Finite Group Databasebeta

← #7711006

Subgroups — #7711006

Order 512.

4738 conjugacy classes of subgroups.

The subgroup lattice has 1082 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59309C214yesmaximal, complemented
2#59136C212yesmaximal, complemented
3#59134C212yesmaximal, complemented
4#46163C214yesmaximal, complemented
5#46022C212yesmaximal, complemented
6#46013C212yesmaximal, complemented
7#40001C214yesmaximal, complemented
8#39796C214yesmaximal, complemented
9#39768C212yesmaximal
10#39752C212yesmaximal, complemented
11#39515C212yesmaximal, complemented
12#39501C212yesmaximal, complemented
13#39493C212yesmaximal, complemented
14#39490C212yesmaximal, complemented
15#38484C214yesmaximal, complemented
16#37555C212yesmaximal, complemented
17#37142C214yesmaximal, complemented
18C2×#2862C211yesmaximal, characteristic, complemented
19#36631C211yesmaximal, characteristic
20#36534C212yesmaximal, complemented
21#36306C214yesmaximal, complemented
22#36286C212yesmaximal, complemented
23#35117C214yesmaximal, complemented
24#34382C212yesmaximal, complemented
25C4×#533C211yesmaximal, characteristic, complemented
26C2×#556C2212yes—
27C2×#554C2212yes—
28C2×#533C2211yescharacteristic
29C22×C4⋊Q8C2211yescharacteristic
30C22×C4⋊Q8C2211yescharacteristic
31C2×#529C2212yes—
32#2863C2214yes—
33#2862C2212yes—
34#2862C2212yes—
35#2862C2212yes—
36#2862C2212yes—
37#2862C2212yes—
38#2862C2212yes—
39#2862C2212yes—
40#2862C2212yes—
41#2861C2212yes—
42#2861C2214yes—
43#2860C2212yes—
44#2860C2212yes—
45#2859C2211yescharacteristic
46#2858C2211yescharacteristic
47#2857C2211yescharacteristic
48#2856C2211yescharacteristic
49#2854C2212yes—
50#2854C2212yes—
51#2850C2212yes—
52#2822C2214yes—
53#2820C2214yes—
54#2809C2214yes—
55#2809C2214yes—
56#2808C2214yes—
57#2808C2214yes—
58#2806C2214yes—
59#2805C2214yes—
60#2804C2214yes—
61#2799C2218yes—
62#2798C2218yes—
63#2766C2218yes—
64#2762C2218yes—
65#2761C2218yes—
66#2759C2218yes—
67#2751C2218yes—
68#2732C2214yes—
69#2729C2218yes—
70#2716C2218yes—
71#2700C2218yes—
72#2689C2218yes—
73#2689C2218yes—
74#2659C2214yes—
75#2650C2218yes—
76#2639C2214yes—
77#2637C2218yes—
78#2628C2214yes—
79#2621C2214yes—
80#2605C2218yes—
81#2592C2214yes—
82#2589C2218yes—
83#2588C2218yes—
84#2581C2214yes—
85#2581C2214yes—
86#2570C2214yes—
87#2569C2218yes—
88#2568C2212yes—
89#2567C2212yes—
90#2565C2214yes—
91#2563C2212yes—
92#2560C2218yes—
93#2560C2218yes—
94#2550C2214yes—
95#2547C2212yes—
96#2545C2214yes—
97#2544C2214yes—
98#2536C2214yes—
99#2536C2214yes—
100#2532C2218yes—
101#2532C2218yes—
102#2532C2218yes—
103#2529C2218yes—
104#2527C2218yes—
105#2515C2218yes—
106#2514C2214yes—
107#2511C2214yes—
108#2510C2218yes—
109#2503C2214yes—
110#2499C2214yes—
111#2498C2218yes—
