2447C2214yescomplemented
105#2446C2214yescomplemented
106#2445C2214yes—
107#2444C2218yescomplemented
108#2442C2214yescomplemented
109#2441C2214yescomplemented
110#2436C2214yes—
111#2436C2214yes—
112#2436C2212yescomplemented
113#2434C2212yescomplemented
114#2432C2212yescomplemented
115#2431C2214yes—
116#2431C2214yes—
117#2431C2212yescomplemented
118#2430C2218yes—
119#2428C2214yes—
120#2427C2214yes—
121#2427C2214yes—
122#2426C2214yes—
123#2424C2218yes—
124#2424C2218yes—
125#2422C2214yes—
126#2420C2214yes—
127#2419C2218yes—
128#2416C2214yes—
129#2414C2214yes—
130#2412C2214yes—
131#2412C2214yes—
132#2412C2218yes—
133#2409C2214yescomplemented
134#2407C2214yescomplemented
135#2404C2214yes—
136#2404C2214yes—
137#2367C2214yes—
138#2366C2214yes—
139#2358C2218yes—
140Q8×C22⋊C4C2214yescomplemented
141#2339C2218yes—
142#2339C2214yescomplemented
143#2335C2218yescomplemented
144#2333C2218yescomplemented
145#2325C2218yescomplemented
146#2324C2214yes—
147#2318C2218yescomplemented
148#2317C2211yescharacteristic
149#2316C2211yescharacteristic
150#2311C2211yescharacteristic
151#2311C2211yescharacteristic
152#2311C2211yescharacteristic
153#2311C2212yescomplemented
154#2310C2211yescharacteristic
155#2310C2211yescharacteristic
156#2310C2212yescomplemented
157C4×C4⋊Q8C2212yescomplemented
158C4×#127C2212yescomplemented
159C4×#126C2214yescomplemented
160C4×#126C2214yescomplemented
161C4×#124C2212yescomplemented
162C4×#124C2212yescomplemented
163C4×#121C2214yes—
164C4×#121C2214yes—
165C4×#121C2214yes—
166#2297C2211yescharacteristic
167#2297C2211yescharacteristic
168#2297C2211yescharacteristic
169#2297C2211yescharacteristic
170#2297C2211yescharacteristic
171#2297C2212yescomplemented
172#2296C2211yescharacteristic
173#2296C2211yescharacteristic
174#2296C2211yescharacteristic
175C2×#391C2211yescharacteristic
176C2×#391C2211yescharacteristic
177C2×#391C2212yescomplemented
178#2293C2214yescomplemented
179C2×#390C2211yescharacteristic
180C2×#390C2211yescharacteristic
181C2×#388C2214yes—
182C2×#388C2214yes—
183#2285C2211yescharacteristic
184#2274C2211yescharacteristic
185C42×D4C2214yescomplemented
186C2×C43C2211yescharacteristic
187C2×2−1+4—28no—
188C2×2−1+4—44no—
189C2×2−1+4—44no—
190C22×#41C2311yescharacteristic
191C22×#41C2311yescharacteristic
192C22×#41C2311yescharacteristic
193C22×#41C2312yes—
194C22×#41C2314yes—
195C22×#41C2312yes—
196C23×Q8C2311yescharacteristic
197C23×Q8C2312yes—
198C23×Q8C2312yes—
199C23×D4C2311yescharacteristic
200#537—44no—
201#536—44no—
202#535—28no—
203#535—44no—
204#535—44no—
205#532—28no—
206C2×C4⋊Q8C2311yescharacteristic
207C2×C4⋊Q8C2312yes—
208C2×#127C2311yescharacteristic
209C2×#127C2312yes—
210C2×#127C2312yes—
211C2×#127C2312yes—
212C2×#126C2314yes—
213C2×#126C2314yes—
214C2×#125—44no—
215C2×#125C2314yes—
216C2×#125C2314yes—
217C2×#124—44no—
218C2×#124C2312yes—
