Finite Group Databasebeta

← #7681819

Subgroups — #7681819

Order 512.

5080 conjugacy classes of subgroups.

The subgroup lattice has 1105 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59682C214yesmaximal, complemented
2#59585C214yesmaximal, complemented
3#59210C218yesmaximal, complemented
4#45156C214yesmaximal, complemented
5#45155C214yesmaximal, complemented
6#43059C218yesmaximal, complemented
7#39820C214yesmaximal, complemented
8#39816C214yesmaximal, complemented
9#39731C214yesmaximal, complemented
10#36605C214yesmaximal, complemented
11#35674C211yesmaximal, characteristic, complemented
12#35630C211yesmaximal, characteristic, complemented
13#35626C211yesmaximal, characteristic, complemented
14#35558C211yesmaximal, characteristic, complemented
15#35327C211yesmaximal, characteristic
16#35327C211yesmaximal, characteristic
17#35316C211yesmaximal, characteristic, complemented
18#34948C211yesmaximal, characteristic, complemented
19C2×#2545C211yesmaximal, characteristic, complemented
20#34269C211yesmaximal, characteristic
21#34268C211yesmaximal, characteristic, complemented
22#34211C211yesmaximal, characteristic, complemented
23#34187C211yesmaximal, characteristic, complemented
24C4⋊C4×#41C211yesmaximal, characteristic, complemented
25C4×#536C211yesmaximal, characteristic, complemented
26C2×#536C2211yescharacteristic
27C2×#536C2211yescharacteristic
28C2×#535C2211yescharacteristic
29C22×C4⋊Q8C2211yescharacteristic
30C22×#124C2211yescharacteristic
31C22×#124C2211yescharacteristic
32C2×#519C2211yescharacteristic
33C2×#518C2211yescharacteristic
34C2×C4×#41C2211yescharacteristic
35C2×C4×#41C2211yescharacteristic
36C2×C4×#41C2211yescharacteristic
37C22×C4×Q8C2211yescharacteristic
38#2857C2214yescomplemented
39#2850C2214yes—
40#2850C2214yes—
41#2793C2218yescomplemented
42#2790C2218yescomplemented
43#2786C2218yescomplemented
44#2783C2218yescomplemented
45#2782C2218yescomplemented
46#2781C2218yescomplemented
47#2779C2218yescomplemented
48#2772C2218yescomplemented
49#2765C2218yescomplemented
50#2757C2218yescomplemented
51#2750C2218yescomplemented
52#2725C2218yescomplemented
53#2621C2214yescomplemented
54#2620C2214yes—
55#2620C2214yes—
56#2608C2218yescomplemented
57#2595C2218yescomplemented
58#2594C2218yescomplemented
59#2587C2218yescomplemented
60#2587C2218yescomplemented
61#2579C2218yescomplemented
62#2578C2218yescomplemented
63#2576C2218yescomplemented
64#2573C2218yescomplemented
65#2571C2212yescomplemented
66#2570C2212yescomplemented
67#2570C2212yescomplemented
68#2569C2214yes—
69#2552C2212yescomplemented
70#2547C2214yescomplemented
71#2546C2214yescomplemented
72#2545C2212yes—
73#2545C2214yes—
74#2545C2214yes—
75#2545C2212yes—
76#2545C2214yes—
77#2545C2212yes—
78#2545C2212yes—
79#2545C2212yes—
80#2545C2212yes—
81#2544C2212yes—
82#2544C2214yes—
83#2544C2212yes—
84#2534C2214yes—
85#2534C2218yes—
86#2534C2214yes—
87#2531C2218yescomplemented
88#2529C2218yescomplemented
89#2525C2218yescomplemented
90#2525C2218yescomplemented
91#2515C2218yescomplemented