112#2495C2214yes—
113#2494C2214yes—
114#2492C2214yes—
115#2492C2214yes—
116#2481C2218yes—
117#2465C2218yes—
118#2453C2214yes—
119#2453C2214yes—
120#2452C2214yes—
121#2451C2214yes—
122#2448C2214yes—
123#2447C2214yes—
124#2447C2214yes—
125#2446C2214yes—
126#2444C2218yes—
127#2442C2214yes—
128#2440C2214yes—
129#2439C2214yes—
130#2436C2214yes—
131#2417C2214yes—
132#2417C2214yes—
133#2409C2218yes—
134#2382C2214yes—
135#2379C2214yes—
136#2369C2212yes—
137#2365C2212yes—
138#2361C2214yes—
139#2359C2218yes—
140#2356C2214yes—
141#2355C2214yes—
142#2353C2218yes—
143#2352C2214yes—
144#2352C2214yes—
145#2352C2214yes—
146D4×C4⋊C4C2214yes—
147Q8×C22⋊C4C2214yes—
148#2334C2218yes—
149#2332C2218yes—
150#2329C2214yes—
151#2325C2214yes—
152#2317C2214yes—
153#2314C2214yes—
154C4×C4⋊Q8C2211yescharacteristic
155C4×C4⋊Q8C2211yescharacteristic
156C4×C4⋊Q8C2211yescharacteristic
157C4×C4⋊Q8C2211yescharacteristic
158C4×C4⋊Q8C2211yescharacteristic
159C4×#127C2211yescharacteristic
160C4×#125C2212yes—
161C4×#125C2212yes—
162C4×#124C2212yes—
163C4×#124C2214yes—
164C4×C22⋊Q8C2212yes—
165C4×C22⋊Q8C2212yes—
166C4×C22⋊Q8C2212yes—
167C4×C22⋊Q8C2212yes—
168C4×#121C2212yes—
169C4×#121C2212yes—
170#2296C2212yes—
171#2295C2212yes—
172#2295C2214yes—
173#2295C2212yes—
174C2×#391C2212yes—
175C2×#391C2212yes—
176C2×#391C2212yes—
177C2×#391C2212yes—
178#2293C2212yes—
179#2293C2212yes—
180#2285C2211yescharacteristic
181C2×#382C2212yes—
182C2×#382C2212yes—
183C42×Q8C2212yes—
184C42×Q8C2212yes—
185C4×#117C2212yes—
186C2×C43C2211yescharacteristic
187C23×Q8C2312yes—
188C23×Q8C2312yes—
189#556—48no—
190#554—48no—
191#533—28no—
192C2×C4⋊Q8—44no—
193C2×C4⋊Q8—44no—
194C2×C4⋊Q8C2311yescharacteristic
195C2×C4⋊Q8C2311yescharacteristic
196C2×C4⋊Q8C2312yes—
197C2×C4⋊Q8C2312yes—
198C2×C4⋊Q8C2311yescharacteristic
199C2×C4⋊Q8C2312yes—
200C2×C4⋊Q8C2312yes—
201C2×C4⋊Q8C2312yes—
202C2×C4⋊Q8C2312yes—
203C2×C4⋊Q8C2312yes—
204C2×C4⋊Q8C2312yes—
205C2×#127C2311yescharacteristic
206#529—216no—
207C2×#126C2314yes—
208C2×#126C2318yes—
209C2×#125C2312yes—
210C2×#125C2312yes—
211C2×#125C2314yes—
212C2×#124C2312yes—
213C2×#124C2314yes—
214C2×#124C2312yes—
215C2×#124C2314yes—
216C2×#123C2314yes—
217C2×C22⋊Q8C2312yes—
218C2×C22⋊Q8C2312yes—
219C2×C22⋊Q8C2312yes—
220C2×C22⋊Q8C2318yes—
221C2×C22⋊Q8C2318yes—
222C2×C22⋊Q8C2314yes—
223C2×C22⋊Q8C2314yes—
224C2×#121C2312yes—
225C2×#121C2312yes—
226C2×#121C2312yes—
227C2×C4×Q8C2312yes—
228C2×C4×Q8C2312yes—
229C2×C4×Q8C2312yes—
230C2×C4×Q8C2312yes—
231C2×C4×Q8C2312yes—
232C2×C4×Q8C2312yes—
233C2×C4×Q8C2312yes—
234C2×C4×Q8C2314yes—
235C2×C4×Q8C2314yes—
236C2×C4×D4C2312yes—
237C2×C4×D4C2312yes—
238C2×C4×D4C2312yes—
239C2×C4×D4C2314yes—
240C2×C4×D4C2318yes—
241C2×C4×D4C2314yes—
242C2×#117C2314yes—
