Finite Group Databasebeta

← #7712029

Subgroups — #7712029

Order 512.

5324 conjugacy classes of subgroups.

The subgroup lattice has 1042 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59862C214yesmaximal, complemented
2#59820C214yesmaximal, complemented
3#46012C218yesmaximal, complemented
4#39810C214yesmaximal, complemented
5#39803C214yesmaximal, complemented
6#39461C218yesmaximal, complemented
7#39201C212yesmaximal, complemented
8#38985C212yesmaximal, complemented
9#38112C214yesmaximal, complemented
10#37632C211yesmaximal, characteristic, complemented
11#37614C211yesmaximal, characteristic
12#37322C212yesmaximal, complemented
13#37321C212yesmaximal, complemented
14#36635C211yesmaximal, characteristic, complemented
15C2×#2858C211yesmaximal, characteristic, complemented
16#36463C212yesmaximal, complemented
17#36300C212yesmaximal, complemented
18#36262C214yesmaximal, complemented
19#35296C212yesmaximal, complemented
20#35268C212yesmaximal, complemented
21#34365C211yesmaximal, characteristic, complemented
22#34364C211yesmaximal, characteristic, complemented
23C4×#529C211yesmaximal, characteristic, complemented
24C2×#551C2218yes—
25C22×C4⋊Q8C2211yescharacteristic
26C22×#127C2211yescharacteristic
27C2×#529C2211yescharacteristic
28C22×#124C2214yes—
29#2864C2211yescharacteristic, complemented
30#2864C2211yescharacteristic, complemented
31#2863C2214yescomplemented
32#2862C2211yescharacteristic, complemented
33#2860C2214yescomplemented
34#2859C2211yescharacteristic, complemented
35#2858C2212yes—
36#2858C2212yes—
37#2858C2214yes—
38#2858C2214yes—
39#2858C2212yes—
40#2858C2212yes—
41#2857C2212yes—
42#2855C2214yes—
43#2854C2214yescomplemented
44#2851C2212yes—
45#2821C2214yescomplemented
46#2818C2214yes—
47#2797C2218yescomplemented
48#2796C2218yescomplemented
49#2786C2218yescomplemented
50#2752C2218yescomplemented
51#2751C2218yescomplemented
52#2740C2218yescomplemented
53#2730C2218yescomplemented
54#2715C2218yescomplemented
55#2715C2218yescomplemented
56#2712C2218yescomplemented
57#2712C2218yescomplemented
58#2710C2218yescomplemented
59#2710C2218yescomplemented
60#2705C2218yescomplemented
61#2700C2218yescomplemented
62#2700C2218yescomplemented
63#2660C2212yescomplemented
64#2657C2212yes—
65#2644C2214yescomplemented
66#2641C2212yes—
67#2640C2212yescomplemented
68#2628C2212yescomplemented
69#2628C2212yescomplemented
70#2624C2214yescomplemented
71#2619C2212yes—
72#2619C2212yes—
73#2614C2214yes—
74#2613C2214yes—
75#2602C2218yescomplemented
76#2601C2218yescomplemented
77#2595C2218yescomplemented
78#2592C2214yescomplemented
79#2580C2214yescomplemented
80#2567C2212yescomplemented
81#2563C2212yescomplemented
82#2561C2218yes—
83#2560C2218yescomplemented
84#2557C2218yescomplemented
85#2557C2218yescomplemented
86#2557C2218yescomplemented
87#2548C2212yes—
88#2548C2214yescomplemented
89#2541C2212yes—
90#2538C2214yescomplemented
91#2534C2218yes—
92#2521C2218yescomplemented
93#2521C2218yescomplemented
