Finite Group Databasebeta

← #7654870

Subgroups — #7654870

Order 512.

5214 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#42075C218yesmaximal, complemented
2#41977C214yesmaximal, complemented
3#39628C212yesmaximal, complemented
4#39269C214yesmaximal, complemented
5#39076C214yesmaximal, complemented
6#38969C212yesmaximal, complemented
7#38250C214yesmaximal, complemented
8#37773C214yesmaximal, complemented
9#37668C214yesmaximal, complemented
10#37628C212yesmaximal, complemented
11#37619C211yesmaximal, characteristic, complemented
12#36609C212yesmaximal, complemented
13#36370C212yesmaximal, complemented
14#36148C214yesmaximal, complemented
15#35994C214yesmaximal, complemented
16#35198C212yesmaximal, complemented
17#35197C212yesmaximal, complemented
18#35192C211yesmaximal, characteristic, complemented
19#35172C211yesmaximal, characteristic, complemented
20#34936C211yesmaximal, characteristic
21#34929C212yesmaximal, complemented
22#34226C211yesmaximal, characteristic, complemented
23#34154C211yesmaximal, characteristic, complemented
24#34126C211yesmaximal, characteristic, complemented
25C2×#542C2214yescomplemented
26C2×#533C2211yescharacteristic
27C2×#533C2214yescomplemented
28C2×#532C2211yescharacteristic
29C2×#525C2214yes—
30C22×C4×D4C2211yescharacteristic
31#2864C2212yescomplemented
32#2862C2212yescomplemented
33#2860C2214yescomplemented
34#2858C2214yes—
35#2854C2214yescomplemented
36#2850C2214yescomplemented
37#2848C2214yes—
38#2836C2218yescomplemented
39#2816C2214yes—
40#2804C2218yescomplemented
41#2797C2218yes—
42#2754C2218yescomplemented
43#2751C2218yescomplemented
44#2732C2218yescomplemented
45#2730C2218yes—
46#2721C2218yescomplemented
47#2697C2218yes—
48#2695C2218yes—
49#2694C2218yescomplemented
50#2687C2218yes—
51#2684C2218yes—
52#2665C2214yes—
53#2662C2218yescomplemented
54#2658C2212yescomplemented
55#2654C2218yescomplemented
56#2648C2218yescomplemented
57#2647C2214yescomplemented
58#2644C2214yes—
59#2640C2212yescomplemented
60#2633C2214yescomplemented
61#2626C2214yes—
62#2625C2214yescomplemented
63#2624C2214yes—
64#2621C2214yescomplemented
65#2605C2214yescomplemented
66#2592C2218yescomplemented
67#2580C2212yes—
68#2580C2212yes—
69#2580C2212yescomplemented
70#2580C2212yescomplemented
71#2575C2218yescomplemented
72#2571C2212yescomplemented
73#2566C2214yes—
74#2563C2212yes—
75#2558C2218yes—
76#2557C2218yes—
77#2556C2218yescomplemented
78#2551C2212yescomplemented
79#2548C2212yescomplemented
80#2546C2212yescomplemented
81#2542C2212yes—
82#2542C2211yescharacteristic
83#2542C2211yescharacteristic
84#2541C2211yescharacteristic
85#2541C2211yescharacteristic
86#2540C2214yes—
87#2539C2214yes—
88#2538C2212yes—
89#2538C2212yes—
90#2513C2214yes—
91#2513C2214yescomplemented
