Finite Group Databasebeta

← #7654836

Subgroups — #7654836

Order 512.

5214 conjugacy classes of subgroups.

The subgroup lattice has 1063 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42072C218yesmaximal, complemented
2#41979C214yesmaximal, complemented
3#39756C212yesmaximal, complemented
4#39273C214yesmaximal, complemented
5#39066C214yesmaximal, complemented
6#38969C212yesmaximal, complemented
7#38260C214yesmaximal, complemented
8#37774C214yesmaximal, complemented
9#37671C214yesmaximal, complemented
10#37625C212yesmaximal, complemented
11#37619C211yesmaximal, characteristic, complemented
12#36573C212yesmaximal, complemented
13#36370C212yesmaximal, complemented
14#36143C214yesmaximal, complemented
15#35690C214yesmaximal, complemented
16#35209C212yesmaximal, complemented
17#35202C211yesmaximal, characteristic, complemented
18#35176C212yesmaximal, complemented
19#35172C211yesmaximal, characteristic, complemented
20#34936C211yesmaximal, characteristic
21#34934C212yesmaximal, complemented
22#34226C211yesmaximal, characteristic, complemented
23#34154C211yesmaximal, characteristic, complemented
24#34126C211yesmaximal, characteristic, complemented
25C2×#541C2214yescomplemented
26C2×#533C2211yescharacteristic
27C2×#532C2211yescharacteristic
28C2×#529C2214yescomplemented
29C2×#525C2214yes—
30C22×C4×D4C2211yescharacteristic
31#2864C2212yescomplemented
32#2860C2214yes—
33#2859C2212yescomplemented
34#2859C2214yescomplemented
35#2857C2214yescomplemented
36#2855C2214yescomplemented
37#2848C2214yes—
38#2829C2218yescomplemented
39#2816C2214yes—
40#2808C2218yescomplemented
41#2773C2218yescomplemented
42#2752C2218yes—
43#2751C2218yescomplemented
44#2727C2218yescomplemented
45#2721C2218yescomplemented
46#2707C2218yes—
47#2705C2218yes—
48#2694C2218yes—
49#2694C2218yescomplemented
50#2685C2218yes—
51#2685C2218yes—
52#2667C2214yes—
53#2667C2218yescomplemented
54#2664C2218yescomplemented
55#2658C2212yescomplemented
56#2644C2214yescomplemented
57#2641C2214yes—
58#2640C2212yescomplemented
59#2633C2214yescomplemented
60#2630C2218yescomplemented
61#2626C2214yes—
62#2624C2214yes—
63#2624C2214yescomplemented
64#2620C2214yescomplemented
65#2606C2214yescomplemented
66#2602C2218yes—
67#2580C2212yes—
68#2580C2212yes—
69#2580C2212yescomplemented
70#2580C2212yescomplemented
71#2580C2218yescomplemented
72#2566C2214yes—
73#2563C2212yes—
74#2554C2218yescomplemented
75#2553C2218yes—
76#2552C2212yescomplemented
77#2552C2212yescomplemented
78#2548C2212yescomplemented
79#2546C2212yescomplemented
80#2542C2212yes—
81#2542C2211yescharacteristic
82#2542C2211yescharacteristic
83#2541C2211yescharacteristic
84#2541C2211yescharacteristic
85#2540C2214yes—
86#2539C2214yes—
87#2538C2212yes—
88#2538C2212yes—
89#2534C2218yes—
90#2522C2218yescomplemented
91#2519C2218yescomplemented
92#2517C2218yescomplemented
93#2512C2214yes—
94#2512C2214yescomplemented
95#2507C2214yescomplemented
96#2506C2214yescomplemented
97#2501C2212yes—