219C2×#124C2311yescharacteristic
220C2×#124C2311yescharacteristic
221C2×#124C2312yes—
222C2×#124C2314yes—
223C2×#124C2314yes—
224C2×#124C2312yes—
225C2×#124C2312yes—
226C2×#123C2318yes—
227C2×#123C2314yes—
228C2×C22⋊Q8C2312yes—
229C2×C22⋊Q8C2314yes—
230C2×C22⋊Q8C2312yes—
231C2×#121C2314yes—
232C2×#121C2314yes—
233C2×#121C2318yes—
234C2×#121C2318yes—
235C2×#121C2314yes—
236C2×#121C2312yes—
237C2×#121C2312yes—
238C2×#121C2312yes—
239C2×#121C2314yes—
240C2×#121C2312yes—
241C2×#120C2314yes—
242C2×#120C2314yes—
243C2×#120C2314yes—
244#520—44no—
245#518—44no—
246C4×#41—44no—
247C4×#41—44no—
248C2×C4×Q8C2312yes—
249C2×C4×Q8C2312yes—
250C2×C4×Q8C2312yes—
251C2×C4×D4C2314yes—
252C2×C4×D4C2314yes—
253C2×C4×D4C2312yes—
254C2×C4×D4C2312yes—
255C2×C4×D4C2314yes—
256C2×C4×D4C2318yes—
257C2×C4×D4C2314yes—
258C2×C4×D4C2314yes—
259C2×C4×D4C2314yes—
260C2×C4×D4C2312yes—
261C2×C4×D4C2314yes—
262C2×C4×D4C2314yes—
263C2×#117C2311yescharacteristic
264C2×#117C2311yescharacteristic
265C2×#117C2311yescharacteristic
266C2×#117C2311yescharacteristic
267C2×#117C2311yescharacteristic
268C2×#117C2312yes—
269C2×#117C2312yes—
270C2×#117C2312yes—
271C22×C4⋊C4C2311yescharacteristic
272C22×C4⋊C4C2311yescharacteristic
273C22×C4⋊C4C2312yes—
274C22×C4⋊C4C2312yes—
275C22×C4⋊C4C2312yes—
276C22×C22⋊C4C2314yes—
277C22×C22⋊C4C2314yes—
278C22×C22⋊C4C2312yes—
279C22×C22⋊C4C2312yes—
280C22×C22⋊C4C2314yes—
281C22×C42C2311yescharacteristic
282C22×C42C2311yescharacteristic
283C22×C42C2311yescharacteristic
284C22×C42C2312yes—
285C22×C42C2312yes—
286C22×C42C2312yes—
287C22×C42C2312yes—
288#401C2318yes—
289#400C2318yes—
290#400C2318yes—
291#400C2318yes—
292#400C2318yes—
293#400C2318yes—
294#400C2318yes—
295#399C2318yes—
296#398C2318yes—
297#398C2318yes—
298#397C2318yes—
299#397C2318yes—
300#397C2318yes—
301#397C2318yes—
302#397C2318yes—
303#397C2318yes—
304#397C2318yes—
305#397C2318yes—
306#396C2318yes—
307#396C2318yes—
308#396C2318yes—
309#395C2318yes—
310#394C2318yes—
311#394C2318yes—
312#394C2318yes—
313#394C2318yes—
314#394C2318yes—
315#394C2318yes—
316#394C2318yes—
317#394C2318yes—
318#394C2318yes—
319#394C2318yes—
320#393C2318yes—
321#393C2318yes—
322#393C2318yes—
323#392C2318yes—
324#392C2318yes—
325#392C2318yes—
326#392C2318yes—
327#392C2318yes—
328#391C2312yes—
329#391C2312yes—
330#391C2312yes—
331#391C2312yes—
332#391C2314yes—
333#391C2314yes—
334#391C2314yes—
335#391C2311yescharacteristic
336#391C2312yes—
337#391C2312yes—
338#391C2318yes—
339#391C2312yes—
340#391C2312yes—
341#391C2318yes—
342#391C2311yescharacteristic
343#391C2314yes—
344#391C2312yes—
345#391C2314yes—
346#391C2312yes—
347#391C2312yes—
348#391C2312yes—
349#391C2312yes—
350#390C2312yes—
351#390C2314yes—
352#390C2314yes—
353#390C2312yes—
354#390C2312yes—
355#390C2312yes—
356#390C2312yes—
357#390C2311yescharacteristic