92#2514C2214yescomplemented
93#2514C2214yescomplemented
94#2513C2214yes—
95#2513C2214yes—
96#2512C2214yes—
97#2512C2214yes—
98#2511C2214yescomplemented
99#2511C2214yescomplemented
100#2510C2218yescomplemented
101#2493C2218yes—
102#2486C2218yes—
103#2484C2218yes—
104#2483C2218yes—
105#2481C2218yescomplemented
106#2480C2218yes—
107#2468C2218yescomplemented
108#2460C2218yescomplemented
109#2447C2214yes—
110#2447C2214yes—
111#2447C2214yes—
112#2447C2214yes—
113#2446C2214yescomplemented
114#2446C2214yescomplemented
115#2446C2214yescomplemented
116#2446C2214yescomplemented
117#2442C2214yes—
118#2402C2214yescomplemented
119C2×#396C2214yes—
120#2373C2218yescomplemented
121#2367C2214yes—
122#2367C2214yes—
123#2367C2214yes—
124#2367C2214yescomplemented
125#2366C2214yes—
126#2365C2214yescomplemented
127#2359C2218yes—
128#2358C2218yes—
129#2356C2214yescomplemented
130#2356C2214yescomplemented
131#2355C2214yescomplemented
132#2355C2214yescomplemented
133#2353C2218yescomplemented
134#2351C2212yescomplemented
135Q8×C4⋊C4C2212yescomplemented
136#2349C2214yes—
137#2349C2212yescomplemented
138D4×C4⋊C4C2214yes—
139D4×C4⋊C4C2212yescomplemented
140#2342C2214yes—
141#2342C2214yes—
142#2327C2212yescomplemented
143#2326C2214yes—
144#2326C2212yescomplemented
145#2324C2214yes—
146#2323C2214yescomplemented
147#2323C2214yescomplemented
148#2322C2214yes—
149#2317C2211yescharacteristic
150#2313C2214yes—
151#2311C2211yescharacteristic
152#2310C2211yescharacteristic
153#2310C2211yescharacteristic
154#2310C2211yescharacteristic
155#2310C2211yescharacteristic
156#2310C2211yescharacteristic
157#2309C2211yescharacteristic
158#2309C2211yescharacteristic
159C4×C4⋊Q8C2212yescomplemented
160C4×#125C2214yescomplemented
161C4×#124C2214yes—
162C4×#124C2212yescomplemented
163C4×C22⋊Q8C2214yescomplemented
164C4×C22⋊Q8C2214yescomplemented
165C4×#123C2214yes—
166C4×#121C2214yes—
167#2296C2211yescharacteristic
168#2296C2211yescharacteristic
169#2296C2211yescharacteristic
170#2296C2211yescharacteristic
171#2296C2212yescomplemented
172#2296C2212yescomplemented
173C2×#391C2211yescharacteristic
174C2×#390C2211yescharacteristic
175C2×#388C2214yes—
176#2285C2211yescharacteristic
177#2285C2211yescharacteristic
178#2285C2211yescharacteristic
179#2285C2211yescharacteristic
180#2285C2212yescomplemented
181#2283C2214yes—
182#2274C2211yescharacteristic
183#2274C2211yescharacteristic
184C4×#117C2211yescharacteristic
185C2×C4×C4⋊C4C2211yescharacteristic
186C2×C4×C4⋊C4C2212yescomplemented
187C22×#41C2311yescharacteristic
188C23×Q8C2311yescharacteristic
189C23×Q8C2311yescharacteristic
190C23×D4C2311yescharacteristic
191#536—28no—
192#536—28no—
193#535—28no—
194C2×C4⋊Q8—44no—
195C2×C4⋊Q8C2312yes—
196C2×C4⋊Q8C2312yes—
197C2×C4⋊Q8C2312yes—
198C2×C4⋊Q8C2312yes—
199C2×C4⋊Q8C2314yes—
200C2×#127C2312yes—
201C2×#126C2318yes—
202C2×#125C2314yes—
203C2×#124—28no—
204C2×#124—44no—
205C2×#124C2312yes—
206C2×#124C2312yes—
207C2×#124C2312yes—
208C2×#124C2312yes—
209C2×#124C2312yes—
210C2×#124C2312yes—
211C2×#124C2312yes—
