Finite Group Databasebeta

← #7683793

Subgroups — #7683793

Order 512.

5072 conjugacy classes of subgroups.

The subgroup lattice has 1125 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59699C214yesmaximal, complemented
2#59575C214yesmaximal, complemented
3#59387C218yesmaximal, complemented
4#59306C214yesmaximal, complemented
5#59302C214yesmaximal, complemented
6#45342C214yesmaximal, complemented
7#45158C214yesmaximal, complemented
8#45130C214yesmaximal, complemented
9#45015C214yesmaximal, complemented
10#44085C218yesmaximal, complemented
11#35661C211yesmaximal, characteristic, complemented
12#35633C211yesmaximal, characteristic, complemented
13#35627C211yesmaximal, characteristic, complemented
14#35621C211yesmaximal, characteristic, complemented
15#35619C211yesmaximal, characteristic, complemented
16#35557C211yesmaximal, characteristic, complemented
17#34814C211yesmaximal, characteristic, complemented
18C2×#2499C211yesmaximal, characteristic, complemented
19#34743C211yesmaximal, characteristic
20#34268C211yesmaximal, characteristic, complemented
21#34254C211yesmaximal, characteristic, complemented
22#34208C211yesmaximal, characteristic, complemented
23#34201C211yesmaximal, characteristic, complemented
24#34201C211yesmaximal, characteristic, complemented
25#34183C211yesmaximal, characteristic, complemented
26C2×#536C2211yescharacteristic
27C2×#536C2211yescharacteristic
28C2×#532C2211yescharacteristic
29C2×#525C2211yescharacteristic
30C2×#525C2211yescharacteristic
31C22×C22⋊Q8C2211yescharacteristic
32C2×#520C2211yescharacteristic
33C2×#520C2211yescharacteristic
34C2×#520C2211yescharacteristic
35C2×#519C2211yescharacteristic
36C2×C4×#41C2211yescharacteristic
37C22×#117C2211yescharacteristic
38#2800C2218yes—
39#2797C2218yes—
40#2793C2218yes—
41#2793C2218yescomplemented
42#2783C2218yes—
43#2781C2218yescomplemented
44#2779C2218yes—
45#2776C2218yescomplemented
46#2772C2218yes—
47#2749C2218yes—
48#2747C2218yescomplemented
49#2691C2218yes—
50#2608C2218yescomplemented
51#2597C2218yes—
52#2595C2218yes—
53#2590C2218yescomplemented
54#2585C2218yescomplemented
55#2578C2218yescomplemented
56#2577C2218yescomplemented
57#2576C2218yescomplemented
58#2571C2214yescomplemented
59#2570C2218yescomplemented
60#2570C2214yescomplemented
61#2547C2212yescomplemented
62#2546C2212yescomplemented
63#2545C2212yescomplemented
64#2544C2212yescomplemented
65#2538C2214yes—
66#2536C2214yes—
67#2534C2214yes—
68#2531C2218yes—
69#2530C2218yescomplemented
70#2526C2218yes—
71#2525C2218yes—
72#2525C2218yescomplemented
73#2512C2218yes—
74#2512C2214yescomplemented
75#2511C2214yescomplemented
76#2509C2214yescomplemented
77#2508C2214yescomplemented
78#2505C2218yes—
79#2504C2218yes—
80#2503C2212yescomplemented
81#2502C2212yescomplemented
82#2499C2214yes—
83#2499C2214yes—
84#2499C2214yes—
85#2499C2214yes—
86#2499C2212yescomplemented
87#2499C2212yescomplemented
88#2497C2212yes—
89#2497C2214yescomplemented
90#2496C2212yes—
91#2496C2214yescomplemented
92#2495C2212yes—
93#2494C2212yes—