92#2507C2214yescomplemented
93#2506C2214yescomplemented
94#2501C2212yes—
95#2492C2214yescomplemented
96#2491C2214yescomplemented
97#2479C2218yescomplemented
98#2472C2218yes—
99#2471C2218yes—
100#2468C2218yescomplemented
101#2461C2218yescomplemented
102#2460C2218yescomplemented
103#2458C2218yes—
104#2458C2218yescomplemented
105#2457C2218yescomplemented
106#2452C2214yes—
107#2452C2214yescomplemented
108#2450C2218yescomplemented
109#2450C2218yescomplemented
110#2448C2218yescomplemented
111#2447C2218yescomplemented
112#2445C2214yes—
113#2445C2214yes—
114#2439C2214yes—
115#2439C2214yes—
116#2433C2212yes—
117#2432C2214yes—
118#2429C2214yescomplemented
119#2429C2214yescomplemented
120#2427C2214yescomplemented
121#2426C2214yescomplemented
122#2423C2218yescomplemented
123#2421C2214yescomplemented
124#2420C2214yescomplemented
125#2419C2218yescomplemented
126#2411C2218yes—
127#2397C2214yes—
128#2396C2218yescomplemented
129#2371C2212yescomplemented
130#2371C2212yescomplemented
131#2367C2218yescomplemented
132#2367C2214yescomplemented
133#2365C2212yescomplemented
134#2365C2212yescomplemented
135#2363C2214yes—
136#2362C2212yes—
137#2362C2212yes—
138#2362C2214yes—
139#2359C2218yescomplemented
140#2357C2211yescharacteristic
141#2357C2211yescharacteristic
142#2357C2212yescomplemented
143#2353C2212yes—
144#2353C2212yes—
145#2349C2211yescharacteristic
146#2349C2211yescharacteristic
147#2349C2212yescomplemented
148#2345C2212yes—
149#2342C2214yes—
150#2341C2212yes—
151#2339C2212yes—
152D4×C22⋊C4C2212yes—
153#2331C2214yescomplemented
154#2328C2214yes—
155#2324C2214yes—
156#2324C2214yescomplemented
157#2319C2214yescomplemented
158#2319C2212yescomplemented
159#2317C2212yes—
160#2309C2212yes—
161C4×C4⋊Q8C2214yescomplemented
162C4×C4⋊Q8C2212yescomplemented
163C4×#127C2212yes—
164C4×#127C2212yes—
165C4×#127C2212yescomplemented
166C4×C22⋊Q8C2214yescomplemented
167#2298C2214yes—
168#2295C2212yescomplemented
169#2295C2212yescomplemented
170#2293C2214yes—
171#2293C2212yes—
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#542—416no—
187#533—28no—
188#533—416no—
189#532—28no—
190C2×C4⋊Q8C2311yescharacteristic
191C2×C4⋊Q8C2311yescharacteristic
192C2×C4⋊Q8C2314yes—
193C2×C4⋊Q8C2311yescharacteristic
194C2×C4⋊Q8C2314yes—
195C2×C4⋊Q8C2314yes—
196C2×#127C2312yes—
197C2×#127C2311yescharacteristic
198C2×#127C2312yes—
199C2×#126C2318yes—
200C2×#125C2312yes—
201C2×#125C2318yes—
202C2×#124C2312yes—
203C2×#124C2318yes—
204C2×#124C2314yes—
205C2×#124C2318yes—
206#525—416no—
207C2×#123C2318yes—
208C2×#123C2318yes—
209C2×#123C2318yes—
210C2×C22⋊Q8C2312yes—
211C2×C22⋊Q8C2312yes—
212C2×C22⋊Q8C2314yes—
213C2×C22⋊Q8C2314yes—
214C2×C22⋊Q8C2314yes—
215C2×C22⋊Q8C2314yes—
216C2×C22⋊Q8C2318yes—
217C2×C22⋊Q8C2318yes—
218C2×#121C2312yes—