98#2490C2214yescomplemented
99#2489C2214yescomplemented
100#2479C2218yescomplemented
101#2470C2218yes—
102#2468C2218yescomplemented
103#2467C2218yes—
104#2466C2218yescomplemented
105#2466C2218yescomplemented
106#2460C2218yescomplemented
107#2458C2218yescomplemented
108#2454C2214yes—
109#2454C2218yescomplemented
110#2454C2218yescomplemented
111#2454C2214yescomplemented
112#2445C2214yes—
113#2445C2214yes—
114#2441C2214yes—
115#2441C2214yes—
116#2441C2218yescomplemented
117#2433C2212yes—
118#2432C2214yes—
119#2429C2214yescomplemented
120#2429C2214yescomplemented
121#2427C2214yescomplemented
122#2426C2214yescomplemented
123#2423C2214yescomplemented
124#2422C2214yescomplemented
125#2419C2218yescomplemented
126#2418C2218yes—
127#2397C2214yes—
128#2392C2218yescomplemented
129#2371C2212yescomplemented
130#2371C2212yescomplemented
131#2367C2214yescomplemented
132#2365C2212yescomplemented
133#2365C2212yescomplemented
134#2363C2214yes—
135#2362C2212yes—
136#2362C2212yes—
137#2362C2214yes—
138#2359C2218yescomplemented
139#2357C2211yescharacteristic
140#2357C2211yescharacteristic
141#2357C2212yescomplemented
142#2353C2212yes—
143#2353C2212yes—
144#2349C2211yescharacteristic
145#2349C2211yescharacteristic
146#2349C2212yescomplemented
147#2349C2218yescomplemented
148#2345C2212yes—
149#2342C2214yes—
150#2341C2212yes—
151#2339C2212yes—
152D4×C22⋊C4C2212yes—
153#2330C2214yescomplemented
154#2330C2214yescomplemented
155#2324C2214yes—
156#2323C2214yescomplemented
157#2319C2214yes—
158#2319C2212yescomplemented
159#2317C2212yes—
160#2309C2212yes—
161C4×C4⋊Q8C2212yescomplemented
162C4×#127C2212yes—
163C4×#127C2212yes—
164C4×#127C2214yes—
165C4×#127C2212yescomplemented
166C4×#121C2214yescomplemented
167#2298C2214yes—
168#2295C2212yescomplemented
169#2295C2212yescomplemented
170#2293C2212yes—
171#2293C2214yescomplemented
172#2290C2214yes—
173#2285C2211yescharacteristic
174#2283C2211yescharacteristic
175#2280C2212yes—
176#2275C2212yescomplemented
177C42×Q8C2212yescomplemented
178C42×Q8C2212yescomplemented
179C42×D4C2212yes—
180C4×#117C2211yescharacteristic
181C4×#117C2211yescharacteristic
182C2×C4×C22⋊C4C2212yes—
183C22×#41C2312yes—
184C23×D4C2311yescharacteristic
185C24×C4C2312yes—
186#541—416no—
187#533—28no—
188#532—28no—
189C2×C4⋊Q8C2311yescharacteristic
190C2×C4⋊Q8C2311yescharacteristic
191C2×C4⋊Q8C2311yescharacteristic
192C2×C4⋊Q8C2314yes—
193C2×#127C2312yes—
194C2×#127C2311yescharacteristic
195C2×#127C2312yes—
196#529—416no—
197C2×#126C2318yes—
198C2×#126C2318yes—
199C2×#126C2318yes—
200C2×#125C2312yes—
201C2×#125C2314yes—
202C2×#125C2314yes—
203C2×#125C2318yes—
204C2×#125C2318yes—
205C2×#124C2312yes—
206C2×#124C2314yes—
207#525—416no—
208C2×#123C2318yes—
209C2×#123C2318yes—
210C2×#123C2318yes—
211C2×C22⋊Q8C2312yes—
212C2×C22⋊Q8C2314yes—
213C2×C22⋊Q8C2312yes—
214C2×C22⋊Q8C2314yes—
215C2×C22⋊Q8C2314yes—
216C2×C22⋊Q8C2314yes—
217C2×#121C2312yes—
218C2×#121C2312yes—
219C2×#121C2314yes—
220C2×#121C2314yes—