94#2493C2214yes—
95#2486C2214yes—
96#2481C2218yes—
97#2481C2218yes—
98#2481C2218yescomplemented
99#2480C2214yes—
100#2447C2214yescomplemented
101#2446C2214yescomplemented
102#2429C2212yes—
103#2429C2214yes—
104#2429C2214yes—
105#2428C2212yes—
106#2427C2214yes—
107#2427C2212yes—
108#2426C2212yes—
109#2426C2214yes—
110#2425C2218yes—
111#2425C2214yes—
112#2424C2214yes—
113#2419C2218yes—
114#2417C2214yes—
115#2417C2214yescomplemented
116#2415C2214yes—
117#2415C2214yescomplemented
118#2413C2214yes—
119#2411C2214yes—
120#2401C2214yes—
121#2392C2214yes—
122C2×#397C2214yes—
123#2373C2218yescomplemented
124#2367C2214yescomplemented
125#2365C2214yescomplemented
126#2364C2218yes—
127#2363C2214yes—
128#2363C2214yes—
129#2362C2214yes—
130#2362C2214yes—
131#2359C2218yes—
132#2356C2214yescomplemented
133#2355C2214yescomplemented
134#2354C2214yes—
135#2354C2214yes—
136#2352C2214yes—
137#2352C2214yes—
138#2352C2214yescomplemented
139#2352C2214yescomplemented
140Q8×C4⋊C4C2214yescomplemented
141D4×C4⋊C4C2218yes—
142D4×C4⋊C4C2214yescomplemented
143#2345C2218yescomplemented
144#2343C2218yes—
145#2328C2212yescomplemented
146#2327C2212yescomplemented
147#2323C2214yescomplemented
148#2321C2214yes—
149#2321C2214yes—
150#2320C2214yescomplemented
151#2317C2211yescharacteristic
152#2317C2211yescharacteristic
153#2317C2211yescharacteristic
154#2317C2212yescomplemented
155#2317C2212yescomplemented
156#2316C2211yescharacteristic
157#2311C2211yescharacteristic
158#2311C2211yescharacteristic
159#2311C2211yescharacteristic
160#2310C2211yescharacteristic
161C4×#126C2214yes—
162C4×#124C2212yescomplemented
163C4×#124C2212yescomplemented
164C4×C22⋊Q8C2214yescomplemented
165C4×#123C2214yes—
166C4×#123C2214yes—
167C4×#121C2214yes—
168#2297C2211yescharacteristic
169#2296C2211yescharacteristic
170#2296C2211yescharacteristic
171#2296C2211yescharacteristic
172#2295C2214yescomplemented
173C2×#391C2211yescharacteristic
174C2×#391C2211yescharacteristic
175C2×#387C2214yes—
176#2285C2211yescharacteristic
177#2285C2212yescomplemented
178C2×#384C2211yescharacteristic
179C2×#384C2212yescomplemented
180C2×#382C2211yescharacteristic
181#2280C2211yescharacteristic
182#2280C2211yescharacteristic
183#2274C2211yescharacteristic
184#2274C2211yescharacteristic
185C4×#117C2211yescharacteristic
186C2×C4×C22⋊C4C2211yescharacteristic
187C22×#41C2311yescharacteristic
188C22×#41C2311yescharacteristic
189C23×Q8C2311yescharacteristic
190C24×C4C2311yescharacteristic
191#536—28no—
192#536—44no—
193#532—28no—
194C2×C4⋊Q8C2311yescharacteristic
195C2×C4⋊Q8C2312yes—
196C2×C4⋊Q8C2312yes—
197C2×#127C2311yescharacteristic
198C2×#126C2314yes—
199C2×#126C2318yes—
200C2×#124C2312yes—
201C2×#124C2311yescharacteristic
202C2×#124C2311yescharacteristic
203C2×#124C2312yes—
204#525—28no—
205#525—28no—
206C2×#123C2314yes—
207C2×#123C2312yes—
208C2×#123C2312yes—
209C2×#123C2314yes—
210C2×C22⋊Q8—44no—
211C2×C22⋊Q8C2314yes—
212C2×C22⋊Q8C2312yes—
213C2×C22⋊Q8C2312yes—
214C2×C22⋊Q8C2314yes—
215C2×C22⋊Q8C2314yes—
216C2×C22⋊Q8C2312yes—