358#390C2312yes—
359#390C2318yes—
360#390C2318yes—
361#390C2318yes—
362#390C2318yes—
363#390C2312yes—
364#390C2311yescharacteristic
365#390C2312yes—
366#390C2312yes—
367#390C2314yes—
368#390C2314yes—
369#390C2312yes—
370#390C2312yes—
371#389C2314yes—
372#389C2314yes—
373#389C2314yes—
374#389C2314yes—
375#389C2314yes—
376#389C2312yes—
377#389C2318yes—
378#389C2312yes—
379#389C2312yes—
380#389C2312yes—
381#389C2312yes—
382#389C2312yes—
383#388C2314yes—
384#388C2314yes—
385#388C2314yes—
386#388C2314yes—
387#388C2314yes—
388#388C2314yes—
389#388C2318yes—
390#388C2318yes—
391#388C2318yes—
392#388C2318yes—
393#388C2318yes—
394#388C2318yes—
395#388C2318yes—
396#388C2318yes—
397#388C2318yes—
398#388C2318yes—
399#388C2318yes—
400#388C2318yes—
401#388C2318yes—
402#388C2318yes—
403#388C2314yes—
404#388C2314yes—
405#388C2314yes—
406#388C2314yes—
407#387C2314yes—
408#387C2314yes—
409#387C2314yes—
410#387C2314yes—
411#387C2314yes—
412#387C2314yes—
413#387C2318yes—
414#387C2318yes—
415#387C2318yes—
416#387C2318yes—
417#387C2318yes—
418#387C2318yes—
419#386C2314yes—
420#386C2314yes—
421#386C2314yes—
422#386C2318yes—
423#386C2318yes—
424#386C2318yes—
425#386C2318yes—
426#386C2318yes—
427#386C2312yes—
428#386C2318yes—
429#386C2318yes—
430#386C2318yes—
431#386C2318yes—
432#386C2318yes—
433#386C2318yes—
434#386C2318yes—
435#386C2318yes—
436#386C2312yes—
437#386C2312yes—
438#386C2314yes—
439#386C2318yes—
440#386C2312yes—
441#386C2314yes—
442#386C2318yes—
443#386C2312yes—
444#386C2312yes—
445#385C2314yes—
446#385C2318yes—
447#385C2318yes—
448#385C2318yes—
449#385C2312yes—
450#385C2318yes—
451#385C2318yes—
452#385C2318yes—
453#385C2314yes—
454#385C2312yes—
455#385C2314yes—
456#384C2312yes—
457#384C2312yes—
458#383C2314yes—
459#383C2314yes—
460#383C2318yes—
461#382C2312yes—
462#382C2318yes—
463#382C2312yes—
464#381C2314yes—
465#381C2314yes—
466#381C2318yes—
467#381C2318yes—
468#381C2318yes—
469#380C2314yes—
470#380C2314yes—
471#380C2314yes—
472#380C2318yes—
473#380C2314yes—
474#380C2318yes—
475#380C2318yes—
476#380C2318yes—
477#380C2314yes—
478C4×C4⋊C4C2314yes—
479C4×C4⋊C4C2314yes—
480C4×C4⋊C4C2312yes—
481C4×C4⋊C4C2312yes—
482C4×C4⋊C4C2314yes—
483C4×C4⋊C4C2314yes—
484C4×C4⋊C4C2314yes—
485C4×C4⋊C4C2314yes—
486C4×C4⋊C4C2314yes—
487C4×C22⋊C4C2314yes—
488C4×C22⋊C4C2312yes—
489C4×C22⋊C4C2312yes—
490C4×C22⋊C4C2314yes—
491C4×C22⋊C4C2314yes—
492C4×C22⋊C4C2318yes—
493C4×C22⋊C4C2314yes—
494C4×C22⋊C4C2314yes—
495C4×C22⋊C4C2318yes—
496C4×C22⋊C4C2314yes—
497C4×C22⋊C4C2314yes—
498C4×C22⋊C4C2314yes—
499C4×C22⋊C4C2314yes—
500C2×#95C2318yes—
501C2×#95C2314yes—
502C2×#95C2314yes—
503C43C2312yes—
504C43C2312yes—
505C43C2312yes—
506C43C2312yes—
507C25C2412yes—
5082−1+4—464no—
509C2×#41—216no—
510C2×#41—28no—
511C2×#41—24no—
512C2×#41—28no—
513C2×#41—24no—
514C2×#41—24no—
515C2×#41—24no—
516C2×#41—24no—
