Finite Group Databasebeta

← #7646818

Subgroups — #7646818

Order 512.

5674 conjugacy classes of subgroups.

The subgroup lattice has 1124 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42641C214yesmaximal, complemented
2#42629C214yesmaximal, complemented
3#42578C214yesmaximal, complemented
4#42565C214yesmaximal, complemented
5#40170C214yesmaximal, complemented
6#40054C214yesmaximal, complemented
7#39402C214yesmaximal, complemented
8#39023C214yesmaximal, complemented
9#37459C214yesmaximal, complemented
10#36759C214yesmaximal, complemented
11#36727C214yesmaximal, complemented
12#35533C212yesmaximal, complemented
13#35530C212yesmaximal, complemented
14#35261C214yesmaximal, complemented
15#35256C212yesmaximal, complemented
16#35168C211yesmaximal, characteristic, complemented
17#35168C211yesmaximal, characteristic, complemented
18#35166C211yesmaximal, characteristic, complemented
19#35159C211yesmaximal, characteristic, complemented
20#34744C212yesmaximal, complemented
21#34274C211yesmaximal, characteristic, complemented
22C2×#2354C211yesmaximal, characteristic, complemented
23C4×#537C211yesmaximal, characteristic, complemented
24C2×#540C2214yescomplemented
25C2×#537C2211yescharacteristic
26C2×#537C2211yescharacteristic
27C2×#537C2212yes—
28C2×#535C2212yes—
29C2×#535C2212yes—
30C2×#532C2212yes—
31C2×#520C2212yes—
32C2×C4×#41C2212yes—
33C22×C4×D4C2211yescharacteristic
34C22×#117C2212yes—
35#2856C2214yes—
36#2856C2214yes—
37#2851C2214yes—
38#2850C2214yes—
39#2847C2214yes—
40#2847C2214yes—
41#2837C2218yescomplemented
42#2828C2218yescomplemented
43#2803C2218yescomplemented
44#2797C2218yescomplemented
45#2793C2218yescomplemented
46#2753C2218yescomplemented
47#2752C2218yescomplemented
48#2748C2218yescomplemented
49#2748C2218yescomplemented
50#2741C2218yescomplemented
51#2741C2218yescomplemented
52#2711C2218yescomplemented
53#2703C2218yescomplemented
54#2703C2218yescomplemented
55#2701C2218yescomplemented
56#2673C2218yescomplemented
57#2671C2218yescomplemented
58#2671C2218yescomplemented
59#2661C2218yescomplemented
60#2656C2214yes—
61#2651C2218yescomplemented
62#2649C2218yescomplemented
63#2646C2214yes—
64#2635C2218yescomplemented
65#2629C2214yescomplemented
66#2624C2214yescomplemented
67#2624C2214yescomplemented
68#2620C2214yes—
69#2619C2214yes—
70#2619C2214yescomplemented
71#2617C2214yes—
72#2617C2214yes—
73#2548C2214yes—
74#2545C2214yes—
75#2544C2214yes—
76#2542C2214yescomplemented
77#2541C2214yes—
78#2541C2214yescomplemented
79#2540C2214yescomplemented
80#2540C2214yescomplemented
81#2516C2218yescomplemented
82#2509C2214yescomplemented
83#2508C2214yescomplemented
84#2507C2214yescomplemented
85#2506C2214yescomplemented
86#2502C2214yescomplemented
87#2501C2214yescomplemented
88#2500C2214yescomplemented
89#2499C2214yescomplemented
90#2476C2218yescomplemented
91#2476C2218yescomplemented
92#2471C2218yescomplemented
93#2471C2218yescomplemented
94#2464C2218yescomplemented
95#2448C2212yescomplemented
96#2448C2212yescomplemented
97#2447C2212yescomplemented
98#2447C2212yescomplemented