212C2×#124C2312yes—
213C2×#124C2312yes—
214C2×#124C2314yes—
215C2×#123C2314yes—
216C2×#123C2314yes—
217C2×C22⋊Q8C2314yes—
218C2×C22⋊Q8C2314yes—
219C2×#121C2314yes—
220C2×#120C2314yes—
221#519—44no—
222#518—44no—
223C4×#41—28no—
224C4×#41—44no—
225C4×#41—44no—
226C2×C4×Q8—28no—
227C2×C4×Q8C2311yescharacteristic
228C2×C4×Q8C2312yes—
229C2×C4×Q8C2312yes—
230C2×C4×Q8C2312yes—
231C2×C4×Q8C2311yescharacteristic
232C2×C4×Q8C2312yes—
233C2×C4×Q8C2314yes—
234C2×C4×Q8C2314yes—
235C2×C4×Q8C2312yes—
236C2×C4×Q8C2312yes—
237C2×C4×D4C2312yes—
238C2×C4×D4C2311yescharacteristic
239C2×C4×D4C2312yes—
240C2×C4×D4C2311yescharacteristic
241C2×C4×D4C2318yes—
242C2×C4×D4C2314yes—
243C2×C4×D4C2314yes—
244C2×C4×D4C2314yes—
245C2×C4×D4C2314yes—
246C2×C4×D4C2312yes—
247C2×C4×D4C2312yes—
248C2×#117C2311yescharacteristic
249C2×#117C2311yescharacteristic
250C2×#117C2311yescharacteristic
251C2×#117C2311yescharacteristic
252C2×#117C2311yescharacteristic
253C2×#117C2311yescharacteristic
254C2×#117C2311yescharacteristic
255C2×#117C2312yes—
256C2×#117C2312yes—
257C2×#117C2312yes—
258C2×#117C2314yes—
259C22×C4⋊C4C2311yescharacteristic
260C22×C4⋊C4C2312yes—
261C22×C4⋊C4C2314yes—
262C22×C4⋊C4C2312yes—
263C22×C4⋊C4C2314yes—
264C22×C22⋊C4C2312yes—
265C22×C22⋊C4C2312yes—
266C22×C22⋊C4C2314yes—
267C22×C22⋊C4C2314yes—
268C22×C22⋊C4C2314yes—
269C22×C42C2312yes—
270C22×C42C2312yes—
271C22×C42C2311yescharacteristic
272C22×C42C2311yescharacteristic
273C22×C42C2312yes—
274C22×C42C2312yes—
275C22×C42C2311yescharacteristic
276#401C2318yes—
277#400C2314yes—
278#400C2314yes—
279#400C2314yes—
280#400C2314yes—
281#400C2318yes—
282#400C2318yes—
283#400C2318yes—
284#400C2318yes—
285#400C2318yes—
286#398C2314yes—
287#398C2314yes—
288#398C2314yes—
289#398C2314yes—
290#398C2318yes—
291#398C2318yes—
292#398C2318yes—
293#398C2318yes—
294#397C2318yes—
295#397C2318yes—
296#397C2318yes—
297#397C2318yes—
298#397C2318yes—
299#397C2318yes—
300#397C2318yes—
301#397C2318yes—
302#397C2318yes—
303#396C2318yes—
304#396C2318yes—
305#396C2318yes—
306#396C2318yes—
307#396C2318yes—
308#396C2318yes—
309#396C2318yes—
310#396C2318yes—
311#396C2318yes—
312#394C2318yes—
313#394C2318yes—
314#394C2318yes—
315#394C2318yes—
316#391C2312yes—
317#391C2312yes—
318#391C2314yes—
319#391C2314yes—
320#391C2312yes—
321#391C2314yes—
322#391C2314yes—
323#391C2314yes—
324#391C2314yes—
325#391C2314yes—
326#391C2314yes—
327#391C2312yes—
328#391C2312yes—
329#391C2312yes—
330#391C2314yes—
331#391C2312yes—
332#390C2314yes—
333#390C2314yes—
334#390C2314yes—
335#390C2312yes—
336#390C2312yes—
337#390C2312yes—
338#390C2312yes—
339#390C2318yes—
340#390C2314yes—
341#390C2312yes—
342#389C2314yes—
343#389C2314yes—
344#389C2318yes—
345#389C2312yes—
346#389C2312yes—
347#389C2312yes—
348#389C2312yes—
349#389C2314yes—
350#389C2318yes—
351#389C2318yes—
352#389C2314yes—
353#389C2314yes—
354#389C2318yes—
355#389C2314yes—
356#389C2312yes—
357#389C2312yes—
358#389C2314yes—
359#389C2312yes—
360#389C2312yes—
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#388C2318yes—