219C2×#121C2314yes—
220C2×#121C2312yes—
221C2×#121C2314yes—
222C2×#120C2318yes—
223C2×C4×Q8C2312yes—
224C2×C4×Q8C2312yes—
225C2×C4×Q8C2312yes—
226C2×C4×Q8C2312yes—
227C2×C4×Q8C2314yes—
228C2×C4×Q8C2318yes—
229C2×C4×Q8C2314yes—
230C2×C4×D4—28no—
231C2×C4×D4C2311yescharacteristic
232C2×C4×D4C2311yescharacteristic
233C2×C4×D4C2312yes—
234C2×C4×D4C2312yes—
235C2×C4×D4C2312yes—
236C2×C4×D4C2312yes—
237C2×C4×D4C2312yes—
238C2×C4×D4C2311yescharacteristic
239C2×C4×D4C2311yescharacteristic
240C2×C4×D4C2318yes—
241C2×C4×D4C2318yes—
242C2×C4×D4C2314yes—
243C2×C4×D4C2314yes—
244C2×C4×D4C2314yes—
245C2×C4×D4C2312yes—
246C2×#117C2312yes—
247C2×#117C2312yes—
248C2×#117C2312yes—
249C2×#117C2312yes—
250C2×#117C2314yes—
251C2×#117C2318yes—
252C22×C4⋊C4C2311yescharacteristic
253C22×C22⋊C4C2312yes—
254C22×C22⋊C4C2314yes—
255C22×C42C2314yes—
256C22×C42C2311yescharacteristic
257#400C2318yes—
258#400C2318yes—
259#400C2318yes—
260#400C2318yes—
261#399C2314yes—
262#399C2314yes—
263#399C2318yes—
264#399C2314yes—
265#399C2314yes—
266#399C2314yes—
267#399C2318yes—
268#399C2314yes—
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#397C2318yes—
282#397C2318yes—
283#396C2318yes—
284#396C2318yes—
285#396C2318yes—
286#396C2318yes—
287#396C2318yes—
288#396C2318yes—
289#395C2318yes—
290#394C2318yes—
291#394C2318yes—
292#394C2318yes—
293#394C2318yes—
294#394C2318yes—
295#394C2318yes—
296#394C2318yes—
297#393C2314yes—
298#393C2314yes—
299#393C2314yes—
300#393C2314yes—
301#393C2318yes—
302#393C2318yes—
303#393C2318yes—
304#392C2314yes—
305#392C2314yes—
306#392C2318yes—
307#391C2318yes—
308#391C2314yes—
309#391C2318yes—
310#391C2318yes—
311#391C2312yes—
312#391C2318yes—
313#391C2312yes—
314#391C2314yes—
315#391C2314yes—
316#390C2312yes—
317#390C2318yes—
318#390C2312yes—
319#390C2312yes—
320#390C2312yes—
321#390C2318yes—
322#390C2314yes—
323#390C2314yes—
324#390C2314yes—
325#390C2314yes—
326#390C2314yes—
327#390C2314yes—
328#390C2314yes—
329#390C2314yes—
330#390C2318yes—
331#390C2318yes—
332#390C2314yes—
333#390C2314yes—
334#390C2312yes—
335#390C2312yes—
336#390C2318yes—
337#389C2314yes—
338#389C2314yes—
339#389C2314yes—
340#389C2314yes—
341#389C2318yes—
342#389C2314yes—
343#389C2314yes—
344#389C2314yes—
345#389C2314yes—
346#389C2314yes—
347#389C2312yes—
348#389C2312yes—
349#389C2312yes—
350#389C2314yes—
351#389C2318yes—
352#389C2312yes—
353#389C2314yes—
354#388C2318yes—
355#388C2318yes—
356#388C2318yes—
357#388C2318yes—
358#388C2318yes—
359#388C2318yes—
360#388C2318yes—
361#388C2314yes—
362#388C2314yes—
363#388C2318yes—
364#388C2318yes—
365#388C2314yes—
366#388C2314yes—
367#388C2318yes—
368#388C2314yes—
369#388C2314yes—
370#388C2314yes—
371#388C2314yes—
372#388C2318yes—
373#388C2318yes—
374#388C2318yes—
375#387C2314yes—