243C2×#117C2312yes—
244C2×#117C2314yes—
245C2×#117C2312yes—
246C22×C4⋊C4C2314yes—
247C22×C4⋊C4C2312yes—
248C22×C4⋊C4C2312yes—
249C22×C4⋊C4C2312yes—
250C22×C4⋊C4C2312yes—
251C22×C42C2311yescharacteristic
252C22×C42C2311yescharacteristic
253C22×C42C2311yescharacteristic
254C22×C42C2311yescharacteristic
255C22×C42C2311yescharacteristic
256C22×C42C2311yescharacteristic
257C22×C42C2311yescharacteristic
258#401C2318yes—
259#400C2318yes—
260#400C2318yes—
261#400C2318yes—
262#400C2318yes—
263#400C2318yes—
264#400C2318yes—
265#400C2318yes—
266#400C2318yes—
267#400C2318yes—
268#399C2318yes—
269#398C2318yes—
270#398C2318yes—
271#398C2318yes—
272#398C2318yes—
273#398C2318yes—
274#398C2318yes—
275#398C2318yes—
276#398C2318yes—
277#397C2318yes—
278#397C2318yes—
279#397C2318yes—
280#397C2318yes—
281#397C2318yes—
282#397C2318yes—
283#397C2318yes—
284#396C2318yes—
285#396C2318yes—
286#396C2318yes—
287#395C2318yes—
288#395C2318yes—
289#395C2318yes—
290#395C2318yes—
291#394C2318yes—
292#394C2318yes—
293#393C2318yes—
294#393C2318yes—
295#393C2318yes—
296#393C2318yes—
297#393C2318yes—
298#391C2314yes—
299#391C2314yes—
300#391C2312yes—
301#391C2312yes—
302#391C2312yes—
303#391C2312yes—
304#391C2312yes—
305#391C2314yes—
306#391C2314yes—
307#391C2314yes—
308#391C2314yes—
309#391C2314yes—
310#391C2314yes—
311#391C2314yes—
312#391C2318yes—
313#391C2314yes—
314#391C2318yes—
315#391C2318yes—
316#391C2314yes—
317#391C2318yes—
318#391C2314yes—
319#391C2318yes—
320#391C2312yes—
321#391C2314yes—
322#391C2314yes—
323#391C2314yes—
324#391C2314yes—
325#391C2314yes—
326#391C2314yes—
327#391C2314yes—
328#391C2314yes—
329#391C2314yes—
330#391C2314yes—
331#390C2312yes—
332#390C2312yes—
333#390C2312yes—
334#390C2314yes—
335#390C2312yes—
336#390C2312yes—
337#390C2312yes—
338#390C2312yes—
339#390C2312yes—
340#390C2312yes—
341#390C2312yes—
342#389C2312yes—
343#389C2312yes—
344#389C2312yes—
345#389C2312yes—
346#389C2312yes—
347#389C2312yes—
348#389C2312yes—
349#389C2312yes—
350#389C2312yes—
351#389C2312yes—
352#389C2314yes—
353#389C2314yes—
354#389C2314yes—
355#389C2314yes—
356#389C2318yes—
357#389C2318yes—
358#389C2312yes—
359#389C2314yes—
360#389C2318yes—
361#389C2312yes—
362#389C2312yes—
363#389C2312yes—
364#389C2312yes—
365#389C2312yes—
366#388C2318yes—
367#388C2318yes—
368#388C2318yes—
369#388C2318yes—
370#388C2318yes—
371#388C2318yes—
372#388C2318yes—
373#388C2318yes—
374#388C2314yes—
375#388C2318yes—
376#388C2318yes—
377#388C2314yes—
378#388C2318yes—
379#388C2314yes—
380#388C2314yes—
381#388C2314yes—
382#388C2314yes—
383#388C2314yes—
384#388C2314yes—
385#388C2318yes—
386#388C2318yes—
387#387C2318yes—
388#387C2318yes—
389#387C2314yes—
390#387C2314yes—
391#387C2314yes—
392#387C2314yes—
393#387C2318yes—