517C2×#41—24no—
518C2×#41—24no—
519C2×#41—24no—
520C2×#41—48no—
521C2×#41—48no—
522C2×#41—44no—
523C2×#41—44no—
524C2×#41—44no—
525C2×#41—44no—
526C2×#41#4118yes—
527C22×Q8—28no—
528C22×Q8—28no—
529C22×Q8—24no—
530C22×Q8—24no—
531C22×Q8—24no—
532C22×Q8—44no—
533C22×Q8—44no—
534C22×Q8—44no—
535C22×Q8—44no—
536C22×Q8C2411yescharacteristic
537C22×Q8C2412yes—
538C22×Q8C2411yescharacteristic
539C22×Q8C2412yes—
540C22×Q8C2411yescharacteristic
541C22×Q8C2414yes—
542C22×D4—24no—
543C22×D4—24no—
544C22×D4—24no—
545C22×D4C2412yes—
546C22×D4C2412yes—
547C22×D4C2412yes—
548C22×D4C2411yescharacteristic
549C22×D4C2412yes—
550C22×D4C2411yescharacteristic
551C22×D4C2414yes—
552C22×D4C2412yes—
553C22×D4C2411yescharacteristic
554C22×D4C2418yes—
555C22×D4C2414yes—
556C22×D4C2414yes—
557C22×D4C2414yes—
558C22×D4C2418yes—
559C22×D4C2414yes—
560C23×C4C2412yes—
561C23×C4C2412yes—
562C23×C4C2412yes—
563C23×C4C2412yes—
564C23×C4C2412yes—
565C23×C4C2412yes—
566C23×C4C2412yes—
567C23×C4C2412yes—
568C23×C4C2411yescharacteristic
569C23×C4C2411yescharacteristic
570C23×C4C2414yes—
571C23×C4C2414yes—
572C23×C4C2414yes—
573C23×C4C2414yes—
574C23×C4C2418yes—
575C23×C4C2414yes—
576C23×C4C2411yescharacteristic
577C4⋊Q8—24no—
578C4⋊Q8—44no—
579#127—24no—
580#127—28no—
581#127—44no—
582#127—44no—
583#126—48no—
584#126—48no—
585#125—48no—
586#125—48no—
587#124—24no—
588#124—28no—
589#124—24no—
590#124—48no—
591#124—48no—
592#124—44no—
593#124—44no—
594#124—44no—
595#123—416no—
596#123—48no—
597C22⋊Q8—48no—
598C22⋊Q8—44no—
599C22⋊Q8—44no—
600#121—216no—
601#121—216no—
602#121—416no—
603#121—416no—
604#121—44no—
605#121—44no—
606#121—48no—
607#121—44no—
608#121—44no—
609#121—48no—
610#120—216no—
611#120—48no—
612#120—48no—
613C4×Q8—44no—
614C4×Q8—44no—
615C4×Q8—44no—
616C4×D4—216no—
617C4×D4—48no—
618C4×D4—44no—
619C4×D4—44no—
620C4×D4—48no—
621C4×D4—48no—
622C4×D4—44no—
623C4×D4—48no—
624C4×D4—416no—
625C4×D4—48no—
626C4×D4—48no—
627C4×D4—48no—
628#117—24no—
629#117—24no—
630#117—24no—
631#117—24no—
632#117—24no—
633#117—44no—
634#117—44no—
635#117—44no—
636C2×C4⋊C4—24no—
637C2×C4⋊C4—24no—
638C2×C4⋊C4—44no—
639C2×C4⋊C4—44no—
640C2×C4⋊C4—44no—
641C2×C4⋊C4C2411yescharacteristic
642C2×C4⋊C4C2412yes—
643C2×C4⋊C4C2412yes—
644C2×C4⋊C4C2412yes—
645C2×C4⋊C4C2412yes—
646C2×C4⋊C4C2411yescharacteristic
647C2×C4⋊C4C2412yes—
648C2×C4⋊C4C2412yes—
649C2×C4⋊C4C2412yes—
650C2×C4⋊C4C2412yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2418yes—
657C2×C4⋊C4C2418yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2418yes—
663C2×C4⋊C4C2418yes—
664C2×C4⋊C4C2418yes—
665C2×C4⋊C4C2414yes—
666C2×C4⋊C4C2414yes—
667C2×C4⋊C4C2414yes—
668C2×C4⋊C4C2414yes—
669C2×C22⋊C4—48no—
670C2×C22⋊C4—48no—
671C2×C22⋊C4—48no—
672C2×C22⋊C4—44no—
673C2×C22⋊C4—44no—
674C2×C22⋊C4C2412yes—
675C2×C22⋊C4C2412yes—
676C2×C22⋊C4C2418yes—