94#2516C2218yescomplemented
95#2513C2214yescomplemented
96#2513C2214yescomplemented
97#2513C2214yescomplemented
98#2512C2214yescomplemented
99#2512C2214yescomplemented
100#2512C2214yescomplemented
101#2503C2212yes—
102#2501C2212yes—
103#2491C2214yescomplemented
104#2490C2214yescomplemented
105#2486C2214yes—
106#2483C2218yes—
107#2482C2218yes—
108#2474C2218yescomplemented
109#2474C2218yescomplemented
110#2471C2218yescomplemented
111#2467C2218yescomplemented
112#2459C2218yescomplemented
113#2459C2218yescomplemented
114#2454C2214yescomplemented
115#2452C2214yescomplemented
116#2448C2214yescomplemented
117#2447C2214yescomplemented
118#2445C2214yescomplemented
119#2445C2214yescomplemented
120#2435C2212yes—
121#2433C2212yes—
122#2422C2214yescomplemented
123#2420C2214yescomplemented
124#2412C2218yes—
125#2411C2218yes—
126#2408C2214yes—
127#2381C2214yescomplemented
128#2380C2214yes—
129#2369C2212yescomplemented
130#2369C2212yescomplemented
131#2367C2214yescomplemented
132#2366C2212yes—
133#2366C2212yes—
134#2366C2214yescomplemented
135#2357C2214yescomplemented
136#2354C2214yescomplemented
137#2344C2214yes—
138#2344C2214yes—
139#2342C2218yes—
140D4×C22⋊C4C2214yes—
141D4×C22⋊C4C2214yes—
142#2331C2214yescomplemented
143#2331C2212yescomplemented
144#2331C2212yescomplemented
145#2328C2214yes—
146#2328C2212yes—
147#2328C2212yes—
148#2324C2214yescomplemented
149#2319C2214yescomplemented
150#2310C2214yes—
151#2308C2214yes—
152C4×C4⋊Q8C2212yescomplemented
153C4×#125C2212yescomplemented
154C4×#125C2212yescomplemented
155C4×#126C2214yescomplemented
156C4×#124C2212yescomplemented
157C4×C22⋊Q8C2214yes—
158C4×C22⋊Q8C2212yes—
159C4×#123C2214yes—
160C4×#121C2212yes—
161C4×#121C2214yescomplemented
162#2298C2212yescomplemented
163#2295C2214yescomplemented
164#2295C2211yescharacteristic, complemented
165#2293C2211yescharacteristic, complemented
166#2293C2214yescomplemented
167C2×#390C2212yes—
168C2×#390C2214yes—
169C2×#390C2212yes—
170#2290C2212yes—
171#2283C2211yescharacteristic
172#2283C2211yescharacteristic
173#2283C2211yescharacteristic
174C42×Q8C2211yescharacteristic, complemented
175C42×D4C2212yes—
176C42×D4C2211yescharacteristic, complemented
177C4×#117C2212yescomplemented
178C2×C43C2211yescharacteristic
179C23×Q8C2312yes—
180C23×D4C2312yes—
181C23×D4C2312yes—
182C23×D4C2312yes—
183#551—432no—
184C2×C4⋊Q8—28no—
185C2×C4⋊Q8C2312yes—
186C2×C4⋊Q8C2312yes—
187C2×C4⋊Q8C2312yes—
188C2×C4⋊Q8C2312yes—
189C2×C4⋊Q8C2312yes—
190C2×#127—28no—
191C2×#127C2312yes—
192C2×#127C2312yes—
193C2×#127C2312yes—
194C2×#127C2312yes—
195C2×#127C2314yes—
196#529—28no—
197C2×#126C2312yes—
198C2×#126C2318yes—
199C2×#126C2318yes—
200C2×#125C2311yescharacteristic
201C2×#125C2312yes—
202C2×#124—416no—
203C2×#124C2311yescharacteristic
204C2×#124C2314yes—
205C2×#124C2314yes—
206C2×#124C2318yes—
207C2×#124C2314yes—
208C2×#124C2314yes—
209C2×#124C2318yes—
210C2×#124C2314yes—
211C2×#124C2318yes—
212C2×#123C2312yes—
213C2×#123C2318yes—
214C2×#123C2318yes—