394#387C2318yes—
395#387C2318yes—
396#387C2318yes—
397#387C2318yes—
398#387C2318yes—
399#387C2318yes—
400#387C2318yes—
401#387C2318yes—
402#387C2318yes—
403#387C2318yes—
404#387C2318yes—
405#387C2318yes—
406#387C2318yes—
407#387C2318yes—
408#387C2318yes—
409#386C2318yes—
410#386C2318yes—
411#386C2318yes—
412#386C2314yes—
413#386C2314yes—
414#386C2318yes—
415#386C2318yes—
416#385C2314yes—
417#385C2318yes—
418#385C2318yes—
419#385C2318yes—
420#385C2318yes—
421#385C2318yes—
422#385C2314yes—
423#384C2311yescharacteristic
424#384C2311yescharacteristic
425#384C2311yescharacteristic
426#384C2311yescharacteristic
427#384C2314yes—
428#383C2318yes—
429#383C2318yes—
430#382C2312yes—
431#382C2314yes—
432#382C2314yes—
433#382C2314yes—
434#382C2314yes—
435#382C2314yes—
436#382C2314yes—
437#382C2314yes—
438#382C2312yes—
439#382C2314yes—
440#382C2314yes—
441#382C2314yes—
442#381C2318yes—
443#381C2318yes—
444#380C2314yes—
445#380C2314yes—
446#380C2312yes—
447#380C2318yes—
448#380C2318yes—
449#380C2314yes—
450#380C2312yes—
451#380C2312yes—
452#380C2312yes—
453#380C2314yes—
454C4×C4⋊C4C2314yes—
455C4×C4⋊C4C2314yes—
456C4×C4⋊C4C2312yes—
457C4×C4⋊C4C2312yes—
458C4×C4⋊C4C2312yes—
459C4×C4⋊C4C2312yes—
460C4×C4⋊C4C2314yes—
461C4×C4⋊C4C2314yes—
462C4×C4⋊C4C2314yes—
463C4×C4⋊C4C2312yes—
464C4×C4⋊C4C2312yes—
465C4×C4⋊C4C2312yes—
466C4×C4⋊C4C2312yes—
467C4×C4⋊C4C2312yes—
468C4×C4⋊C4C2312yes—
469C4×C4⋊C4C2314yes—
470C4×C4⋊C4C2314yes—
471C4×C4⋊C4C2314yes—
472C4×C4⋊C4C2318yes—
473C4×C4⋊C4C2312yes—
474C4×C4⋊C4C2314yes—
475C4×C4⋊C4C2312yes—
476C4×C22⋊C4C2318yes—
477C4×C22⋊C4C2318yes—
478C4×C22⋊C4C2318yes—
479C4×C22⋊C4C2314yes—
480C4×C22⋊C4C2314yes—
481C4×C22⋊C4C2314yes—
482C4×C22⋊C4C2314yes—
483#376C2318yes—
484#376C2314yes—
485C2×#95C2314yes—
486C2×#95C2314yes—
487C2×#95C2314yes—
488C2×#95C2314yes—
489C43C2311yescharacteristic
490C43C2311yescharacteristic
491C43C2311yescharacteristic
492C43C2311yescharacteristic
493C43C2311yescharacteristic
494C43C2311yescharacteristic
495C43C2311yescharacteristic
496C43C2314yes—
497C43C2311yescharacteristic
498C22×Q8—28no—
499C22×Q8—44no—
500C22×Q8—44no—
501C22×Q8—44no—
502C22×Q8—44no—
503C22×Q8—44no—
504C22×Q8C2412yes—
505C22×Q8C2414yes—
506C22×Q8C2412yes—
507C22×Q8C2412yes—
508C22×Q8C2414yes—
509C22×Q8C2414yes—
510C22×Q8C2414yes—
511C22×D4C2414yes—
512C22×D4C2412yes—
513C22×D4C2412yes—
514C22×D4C2412yes—
515C23×C4C2411yescharacteristic
516C23×C4C2414yes—
517C23×C4C2411yescharacteristic
518C23×C4C2411yescharacteristic
519C23×C4C2411yescharacteristic
520C23×C4C2411yescharacteristic
521C23×C4C2411yescharacteristic
522C23×C4C2414yes—
523C23×C4C2414yes—
524C23×C4C2418yes—
525C23×C4C2411yescharacteristic
526C4⋊Q8—24no—
527C4⋊Q8—24no—
528C4⋊Q8—28no—
