Finite Group Databasebeta

← #7646718

Subgroups — #7646718

Order 512.

5042 conjugacy classes of subgroups.

The subgroup lattice has 1022 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42976C214yesmaximal, complemented
2#42939C214yesmaximal, complemented
3#41979C214yesmaximal, complemented
4#41977C214yesmaximal, complemented
5#39387C212yesmaximal, complemented
6#39385C212yesmaximal, complemented
7#39202C212yesmaximal, complemented
8#39200C212yesmaximal, complemented
9#37671C214yesmaximal, complemented
10#37668C214yesmaximal, complemented
11#37579C214yesmaximal, complemented
12#37016C214yesmaximal, complemented
13#37010C214yesmaximal, complemented
14#35561C214yesmaximal, complemented
15#35298C211yesmaximal, characteristic, complemented
16#35240C211yesmaximal, characteristic, complemented
17#35220C214yesmaximal, complemented
18#35186C214yesmaximal, complemented
19#34936C211yesmaximal, characteristic
20#34912C211yesmaximal, characteristic, complemented
21#34232C211yesmaximal, characteristic, complemented
22#34154C211yesmaximal, characteristic, complemented
23#34058C211yesmaximal, characteristic, complemented
24C2×#542C2214yescomplemented
25C2×#541C2214yescomplemented
26C2×#533C2211yescharacteristic
27C2×#532C2211yescharacteristic
28C2×#525C2214yes—
29C22×C4×D4C2211yescharacteristic
30#2868C2211yescharacteristic, complemented
31#2862C2211yescharacteristic, complemented
32#2861C2218yescomplemented
33#2860C2218yescomplemented
34#2858C2211yescharacteristic, complemented
35#2858C2211yescharacteristic, complemented
36#2848C2212yes—
37#2848C2212yes—
38#2836C2218yescomplemented
39#2829C2218yes—
40#2797C2218yescomplemented
41#2773C2218yescomplemented
42#2754C2218yescomplemented
43#2752C2218yescomplemented
44#2730C2218yescomplemented
45#2721C2218yescomplemented
46#2721C2218yescomplemented
47#2707C2218yes—
48#2705C2218yescomplemented
49#2697C2218yes—
50#2695C2218yes—
51#2694C2218yes—
52#2687C2218yes—
53#2685C2218yes—
54#2685C2218yes—
55#2684C2218yes—
56#2667C2218yescomplemented
57#2664C2218yescomplemented
58#2662C2218yes—
59#2651C2218yescomplemented
60#2651C2218yescomplemented
61#2648C2218yes—
62#2633C2214yes—
63#2625C2214yescomplemented
64#2624C2214yescomplemented
65#2621C2214yescomplemented
66#2620C2214yes—
67#2620C2214yescomplemented
68#2608C2212yes—
69#2607C2212yes—
70#2606C2212yescomplemented
71#2605C2212yescomplemented
72#2592C2214yes—
73#2582C2214yescomplemented
74#2570C2212yescomplemented
75#2566C2212yescomplemented
76#2566C2212yescomplemented
77#2560C2218yescomplemented
78#2558C2218yescomplemented
79#2556C2218yescomplemented
80#2554C2218yes—
81#2552C2214yescomplemented
82#2552C2214yescomplemented
83#2550C2212yescomplemented
84#2548C2214yes—
85#2548C2214yes—
86#2547C2212yes—
87#2545C2214yescomplemented
88#2544C2214yes—
89#2542C2212yes—
90#2542C2212yes—
