Finite Group Databasebeta

← #7644122

Subgroups — #7644122

Order 512.

4704 conjugacy classes of subgroups.

The subgroup lattice has 1071 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42672C214yesmaximal, complemented
2#42666C214yesmaximal, complemented
3#42662C214yesmaximal, complemented
4#42659C214yesmaximal, complemented
5#42472C214yesmaximal, complemented
6#42466C214yesmaximal, complemented
7#42458C214yesmaximal, complemented
8#42457C214yesmaximal, complemented
9#37463C214yesmaximal, complemented
10#37462C214yesmaximal, complemented
11#36766C214yesmaximal, complemented
12#36764C214yesmaximal, complemented
13#35629C212yesmaximal, complemented
14#35542C212yesmaximal, complemented
15#35532C212yesmaximal, complemented
16#35516C212yesmaximal, complemented
17#35180C211yesmaximal, characteristic, complemented
18#35167C211yesmaximal, characteristic, complemented
19#34634C211yesmaximal, characteristic, complemented
20#34633C211yesmaximal, characteristic
21#34213C211yesmaximal, characteristic, complemented
22#34206C211yesmaximal, characteristic, complemented
23C2×#2314C211yesmaximal, characteristic, complemented
24C2×#544C2212yes—
25C2×#533C2211yescharacteristic
26C2×#532C2211yescharacteristic
27C2×#525C2212yes—
28C2×#520C2212yes—
29C22×#117C2211yescharacteristic
30#2857C2214yes—
31#2850C2214yes—
32#2838C2218yes—
33#2838C2218yescomplemented
34#2831C2218yescomplemented
35#2829C2218yes—
36#2801C2218yes—
37#2796C2218yescomplemented
38#2795C2218yes—
39#2793C2218yescomplemented
40#2777C2218yescomplemented
41#2773C2218yes—
42#2765C2218yescomplemented
43#2762C2218yescomplemented
44#2759C2218yes—
45#2757C2218yes—
46#2755C2218yescomplemented
47#2730C2218yes—
48#2729C2218yescomplemented
49#2710C2218yes—
50#2700C2218yescomplemented
51#2674C2218yes—
52#2666C2218yescomplemented
53#2663C2218yes—
54#2659C2214yes—
55#2655C2218yescomplemented
56#2653C2218yes—
57#2651C2218yes—
58#2651C2218yescomplemented
59#2639C2214yes—
60#2638C2218yescomplemented
61#2632C2218yes—
62#2629C2212yes—
63#2629C2212yes—
64#2628C2212yes—
65#2628C2212yes—
66#2627C2212yes—
67#2627C2212yes—
68#2626C2212yes—
69#2626C2212yes—
70#2621C2212yes—
71#2620C2212yes—
72#2620C2212yes—
73#2619C2212yes—
74#2618C2212yes—
75#2618C2212yes—
76#2617C2212yes—
77#2617C2212yes—
78#2592C2214yescomplemented
79#2568C2212yescomplemented
80#2567C2214yescomplemented
81#2566C2214yescomplemented
82#2565C2214yescomplemented
83#2563C2214yes—
84#2563C2212yescomplemented
85#2562C2214yes—
86#2562C2214yes—
87#2562C2214yescomplemented
88#2552C2212yescomplemented
89#2552C2212yescomplemented
90#2551C2212yescomplemented
91#2551C2212yescomplemented
92#2550C2214yescomplemented
93#2550C2214yescomplemented
94#2548C2212yescomplemented
95#2547C2214yes—
96#2547C2212yescomplemented
97#2542C2214yescomplemented
98#2525C2218yes—
99#2515C2218yescomplemented
100#2514C2214yescomplemented