221C2×#120C2318yes—
222C2×C4×Q8C2312yes—
223C2×C4×Q8C2312yes—
224C2×C4×Q8C2312yes—
225C2×C4×Q8C2312yes—
226C2×C4×Q8C2314yes—
227C2×C4×Q8C2314yes—
228C2×C4×D4—28no—
229C2×C4×D4C2311yescharacteristic
230C2×C4×D4C2311yescharacteristic
231C2×C4×D4C2312yes—
232C2×C4×D4C2312yes—
233C2×C4×D4C2312yes—
234C2×C4×D4C2312yes—
235C2×C4×D4C2312yes—
236C2×C4×D4C2311yescharacteristic
237C2×C4×D4C2311yescharacteristic
238C2×C4×D4C2312yes—
239C2×C4×D4C2314yes—
240C2×C4×D4C2318yes—
241C2×C4×D4C2318yes—
242C2×C4×D4C2318yes—
243C2×C4×D4C2318yes—
244C2×C4×D4C2314yes—
245C2×C4×D4C2314yes—
246C2×#117C2312yes—
247C2×#117C2312yes—
248C2×#117C2312yes—
249C2×#117C2314yes—
250C2×#117C2312yes—
251C2×#117C2318yes—
252C22×C4⋊C4C2311yescharacteristic
253C22×C22⋊C4C2312yes—
254C22×C22⋊C4C2314yes—
255C22×C42C2314yes—
256C22×C42C2311yescharacteristic
257#400C2318yes—
258#399C2314yes—
259#399C2314yes—
260#399C2318yes—
261#399C2314yes—
262#399C2314yes—
263#399C2318yes—
264#399C2318yes—
265#399C2314yes—
266#399C2314yes—
267#399C2318yes—
268#399C2318yes—
269#398C2318yes—
270#398C2318yes—
271#398C2318yes—
272#398C2318yes—
273#398C2318yes—
274#398C2318yes—
275#397C2318yes—
276#397C2318yes—
277#397C2318yes—
278#397C2318yes—
279#397C2318yes—
280#397C2318yes—
281#396C2318yes—
282#396C2318yes—
283#396C2318yes—
284#396C2318yes—
285#396C2318yes—
286#396C2318yes—
287#396C2318yes—
288#396C2318yes—
289#394C2318yes—
290#394C2318yes—
291#394C2318yes—
292#394C2318yes—
293#394C2318yes—
294#394C2318yes—
295#394C2318yes—
296#394C2318yes—
297#394C2318yes—
298#394C2318yes—
299#394C2318yes—
300#393C2314yes—
301#393C2314yes—
302#393C2314yes—
303#393C2314yes—
304#392C2314yes—
305#392C2318yes—
306#392C2314yes—
307#391C2314yes—
308#391C2314yes—
309#391C2312yes—
310#391C2312yes—
311#391C2314yes—
312#390C2314yes—
313#390C2312yes—
314#390C2314yes—
315#390C2318yes—
316#390C2318yes—
317#390C2312yes—
318#390C2312yes—
319#390C2318yes—
320#390C2318yes—
321#390C2312yes—
322#390C2314yes—
323#390C2314yes—
324#390C2314yes—
325#390C2314yes—
326#390C2314yes—
327#390C2314yes—
328#390C2318yes—
329#390C2314yes—
330#390C2312yes—
331#390C2312yes—
332#390C2314yes—
333#389C2314yes—
334#389C2314yes—
335#389C2314yes—
336#389C2314yes—
337#389C2314yes—
338#389C2314yes—
339#389C2318yes—
340#389C2314yes—
341#389C2314yes—
342#389C2318yes—
343#389C2314yes—
344#389C2318yes—
345#389C2318yes—
346#389C2318yes—
347#389C2312yes—
348#389C2312yes—
349#389C2312yes—
350#389C2318yes—
351#389C2318yes—
352#389C2318yes—
353#389C2314yes—
354#389C2312yes—
355#389C2314yes—
356#388C2314yes—
357#388C2318yes—
358#388C2318yes—
359#388C2318yes—
360#388C2318yes—
361#388C2318yes—
362#388C2318yes—
363#388C2314yes—
364#388C2314yes—
365#388C2314yes—
366#388C2318yes—
367#388C2318yes—
368#388C2314yes—
369#388C2314yes—
370#388C2314yes—
371#388C2314yes—
372#388C2318yes—
373#388C2318yes—
374#388C2318yes—
375#387C2314yes—
376#387C2318yes—
377#387C2318yes—
378#387C2318yes—
379#387C2318yes—