91#2541C2212yes—
92#2540C2212yes—
93#2540C2212yes—
94#2539C2214yes—
95#2538C2214yescomplemented
96#2536C2214yes—
97#2531C2218yescomplemented
98#2526C2218yescomplemented
99#2512C2214yes—
100#2512C2214yes—
101#2512C2214yescomplemented
102#2511C2214yescomplemented
103#2502C2212yes—
104#2501C2212yes—
105#2500C2212yes—
106#2500C2212yes—
107#2492C2214yescomplemented
108#2490C2214yescomplemented
109#2482C2214yes—
110#2468C2218yescomplemented
111#2468C2218yescomplemented
112#2466C2218yescomplemented
113#2460C2218yescomplemented
114#2454C2218yescomplemented
115#2450C2218yescomplemented
116#2448C2214yes—
117#2448C2214yescomplemented
118#2447C2214yescomplemented
119#2447C2218yescomplemented
120#2445C2214yes—
121#2441C2212yes—
122#2439C2212yes—
123#2435C2212yes—
124#2433C2212yes—
125#2432C2214yes—
126#2429C2214yescomplemented
127#2429C2214yescomplemented
128#2427C2214yescomplemented
129#2426C2214yescomplemented
130#2423C2214yescomplemented
131#2420C2214yescomplemented
132#2419C2218yescomplemented
133#2397C2214yes—
134#2396C2214yes—
135#2371C2214yescomplemented
136#2366C2212yescomplemented
137#2365C2212yescomplemented
138#2365C2212yescomplemented
139#2365C2212yescomplemented
140#2363C2214yes—
141#2362C2214yes—
142#2362C2214yes—
143#2353C2214yescomplemented
144#2341C2212yes—
145#2339C2212yes—
146#2333C2214yes—
147#2326C2214yes—
148#2326C2214yescomplemented
149#2324C2214yescomplemented
150#2323C2214yescomplemented
151#2319C2212yes—
152#2319C2212yes—
153#2319C2212yes—
154#2319C2212yes—
155#2319C2212yescomplemented
156#2316C2212yes—
157#2312C2212yes—
158#2312C2212yes—
159#2309C2212yes—
160C4×C4⋊Q8C2212yescomplemented
161C4×#127C2214yes—
162C4×#125C2212yescomplemented
163C4×#124C2214yescomplemented
164#2298C2214yes—
165#2295C2214yescomplemented
166#2295C2212yescomplemented
167#2295C2212yescomplemented
168#2293C2212yes—
169#2293C2212yes—
170#2293C2214yes—
171#2283C2211yescharacteristic
172#2280C2214yes—
173#2275C2212yescomplemented
174C42×Q8C2212yescomplemented
175C42×Q8C2212yescomplemented
176C4×#117C2211yescharacteristic
177C4×#117C2211yescharacteristic
178C4×#117C2211yescharacteristic
179C22×#41C2312yes—
180C23×D4C2311yescharacteristic
181C24×C4C2312yes—
182#542—416no—
183#541—416no—
184#533—28no—
185#532—28no—
186C2×C4⋊Q8C2312yes—
187C2×C4⋊Q8C2311yescharacteristic
188C2×C4⋊Q8C2311yescharacteristic
189C2×C4⋊Q8C2311yescharacteristic
190C2×C4⋊Q8C2314yes—
191C2×#127C2311yescharacteristic
192C2×#127C2314yes—
193C2×#126C2318yes—
194C2×#126C2318yes—
195C2×#126C2318yes—
196C2×#125C2312yes—
197C2×#125C2312yes—
198C2×#125C2318yes—
199C2×#125C2318yes—
200C2×#124C2312yes—
201C2×#124C2314yes—
202C2×#124C2314yes—
203C2×#124C2314yes—
204C2×#124C2318yes—
205#525—416no—
206C2×#123C2318yes—
207C2×#123C2318yes—
208C2×C22⋊Q8C2314yes—
209C2×C22⋊Q8C2312yes—
210C2×C22⋊Q8C2312yes—