677C2×C22⋊C4C2418yes—
678C2×C22⋊C4C2412yes—
679C2×C22⋊C4C2412yes—
680C2×C22⋊C4C2412yes—
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2414yes—
683C2×C22⋊C4C2418yes—
684C2×C22⋊C4C2414yes—
685C2×C22⋊C4C2414yes—
686C2×C22⋊C4C2418yes—
687C2×C22⋊C4C2418yes—
688C2×C22⋊C4C2418yes—
689C2×C22⋊C4C2418yes—
690C2×C22⋊C4C2418yes—
691C2×C22⋊C4C2414yes—
692C2×C22⋊C4C2414yes—
693C2×C22⋊C4C2414yes—
694C2×C22⋊C4C2414yes—
695C2×C22⋊C4C2414yes—
696C2×C22⋊C4C2414yes—
697C2×C22⋊C4C2414yes—
698C2×C22⋊C4C2418yes—
699C2×C22⋊C4C2414yes—
700C2×C22⋊C4C2414yes—
701C2×C22⋊C4C2418yes—
702C2×C22⋊C4C2414yes—
703C2×C22⋊C4C2414yes—
704C2×C22⋊C4C2418yes—
705C2×C22⋊C4C2418yes—
706C2×C22⋊C4C2418yes—
707C2×C22⋊C4C2414yes—
708C2×C22⋊C4C2414yes—
709C2×C22⋊C4C2414yes—
710C2×C22⋊C4C2414yes—
711C2×C42—24no—
712C2×C42—24no—
713C2×C42—24no—
714C2×C42—44no—
715C2×C42—44no—
716C2×C42—44no—
717C2×C42—44no—
718C2×C42C2411yescharacteristic
719C2×C42C2412yes—
720C2×C42C2412yes—
721C2×C42C2412yes—
722C2×C42C2412yes—
723C2×C42C2412yes—
724C2×C42C2412yes—
725C2×C42C2412yes—
726C2×C42C2412yes—
727C2×C42C2412yes—
728C2×C42C2412yes—
729C2×C42C2412yes—
730C2×C42C2411yescharacteristic
731C2×C42C2412yes—
732C2×C42C2412yes—
733C2×C42C2411yescharacteristic
734C2×C42C2411yescharacteristic
735C2×C42C2414yes—
736C2×C42C2414yes—
737C2×C42C2414yes—
738C2×C42C2418yes—
739C2×C42C2412yes—
740C2×C42C2412yes—
741C2×C42C2412yes—
742C2×C42C2412yes—
743#95C2418yes—
744#95C2414yes—
745#95C2418yes—
746#95C2418yes—
747#95C2418yes—
748#95C2418yes—
749#95C2418yes—
750#95C2414yes—
751#95C2414yes—
752#95C2414yes—
753#95C2414yes—
754#95C2414yes—
755#95C2414yes—
756#95C2414yes—
757#95C2418yes—
758#95C2418yes—
759#95C2418yes—
760#95C2414yes—
761#95C2414yes—
762#95C2414yes—
763#95C2414yes—
764#95C2414yes—
765#95C2414yes—
766#95C2414yes—
767#95C2414yes—
768#95C2414yes—
769#95C2414yes—
770#95C2418yes—
771#95C2418yes—
772#95C2418yes—
773#95C2418yes—
774#95C2418yes—
775C24—24no—
776C24—24no—
777C24—24no—
778C24—44no—
779C24—44no—
780C24C2514yes—
781C24C2512yes—
782C24C2512yes—
783C24C2512yes—
784C24C2511yescharacteristic
785#41—232no—
786#41—432no—
787#41—464no—
788#41—432no—
789#41—416no—
790#41—416no—
791C2×Q8—22no—
792C2×Q8—28no—
793C2×Q8—24no—
794C2×Q8—24no—
795C2×Q8—22no—
796C2×Q8—22no—
797C2×Q8—22no—
798C2×Q8—22no—
799C2×Q8—22no—
800C2×Q8—24no—
801C2×Q8—22no—
802C2×Q8—24no—
803C2×Q8—24no—
804C2×Q8—22no—
805C2×Q8—24no—
806C2×Q8—44no—
807C2×Q8—44no—
808C2×Q8—432no—
809C2×Q8—432no—
810C2×Q8—416no—
811C2×Q8C2×#4114yes—
812C2×D4—24no—
813C2×D4—24no—
814C2×D4—28no—
815C2×D4—24no—
816C2×D4—28no—
817C2×D4—24no—
818C2×D4—24no—
819C2×D4—24no—
820C2×D4—24no—
821C2×D4—24no—
822C2×D4—216no—
823C2×D4—24no—
824C2×D4—24no—
825C2×D4—22no—
826C2×D4—22no—
827C2×D4—22no—
828C2×D4—22no—
829C2×D4—24no—
830C2×D4—22no—
831C2×D4—24no—
832C2×D4—24no—
833C2×D4—22no—
