Finite Group Databasebeta

← #7678745

Subgroups — #7678745

Order 512.

5026 conjugacy classes of subgroups.

The subgroup lattice has 1064 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59908C214yesmaximal, complemented
2#59427C214yesmaximal, complemented
3#59237C214yesmaximal, complemented
4#59231C214yesmaximal, complemented
5#45436C212yesmaximal, complemented
6#45428C212yesmaximal, complemented
7#45228C214yesmaximal, complemented
8#45151C212yesmaximal, complemented
9#45078C214yesmaximal, complemented
10#44963C212yesmaximal, complemented
11#38935C214yesmaximal, complemented
12#38281C218yesmaximal, complemented
13#36359C214yesmaximal, complemented
14#35628C212yesmaximal, complemented
15#35621C212yesmaximal, complemented
16#35180C212yesmaximal, complemented
17#35178C211yesmaximal, characteristic, complemented
18#34938C211yesmaximal, characteristic, complemented
19#34937C211yesmaximal, characteristic
20#34252C212yesmaximal, complemented
21#34208C211yesmaximal, characteristic, complemented
22#34189C211yesmaximal, characteristic, complemented
23C2×#2356C211yesmaximal, characteristic, complemented
24C4×#536C211yesmaximal, characteristic, complemented
25C2×#536C2211yescharacteristic
26C2×#536C2212yes—
27C2×#533C2212yes—
28C2×#532C2211yescharacteristic
29C2×#532C2212yes—
30C2×#520C2212yes—
31C2×C4×#41C2211yescharacteristic
32C22×C4×Q8C2211yescharacteristic
33#2854C2214yes—
34#2850C2218yes—
35#2795C2218yes—
36#2783C2218yes—
37#2783C2218yes—
38#2775C2218yes—
39#2769C2218yes—
40#2769C2218yes—
41#2756C2218yes—
42#2744C2218yes—
43#2737C2218yes—
44#2737C2218yes—
45#2731C2218yes—
46#2686C2218yes—
47#2639C2218yes—
48#2618C2214yes—
49#2612C2218yes—
50#2612C2218yes—
51#2610C2218yes—
52#2592C2214yes—
53#2592C2214yes—
54#2592C2214yes—
55#2592C2214yes—
56#2574C2218yes—
57#2572C2218yes—
58#2568C2214yes—
59#2568C2214yes—
60#2568C2214yes—
61#2563C2214yes—
62#2562C2214yes—
63#2562C2214yes—
64#2552C2212yes—
65#2551C2212yes—
66#2550C2212yes—
67#2550C2212yes—
68#2549C2212yes—
69#2549C2212yes—
70#2548C2214yes—
71#2548C2212yes—
72#2548C2211yescharacteristic
73#2547C2214yes—
74#2547C2214yes—
75#2547C2211yescharacteristic
76#2546C2214yes—
77#2546C2212yes—
78#2546C2211yescharacteristic
79#2545C2214yes—
80#2545C2214yes—
81#2545C2212yes—
82#2544C2212yes—
83#2544C2214yes—
84#2543C2212yes—
85#2543C2212yes—
86#2541C2211yescharacteristic
87#2538C2214yes—
88#2536C2212yes—
89#2536C2212yes—
90#2532C2218yes—
91#2532C2218yes—
92#2531C2218yes—
93#2531C2218yes—
94#2529C2218yes—
95#2526C2218yes—
96#2526C2218yes—
97#2518C2218yes—
98#2518C2218yes—
99#2497C2218yes—
100#2495C2218yes—
101#2492C2214yes—