215C2×#123C2318yes—
216C2×C22⋊Q8C2314yes—
217C2×C22⋊Q8C2311yescharacteristic
218C2×C22⋊Q8C2318yes—
219C2×#121C2311yescharacteristic
220C2×#121C2314yes—
221C2×#121C2314yes—
222C2×#120C2318yes—
223C2×C4×Q8C2311yescharacteristic
224C2×C4×Q8C2314yes—
225C2×C4×Q8C2312yes—
226C2×C4×D4C2311yescharacteristic
227C2×C4×D4C2312yes—
228C2×C4×D4C2314yes—
229C2×C4×D4C2314yes—
230C2×C4×D4C2314yes—
231C2×C4×D4C2314yes—
232C2×C4×D4C2314yes—
233C2×C4×D4C2318yes—
234C2×C4×D4C2312yes—
235C2×#117C2312yes—
236C2×#117C2318yes—
237C2×#117C2312yes—
238C2×#117C2318yes—
239C22×C4⋊C4C2312yes—
240C22×C4⋊C4C2312yes—
241C22×C22⋊C4C2318yes—
242C22×C22⋊C4C2318yes—
243C22×C22⋊C4C2318yes—
244C22×C42C2312yes—
245C22×C42C2311yescharacteristic
246C22×C42C2312yes—
247C22×C42C2311yescharacteristic
248C22×C42C2312yes—
249C22×C42C2311yescharacteristic
250#400C2314yes—
251#400C2314yes—
252#399C2314yes—
253#399C2314yes—
254#399C2318yes—
255#399C2318yes—
256#398C2318yes—
257#397C2318yes—
258#397C2318yes—
259#397C2318yes—
260#397C2318yes—
261#397C2318yes—
262#397C2318yes—
263#397C2318yes—
264#397C2318yes—
265#397C2318yes—
266#397C2318yes—
267#397C2318yes—
268#396C2318yes—
269#396C2318yes—
270#396C2318yes—
271#396C2318yes—
272#395C2318yes—
273#395C2314yes—
274#395C2314yes—
275#394C2318yes—
276#394C2314yes—
277#394C2318yes—
278#394C2314yes—
279#394C2318yes—
280#394C2318yes—
281#394C2314yes—
282#394C2314yes—
283#394C2318yes—
284#394C2318yes—
285#394C2318yes—
286#394C2318yes—
287#393C2318yes—
288#393C2318yes—
289#393C2318yes—
290#393C2314yes—
291#393C2314yes—
292#392C2318yes—
293#392C2318yes—
294#392C2314yes—
295#392C2314yes—
296#392C2314yes—
297#392C2314yes—
298#391C2314yes—
299#391C2314yes—
300#391C2318yes—
301#391C2318yes—
302#391C2318yes—
303#391C2318yes—
304#391C2314yes—
305#391C2312yes—
306#391C2314yes—
307#391C2314yes—
308#390C2318yes—
309#390C2314yes—
310#390C2314yes—
311#390C2314yes—
312#390C2318yes—
313#390C2314yes—
314#390C2314yes—
315#390C2314yes—
316#390C2314yes—
317#390C2314yes—
318#390C2314yes—
319#390C2314yes—
320#390C2318yes—
321#390C2314yes—
322#390C2314yes—
323#390C2314yes—
324#390C2314yes—
325#390C2314yes—
326#390C2318yes—
327#390C2318yes—
328#390C2314yes—
329#390C2314yes—
330#390C2318yes—
331#390C2312yes—
332#389C2312yes—
333#389C2312yes—
334#389C2312yes—
335#389C2312yes—
336#389C2312yes—
337#389C2312yes—
338#389C2314yes—
339#389C2314yes—
340#389C2314yes—
341#389C2314yes—
342#389C2314yes—
343#389C2314yes—
344#389C2314yes—
345#389C2314yes—
346#389C2314yes—
347#389C2314yes—
348#388C2314yes—
349#388C2314yes—
350#388C2314yes—
351#388C2318yes—
352#388C2318yes—
353#388C2318yes—
354#388C2318yes—
355#388C2318yes—
356#388C2318yes—
357#388C2318yes—
358#388C2318yes—
359#388C2318yes—
360#388C2318yes—
361#388C2318yes—
362#388C2318yes—
363#388C2318yes—
364#388C2318yes—
365#388C2318yes—
366#388C2318yes—
367#388C2314yes—
368#387C2314yes—
369#387C2314yes—
370#387C2314yes—
371#387C2318yes—
372#387C2314yes—
373#387C2314yes—
374#387C2314yes—
375#387C2318yes—