834C2×D4—22no—
835C2×D4—24no—
836C2×D4—22no—
837C2×D4—28no—
838C2×D4—44no—
839C2×D4—44no—
840C2×D4—44no—
841C2×D4—48no—
842C2×D4—48no—
843C2×D4—44no—
844C2×D4—48no—
845C2×D4—44no—
846C2×D4—44no—
847C2×D4—48no—
848C2×D4—48no—
849C2×D4—48no—
850C2×D4—48no—
851C2×D4—48no—
852C2×D4—416no—
853C2×D4C2×#4118yes—
854C2×D4C2×#4114yes—
855C22×C4—24no—
856C22×C4—24no—
857C22×C4—24no—
858C22×C4—28no—
859C22×C4—24no—
860C22×C4—22no—
861C22×C4—22no—
862C22×C4—24no—
863C22×C4—24no—
864C22×C4—24no—
865C22×C4—24no—
866C22×C4—24no—
867C22×C4—24no—
868C22×C4—28no—
869C22×C4—24no—
870C22×C4—24no—
871C22×C4—24no—
872C22×C4—24no—
873C22×C4—24no—
874C22×C4—24no—
875C22×C4—24no—
876C22×C4—28no—
877C22×C4—28no—
878C22×C4—42no—
879C22×C4—42no—
880C22×C4—42no—
881C22×C4—42no—
882C22×C4—44no—
883C22×C4—44no—
884C22×C4—44no—
885C22×C4—44no—
886C22×C4—44no—
887C22×C4—44no—
888C22×C4—44no—
889C22×C4—44no—
890C22×C4—44no—
891C22×C4—44no—
892C22×C4—48no—
893C22×C4—44no—
894C22×C4—48no—
895C22×C4—48no—
896C22×C4—48no—
897C22×C4C2×#4118yes—
898C22×C4C2×#4114yes—
899C22×C4H(5,𝔽2)14yes—
900C22×C4H(5,𝔽2)14yes—
901C22×C4C2512yes—
902C22×C4C2514yes—
903C22×C4C2514yes—
904C22×C4C2512yes—
905C22×C4C2512yes—
906C22×C4C2514yes—
907C22×C4C2514yes—
908C22×C4C2512yes—
909C22×C4C2514yes—
910C22×C4C2514yes—
911C22×C4C2514yes—
912C22×C4C2512yes—
913C22×C4C2512yes—
914C22×C4C2512yes—
915C22×C4C2512yes—
916C22×C4C2512yes—
917C22×C4C2512yes—
918C22×C4C2512yes—
919C22×C4C2511yescharacteristic
920C22×C4C2511yescharacteristic
921C4⋊C4—24no—
922C4⋊C4—28no—
923C4⋊C4—24no—
924C4⋊C4—24no—
925C4⋊C4—24no—
926C4⋊C4—24no—
927C4⋊C4—22no—
928C4⋊C4—22no—
929C4⋊C4—24no—
930C4⋊C4—24no—
931C4⋊C4—24no—
932C4⋊C4—28no—
933C4⋊C4—28no—
934C4⋊C4—28no—
935C4⋊C4—44no—
936C4⋊C4—48no—
937C4⋊C4—48no—
938C4⋊C4—44no—
939C4⋊C4—44no—
940C4⋊C4—44no—
941C4⋊C4—48no—
942C4⋊C4—44no—
943C4⋊C4—48no—
944C4⋊C4—48no—
945C4⋊C4—44no—
946C4⋊C4—44no—
947C4⋊C4—44no—
948C4⋊C4—44no—
949C22⋊C4—24no—
950C22⋊C4—28no—
951C22⋊C4—24no—
952C22⋊C4—24no—
953C22⋊C4—24no—
954C22⋊C4—24no—
955C22⋊C4—28no—
956C22⋊C4—216no—
957C22⋊C4—216no—
958C22⋊C4—216no—
959C22⋊C4—28no—
960C22⋊C4—28no—
961C22⋊C4—48no—
962C22⋊C4—48no—
963C22⋊C4—48no—
964C22⋊C4—48no—
965C22⋊C4—48no—
966C22⋊C4—44no—
967C22⋊C4—44no—
968C22⋊C4—44no—
969C22⋊C4—44no—
970C22⋊C4—44no—
971C22⋊C4—44no—
972C22⋊C4—44no—
973C22⋊C4—48no—
974C22⋊C4—44no—
975C22⋊C4—48no—
976C22⋊C4—44no—
977C22⋊C4—48no—
978C22⋊C4—44no—
979C22⋊C4—44no—
980C22⋊C4—48no—
981C22⋊C4—48no—
982C22⋊C4—44no—
983C22⋊C4—44no—
984C22⋊C4—44no—
985C22⋊C4—44no—
986C42—24no—
987C42—22no—
988C42—22no—
989C42—24no—
990C42—22no—
991C42—22no—
992C42—24no—
993C42—24no—
994C42—24no—
995C42—24no—
996C42—24no—
997C42—24no—
998C42—24no—
999C42—24no—
1000C42—24no—
1001C42—24no—
1002C42—24no—
1003C42—42no—
1004C42—42no—
1005C42—42no—
1006C42—42no—
1007C42—44no—