211C2×C22⋊Q8C2318yes—
212C2×C22⋊Q8C2314yes—
213C2×C22⋊Q8C2314yes—
214C2×C22⋊Q8C2314yes—
215C2×#121C2314yes—
216C2×#121C2312yes—
217C2×#121C2312yes—
218C2×#121C2314yes—
219C2×#120C2318yes—
220C2×C4×Q8C2312yes—
221C2×C4×Q8C2314yes—
222C2×C4×Q8C2312yes—
223C2×C4×Q8C2314yes—
224C2×C4×Q8C2314yes—
225C2×C4×Q8C2314yes—
226C2×C4×D4—28no—
227C2×C4×D4C2312yes—
228C2×C4×D4C2312yes—
229C2×C4×D4C2312yes—
230C2×C4×D4C2312yes—
231C2×C4×D4C2312yes—
232C2×C4×D4C2312yes—
233C2×C4×D4C2318yes—
234C2×C4×D4C2318yes—
235C2×C4×D4C2314yes—
236C2×C4×D4C2314yes—
237C2×#117C2312yes—
238C2×#117C2312yes—
239C2×#117C2312yes—
240C2×#117C2312yes—
241C2×#117C2314yes—
242C2×#117C2314yes—
243C22×C4⋊C4C2311yescharacteristic
244C22×C22⋊C4C2312yes—
245C22×C42C2311yescharacteristic
246#400C2314yes—
247#400C2318yes—
248#400C2318yes—
249#399C2318yes—
250#399C2314yes—
251#399C2314yes—
252#399C2318yes—
253#399C2318yes—
254#399C2314yes—
255#399C2318yes—
256#398C2318yes—
257#398C2314yes—
258#398C2318yes—
259#398C2318yes—
260#398C2318yes—
261#398C2318yes—
262#398C2318yes—
263#398C2314yes—
264#398C2318yes—
265#397C2318yes—
266#397C2318yes—
267#397C2318yes—
268#397C2318yes—
269#397C2318yes—
270#397C2318yes—
271#397C2318yes—
272#397C2318yes—
273#397C2318yes—
274#396C2318yes—
275#396C2318yes—
276#396C2318yes—
277#396C2318yes—
278#396C2314yes—
279#396C2314yes—
280#396C2318yes—
281#396C2318yes—
282#396C2318yes—
283#395C2314yes—
284#394C2318yes—
285#394C2318yes—
286#394C2318yes—
287#394C2318yes—
288#394C2318yes—
289#394C2318yes—
290#394C2318yes—
291#394C2318yes—
292#394C2318yes—
293#394C2318yes—
294#394C2318yes—
295#393C2318yes—
296#393C2314yes—
297#392C2314yes—
298#392C2314yes—
299#392C2318yes—
300#391C2314yes—
301#391C2314yes—
302#391C2314yes—
303#391C2314yes—
304#391C2314yes—
305#391C2318yes—
306#391C2314yes—
307#391C2314yes—
308#391C2314yes—
309#391C2314yes—
310#390C2318yes—
311#390C2314yes—
312#390C2318yes—
313#390C2314yes—
314#390C2314yes—
315#390C2312yes—
316#390C2314yes—
317#390C2312yes—
318#390C2312yes—
319#390C2312yes—
320#390C2312yes—
321#390C2312yes—
322#390C2312yes—
323#390C2312yes—
324#390C2314yes—
325#390C2314yes—
326#390C2318yes—
327#390C2314yes—
328#390C2314yes—
329#390C2318yes—
330#390C2314yes—
331#390C2318yes—
332#390C2318yes—
333#389C2312yes—
334#389C2312yes—
335#389C2312yes—
336#389C2312yes—
337#389C2314yes—
338#389C2314yes—
339#389C2312yes—
340#389C2314yes—
341#389C2312yes—
342#389C2312yes—
343#389C2312yes—
344#389C2314yes—
345#389C2318yes—
346#389C2314yes—
347#389C2318yes—
348#389C2314yes—
349#389C2314yes—
350#389C2314yes—
351#389C2318yes—
352#388C2314yes—
353#388C2318yes—
354#388C2318yes—
355#388C2314yes—
356#388C2314yes—
357#388C2314yes—
358#388C2314yes—
359#388C2314yes—
360#388C2314yes—
361#388C2314yes—
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#387C2318yes—
378#387C2314yes—