377#388C2318yes—
378#388C2318yes—
379#388C2318yes—
380#388C2318yes—
381#388C2318yes—
382#387C2314yes—
383#387C2314yes—
384#387C2314yes—
385#387C2314yes—
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#386C2314yes—
402#386C2318yes—
403#386C2318yes—
404#386C2318yes—
405#386C2318yes—
406#386C2318yes—
407#386C2318yes—
408#385C2314yes—
409#385C2314yes—
410#385C2314yes—
411#385C2318yes—
412#385C2314yes—
413#385C2318yes—
414#385C2318yes—
415#385C2318yes—
416#385C2318yes—
417#385C2318yes—
418#385C2318yes—
419#385C2314yes—
420#385C2314yes—
421#385C2314yes—
422#385C2314yes—
423#385C2314yes—
424#384C2312yes—
425#384C2312yes—
426#384C2312yes—
427#384C2312yes—
428#384C2312yes—
429#384C2314yes—
430#383C2318yes—
431#383C2318yes—
432#382C2314yes—
433#382C2312yes—
434#382C2312yes—
435#382C2312yes—
436#382C2312yes—
437#382C2314yes—
438#382C2312yes—
439#382C2318yes—
440#381C2314yes—
441#381C2314yes—
442#381C2314yes—
443#381C2314yes—
444#381C2314yes—
445#381C2318yes—
446#381C2318yes—
447#380C2314yes—
448#380C2312yes—
449#380C2312yes—
450#380C2312yes—
451#380C2314yes—
452#380C2314yes—
453#380C2314yes—
454#380C2318yes—
455#380C2312yes—
456#380C2318yes—
457#380C2314yes—
458#379C2314yes—
459#379C2314yes—
460C4×C4⋊C4C2312yes—
461C4×C4⋊C4C2312yes—
462C4×C4⋊C4C2314yes—
463C4×C4⋊C4C2314yes—
464C4×C4⋊C4C2314yes—
465C4×C4⋊C4C2314yes—
466C4×C4⋊C4C2318yes—
467C4×C4⋊C4C2312yes—
468C4×C4⋊C4C2311yescharacteristic
469C4×C4⋊C4C2311yescharacteristic
470C4×C4⋊C4C2311yescharacteristic
471C4×C4⋊C4C2312yes—
472C4×C4⋊C4C2314yes—
473C4×C4⋊C4C2314yes—
474C4×C4⋊C4C2314yes—
475C4×C4⋊C4C2318yes—
476C4×C4⋊C4C2318yes—
477C4×C4⋊C4C2312yes—
478C4×C4⋊C4C2314yes—
479C4×C4⋊C4C2312yes—
480C4×C4⋊C4C2312yes—
481C4×C4⋊C4C2314yes—
482C4×C4⋊C4C2314yes—
483C4×C4⋊C4C2312yes—
484C4×C4⋊C4C2312yes—
485C4×C4⋊C4C2312yes—
486C4×C4⋊C4C2312yes—
487C4×C4⋊C4C2312yes—
488C4×C4⋊C4C2311yescharacteristic
489C4×C22⋊C4C2314yes—
490C4×C22⋊C4C2314yes—
491C4×C22⋊C4C2312yes—
492C4×C22⋊C4C2318yes—
493C4×C22⋊C4C2318yes—
494C4×C22⋊C4C2318yes—
495C4×C22⋊C4C2312yes—
496C4×C22⋊C4C2318yes—
497C4×C22⋊C4C2318yes—
498#376C2312yes—
499#376C2318yes—
500C2×#95C2312yes—
501C2×#95C2314yes—
502C2×#95C2314yes—
503C43C2312yes—
504C25C2412yes—
505C2×#41—24no—
506C2×#41—24no—
507C2×#41#4118yes—
508C22×Q8—24no—
509C22×Q8—24no—
510C22×Q8—24no—
511C22×Q8—24no—
512C22×Q8—24no—
513C22×Q8—24no—
514C22×Q8C2412yes—
515C22×Q8C2412yes—
516C22×Q8C2412yes—
517C22×Q8C2412yes—
518C22×Q8C2411yescharacteristic
519C22×D4—24no—
520C22×D4—24no—
521C22×D4—24no—
522C22×D4C2412yes—
523C22×D4C2412yes—
524C22×D4C2412yes—
525C22×D4C2411yescharacteristic
526C22×D4C2418yes—
527C23×C4C2412yes—
528C23×C4C2412yes—
529C23×C4C2412yes—
530C23×C4C2412yes—
531C23×C4C2412yes—
532C23×C4C2412yes—
533C23×C4C2412yes—
534C23×C4C2414yes—
535C23×C4C2412yes—
536C23×C4C2418yes—
537C23×C4C2414yes—
538C23×C4C2411yescharacteristic
539C23×C4C2411yescharacteristic
540C23×C4C2411yescharacteristic
541C4⋊Q8—28no—
542C4⋊Q8—28no—
543C4⋊Q8—44no—
544C4⋊Q8—44no—
545C4⋊Q8—48no—