529C4⋊Q8—28no—
530C4⋊Q8—44no—
531C4⋊Q8—44no—
532C4⋊Q8—44no—
533C4⋊Q8—44no—
534C4⋊Q8—42no—
535C4⋊Q8—44no—
536C4⋊Q8—44no—
537#127—42no—
538#126—216no—
539#126—416no—
540#125—28no—
541#125—28no—
542#125—48no—
543#124—28no—
544#124—44no—
545#124—48no—
546#124—48no—
547#123—216no—
548C22⋊Q8—28no—
549C22⋊Q8—28no—
550C22⋊Q8—28no—
551C22⋊Q8—416no—
552C22⋊Q8—416no—
553C22⋊Q8—48no—
554C22⋊Q8—48no—
555#121—28no—
556#121—28no—
557#121—44no—
558C4×Q8—28no—
559C4×Q8—28no—
560C4×Q8—28no—
561C4×Q8—28no—
562C4×Q8—28no—
563C4×Q8—44no—
564C4×Q8—44no—
565C4×Q8—48no—
566C4×Q8—48no—
567C4×D4—216no—
568C4×D4—28no—
569C4×D4—28no—
570C4×D4—28no—
571C4×D4—48no—
572C4×D4—416no—
573#117—28no—
574#117—216no—
575#117—44no—
576#117—48no—
577C2×C4⋊C4—44no—
578C2×C4⋊C4—44no—
579C2×C4⋊C4—44no—
580C2×C4⋊C4—44no—
581C2×C4⋊C4—48no—
582C2×C4⋊C4C2412yes—
583C2×C4⋊C4C2414yes—
584C2×C4⋊C4C2414yes—
585C2×C4⋊C4C2414yes—
586C2×C4⋊C4C2414yes—
587C2×C4⋊C4C2414yes—
588C2×C4⋊C4C2414yes—
589C2×C4⋊C4C2412yes—
590C2×C4⋊C4C2412yes—
591C2×C4⋊C4C2412yes—
592C2×C4⋊C4C2412yes—
593C2×C4⋊C4C2414yes—
594C2×C4⋊C4C2412yes—
595C2×C4⋊C4C2412yes—
596C2×C4⋊C4C2412yes—
597C2×C4⋊C4C2414yes—
598C2×C4⋊C4C2414yes—
599C2×C4⋊C4C2414yes—
600C2×C4⋊C4C2414yes—
601C2×C4⋊C4C2412yes—
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2414yes—
604C2×C4⋊C4C2412yes—
605C2×C4⋊C4C2414yes—
606C2×C4⋊C4C2412yes—
607C2×C4⋊C4C2418yes—
608C2×C4⋊C4C2414yes—
609C2×C4⋊C4C2414yes—
610C2×C4⋊C4C2414yes—
611C2×C4⋊C4C2414yes—
612C2×C4⋊C4C2412yes—
613C2×C4⋊C4C2412yes—
614C2×C4⋊C4C2418yes—
615C2×C4⋊C4C2418yes—
616C2×C4⋊C4C2412yes—
617C2×C4⋊C4C2412yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2418yes—
620C2×C4⋊C4C2412yes—
621C2×C4⋊C4C2418yes—
622C2×C4⋊C4C2418yes—
623C2×C4⋊C4C2418yes—
624C2×C4⋊C4C2412yes—
625C2×C22⋊C4C2414yes—
626C2×C22⋊C4C2414yes—
627C2×C22⋊C4C2414yes—
628C2×C22⋊C4C2414yes—
629C2×C22⋊C4C2414yes—
630C2×C22⋊C4C2414yes—
631C2×C22⋊C4C2414yes—
632C2×C22⋊C4C2414yes—
633C2×C22⋊C4C2414yes—
634C2×C22⋊C4C2414yes—
635C2×C22⋊C4C2414yes—
636C2×C22⋊C4C2418yes—
637C2×C22⋊C4C2418yes—
638C2×C22⋊C4C2418yes—
639C2×C22⋊C4C2414yes—
640C2×C22⋊C4C2418yes—
641C2×C22⋊C4C2418yes—
642C2×C22⋊C4C2418yes—
643C2×C22⋊C4C2418yes—
644C2×C22⋊C4C2414yes—
645C2×C42—24no—
646C2×C42—24no—
647C2×C42—24no—
648C2×C42—42no—
649C2×C42—42no—
650C2×C42—42no—
651C2×C42#4118yes—
652C2×C42C2414yes—
653C2×C42C2414yes—
654C2×C42C2414yes—
655C2×C42C2414yes—
656C2×C42C2411yescharacteristic
657C2×C42C2411yescharacteristic
658C2×C42C2414yes—
659C2×C42C2411yescharacteristic
660C2×C42C2411yescharacteristic
661C2×C42C2411yescharacteristic
662C2×C42C2411yescharacteristic
663C2×C42C2411yescharacteristic
664C2×C42C2411yescharacteristic
665C2×C42C2411yescharacteristic
666C2×C42C2411yescharacteristic