217C2×C22⋊Q8C2312yes—
218C2×#121C2312yes—
219C2×#121C2312yes—
220C2×#121C2314yes—
221C2×#121C2314yes—
222C2×#120C2312yes—
223C2×#120C2312yes—
224#520—44no—
225#520—44no—
226#520—44no—
227#519—28no—
228C4×#41—28no—
229C2×C4×Q8C2314yes—
230C2×C4×Q8C2314yes—
231C2×C4×Q8C2312yes—
232C2×C4×Q8C2312yes—
233C2×C4×Q8C2312yes—
234C2×C4×Q8C2312yes—
235C2×C4×D4C2314yes—
236C2×C4×D4C2312yes—
237C2×C4×D4C2314yes—
238C2×C4×D4C2314yes—
239C2×C4×D4C2314yes—
240C2×C4×D4C2314yes—
241C2×C4×D4C2314yes—
242C2×C4×D4C2312yes—
243C2×C4×D4C2312yes—
244C2×C4×D4C2314yes—
245C2×C4×D4C2312yes—
246C2×#117—44no—
247C2×#117C2311yescharacteristic
248C2×#117C2311yescharacteristic
249C2×#117C2311yescharacteristic
250C2×#117C2311yescharacteristic
251C2×#117C2311yescharacteristic
252C2×#117C2312yes—
253C2×#117C2314yes—
254C2×#117C2312yes—
255C2×#117C2312yes—
256C2×#117C2314yes—
257C2×#117C2312yes—
258C2×#117C2314yes—
259C2×#117C2311yescharacteristic
260C22×C4⋊C4C2311yescharacteristic
261C22×C4⋊C4C2311yescharacteristic
262C22×C4⋊C4C2311yescharacteristic
263C22×C4⋊C4C2312yes—
264C22×C4⋊C4C2312yes—
265C22×C4⋊C4C2318yes—
266C22×C4⋊C4C2314yes—
267C22×C4⋊C4C2312yes—
268C22×C4⋊C4C2312yes—
269C22×C22⋊C4C2312yes—
270C22×C22⋊C4C2312yes—
271C22×C22⋊C4C2312yes—
272C22×C42C2311yescharacteristic
273C22×C42C2312yes—
274C22×C42C2311yescharacteristic
275C22×C42C2312yes—
276#401C2314yes—
277#400C2314yes—
278#400C2318yes—
279#400C2318yes—
280#400C2318yes—
281#400C2318yes—
282#400C2318yes—
283#400C2314yes—
284#400C2314yes—
285#400C2318yes—
286#398C2318yes—
287#398C2318yes—
288#398C2318yes—
289#398C2318yes—
290#398C2318yes—
291#398C2314yes—
292#397C2318yes—
293#397C2314yes—
294#397C2318yes—
295#397C2318yes—
296#397C2318yes—
297#397C2318yes—
298#397C2318yes—
299#397C2318yes—
300#397C2314yes—
301#397C2314yes—
302#397C2314yes—
303#397C2318yes—
304#397C2318yes—
305#396C2318yes—
306#396C2314yes—
307#396C2318yes—
308#396C2318yes—
309#396C2314yes—
310#396C2314yes—
311#396C2318yes—
312#396C2318yes—
313#394C2314yes—
314#394C2318yes—
315#394C2314yes—
316#394C2318yes—
317#394C2314yes—
318#394C2318yes—
319#392C2314yes—
320#391C2314yes—
321#391C2312yes—
322#391C2312yes—
323#391C2312yes—
324#391C2312yes—
325#391C2312yes—
326#391C2312yes—
327#391C2312yes—
328#391C2314yes—
329#391C2314yes—
330#391C2312yes—
331#391C2312yes—
332#391C2312yes—
333#390C2312yes—
334#390C2312yes—
335#390C2312yes—
336#390C2318yes—
337#390C2318yes—
338#390C2314yes—
339#390C2318yes—
340#390C2312yes—
341#389C2314yes—
342#389C2312yes—
343#389C2314yes—
344#389C2318yes—
345#389C2312yes—
346#389C2318yes—
347#389C2314yes—
348#389C2314yes—
349#389C2314yes—
350#389C2314yes—
351#389C2318yes—
352#389C2318yes—
353#389C2312yes—
354#389C2312yes—
355#389C2318yes—
356#389C2318yes—
357#389C2318yes—
358#389C2312yes—
359#389C2312yes—
360#388C2314yes—
361#388C2314yes—
362#388C2314yes—
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#388C2318yes—
377#388C2318yes—
378#388C2314yes—
379#388C2314yes—
380#387C2314yes—
381#387C2314yes—
382#387C2314yes—