102#2492C2214yes—
103#2489C2214yes—
104#2489C2214yes—
105#2488C2218yes—
106#2488C2218yes—
107#2476C2218yes—
108#2440C2214yes—
109#2439C2218yes—
110#2425C2218yes—
111#2425C2218yes—
112#2417C2214yes—
113#2417C2214yes—
114#2416C2214yes—
115#2415C2214yes—
116#2415C2214yes—
117#2399C2212yes—
118#2399C2212yes—
119#2392C2212yes—
120#2392C2212yes—
121#2372C2218yes—
122#2364C2214yes—
123#2364C2214yes—
124#2357C2212yes—
125#2357C2214yes—
126#2357C2212yes—
127#2356C2214yes—
128#2356C2214yes—
129#2356C2212yes—
130#2356C2212yes—
131#2356C2212yes—
132#2356C2214yes—
133#2356C2212yes—
134#2356C2212yes—
135#2356C2212yes—
136#2355C2214yes—
137#2354C2214yes—
138#2353C2214yes—
139#2353C2214yes—
140#2352C2214yes—
141#2352C2214yes—
142#2347C2214yes—
143#2346C2218yes—
144#2346C2214yes—
145#2345C2214yes—
146#2344C2214yes—
147#2328C2212yes—
148#2327C2212yes—
149#2327C2212yes—
150#2326C2212yes—
151#2323C2214yes—
152#2322C2214yes—
153#2318C2218yes—
154#2317C2211yescharacteristic
155#2314C2214yes—
156#2311C2212yes—
157#2311C2211yescharacteristic
158#2311C2212yes—
159#2311C2212yes—
160#2310C2211yescharacteristic
161C4×C4⋊Q8C2214yes—
162C4×C4⋊Q8C2212yes—
163C4×#124C2212yes—
164C4×#124C2214yes—
165C4×C22⋊Q8C2214yes—
166C4×#123C2214yes—
167C4×#121C2214yes—
168#2297C2212yes—
169#2296C2212yes—
170C2×#391C2212yes—
171#2290C2218yes—
172C2×#387C2214yes—
173#2285C2211yescharacteristic
174#2283C2212yes—
175#2283C2212yes—
176C2×#383C2212yes—
177C2×#382C2211yescharacteristic
178#2274C2212yes—
179C4×#117C2211yescharacteristic
180C2×C4×C4⋊C4C2212yes—
181C2×C4×C4⋊C4C2211yescharacteristic
182C2×#376C2212yes—
183C22×#41C2311yescharacteristic
184C22×#41C2312yes—
185C23×Q8C2311yescharacteristic
186#536—28no—
187#536—48no—
188#533—48no—
189#532—28no—
190#532—48no—
191C2×C4⋊Q8C2312yes—
192C2×C4⋊Q8C2311yescharacteristic
193C2×C4⋊Q8C2314yes—
194C2×C4⋊Q8C2312yes—
195C2×C4⋊Q8C2312yes—
196C2×C4⋊Q8C2314yes—
197C2×C4⋊Q8C2312yes—
198C2×#127C2311yescharacteristic
199C2×#127C2312yes—
200C2×#125C2312yes—
201C2×#125C2312yes—
202C2×#124C2312yes—
203C2×#124C2312yes—
204C2×#124C2312yes—
205C2×#124C2312yes—
206C2×#124C2314yes—
207C2×#124C2318yes—
208C2×#123C2314yes—
209C2×#123C2318yes—
210C2×C22⋊Q8C2314yes—
211C2×C22⋊Q8C2314yes—
212C2×C22⋊Q8C2314yes—
213C2×C22⋊Q8C2314yes—
214C2×C22⋊Q8C2314yes—
215C2×#121C2312yes—
216C2×#121C2312yes—
217C2×#121C2314yes—
218C2×#121C2314yes—
219C2×#121C2314yes—
220#520—216no—
221C4×#41—28no—
222C2×C4×Q8—28no—
223C2×C4×Q8C2311yescharacteristic
224C2×C4×Q8C2312yes—
225C2×C4×Q8C2312yes—
226C2×C4×Q8C2312yes—
227C2×C4×Q8C2311yescharacteristic
228C2×C4×Q8C2314yes—
229C2×C4×Q8C2312yes—