101#2514C2214yescomplemented
102#2513C2214yescomplemented
103#2513C2214yescomplemented
104#2510C2218yes—
105#2510C2218yes—
106#2495C2214yescomplemented
107#2495C2214yescomplemented
108#2494C2214yescomplemented
109#2494C2214yescomplemented
110#2492C2214yes—
111#2491C2214yes—
112#2490C2214yes—
113#2489C2214yes—
114#2488C2218yes—
115#2487C2214yes—
116#2486C2214yes—
117#2485C2214yes—
118#2485C2214yes—
119#2472C2218yes—
120#2465C2218yescomplemented
121#2461C2218yes—
122#2449C2218yes—
123#2449C2218yes—
124#2441C2214yescomplemented
125#2441C2214yescomplemented
126#2440C2214yescomplemented
127#2440C2214yescomplemented
128#2423C2214yes—
129#2422C2214yes—
130#2421C2214yes—
131#2420C2214yes—
132#2419C2218yes—
133#2418C2218yes—
134#2396C2214yes—
135#2396C2214yes—
136#2392C2214yes—
137#2392C2214yes—
138#2370C2214yescomplemented
139#2369C2212yescomplemented
140#2367C2214yescomplemented
141#2366C2212yescomplemented
142#2365C2212yescomplemented
143#2365C2212yescomplemented
144#2355C2212yescomplemented
145#2355C2214yescomplemented
146#2354C2212yescomplemented
147#2352C2214yescomplemented
148Q8×C4⋊C4C2212yescomplemented
149D4×C4⋊C4C2212yescomplemented
150#2329C2214yes—
151#2325C2214yes—
152#2317C2212yes—
153#2316C2212yes—
154#2314C2214yes—
155#2314C2214yes—
156#2314C2214yes—
157#2314C2214yes—
158#2311C2212yes—
159#2311C2212yes—
160#2311C2212yes—
161C4×C22⋊Q8C2214yes—
162C4×#121C2214yes—
163#2297C2212yes—
164#2296C2212yes—
165C2×#388C2212yes—
166C2×#388C2212yes—
167C2×#387C2212yes—
168C2×#387C2212yes—
169#2285C2211yescharacteristic
170#2285C2211yescharacteristic
171C2×#384C2211yescharacteristic
172C2×#382C2211yescharacteristic
173#2280C2212yes—
174C2×#380C2211yescharacteristic
175C2×#380C2211yescharacteristic
176#2274C2212yes—
177C2×C4×C4⋊C4C2211yescharacteristic
178C2×C4×C4⋊C4C2211yescharacteristic
179C22×#41C2312yes—
180C24×C4C2311yescharacteristic
181#544—48no—
182#533—28no—
183#532—28no—
184C2×C4⋊Q8C2311yescharacteristic
185C2×C4⋊Q8C2311yescharacteristic
186C2×C4⋊Q8C2311yescharacteristic
187C2×C4⋊Q8C2314yes—
188C2×C4⋊Q8C2314yes—
189C2×C4⋊Q8C2314yes—
190C2×#127C2311yescharacteristic
191C2×#125C2312yes—
192C2×#125C2314yes—
193C2×#125C2314yes—
194C2×#124C2312yes—
195C2×#124C2314yes—
196C2×#124C2318yes—
197#525—48no—
198C2×#123C2314yes—
199C2×#123C2318yes—
200C2×C22⋊Q8C2312yes—
201C2×C22⋊Q8C2312yes—
202C2×C22⋊Q8C2318yes—
203C2×C22⋊Q8C2312yes—
204C2×C22⋊Q8C2312yes—
205C2×C22⋊Q8C2318yes—
206C2×C22⋊Q8C2318yes—
207C2×#121C2312yes—
208C2×#121C2312yes—
209C2×#121C2312yes—
210C2×#121C2312yes—
211C2×#120C2314yes—
212#520—48no—
213C2×C4×Q8C2312yes—
214C2×C4×Q8C2312yes—
215C2×C4×Q8C2314yes—
216C2×C4×Q8C2314yes—
217C2×C4×D4C2312yes—
218C2×C4×D4C2312yes—
219C2×C4×D4C2314yes—
220C2×C4×D4C2314yes—
221C2×C4×D4C2314yes—
222C2×C4×D4C2318yes—
223C2×C4×D4C2314yes—
224C2×#117—28no—
225C2×#117C2312yes—
226C2×#117C2312yes—
227C2×#117C2312yes—
228C2×#117C2312yes—