376#387C2314yes—
377#387C2318yes—
378#387C2318yes—
379#387C2314yes—
380#387C2318yes—
381#387C2314yes—
382#387C2318yes—
383#387C2314yes—
384#387C2314yes—
385#387C2314yes—
386#387C2314yes—
387#387C2314yes—
388#387C2314yes—
389#387C2318yes—
390#386C2318yes—
391#386C2318yes—
392#386C2318yes—
393#386C2318yes—
394#386C2318yes—
395#386C2318yes—
396#386C2314yes—
397#386C2314yes—
398#386C2318yes—
399#385C2318yes—
400#385C2318yes—
401#385C2318yes—
402#385C2318yes—
403#385C2318yes—
404#385C2318yes—
405#385C2318yes—
406#385C2314yes—
407#385C2314yes—
408#385C2318yes—
409#384C2312yes—
410#384C2312yes—
411#384C2312yes—
412#384C2314yes—
413#383C2312yes—
414#382C2314yes—
415#382C2314yes—
416#382C2314yes—
417#382C2312yes—
418#382C2311yescharacteristic
419#382C2311yescharacteristic
420#381C2312yes—
421#381C2318yes—
422#381C2314yes—
423#381C2312yes—
424#381C2312yes—
425#380C2314yes—
426#380C2314yes—
427#380C2314yes—
428#380C2318yes—
429#380C2312yes—
430#380C2312yes—
431#380C2312yes—
432#380C2314yes—
433#380C2312yes—
434#380C2312yes—
435#379C2318yes—
436#379C2314yes—
437C4×C4⋊C4C2312yes—
438C4×C4⋊C4C2314yes—
439C4×C4⋊C4C2318yes—
440C4×C4⋊C4C2314yes—
441C4×C4⋊C4C2312yes—
442C4×C4⋊C4C2312yes—
443C4×C4⋊C4C2311yescharacteristic
444C4×C4⋊C4C2312yes—
445C4×C4⋊C4C2312yes—
446C4×C4⋊C4C2312yes—
447C4×C4⋊C4C2312yes—
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2314yes—
451C4×C4⋊C4C2314yes—
452C4×C4⋊C4C2312yes—
453C4×C4⋊C4C2314yes—
454C4×C4⋊C4C2314yes—
455C4×C4⋊C4C2314yes—
456C4×C4⋊C4C2312yes—
457C4×C4⋊C4C2314yes—
458C4×C4⋊C4C2314yes—
459C4×C4⋊C4C2311yescharacteristic
460C4×C22⋊C4C2318yes—
461C4×C22⋊C4C2312yes—
462C4×C22⋊C4C2311yescharacteristic
463C4×C22⋊C4C2311yescharacteristic
464C4×C22⋊C4C2314yes—
465C4×C22⋊C4C2314yes—
466C4×C22⋊C4C2314yes—
467C4×C22⋊C4C2314yes—
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#376C2311yescharacteristic
477#376C2314yes—
478#376C2312yes—
479#376C2312yes—
480#376C2311yescharacteristic
481C2×#95C2314yes—
482C2×#95C2312yes—
483C2×#95C2312yes—
484C43C2312yes—
485C43C2312yes—
486C43C2314yes—
487C25C2412yes—
488C2×#41—28no—
489C2×#41—48no—
490C22×Q8C2412yes—
491C22×Q8C2412yes—
492C22×Q8C2412yes—
493C22×Q8C2418yes—
494C22×D4—24no—
495C22×D4—24no—
496C22×D4—42no—
497C22×D4C2412yes—
498C22×D4C2412yes—
499C22×D4C2411yescharacteristic
500C22×D4C2412yes—
501C22×D4C2411yescharacteristic
502C22×D4C2412yes—
503C22×D4C2418yes—
504C22×D4C2418yes—
505C22×D4C2414yes—
506C23×C4—28no—
507C23×C4—48no—
508C23×C4C2412yes—
509C23×C4C2412yes—
510C23×C4C2414yes—
511C23×C4C2411yescharacteristic
512C23×C4C2411yescharacteristic
513C23×C4C2412yes—
514C23×C4C2412yes—
515C23×C4C2412yes—
516C23×C4C2414yes—
517C23×C4C2414yes—
518C23×C4C2418yes—
519C23×C4C2411yescharacteristic
520C4⋊Q8—216no—
521C4⋊Q8—24no—