230C2×C4×Q8C2314yes—
231C2×C4×Q8C2314yes—
232C2×C4×D4C2318yes—
233C2×C4×D4C2312yes—
234C2×C4×D4C2311yescharacteristic
235C2×C4×D4C2314yes—
236C2×C4×D4C2312yes—
237C2×C4×D4C2312yes—
238C2×C4×D4C2312yes—
239C2×C4×D4C2311yescharacteristic
240C2×C4×D4C2314yes—
241C2×C4×D4C2314yes—
242C2×#117C2311yescharacteristic
243C2×#117C2311yescharacteristic
244C2×#117C2312yes—
245C2×#117C2312yes—
246C2×#117C2314yes—
247C2×#117C2318yes—
248C2×#117C2311yescharacteristic
249C22×C4⋊C4C2311yescharacteristic
250C22×C4⋊C4C2312yes—
251C22×C4⋊C4C2312yes—
252C22×C4⋊C4C2314yes—
253C22×C4⋊C4C2312yes—
254C22×C42C2312yes—
255C22×C42C2312yes—
256C22×C42C2312yes—
257C22×C42C2314yes—
258C22×C42C2311yescharacteristic
259#400C2318yes—
260#400C2318yes—
261#400C2318yes—
262#400C2318yes—
263#400C2318yes—
264#400C2318yes—
265#398C2314yes—
266#398C2312yes—
267#398C2314yes—
268#398C2318yes—
269#398C2312yes—
270#398C2314yes—
271#398C2314yes—
272#398C2314yes—
273#398C2314yes—
274#398C2318yes—
275#397C2318yes—
276#397C2318yes—
277#397C2318yes—
278#397C2318yes—
279#397C2312yes—
280#397C2312yes—
281#397C2318yes—
282#397C2318yes—
283#396C2318yes—
284#396C2318yes—
285#396C2318yes—
286#396C2314yes—
287#396C2314yes—
288#396C2318yes—
289#395C2314yes—
290#395C2314yes—
291#395C2314yes—
292#395C2314yes—
293#394C2318yes—
294#394C2318yes—
295#394C2318yes—
296#394C2314yes—
297#394C2314yes—
298#394C2314yes—
299#394C2314yes—
300#394C2312yes—
301#394C2312yes—
302#394C2318yes—
303#393C2318yes—
304#393C2318yes—
305#393C2318yes—
306#393C2318yes—
307#392C2312yes—
308#392C2312yes—
309#391C2312yes—
310#391C2312yes—
311#391C2314yes—
312#391C2314yes—
313#391C2312yes—
314#391C2314yes—
315#391C2314yes—
316#391C2314yes—
317#391C2314yes—
318#391C2312yes—
319#391C2312yes—
320#391C2318yes—
321#391C2314yes—
322#391C2314yes—
323#391C2318yes—
324#391C2318yes—
325#391C2314yes—
326#391C2314yes—
327#390C2318yes—
328#390C2312yes—
329#390C2314yes—
330#390C2314yes—
331#390C2314yes—
332#390C2312yes—
333#390C2312yes—
334#390C2318yes—
335#390C2314yes—
336#389C2318yes—
337#389C2314yes—
338#389C2314yes—
339#389C2314yes—
340#389C2314yes—
341#389C2314yes—
342#389C2318yes—
343#389C2312yes—
344#389C2312yes—
345#389C2312yes—
346#389C2318yes—
347#389C2312yes—
348#389C2314yes—
349#389C2318yes—
350#388C2318yes—
351#388C2318yes—
352#388C2318yes—
353#388C2318yes—
354#388C2318yes—
355#388C2318yes—
356#388C2318yes—
357#388C2318yes—
358#388C2318yes—
359#388C2318yes—
360#388C2318yes—
361#388C2318yes—
362#388C2318yes—
363#388C2318yes—
364#388C2318yes—
365#388C2318yes—
366#388C2318yes—
367#388C2314yes—
368#388C2318yes—
369#388C2318yes—
370#388C2318yes—
371#388C2318yes—