99#2446C2212yescomplemented
100#2446C2212yescomplemented
101#2445C2212yescomplemented
102#2445C2212yescomplemented
103#2444C2214yes—
104#2444C2214yes—
105#2443C2218yes—
106#2443C2214yes—
107#2443C2218yes—
108#2443C2214yes—
109#2428C2214yes—
110#2428C2214yes—
111#2428C2214yes—
112#2428C2214yes—
113#2428C2214yes—
114#2428C2214yes—
115#2427C2214yes—
116#2427C2214yes—
117#2427C2214yes—
118#2427C2214yes—
119#2426C2214yes—
120#2426C2214yes—
121#2424C2218yes—
122#2424C2218yes—
123#2424C2218yes—
124#2424C2218yes—
125#2423C2214yescomplemented
126#2423C2214yescomplemented
127#2422C2214yescomplemented
128#2422C2214yescomplemented
129#2416C2214yes—
130#2416C2214yes—
131#2414C2214yes—
132#2414C2214yes—
133#2395C2214yescomplemented
134#2395C2214yescomplemented
135#2363C2214yescomplemented
136#2362C2214yescomplemented
137#2361C2214yescomplemented
138#2360C2214yescomplemented
139#2354C2214yes—
140#2354C2214yes—
141#2354C2214yes—
142#2354C2214yes—
143#2325C2214yes—
144#2325C2214yes—
145#2324C2214yescomplemented
146#2324C2214yescomplemented
147#2324C2214yescomplemented
148#2323C2214yescomplemented
149#2317C2212yes—
150#2316C2211yescharacteristic
151#2316C2211yescharacteristic
152#2314C2214yescomplemented
153#2311C2212yes—
154C4×C22⋊Q8C2214yescomplemented
155C4×#123C2214yescomplemented
156C4×#123C2214yescomplemented
157C4×#121C2214yes—
158C4×#121C2214yes—
159C4×#121C2214yescomplemented
160#2297C2212yes—
161#2297C2212yes—
162#2297C2212yes—
163#2296C2212yes—
164C2×#390C2211yescharacteristic
165C2×#390C2211yescharacteristic
166C2×#388C2212yes—
167C2×#388C2212yes—
168C2×#384C2211yescharacteristic
169C2×#380C2212yes—
170C2×C4×C4⋊C4C2211yescharacteristic
171C2×C4×C4⋊C4C2211yescharacteristic
172C2×C4×C4⋊C4C2211yescharacteristic
173C22×#41C2312yes—
174C22×#41C2312yes—
175C23×D4C2311yescharacteristic
176C24×C4C2312yes—
177#540—416no—
178#537—28no—
179#537—28no—
180#537—48no—
181#535—48no—
182#535—48no—
183#532—48no—
184C2×C4⋊Q8C2312yes—
185C2×#127C2314yes—
186C2×#127C2314yes—
187C2×#127C2312yes—
188C2×#127C2314yes—
189C2×#125C2314yes—
190C2×#124C2314yes—
191C2×#124C2312yes—
192C2×#124C2312yes—
193C2×#124C2314yes—
194C2×#123C2314yes—
195C2×#123C2314yes—
196C2×#123C2318yes—
197C2×#123C2318yes—
198C2×C22⋊Q8C2314yes—
199C2×C22⋊Q8C2314yes—
200C2×C22⋊Q8C2314yes—
201C2×C22⋊Q8C2314yes—
202C2×#121C2314yes—
203C2×#121C2314yes—
204C2×#121C2314yes—
205C2×#121C2314yes—
206C2×#121C2314yes—
207C2×#121C2314yes—
208C2×#121C2314yes—
209C2×#121C2314yes—
210C2×#121C2314yes—
211C2×#121C2314yes—
212C2×#121C2314yes—
213C2×#121C2314yes—
214C2×#121C2318yes—
215C2×#121C2318yes—
216C2×#121C2314yes—
217C2×#121C2314yes—
218C2×#121C2314yes—
219C2×#121C2318yes—
220C2×#121C2314yes—
221C2×#121C2318yes—
222C2×#121C2318yes—
223C2×#120C2318yes—
224C2×#120C2318yes—
225#520—48no—
226C4×#41—48no—
227C2×C4×Q8C2312yes—
228C2×C4×Q8C2314yes—
229C2×C4×Q8C2312yes—
230C2×C4×D4—28no—
231C2×C4×D4C2314yes—
232C2×C4×D4C2314yes—
233C2×C4×D4C2312yes—
234C2×C4×D4C2314yes—
235C2×C4×D4C2314yes—
236C2×C4×D4C2314yes—
237C2×C4×D4C2318yes—