229C2×#117C2312yes—
230C2×#117C2312yes—
231C2×#117C2312yes—
232C2×#117C2314yes—
233C22×C4⋊C4C2311yescharacteristic
234C22×C4⋊C4C2311yescharacteristic
235C22×C4⋊C4C2311yescharacteristic
236C22×C4⋊C4C2311yescharacteristic
237C22×C4⋊C4C2311yescharacteristic
238C22×C4⋊C4C2311yescharacteristic
239C22×C4⋊C4C2314yes—
240C22×C4⋊C4C2312yes—
241C22×C4⋊C4C2312yes—
242C22×C22⋊C4C2311yescharacteristic
243C22×C22⋊C4C2311yescharacteristic
244C22×C22⋊C4C2312yes—
245C22×C22⋊C4C2312yes—
246C22×C42C2311yescharacteristic
247C22×C42C2312yes—
248C22×C42C2312yes—
249C22×C42C2311yescharacteristic
250#401C2318yes—
251#401C2318yes—
252#400C2318yes—
253#400C2318yes—
254#400C2318yes—
255#400C2318yes—
256#400C2318yes—
257#400C2318yes—
258#400C2314yes—
259#400C2314yes—
260#399C2318yes—
261#399C2318yes—
262#399C2318yes—
263#399C2314yes—
264#399C2314yes—
265#398C2318yes—
266#398C2318yes—
267#398C2318yes—
268#398C2318yes—
269#398C2318yes—
270#398C2314yes—
271#398C2314yes—
272#398C2314yes—
273#398C2314yes—
274#398C2314yes—
275#398C2314yes—
276#397C2318yes—
277#397C2318yes—
278#397C2318yes—
279#397C2318yes—
280#397C2318yes—
281#397C2314yes—
282#397C2318yes—
283#397C2318yes—
284#397C2318yes—
285#397C2318yes—
286#397C2318yes—
287#397C2314yes—
288#396C2318yes—
289#396C2318yes—
290#396C2314yes—
291#396C2314yes—
292#396C2314yes—
293#396C2314yes—
294#396C2314yes—
295#396C2314yes—
296#396C2314yes—
297#396C2314yes—
298#395C2318yes—
299#395C2318yes—
300#395C2314yes—
301#395C2318yes—
302#395C2318yes—
303#395C2314yes—
304#394C2318yes—
305#394C2318yes—
306#394C2318yes—
307#394C2318yes—
308#394C2318yes—
309#394C2314yes—
310#394C2314yes—
311#394C2314yes—
312#394C2314yes—
313#394C2314yes—
314#394C2314yes—
315#393C2318yes—
316#393C2318yes—
317#393C2318yes—
318#393C2314yes—
319#393C2314yes—
320#392C2314yes—
321#392C2314yes—
322#391C2312yes—
323#391C2314yes—
324#391C2314yes—
325#391C2314yes—
326#391C2312yes—
327#391C2314yes—
328#391C2314yes—
329#391C2318yes—
330#391C2318yes—
331#391C2318yes—
332#390C2318yes—
333#390C2314yes—
334#390C2312yes—
335#390C2314yes—
336#390C2314yes—
337#390C2314yes—
338#390C2314yes—
339#390C2312yes—
340#389C2318yes—
341#389C2318yes—
342#389C2314yes—
343#389C2314yes—
344#389C2314yes—
345#389C2314yes—
346#389C2314yes—
347#389C2314yes—
348#389C2314yes—
349#389C2314yes—
350#389C2318yes—
351#389C2318yes—
352#389C2314yes—
353#389C2314yes—
354#389C2312yes—
355#389C2312yes—
356#389C2312yes—
357#389C2312yes—
358#388C2318yes—
359#388C2318yes—
360#388C2318yes—
361#388C2318yes—
362#388C2318yes—
363#388C2318yes—
364#388C2318yes—
365#388C2318yes—
366#388C2318yes—
367#388C2318yes—
368#388C2318yes—
369#388C2318yes—
370#388C2318yes—
371#388C2318yes—
372#388C2318yes—
373#388C2318yes—
374#388C2318yes—
375#388C2318yes—
376#387C2318yes—
377#387C2318yes—
378#387C2318yes—
379#387C2318yes—
380#387C2318yes—
381#387C2318yes—
382#387C2318yes—
383#387C2318yes—