383#387C2318yes—
384#387C2318yes—
385#387C2318yes—
386#387C2318yes—
387#387C2318yes—
388#387C2318yes—
389#387C2318yes—
390#387C2318yes—
391#387C2318yes—
392#387C2318yes—
393#387C2318yes—
394#387C2318yes—
395#387C2318yes—
396#387C2318yes—
397#387C2318yes—
398#387C2318yes—
399#387C2318yes—
400#387C2318yes—
401#387C2318yes—
402#387C2318yes—
403#386C2314yes—
404#386C2314yes—
405#386C2314yes—
406#386C2318yes—
407#386C2318yes—
408#386C2318yes—
409#386C2318yes—
410#386C2314yes—
411#386C2318yes—
412#386C2318yes—
413#386C2314yes—
414#386C2314yes—
415#385C2314yes—
416#385C2314yes—
417#385C2314yes—
418#385C2318yes—
419#385C2318yes—
420#385C2318yes—
421#385C2314yes—
422#385C2314yes—
423#385C2318yes—
424#385C2314yes—
425#384C2312yes—
426#384C2318yes—
427#384C2312yes—
428#384C2312yes—
429#384C2312yes—
430#384C2314yes—
431#384C2311yescharacteristic
432#384C2312yes—
433#384C2311yescharacteristic
434#383C2314yes—
435#383C2318yes—
436#382C2312yes—
437#382C2318yes—
438#382C2314yes—
439#382C2318yes—
440#382C2312yes—
441#382C2312yes—
442#382C2311yescharacteristic
443#382C2311yescharacteristic
444#382C2312yes—
445#382C2312yes—
446#381C2314yes—
447#381C2318yes—
448#381C2312yes—
449#381C2312yes—
450#380C2314yes—
451#380C2314yes—
452#380C2314yes—
453#380C2314yes—
454#380C2318yes—
455#380C2318yes—
456#380C2314yes—
457#380C2318yes—
458#380C2314yes—
459#380C2312yes—
460#380C2312yes—
461#380C2312yes—
462#380C2312yes—
463#379C2312yes—
464#379C2312yes—
465C4×C4⋊C4C2312yes—
466C4×C4⋊C4C2314yes—
467C4×C4⋊C4C2314yes—
468C4×C4⋊C4C2314yes—
469C4×C4⋊C4C2314yes—
470C4×C4⋊C4C2318yes—
471C4×C4⋊C4C2318yes—
472C4×C4⋊C4C2314yes—
473C4×C4⋊C4C2318yes—
474C4×C4⋊C4C2318yes—
475C4×C4⋊C4C2318yes—
476C4×C4⋊C4C2314yes—
477C4×C4⋊C4C2312yes—
478C4×C4⋊C4C2312yes—
479C4×C4⋊C4C2314yes—
480C4×C4⋊C4C2312yes—
481C4×C22⋊C4C2312yes—
482C4×C22⋊C4C2314yes—
483C4×C22⋊C4C2314yes—
484C4×C22⋊C4C2318yes—
485C4×C22⋊C4C2318yes—
486C4×C22⋊C4C2314yes—
487C4×C22⋊C4C2314yes—
488C4×C22⋊C4C2318yes—
489C4×C22⋊C4C2318yes—
490C4×C22⋊C4C2318yes—
491C4×C22⋊C4C2314yes—
492C4×C22⋊C4C2312yes—
493C4×C22⋊C4C2312yes—
494C4×C22⋊C4C2312yes—
495C4×C22⋊C4C2312yes—
496C4×C22⋊C4C2312yes—
497#376C2312yes—
498#376C2318yes—
499C2×#95C2314yes—
500C2×#95C2314yes—
501C2×#95C2314yes—
502C2×#95C2312yes—
503C43C2312yes—
504C25C2411yescharacteristic
505C2×#41—24no—
506C2×#41—24no—
507C2×#41—24no—
508C2×#41—24no—
509C2×#41—24no—
510C2×#41#4118yes—
511C22×Q8—24no—
512C22×Q8—24no—
513C22×Q8—24no—
514C22×Q8C2412yes—
515C22×Q8C2412yes—
516C22×Q8C2411yescharacteristic
517C22×Q8C2411yescharacteristic
518C22×D4C2412yes—
519C22×D4C2411yescharacteristic
520C22×D4C2412yes—
521C22×D4C2411yescharacteristic
522C22×D4C2414yes—
523C22×D4C2414yes—
524C22×D4C2414yes—
525C23×C4—24no—
526C23×C4—24no—
527C23×C4—24no—
528C23×C4C2412yes—
529C23×C4C2411yescharacteristic
530C23×C4C2412yes—
531C23×C4C2412yes—
532C23×C4C2412yes—
533C23×C4C2412yes—
534C23×C4C2414yes—
535C23×C4C2412yes—
536C23×C4C2412yes—
537C23×C4C2412yes—
538C23×C4C2412yes—
539C23×C4C2412yes—
540C23×C4C2414yes—