379#387C2314yes—
380#387C2314yes—
381#387C2314yes—
382#387C2318yes—
383#387C2318yes—
384#387C2314yes—
385#387C2314yes—
386#387C2318yes—
387#387C2318yes—
388#387C2318yes—
389#387C2318yes—
390#386C2318yes—
391#386C2318yes—
392#386C2318yes—
393#386C2318yes—
394#386C2318yes—
395#385C2318yes—
396#385C2318yes—
397#385C2318yes—
398#385C2318yes—
399#385C2318yes—
400#385C2314yes—
401#385C2314yes—
402#384C2314yes—
403#384C2312yes—
404#384C2312yes—
405#384C2312yes—
406#384C2314yes—
407#384C2314yes—
408#383C2312yes—
409#382C2312yes—
410#382C2312yes—
411#382C2312yes—
412#382C2312yes—
413#381C2314yes—
414#381C2314yes—
415#381C2314yes—
416#381C2312yes—
417#381C2318yes—
418#380C2314yes—
419#380C2314yes—
420#380C2314yes—
421#380C2314yes—
422#380C2314yes—
423#380C2314yes—
424#380C2314yes—
425#380C2311yescharacteristic
426#380C2311yescharacteristic
427#380C2318yes—
428#379C2314yes—
429#379C2314yes—
430#379C2314yes—
431#379C2314yes—
432C4×C4⋊C4C2314yes—
433C4×C4⋊C4C2312yes—
434C4×C4⋊C4C2312yes—
435C4×C4⋊C4C2314yes—
436C4×C4⋊C4C2314yes—
437C4×C4⋊C4C2314yes—
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441C4×C4⋊C4C2312yes—
442C4×C4⋊C4C2311yescharacteristic
443C4×C4⋊C4C2311yescharacteristic
444C4×C4⋊C4C2314yes—
445C4×C4⋊C4C2314yes—
446C4×C4⋊C4C2314yes—
447C4×C4⋊C4C2318yes—
448C4×C4⋊C4C2318yes—
449C4×C4⋊C4C2312yes—
450C4×C4⋊C4C2314yes—
451C4×C4⋊C4C2311yescharacteristic
452C4×C22⋊C4C2318yes—
453C4×C22⋊C4C2312yes—
454C4×C22⋊C4C2311yescharacteristic
455C4×C22⋊C4C2311yescharacteristic
456C4×C22⋊C4C2312yes—
457C4×C22⋊C4C2314yes—
458C4×C22⋊C4C2312yes—
459C4×C22⋊C4C2318yes—
460C4×C22⋊C4C2312yes—
461C4×C22⋊C4C2312yes—
462C4×C22⋊C4C2314yes—
463C4×C22⋊C4C2314yes—
464C4×C22⋊C4C2312yes—
465#376C2312yes—
466#376C2312yes—
467#376C2312yes—
468#376C2312yes—
469#376C2314yes—
470C2×#95C2314yes—
471C43C2311yescharacteristic
472C43C2312yes—
473C43C2311yescharacteristic
474C43C2314yes—
475C43C2312yes—
476C25C2412yes—
477C2×#41—28no—
478C2×#41—48no—
479C22×Q8C2412yes—
480C22×Q8C2412yes—
481C22×Q8C2412yes—
482C22×Q8C2414yes—
483C22×D4—24no—
484C22×D4—44no—
485C22×D4C2412yes—
486C22×D4C2412yes—
487C22×D4C2412yes—
488C22×D4C2412yes—
489C22×D4C2418yes—
490C22×D4C2412yes—
491C22×D4C2414yes—
492C22×D4C2418yes—
493C23×C4—28no—
494C23×C4—48no—
495C23×C4C2414yes—
496C23×C4C2411yescharacteristic
497C23×C4C2411yescharacteristic
498C23×C4C2412yes—
499C23×C4C2414yes—
500C23×C4C2414yes—
501C23×C4C2418yes—
502C23×C4C2411yescharacteristic
503C4⋊Q8—28no—
504C4⋊Q8—24no—
505C4⋊Q8—24no—
506C4⋊Q8—24no—
507C4⋊Q8—48no—
508#127—24no—
509#127—48no—
510#126—416no—
511#126—416no—
512#126—416no—
513#125—28no—
514#125—28no—
515#125—416no—
516#125—416no—
517#124—28no—
518#124—48no—
519#124—48no—
520#124—48no—
521#124—416no—
522#123—416no—
523#123—416no—
524C22⋊Q8—28no—
525C22⋊Q8—28no—
526C22⋊Q8—216no—
527C22⋊Q8—416no—