384#387C2318yes—
385#387C2318yes—
386#387C2318yes—
387#387C2318yes—
388#387C2318yes—
389#387C2318yes—
390#386C2318yes—
391#386C2318yes—
392#386C2318yes—
393#386C2318yes—
394#386C2314yes—
395#386C2314yes—
396#386C2318yes—
397#385C2318yes—
398#385C2318yes—
399#385C2318yes—
400#385C2318yes—
401#385C2314yes—
402#385C2314yes—
403#385C2318yes—
404#384C2314yes—
405#384C2314yes—
406#384C2314yes—
407#384C2314yes—
408#384C2311yescharacteristic
409#384C2311yescharacteristic
410#384C2311yescharacteristic
411#384C2311yescharacteristic
412#383C2318yes—
413#383C2318yes—
414#382C2318yes—
415#382C2314yes—
416#382C2314yes—
417#382C2314yes—
418#382C2314yes—
419#382C2312yes—
420#382C2312yes—
421#381C2314yes—
422#381C2318yes—
423#380C2314yes—
424#380C2314yes—
425#380C2312yes—
426#380C2312yes—
427#380C2314yes—
428#380C2314yes—
429#380C2314yes—
430#380C2314yes—
431#380C2312yes—
432#380C2314yes—
433#380C2314yes—
434#380C2314yes—
435#380C2314yes—
436#380C2318yes—
437#380C2312yes—
438#380C2312yes—
439#380C2312yes—
440#380C2312yes—
441#380C2312yes—
442#379C2314yes—
443C4×C4⋊C4C2314yes—
444C4×C4⋊C4C2314yes—
445C4×C4⋊C4C2312yes—
446C4×C4⋊C4C2312yes—
447C4×C4⋊C4C2314yes—
448C4×C4⋊C4C2314yes—
449C4×C4⋊C4C2312yes—
450C4×C4⋊C4C2312yes—
451C4×C4⋊C4C2312yes—
452C4×C4⋊C4C2312yes—
453C4×C4⋊C4C2312yes—
454C4×C4⋊C4C2312yes—
455C4×C4⋊C4C2314yes—
456C4×C4⋊C4C2314yes—
457C4×C4⋊C4C2314yes—
458C4×C4⋊C4C2314yes—
459C4×C4⋊C4C2318yes—
460C4×C4⋊C4C2312yes—
461C4×C4⋊C4C2312yes—
462C4×C4⋊C4C2312yes—
463C4×C4⋊C4C2312yes—
464C4×C22⋊C4C2318yes—
465C4×C22⋊C4C2318yes—
466C4×C22⋊C4C2314yes—
467C4×C22⋊C4C2314yes—
468C4×C22⋊C4C2314yes—
469C4×C22⋊C4C2314yes—
470C2×#95C2312yes—
471C2×#95C2312yes—
472C2×#95C2312yes—
473C2×#95C2312yes—
474C2×#95C2312yes—
475C2×#95C2312yes—
476C25C2411yescharacteristic
477C2×#41—28no—
478C2×#41—28no—
479C2×#41—28no—
480C22×Q8C2412yes—
481C22×Q8C2412yes—
482C22×Q8C2412yes—
483C22×Q8C2418yes—
484C22×D4C2414yes—
485C22×D4C2412yes—
486C22×D4C2412yes—
487C22×D4C2412yes—
488C22×D4C2414yes—
489C22×D4C2414yes—
490C23×C4—24no—
491C23×C4—24no—
492C23×C4—24no—
493C23×C4C2411yescharacteristic
494C23×C4C2414yes—
495C23×C4C2412yes—
496C23×C4C2412yes—
497C23×C4C2412yes—
498C23×C4C2412yes—
499C23×C4C2411yescharacteristic
500C23×C4C2411yescharacteristic
501C23×C4C2412yes—
502C23×C4C2412yes—
503C23×C4C2418yes—
504C23×C4C2411yescharacteristic
505C23×C4C2411yescharacteristic
506C23×C4C2411yescharacteristic
507C4⋊Q8—24no—
508C4⋊Q8—24no—
509C4⋊Q8—24no—
510C4⋊Q8—48no—
511C4⋊Q8—48no—
512C4⋊Q8—84no—
513#127—24no—
514#125—28no—
515#125—48no—
516#125—48no—
517#124—28no—
518#124—84no—
519#124—88no—
520#123—48no—
521#123—88no—
522C22⋊Q8—28no—
523C22⋊Q8—28no—
524C22⋊Q8—416no—
525C22⋊Q8—44no—
526C22⋊Q8—44no—
527C22⋊Q8—88no—
528C22⋊Q8—88no—
529#121—28no—
530#121—28no—
531#121—44no—
532#121—44no—
533#120—48no—
534C4×Q8—28no—
535C4×Q8—28no—
536C4×Q8—48no—