522C4⋊Q8—24no—
523C4⋊Q8—24no—
524C4⋊Q8—48no—
525C4⋊Q8—48no—
526#127—28no—
527#127—24no—
528#127—44no—
529#126—416no—
530#125—28no—
531#125—416no—
532#124—28no—
533#124—416no—
534#124—48no—
535#124—416no—
536#123—416no—
537#123—416no—
538#123—416no—
539C22⋊Q8—28no—
540C22⋊Q8—28no—
541C22⋊Q8—216no—
542C22⋊Q8—416no—
543C22⋊Q8—416no—
544C22⋊Q8—48no—
545C22⋊Q8—48no—
546C22⋊Q8—48no—
547#121—28no—
548#121—28no—
549#121—216no—
550#121—48no—
551#120—416no—
552C4×Q8—28no—
553C4×Q8—28no—
554C4×Q8—28no—
555C4×Q8—28no—
556C4×Q8—48no—
557C4×Q8—48no—
558C4×Q8—416no—
559C4×D4—28no—
560C4×D4—24no—
561C4×D4—24no—
562C4×D4—28no—
563C4×D4—24no—
564C4×D4—24no—
565C4×D4—28no—
566C4×D4—28no—
567C4×D4—28no—
568C4×D4—48no—
569C4×D4—416no—
570C4×D4—48no—
571C4×D4—44no—
572C4×D4—416no—
573C4×D4—48no—
574#117—28no—
575#117—28no—
576#117—48no—
577#117—44no—
578#117—416no—
579#117—44no—
580C2×C4⋊C4—24no—
581C2×C4⋊C4C2411yescharacteristic
582C2×C4⋊C4C2412yes—
583C2×C4⋊C4C2411yescharacteristic
584C2×C4⋊C4C2414yes—
585C2×C4⋊C4C2412yes—
586C2×C4⋊C4C2412yes—
587C2×C4⋊C4C2418yes—
588C2×C4⋊C4C2412yes—
589C2×C4⋊C4C2412yes—
590C2×C4⋊C4C2414yes—
591C2×C4⋊C4C2418yes—
592C2×C4⋊C4C2412yes—
593C2×C4⋊C4C2412yes—
594C2×C4⋊C4C2412yes—
595C2×C4⋊C4C2412yes—
596C2×C4⋊C4C2414yes—
597C2×C4⋊C4C2414yes—
598C2×C4⋊C4C2414yes—
599C2×C4⋊C4C2414yes—
600C2×C4⋊C4C2412yes—
601C2×C4⋊C4C2412yes—
602C2×C4⋊C4C2414yes—
603C2×C4⋊C4C2414yes—
604C2×C4⋊C4C2418yes—
605C2×C4⋊C4C2414yes—
606C2×C4⋊C4C2412yes—
607C2×C4⋊C4C2418yes—
608C2×C4⋊C4C2414yes—
609C2×C4⋊C4C2418yes—
610C2×C4⋊C4C2418yes—
611C2×C4⋊C4C2418yes—
612C2×C4⋊C4C2414yes—
613C2×C4⋊C4C2418yes—
614C2×C4⋊C4C2418yes—
615C2×C4⋊C4C2418yes—
616C2×C4⋊C4C2412yes—
617C2×C22⋊C4—28no—
618C2×C22⋊C4—48no—
619C2×C22⋊C4C2412yes—
620C2×C22⋊C4C2412yes—
621C2×C22⋊C4C2412yes—
622C2×C22⋊C4C2412yes—
623C2×C22⋊C4C2412yes—
624C2×C22⋊C4C2414yes—
625C2×C22⋊C4C2418yes—
626C2×C22⋊C4C2414yes—
627C2×C22⋊C4C2414yes—
628C2×C22⋊C4C2418yes—
629C2×C22⋊C4C2414yes—
630C2×C22⋊C4C2414yes—
631C2×C22⋊C4C2418yes—
632C2×C22⋊C4C2414yes—
633C2×C22⋊C4C2414yes—
634C2×C22⋊C4C2414yes—
635C2×C22⋊C4C2418yes—
636C2×C22⋊C4C2414yes—
637C2×C22⋊C4C2414yes—
638C2×C22⋊C4C2412yes—
639C2×C22⋊C4C2414yes—
640C2×C22⋊C4C2418yes—
641C2×C22⋊C4C2418yes—
642C2×C22⋊C4C2418yes—
643C2×C22⋊C4C2414yes—
644C2×C22⋊C4C2418yes—
645C2×C22⋊C4C2418yes—
646C2×C22⋊C4C2418yes—
647C2×C22⋊C4C2418yes—
648C2×C22⋊C4C2418yes—
649C2×C22⋊C4C2418yes—
650C2×C22⋊C4C2418yes—
651C2×C22⋊C4C2418yes—
652C2×C42—48no—
653C2×C42#4118yes—
654C2×C42C2412yes—
655C2×C42C2414yes—
656C2×C42C2414yes—
657C2×C42C2412yes—
658C2×C42C2414yes—
659C2×C42C2414yes—
660C2×C42C2412yes—
661C2×C42C2412yes—
662C2×C42C2412yes—
663C2×C42C2414yes—
664C2×C42C2414yes—
665C2×C42C2412yes—
666C2×C42C2412yes—
667C2×C42C2418yes—