1008C42—44no—
1009C42—44no—
1010C42—48no—
1011C23—22no—
1012C23—22no—
1013C23—22no—
1014C23—22no—
1015C23—24no—
1016C23—24no—
1017C23—22no—
1018C23—24no—
1019C23—22no—
1020C23—22no—
1021C23—24no—
1022C23—24no—
1023C23—22no—
1024C23—22no—
1025C23—22no—
1026C23—24no—
1027C23—24no—
1028C23—28no—
1029C23—28no—
1030C23—24no—
1031C23—24no—
1032C23—48no—
1033C23—88no—
1034C23—88no—
1035C23—84no—
1036C23—84no—
1037C23C22×#4114yes—
1038C23C22×#4112yes—
1039C23C2×H(5,𝔽2)12yes—
1040C23C2×H(5,𝔽2)12yes—
1041C23C2611yescharacteristic
1042Q8—28no—
1043Q8—416no—
1044Q8—48no—
1045Q8—44no—
1046Q8—48no—
1047Q8—44no—
1048D4—216no—
1049D4—28no—
1050D4—416no—
1051D4—416no—
1052D4—48no—
1053D4—48no—
1054D4—48no—
1055D4—48no—
1056D4—44no—
1057D4—44no—
1058D4—816no—
1059D4—168no—
1060D4—164no—
1061D4—164no—
1062D4—164no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—216no—
1070C2×C4—22no—
1071C2×C4—24no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—24no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—24no—
1080C2×C4—24no—
1081C2×C4—24no—
1082C2×C4—22no—
1083C2×C4—22no—
1084C2×C4—24no—
1085C2×C4—22no—
1086C2×C4—22no—
1087C2×C4—24no—
1088C2×C4—24no—
1089C2×C4—22no—
1090C2×C4—24no—
1091C2×C4—22no—
1092C2×C4—22no—
1093C2×C4—22no—
1094C2×C4—22no—
1095C2×C4—22no—
1096C2×C4—22no—
1097C2×C4—22no—
1098C2×C4—22no—
1099C2×C4—24no—
1100C2×C4—24no—
1101C2×C4—28no—
1102C2×C4—28no—
1103C2×C4—24no—
1104C2×C4—24no—
1105C2×C4—24no—
1106C2×C4—24no—
1107C2×C4—24no—
1108C2×C4—24no—
1109C2×C4—24no—
1110C2×C4—24no—
1111C2×C4—48no—
1112C2×C4—48no—
1113C2×C4—416no—
1114C2×C4—44no—
1115C2×C4—44no—
1116C2×C4—416no—
1117C2×C4—48no—
1118C2×C4—48no—
1119C2×C4—48no—
1120C2×C4—88no—
1121C2×C4—88no—
1122C2×C4—84no—
1123C2×C4—84no—
1124C2×C4—168no—
1125C2×C4—164no—
1126C2×C4#538116yes—
1127C2×C4C22×#4114yes—
1128C2×C4C22×#4112yes—
1129C2×C4C22×#4112yes—
1130C2×C4C2×H(5,𝔽2)12yes—
1131C2×C4C2×H(5,𝔽2)12yes—
1132C2×C4C2×H(5,𝔽2)12yes—
1133C2×C4C2×H(5,𝔽2)12yes—
1134C2×C4#58514yes—
1135C2×C4#58514yes—
1136C22—24no—
1137C22—24no—
1138C22—22no—
1139C22—22no—
1140C22—28no—
1141C22—24no—
1142C22—44no—
1143C22—42no—
1144C22—42no—
1145C22—44no—
1146C22—48no—
1147C22—44no—
1148C22—44no—
1149C22—48no—
1150C22—44no—
1151C22—42no—
1152C22—42no—
1153C22—42no—
1154C22—44no—
1155C22—44no—
1156C22—42no—
1157C22—42no—
1158C22—42no—
1159C22—44no—
1160C22—168no—
1161C22C2×#53814yes—
1162C22C23×#4111yescharacteristic
1163C22C22×H(5,𝔽2)11yescharacteristic
1164C22C22×H(5,𝔽2)11yescharacteristic
1165C22C2×#58512yes—
1166C22C2×#58512yes—
1167C4—24no—
1168C4—24no—
1169C4—24no—
1170C4—42no—
1171C4—44no—
1172C4—42no—
1173C4—44no—
1174C4—44no—
1175C4—44no—
1176C4—42no—
1177C4—42no—
1178C4—44no—
1179C4—44no—
1180C4—42no—
1181C4—42no—
1182C4—42no—
1183C4—44no—
1184C4—42no—
1185C4C2×#53814yes—
1186C4C2×#53814yes—
1187C2—24no—