537C4×Q8—84no—
538C4×D4—28no—
539C4×D4—28no—
540C4×D4—48no—
541C4×D4—48no—
542C4×D4—48no—
543C4×D4—416no—
544C4×D4—84no—
545#117—28no—
546#117—28no—
547#117—28no—
548#117—28no—
549#117—28no—
550#117—28no—
551#117—28no—
552#117—48no—
553C2×C4⋊C4—24no—
554C2×C4⋊C4—24no—
555C2×C4⋊C4—24no—
556C2×C4⋊C4—24no—
557C2×C4⋊C4—24no—
558C2×C4⋊C4—24no—
559C2×C4⋊C4—48no—
560C2×C4⋊C4—82no—
561C2×C4⋊C4—82no—
562C2×C4⋊C4C2412yes—
563C2×C4⋊C4C2412yes—
564C2×C4⋊C4C2412yes—
565C2×C4⋊C4C2412yes—
566C2×C4⋊C4C2412yes—
567C2×C4⋊C4C2412yes—
568C2×C4⋊C4C2412yes—
569C2×C4⋊C4C2412yes—
570C2×C4⋊C4C2412yes—
571C2×C4⋊C4C2412yes—
572C2×C4⋊C4C2412yes—
573C2×C4⋊C4C2412yes—
574C2×C4⋊C4C2412yes—
575C2×C4⋊C4C2412yes—
576C2×C4⋊C4C2412yes—
577C2×C4⋊C4C2412yes—
578C2×C4⋊C4C2412yes—
579C2×C4⋊C4C2412yes—
580C2×C4⋊C4C2412yes—
581C2×C4⋊C4C2412yes—
582C2×C4⋊C4C2414yes—
583C2×C4⋊C4C2414yes—
584C2×C4⋊C4C2412yes—
585C2×C4⋊C4C2412yes—
586C2×C4⋊C4C2418yes—
587C2×C4⋊C4C2418yes—
588C2×C4⋊C4C2418yes—
589C2×C4⋊C4C2412yes—
590C2×C4⋊C4C2414yes—
591C2×C4⋊C4C2414yes—
592C2×C4⋊C4C2412yes—
593C2×C4⋊C4C2418yes—
594C2×C4⋊C4C2414yes—
595C2×C4⋊C4C2414yes—
596C2×C4⋊C4C2418yes—
597C2×C4⋊C4C2418yes—
598C2×C4⋊C4C2418yes—
599C2×C4⋊C4C2418yes—
600C2×C4⋊C4C2418yes—
601C2×C4⋊C4C2412yes—
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2412yes—
604C2×C4⋊C4C2412yes—
605C2×C4⋊C4C2412yes—
606C2×C4⋊C4C2412yes—
607C2×C4⋊C4C2414yes—
608C2×C4⋊C4C2414yes—
609C2×C4⋊C4C2418yes—
610C2×C22⋊C4—24no—
611C2×C22⋊C4—24no—
612C2×C22⋊C4—82no—
613C2×C22⋊C4—82no—
614C2×C22⋊C4C2412yes—
615C2×C22⋊C4C2412yes—
616C2×C22⋊C4C2412yes—
617C2×C22⋊C4C2412yes—
618C2×C22⋊C4C2414yes—
619C2×C22⋊C4C2414yes—
620C2×C22⋊C4C2414yes—
621C2×C22⋊C4C2414yes—
622C2×C22⋊C4C2414yes—
623C2×C22⋊C4C2418yes—
624C2×C22⋊C4C2418yes—
625C2×C22⋊C4C2418yes—
626C2×C22⋊C4C2414yes—
627C2×C22⋊C4C2414yes—
628C2×C22⋊C4C2414yes—
629C2×C22⋊C4C2414yes—
630C2×C22⋊C4C2418yes—
631C2×C22⋊C4C2414yes—
632C2×C22⋊C4C2414yes—
633C2×C22⋊C4C2418yes—
634C2×C22⋊C4C2418yes—
635C2×C22⋊C4C2414yes—
636C2×C22⋊C4C2418yes—
637C2×C22⋊C4C2414yes—
638C2×C22⋊C4C2414yes—
639C2×C22⋊C4C2414yes—
640C2×C22⋊C4C2418yes—
641C2×C22⋊C4C2414yes—
642C2×C22⋊C4C2414yes—
643C2×C22⋊C4C2418yes—
644C2×C42—24no—
645C2×C42—82no—
646C2×C42—82no—
647C2×C42#4118yes—
648C2×C42C2412yes—
649C2×C42C2412yes—
650C2×C42C2414yes—
651C2×C42C2414yes—
652C2×C42C2414yes—
653C2×C42C2418yes—
654C2×C42C2414yes—
655C2×C42C2418yes—
656C2×C42C2414yes—
657C2×C42C2414yes—
658C2×C42C2414yes—
659C2×C42C2418yes—
660C2×C42C2411yescharacteristic
661C2×C42C2411yescharacteristic
662C2×C42C2411yescharacteristic
663C2×C42C2411yescharacteristic
664#95C2414yes—
665#95C2414yes—
666#95C2414yes—
667#95C2414yes—
668#95C2418yes—
669#95C2418yes—
670#95C2418yes—
671#95C2418yes—
672#95C2414yes—
673#95C2418yes—
674#95C2418yes—
675#95C2414yes—
676#95C2414yes—
677#95C2414yes—
678#95C2414yes—
679#95C2418yes—
680#95C2414yes—