668C2×C42C2412yes—
669C2×C42C2414yes—
670C2×C42C2414yes—
671C2×C42C2414yes—
672C2×C42C2414yes—
673C2×C42C2414yes—
674C2×C42C2411yescharacteristic
675C2×C42C2411yescharacteristic
676C2×C42C2411yescharacteristic
677C2×C42C2411yescharacteristic
678#95C2411yescharacteristic
679#95C2411yescharacteristic
680#95C2411yescharacteristic
681#95C2412yes—
682#95C2412yes—
683#95C2414yes—
684#95C2414yes—
685#95C2414yes—
686#95C2418yes—
687#95C2412yes—
688#95C2411yescharacteristic
689#95C2412yes—
690#95C2412yes—
691#95C2414yes—
692#95C2412yes—
693#95C2414yes—
694#95C2414yes—
695#95C2414yes—
696#95C2412yes—
697#95C2412yes—
698#95C2414yes—
699#95C2414yes—
700#95C2414yes—
701#95C2414yes—
702#95C2414yes—
703#95C2418yes—
704#95C2418yes—
705#95C2414yes—
706#95C2414yes—
707#95C2414yes—
708#95C2414yes—
709#95C2418yes—
710#95C2414yes—
711#95C2418yes—
712#95C2418yes—
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—216no—
734C2×Q8—44no—
735C2×Q8—48no—
736C2×Q8—48no—
737C2×D4—24no—
738C2×D4—28no—
739C2×D4—216no—
740C2×D4—22no—
741C2×D4—24no—
742C2×D4—22no—
743C2×D4—24no—
744C2×D4—24no—
745C2×D4—24no—
746C2×D4—28no—
747C2×D4—216no—
748C2×D4—24no—
749C2×D4—22no—
750C2×D4—22no—
751C2×D4—24no—
752C2×D4—22no—
753C2×D4—416no—
754C2×D4—44no—
755C2×D4—42no—
756C2×D4—48no—
757C2×D4—48no—
758C2×D4—48no—
759C2×D4—48no—
760C2×D4—48no—
761C2×D42−1+414yes—
762C22×C4—24no—
763C22×C4—22no—
764C22×C4—22no—
765C22×C4—28no—
766C22×C4—24no—
767C22×C4—24no—
768C22×C4—24no—
769C22×C4—28no—
770C22×C4—28no—
771C22×C4—28no—
772C22×C4—24no—
773C22×C4—24no—
774C22×C4—28no—
775C22×C4—44no—
776C22×C4—42no—
777C22×C4—44no—
778C22×C4—44no—
779C22×C4—44no—
780C22×C4—44no—
781C22×C4—48no—
782C22×C4—44no—
783C22×C4—44no—
784C22×C4—48no—
785C22×C4—48no—
786C22×C4—48no—
787C22×C4—816no—
788C22×C4C2×#4114yes—
789C22×C4C2×#4114yes—
790C22×C4C2×#4114yes—
791C22×C4C2514yes—
792C22×C4C2512yes—
793C22×C4C2514yes—
794C22×C4C2514yes—
795C22×C4C2514yes—
796C22×C4C2512yes—
797C22×C4C2512yes—
798C22×C4C2518yes—
799C22×C4C2512yes—
800C22×C4C2514yes—
801C22×C4C2512yes—
802C22×C4C2514yes—
803C22×C4C2511yescharacteristic
804C22×C4C2511yescharacteristic
805C22×C4C2511yescharacteristic
806C22×C4C2511yescharacteristic
807C22×C4C2514yes—
808C22×C4C2512yes—
809C22×C4C2511yescharacteristic
810C22×C4C2511yescharacteristic
811C4⋊C4—24no—
812C4⋊C4—22no—
813C4⋊C4—22no—
814C4⋊C4—24no—
815C4⋊C4—24no—
816C4⋊C4—24no—
817C4⋊C4—24no—
818C4⋊C4—28no—
819C4⋊C4—28no—
820C4⋊C4—24no—
821C4⋊C4—24no—
822C4⋊C4—24no—
823C4⋊C4—216no—
824C4⋊C4—216no—
825C4⋊C4—28no—
826C4⋊C4—28no—
827C4⋊C4—28no—
828C4⋊C4—24no—
829C4⋊C4—28no—
830C4⋊C4—24no—
831C4⋊C4—24no—
832C4⋊C4—28no—
833C4⋊C4—42no—
834C4⋊C4—44no—
835C4⋊C4—48no—
836C4⋊C4—44no—
837C4⋊C4—44no—
838C4⋊C4—48no—
839C4⋊C4—44no—