380#387C2318yes—
381#387C2318yes—
382#387C2314yes—
383#387C2314yes—
384#387C2314yes—
385#387C2318yes—
386#387C2314yes—
387#387C2314yes—
388#387C2314yes—
389#387C2314yes—
390#387C2314yes—
391#387C2314yes—
392#386C2318yes—
393#386C2314yes—
394#386C2314yes—
395#386C2318yes—
396#386C2318yes—
397#385C2318yes—
398#385C2318yes—
399#385C2318yes—
400#385C2318yes—
401#385C2314yes—
402#385C2318yes—
403#385C2318yes—
404#385C2318yes—
405#385C2318yes—
406#385C2314yes—
407#384C2312yes—
408#384C2314yes—
409#384C2312yes—
410#384C2312yes—
411#384C2314yes—
412#384C2314yes—
413#383C2312yes—
414#382C2314yes—
415#382C2312yes—
416#382C2311yescharacteristic
417#382C2311yescharacteristic
418#382C2318yes—
419#381C2312yes—
420#381C2318yes—
421#381C2314yes—
422#381C2312yes—
423#381C2312yes—
424#380C2314yes—
425#380C2314yes—
426#380C2318yes—
427#380C2314yes—
428#380C2312yes—
429#380C2312yes—
430#380C2312yes—
431#380C2314yes—
432#380C2318yes—
433#380C2312yes—
434#380C2312yes—
435#380C2318yes—
436#379C2318yes—
437#379C2314yes—
438C4×C4⋊C4C2314yes—
439C4×C4⋊C4C2314yes—
440C4×C4⋊C4C2312yes—
441C4×C4⋊C4C2312yes—
442C4×C4⋊C4C2312yes—
443C4×C4⋊C4C2312yes—
444C4×C4⋊C4C2312yes—
445C4×C4⋊C4C2312yes—
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2314yes—
449C4×C4⋊C4C2314yes—
450C4×C4⋊C4C2312yes—
451C4×C4⋊C4C2314yes—
452C4×C4⋊C4C2314yes—
453C4×C4⋊C4C2314yes—
454C4×C4⋊C4C2312yes—
455C4×C4⋊C4C2314yes—
456C4×C4⋊C4C2314yes—
457C4×C4⋊C4C2311yescharacteristic
458C4×C4⋊C4C2311yescharacteristic
459C4×C4⋊C4C2312yes—
460C4×C22⋊C4C2312yes—
461C4×C22⋊C4C2311yescharacteristic
462C4×C22⋊C4C2311yescharacteristic
463C4×C22⋊C4C2314yes—
464C4×C22⋊C4C2314yes—
465C4×C22⋊C4C2314yes—
466C4×C22⋊C4C2314yes—
467C4×C22⋊C4C2318yes—
468C4×C22⋊C4C2312yes—
469C4×C22⋊C4C2312yes—
470C4×C22⋊C4C2318yes—
471C4×C22⋊C4C2312yes—
472C4×C22⋊C4C2314yes—
473C4×C22⋊C4C2314yes—
474C4×C22⋊C4C2312yes—
475C4×C22⋊C4C2312yes—
476#376C2314yes—
477#376C2311yescharacteristic
478#376C2312yes—
479#376C2312yes—
480#376C2311yescharacteristic
481C2×#95C2314yes—
482C2×#95C2312yes—
483C2×#95C2312yes—
484C43C2312yes—
485C43C2314yes—
486C43C2312yes—
487C25C2412yes—
488C2×#41—28no—
489C2×#41—48no—
490C22×Q8C2412yes—
491C22×Q8C2412yes—
492C22×Q8C2412yes—
493C22×D4—24no—
494C22×D4—24no—
495C22×D4—42no—
496C22×D4C2412yes—
497C22×D4C2412yes—
498C22×D4C2411yescharacteristic
499C22×D4C2418yes—
500C22×D4C2412yes—
501C22×D4C2411yescharacteristic
502C22×D4C2412yes—
503C22×D4C2414yes—
504C22×D4C2418yes—
505C23×C4—28no—
506C23×C4—48no—
507C23×C4C2412yes—
508C23×C4C2412yes—
509C23×C4C2411yescharacteristic
510C23×C4C2411yescharacteristic
511C23×C4C2412yes—
512C23×C4C2414yes—
513C23×C4C2414yes—
514C23×C4C2418yes—
515C23×C4C2412yes—
516C23×C4C2412yes—
517C23×C4C2414yes—
518C23×C4C2411yescharacteristic
519C4⋊Q8—24no—
520C4⋊Q8—24no—
521C4⋊Q8—24no—
522C4⋊Q8—48no—
523#127—28no—
524#127—24no—
525#127—44no—
526#126—416no—
527#126—416no—
528#126—416no—
529#125—216no—
530#125—28no—
531#125—48no—