681#95C2414yes—
682#95C2414yes—
683#95C2414yes—
684#95C2414yes—
685#95C2414yes—
686#95C2414yes—
687#95C2418yes—
688#95C2418yes—
689#95C2418yes—
690#95C2414yes—
691#95C2414yes—
692#95C2414yes—
693#95C2414yes—
694#95C2418yes—
695#95C2418yes—
696#95C2418yes—
697#95C2418yes—
698#95C2418yes—
699#95C2418yes—
700C24—22no—
701C24—22no—
702C24—22no—
703C24—41no—
704C24—41no—
705C24—41no—
706C24—41no—
707C24C2512yes—
708C24C2514yes—
709C24C2511yescharacteristic
710#41—432no—
711C2×Q8—24no—
712C2×Q8—24no—
713C2×Q8—24no—
714C2×Q8—24no—
715C2×Q8—24no—
716C2×Q8—42no—
717C2×Q8—42no—
718C2×Q8—42no—
719C2×Q8—42no—
720C2×Q8—48no—
721C2×Q8—48no—
722C2×Q8—48no—
723C2×D4—28no—
724C2×D4—28no—
725C2×D4—28no—
726C2×D4—24no—
727C2×D4—24no—
728C2×D4—24no—
729C2×D4—24no—
730C2×D4—24no—
731C2×D4—42no—
732C2×D4—42no—
733C2×D4—44no—
734C2×D4—44no—
735C2×D4—44no—
736C2×D4—42no—
737C2×D4—44no—
738C2×D4—42no—
739C2×D4—44no—
740C2×D4—44no—
741C22×C4—22no—
742C22×C4—22no—
743C22×C4—22no—
744C22×C4—22no—
745C22×C4—22no—
746C22×C4—24no—
747C22×C4—24no—
748C22×C4—24no—
749C22×C4—24no—
750C22×C4—24no—
751C22×C4—24no—
752C22×C4—28no—
753C22×C4—28no—
754C22×C4—24no—
755C22×C4—24no—
756C22×C4—24no—
757C22×C4—24no—
758C22×C4—28no—
759C22×C4—41no—
760C22×C4—41no—
761C22×C4—41no—
762C22×C4—41no—
763C22×C4—41no—
764C22×C4—41no—
765C22×C4—41no—
766C22×C4—41no—
767C22×C4—42no—
768C22×C4—42no—
769C22×C4—42no—
770C22×C4—42no—
771C22×C4—42no—
772C22×C4—42no—
773C22×C4—42no—
774C22×C4—42no—
775C22×C4—48no—
776C22×C4—48no—
777C22×C4—48no—
778C22×C4—416no—
779C22×C4C2×#4114yes—
780C22×C4C2×#4114yes—
781C22×C4C2×#4114yes—
782C22×C4H(5,𝔽2)14yes—
783C22×C42−1+414yes—
784C22×C4C2514yes—
785C22×C4C2514yes—
786C22×C4C2514yes—
787C22×C4C2512yes—
788C22×C4C2514yes—
789C22×C4C2514yes—
790C22×C4C2514yes—
791C22×C4C2512yes—
792C22×C4C2512yes—
793C22×C4C2514yes—
794C22×C4C2514yes—
795C22×C4C2514yes—
796C22×C4C2514yes—
797C22×C4C2514yes—
798C22×C4C2511yescharacteristic
799C22×C4C2511yescharacteristic
800C22×C4C2511yescharacteristic
801C22×C4C2511yescharacteristic
802C22×C4C2511yescharacteristic
803C22×C4C2511yescharacteristic
804C4⋊C4—24no—
805C4⋊C4—24no—
806C4⋊C4—24no—
807C4⋊C4—24no—
808C4⋊C4—24no—
809C4⋊C4—24no—
810C4⋊C4—24no—
811C4⋊C4—24no—
812C4⋊C4—28no—
813C4⋊C4—28no—
814C4⋊C4—24no—
815C4⋊C4—24no—
816C4⋊C4—24no—
817C4⋊C4—24no—
818C4⋊C4—24no—
819C4⋊C4—24no—
820C4⋊C4—24no—
821C4⋊C4—24no—
822C4⋊C4—24no—
823C4⋊C4—24no—
824C4⋊C4—24no—
825C4⋊C4—24no—
826C4⋊C4—24no—
827C4⋊C4—24no—
828C4⋊C4—48no—
829C4⋊C4—48no—
830C4⋊C4—48no—
831C4⋊C4—42no—
832C4⋊C4—42no—
833C4⋊C4—42no—
834C4⋊C4—42no—
835C4⋊C4—44no—
836C4⋊C4—44no—
837C4⋊C4—48no—
838C4⋊C4—44no—
839C4⋊C4—44no—
840C4⋊C4—42no—
841C4⋊C4—42no—
842C4⋊C4—48no—
843C4⋊C4—48no—
844C4⋊C4—48no—
845C4⋊C4—48no—
846C4⋊C4—44no—
847C4⋊C4—44no—
848C4⋊C4—48no—
849C4⋊C4—48no—
850C4⋊C4—42no—
851C4⋊C4—42no—
852C22⋊C4—28no—
853C22⋊C4—28no—
854C22⋊C4—28no—