238C2×C4×D4C2314yes—
239C2×C4×D4C2314yes—
240C2×C4×D4C2314yes—
241C2×C4×D4C2314yes—
242C2×C4×D4C2312yes—
243C2×#117—48no—
244C2×#117C2312yes—
245C2×#117C2314yes—
246C2×#117C2312yes—
247C2×#117C2314yes—
248C2×#117C2314yes—
249C2×#117C2314yes—
250C2×#117C2314yes—
251C2×#117C2314yes—
252C22×C4⋊C4C2311yescharacteristic
253C22×C4⋊C4C2311yescharacteristic
254C22×C4⋊C4C2311yescharacteristic
255C22×C4⋊C4C2314yes—
256C22×C4⋊C4C2312yes—
257C22×C4⋊C4C2311yescharacteristic
258C22×C4⋊C4C2312yes—
259C22×C4⋊C4C2311yescharacteristic
260C22×C22⋊C4C2312yes—
261C22×C22⋊C4C2312yes—
262C22×C22⋊C4C2312yes—
263C22×C22⋊C4C2312yes—
264C22×C22⋊C4C2312yes—
265C22×C42C2311yescharacteristic
266C22×C42C2311yescharacteristic
267C22×C42C2311yescharacteristic
268C22×C42C2314yes—
269C22×C42C2312yes—
270C22×C42C2312yes—
271#400C2318yes—
272#400C2314yes—
273#400C2318yes—
274#400C2314yes—
275#399C2318yes—
276#399C2318yes—
277#399C2314yes—
278#399C2318yes—
279#399C2318yes—
280#399C2314yes—
281#398C2318yes—
282#398C2318yes—
283#398C2314yes—
284#398C2318yes—
285#398C2318yes—
286#398C2314yes—
287#397C2314yes—
288#397C2318yes—
289#397C2314yes—
290#397C2318yes—
291#397C2318yes—
292#397C2314yes—
293#397C2318yes—
294#397C2314yes—
295#397C2314yes—
296#397C2314yes—
297#396C2318yes—
298#396C2318yes—
299#396C2318yes—
300#396C2318yes—
301#394C2314yes—
302#394C2318yes—
303#394C2318yes—
304#394C2318yes—
305#394C2318yes—
306#394C2318yes—
307#394C2318yes—
308#394C2318yes—
309#394C2318yes—
310#394C2318yes—
311#394C2318yes—
312#394C2314yes—
313#394C2318yes—
314#394C2318yes—
315#394C2318yes—
316#394C2318yes—
317#394C2314yes—
318#394C2314yes—
319#392C2318yes—
320#392C2318yes—
321#392C2318yes—
322#392C2318yes—
323#392C2318yes—
324#392C2318yes—
325#392C2318yes—
326#392C2318yes—
327#391C2314yes—
328#391C2312yes—
329#391C2312yes—
330#391C2312yes—
331#391C2312yes—
332#391C2312yes—
333#391C2312yes—
334#390C2314yes—
335#390C2314yes—
336#390C2314yes—
337#390C2314yes—
338#390C2314yes—
339#390C2318yes—
340#390C2318yes—
341#390C2314yes—
342#390C2312yes—
343#390C2318yes—
344#390C2318yes—
345#390C2318yes—
346#390C2314yes—
347#390C2314yes—
348#390C2314yes—
349#390C2312yes—
350#390C2318yes—
351#390C2312yes—
352#390C2312yes—
353#390C2312yes—
354#390C2312yes—
355#389C2314yes—
356#389C2314yes—
357#389C2314yes—
358#389C2314yes—
359#389C2314yes—
360#389C2314yes—
361#389C2314yes—
362#389C2314yes—
363#389C2314yes—
364#389C2314yes—
365#389C2312yes—
366#389C2312yes—
367#389C2312yes—
368#389C2312yes—
369#388C2318yes—
370#388C2318yes—
371#388C2318yes—
372#388C2318yes—
373#388C2318yes—
374#388C2314yes—
375#388C2318yes—
376#388C2318yes—
377#388C2318yes—
378#388C2318yes—
379#388C2318yes—
380#388C2318yes—
381#388C2318yes—
382#388C2318yes—
383#388C2314yes—
384#388C2318yes—
385#388C2314yes—
386#388C2314yes—
387#387C2314yes—
388#387C2318yes—
389#387C2318yes—
390#387C2318yes—
391#387C2318yes—
392#387C2318yes—
393#387C2318yes—
394#387C2314yes—
395#387C2314yes—
396#387C2314yes—
397#386C2318yes—
398#386C2318yes—
399#386C2318yes—
400#386C2318yes—