376#387C2318yes—
377#387C2318yes—
378#387C2314yes—
379#387C2314yes—
380#387C2314yes—
381#387C2314yes—
382#387C2314yes—
383#387C2314yes—
384#386C2318yes—
385#386C2318yes—
386#386C2318yes—
387#386C2318yes—
388#386C2318yes—
389#386C2318yes—
390#386C2318yes—
391#386C2318yes—
392#386C2318yes—
393#386C2318yes—
394#386C2318yes—
395#386C2314yes—
396#386C2318yes—
397#385C2318yes—
398#385C2318yes—
399#385C2314yes—
400#385C2314yes—
401#385C2318yes—
402#385C2318yes—
403#385C2314yes—
404#384C2312yes—
405#384C2314yes—
406#383C2312yes—
407#383C2312yes—
408#383C2312yes—
409#382C2312yes—
410#382C2312yes—
411#382C2314yes—
412#382C2311yescharacteristic
413#382C2311yescharacteristic
414#382C2311yescharacteristic
415#382C2311yescharacteristic
416#381C2318yes—
417#381C2318yes—
418#381C2312yes—
419#381C2312yes—
420#381C2312yes—
421#381C2318yes—
422#381C2318yes—
423#380C2314yes—
424#380C2314yes—
425#380C2318yes—
426#380C2312yes—
427#380C2312yes—
428#380C2312yes—
429#380C2314yes—
430#380C2318yes—
431#379C2318yes—
432#379C2318yes—
433C4×C4⋊C4C2314yes—
434C4×C4⋊C4C2314yes—
435C4×C4⋊C4C2314yes—
436C4×C4⋊C4C2312yes—
437C4×C4⋊C4C2312yes—
438C4×C4⋊C4C2312yes—
439C4×C4⋊C4C2314yes—
440C4×C4⋊C4C2312yes—
441C4×C4⋊C4C2314yes—
442C4×C4⋊C4C2314yes—
443C4×C4⋊C4C2314yes—
444C4×C4⋊C4C2314yes—
445C4×C4⋊C4C2314yes—
446C4×C4⋊C4C2314yes—
447C4×C4⋊C4C2314yes—
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2312yes—
451C4×C4⋊C4C2312yes—
452C4×C22⋊C4C2314yes—
453C4×C22⋊C4C2314yes—
454C4×C22⋊C4C2314yes—
455C4×C22⋊C4C2318yes—
456C4×C22⋊C4C2314yes—
457C4×C22⋊C4C2312yes—
458C4×C22⋊C4C2312yes—
459C4×C22⋊C4C2318yes—
460C4×C22⋊C4C2312yes—
461C4×C22⋊C4C2312yes—
462C4×C22⋊C4C2312yes—
463C4×C22⋊C4C2314yes—
464#376C2312yes—
465#376C2312yes—
466#376C2312yes—
467#376C2312yes—
468C43C2312yes—
469C43C2311yescharacteristic
470C43C2312yes—
471C43C2311yescharacteristic
472C43C2311yescharacteristic
473C43C2311yescharacteristic
474C43C2312yes—
475C25C2414yes—
476C22×Q8—28no—
477C22×Q8—48no—
478C22×Q8C2411yescharacteristic
479C22×Q8C2414yes—
480C22×Q8C2414yes—
481C22×Q8C2414yes—
482C22×D4—28no—
483C22×D4—28no—
484C22×D4—28no—
485C22×D4—44no—
486C22×D4—44no—
487C22×D4—48no—
488C22×D4—48no—
489C22×D4C2412yes—
490C22×D4C2411yescharacteristic
491C22×D4C2414yes—
492C22×D4C2414yes—
493C22×D4C2414yes—
494C22×D4C2414yes—
495C22×D4C2414yes—
496C22×D4C2414yes—
497C22×D4C2418yes—
498C22×D4C2418yes—
499C23×C4C2414yes—
500C23×C4C2412yes—
501C23×C4C2411yescharacteristic
502C23×C4C2411yescharacteristic
503C23×C4C2411yescharacteristic
504C23×C4C2412yes—
505C23×C4C2414yes—
506C23×C4C2418yes—
507C23×C4C2418yes—
508C23×C4C2412yes—
509C4⋊Q8—28no—
510C4⋊Q8—28no—
511C4⋊Q8—28no—
512C4⋊Q8—28no—
513C4⋊Q8—44no—
514#127—28no—
515#127—28no—
516#127—28no—
517#127—28no—
518#127—48no—
519#126—28no—
520#126—416no—
521#126—416no—
522#125—24no—
523#125—44no—
524#124—24no—
525#124—48no—
526#124—416no—
527#124—48no—
528#124—416no—
529#124—48no—
530#124—48no—
531#124—48no—
532#124—416no—