855C22⋊C4—24no—
856C22⋊C4—24no—
857C22⋊C4—24no—
858C22⋊C4—24no—
859C22⋊C4—28no—
860C22⋊C4—28no—
861C22⋊C4—48no—
862C22⋊C4—48no—
863C22⋊C4—48no—
864C22⋊C4—44no—
865C22⋊C4—44no—
866C22⋊C4—48no—
867C22⋊C4—44no—
868C22⋊C4—44no—
869C22⋊C4—48no—
870C22⋊C4—44no—
871C22⋊C4—44no—
872C22⋊C4—44no—
873C22⋊C4—44no—
874C22⋊C4—48no—
875C22⋊C4—44no—
876C22⋊C4—44no—
877C22⋊C4—48no—
878C22⋊C4—48no—
879C22⋊C4—44no—
880C22⋊C4—48no—
881C22⋊C4—44no—
882C42—24no—
883C42—24no—
884C42—28no—
885C42—28no—
886C42—28no—
887C42—44no—
888C42—44no—
889C42—44no—
890C42—44no—
891C42—48no—
892C42—48no—
893C42—48no—
894C42C2×#4114yes—
895C42C2×#4114yes—
896C42C2×#4114yes—
897C42C2×#4114yes—
898C23—21no—
899C23—21no—
900C23—21no—
901C23—21no—
902C23—22no—
903C23—24no—
904C23—22no—
905C23—24no—
906C23—22no—
907C23—24no—
908C23—22no—
909C23—22no—
910C23—24no—
911C23—24no—
912C23—24no—
913C23—24no—
914C23—22no—
915C23—22no—
916C23—44no—
917C23—44no—
918C23—44no—
919C23—82no—
920C23—82no—
921C23—82no—
922C23—82no—
923C23C22×#4112yes—
924C23C2×H(5,𝔽2)12yes—
925C23C2×2−1+412yes—
926C23C2611yescharacteristic
927Q8—48no—
928Q8—48no—
929Q8—84no—
930Q8—168no—
931D4—48no—
932D4—416no—
933D4—48no—
934D4—84no—
935D4—88no—
936D4—88no—
937C2×C4—21no—
938C2×C4—21no—
939C2×C4—21no—
940C2×C4—21no—
941C2×C4—21no—
942C2×C4—21no—
943C2×C4—21no—
944C2×C4—21no—
945C2×C4—22no—
946C2×C4—22no—
947C2×C4—24no—
948C2×C4—24no—
949C2×C4—24no—
950C2×C4—22no—
951C2×C4—24no—
952C2×C4—24no—
953C2×C4—24no—
954C2×C4—24no—
955C2×C4—24no—
956C2×C4—24no—
957C2×C4—22no—
958C2×C4—24no—
959C2×C4—24no—
960C2×C4—24no—
961C2×C4—22no—
962C2×C4—24no—
963C2×C4—24no—
964C2×C4—24no—
965C2×C4—24no—
966C2×C4—24no—
967C2×C4—24no—
968C2×C4—24no—
969C2×C4—24no—
970C2×C4—24no—
971C2×C4—24no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—24no—
975C2×C4—24no—
976C2×C4—24no—
977C2×C4—24no—
978C2×C4—24no—
979C2×C4—24no—
980C2×C4—24no—
981C2×C4—24no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—24no—
985C2×C4—24no—
986C2×C4—24no—
987C2×C4—44no—
988C2×C4—44no—
989C2×C4—44no—
990C2×C4—44no—
991C2×C4—44no—
992C2×C4—48no—
993C2×C4—48no—
994C2×C4—416no—
995C2×C4—84no—
996C2×C4—84no—
997C2×C4—84no—
998C2×C4—84no—
999C2×C4—168no—
1000C2×C4#542116yes—
1001C2×C4C22×#4112yes—
1002C2×C4C22×#4112yes—
1003C2×C4C22×#4112yes—
1004C2×C4C22×#4112yes—
1005C2×C4C22×#4112yes—
1006C2×C4C22×#4112yes—
1007C2×C4C2×H(5,𝔽2)12yes—
1008C2×C4C2×H(5,𝔽2)12yes—
1009C2×C4C2×2−1+412yes—
1010C2×C4C2×2−1+412yes—
1011C22—22no—
1012C22—22no—
1013C22—22no—
1014C22—22no—
1015C22—22no—
1016C22—22no—
1017C22—44no—
1018C22—42no—
1019C22—44no—
1020C22—42no—
1021C22—44no—
1022C22—44no—
1023C22—42no—
1024C22—42no—
1025C22—44no—
1026C22—42no—
1027C22—42no—
1028C22—44no—
1029C22—42no—
1030C22—44no—
1031C22—88no—
1032C22C2×#54214yes—
1033C22C23×#4111yescharacteristic
1034C22C22×H(5,𝔽2)11yescharacteristic
1035C22C22×2−1+411yescharacteristic