1188C2—44no—
1189C2—82no—
1190C2—82no—
1191C2—84no—
1192C2C22×#53811yescharacteristic
1193C2#6281012yes—
1194C2#6283012yes—
1195C2#6283611yescharacteristic
1196C2#6283611yescharacteristic
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. #40200C2semidirect
2. #40153C2semidirect
3. #39248C2semidirect
4. #39009C2semidirect
5. #38512C2semidirect
6. #38132C2semidirect
7. #37411C2semidirect
8. #37356C2semidirect
9. #36641C2semidirect
10. C2×#2861C2semidirect
11. #35676C2semidirect
12. #35660C2semidirect
13. #35649C2semidirect
14. #35639C2semidirect
15. #35630C2semidirect
16. #35617C2semidirect
17. #35541C2semidirect
18. #35533C2semidirect
19. #35307C2semidirect
20. #35256C2semidirect
21. #35038C2semidirect
22. #35030C2semidirect
23. #34269C2semidirect
24. #34259C2semidirect
25. C4×#532C2semidirect
39. #2863C22semidirect
40. #2863C22semidirect
45. #2860C22semidirect
46. #2860C22semidirect
48. #2855C22semidirect
52. #2808C22semidirect
53. #2788C22semidirect
54. #2779C22semidirect
55. #2778C22semidirect
56. #2778C22semidirect
57. #2775C22semidirect
58. #2761C22semidirect
59. #2756C22semidirect
60. #2756C22semidirect
61. #2752C22semidirect
62. #2751C22semidirect
63. #2749C22semidirect
64. #2743C22semidirect
65. #2714C22semidirect
66. #2703C22semidirect
67. #2695C22semidirect
68. #2653C22semidirect
69. #2650C22semidirect
70. #2648C22semidirect
71. #2635C22semidirect
72. #2625C22semidirect
75. #2595C22semidirect
78. #2574C22semidirect
79. #2572C22semidirect
80. #2559C22semidirect
87. #2514C22semidirect
88. #2514C22semidirect
89. #2511C22semidirect
90. #2511C22semidirect
91. #2510C22semidirect
94. #2490C22semidirect
95. #2490C22semidirect
96. #2489C22semidirect
97. #2489C22semidirect
99. #2467C22semidirect
100. #2456C22semidirect
101. #2454C22semidirect
102. #2453C22semidirect
104. #2447C22semidirect
105. #2446C22semidirect
107. #2444C22semidirect
108. #2442C22semidirect
109. #2441C22semidirect
112. #2436C22semidirect
113. #2434C22semidirect
114. #2432C22semidirect
117. #2431C22semidirect
133. #2409C22semidirect
134. #2407C22semidirect
140. Q8×C22⋊C4C22semidirect
142. #2339C22semidirect
143. #2335C22semidirect
144. #2333C22semidirect
145. #2325C22semidirect
147. #2318C22semidirect
153. #2311C22semidirect
156. #2310C22semidirect
157. C4×C4⋊Q8C22semidirect
158. C4×#127C22semidirect
159. C4×#126C22semidirect
160. C4×#126C22semidirect
161. C4×#124C22semidirect
162. C4×#124C22semidirect
171. #2297C22semidirect
177. C2×#391C22semidirect
178. #2293C22semidirect
185. C42×D4C22semidirect

Maximal subgroups

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

subgroupindex
#402002
#401532
#392482
#390092
#385122
#381322
#374112
#373562
#366412
C2×#28612
#356762
#356602
#356492
#356392
#356302
#356172
#355412
#355332
#353072
#352562
#350382
#350302
#342692
#342592
C4×#5322