667C2×C42C2411yescharacteristic
668C2×C42C2411yescharacteristic
669C2×C42C2411yescharacteristic
670C2×C42C2411yescharacteristic
671C2×C42C2418yes—
672C2×C42C2414yes—
673C2×C42C2418yes—
674C2×C42C2414yes—
675C2×C42C2418yes—
676C2×C42C2411yescharacteristic
677C2×C42C2411yescharacteristic
678C2×C42C2411yescharacteristic
679C2×C42C2411yescharacteristic
680C2×C42C2411yescharacteristic
681C2×C42C2411yescharacteristic
682C2×C42C2411yescharacteristic
683C2×C42C2411yescharacteristic
684C2×C42C2411yescharacteristic
685C2×C42C2411yescharacteristic
686C2×C42C2411yescharacteristic
687C2×C42C2411yescharacteristic
688C2×C42C2411yescharacteristic
689C2×C42C2411yescharacteristic
690#95C2418yes—
691#95C2418yes—
692#95C2418yes—
693#95C2418yes—
694#95C2418yes—
695#95C2418yes—
696#95C2418yes—
697#95C2418yes—
698#95C2414yes—
699#95C2414yes—
700#95C2414yes—
701#95C2414yes—
702#95C2414yes—
703#95C2418yes—
704#95C2418yes—
705#95C2418yes—
706#95C2418yes—
707#95C2418yes—
708#95C2414yes—
709#95C2414yes—
710#95C2418yes—
711#95C2414yes—
712#95C2414yes—
713#95C2414yes—
714#95C2414yes—
715#95C2414yes—
716#95C2414yes—
717#95C2414yes—
718#95C2414yes—
719#95C2418yes—
720#95C2418yes—
721#95C2418yes—
722#95C2418yes—
723#95C2414yes—
724#95C2418yes—
725#95C2418yes—
726#95C2418yes—
727#95C2418yes—
728C24C2514yes—
729C24C2511yescharacteristic
730C2×Q8—24no—
731C2×Q8—24no—
732C2×Q8—24no—
733C2×Q8—24no—
734C2×Q8—28no—
735C2×Q8—28no—
736C2×Q8—24no—
737C2×Q8—28no—
738C2×Q8—28no—
739C2×Q8—28no—
740C2×Q8—28no—
741C2×Q8—42no—
742C2×Q8—42no—
743C2×Q8—42no—
744C2×Q8—44no—
745C2×Q8—44no—
746C2×Q8—42no—
747C2×Q8—44no—
748C2×Q8—44no—
749C2×Q8—44no—
750C2×Q8—44no—
751C2×Q8—816no—
752C2×Q8—816no—
753C2×D4—28no—
754C2×D4—28no—
755C2×D4—28no—
756C2×D4—24no—
757C2×D4—24no—
758C2×D4—24no—
759C2×D4—24no—
760C2×D4—24no—
761C2×D4—42no—
762C2×D4—42no—
763C2×D4—42no—
764C2×D4—42no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—22no—
768C22×C4—22no—
769C22×C4—22no—
770C22×C4—22no—
771C22×C4—22no—
772C22×C4—22no—
773C22×C4—22no—
774C22×C4—22no—
775C22×C4—22no—
776C22×C4—28no—
777C22×C4—28no—
778C22×C4—28no—
779C22×C4—28no—
780C22×C4—22no—
781C22×C4—22no—
782C22×C4—28no—
783C22×C4—41no—
784C22×C4—41no—
785C22×C4—41no—
786C22×C4—41no—
787C22×C4—44no—
788C22×C4—44no—
789C22×C4—44no—
790C22×C4—44no—
791C22×C4—48no—
792C22×C4—48no—
793C22×C4—48no—
794C22×C4C2×#4114yes—
795C22×C4C2×#4114yes—
796C22×C4C2×#4114yes—
797C22×C42−1+414yes—
798C22×C4C2511yescharacteristic
799C22×C4C2511yescharacteristic
800C22×C4C2514yes—
801C22×C4C2518yes—
802C22×C4C2514yes—
803C22×C4C2518yes—
804C22×C4C2514yes—
805C22×C4C2514yes—
806C22×C4C2514yes—
807C22×C4C2514yes—
808C22×C4C2514yes—
809C22×C4C2511yescharacteristic
810C22×C4C2511yescharacteristic