546#127—28no—
547#126—416no—
548#125—48no—
549#124—28no—
550#124—28no—
551#124—28no—
552#124—28no—
553#124—28no—
554#124—28no—
555#124—28no—
556#124—44no—
557#124—44no—
558#124—48no—
559#123—216no—
560#123—216no—
561C22⋊Q8—216no—
562C22⋊Q8—216no—
563#121—216no—
564#120—216no—
565C4×Q8—28no—
566C4×Q8—28no—
567C4×Q8—28no—
568C4×Q8—28no—
569C4×Q8—24no—
570C4×Q8—24no—
571C4×Q8—44no—
572C4×Q8—44no—
573C4×Q8—48no—
574C4×Q8—48no—
575C4×D4—28no—
576C4×D4—28no—
577C4×D4—24no—
578C4×D4—24no—
579C4×D4—44no—
580C4×D4—44no—
581C4×D4—48no—
582C4×D4—48no—
583C4×D4—416no—
584C4×D4—48no—
585C4×D4—48no—
586#117—24no—
587#117—24no—
588#117—24no—
589#117—24no—
590#117—24no—
591#117—24no—
592#117—24no—
593#117—28no—
594#117—44no—
595#117—44no—
596#117—48no—
597C2×C4⋊C4—28no—
598C2×C4⋊C4—24no—
599C2×C4⋊C4—44no—
600C2×C4⋊C4—48no—
601C2×C4⋊C4—48no—
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2412yes—
604C2×C4⋊C4C2412yes—
605C2×C4⋊C4C2414yes—
606C2×C4⋊C4C2414yes—
607C2×C4⋊C4C2412yes—
608C2×C4⋊C4C2414yes—
609C2×C4⋊C4C2412yes—
610C2×C4⋊C4C2412yes—
611C2×C4⋊C4C2412yes—
612C2×C4⋊C4C2411yescharacteristic
613C2×C4⋊C4C2411yescharacteristic
614C2×C4⋊C4C2412yes—
615C2×C4⋊C4C2412yes—
616C2×C4⋊C4C2412yes—
617C2×C4⋊C4C2412yes—
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2414yes—
620C2×C4⋊C4C2418yes—
621C2×C4⋊C4C2418yes—
622C2×C4⋊C4C2414yes—
623C2×C4⋊C4C2418yes—
624C2×C4⋊C4C2418yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2418yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2418yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2414yes—
644C2×C22⋊C4—28no—
645C2×C22⋊C4—28no—
646C2×C22⋊C4—48no—
647C2×C22⋊C4—48no—
648C2×C22⋊C4—48no—
649C2×C22⋊C4C2412yes—
650C2×C22⋊C4C2412yes—
651C2×C22⋊C4C2418yes—
652C2×C22⋊C4C2414yes—
653C2×C22⋊C4C2414yes—
654C2×C22⋊C4C2414yes—
655C2×C22⋊C4C2414yes—
656C2×C22⋊C4C2412yes—
657C2×C22⋊C4C2412yes—
658C2×C22⋊C4C2412yes—
659C2×C22⋊C4C2412yes—
660C2×C22⋊C4C2412yes—
661C2×C22⋊C4C2412yes—
662C2×C22⋊C4C2412yes—
663C2×C22⋊C4C2418yes—
664C2×C22⋊C4C2418yes—
665C2×C22⋊C4C2418yes—
666C2×C22⋊C4C2418yes—
667C2×C22⋊C4C2418yes—
668C2×C22⋊C4C2418yes—
669C2×C22⋊C4C2418yes—
670C2×C22⋊C4C2414yes—
671C2×C22⋊C4C2414yes—
672C2×C22⋊C4C2418yes—
673C2×C22⋊C4C2418yes—
674C2×C22⋊C4C2418yes—
675C2×C22⋊C4C2418yes—
676C2×C22⋊C4C2418yes—
677C2×C42—28no—
678C2×C42—24no—
679C2×C42—24no—
680C2×C42—28no—
681C2×C42—44no—
682C2×C42—44no—
683C2×C42#4118yes—
684C2×C42C2412yes—
685C2×C42C2412yes—
686C2×C42C2411yescharacteristic
687C2×C42C2411yescharacteristic
688C2×C42C2412yes—
689C2×C42C2412yes—
690C2×C42C2412yes—
691C2×C42C2412yes—
692C2×C42C2412yes—
693C2×C42C2412yes—
694C2×C42C2412yes—
695C2×C42C2412yes—
696C2×C42C2412yes—
697C2×C42C2414yes—
698C2×C42C2414yes—
699C2×C42C2411yescharacteristic
700C2×C42C2411yescharacteristic
701C2×C42C2418yes—
702C2×C42C2414yes—
703C2×C42C2414yes—
704C2×C42C2418yes—
705C2×C42C2414yes—
706C2×C42C2418yes—
707C2×C42C2414yes—
708C2×C42C2411yescharacteristic
709C2×C42C2411yescharacteristic
710C2×C42C2411yescharacteristic