372#388C2318yes—
373#388C2314yes—
374#387C2318yes—
375#387C2318yes—
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#386C2318yes—
389#386C2314yes—
390#386C2318yes—
391#386C2318yes—
392#386C2314yes—
393#386C2318yes—
394#386C2314yes—
395#386C2318yes—
396#386C2318yes—
397#386C2318yes—
398#386C2314yes—
399#386C2314yes—
400#385C2314yes—
401#385C2314yes—
402#385C2318yes—
403#385C2314yes—
404#384C2312yes—
405#384C2314yes—
406#384C2312yes—
407#383C2318yes—
408#383C2318yes—
409#383C2314yes—
410#383C2314yes—
411#383C2314yes—
412#383C2314yes—
413#382C2318yes—
414#382C2318yes—
415#382C2318yes—
416#382C2312yes—
417#382C2312yes—
418#382C2318yes—
419#382C2312yes—
420#382C2312yes—
421#382C2312yes—
422#382C2311yescharacteristic
423#382C2311yescharacteristic
424#381C2314yes—
425#381C2314yes—
426#381C2318yes—
427#381C2314yes—
428#380C2314yes—
429#380C2314yes—
430#380C2314yes—
431#380C2314yes—
432#380C2314yes—
433#380C2314yes—
434#380C2314yes—
435#380C2318yes—
436#380C2314yes—
437#380C2312yes—
438#380C2318yes—
439#380C2312yes—
440#380C2318yes—
441C4×C4⋊C4C2314yes—
442C4×C4⋊C4C2312yes—
443C4×C4⋊C4C2312yes—
444C4×C4⋊C4C2318yes—
445C4×C4⋊C4C2314yes—
446C4×C4⋊C4C2314yes—
447C4×C4⋊C4C2314yes—
448C4×C4⋊C4C2314yes—
449C4×C4⋊C4C2314yes—
450C4×C4⋊C4C2314yes—
451C4×C4⋊C4C2314yes—
452C4×C4⋊C4C2314yes—
453C4×C4⋊C4C2318yes—
454C4×C4⋊C4C2312yes—
455C4×C4⋊C4C2314yes—
456C4×C4⋊C4C2312yes—
457C4×C4⋊C4C2311yescharacteristic
458C4×C4⋊C4C2311yescharacteristic
459C4×C4⋊C4C2311yescharacteristic
460C4×C4⋊C4C2311yescharacteristic
461C4×C4⋊C4C2312yes—
462C4×C4⋊C4C2312yes—
463C4×C22⋊C4C2318yes—
464C4×C22⋊C4C2318yes—
465C4×C22⋊C4C2318yes—
466C4×C22⋊C4C2314yes—
467C4×C22⋊C4C2312yes—
468C4×C22⋊C4C2314yes—
469C4×C22⋊C4C2314yes—
470C4×C22⋊C4C2318yes—
471C4×C22⋊C4C2318yes—
472C4×C22⋊C4C2314yes—
473C4×C22⋊C4C2312yes—
474#376C2312yes—
475#376C2314yes—
476#376C2318yes—
477#376C2318yes—
478#376C2314yes—
479#376C2314yes—
480#376C2314yes—
481C2×#95C2314yes—
482C2×#95C2312yes—
483C2×#95C2312yes—
484C2×#95C2314yes—
485C2×#95C2314yes—
486C2×#95C2311yescharacteristic
487C2×#95C2311yescharacteristic
488C43C2312yes—
489C2×#41—24no—
490C2×#41—28no—
491C2×#41—28no—
492C2×#41—24no—
493C2×#41—24no—
494C2×#41—28no—
495C22×Q8—24no—
496C22×Q8—24no—
497C22×Q8—24no—
498C22×Q8C2412yes—
499C22×Q8C2412yes—
500C22×Q8C2412yes—
501C22×Q8C2411yescharacteristic
502C22×Q8C2414yes—
503C22×Q8C2414yes—
504C22×D4C2414yes—
505C22×D4C2412yes—
506C22×D4C2411yescharacteristic
507C22×D4C2412yes—
508C22×D4C2412yes—
509C22×D4C2414yes—
510C22×D4C2412yes—
511C22×D4C2414yes—
512C23×C4C2414yes—
513C23×C4C2412yes—
514C23×C4C2412yes—