401#386C2314yes—
402#386C2318yes—
403#386C2314yes—
404#386C2314yes—
405#386C2318yes—
406#386C2318yes—
407#386C2318yes—
408#386C2318yes—
409#386C2318yes—
410#386C2314yes—
411#386C2314yes—
412#386C2314yes—
413#386C2318yes—
414#386C2314yes—
415#386C2314yes—
416#385C2318yes—
417#385C2314yes—
418#385C2318yes—
419#385C2318yes—
420#385C2318yes—
421#385C2314yes—
422#385C2314yes—
423#385C2318yes—
424#385C2314yes—
425#384C2314yes—
426#384C2314yes—
427#384C2314yes—
428#384C2314yes—
429#382C2314yes—
430#382C2314yes—
431#381C2314yes—
432#381C2314yes—
433#380C2314yes—
434#380C2314yes—
435#380C2314yes—
436#380C2314yes—
437#380C2314yes—
438#380C2314yes—
439#380C2314yes—
440#380C2314yes—
441#380C2318yes—
442#380C2318yes—
443C4×C4⋊C4C2314yes—
444C4×C4⋊C4C2314yes—
445C4×C4⋊C4C2314yes—
446C4×C4⋊C4C2314yes—
447C4×C4⋊C4C2312yes—
448C4×C4⋊C4C2312yes—
449C4×C4⋊C4C2312yes—
450C4×C4⋊C4C2312yes—
451C4×C4⋊C4C2314yes—
452C4×C4⋊C4C2314yes—
453C4×C4⋊C4C2314yes—
454C4×C4⋊C4C2314yes—
455C4×C22⋊C4C2318yes—
456C4×C22⋊C4C2314yes—
457C4×C22⋊C4C2314yes—
458C4×C22⋊C4C2314yes—
459C4×C22⋊C4C2314yes—
460C4×C22⋊C4C2314yes—
461C4×C22⋊C4C2314yes—
462C4×C22⋊C4C2318yes—
463C2×#95C2312yes—
464C2×#95C2312yes—
465C2×#95C2311yescharacteristic
466C2×#95C2311yescharacteristic
467C25C2412yes—
468C2×#41—28no—
469C2×#41—28no—
470C2×#41—28no—
471C2×#41—28no—
472C2×#41—28no—
473C2×#41—28no—
474C22×Q8C2412yes—
475C22×Q8C2412yes—
476C22×D4—24no—
477C22×D4—24no—
478C22×D4—24no—
479C22×D4C2414yes—
480C22×D4C2414yes—
481C22×D4C2414yes—
482C22×D4C2412yes—
483C22×D4C2412yes—
484C22×D4C2414yes—
485C22×D4C2414yes—
486C22×D4C2414yes—
487C22×D4C2414yes—
488C22×D4C2418yes—
489C22×D4C2418yes—
490C22×D4C2418yes—
491C22×D4C2418yes—
492C22×D4C2418yes—
493C23×C4—28no—
494C23×C4—44no—
495C23×C4—44no—
496C23×C4C2411yescharacteristic
497C23×C4C2414yes—
498C23×C4C2414yes—
499C23×C4C2411yescharacteristic
500C23×C4C2411yescharacteristic
501C23×C4C2414yes—
502C23×C4C2414yes—
503C23×C4C2412yes—
504C23×C4C2412yes—
505C23×C4C2411yescharacteristic
506C23×C4C2411yescharacteristic
507C23×C4C2411yescharacteristic
508C23×C4C2414yes—
509C23×C4C2418yes—
510C23×C4C2414yes—
511C23×C4C2412yes—
512C23×C4C2411yescharacteristic
513C4⋊Q8—44no—
514#127—44no—
515#127—48no—
516#127—48no—
517#127—48no—
518#125—48no—
519#124—44no—
520#124—44no—
521#124—48no—
522#124—48no—
523#123—216no—
524#123—48no—
525#123—416no—
526#123—88no—
527C22⋊Q8—216no—
528C22⋊Q8—216no—
529C22⋊Q8—48no—
530C22⋊Q8—48no—
531#121—216no—
532#121—216no—
533#121—216no—
534#121—216no—
535#121—48no—
536#121—48no—
537#121—416no—
538#121—48no—
539#121—48no—
540#121—416no—
541#121—48no—
542#121—48no—
543#121—48no—
544#121—48no—
545#121—48no—
546#121—48no—
547#121—48no—
548#121—48no—
549#121—416no—
550#121—88no—
551#121—88no—
552#120—416no—
553#120—416no—
554C4×Q8—44no—
555C4×Q8—44no—
556C4×Q8—48no—
557C4×D4—216no—
558C4×D4—216no—
559C4×D4—48no—
560C4×D4—44no—
561C4×D4—44no—
562C4×D4—48no—
563C4×D4—48no—
564C4×D4—48no—
565C4×D4—48no—
566C4×D4—48no—
567C4×D4—48no—
568C4×D4—416no—
569#117—28no—
570#117—28no—