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—216no—
861C22⋊C4—44no—
862C22⋊C4—44no—
863C22⋊C4—42no—
864C22⋊C4—44no—
865C22⋊C4—48no—
866C22⋊C4—44no—
867C22⋊C4—44no—
868C22⋊C4—48no—
869C22⋊C4—44no—
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—24no—
885C42—28no—
886C42—28no—
887C42—24no—
888C42—24no—
889C42—24no—
890C42—24no—
891C42—28no—
892C42—24no—
893C42—44no—
894C42—44no—
895C42—42no—
896C42—44no—
897C42—48no—
898C42—44no—
899C42—44no—
900C42C2×#4114yes—
901C42C2×#4114yes—
902C42C2×#4114yes—
903C42C2×#4114yes—
904C23—22no—
905C23—24no—
906C23—22no—
907C23—21no—
908C23—22no—
909C23—21no—
910C23—24no—
911C23—22no—
912C23—22no—
913C23—24no—
914C23—28no—
915C23—24no—
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—
933Q8—816no—
934D4—28no—
935D4—48no—
936D4—48no—
937D4—48no—
938D4—44no—
939D4—48no—
940D4—816no—
941D4—816no—
942D4—88no—
943C2×C4—22no—
944C2×C4—22no—
945C2×C4—22no—
946C2×C4—21no—
947C2×C4—24no—
948C2×C4—22no—
949C2×C4—24no—
950C2×C4—21no—
951C2×C4—22no—
952C2×C4—28no—
953C2×C4—28no—
954C2×C4—24no—
955C2×C4—24no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—24no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—24no—
962C2×C4—24no—
963C2×C4—24no—
964C2×C4—24no—
965C2×C4—22no—
966C2×C4—24no—
967C2×C4—24no—
968C2×C4—28no—
969C2×C4—28no—
970C2×C4—24no—
971C2×C4—22no—
972C2×C4—24no—
973C2×C4—24no—
974C2×C4—24no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—24no—
981C2×C4—28no—
982C2×C4—24no—
983C2×C4—24no—
984C2×C4—28no—
985C2×C4—24no—
986C2×C4—24no—
987C2×C4—44no—
988C2×C4—416no—
989C2×C4—48no—
990C2×C4—48no—
991C2×C4—84no—
992C2×C4—84no—
993C2×C4—88no—
994C2×C4—84no—
995C2×C4—88no—
996C2×C4—168no—
997C2×C4C22×#4112yes—
998C2×C4C22×#4112yes—
999C2×C4C22×#4112yes—
1000C2×C4C22×#4112yes—
1001C2×C4C22×#4112yes—
1002C2×C4C22×#4112yes—
1003C2×C4C2×H(5,𝔽2)18yes—
1004C2×C4C2×H(5,𝔽2)14yes—
1005C2×C4C2×2−1+412yes—
1006C2×C4#58514yes—
1007C2×C4#58512yes—
1008C22—28no—
1009C22—22no—
1010C22—22no—
1011C22—24no—
1012C22—22no—
1013C22—42no—
1014C22—44no—
1015C22—42no—
1016C22—42no—
1017C22—42no—
1018C22—48no—
1019C22—44no—
1020C22—48no—
1021C22—44no—
1022C22—42no—
1023C22—44no—
1024C22—42no—
1025C22—44no—
1026C22—44no—
1027C22—42no—
1028C22—816no—
1029C22C23×#4111yescharacteristic
1030C22C22×H(5,𝔽2)12yes—
1031C22C22×2−1+411yescharacteristic
1032C22C2×#58512yes—
1033C22C2×#58511yescharacteristic
1034C4—24no—
1035C4—28no—
1036C4—22no—
1037C4—22no—
1038C4—22no—
1039C4—22no—
1040C4—42no—
1041C4—44no—
1042C4—44no—
1043C4—42no—
1044C4—44no—
1045C4—42no—
1046C4—48no—
1047C4—42no—
1048C4—42no—
1049C4—44no—
1050C4—44no—
1051C4—44no—
1052C4#349514yes—
1053C4#350814yes—
1054C2—44no—
1055C2—42no—
1056C2—84no—
1057C2—82no—
1058C2#6268611yescharacteristic