811C22×C4C2511yescharacteristic
812C22×C4C2511yescharacteristic
813C22×C4C2511yescharacteristic
814C22×C4C2511yescharacteristic
815C22×C4C2511yescharacteristic
816C22×C4C2511yescharacteristic
817C22×C4C2511yescharacteristic
818C22×C4C2511yescharacteristic
819C22×C4C2511yescharacteristic
820C22×C4C2511yescharacteristic
821C4⋊C4—28no—
822C4⋊C4—28no—
823C4⋊C4—24no—
824C4⋊C4—24no—
825C4⋊C4—24no—
826C4⋊C4—28no—
827C4⋊C4—24no—
828C4⋊C4—28no—
829C4⋊C4—28no—
830C4⋊C4—24no—
831C4⋊C4—24no—
832C4⋊C4—28no—
833C4⋊C4—24no—
834C4⋊C4—28no—
835C4⋊C4—28no—
836C4⋊C4—28no—
837C4⋊C4—28no—
838C4⋊C4—24no—
839C4⋊C4—28no—
840C4⋊C4—24no—
841C4⋊C4—24no—
842C4⋊C4—28no—
843C4⋊C4—24no—
844C4⋊C4—24no—
845C4⋊C4—28no—
846C4⋊C4—48no—
847C4⋊C4—44no—
848C4⋊C4—44no—
849C4⋊C4—44no—
850C4⋊C4—44no—
851C4⋊C4—42no—
852C4⋊C4—42no—
853C4⋊C4—48no—
854C4⋊C4—42no—
855C4⋊C4—42no—
856C4⋊C4—44no—
857C4⋊C4—48no—
858C4⋊C4—48no—
859C4⋊C4—42no—
860C4⋊C4—48no—
861C4⋊C4—48no—
862C4⋊C4—48no—
863C4⋊C4—42no—
864C22⋊C4—28no—
865C22⋊C4—28no—
866C22⋊C4—28no—
867C22⋊C4—28no—
868C22⋊C4—28no—
869C22⋊C4—28no—
870C22⋊C4—28no—
871C22⋊C4—28no—
872C22⋊C4—28no—
873C22⋊C4—28no—
874C22⋊C4—28no—
875C22⋊C4—48no—
876C22⋊C4—48no—
877C22⋊C4—48no—
878C22⋊C4—44no—
879C22⋊C4—48no—
880C22⋊C4—48no—
881C22⋊C4—48no—
882C22⋊C4—44no—
883C22⋊C4—48no—
884C42—28no—
885C42—28no—
886C42—22no—
887C42—22no—
888C42—22no—
889C42—28no—
890C42—22no—
891C42—22no—
892C42—22no—
893C42—22no—
894C42—22no—
895C42—22no—
896C42—22no—
897C42—28no—
898C42—22no—
899C42—22no—
900C42—22no—
901C42—22no—
902C42—28no—
903C42—41no—
904C42—41no—
905C42—41no—
906C42—41no—
907C42—41no—
908C42—41no—
909C42—41no—
910C42—41no—
911C42—44no—
912C42—48no—
913C42—48no—
914C42—44no—
915C42—48no—
916C42C2×#4114yes—
917C42C2×#4114yes—
918C42C2×#4114yes—
919C42C2×#4114yes—
920C42H(5,𝔽2)14yes—
921C422−1+414yes—
922C23—21no—
923C23—21no—
924C23—21no—
925C23—21no—
926C23—24no—
927C23—24no—
928C23—24no—
929C23—24no—
930C23—24no—
931C23—24no—
932C23—24no—
933C23C22×#4112yes—
934C23C2×2−1+412yes—
935C23#58512yes—
936C23C2611yescharacteristic
937Q8—48no—
938Q8—48no—
939Q8—416no—
940Q8—84no—
941Q8—88no—
942Q8—88no—
943Q8—88no—
944D4—416no—
945D4—48no—
946D4—84no—
947D4—84no—
948C2×C4—28no—
949C2×C4—21no—
950C2×C4—21no—
951C2×C4—21no—
952C2×C4—21no—
953C2×C4—21no—
954C2×C4—21no—
955C2×C4—21no—
956C2×C4—21no—
957C2×C4—21no—
958C2×C4—21no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—21no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—21no—
969C2×C4—28no—
970C2×C4—28no—
971C2×C4—28no—
972C2×C4—24no—
973C2×C4—24no—
974C2×C4—24no—
975C2×C4—24no—
976C2×C4—24no—
977C2×C4—24no—
978C2×C4—24no—
979C2×C4—24no—
980C2×C4—28no—
981C2×C4—28no—
982C2×C4—21no—
983C2×C4—21no—
984C2×C4—21no—