571#117—216no—
572#117—48no—
573#117—48no—
574#117—48no—
575#117—48no—
576#117—48no—
577C2×C4⋊C4—24no—
578C2×C4⋊C4—24no—
579C2×C4⋊C4—24no—
580C2×C4⋊C4—42no—
581C2×C4⋊C4—44no—
582C2×C4⋊C4—48no—
583C2×C4⋊C4—82no—
584C2×C4⋊C4#4118yes—
585C2×C4⋊C4C2414yes—
586C2×C4⋊C4C2412yes—
587C2×C4⋊C4C2411yescharacteristic
588C2×C4⋊C4C2411yescharacteristic
589C2×C4⋊C4C2411yescharacteristic
590C2×C4⋊C4C2414yes—
591C2×C4⋊C4C2414yes—
592C2×C4⋊C4C2412yes—
593C2×C4⋊C4C2412yes—
594C2×C4⋊C4C2412yes—
595C2×C4⋊C4C2412yes—
596C2×C4⋊C4C2414yes—
597C2×C4⋊C4C2414yes—
598C2×C4⋊C4C2414yes—
599C2×C4⋊C4C2414yes—
600C2×C4⋊C4C2418yes—
601C2×C4⋊C4C2418yes—
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2414yes—
604C2×C4⋊C4C2414yes—
605C2×C4⋊C4C2414yes—
606C2×C4⋊C4C2414yes—
607C2×C4⋊C4C2414yes—
608C2×C4⋊C4C2414yes—
609C2×C4⋊C4C2414yes—
610C2×C4⋊C4C2418yes—
611C2×C4⋊C4C2418yes—
612C2×C4⋊C4C2418yes—
613C2×C4⋊C4C2414yes—
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2414yes—
616C2×C4⋊C4C2414yes—
617C2×C4⋊C4C2414yes—
618C2×C4⋊C4C2411yescharacteristic
619C2×C22⋊C4—28no—
620C2×C22⋊C4—44no—
621C2×C22⋊C4—44no—
622C2×C22⋊C4—82no—
623C2×C22⋊C4—82no—
624C2×C22⋊C4C2414yes—
625C2×C22⋊C4C2414yes—
626C2×C22⋊C4C2418yes—
627C2×C22⋊C4C2414yes—
628C2×C22⋊C4C2414yes—
629C2×C22⋊C4C2414yes—
630C2×C22⋊C4C2418yes—
631C2×C22⋊C4C2418yes—
632C2×C22⋊C4C2414yes—
633C2×C22⋊C4C2414yes—
634C2×C22⋊C4C2414yes—
635C2×C22⋊C4C2414yes—
636C2×C22⋊C4C2414yes—
637C2×C22⋊C4C2414yes—
638C2×C22⋊C4C2418yes—
639C2×C22⋊C4C2418yes—
640C2×C22⋊C4C2414yes—
641C2×C22⋊C4C2418yes—
642C2×C22⋊C4C2414yes—
643C2×C22⋊C4C2418yes—
644C2×C22⋊C4C2414yes—
645C2×C22⋊C4C2414yes—
646C2×C22⋊C4C2414yes—
647C2×C22⋊C4C2414yes—
648C2×C22⋊C4C2418yes—
649C2×C22⋊C4C2418yes—
650C2×C22⋊C4C2418yes—
651C2×C22⋊C4C2418yes—
652C2×C22⋊C4C2418yes—
653C2×C22⋊C4C2418yes—
654C2×C22⋊C4C2414yes—
655C2×C22⋊C4C2418yes—
656C2×C22⋊C4C2414yes—
657C2×C22⋊C4C2414yes—
658C2×C22⋊C4C2414yes—
659C2×C22⋊C4C2414yes—
660C2×C22⋊C4C2414yes—
661C2×C22⋊C4C2414yes—
662C2×C42—24no—
663C2×C42—24no—
664C2×C42—24no—
665C2×C42—44no—
666C2×C42—44no—
667C2×C42—48no—
668C2×C42C2414yes—
669C2×C42C2412yes—
670C2×C42C2414yes—
671C2×C42C2414yes—
672C2×C42C2414yes—
673C2×C42C2412yes—
674C2×C42C2412yes—
675C2×C42C2412yes—
676C2×C42C2412yes—
677C2×C42C2412yes—
678C2×C42C2414yes—
679C2×C42C2414yes—
680C2×C42C2418yes—
681C2×C42C2414yes—
682C2×C42C2414yes—
683#95C2418yes—
684#95C2418yes—
685#95C2412yes—
686#95C2412yes—
687#95C2412yes—
688#95C2412yes—
689#95C2414yes—
690#95C2414yes—
691#95C2414yes—
692#95C2414yes—
693#95C2414yes—
694#95C2414yes—
695#95C2418yes—
696#95C2418yes—
697#95C2418yes—
698#95C2414yes—
699#95C2414yes—
700#95C2414yes—
701#95C2414yes—
702#95C2414yes—
703#95C2414yes—
704#95C2418yes—
705#95C2414yes—
706#95C2414yes—
707#95C2414yes—
708#95C2414yes—
709#95C2418yes—
710#95C2418yes—
711C24—24no—
712C24—24no—
713C24—24no—
714C24—42no—
715C24—42no—
716C24—42no—
717C24—42no—
718C24C2514yes—
719C24C2514yes—
720C24C2514yes—
721C24C2511yescharacteristic
722#41—432no—
723#41—432no—
724C2×Q8—24no—