541C23×C4C2414yes—
542C23×C4C2414yes—
543C23×C4C2411yescharacteristic
544C4⋊Q8—24no—
545C4⋊Q8—28no—
546C4⋊Q8—44no—
547#127—24no—
548#126—48no—
549#126—416no—
550#124—24no—
551#124—24no—
552#124—28no—
553#124—44no—
554#123—28no—
555#123—216no—
556#123—28no—
557#123—48no—
558C22⋊Q8—28no—
559C22⋊Q8—216no—
560C22⋊Q8—28no—
561C22⋊Q8—48no—
562C22⋊Q8—48no—
563C22⋊Q8—44no—
564C22⋊Q8—44no—
565#121—28no—
566#121—216no—
567#121—28no—
568#121—48no—
569#120—28no—
570#120—28no—
571C4×Q8—28no—
572C4×Q8—216no—
573C4×Q8—216no—
574C4×Q8—44no—
575C4×Q8—44no—
576C4×Q8—44no—
577C4×D4—216no—
578C4×D4—216no—
579C4×D4—28no—
580C4×D4—216no—
581C4×D4—216no—
582C4×D4—44no—
583C4×D4—44no—
584C4×D4—44no—
585C4×D4—48no—
586C4×D4—48no—
587C4×D4—48no—
588#117—24no—
589#117—24no—
590#117—24no—
591#117—24no—
592#117—24no—
593#117—216no—
594#117—28no—
595#117—48no—
596#117—48no—
597#117—44no—
598#117—44no—
599#117—44no—
600#117#4118yes—
601C2×C4⋊C4—24no—
602C2×C4⋊C4—24no—
603C2×C4⋊C4—24no—
604C2×C4⋊C4—48no—
605C2×C4⋊C4—416no—
606C2×C4⋊C4—44no—
607C2×C4⋊C4—44no—
608C2×C4⋊C4—44no—
609C2×C4⋊C4—44no—
610C2×C4⋊C4C2412yes—
611C2×C4⋊C4C2411yescharacteristic
612C2×C4⋊C4C2412yes—
613C2×C4⋊C4C2411yescharacteristic
614C2×C4⋊C4C2412yes—
615C2×C4⋊C4C2411yescharacteristic
616C2×C4⋊C4C2414yes—
617C2×C4⋊C4C2418yes—
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2412yes—
620C2×C4⋊C4C2412yes—
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2414yes—
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2418yes—
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2418yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2418yes—
636C2×C4⋊C4C2418yes—
637C2×C4⋊C4C2418yes—
638C2×C4⋊C4C2418yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2418yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2418yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2412yes—
650C2×C22⋊C4—44no—
651C2×C22⋊C4—44no—
652C2×C22⋊C4—44no—
653C2×C22⋊C4C2412yes—
654C2×C22⋊C4C2412yes—
655C2×C22⋊C4C2412yes—
656C2×C22⋊C4C2412yes—
657C2×C22⋊C4C2412yes—
658C2×C22⋊C4C2414yes—
659C2×C22⋊C4C2412yes—
660C2×C22⋊C4C2412yes—
661C2×C22⋊C4C2414yes—
662C2×C22⋊C4C2414yes—
663C2×C22⋊C4C2414yes—
664C2×C22⋊C4C2414yes—
665C2×C22⋊C4C2414yes—
666C2×C22⋊C4C2414yes—
667C2×C22⋊C4C2414yes—
668C2×C22⋊C4C2418yes—
669C2×C22⋊C4C2418yes—
670C2×C22⋊C4C2418yes—
671C2×C22⋊C4C2412yes—
672C2×C22⋊C4C2412yes—
673C2×C22⋊C4C2414yes—
674C2×C22⋊C4C2414yes—
675C2×C22⋊C4C2414yes—
676C2×C22⋊C4C2414yes—
677C2×C22⋊C4C2414yes—
678C2×C22⋊C4C2414yes—
679C2×C22⋊C4C2414yes—
680C2×C22⋊C4C2418yes—
681C2×C22⋊C4C2418yes—
682C2×C22⋊C4C2418yes—
683C2×C22⋊C4C2414yes—
684C2×C22⋊C4C2414yes—
685C2×C22⋊C4C2414yes—
686C2×C22⋊C4C2412yes—
687C2×C42—24no—
688C2×C42—24no—
689C2×C42—28no—
690C2×C42—44no—
691C2×C42C2411yescharacteristic
692C2×C42C2412yes—
693C2×C42C2412yes—
694C2×C42C2412yes—
695C2×C42C2412yes—
696C2×C42C2418yes—
697C2×C42C2412yes—
698C2×C42C2412yes—
699C2×C42C2412yes—
700C2×C42C2414yes—
701C2×C42C2411yescharacteristic
702C2×C42C2411yescharacteristic