711C2×C42C2411yescharacteristic
712#95C2412yes—
713#95C2414yes—
714#95C2418yes—
715#95C2412yes—
716#95C2414yes—
717#95C2414yes—
718#95C2412yes—
719#95C2412yes—
720#95C2418yes—
721#95C2414yes—
722#95C2414yes—
723#95C2414yes—
724#95C2418yes—
725#95C2418yes—
726#95C2414yes—
727#95C2414yes—
728#95C2414yes—
729#95C2418yes—
730#95C2418yes—
731#95C2418yes—
732#95C2418yes—
733#95C2418yes—
734#95C2418yes—
735#95C2418yes—
736#95C2414yes—
737#95C2418yes—
738#95C2414yes—
739#95C2414yes—
740#95C2414yes—
741#95C2414yes—
742#95C2414yes—
743#95C2414yes—
744#95C2418yes—
745#95C2414yes—
746#95C2418yes—
747#95C2414yes—
748#95C2418yes—
749#95C2418yes—
750C24—24no—
751C24—24no—
752C24—24no—
753C24—44no—
754C24—44no—
755C24C2514yes—
756C24C2512yes—
757C24C2511yescharacteristic
758#41—232no—
759C2×Q8—22no—
760C2×Q8—24no—
761C2×Q8—24no—
762C2×Q8—24no—
763C2×Q8—24no—
764C2×Q8—24no—
765C2×Q8—24no—
766C2×Q8—24no—
767C2×Q8—24no—
768C2×Q8—22no—
769C2×Q8—24no—
770C2×Q8—24no—
771C2×Q8—24no—
772C2×Q8—24no—
773C2×Q8—416no—
774C2×Q8—416no—
775C2×Q8C2×#4114yes—
776C2×D4—24no—
777C2×D4—24no—
778C2×D4—216no—
779C2×D4—22no—
780C2×D4—24no—
781C2×D4—24no—
782C2×D4—24no—
783C2×D4—24no—
784C2×D4—22no—
785C2×D4—24no—
786C2×D4—24no—
787C2×D4—48no—
788C2×D4—48no—
789C2×D4—416no—
790C2×D4C2×#4118yes—
791C2×D4C2×#4114yes—
792C22×C4—24no—
793C22×C4—24no—
794C22×C4—24no—
795C22×C4—24no—
796C22×C4—24no—
797C22×C4—24no—
798C22×C4—24no—
799C22×C4—24no—
800C22×C4—24no—
801C22×C4—24no—
802C22×C4—24no—
803C22×C4—24no—
804C22×C4—24no—
805C22×C4—24no—
806C22×C4—28no—
807C22×C4—42no—
808C22×C4—44no—
809C22×C4—42no—
810C22×C4—42no—
811C22×C4—44no—
812C22×C4—44no—
813C22×C4—44no—
814C22×C4—44no—
815C22×C4—42no—
816C22×C4—44no—
817C22×C4—44no—
818C22×C4—44no—
819C22×C4—42no—
820C22×C4—48no—
821C22×C4—48no—
822C22×C4—48no—
823C22×C4C2×#4118yes—
824C22×C4C2×#4114yes—
825C22×C4C2×#4114yes—
826C22×C4C2×#4114yes—
827C22×C4C2×#4114yes—
828C22×C4H(5,𝔽2)14yes—
829C22×C4C2514yes—
830C22×C4C2512yes—
831C22×C4C2512yes—
832C22×C4C2514yes—
833C22×C4C2514yes—
834C22×C4C2514yes—
835C22×C4C2514yes—
836C22×C4C2514yes—
837C22×C4C2512yes—
838C22×C4C2514yes—
839C22×C4C2514yes—
840C22×C4C2514yes—
841C22×C4C2512yes—
842C22×C4C2512yes—
843C22×C4C2511yescharacteristic
844C22×C4C2511yescharacteristic
845C22×C4C2511yescharacteristic
846C22×C4C2511yescharacteristic
847C22×C4C2512yes—
848C22×C4C2512yes—
849C22×C4C2511yescharacteristic
850C22×C4C2511yescharacteristic
851C4⋊C4—24no—
852C4⋊C4—24no—
853C4⋊C4—28no—
854C4⋊C4—28no—
855C4⋊C4—24no—
856C4⋊C4—24no—
857C4⋊C4—22no—
858C4⋊C4—22no—
859C4⋊C4—24no—
860C4⋊C4—24no—
861C4⋊C4—24no—
862C4⋊C4—216no—
863C4⋊C4—216no—
864C4⋊C4—24no—
865C4⋊C4—24no—
866C4⋊C4—24no—
867C4⋊C4—24no—
868C4⋊C4—24no—
869C4⋊C4—28no—
870C4⋊C4—28no—
871C4⋊C4—28no—
872C4⋊C4—42no—
873C4⋊C4—44no—
874C4⋊C4—42no—
875C4⋊C4—44no—
876C4⋊C4—48no—
877C4⋊C4—48no—
878C4⋊C4—44no—
879C4⋊C4—44no—
880C4⋊C4—44no—
881C4⋊C4—44no—
882C4⋊C4—44no—
883C4⋊C4—44no—
884C4⋊C4—44no—
885C4⋊C4—44no—
886C4⋊C4—44no—
887C4⋊C4—44no—
888C4⋊C4—48no—