725C2×Q8—24no—
726C2×Q8—24no—
727C2×Q8—24no—
728C2×Q8—24no—
729C2×Q8—24no—
730C2×D4—28no—
731C2×D4—28no—
732C2×D4—28no—
733C2×D4—28no—
734C2×D4—28no—
735C2×D4—28no—
736C2×D4—28no—
737C2×D4—24no—
738C2×D4—24no—
739C2×D4—28no—
740C2×D4—28no—
741C2×D4—24no—
742C2×D4—24no—
743C2×D4—28no—
744C2×D4—28no—
745C2×D4—24no—
746C2×D4—24no—
747C2×D4—28no—
748C2×D4—44no—
749C2×D4—44no—
750C2×D4—44no—
751C2×D4—44no—
752C2×D4—44no—
753C2×D4—44no—
754C2×D4—44no—
755C2×D4—44no—
756C2×D4—44no—
757C2×D4—48no—
758C2×D4—48no—
759C2×D4—48no—
760C2×D4—48no—
761C2×D4—48no—
762C2×D4—48no—
763C2×D4—48no—
764C2×D4—48no—
765C2×D4—48no—
766C2×D4—48no—
767C2×D4—48no—
768C2×D4—48no—
769C2×D4—48no—
770C2×D4—48no—
771C2×D4—48no—
772C2×D4—416no—
773C22×C4—22no—
774C22×C4—22no—
775C22×C4—22no—
776C22×C4—22no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—22no—
780C22×C4—22no—
781C22×C4—24no—
782C22×C4—24no—
783C22×C4—28no—
784C22×C4—28no—
785C22×C4—28no—
786C22×C4—28no—
787C22×C4—22no—
788C22×C4—22no—
789C22×C4—28no—
790C22×C4—28no—
791C22×C4—28no—
792C22×C4—28no—
793C22×C4—28no—
794C22×C4—28no—
795C22×C4—28no—
796C22×C4—42no—
797C22×C4—41no—
798C22×C4—44no—
799C22×C4—44no—
800C22×C4—42no—
801C22×C4—41no—
802C22×C4—41no—
803C22×C4—41no—
804C22×C4—42no—
805C22×C4—42no—
806C22×C4—44no—
807C22×C4—44no—
808C22×C4—41no—
809C22×C4—41no—
810C22×C4—42no—
811C22×C4—42no—
812C22×C4—41no—
813C22×C4—41no—
814C22×C4—44no—
815C22×C4—44no—
816C22×C4—44no—
817C22×C4—48no—
818C22×C4—48no—
819C22×C4—48no—
820C22×C4—432no—
821C22×C4C2×#4118yes—
822C22×C4C2×#4114yes—
823C22×C4H(5,𝔽2)14yes—
824C22×C4H(5,𝔽2)14yes—
825C22×C4C2514yes—
826C22×C4C2512yes—
827C22×C4C2512yes—
828C22×C4C2512yes—
829C22×C4C2514yes—
830C22×C4C2514yes—
831C22×C4C2514yes—
832C22×C4C2514yes—
833C22×C4C2514yes—
834C22×C4C2511yescharacteristic
835C22×C4C2511yescharacteristic
836C22×C4C2514yes—
837C22×C4C2514yes—
838C22×C4C2514yes—
839C22×C4C2511yescharacteristic
840C22×C4C2511yescharacteristic
841C22×C4C2511yescharacteristic
842C22×C4C2511yescharacteristic
843C22×C4C2512yes—
844C4⋊C4—28no—
845C4⋊C4—28no—
846C4⋊C4—28no—
847C4⋊C4—22no—
848C4⋊C4—22no—
849C4⋊C4—22no—
850C4⋊C4—28no—
851C4⋊C4—24no—
852C4⋊C4—28no—
853C4⋊C4—24no—
854C4⋊C4—24no—
855C4⋊C4—24no—
856C4⋊C4—28no—
857C4⋊C4—24no—
858C4⋊C4—42no—
859C4⋊C4—44no—
860C4⋊C4—48no—
861C4⋊C4—48no—
862C4⋊C4—44no—
863C4⋊C4—44no—
864C4⋊C4—44no—
865C4⋊C4—44no—
866C4⋊C4—44no—
867C4⋊C4—44no—
868C4⋊C4—44no—
869C4⋊C4—44no—
870C4⋊C4—44no—
871C4⋊C4—48no—
872C4⋊C4—48no—
873C4⋊C4—44no—
874C4⋊C4—48no—
875C4⋊C4—44no—
876C4⋊C4C2×#41116yes—
877C4⋊C4H(5,𝔽2)14yes—
878C22⋊C4—28no—
879C22⋊C4—28no—
880C22⋊C4—216no—
881C22⋊C4—216no—
882C22⋊C4—216no—
883C22⋊C4—28no—
884C22⋊C4—28no—
885C22⋊C4—28no—
886C22⋊C4—28no—
887C22⋊C4—28no—
888C22⋊C4—28no—
889C22⋊C4—28no—
890C22⋊C4—44no—
891C22⋊C4—44no—
892C22⋊C4—48no—
893C22⋊C4—48no—
894C22⋊C4—44no—
895C22⋊C4—44no—
896C22⋊C4—44no—
897C22⋊C4—44no—
898C22⋊C4—44no—
899C22⋊C4—48no—
900C22⋊C4—48no—
901C22⋊C4—44no—
902C22⋊C4—44no—
903C22⋊C4—44no—
904C22⋊C4—44no—
905C22⋊C4—48no—
906C22⋊C4—48no—