532#125—416no—
533#125—416no—
534#124—28no—
535#124—48no—
536#123—416no—
537#123—416no—
538#123—416no—
539C22⋊Q8—28no—
540C22⋊Q8—28no—
541C22⋊Q8—216no—
542C22⋊Q8—48no—
543C22⋊Q8—48no—
544C22⋊Q8—48no—
545#121—28no—
546#121—28no—
547#121—216no—
548#121—48no—
549#120—416no—
550C4×Q8—28no—
551C4×Q8—28no—
552C4×Q8—28no—
553C4×Q8—28no—
554C4×Q8—48no—
555C4×Q8—48no—
556C4×D4—28no—
557C4×D4—24no—
558C4×D4—24no—
559C4×D4—28no—
560C4×D4—24no—
561C4×D4—24no—
562C4×D4—28no—
563C4×D4—28no—
564C4×D4—28no—
565C4×D4—416no—
566C4×D4—48no—
567C4×D4—44no—
568C4×D4—416no—
569C4×D4—48no—
570C4×D4—416no—
571C4×D4—48no—
572C4×D4—416no—
573#117—28no—
574#117—28no—
575#117—48no—
576#117—44no—
577#117—416no—
578#117—44no—
579C2×C4⋊C4—24no—
580C2×C4⋊C4C2411yescharacteristic
581C2×C4⋊C4C2412yes—
582C2×C4⋊C4C2411yescharacteristic
583C2×C4⋊C4C2414yes—
584C2×C4⋊C4C2412yes—
585C2×C4⋊C4C2412yes—
586C2×C4⋊C4C2418yes—
587C2×C4⋊C4C2412yes—
588C2×C4⋊C4C2412yes—
589C2×C4⋊C4C2414yes—
590C2×C4⋊C4C2412yes—
591C2×C4⋊C4C2412yes—
592C2×C4⋊C4C2418yes—
593C2×C4⋊C4C2418yes—
594C2×C4⋊C4C2412yes—
595C2×C4⋊C4C2412yes—
596C2×C4⋊C4C2414yes—
597C2×C4⋊C4C2414yes—
598C2×C4⋊C4C2412yes—
599C2×C4⋊C4C2412yes—
600C2×C4⋊C4C2414yes—
601C2×C4⋊C4C2414yes—
602C2×C4⋊C4C2414yes—
603C2×C4⋊C4C2418yes—
604C2×C4⋊C4C2414yes—
605C2×C4⋊C4C2414yes—
606C2×C4⋊C4C2412yes—
607C2×C4⋊C4C2418yes—
608C2×C4⋊C4C2414yes—
609C2×C4⋊C4C2418yes—
610C2×C4⋊C4C2418yes—
611C2×C4⋊C4C2414yes—
612C2×C4⋊C4C2418yes—
613C2×C4⋊C4C2418yes—
614C2×C4⋊C4C2418yes—
615C2×C4⋊C4C2418yes—
616C2×C4⋊C4C2418yes—
617C2×C4⋊C4C2418yes—
618C2×C4⋊C4C2412yes—
619C2×C22⋊C4—28no—
620C2×C22⋊C4—48no—
621C2×C22⋊C4C2412yes—
622C2×C22⋊C4C2412yes—
623C2×C22⋊C4C2412yes—
624C2×C22⋊C4C2412yes—
625C2×C22⋊C4C2412yes—
626C2×C22⋊C4C2414yes—
627C2×C22⋊C4C2418yes—
628C2×C22⋊C4C2414yes—
629C2×C22⋊C4C2414yes—
630C2×C22⋊C4C2418yes—
631C2×C22⋊C4C2414yes—
632C2×C22⋊C4C2414yes—
633C2×C22⋊C4C2414yes—
634C2×C22⋊C4C2414yes—
635C2×C22⋊C4C2414yes—
636C2×C22⋊C4C2418yes—
637C2×C22⋊C4C2414yes—
638C2×C22⋊C4C2414yes—
639C2×C22⋊C4C2412yes—
640C2×C22⋊C4C2414yes—
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⋊C4C2418yes—
650C2×C22⋊C4C2418yes—
651C2×C22⋊C4C2418yes—
652C2×C22⋊C4C2418yes—
653C2×C22⋊C4C2418yes—
654C2×C42—48no—
655C2×C42#4118yes—
656C2×C42C2414yes—
657C2×C42C2412yes—
658C2×C42C2414yes—
659C2×C42C2412yes—
660C2×C42C2414yes—
661C2×C42C2414yes—
662C2×C42C2412yes—
663C2×C42C2412yes—
664C2×C42C2414yes—
665C2×C42C2412yes—
666C2×C42C2414yes—
667C2×C42C2412yes—
668C2×C42C2412yes—
669C2×C42C2414yes—
670C2×C42C2412yes—
671C2×C42C2414yes—
672C2×C42C2418yes—
673C2×C42C2414yes—
674C2×C42C2414yes—
675C2×C42C2414yes—
676C2×C42C2411yescharacteristic
677C2×C42C2411yescharacteristic
678C2×C42C2411yescharacteristic
679C2×C42C2411yescharacteristic
680#95C2411yescharacteristic
681#95C2411yescharacteristic
682#95C2414yes—
683#95C2412yes—
684#95C2412yes—
685#95C2414yes—
686#95C2414yes—
687#95C2418yes—
688#95C2411yescharacteristic