515C23×C4C2412yes—
516C23×C4C2412yes—
517C23×C4C2418yes—
518C23×C4C2414yes—
519C23×C4C2412yes—
520C23×C4C2412yes—
521C23×C4C2412yes—
522C23×C4C2411yescharacteristic
523C23×C4C2411yescharacteristic
524C23×C4C2411yescharacteristic
525C4⋊Q8—24no—
526C4⋊Q8—28no—
527C4⋊Q8—44no—
528C4⋊Q8—44no—
529C4⋊Q8—44no—
530C4⋊Q8—48no—
531C4⋊Q8—48no—
532#127—24no—
533#127—44no—
534#125—44no—
535#125—44no—
536#124—28no—
537#124—28no—
538#124—416no—
539#124—44no—
540#124—44no—
541#124—48no—
542#123—216no—
543#123—416no—
544C22⋊Q8—216no—
545C22⋊Q8—48no—
546C22⋊Q8—48no—
547C22⋊Q8—48no—
548C22⋊Q8—48no—
549#121—28no—
550#121—28no—
551#121—48no—
552#121—48no—
553#121—48no—
554C4×Q8—28no—
555C4×Q8—28no—
556C4×Q8—28no—
557C4×Q8—28no—
558C4×Q8—24no—
559C4×Q8—24no—
560C4×Q8—216no—
561C4×Q8—48no—
562C4×Q8—48no—
563C4×D4—28no—
564C4×D4—28no—
565C4×D4—232no—
566C4×D4—24no—
567C4×D4—24no—
568C4×D4—216no—
569C4×D4—28no—
570C4×D4—28no—
571C4×D4—48no—
572C4×D4—48no—
573#117—24no—
574#117—24no—
575#117—28no—
576#117—216no—
577#117—28no—
578#117—416no—
579#117#4118yes—
580C2×C4⋊C4—24no—
581C2×C4⋊C4—28no—
582C2×C4⋊C4—28no—
583C2×C4⋊C4—216no—
584C2×C4⋊C4—44no—
585C2×C4⋊C4C2414yes—
586C2×C4⋊C4C2414yes—
587C2×C4⋊C4C2418yes—
588C2×C4⋊C4C2412yes—
589C2×C4⋊C4C2412yes—
590C2×C4⋊C4C2414yes—
591C2×C4⋊C4C2414yes—
592C2×C4⋊C4C2412yes—
593C2×C4⋊C4C2412yes—
594C2×C4⋊C4C2414yes—
595C2×C4⋊C4C2411yescharacteristic
596C2×C4⋊C4C2411yescharacteristic
597C2×C4⋊C4C2412yes—
598C2×C4⋊C4C2412yes—
599C2×C4⋊C4C2412yes—
600C2×C4⋊C4C2412yes—
601C2×C4⋊C4C2412yes—
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2412yes—
604C2×C4⋊C4C2418yes—
605C2×C4⋊C4C2412yes—
606C2×C4⋊C4C2412yes—
607C2×C4⋊C4C2418yes—
608C2×C4⋊C4C2414yes—
609C2×C4⋊C4C2414yes—
610C2×C4⋊C4C2414yes—
611C2×C4⋊C4C2414yes—
612C2×C4⋊C4C2414yes—
613C2×C4⋊C4C2414yes—
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2414yes—
616C2×C4⋊C4C2418yes—
617C2×C4⋊C4C2418yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2414yes—
620C2×C4⋊C4C2414yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2414yes—
623C2×C4⋊C4C2412yes—
624C2×C22⋊C4C2414yes—
625C2×C22⋊C4C2412yes—
626C2×C22⋊C4C2418yes—
627C2×C22⋊C4C2412yes—
628C2×C22⋊C4C2412yes—
629C2×C22⋊C4C2412yes—
630C2×C22⋊C4C2414yes—
631C2×C22⋊C4C2414yes—
632C2×C22⋊C4C2414yes—
633C2×C22⋊C4C2418yes—
634C2×C22⋊C4C2418yes—
635C2×C22⋊C4C2414yes—
636C2×C22⋊C4C2414yes—
637C2×C22⋊C4C2414yes—
638C2×C22⋊C4C2414yes—
639C2×C22⋊C4C2414yes—
640C2×C22⋊C4C2418yes—
641C2×C22⋊C4C2418yes—
642C2×C22⋊C4C2418yes—
643C2×C22⋊C4C2418yes—
644C2×C22⋊C4C2418yes—
645C2×C22⋊C4C2418yes—
646C2×C22⋊C4C2414yes—
647C2×C22⋊C4C2418yes—
648C2×C22⋊C4C2418yes—