907C22⋊C4—48no—
908C22⋊C4—48no—
909C22⋊C4—48no—
910C22⋊C4—48no—
911C22⋊C4—44no—
912C22⋊C4—48no—
913C22⋊C4—44no—
914C22⋊C4—44no—
915C22⋊C4—44no—
916C42—24no—
917C42—24no—
918C42—24no—
919C42—24no—
920C42—24no—
921C42—24no—
922C42—28no—
923C42—28no—
924C42—28no—
925C42—28no—
926C42—44no—
927C42—44no—
928C42—44no—
929C42—44no—
930C42—48no—
931C23—21no—
932C23—21no—
933C23—21no—
934C23—21no—
935C23—24no—
936C23—24no—
937C23—24no—
938C23—24no—
939C23—24no—
940C23—24no—
941C23—24no—
942C23—24no—
943C23—24no—
944C23—24no—
945C23—24no—
946C23—24no—
947C23—24no—
948C23—24no—
949C23—24no—
950C23—24no—
951C23—24no—
952C23—24no—
953C23—24no—
954C23—24no—
955C23—24no—
956C23—48no—
957C23—48no—
958C23—48no—
959C23—84no—
960C23—84no—
961C23—84no—
962C23—84no—
963C23C22×#4112yes—
964C23C2×H(5,𝔽2)12yes—
965C23C2×H(5,𝔽2)12yes—
966C23C2611yescharacteristic
967Q8—48no—
968Q8—48no—
969D4—416no—
970D4—416no—
971D4—416no—
972D4—48no—
973D4—48no—
974D4—88no—
975D4—88no—
976D4—88no—
977D4—88no—
978D4—168no—
979D4—168no—
980D4—168no—
981D4—168no—
982D4—168no—
983C2×C4—28no—
984C2×C4—21no—
985C2×C4—21no—
986C2×C4—21no—
987C2×C4—24no—
988C2×C4—21no—
989C2×C4—21no—
990C2×C4—21no—
991C2×C4—24no—
992C2×C4—21no—
993C2×C4—21no—
994C2×C4—22no—
995C2×C4—24no—
996C2×C4—24no—
997C2×C4—22no—
998C2×C4—21no—
999C2×C4—21no—
1000C2×C4—22no—
1001C2×C4—24no—
1002C2×C4—24no—
1003C2×C4—24no—
1004C2×C4—24no—
1005C2×C4—24no—
1006C2×C4—24no—
1007C2×C4—21no—
1008C2×C4—21no—
1009C2×C4—24no—
1010C2×C4—24no—
1011C2×C4—24no—
1012C2×C4—24no—
1013C2×C4—24no—
1014C2×C4—24no—
1015C2×C4—24no—
1016C2×C4—24no—
1017C2×C4—24no—
1018C2×C4—24no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—24no—
1024C2×C4—22no—
1025C2×C4—24no—
1026C2×C4—24no—
1027C2×C4—24no—
1028C2×C4—22no—
1029C2×C4—21no—
1030C2×C4—24no—
1031C2×C4—24no—
1032C2×C4—21no—
1033C2×C4—48no—
1034C2×C4—416no—
1035C2×C4—416no—
1036C2×C4—44no—
1037C2×C4—44no—
1038C2×C4—44no—
1039C2×C4—416no—
1040C2×C4—416no—
1041C2×C4—88no—
1042C2×C4—84no—
1043C2×C4—84no—
1044C2×C4—82no—
1045C2×C4—82no—
1046C2×C4—88no—
1047C2×C4—168no—
1048C2×C4#540116yescomplemented
1049C2×C4C22×#4118yes—
1050C2×C4C22×#4114yes—
1051C2×C4C2×H(5,𝔽2)12yes—
1052C2×C4C2×H(5,𝔽2)12yes—
1053C2×C4C2×H(5,𝔽2)12yes—
1054C2×C4C2×H(5,𝔽2)14yes—
1055C2×C4C2×H(5,𝔽2)14yes—
1056C2×C4#58512yes—
1057C22—22no—
1058C22—22no—
1059C22—22no—
1060C22—22no—
1061C22—22no—
1062C22—22no—
1063C22—44no—
1064C22—44no—
1065C22—44no—
1066C22—44no—
1067C22—44no—
1068C22—44no—
1069C22—44no—
1070C22—44no—
1071C22—44no—
1072C22—44no—
1073C22—44no—
1074C22—44no—
1075C22—44no—
1076C22—44no—
1077C22—44no—
1078C22—44no—
1079C22—44no—
1080C22—44no—
1081C22—44no—
1082C22—44no—
1083C22—44no—
1084C22—816no—
1085C22C2×#54014yes—
1086C22C23×#4111yescharacteristic
1087C22C22×H(5,𝔽2)11yescharacteristic
1088C22C22×H(5,𝔽2)11yescharacteristic
1089C22C22×H(5,𝔽2)11yescharacteristic
1090C22C2×#58511yescharacteristic
1091C22H(7,𝔽2)11yescharacteristic
1092C222−1+611yescharacteristic
1093C4—22no—
1094C4—22no—
1095C4—28no—
1096C4—22no—
1097C4—22no—
1098C4—42no—