533#123—28no—
534#123—416no—
535#123—416no—
536#123—416no—
537C22⋊Q8—24no—
538C22⋊Q8—216no—
539C22⋊Q8—416no—
540#121—24no—
541#121—48no—
542#121—48no—
543#120—416no—
544C4×Q8—24no—
545C4×Q8—48no—
546C4×Q8—44no—
547C4×D4—28no—
548C4×D4—216no—
549C4×D4—24no—
550C4×D4—48no—
551C4×D4—44no—
552C4×D4—48no—
553C4×D4—48no—
554C4×D4—48no—
555C4×D4—416no—
556#117—28no—
557#117—44no—
558#117—416no—
559#117—416no—
560C2×C4⋊C4—28no—
561C2×C4⋊C4—28no—
562C2×C4⋊C4C2414yes—
563C2×C4⋊C4C2414yes—
564C2×C4⋊C4C2414yes—
565C2×C4⋊C4C2414yes—
566C2×C4⋊C4C2414yes—
567C2×C4⋊C4C2412yes—
568C2×C4⋊C4C2412yes—
569C2×C4⋊C4C2412yes—
570C2×C4⋊C4C2412yes—
571C2×C4⋊C4C2414yes—
572C2×C4⋊C4C2412yes—
573C2×C4⋊C4C2412yes—
574C2×C4⋊C4C2414yes—
575C2×C4⋊C4C2411yescharacteristic
576C2×C4⋊C4C2412yes—
577C2×C4⋊C4C2411yescharacteristic
578C2×C4⋊C4C2412yes—
579C2×C4⋊C4C2412yes—
580C2×C4⋊C4C2412yes—
581C2×C4⋊C4C2414yes—
582C2×C4⋊C4C2418yes—
583C2×C4⋊C4C2418yes—
584C2×C4⋊C4C2418yes—
585C2×C4⋊C4C2414yes—
586C2×C4⋊C4C2414yes—
587C2×C4⋊C4C2414yes—
588C2×C4⋊C4C2414yes—
589C2×C4⋊C4C2414yes—
590C2×C4⋊C4C2418yes—
591C2×C4⋊C4C2414yes—
592C2×C4⋊C4C2414yes—
593C2×C4⋊C4C2414yes—
594C2×C22⋊C4—232no—
595C2×C22⋊C4—416no—
596C2×C22⋊C4—416no—
597C2×C22⋊C4C2414yes—
598C2×C22⋊C4C2414yes—
599C2×C22⋊C4C2418yes—
600C2×C22⋊C4C2418yes—
601C2×C22⋊C4C2418yes—
602C2×C22⋊C4C2418yes—
603C2×C22⋊C4C2414yes—
604C2×C22⋊C4C2412yes—
605C2×C22⋊C4C2412yes—
606C2×C22⋊C4C2412yes—
607C2×C22⋊C4C2414yes—
608C2×C22⋊C4C2412yes—
609C2×C22⋊C4C2412yes—
610C2×C22⋊C4C2418yes—
611C2×C22⋊C4C2418yes—
612C2×C22⋊C4C2418yes—
613C2×C22⋊C4C2418yes—
614C2×C22⋊C4C2418yes—
615C2×C22⋊C4C2418yes—
616C2×C22⋊C4C2418yes—
617C2×C22⋊C4C2414yes—
618C2×C22⋊C4C2418yes—
619C2×C22⋊C4C2414yes—
620C2×C22⋊C4C2418yes—
621C2×C22⋊C4C2418yes—
622C2×C22⋊C4C2418yes—
623C2×C22⋊C4C2418yes—
624C2×C22⋊C4C2418yes—
625C2×C22⋊C4C2418yes—
626C2×C22⋊C4C2418yes—
627C2×C22⋊C4C2418yes—
628C2×C22⋊C4C2418yes—
629C2×C22⋊C4C2418yes—
630C2×C42—28no—
631C2×C42—44no—
632C2×C42—42no—
633C2×C42—42no—
634C2×C42—44no—
635C2×C42#4118yes—
636C2×C42C2414yes—
637C2×C42C2411yescharacteristic
638C2×C42C2412yes—
639C2×C42C2412yes—
640C2×C42C2414yes—
641C2×C42C2412yes—
642C2×C42C2412yes—
643C2×C42C2412yes—
644C2×C42C2414yes—
645C2×C42C2412yes—
646C2×C42C2412yes—
647C2×C42C2412yes—
648C2×C42C2412yes—
649C2×C42C2411yescharacteristic
650C2×C42C2411yescharacteristic
651C2×C42C2411yescharacteristic
652C2×C42C2418yes—
653C2×C42C2418yes—
654C2×C42C2414yes—
655C2×C42C2412yes—
656C2×C42C2412yes—
657C2×C42C2412yes—
658C2×C42C2412yes—
659C2×C42C2414yes—
660C2×C42C2411yescharacteristic
661C2×C42C2411yescharacteristic
662C2×C42C2411yescharacteristic
663C2×C42C2411yescharacteristic
664#95C2414yes—
665#95C2414yes—
666#95C2414yes—
667#95C2414yes—
668#95C2414yes—
669#95C2414yes—
670#95C2412yes—
671#95C2412yes—
672#95C2412yes—
673#95C2412yes—
674#95C2414yes—
675#95C2414yes—
676#95C2414yes—
677#95C2412yes—
678#95C2414yes—
679#95C2414yes—
680#95C2414yes—
681#95C2418yes—