889C4⋊C4—44no—
890C4⋊C4—44no—
891C4⋊C4—44no—
892C4⋊C4—48no—
893C22⋊C4—24no—
894C22⋊C4—24no—
895C22⋊C4—24no—
896C22⋊C4—24no—
897C22⋊C4—216no—
898C22⋊C4—216no—
899C22⋊C4—24no—
900C22⋊C4—24no—
901C22⋊C4—24no—
902C22⋊C4—28no—
903C22⋊C4—28no—
904C22⋊C4—28no—
905C22⋊C4—28no—
906C22⋊C4—24no—
907C22⋊C4—24no—
908C22⋊C4—216no—
909C22⋊C4—216no—
910C22⋊C4—48no—
911C22⋊C4—48no—
912C22⋊C4—48no—
913C22⋊C4—48no—
914C22⋊C4—48no—
915C22⋊C4—48no—
916C22⋊C4—44no—
917C22⋊C4—44no—
918C22⋊C4—48no—
919C22⋊C4—48no—
920C22⋊C4—48no—
921C42—24no—
922C42—24no—
923C42—24no—
924C42—28no—
925C42—28no—
926C42—24no—
927C42—24no—
928C42—24no—
929C42—22no—
930C42—22no—
931C42—22no—
932C42—22no—
933C42—24no—
934C42—24no—
935C42—24no—
936C42—24no—
937C42—24no—
938C42—44no—
939C42—44no—
940C42—44no—
941C42—48no—
942C42—48no—
943C42—44no—
944C42—48no—
945C42C2×#4114yes—
946C42C2×#4114yes—
947C42C2×#4114yes—
948C42C2×#4114yes—
949C23—22no—
950C23—22no—
951C23—22no—
952C23—22no—
953C23—24no—
954C23—24no—
955C23—24no—
956C23—24no—
957C23—24no—
958C23—28no—
959C23—28no—
960C23—48no—
961C23—88no—
962C23—84no—
963C23—84no—
964C23—88no—
965C23C22×#4114yes—
966C23C22×#4112yes—
967C23C22×#4112yes—
968C23C2×H(5,𝔽2)12yes—
969C23C2611yescharacteristic
970Q8—28no—
971Q8—48no—
972Q8—48no—
973Q8—48no—
974Q8—48no—
975D4—216no—
976D4—28no—
977D4—48no—
978D4—48no—
979D4—816no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—216no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—24no—
992C2×C4—24no—
993C2×C4—24no—
994C2×C4—24no—
995C2×C4—24no—
996C2×C4—24no—
997C2×C4—24no—
998C2×C4—24no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—24no—
1003C2×C4—24no—
1004C2×C4—24no—
1005C2×C4—24no—
1006C2×C4—24no—
1007C2×C4—28no—
1008C2×C4—24no—
1009C2×C4—24no—
1010C2×C4—24no—
1011C2×C4—24no—
1012C2×C4—24no—
1013C2×C4—24no—
1014C2×C4—22no—
1015C2×C4—24no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—24no—
1019C2×C4—24no—
1020C2×C4—24no—
1021C2×C4—24no—
1022C2×C4—24no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—24no—
1026C2×C4—22no—
1027C2×C4—24no—
1028C2×C4—44no—
1029C2×C4—44no—
1030C2×C4—48no—
1031C2×C4—48no—
1032C2×C4—48no—
1033C2×C4—48no—
1034C2×C4—84no—
1035C2×C4—88no—
1036C2×C4—84no—
1037C2×C4—84no—
1038C2×C4—88no—
1039C2×C4—168no—
1040C2×C4#553116yes—
1041C2×C4C22×#4112yes—
1042C2×C4C22×#4112yes—
1043C2×C4C22×#4112yes—
1044C2×C4C22×#4112yes—
1045C2×C4C22×#4114yes—
1046C2×C4C22×#4112yes—
1047C2×C4C22×#4112yes—
1048C2×C4C22×#4112yes—
1049C2×C4C22×#4112yes—
1050C2×C4C2×H(5,𝔽2)12yes—
1051C2×C4C2×H(5,𝔽2)12yes—
1052C2×C4#58514yes—
1053C22—24no—
1054C22—22no—
1055C22—22no—
1056C22—24no—
1057C22—28no—
1058C22—24no—
1059C22—42no—
1060C22—42no—
1061C22—44no—
1062C22—48no—
1063C22—44no—
1064C22—44no—
1065C22—48no—
1066C22—44no—
1067C22—168no—
1068C22C2×#55314yes—
1069C22C23×#4111yescharacteristic
1070C22C23×#4111yescharacteristic
1071C22C22×H(5,𝔽2)11yescharacteristic
1072C22C2×#58512yes—
1073C222−1+612yes—
1074C4—22no—
1075C4—22no—
1076C4—22no—
1077C4—22no—
1078C4—24no—
1079C4—24no—
1080C4—44no—