689#95C2412yes—
690#95C2411yescharacteristic
691#95C2412yes—
692#95C2412yes—
693#95C2414yes—
694#95C2412yes—
695#95C2414yes—
696#95C2414yes—
697#95C2414yes—
698#95C2412yes—
699#95C2412yes—
700#95C2414yes—
701#95C2414yes—
702#95C2414yes—
703#95C2414yes—
704#95C2414yes—
705#95C2418yes—
706#95C2418yes—
707#95C2414yes—
708#95C2414yes—
709#95C2414yes—
710#95C2414yes—
711#95C2418yes—
712#95C2414yes—
713#95C2418yes—
714#95C2418yes—
715#95C2418yes—
716#95C2418yes—
717C24—24no—
718C24—24no—
719C24—44no—
720C24—42no—
721C24—44no—
722C24C2512yes—
723C24C2514yes—
724C24C2511yescharacteristic
725C24C2512yes—
726#41—816no—
727C2×Q8—24no—
728C2×Q8—24no—
729C2×Q8—24no—
730C2×Q8—24no—
731C2×Q8—24no—
732C2×Q8—28no—
733C2×Q8—44no—
734C2×D4—216no—
735C2×D4—24no—
736C2×D4—28no—
737C2×D4—22no—
738C2×D4—24no—
739C2×D4—22no—
740C2×D4—24no—
741C2×D4—24no—
742C2×D4—24no—
743C2×D4—216no—
744C2×D4—28no—
745C2×D4—24no—
746C2×D4—22no—
747C2×D4—22no—
748C2×D4—24no—
749C2×D4—22no—
750C2×D4—416no—
751C2×D4—48no—
752C2×D4—44no—
753C2×D4—42no—
754C2×D4—48no—
755C2×D4—48no—
756C2×D4—48no—
757C2×D4—48no—
758C2×D42−1+414yes—
759C22×C4—24no—
760C22×C4—22no—
761C22×C4—22no—
762C22×C4—24no—
763C22×C4—28no—
764C22×C4—24no—
765C22×C4—24no—
766C22×C4—28no—
767C22×C4—28no—
768C22×C4—24no—
769C22×C4—24no—
770C22×C4—28no—
771C22×C4—28no—
772C22×C4—216no—
773C22×C4—42no—
774C22×C4—44no—
775C22×C4—44no—
776C22×C4—44no—
777C22×C4—48no—
778C22×C4—44no—
779C22×C4—44no—
780C22×C4—48no—
781C22×C4—48no—
782C22×C4—44no—
783C22×C4—44no—
784C22×C4—816no—
785C22×C4C2×#4114yes—
786C22×C4C2×#4114yes—
787C22×C4C2×#4114yes—
788C22×C4C2512yes—
789C22×C4C2514yes—
790C22×C4C2514yes—
791C22×C4C2512yes—
792C22×C4C2514yes—
793C22×C4C2512yes—
794C22×C4C2514yes—
795C22×C4C2518yes—
796C22×C4C2514yes—
797C22×C4C2512yes—
798C22×C4C2512yes—
799C22×C4C2514yes—
800C22×C4C2511yescharacteristic
801C22×C4C2511yescharacteristic
802C22×C4C2511yescharacteristic
803C22×C4C2511yescharacteristic
804C22×C4C2514yes—
805C22×C4C2512yes—
806C22×C4C2511yescharacteristic
807C22×C4C2511yescharacteristic
808C4⋊C4—24no—
809C4⋊C4—22no—
810C4⋊C4—22no—
811C4⋊C4—24no—
812C4⋊C4—24no—
813C4⋊C4—24no—
814C4⋊C4—24no—
815C4⋊C4—28no—
816C4⋊C4—28no—
817C4⋊C4—24no—
818C4⋊C4—24no—
819C4⋊C4—24no—
820C4⋊C4—216no—
821C4⋊C4—28no—
822C4⋊C4—216no—
823C4⋊C4—216no—
824C4⋊C4—28no—
825C4⋊C4—28no—
826C4⋊C4—24no—
827C4⋊C4—28no—
828C4⋊C4—24no—
829C4⋊C4—24no—
830C4⋊C4—28no—
831C4⋊C4—42no—
832C4⋊C4—48no—
833C4⋊C4—44no—
834C4⋊C4—44no—
835C4⋊C4—48no—
836C4⋊C4—44no—
837C4⋊C4—48no—
838C4⋊C4—44no—
839C4⋊C4—48no—
840C4⋊C4—48no—
841C4⋊C4—48no—
842C4⋊C4—48no—
843C4⋊C4—48no—
844C4⋊C4—48no—
845C4⋊C4—48no—
846C4⋊C4H(5,𝔽2)18yes—
847C22⋊C4—28no—
848C22⋊C4—28no—
849C22⋊C4—24no—
850C22⋊C4—24no—
851C22⋊C4—24no—
852C22⋊C4—24no—
853C22⋊C4—28no—
854C22⋊C4—28no—
855C22⋊C4—28no—
856C22⋊C4—216no—
857C22⋊C4—216no—
858C22⋊C4—24no—
859C22⋊C4—28no—
860C22⋊C4—44no—
861C22⋊C4—44no—
862C22⋊C4—42no—
863C22⋊C4—44no—
864C22⋊C4—48no—