528C22⋊Q8—48no—
529C22⋊Q8—48no—
530C22⋊Q8—48no—
531#121—28no—
532#121—28no—
533#121—216no—
534#121—48no—
535#120—416no—
536C4×Q8—216no—
537C4×Q8—28no—
538C4×Q8—28no—
539C4×Q8—48no—
540C4×Q8—48no—
541C4×Q8—48no—
542C4×D4—28no—
543C4×D4—28no—
544C4×D4—28no—
545C4×D4—28no—
546C4×D4—28no—
547C4×D4—28no—
548C4×D4—416no—
549C4×D4—48no—
550C4×D4—416no—
551C4×D4—48no—
552#117—28no—
553#117—28no—
554#117—44no—
555#117—48no—
556#117—48no—
557#117—44no—
558C2×C4⋊C4—24no—
559C2×C4⋊C4C2412yes—
560C2×C4⋊C4C2412yes—
561C2×C4⋊C4C2412yes—
562C2×C4⋊C4C2412yes—
563C2×C4⋊C4C2412yes—
564C2×C4⋊C4C2412yes—
565C2×C4⋊C4C2412yes—
566C2×C4⋊C4C2412yes—
567C2×C4⋊C4C2412yes—
568C2×C4⋊C4C2412yes—
569C2×C4⋊C4C2418yes—
570C2×C4⋊C4C2412yes—
571C2×C4⋊C4C2418yes—
572C2×C4⋊C4C2414yes—
573C2×C4⋊C4C2414yes—
574C2×C4⋊C4C2412yes—
575C2×C4⋊C4C2412yes—
576C2×C4⋊C4C2414yes—
577C2×C4⋊C4C2414yes—
578C2×C4⋊C4C2414yes—
579C2×C4⋊C4C2414yes—
580C2×C4⋊C4C2414yes—
581C2×C4⋊C4C2414yes—
582C2×C4⋊C4C2414yes—
583C2×C4⋊C4C2412yes—
584C2×C4⋊C4C2412yes—
585C2×C4⋊C4C2418yes—
586C2×C4⋊C4C2418yes—
587C2×C4⋊C4C2418yes—
588C2×C4⋊C4C2414yes—
589C2×C4⋊C4C2414yes—
590C2×C4⋊C4C2414yes—
591C2×C4⋊C4C2418yes—
592C2×C4⋊C4C2418yes—
593C2×C4⋊C4C2418yes—
594C2×C4⋊C4C2418yes—
595C2×C4⋊C4C2414yes—
596C2×C4⋊C4C2414yes—
597C2×C4⋊C4C2414yes—
598C2×C4⋊C4C2412yes—
599C2×C22⋊C4—28no—
600C2×C22⋊C4C2414yes—
601C2×C22⋊C4C2414yes—
602C2×C22⋊C4C2414yes—
603C2×C22⋊C4C2414yes—
604C2×C22⋊C4C2418yes—
605C2×C22⋊C4C2418yes—
606C2×C22⋊C4C2414yes—
607C2×C22⋊C4C2414yes—
608C2×C22⋊C4C2414yes—
609C2×C22⋊C4C2414yes—
610C2×C22⋊C4C2414yes—
611C2×C22⋊C4C2414yes—
612C2×C22⋊C4C2414yes—
613C2×C22⋊C4C2412yes—
614C2×C22⋊C4C2412yes—
615C2×C22⋊C4C2418yes—
616C2×C22⋊C4C2418yes—
617C2×C22⋊C4C2418yes—
618C2×C22⋊C4C2418yes—
619C2×C22⋊C4C2418yes—
620C2×C22⋊C4C2418yes—
621C2×C22⋊C4C2418yes—
622C2×C22⋊C4C2418yes—
623C2×C22⋊C4C2418yes—
624C2×C22⋊C4C2418yes—
625C2×C22⋊C4C2418yes—
626C2×C22⋊C4C2418yes—
627C2×C22⋊C4C2412yes—
628C2×C22⋊C4C2412yes—
629C2×C22⋊C4C2414yes—
630C2×C22⋊C4C2414yes—
631C2×C22⋊C4C2414yes—
632C2×C22⋊C4C2414yes—
633C2×C22⋊C4C2418yes—
634C2×C42#4118yes—
635C2×C42C2414yes—
636C2×C42C2412yes—
637C2×C42C2412yes—
638C2×C42C2414yes—
639C2×C42C2414yes—
640C2×C42C2412yes—
641C2×C42C2412yes—
642C2×C42C2414yes—
643C2×C42C2414yes—
644C2×C42C2418yes—
645C2×C42C2414yes—
646C2×C42C2418yes—
647C2×C42C2418yes—
648C2×C42C2412yes—
649C2×C42C2412yes—
650C2×C42C2412yes—
651C2×C42C2412yes—
652C2×C42C2411yescharacteristic
653C2×C42C2411yescharacteristic
654C2×C42C2411yescharacteristic
655C2×C42C2411yescharacteristic
656C2×C42C2411yescharacteristic
657C2×C42C2411yescharacteristic
658C2×C42C2411yescharacteristic
659C2×C42C2411yescharacteristic
660#95C2412yes—
661#95C2412yes—
662#95C2418yes—
663#95C2412yes—
664#95C2414yes—
665#95C2412yes—
666#95C2412yes—
667#95C2412yes—