682#95C2418yes—
683#95C2412yes—
684#95C2412yes—
685#95C2412yes—
686#95C2412yes—
687#95C2414yes—
688#95C2412yes—
689#95C2418yes—
690#95C2418yes—
691#95C2414yes—
692#95C2414yes—
693#95C2418yes—
694#95C2414yes—
695#95C2414yes—
696#95C2418yes—
697#95C2414yes—
698#95C2414yes—
699#95C2418yes—
700#95C2418yes—
701C24—28no—
702C24—216no—
703C24—48no—
704C24—44no—
705C24—44no—
706C24C2518yes—
707C24C2512yes—
708C24C2511yescharacteristic
709C2×Q8—22no—
710C2×Q8—28no—
711C2×Q8—28no—
712C2×Q8—28no—
713C2×Q8—24no—
714C2×Q8—44no—
715C2×Q8—44no—
716C2×Q8—48no—
717C2×Q8—44no—
718C2×Q8—44no—
719C2×Q8—816no—
720C2×D4—24no—
721C2×D4—28no—
722C2×D4—22no—
723C2×D4—28no—
724C2×D4—28no—
725C2×D4—28no—
726C2×D4—28no—
727C2×D4—28no—
728C2×D4—28no—
729C2×D4—28no—
730C2×D4—28no—
731C2×D4—28no—
732C2×D4—24no—
733C2×D4—28no—
734C2×D4—48no—
735C2×D4—48no—
736C2×D4—44no—
737C2×D4—48no—
738C2×D4—44no—
739C2×D4—48no—
740C2×D4—48no—
741C2×D4—44no—
742C2×D4—44no—
743C2×D4—48no—
744C2×D4—48no—
745C2×D4—48no—
746C2×D4—816no—
747C2×D4—816no—
748C2×D4—816no—
749C22×C4—24no—
750C22×C4—24no—
751C22×C4—22no—
752C22×C4—22no—
753C22×C4—28no—
754C22×C4—24no—
755C22×C4—216no—
756C22×C4—24no—
757C22×C4—24no—
758C22×C4—24no—
759C22×C4—28no—
760C22×C4—42no—
761C22×C4—42no—
762C22×C4—42no—
763C22×C4—42no—
764C22×C4—44no—
765C22×C4—48no—
766C22×C4—44no—
767C22×C4—48no—
768C22×C4—48no—
769C22×C4—48no—
770C22×C4—48no—
771C22×C4—48no—
772C22×C4C2×#4114yes—
773C22×C4C2×#4114yes—
774C22×C4C2×#4114yes—
775C22×C4H(5,𝔽2)18yes—
776C22×C4C2514yes—
777C22×C4C2512yes—
778C22×C4C2514yes—
779C22×C4C2512yes—
780C22×C4C2514yes—
781C22×C4C2514yes—
782C22×C4C2514yes—
783C22×C4C2514yes—
784C22×C4C2512yes—
785C22×C4C2512yes—
786C22×C4C2518yes—
787C22×C4C2512yes—
788C22×C4C2511yescharacteristic
789C22×C4C2511yescharacteristic
790C22×C4C2511yescharacteristic
791C22×C4C2511yescharacteristic
792C22×C4C2512yes—
793C22×C4C2512yes—
794C22×C4C2511yescharacteristic
795C22×C4C2511yescharacteristic
796C4⋊C4—28no—
797C4⋊C4—28no—
798C4⋊C4—28no—
799C4⋊C4—28no—
800C4⋊C4—24no—
801C4⋊C4—24no—
802C4⋊C4—22no—
803C4⋊C4—24no—
804C4⋊C4—22no—
805C4⋊C4—24no—
806C4⋊C4—28no—
807C4⋊C4—28no—
808C4⋊C4—28no—
809C4⋊C4—28no—
810C4⋊C4—24no—
811C4⋊C4—24no—
812C4⋊C4—24no—
813C4⋊C4—24no—
814C4⋊C4—24no—
815C4⋊C4—24no—
816C4⋊C4—44no—
817C4⋊C4—48no—
818C4⋊C4—48no—
819C4⋊C4—48no—
820C4⋊C4—44no—
821C4⋊C4—44no—
822C4⋊C4—44no—
823C4⋊C4—44no—
824C4⋊C4—48no—
825C4⋊C4—44no—
826C4⋊C4—44no—
827C4⋊C4—44no—
828C22⋊C4—24no—
829C22⋊C4—28no—
830C22⋊C4—28no—
831C22⋊C4—28no—
832C22⋊C4—24no—
833C22⋊C4—24no—
834C22⋊C4—24no—
835C22⋊C4—24no—
836C22⋊C4—216no—
837C22⋊C4—216no—
838C22⋊C4—216no—
839C22⋊C4—216no—
840C22⋊C4—28no—
841C22⋊C4—48no—
842C22⋊C4—48no—
843C22⋊C4—48no—
844C22⋊C4—48no—
845C22⋊C4—48no—
846C22⋊C4—48no—
847C22⋊C4—44no—
848C22⋊C4—48no—
849C22⋊C4—44no—
850C22⋊C4—48no—
851C22⋊C4—48no—
852C22⋊C4—48no—
853C22⋊C4—48no—
854C22⋊C4—48no—
855C22⋊C4—48no—
856C22⋊C4—48no—
857C22⋊C4—48no—
858C22⋊C4—48no—
859C22⋊C4—48no—