985C2×C4—24no—
986C2×C4—24no—
987C2×C4—24no—
988C2×C4—24no—
989C2×C4—28no—
990C2×C4—24no—
991C2×C4—21no—
992C2×C4—21no—
993C2×C4—24no—
994C2×C4—24no—
995C2×C4—21no—
996C2×C4—24no—
997C2×C4—24no—
998C2×C4—24no—
999C2×C4—24no—
1000C2×C4—28no—
1001C2×C4—28no—
1002C2×C4—24no—
1003C2×C4—24no—
1004C2×C4—28no—
1005C2×C4—44no—
1006C2×C4—44no—
1007C2×C4—44no—
1008C2×C4—416no—
1009C2×C4—88no—
1010C2×C4—88no—
1011C2×C4—168no—
1012C2×C4C22×#4112yes—
1013C2×C4C22×#4112yes—
1014C2×C4C22×#4112yes—
1015C2×C4C22×#4112yes—
1016C2×C4C22×#4112yes—
1017C2×C4C22×#4112yes—
1018C2×C4C2×H(5,𝔽2)12yes—
1019C2×C4C2×H(5,𝔽2)12yes—
1020C2×C4C2×H(5,𝔽2)12yes—
1021C2×C4C2×2−1+412yes—
1022C2×C4C2×2−1+412yes—
1023C2×C4C2×2−1+412yes—
1024C2×C4C2×2−1+412yes—
1025C2×C4C2×2−1+412yes—
1026C2×C4#58512yes—
1027C2×C4#58512yes—
1028C22—22no—
1029C22—22no—
1030C22—22no—
1031C22—22no—
1032C22—22no—
1033C22—22no—
1034C22—44no—
1035C22—44no—
1036C22—44no—
1037C22—44no—
1038C22—44no—
1039C22—44no—
1040C22—44no—
1041C22#350714yes—
1042C22C23×#4111yescharacteristic
1043C22C22×H(5,𝔽2)11yescharacteristic
1044C22C22×2−1+411yescharacteristic
1045C22C22×2−1+411yescharacteristic
1046C22C2×#58511yescharacteristic
1047C22C2×#58511yescharacteristic
1048C22C2×#58511yescharacteristic
1049C4—22no—
1050C4—22no—
1051C4—22no—
1052C4—22no—
1053C4—22no—
1054C4—22no—
1055C4—22no—
1056C4—22no—
1057C4—22no—
1058C4—22no—
1059C4—48no—
1060C4—44no—
1061C4—41no—
1062C4—44no—
1063C4—44no—
1064C4—44no—
1065C4—44no—
1066C4—44no—
1067C4—48no—
1068C4—44no—
1069C4—41no—
1070C4#351114yes—
1071C4#356114yes—
1072C2—24no—
1073C2—84no—
1074C2C2×#356111yescharacteristic
1075C2#6275211yescharacteristic
1076C2C2×#350711yescharacteristic
1077C2C2×#351111yescharacteristic
1078C2#6281511yescharacteristic
1079C2#6282411yescharacteristic
1080C2#6283711yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2856C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59309C2semidirect
2. #59136C2semidirect
3. #59134C2semidirect
4. #46163C2semidirect
5. #46022C2semidirect
6. #46013C2semidirect
7. #40001C2semidirect
8. #39796C2semidirect
10. #39752C2semidirect
11. #39515C2semidirect
12. #39501C2semidirect
13. #39493C2semidirect
14. #39490C2semidirect
15. #38484C2semidirect
16. #37555C2semidirect
17. #37142C2semidirect
18. C2×#2862C2semidirect
20. #36534C2semidirect
21. #36306C2semidirect
22. #36286C2semidirect
23. #35117C2semidirect
24. #34382C2semidirect
25. C4×#533C2semidirect

Maximal subgroups

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

subgroupindex
#593092
#591362
#591342
#461632
#460222
#460132
#400012
#397962
#397682
#397522
#395152
#395012
#394932
#394902
#384842
#375552
#371422
C2×#28622
#366312
#365342
#363062
#362862
#351172
#343822
C4×#5332