703C2×C42C2411yescharacteristic
704C2×C42C2418yes—
705C2×C42C2414yes—
706C2×C42C2414yes—
707C2×C42C2414yes—
708C2×C42C2414yes—
709C2×C42C2418yes—
710C2×C42C2414yes—
711C2×C42C2418yes—
712C2×C42C2412yes—
713#95C2418yes—
714#95C2412yes—
715#95C2418yes—
716#95C2412yes—
717#95C2412yes—
718#95C2412yes—
719#95C2418yes—
720#95C2418yes—
721#95C2418yes—
722#95C2418yes—
723#95C2414yes—
724#95C2418yes—
725#95C2414yes—
726#95C2414yes—
727#95C2418yes—
728#95C2414yes—
729#95C2414yes—
730#95C2414yes—
731#95C2414yes—
732#95C2414yes—
733#95C2418yes—
734#95C2418yes—
735#95C2418yes—
736#95C2414yes—
737#95C2418yes—
738#95C2418yes—
739#95C2414yes—
740#95C2418yes—
741#95C2414yes—
742#95C2418yes—
743#95C2414yes—
744#95C2418yes—
745#95C2414yes—
746#95C2414yes—
747#95C2414yes—
748#95C2414yes—
749#95C2418yes—
750C24—22no—
751C24—22no—
752C24—22no—
753C24—42no—
754C24—42no—
755C24C2512yes—
756C24C2512yes—
757C24C2512yes—
758C24C2511yescharacteristic
759#41—232no—
760#41—416no—
761C2×Q8—22no—
762C2×Q8—24no—
763C2×Q8—24no—
764C2×Q8—24no—
765C2×Q8—22no—
766C2×Q8—24no—
767C2×Q8—22no—
768C2×Q8—22no—
769C2×Q8—22no—
770C2×Q8—24no—
771C2×Q8—24no—
772C2×Q8—416no—
773C2×Q8C2×#4114yes—
774C2×D4—24no—
775C2×D4—24no—
776C2×D4—24no—
777C2×D4—24no—
778C2×D4—24no—
779C2×D4—28no—
780C2×D4—28no—
781C2×D4—22no—
782C2×D4—22no—
783C2×D4—22no—
784C2×D4—28no—
785C2×D4—22no—
786C2×D4—22no—
787C2×D4—44no—
788C2×D4—44no—
789C2×D4—44no—
790C2×D4—44no—
791C2×D4—44no—
792C2×D4—44no—
793C2×D4C2×#4118yes—
794C2×D4C2×#4114yes—
795C22×C4—24no—
796C22×C4—24no—
797C22×C4—24no—
798C22×C4—24no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—24no—
802C22×C4—22no—
803C22×C4—24no—
804C22×C4—24no—
805C22×C4—24no—
806C22×C4—24no—
807C22×C4—24no—
808C22×C4—28no—
809C22×C4—24no—
810C22×C4—24no—
811C22×C4—24no—
812C22×C4—24no—
813C22×C4—24no—
814C22×C4—24no—
815C22×C4—24no—
816C22×C4—24no—
817C22×C4—24no—
818C22×C4—24no—
819C22×C4—28no—
820C22×C4—44no—
821C22×C4—42no—
822C22×C4—42no—
823C22×C4—44no—
824C22×C4—44no—
825C22×C4—42no—
826C22×C4—44no—
827C22×C4—44no—
828C22×C4—44no—
829C22×C4—44no—
830C22×C4—48no—
831C22×C4—48no—
832C22×C4—48no—
833C22×C4—416no—
834C22×C4C2×#4118yes—
835C22×C4C2×#4114yes—
836C22×C4C2×#4114yes—
837C22×C4H(5,𝔽2)14yes—
838C22×C4C2512yes—
839C22×C4C2512yes—
840C22×C4C2512yes—
841C22×C4C2514yes—
842C22×C4C2514yes—
843C22×C4C2512yes—
844C22×C4C2514yes—
845C22×C4C2512yes—
846C22×C4C2514yes—
847C22×C4C2514yes—
848C22×C4C2512yes—
849C22×C4C2512yes—
850C22×C4C2514yes—
851C22×C4C2512yes—
852C22×C4C2512yes—
853C22×C4C2514yes—
854C22×C4C2514yes—
855C22×C4C2512yes—
856C22×C4C2512yes—
857C22×C4C2511yescharacteristic
858C22×C4C2511yescharacteristic
859C4⋊C4—28no—
860C4⋊C4—24no—
861C4⋊C4—216no—
862C4⋊C4—24no—
863C4⋊C4—24no—
864C4⋊C4—28no—
865C4⋊C4—28no—
866C4⋊C4—28no—
867C4⋊C4—216no—
868C4⋊C4—24no—
869C4⋊C4—24no—
870C4⋊C4—24no—
871C4⋊C4—24no—
872C4⋊C4—24no—
873C4⋊C4—24no—
874C4⋊C4—22no—
875C4⋊C4—22no—
876C4⋊C4—22no—
877C4⋊C4—22no—
878C4⋊C4—216no—
879C4⋊C4—28no—
880C4⋊C4—28no—
881C4⋊C4—48no—
882C4⋊C4—48no—