1036C22H(7,𝔽2)11yescharacteristic
1037C22H(7,𝔽2)11yescharacteristic
1038C222−1+611yescharacteristic
1039C222−1+611yescharacteristic
1040C4—22no—
1041C4—22no—
1042C4—22no—
1043C4—22no—
1044C4—42no—
1045C4—44no—
1046C4—42no—
1047C4—44no—
1048C4—44no—
1049C4—44no—
1050C4—44no—
1051C4—44no—
1052C4—44no—
1053C4—44no—
1054C4—44no—
1055C4—44no—
1056C4—42no—
1057C4—44no—
1058C4C2×#54214yes—
1059C4C2×#54214yes—
1060C2—24no—
1061C2—84no—
1062C2—82no—
1063C2C22×#54211yescharacteristic
1064C2#6284511yescharacteristic
1065C2#6285611yescharacteristic
1066C2#6287911yescharacteristic
1067C2#6287911yescharacteristic
1068C2#6288011yescharacteristic
1069C2#6288811yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#34633C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #42672C2semidirect
2. #42666C2semidirect
3. #42662C2semidirect
4. #42659C2semidirect
5. #42472C2semidirect
6. #42466C2semidirect
7. #42458C2semidirect
8. #42457C2semidirect
9. #37463C2semidirect
10. #37462C2semidirect
11. #36766C2semidirect
12. #36764C2semidirect
13. #35629C2semidirect
14. #35542C2semidirect
15. #35532C2semidirect
16. #35516C2semidirect
17. #35180C2semidirect
18. #35167C2semidirect
19. #34634C2semidirect
21. #34213C2semidirect
22. #34206C2semidirect
23. C2×#2314C2semidirect
33. #2838C22semidirect
34. #2831C22semidirect
37. #2796C22semidirect
39. #2793C22semidirect
40. #2777C22semidirect
42. #2765C22semidirect
43. #2762C22semidirect
46. #2755C22semidirect
48. #2729C22semidirect
50. #2700C22semidirect
52. #2666C22semidirect
55. #2655C22semidirect
58. #2651C22semidirect
60. #2638C22semidirect
78. #2592C22semidirect
79. #2568C22semidirect
80. #2567C22semidirect
81. #2566C22semidirect
82. #2565C22semidirect
84. #2563C22semidirect
87. #2562C22semidirect
88. #2552C22semidirect
89. #2552C22semidirect
90. #2551C22semidirect
91. #2551C22semidirect
92. #2550C22semidirect
93. #2550C22semidirect
94. #2548C22semidirect
96. #2547C22semidirect
97. #2542C22semidirect
99. #2515C22semidirect
100. #2514C22semidirect
101. #2514C22semidirect
102. #2513C22semidirect
103. #2513C22semidirect
106. #2495C22semidirect
107. #2495C22semidirect
108. #2494C22semidirect
109. #2494C22semidirect
120. #2465C22semidirect
124. #2441C22semidirect
125. #2441C22semidirect
126. #2440C22semidirect
127. #2440C22semidirect
138. #2370C22semidirect
139. #2369C22semidirect
140. #2367C22semidirect
141. #2366C22semidirect
142. #2365C22semidirect
143. #2365C22semidirect
144. #2355C22semidirect
145. #2355C22semidirect
146. #2354C22semidirect
147. #2352C22semidirect
148. Q8×C4⋊C4C22semidirect
149. D4×C4⋊C4C22semidirect

Maximal subgroups

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

subgroupindex
#426722
#426662
#426622
#426592
#424722
#424662
#424582
#424572
#374632
#374622
#367662
#367642
#356292
#355422
#355322
#355162
#351802
#351672
#346342
#346332
#342132
#342062
C2×#23142