649C2×C22⋊C4C2414yes—
650C2×C22⋊C4C2412yes—
651C2×C42—28no—
652C2×C42—28no—
653C2×C42—28no—
654C2×C42—48no—
655C2×C42#4118yes—
656C2×C42C2412yes—
657C2×C42C2418yes—
658C2×C42C2412yes—
659C2×C42C2414yes—
660C2×C42C2418yes—
661C2×C42C2412yes—
662C2×C42C2412yes—
663C2×C42C2412yes—
664C2×C42C2412yes—
665C2×C42C2412yes—
666C2×C42C2412yes—
667C2×C42C2414yes—
668C2×C42C2414yes—
669C2×C42C2418yes—
670C2×C42C2414yes—
671C2×C42C2414yes—
672C2×C42C2418yes—
673C2×C42C2418yes—
674C2×C42C2411yescharacteristic
675C2×C42C2412yes—
676C2×C42C2411yescharacteristic
677C2×C42C2411yescharacteristic
678C2×C42C2411yescharacteristic
679#95C2412yes—
680#95C2411yescharacteristic
681#95C2411yescharacteristic
682#95C2414yes—
683#95C2418yes—
684#95C2414yes—
685#95C2418yes—
686#95C2414yes—
687#95C2414yes—
688#95C2418yes—
689#95C2418yes—
690#95C2412yes—
691#95C2411yescharacteristic
692#95C2411yescharacteristic
693#95C2418yes—
694#95C2418yes—
695#95C2414yes—
696#95C2412yes—
697#95C2412yes—
698#95C2414yes—
699#95C2418yes—
700#95C2414yes—
701#95C2414yes—
702#95C2418yes—
703#95C2418yes—
704#95C2418yes—
705#95C2412yes—
706#95C2412yes—
707#95C2414yes—
708#95C2418yes—
709#95C2414yes—
710#95C2418yes—
711#95C2418yes—
712#95C2414yes—
713#95C2418yes—
714#95C2418yes—
715#95C2414yes—
716#95C2418yes—
717#95C2418yes—
718#95C2414yes—
719#95C2418yes—
720#95C2414yes—
721C24C2512yes—
722C24C2514yes—
723C24C2511yescharacteristic
724#41—416no—
725#41—432no—
726C2×Q8—24no—
727C2×Q8—24no—
728C2×Q8—22no—
729C2×Q8—24no—
730C2×Q8—24no—
731C2×Q8—24no—
732C2×Q8—24no—
733C2×Q8—22no—
734C2×Q8—24no—
735C2×Q8—24no—
736C2×Q8—22no—
737C2×Q8—24no—
738C2×Q8—28no—
739C2×Q8—44no—
740C2×Q8—44no—
741C2×Q8—44no—
742C2×Q8—44no—
743C2×Q8—44no—
744C2×Q8—416no—
745C2×D4—24no—
746C2×D4—28no—
747C2×D4—28no—
748C2×D4—24no—
749C2×D4—24no—
750C2×D4—28no—
751C2×D4—22no—
752C2×D4—24no—
753C2×D4—22no—
754C2×D4—24no—
755C2×D4—24no—
756C2×D4—24no—
757C2×D4—24no—
758C2×D4—22no—
759C2×D4—28no—
760C2×D4—44no—
761C2×D4—44no—
762C2×D4—44no—
763C2×D4—44no—
764C2×D4—44no—
765C2×D4—44no—
766C2×D4—44no—
767C22×C4—24no—
768C22×C4—24no—
769C22×C4—24no—
770C22×C4—24no—
771C22×C4—24no—
772C22×C4—28no—
773C22×C4—24no—
774C22×C4—24no—
775C22×C4—28no—
776C22×C4—28no—
777C22×C4—24no—
778C22×C4—24no—
779C22×C4—28no—
780C22×C4—24no—
781C22×C4—24no—
782C22×C4—24no—
783C22×C4—216no—
784C22×C4—44no—
785C22×C4—42no—
786C22×C4—42no—
787C22×C4—42no—
788C22×C4—44no—
789C22×C4—42no—
790C22×C4—48no—
791C22×C4—44no—
792C22×C4—44no—
793C22×C4—48no—
794C22×C4—44no—
795C22×C4—42no—
796C22×C4C2×#4114yes—
797C22×C4C2×#4114yes—
798C22×C4C2×#4114yes—
799C22×C4C2×#4114yes—