865C22⋊C4—44no—
866C22⋊C4—44no—
867C22⋊C4—48no—
868C22⋊C4—44no—
869C22⋊C4—48no—
870C22⋊C4—48no—
871C22⋊C4—48no—
872C22⋊C4—48no—
873C22⋊C4—48no—
874C22⋊C4—48no—
875C22⋊C4—48no—
876C22⋊C4—48no—
877C22⋊C4—48no—
878C22⋊C4—48no—
879C22⋊C4—48no—
880C42—28no—
881C42—24no—
882C42—28no—
883C42—28no—
884C42—28no—
885C42—24no—
886C42—28no—
887C42—24no—
888C42—24no—
889C42—24no—
890C42—24no—
891C42—28no—
892C42—24no—
893C42—44no—
894C42—44no—
895C42—42no—
896C42—44no—
897C42—44no—
898C42—44no—
899C42—48no—
900C42C2×#4114yes—
901C42C2×#4114yes—
902C42C2×#4114yes—
903C42C2×#4114yes—
904C23—22no—
905C23—22no—
906C23—24no—
907C23—21no—
908C23—22no—
909C23—21no—
910C23—24no—
911C23—22no—
912C23—22no—
913C23—24no—
914C23—24no—
915C23—28no—
916C23—24no—
917C23—22no—
918C23—24no—
919C23—28no—
920C23—24no—
921C23—22no—
922C23—48no—
923C23—48no—
924C23—84no—
925C23—88no—
926C23—88no—
927C23C22×#4112yes—
928C23C2×2−1+414yes—
929C23C2611yescharacteristic
930Q8—48no—
931Q8—48no—
932Q8—48no—
933D4—28no—
934D4—432no—
935D4—48no—
936D4—48no—
937D4—48no—
938D4—44no—
939D4—48no—
940D4—88no—
941D4—816no—
942C2×C4—22no—
943C2×C4—22no—
944C2×C4—24no—
945C2×C4—21no—
946C2×C4—24no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—21no—
950C2×C4—22no—
951C2×C4—28no—
952C2×C4—28no—
953C2×C4—24no—
954C2×C4—24no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—24no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—24no—
962C2×C4—24no—
963C2×C4—24no—
964C2×C4—24no—
965C2×C4—24no—
966C2×C4—24no—
967C2×C4—28no—
968C2×C4—28no—
969C2×C4—24no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—24no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—24no—
976C2×C4—24no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—24no—
980C2×C4—28no—
981C2×C4—24no—
982C2×C4—24no—
983C2×C4—24no—
984C2×C4—28no—
985C2×C4—24no—
986C2×C4—44no—
987C2×C4—48no—
988C2×C4—48no—
989C2×C4—88no—
990C2×C4—816no—
991C2×C4—84no—
992C2×C4—84no—
993C2×C4—88no—
994C2×C4—88no—
995C2×C4—84no—
996C2×C4C22×#4112yes—
997C2×C4C22×#4112yes—
998C2×C4C22×#4112yes—
999C2×C4C22×#4112yes—
1000C2×C4C22×#4112yes—
1001C2×C4C22×#4112yes—
1002C2×C4C2×H(5,𝔽2)18yes—
1003C2×C4C2×H(5,𝔽2)14yes—
1004C2×C4C2×2−1+412yes—
1005C2×C4#58514yes—
1006C2×C4#58512yes—
1007C22—28no—
1008C22—22no—
1009C22—22no—
1010C22—24no—
1011C22—22no—
1012C22—42no—
1013C22—44no—
1014C22—42no—
1015C22—42no—
1016C22—42no—
1017C22—48no—
1018C22—44no—
1019C22—48no—
1020C22—44no—
1021C22—42no—
1022C22—44no—
1023C22—42no—
1024C22—44no—
1025C22—44no—
1026C22—42no—
1027C22—816no—
1028C22C23×#4111yescharacteristic
1029C22C22×H(5,𝔽2)12yes—
1030C22C22×2−1+411yescharacteristic
1031C22C2×#58512yes—
1032C22C2×#58511yescharacteristic
1033C4—28no—
1034C4—24no—
1035C4—22no—
1036C4—22no—
1037C4—22no—
1038C4—22no—
1039C4—42no—
1040C4—44no—
1041C4—42no—
1042C4—42no—
1043C4—44no—
1044C4—48no—
1045C4—44no—
1046C4—42no—
1047C4—42no—
1048C4—44no—
1049C4—44no—
1050C4—44no—
1051C4#349514yes—
1052C4#350814yes—