883C4⋊C4—48no—
884C4⋊C4—44no—
885C4⋊C4—44no—
886C4⋊C4—44no—
887C4⋊C4—48no—
888C4⋊C4—44no—
889C4⋊C4—44no—
890C4⋊C4—44no—
891C4⋊C4—44no—
892C4⋊C4—48no—
893C4⋊C4—44no—
894C4⋊C4—44no—
895C4⋊C4—44no—
896C4⋊C4—44no—
897C4⋊C4—48no—
898C4⋊C4C2×#4118yes—
899C22⋊C4—24no—
900C22⋊C4—24no—
901C22⋊C4—24no—
902C22⋊C4—28no—
903C22⋊C4—28no—
904C22⋊C4—216no—
905C22⋊C4—24no—
906C22⋊C4—24no—
907C22⋊C4—28no—
908C22⋊C4—28no—
909C22⋊C4—28no—
910C22⋊C4—28no—
911C22⋊C4—28no—
912C22⋊C4—24no—
913C22⋊C4—24no—
914C22⋊C4—28no—
915C22⋊C4—42no—
916C22⋊C4—42no—
917C22⋊C4—48no—
918C22⋊C4—48no—
919C22⋊C4—44no—
920C22⋊C4—48no—
921C22⋊C4—44no—
922C22⋊C4—44no—
923C22⋊C4—44no—
924C22⋊C4—44no—
925C22⋊C4—44no—
926C22⋊C4—44no—
927C22⋊C4—44no—
928C22⋊C4—44no—
929C22⋊C4—48no—
930C22⋊C4—44no—
931C22⋊C4—48no—
932C22⋊C4C2×#4118yes—
933C42—22no—
934C42—22no—
935C42—24no—
936C42—28no—
937C42—24no—
938C42—22no—
939C42—22no—
940C42—24no—
941C42—24no—
942C42—216no—
943C42—24no—
944C42—24no—
945C42—24no—
946C42—48no—
947C42—48no—
948C42—44no—
949C42—44no—
950C42—44no—
951C42—44no—
952C42—44no—
953C42—48no—
954C42C2×#4118yes—
955C23—22no—
956C23—22no—
957C23—22no—
958C23—22no—
959C23—24no—
960C23—24no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—22no—
966C23—22no—
967C23—22no—
968C23—24no—
969C23—22no—
970C23—22no—
971C23—22no—
972C23—24no—
973C23—44no—
974C23—44no—
975C23—44no—
976C23—84no—
977C23—84no—
978C23C22×#4114yes—
979C23C22×#4112yes—
980C23C22×#4112yes—
981C23C2×H(5,𝔽2)12yes—
982C23C2611yescharacteristic
983Q8—28no—
984Q8—48no—
985Q8—48no—
986Q8—44no—
987D4—216no—
988D4—28no—
989D4—48no—
990D4—44no—
991D4—88no—
992D4—88no—
993D4—88no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—24no—
998C2×C4—24no—
999C2×C4—22no—
1000C2×C4—216no—
1001C2×C4—24no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—24no—
1006C2×C4—24no—
1007C2×C4—24no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—24no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—24no—
1019C2×C4—24no—
1020C2×C4—22no—
1021C2×C4—24no—
1022C2×C4—24no—
1023C2×C4—24no—
1024C2×C4—22no—
1025C2×C4—24no—
1026C2×C4—28no—
1027C2×C4—24no—
1028C2×C4—22no—
1029C2×C4—24no—
1030C2×C4—22no—
1031C2×C4—28no—
1032C2×C4—24no—
1033C2×C4—24no—
1034C2×C4—22no—
1035C2×C4—24no—
1036C2×C4—28no—
1037C2×C4—24no—
1038C2×C4—22no—
1039C2×C4—24no—
1040C2×C4—24no—
1041C2×C4—22no—
1042C2×C4—416no—
1043C2×C4—48no—
1044C2×C4—44no—
1045C2×C4—48no—
1046C2×C4—48no—
1047C2×C4—48no—
1048C2×C4—48no—
1049C2×C4—84no—
1050C2×C4—84no—
1051C2×C4—84no—
1052C2×C4—84no—
1053C2×C4—164no—
1054C2×C4—164no—
1055C2×C4—164no—
1056C2×C4#553116yes—
1057C2×C4C22×#4118yes—
1058C2×C4C22×#4114yes—
1059C2×C4C22×#4112yes—
1060C2×C4C22×#4112yes—
1061C2×C4C22×#4112yes—
1062C2×C4C22×#4112yes—
1063C2×C4C2×H(5,𝔽2)12yes—
1064C2×C4C2×H(5,𝔽2)12yes—
1065C2×C4#58514yes—
1066C22—24no—
1067C22—24no—
1068C22—22no—
1069C22—22no—
1070C22—28no—
1071C22—24no—
1072C22—44no—
1073C22—42no—
1074C22—42no—
1075C22—42no—
1076C22—44no—
1077C22—42no—
1078C22—42no—
1079C22—44no—
1080C22—42no—