800C22×C4H(5,𝔽2)14yes—
801C22×C4C2512yes—
802C22×C4C2518yes—
803C22×C4C2512yes—
804C22×C4C2512yes—
805C22×C4C2512yes—
806C22×C4C2514yes—
807C22×C4C2514yes—
808C22×C4C2514yes—
809C22×C4C2514yes—
810C22×C4C2512yes—
811C22×C4C2512yes—
812C22×C4C2514yes—
813C22×C4C2514yes—
814C22×C4C2511yescharacteristic
815C22×C4C2511yescharacteristic
816C22×C4C2511yescharacteristic
817C22×C4C2514yes—
818C22×C4C2511yescharacteristic
819C22×C4C2512yes—
820C22×C4C2511yescharacteristic
821C22×C4C2511yescharacteristic
822C4⋊C4—28no—
823C4⋊C4—216no—
824C4⋊C4—28no—
825C4⋊C4—24no—
826C4⋊C4—24no—
827C4⋊C4—28no—
828C4⋊C4—28no—
829C4⋊C4—22no—
830C4⋊C4—22no—
831C4⋊C4—24no—
832C4⋊C4—24no—
833C4⋊C4—24no—
834C4⋊C4—24no—
835C4⋊C4—216no—
836C4⋊C4—24no—
837C4⋊C4—24no—
838C4⋊C4—24no—
839C4⋊C4—24no—
840C4⋊C4—24no—
841C4⋊C4—28no—
842C4⋊C4—42no—
843C4⋊C4—42no—
844C4⋊C4—44no—
845C4⋊C4—44no—
846C4⋊C4—44no—
847C4⋊C4—48no—
848C4⋊C4—44no—
849C4⋊C4—44no—
850C4⋊C4—44no—
851C4⋊C4—44no—
852C4⋊C4—44no—
853C4⋊C4—44no—
854C4⋊C4—44no—
855C4⋊C4—44no—
856C4⋊C4—48no—
857C4⋊C4—48no—
858C4⋊C4—44no—
859C4⋊C4—44no—
860C4⋊C4C2×#4118yes—
861C22⋊C4—24no—
862C22⋊C4—24no—
863C22⋊C4—28no—
864C22⋊C4—24no—
865C22⋊C4—24no—
866C22⋊C4—216no—
867C22⋊C4—28no—
868C22⋊C4—28no—
869C22⋊C4—216no—
870C22⋊C4—28no—
871C22⋊C4—44no—
872C22⋊C4—44no—
873C22⋊C4—48no—
874C22⋊C4—48no—
875C22⋊C4—48no—
876C22⋊C4—44no—
877C22⋊C4—44no—
878C22⋊C4—44no—
879C22⋊C4—44no—
880C22⋊C4—44no—
881C22⋊C4—48no—
882C22⋊C4—48no—
883C22⋊C4—48no—
884C22⋊C4—48no—
885C22⋊C4—48no—
886C22⋊C4—48no—
887C22⋊C4C2×#4118yes—
888C42—24no—
889C42—24no—
890C42—24no—
891C42—28no—
892C42—28no—
893C42—216no—
894C42—24no—
895C42—24no—
896C42—24no—
897C42—24no—
898C42—24no—
899C42—28no—
900C42—216no—
901C42—48no—
902C42—44no—
903C42—48no—
904C42—48no—
905C42—44no—
906C42C2×#4114yes—
907C42C2×#4114yes—
908C42C2×#4114yes—
909C42C2×#4114yes—
910C42C2×#4118yes—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—24no—
915C23—22no—
916C23—24no—
917C23—24no—
918C23—22no—
919C23—24no—
920C23—24no—
921C23—24no—
922C23—24no—
923C23—24no—
924C23—24no—
925C23C22×#4112yes—
926C23C22×#4112yes—
927C23C2×H(5,𝔽2)12yes—
928C23C2611yescharacteristic
929Q8—48no—
930Q8—48no—
931Q8—48no—
932Q8—44no—
933Q8—88no—
934Q8—88no—
935D4—416no—
936D4—48no—
937D4—44no—
938D4—48no—
939D4—84no—
940D4—84no—
941D4—88no—
942D4—88no—
943C2×C4—22no—
944C2×C4—22no—
945C2×C4—24no—
946C2×C4—22no—
947C2×C4—22no—
948C2×C4—24no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—24no—
954C2×C4—24no—
955C2×C4—22no—
956C2×C4—24no—
957C2×C4—28no—
958C2×C4—24no—
959C2×C4—24no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—24no—