668#95C2412yes—
669#95C2414yes—
670#95C2414yes—
671#95C2412yes—
672#95C2412yes—
673#95C2412yes—
674#95C2418yes—
675#95C2418yes—
676#95C2414yes—
677#95C2414yes—
678#95C2414yes—
679#95C2414yes—
680#95C2414yes—
681#95C2418yes—
682#95C2418yes—
683#95C2418yes—
684#95C2414yes—
685#95C2414yes—
686#95C2414yes—
687#95C2414yes—
688#95C2414yes—
689#95C2414yes—
690#95C2414yes—
691#95C2418yes—
692#95C2418yes—
693#95C2418yes—
694#95C2418yes—
695C24—24no—
696C24—44no—
697C24—44no—
698C24—42no—
699C24—42no—
700C24C2514yes—
701C24C2514yes—
702C24C2511yescharacteristic
703#41—816no—
704C2×Q8—24no—
705C2×Q8—24no—
706C2×Q8—24no—
707C2×Q8—28no—
708C2×Q8—28no—
709C2×Q8—28no—
710C2×Q8—28no—
711C2×Q8—44no—
712C2×Q8—44no—
713C2×D4—28no—
714C2×D4—24no—
715C2×D4—24no—
716C2×D4—24no—
717C2×D4—24no—
718C2×D4—24no—
719C2×D4—28no—
720C2×D4—216no—
721C2×D4—28no—
722C2×D4—24no—
723C2×D4—24no—
724C2×D4—44no—
725C2×D4—416no—
726C2×D4—48no—
727C2×D4—48no—
728C2×D4—48no—
729C2×D4—48no—
730C2×D4—42no—
731C2×D4—42no—
732C2×D4—48no—
733C2×D4—48no—
734C22×C4—24no—
735C22×C4—24no—
736C22×C4—24no—
737C22×C4—28no—
738C22×C4—28no—
739C22×C4—28no—
740C22×C4—28no—
741C22×C4—28no—
742C22×C4—41no—
743C22×C4—41no—
744C22×C4—44no—
745C22×C4—44no—
746C22×C4—48no—
747C22×C4—44no—
748C22×C4—48no—
749C22×C4—48no—
750C22×C4—48no—
751C22×C4—816no—
752C22×C4C2×#4114yes—
753C22×C4C2×#4114yes—
754C22×C4C2×#4114yes—
755C22×C4C2514yes—
756C22×C4C2514yes—
757C22×C4C2514yes—
758C22×C4C2512yes—
759C22×C4C2514yes—
760C22×C4C2514yes—
761C22×C4C2512yes—
762C22×C4C2512yes—
763C22×C4C2512yes—
764C22×C4C2514yes—
765C22×C4C2514yes—
766C22×C4C2514yes—
767C22×C4C2514yes—
768C22×C4C2511yescharacteristic
769C22×C4C2511yescharacteristic
770C22×C4C2511yescharacteristic
771C22×C4C2511yescharacteristic
772C22×C4C2514yes—
773C22×C4C2511yescharacteristic
774C22×C4C2511yescharacteristic
775C4⋊C4—24no—
776C4⋊C4—24no—
777C4⋊C4—24no—
778C4⋊C4—24no—
779C4⋊C4—24no—
780C4⋊C4—24no—
781C4⋊C4—28no—
782C4⋊C4—28no—
783C4⋊C4—24no—
784C4⋊C4—24no—
785C4⋊C4—24no—
786C4⋊C4—24no—
787C4⋊C4—216no—
788C4⋊C4—216no—
789C4⋊C4—24no—
790C4⋊C4—28no—
791C4⋊C4—28no—
792C4⋊C4—28no—
793C4⋊C4—24no—
794C4⋊C4—24no—
795C4⋊C4—44no—
796C4⋊C4—44no—
797C4⋊C4—44no—
798C4⋊C4—42no—
799C4⋊C4—42no—
800C4⋊C4—44no—
801C4⋊C4—44no—
802C4⋊C4—44no—
803C4⋊C4—44no—
804C4⋊C4—48no—
805C4⋊C4—44no—
806C4⋊C4—44no—
807C4⋊C4—44no—
808C4⋊C4—48no—
809C4⋊C4—48no—
810C4⋊C4—48no—
811C4⋊C4—48no—
812C4⋊C4—48no—
813C4⋊C4—48no—
814C4⋊C4H(5,𝔽2)18yes—
815C22⋊C4—28no—
816C22⋊C4—28no—
817C22⋊C4—28no—
818C22⋊C4—28no—
819C22⋊C4—28no—
820C22⋊C4—28no—
821C22⋊C4—216no—
822C22⋊C4—216no—
823C22⋊C4—44no—
824C22⋊C4—44no—
825C22⋊C4—48no—
826C22⋊C4—44no—
827C22⋊C4—44no—
828C22⋊C4—42no—
829C22⋊C4—42no—
830C22⋊C4—42no—
831C22⋊C4—42no—
832C22⋊C4—44no—
833C22⋊C4—44no—
834C22⋊C4—44no—
835C22⋊C4—44no—
836C22⋊C4—44no—