1059C2C2×#350811yescharacteristic
1060C2C2×#349511yescharacteristic
1061C2#6301512yes—
1062C2#6302112yes—
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. #42075C2semidirect
2. #41977C2semidirect
3. #39628C2semidirect
4. #39269C2semidirect
5. #39076C2semidirect
6. #38969C2semidirect
7. #38250C2semidirect
8. #37773C2semidirect
9. #37668C2semidirect
10. #37628C2semidirect
11. #37619C2semidirect
12. #36609C2semidirect
13. #36370C2semidirect
14. #36148C2semidirect
15. #35994C2semidirect
16. #35198C2semidirect
17. #35197C2semidirect
18. #35192C2semidirect
19. #35172C2semidirect
21. #34929C2semidirect
22. #34226C2semidirect
23. #34154C2semidirect
24. #34126C2semidirect
25. C2×#542C22semidirect
27. C2×#533C22semidirect
31. #2864C22semidirect
32. #2862C22semidirect
33. #2860C22semidirect
35. #2854C22semidirect
36. #2850C22semidirect
38. #2836C22semidirect
40. #2804C22semidirect
42. #2754C22semidirect
43. #2751C22semidirect
44. #2732C22semidirect
46. #2721C22semidirect
49. #2694C22semidirect
53. #2662C22semidirect
54. #2658C22semidirect
55. #2654C22semidirect
56. #2648C22semidirect
57. #2647C22semidirect
59. #2640C22semidirect
60. #2633C22semidirect
62. #2625C22semidirect
64. #2621C22semidirect
65. #2605C22semidirect
66. #2592C22semidirect
69. #2580C22semidirect
70. #2580C22semidirect
71. #2575C22semidirect
72. #2571C22semidirect
77. #2556C22semidirect
78. #2551C22semidirect
79. #2548C22semidirect
80. #2546C22semidirect
91. #2513C22semidirect
92. #2507C22semidirect
93. #2506C22semidirect
95. #2492C22semidirect
96. #2491C22semidirect
97. #2479C22semidirect
100. #2468C22semidirect
101. #2461C22semidirect
102. #2460C22semidirect
104. #2458C22semidirect
105. #2457C22semidirect
107. #2452C22semidirect
108. #2450C22semidirect
109. #2450C22semidirect
110. #2448C22semidirect
111. #2447C22semidirect
118. #2429C22semidirect
119. #2429C22semidirect
120. #2427C22semidirect
121. #2426C22semidirect
122. #2423C22semidirect
123. #2421C22semidirect
124. #2420C22semidirect
125. #2419C22semidirect
128. #2396C22semidirect
129. #2371C22semidirect
130. #2371C22semidirect
131. #2367C22semidirect
132. #2367C22semidirect
133. #2365C22semidirect
134. #2365C22semidirect
139. #2359C22semidirect
142. #2357C22semidirect
147. #2349C22semidirect
153. #2331C22semidirect
156. #2324C22semidirect
157. #2319C22semidirect
158. #2319C22semidirect
161. C4×C4⋊Q8C22semidirect
162. C4×C4⋊Q8C22semidirect
165. C4×#127C22semidirect
166. C4×C22⋊Q8C22semidirect
168. #2295C22semidirect
169. #2295C22semidirect
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
#420752
#419772
#396282
#392692
#390762
#389692
#382502
#377732
#376682
#376282
#376192
#366092
#363702
#361482
#359942
#351982
#351972
#351922
#351722
#349362
#349292
#342262
#341542
#341262