965C2×C4—24no—
966C2×C4—24no—
967C2×C4—22no—
968C2×C4—24no—
969C2×C4—24no—
970C2×C4—28no—
971C2×C4—28no—
972C2×C4—22no—
973C2×C4—24no—
974C2×C4—24no—
975C2×C4—24no—
976C2×C4—24no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—24no—
980C2×C4—24no—
981C2×C4—28no—
982C2×C4—24no—
983C2×C4—22no—
984C2×C4—24no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—44no—
988C2×C4—44no—
989C2×C4—48no—
990C2×C4—48no—
991C2×C4—48no—
992C2×C4—48no—
993C2×C4—416no—
994C2×C4—816no—
995C2×C4—84no—
996C2×C4—84no—
997C2×C4—88no—
998C2×C4—84no—
999C2×C4#555116yes—
1000C2×C4C22×#4112yes—
1001C2×C4C22×#4112yes—
1002C2×C4C22×#4112yes—
1003C2×C4C22×#4118yes—
1004C2×C4C22×#4112yes—
1005C2×C4C22×#4112yes—
1006C2×C4C22×#4112yes—
1007C2×C4C22×#4112yes—
1008C2×C4C22×#4112yes—
1009C2×C4C2×H(5,𝔽2)12yes—
1010C2×C4C2×H(5,𝔽2)12yes—
1011C2×C4#58514yes—
1012C22—24no—
1013C22—22no—
1014C22—22no—
1015C22—24no—
1016C22—44no—
1017C22—44no—
1018C22—44no—
1019C22—42no—
1020C22—44no—
1021C22—42no—
1022C22—44no—
1023C22—44no—
1024C22—44no—
1025C22—44no—
1026C22—42no—
1027C22—44no—
1028C22C2×#55514yes—
1029C22C23×#4111yescharacteristic
1030C22C23×#4111yescharacteristic
1031C22C22×H(5,𝔽2)11yescharacteristic
1032C22C2×#58512yes—
1033C222−1+612yes—
1034C4—28no—
1035C4—22no—
1036C4—22no—
1037C4—22no—
1038C4—22no—
1039C4—24no—
1040C4—48no—
1041C4—44no—
1042C4—42no—
1043C4—42no—
1044C4—42no—
1045C4—42no—
1046C4—42no—
1047C4—44no—
1048C4—44no—
1049C4—44no—
1050C4—44no—
1051C4—42no—
1052C4—44no—
1053C4C2×#55514yes—
1054C4C2×#55514yes—
1055C2—24no—
1056C2—84no—
1057C2—82no—
1058C2C22×#55511yescharacteristic
1059C2#6281511yescharacteristic
1060C2#6286011yescharacteristic
1061C2#6292712yes—
1062C2#6299512yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#34937C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59908C2semidirect
2. #59427C2semidirect
3. #59237C2semidirect
4. #59231C2semidirect
5. #45436C2semidirect
6. #45428C2semidirect
7. #45228C2semidirect
8. #45151C2semidirect
9. #45078C2semidirect
10. #44963C2semidirect
11. #38935C2semidirect
12. #38281C2semidirect
13. #36359C2semidirect
14. #35628C2semidirect
15. #35621C2semidirect
16. #35180C2semidirect
17. #35178C2semidirect
18. #34938C2semidirect
20. #34252C2semidirect
21. #34208C2semidirect
22. #34189C2semidirect
23. C2×#2356C2semidirect
24. C4×#536C2semidirect

Maximal subgroups

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

subgroupindex
#599082
#594272
#592372
#592312
#454362
#454282
#452282
#451512
#450782
#449632
#389352
#382812
#363592
#356282
#356212
#351802
#351782
#349382
#349372
#342522
#342082
#341892
C2×#23562
C4×#5362