837C22⋊C4—48no—
838C22⋊C4—48no—
839C22⋊C4—48no—
840C22⋊C4—48no—
841C22⋊C4—48no—
842C22⋊C4—48no—
843C22⋊C4—48no—
844C22⋊C4—48no—
845C22⋊C4—48no—
846C22⋊C4—48no—
847C22⋊C4—48no—
848C22⋊C4—48no—
849C42—28no—
850C42—28no—
851C42—28no—
852C42—24no—
853C42—24no—
854C42—216no—
855C42—24no—
856C42—24no—
857C42—28no—
858C42—28no—
859C42—42no—
860C42—42no—
861C42—42no—
862C42—42no—
863C42—41no—
864C42—41no—
865C42—41no—
866C42—41no—
867C42—44no—
868C42—48no—
869C42—48no—
870C42C2×#4114yes—
871C42C2×#4114yes—
872C42C2×#4114yes—
873C42C2×#4114yes—
874C23—22no—
875C23—22no—
876C23—21no—
877C23—21no—
878C23—24no—
879C23—24no—
880C23—24no—
881C23—28no—
882C23—24no—
883C23—24no—
884C23—28no—
885C23—24no—
886C23—24no—
887C23—24no—
888C23—24no—
889C23—24no—
890C23—48no—
891C23—84no—
892C23—84no—
893C23—88no—
894C23—88no—
895C23C22×#4112yes—
896C23C2611yescharacteristic
897Q8—48no—
898Q8—48no—
899Q8—48no—
900Q8—88no—
901D4—48no—
902D4—48no—
903D4—48no—
904D4—48no—
905D4—84no—
906D4—816no—
907D4—88no—
908D4—816no—
909C2×C4—22no—
910C2×C4—24no—
911C2×C4—22no—
912C2×C4—21no—
913C2×C4—21no—
914C2×C4—21no—
915C2×C4—21no—
916C2×C4—24no—
917C2×C4—28no—
918C2×C4—28no—
919C2×C4—24no—
920C2×C4—24no—
921C2×C4—24no—
922C2×C4—24no—
923C2×C4—24no—
924C2×C4—24no—
925C2×C4—24no—
926C2×C4—22no—
927C2×C4—22no—
928C2×C4—28no—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—24no—
932C2×C4—28no—
933C2×C4—24no—
934C2×C4—24no—
935C2×C4—24no—
936C2×C4—22no—
937C2×C4—22no—
938C2×C4—24no—
939C2×C4—24no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—24no—
943C2×C4—24no—
944C2×C4—28no—
945C2×C4—24no—
946C2×C4—24no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—24no—
951C2×C4—22no—
952C2×C4—24no—
953C2×C4—24no—
954C2×C4—24no—
955C2×C4—44no—
956C2×C4—416no—
957C2×C4—88no—
958C2×C4—88no—
959C2×C4—84no—
960C2×C4—168no—
961C2×C4C22×#4112yes—
962C2×C4C22×#4112yes—
963C2×C4C22×#4112yes—
964C2×C4C22×#4112yes—
965C2×C4C22×#4112yes—
966C2×C4C22×#4112yes—
967C2×C4C2×H(5,𝔽2)18yes—
968C2×C4C2×H(5,𝔽2)14yes—
969C2×C4#58514yes—
970C22—22no—
971C22—22no—
972C22—22no—
973C22—42no—
974C22—42no—
975C22—44no—
976C22—44no—
977C22—44no—
978C22—44no—
979C22—48no—
980C22—44no—
981C22—44no—
982C22—44no—
983C22—48no—
984C22—44no—
985C22—44no—
986C22—44no—
987C22—816no—
988C22C23×#4111yescharacteristic
989C22C22×H(5,𝔽2)12yes—
990C22C2×#58512yes—
991C222−1+611yescharacteristic
992C222−1+611yescharacteristic
993C4—22no—
994C4—22no—
995C4—22no—
996C4—28no—
997C4—22no—
998C4—44no—
999C4—44no—
1000C4—44no—
1001C4—42no—
1002C4—44no—
1003C4—44no—
1004C4—42no—
1005C4—44no—
1006C4—42no—
1007C4—42no—
1008C4—44no—
1009C4—44no—
1010C4—44no—
1011C4#345514yes—
1012C4#350814yes—
1013C2—42no—
1014C2—84no—
1015C2—84no—
1016C2C2×#345511yescharacteristic
1017C2C2×#350811yescharacteristic
1018C2#6286011yescharacteristic