1099C4—41no—
1100C4—41no—
1101C4—44no—
1102C4—44no—
1103C4—44no—
1104C4—44no—
1105C4—42no—
1106C4—42no—
1107C4—44no—
1108C4—44no—
1109C4—44no—
1110C4—44no—
1111C4C2×#54018yes—
1112C2—24no—
1113C2—84no—
1114C2—84no—
1115C2—84no—
1116C2C22×#54011yescharacteristic
1117C2#6277311yescharacteristic
1118C2#6285111yescharacteristic
1119C2#6291411yescharacteristic
1120C2#6291611yescharacteristic
1121C2#6293011yescharacteristic
1122C2#6293111yescharacteristic
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. #42641C2semidirect
2. #42629C2semidirect
3. #42578C2semidirect
4. #42565C2semidirect
5. #40170C2semidirect
6. #40054C2semidirect
7. #39402C2semidirect
8. #39023C2semidirect
9. #37459C2semidirect
10. #36759C2semidirect
11. #36727C2semidirect
12. #35533C2semidirect
13. #35530C2semidirect
14. #35261C2semidirect
15. #35256C2semidirect
16. #35168C2semidirect
17. #35168C2semidirect
18. #35166C2semidirect
19. #35159C2semidirect
20. #34744C2semidirect
21. #34274C2semidirect
22. C2×#2354C2semidirect
23. C4×#537C2semidirect
24. C2×#540C22semidirect
41. #2837C22semidirect
42. #2828C22semidirect
43. #2803C22semidirect
44. #2797C22semidirect
45. #2793C22semidirect
46. #2753C22semidirect
47. #2752C22semidirect
48. #2748C22semidirect
49. #2748C22semidirect
50. #2741C22semidirect
51. #2741C22semidirect
52. #2711C22semidirect
53. #2703C22semidirect
54. #2703C22semidirect
55. #2701C22semidirect
56. #2673C22semidirect
57. #2671C22semidirect
58. #2671C22semidirect
59. #2661C22semidirect
61. #2651C22semidirect
62. #2649C22semidirect
64. #2635C22semidirect
65. #2629C22semidirect
66. #2624C22semidirect
67. #2624C22semidirect
70. #2619C22semidirect
76. #2542C22semidirect
78. #2541C22semidirect
79. #2540C22semidirect
80. #2540C22semidirect
81. #2516C22semidirect
82. #2509C22semidirect
83. #2508C22semidirect
84. #2507C22semidirect
85. #2506C22semidirect
86. #2502C22semidirect
87. #2501C22semidirect
88. #2500C22semidirect
89. #2499C22semidirect
90. #2476C22semidirect
91. #2476C22semidirect
92. #2471C22semidirect
93. #2471C22semidirect
94. #2464C22semidirect
95. #2448C22semidirect
96. #2448C22semidirect
97. #2447C22semidirect
98. #2447C22semidirect
99. #2446C22semidirect
100. #2446C22semidirect
101. #2445C22semidirect
102. #2445C22semidirect
125. #2423C22semidirect
126. #2423C22semidirect
127. #2422C22semidirect
128. #2422C22semidirect
133. #2395C22semidirect
134. #2395C22semidirect
135. #2363C22semidirect
136. #2362C22semidirect
137. #2361C22semidirect
138. #2360C22semidirect
145. #2324C22semidirect
146. #2324C22semidirect
147. #2324C22semidirect
148. #2323C22semidirect
152. #2314C22semidirect
154. C4×C22⋊Q8C22semidirect
155. C4×#123C22semidirect
156. C4×#123C22semidirect
159. C4×#121C22semidirect
1048. C2×C4#540semidirect

Maximal subgroups

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

subgroupindex
#426412
#426292
#425782
#425652
#401702
#400542
#394022
#390232
#374592
#367592
#367272
#355332
#355302
#352612
#352562
#351682
#351662
#351592
#347442
#342742
C2×#23542
C4×#5372