860C22⋊C4—48no—
861C42—24no—
862C42—24no—
863C42—24no—
864C42—24no—
865C42—24no—
866C42—28no—
867C42—22no—
868C42—22no—
869C42—24no—
870C42—24no—
871C42—24no—
872C42—22no—
873C42—22no—
874C42—24no—
875C42—28no—
876C42—28no—
877C42—42no—
878C42—42no—
879C42—44no—
880C42—42no—
881C42—42no—
882C42—48no—
883C42—48no—
884C42—44no—
885C42C2×#4114yes—
886C42C2×#4114yes—
887C42C2×#4114yes—
888C42C2×#4114yes—
889C23—21no—
890C23—22no—
891C23—21no—
892C23—22no—
893C23—28no—
894C23—28no—
895C23—28no—
896C23—24no—
897C23—28no—
898C23—22no—
899C23—28no—
900C23—28no—
901C23—24no—
902C23—28no—
903C23—22no—
904C23—416no—
905C23—88no—
906C23—88no—
907C23—816no—
908C23—816no—
909C23C22×#4112yes—
910C23C2×H(5,𝔽2)14yes—
911C23C2611yescharacteristic
912Q8—44no—
913Q8—88no—
914Q8—88no—
915Q8—88no—
916D4—48no—
917D4—44no—
918D4—416no—
919D4—416no—
920D4—88no—
921D4—88no—
922D4—88no—
923D4—88no—
924D4—816no—
925D4—168no—
926C2×C4—22no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—21no—
933C2×C4—22no—
934C2×C4—21no—
935C2×C4—28no—
936C2×C4—28no—
937C2×C4—28no—
938C2×C4—22no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—28no—
942C2×C4—22no—
943C2×C4—22no—
944C2×C4—24no—
945C2×C4—24no—
946C2×C4—28no—
947C2×C4—24no—
948C2×C4—24no—
949C2×C4—24no—
950C2×C4—28no—
951C2×C4—24no—
952C2×C4—24no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—24no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—24no—
959C2×C4—24no—
960C2×C4—24no—
961C2×C4—24no—
962C2×C4—24no—
963C2×C4—22no—
964C2×C4—24no—
965C2×C4—24no—
966C2×C4—22no—
967C2×C4—24no—
968C2×C4—24no—
969C2×C4—24no—
970C2×C4—24no—
971C2×C4—24no—
972C2×C4—48no—
973C2×C4—48no—
974C2×C4—416no—
975C2×C4—48no—
976C2×C4—88no—
977C2×C4—816no—
978C2×C4—168no—
979C2×C4C22×#4112yes—
980C2×C4C22×#4112yes—
981C2×C4C22×#4112yes—
982C2×C4C22×#4112yes—
983C2×C4C22×#4112yes—
984C2×C4C22×#4112yes—
985C2×C4C2×H(5,𝔽2)14yes—
986C2×C4C2×H(5,𝔽2)14yes—
987C2×C4#58514yes—
988C2×C4#58512yes—
989C2×C4#58512yes—
990C22—24no—
991C22—22no—
992C22—22no—
993C22—24no—
994C22—48no—
995C22—44no—
996C22—48no—
997C22—42no—
998C22—48no—
999C22—42no—
1000C22—48no—
1001C22—48no—
1002C22—42no—
1003C22—44no—
1004C22—48no—
1005C22—48no—
1006C22—1616no—
1007C22#350814yes—
1008C22C23×#4111yescharacteristic
1009C22C22×H(5,𝔽2)12yes—
1010C22C2×#58511yescharacteristic
1011C22C2×#58512yes—
1012C22C2×#58511yescharacteristic
1013C4—22no—
1014C4—22no—
1015C4—22no—
1016C4—22no—
1017C4—24no—
1018C4—24no—
1019C4—42no—
1020C4—42no—
1021C4—44no—
1022C4—44no—
1023C4—44no—
1024C4—48no—
1025C4—42no—
1026C4—42no—
1027C4—42no—
1028C4—44no—
1029C4—44no—
1030C4—44no—
1031C4#351014yes—
1032C4#351014yes—
1033C2—24no—
1034C2—82no—
1035C2—88no—
1036C2#6275912yes—
1037C2C2×#350811yescharacteristic
1038C2C2×#351011yescharacteristic
1039C2C2×#351011yescharacteristic
1040C2#6282212yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#37614C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59862C2semidirect
2. #59820C2semidirect