1081C22—42no—
1082C22—42no—
1083C22—42no—
1084C22—42no—
1085C22—42no—
1086C22—42no—
1087C22—88no—
1088C22C2×#55314yes—
1089C22C23×#4111yescharacteristic
1090C22C23×#4111yescharacteristic
1091C22C22×H(5,𝔽2)11yescharacteristic
1092C22C2×#58512yes—
1093C222−1+612yes—
1094C4—24no—
1095C4—28no—
1096C4—24no—
1097C4—44no—
1098C4—42no—
1099C4—44no—
1100C4—42no—
1101C4—42no—
1102C4—44no—
1103C4—44no—
1104C4—44no—
1105C4—42no—
1106C4—42no—
1107C4—42no—
1108C4—44no—
1109C4—42no—
1110C4—42no—
1111C4—42no—
1112C4—44no—
1113C4C2×#55314yes—
1114C4C2×#55314yes—
1115C2—24no—
1116C2—44no—
1117C2—82no—
1118C2—82no—
1119C2C22×#55311yescharacteristic
1120C2#6283611yescharacteristic
1121C2#6288711yescharacteristic
1122C2#6299312yes—
1123C2#6300912yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#34743C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59699C2semidirect
2. #59575C2semidirect
3. #59387C2semidirect
4. #59306C2semidirect
5. #59302C2semidirect
6. #45342C2semidirect
7. #45158C2semidirect
8. #45130C2semidirect
9. #45015C2semidirect
10. #44085C2semidirect
11. #35661C2semidirect
12. #35633C2semidirect
13. #35627C2semidirect
14. #35621C2semidirect
15. #35619C2semidirect
16. #35557C2semidirect
17. #34814C2semidirect
18. C2×#2499C2semidirect
20. #34268C2semidirect
21. #34254C2semidirect
22. #34208C2semidirect
23. #34201C2semidirect
24. #34201C2semidirect
25. #34183C2semidirect
41. #2793C22semidirect
43. #2781C22semidirect
45. #2776C22semidirect
48. #2747C22semidirect
50. #2608C22semidirect
53. #2590C22semidirect
54. #2585C22semidirect
55. #2578C22semidirect
56. #2577C22semidirect
57. #2576C22semidirect
58. #2571C22semidirect
59. #2570C22semidirect
60. #2570C22semidirect
61. #2547C22semidirect
62. #2546C22semidirect
63. #2545C22semidirect
64. #2544C22semidirect
69. #2530C22semidirect
72. #2525C22semidirect
74. #2512C22semidirect
75. #2511C22semidirect
76. #2509C22semidirect
77. #2508C22semidirect
80. #2503C22semidirect
81. #2502C22semidirect
86. #2499C22semidirect
87. #2499C22semidirect
89. #2497C22semidirect
91. #2496C22semidirect
98. #2481C22semidirect
100. #2447C22semidirect
101. #2446C22semidirect
115. #2417C22semidirect
117. #2415C22semidirect
123. #2373C22semidirect
124. #2367C22semidirect
125. #2365C22semidirect
132. #2356C22semidirect
133. #2355C22semidirect
138. #2352C22semidirect
139. #2352C22semidirect
140. Q8×C4⋊C4C22semidirect
142. D4×C4⋊C4C22semidirect
143. #2345C22semidirect
145. #2328C22semidirect
146. #2327C22semidirect
147. #2323C22semidirect
150. #2320C22semidirect
154. #2317C22semidirect
155. #2317C22semidirect
162. C4×#124C22semidirect
163. C4×#124C22semidirect
164. C4×C22⋊Q8C22semidirect
172. #2295C22semidirect
177. #2285C22semidirect
179. C2×#384C22semidirect

Maximal subgroups

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

subgroupindex
#596992
#595752
#593872
#593062
#593022
#453422
#451582
#451302
#450152
#440852
#356612
#356332
#356272
#356212
#356192
#355572
#348142
C2×#24992
#347432
#342682
#342542
#342082
#342012
#341832