1019C2#6292112yes—
1020C2#6292212yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#34936C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42976C2semidirect
2. #42939C2semidirect
3. #41979C2semidirect
4. #41977C2semidirect
5. #39387C2semidirect
6. #39385C2semidirect
7. #39202C2semidirect
8. #39200C2semidirect
9. #37671C2semidirect
10. #37668C2semidirect
11. #37579C2semidirect
12. #37016C2semidirect
13. #37010C2semidirect
14. #35561C2semidirect
15. #35298C2semidirect
16. #35240C2semidirect
17. #35220C2semidirect
18. #35186C2semidirect
20. #34912C2semidirect
21. #34232C2semidirect
22. #34154C2semidirect
23. #34058C2semidirect
24. C2×#542C22semidirect
25. C2×#541C22semidirect
30. #2868C22semidirect
31. #2862C22semidirect
32. #2861C22semidirect
33. #2860C22semidirect
34. #2858C22semidirect
35. #2858C22semidirect
38. #2836C22semidirect
40. #2797C22semidirect
41. #2773C22semidirect
42. #2754C22semidirect
43. #2752C22semidirect
44. #2730C22semidirect
45. #2721C22semidirect
46. #2721C22semidirect
48. #2705C22semidirect
56. #2667C22semidirect
57. #2664C22semidirect
59. #2651C22semidirect
60. #2651C22semidirect
63. #2625C22semidirect
64. #2624C22semidirect
65. #2621C22semidirect
67. #2620C22semidirect
70. #2606C22semidirect
71. #2605C22semidirect
73. #2582C22semidirect
74. #2570C22semidirect
75. #2566C22semidirect
76. #2566C22semidirect
77. #2560C22semidirect
78. #2558C22semidirect
79. #2556C22semidirect
81. #2552C22semidirect
82. #2552C22semidirect
83. #2550C22semidirect
87. #2545C22semidirect
95. #2538C22semidirect
97. #2531C22semidirect
98. #2526C22semidirect
101. #2512C22semidirect
102. #2511C22semidirect
107. #2492C22semidirect
108. #2490C22semidirect
110. #2468C22semidirect
111. #2468C22semidirect
112. #2466C22semidirect
113. #2460C22semidirect
114. #2454C22semidirect
115. #2450C22semidirect
117. #2448C22semidirect
118. #2447C22semidirect
119. #2447C22semidirect
126. #2429C22semidirect
127. #2429C22semidirect
128. #2427C22semidirect
129. #2426C22semidirect
130. #2423C22semidirect
131. #2420C22semidirect
132. #2419C22semidirect
135. #2371C22semidirect
136. #2366C22semidirect
137. #2365C22semidirect
138. #2365C22semidirect
139. #2365C22semidirect
143. #2353C22semidirect
148. #2326C22semidirect
149. #2324C22semidirect
150. #2323C22semidirect
155. #2319C22semidirect
160. C4×C4⋊Q8C22semidirect
162. C4×#125C22semidirect
163. C4×#124C22semidirect
165. #2295C22semidirect
166. #2295C22semidirect
167. #2295C22semidirect
173. #2275C22semidirect
174. C42×Q8C22semidirect
175. C42×Q8C22semidirect

Maximal subgroups

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

subgroupindex
#429762
#429392
#419792
#419772
#393872
#393852
#392022
#392002
#376712
#376682
#375792
#370162
#370102
#355612
#352982
#352402
#352202
#351862
#349362
#349122
#342322
#341542
#340582