3. #46012C2semidirect
4. #39810C2semidirect
5. #39803C2semidirect
6. #39461C2semidirect
7. #39201C2semidirect
8. #38985C2semidirect
9. #38112C2semidirect
10. #37632C2semidirect
12. #37322C2semidirect
13. #37321C2semidirect
14. #36635C2semidirect
15. C2×#2858C2semidirect
16. #36463C2semidirect
17. #36300C2semidirect
18. #36262C2semidirect
19. #35296C2semidirect
20. #35268C2semidirect
21. #34365C2semidirect
22. #34364C2semidirect
23. C4×#529C2semidirect
29. #2864C22semidirect
30. #2864C22semidirect
31. #2863C22semidirect
32. #2862C22semidirect
33. #2860C22semidirect
34. #2859C22semidirect
43. #2854C22semidirect
45. #2821C22semidirect
47. #2797C22semidirect
48. #2796C22semidirect
49. #2786C22semidirect
50. #2752C22semidirect
51. #2751C22semidirect
52. #2740C22semidirect
53. #2730C22semidirect
54. #2715C22semidirect
55. #2715C22semidirect
56. #2712C22semidirect
57. #2712C22semidirect
58. #2710C22semidirect
59. #2710C22semidirect
60. #2705C22semidirect
61. #2700C22semidirect
62. #2700C22semidirect
63. #2660C22semidirect
65. #2644C22semidirect
67. #2640C22semidirect
68. #2628C22semidirect
69. #2628C22semidirect
70. #2624C22semidirect
75. #2602C22semidirect
76. #2601C22semidirect
77. #2595C22semidirect
78. #2592C22semidirect
79. #2580C22semidirect
80. #2567C22semidirect
81. #2563C22semidirect
83. #2560C22semidirect
84. #2557C22semidirect
85. #2557C22semidirect
86. #2557C22semidirect
88. #2548C22semidirect
90. #2538C22semidirect
92. #2521C22semidirect
93. #2521C22semidirect
94. #2516C22semidirect
95. #2513C22semidirect
96. #2513C22semidirect
97. #2513C22semidirect
98. #2512C22semidirect
99. #2512C22semidirect
100. #2512C22semidirect
103. #2491C22semidirect
104. #2490C22semidirect
108. #2474C22semidirect
109. #2474C22semidirect
110. #2471C22semidirect
111. #2467C22semidirect
112. #2459C22semidirect
113. #2459C22semidirect
114. #2454C22semidirect
115. #2452C22semidirect
116. #2448C22semidirect
117. #2447C22semidirect
118. #2445C22semidirect
119. #2445C22semidirect
122. #2422C22semidirect
123. #2420C22semidirect
127. #2381C22semidirect
129. #2369C22semidirect
130. #2369C22semidirect
131. #2367C22semidirect
134. #2366C22semidirect
135. #2357C22semidirect
136. #2354C22semidirect
142. #2331C22semidirect
143. #2331C22semidirect
144. #2331C22semidirect
148. #2324C22semidirect
149. #2319C22semidirect
152. C4×C4⋊Q8C22semidirect
153. C4×#125C22semidirect
154. C4×#125C22semidirect
155. C4×#126C22semidirect
156. C4×#124C22semidirect
161. C4×#121C22semidirect
162. #2298C22semidirect
163. #2295C22semidirect
164. #2295C22semidirect
165. #2293C22semidirect
166. #2293C22semidirect
174. C42×Q8C22semidirect
176. C42×D4C22semidirect
177. C4×#117C22semidirect

Maximal subgroups

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

subgroupindex
#598622
#598202
#460122
#398102
#398032
#394612
#392012
#389852
#381122
#376322
#376142
#373222
#373212
#366352
C2×#28582
#364632
#363002
#362622
#352962
#352682
#343652
#343642
C4×#5292