1053C2—44no—
1054C2—42no—
1055C2—84no—
1056C2—82no—
1057C2#6268611yescharacteristic
1058C2C2×#350811yescharacteristic
1059C2C2×#349511yescharacteristic
1060C2#6301312yes—
1061C2#6301912yes—
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. #42072C2semidirect
2. #41979C2semidirect
3. #39756C2semidirect
4. #39273C2semidirect
5. #39066C2semidirect
6. #38969C2semidirect
7. #38260C2semidirect
8. #37774C2semidirect
9. #37671C2semidirect
10. #37625C2semidirect
11. #37619C2semidirect
12. #36573C2semidirect
13. #36370C2semidirect
14. #36143C2semidirect
15. #35690C2semidirect
16. #35209C2semidirect
17. #35202C2semidirect
18. #35176C2semidirect
19. #35172C2semidirect
21. #34934C2semidirect
22. #34226C2semidirect
23. #34154C2semidirect
24. #34126C2semidirect
25. C2×#541C22semidirect
28. C2×#529C22semidirect
31. #2864C22semidirect
33. #2859C22semidirect
34. #2859C22semidirect
35. #2857C22semidirect
36. #2855C22semidirect
38. #2829C22semidirect
40. #2808C22semidirect
41. #2773C22semidirect
43. #2751C22semidirect
44. #2727C22semidirect
45. #2721C22semidirect
49. #2694C22semidirect
53. #2667C22semidirect
54. #2664C22semidirect
55. #2658C22semidirect
56. #2644C22semidirect
58. #2640C22semidirect
59. #2633C22semidirect
60. #2630C22semidirect
63. #2624C22semidirect
64. #2620C22semidirect
65. #2606C22semidirect
69. #2580C22semidirect
70. #2580C22semidirect
71. #2580C22semidirect
74. #2554C22semidirect
76. #2552C22semidirect
77. #2552C22semidirect
78. #2548C22semidirect
79. #2546C22semidirect
90. #2522C22semidirect
91. #2519C22semidirect
92. #2517C22semidirect
94. #2512C22semidirect
95. #2507C22semidirect
96. #2506C22semidirect
98. #2490C22semidirect
99. #2489C22semidirect
100. #2479C22semidirect
102. #2468C22semidirect
104. #2466C22semidirect
105. #2466C22semidirect
106. #2460C22semidirect
107. #2458C22semidirect
109. #2454C22semidirect
110. #2454C22semidirect
111. #2454C22semidirect
116. #2441C22semidirect
119. #2429C22semidirect
120. #2429C22semidirect
121. #2427C22semidirect
122. #2426C22semidirect
123. #2423C22semidirect
124. #2422C22semidirect
125. #2419C22semidirect
128. #2392C22semidirect
129. #2371C22semidirect
130. #2371C22semidirect
131. #2367C22semidirect
132. #2365C22semidirect
133. #2365C22semidirect
138. #2359C22semidirect
141. #2357C22semidirect
146. #2349C22semidirect
147. #2349C22semidirect
153. #2330C22semidirect
154. #2330C22semidirect
156. #2323C22semidirect
158. #2319C22semidirect
161. C4×C4⋊Q8C22semidirect
165. C4×#127C22semidirect
166. C4×#121C22semidirect
168. #2295C22semidirect
169. #2295C22semidirect
171. #2293C22semidirect
176. #2275C22semidirect
177. C42×Q8C22semidirect
178. C42×Q8C22semidirect

Maximal subgroups

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

subgroupindex
#420722
#419792
#397562
#392732
#390662
#389692
#382602
#377742
#376712
#376252
#376192
#365732
#363702
#361432
#356902
#352092
#352022
#351762
#351722
#349362
#349342
#342262
#341542
#341262