1081C4—44no—
1082C4—44no—
1083C4—42no—
1084C4—44no—
1085C4—42no—
1086C4—42no—
1087C4—42no—
1088C4—44no—
1089C4—42no—
1090C4—44no—
1091C4—44no—
1092C4—44no—
1093C4—44no—
1094C4C2×#55314yes—
1095C4C2×#55314yes—
1096C2—24no—
1097C2—44no—
1098C2—84no—
1099C2C22×#55311yescharacteristic
1100C2#6281511yescharacteristic
1101C2#6286011yescharacteristic
1102C2#6295412yes—
1103C2#6299512yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#535C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59682C2semidirect
2. #59585C2semidirect
3. #59210C2semidirect
4. #45156C2semidirect
5. #45155C2semidirect
6. #43059C2semidirect
7. #39820C2semidirect
8. #39816C2semidirect
9. #39731C2semidirect
10. #36605C2semidirect
11. #35674C2semidirect
12. #35630C2semidirect
13. #35626C2semidirect
14. #35558C2semidirect
17. #35316C2semidirect
18. #34948C2semidirect
19. C2×#2545C2semidirect
21. #34268C2semidirect
22. #34211C2semidirect
23. #34187C2semidirect
24. C4⋊C4×#41C2semidirect
25. C4×#536C2semidirect
38. #2857C22semidirect
41. #2793C22semidirect
42. #2790C22semidirect
43. #2786C22semidirect
44. #2783C22semidirect
45. #2782C22semidirect
46. #2781C22semidirect
47. #2779C22semidirect
48. #2772C22semidirect
49. #2765C22semidirect
50. #2757C22semidirect
51. #2750C22semidirect
52. #2725C22semidirect
53. #2621C22semidirect
56. #2608C22semidirect
57. #2595C22semidirect
58. #2594C22semidirect
59. #2587C22semidirect
60. #2587C22semidirect
61. #2579C22semidirect
62. #2578C22semidirect
63. #2576C22semidirect
64. #2573C22semidirect
65. #2571C22semidirect
66. #2570C22semidirect
67. #2570C22semidirect
69. #2552C22semidirect
70. #2547C22semidirect
71. #2546C22semidirect
87. #2531C22semidirect
88. #2529C22semidirect
89. #2525C22semidirect
90. #2525C22semidirect
91. #2515C22semidirect
92. #2514C22semidirect
93. #2514C22semidirect
98. #2511C22semidirect
99. #2511C22semidirect
100. #2510C22semidirect
105. #2481C22semidirect
107. #2468C22semidirect
108. #2460C22semidirect
113. #2446C22semidirect
114. #2446C22semidirect
115. #2446C22semidirect
116. #2446C22semidirect
118. #2402C22semidirect
120. #2373C22semidirect
124. #2367C22semidirect
126. #2365C22semidirect
129. #2356C22semidirect
130. #2356C22semidirect
131. #2355C22semidirect
132. #2355C22semidirect
133. #2353C22semidirect
134. #2351C22semidirect
135. Q8×C4⋊C4C22semidirect
137. #2349C22semidirect
139. D4×C4⋊C4C22semidirect
142. #2327C22semidirect
144. #2326C22semidirect
146. #2323C22semidirect
147. #2323C22semidirect
159. C4×C4⋊Q8C22semidirect
160. C4×#125C22semidirect
162. C4×#124C22semidirect
163. C4×C22⋊Q8C22semidirect
164. C4×C22⋊Q8C22semidirect
171. #2296C22semidirect
172. #2296C22semidirect
180. #2285C22semidirect
186. C2×C4×C4⋊C4C22semidirect

Maximal subgroups

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

subgroupindex
#596822
#595852
#592102
#451562
#451552
#430592
#398202
#398162
#397312
#366052
#356742
#356302
#356262
#355582
#353272
#353162
#349482
C2×#25452
#342692
#342682
#342112
#341872
C4⋊C4×#412
C4×#5362