Finite Group Databasebeta

← #7644124

Subgroups — #7644124

Order 512.

4880 conjugacy classes of subgroups.

The subgroup lattice has 1084 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42699C214yesmaximal, complemented
2#42698C214yesmaximal, complemented
3#42694C214yesmaximal, complemented
4#42693C214yesmaximal, complemented
5#42524C214yesmaximal, complemented
6#42523C214yesmaximal, complemented
7#42515C214yesmaximal, complemented
8#42514C214yesmaximal, complemented
9#37462C214yesmaximal, complemented
10#37461C214yesmaximal, complemented
11#36730C214yesmaximal, complemented
12#36729C214yesmaximal, complemented
13#35556C212yesmaximal, complemented
14#35545C212yesmaximal, complemented
15#35531C212yesmaximal, complemented
16#35519C212yesmaximal, complemented
17#35172C211yesmaximal, characteristic, complemented
18#35165C211yesmaximal, characteristic
19#34642C211yesmaximal, characteristic, complemented
20#34637C211yesmaximal, characteristic, complemented
21#34213C211yesmaximal, characteristic, complemented
22#34206C211yesmaximal, characteristic, complemented
23C2×#2319C211yesmaximal, characteristic, complemented
24C2×#535C2212yes—
25C2×#533C2211yescharacteristic
26C2×#533C2212yes—
27C2×#532C2211yescharacteristic
28C2×#520C2212yes—
29C22×C4×D4C2211yescharacteristic
30#2848C2214yes—
31#2847C2214yes—
32#2838C2218yescomplemented
33#2837C2218yescomplemented
34#2832C2218yescomplemented
35#2829C2218yescomplemented
36#2747C2218yescomplemented
37#2746C2218yescomplemented
38#2745C2218yescomplemented
39#2742C2218yescomplemented
40#2741C2218yescomplemented
41#2738C2218yescomplemented
42#2737C2218yescomplemented
43#2717C2218yescomplemented
44#2702C2218yescomplemented
45#2701C2218yescomplemented
46#2700C2218yescomplemented
47#2692C2218yescomplemented
48#2691C2218yescomplemented
49#2687C2218yescomplemented
50#2686C2218yescomplemented
51#2672C2218yescomplemented
52#2663C2218yescomplemented
53#2662C2218yescomplemented
54#2660C2212yescomplemented
55#2660C2212yescomplemented
56#2660C2212yescomplemented
57#2660C2212yescomplemented
58#2659C2212yes—
59#2659C2212yes—
60#2659C2212yes—
61#2659C2212yes—
62#2654C2218yescomplemented
63#2653C2218yescomplemented
64#2651C2218yescomplemented
65#2650C2218yescomplemented
66#2642C2212yescomplemented
67#2641C2212yescomplemented
68#2640C2212yescomplemented
69#2640C2212yescomplemented
70#2639C2212yes—
71#2639C2212yes—
72#2639C2212yes—
73#2639C2212yes—
74#2632C2218yescomplemented
75#2630C2218yescomplemented
76#2626C2214yes—
77#2617C2214yes—
78#2592C2214yes—
79#2592C2214yes—
80#2582C2214yescomplemented
81#2581C2214yescomplemented
82#2580C2214yes—
83#2580C2214yescomplemented
84#2566C2214yes—
85#2563C2212yes—
86#2548C2214yes—
87#2548C2214yes—
88#2547C2212yes—
89#2544C2214yes—
90#2542C2212yes—
91#2541C2212yes—
92#2538C2212yes—
93#2538C2212yes—
94#2538C2214yescomplemented
95#2537C2212yes—
96#2537C2212yes—
97#2535C2214yes—
98#2525C2218yescomplemented
99#2521C2218yescomplemented
100#2514C2214yescomplemented
101#2513C2214yescomplemented
102#2512C2214yescomplemented
103#2511C2214yescomplemented
104#2510C2218yes—
105#2504C2214yes—
106#2501C2214yes—
107#2500C2214yes—
108#2500C2214yes—
109#2497C2214yescomplemented
110#2496C2214yescomplemented
111#2495C2214yescomplemented
112#2494C2214yescomplemented
113#2491C2214yes—
114#2491C2214yes—
115#2490C2214yes—
116#2490C2214yes—
117#2481C2218yes—
118#2472C2218yes—
119#2472C2218yes—
120#2461C2218yescomplemented
121#2458C2218yescomplemented
122#2450C2218yes—
123#2449C2218yes—
124#2448C2214yes—
125#2448C2214yes—
126#2445C2214yes—
127#2445C2214yes—
128#2442C2214yescomplemented
129#2441C2214yescomplemented
130#2440C2214yescomplemented
131#2439C2214yescomplemented
132#2418C2218yes—
133#2418C2218yes—
134#2399C2214yescomplemented
135#2399C2214yescomplemented
136#2398C2214yescomplemented
137#2398C2214yescomplemented
138#2370C2214yescomplemented
139#2369C2212yescomplemented
140#2367C2214yescomplemented
141#2366C2212yescomplemented
142#2365C2212yescomplemented
143#2365C2212yescomplemented
144#2355C2214yescomplemented
145#2355C2212yescomplemented
146#2354C2212yescomplemented
147#2352C2214yescomplemented
148Q8×C4⋊C4C2212yescomplemented
149D4×C4⋊C4C2212yescomplemented
150#2329C2214yes—
151#2325C2214yes—
152#2319C2214yes—
153#2319C2214yes—
154#2319C2214yes—
155#2319C2214yes—
156#2317C2212yes—
157#2317C2212yes—
158#2311C2212yes—
159#2311C2212yes—
160#2309C2212yes—
161C4×C22⋊Q8C2214yes—
162C4×#121C2214yes—
163#2297C2212yes—
164#2297C2212yes—
165C2×#390C2211yescharacteristic
166C2×#390C2211yescharacteristic
167C2×#389C2211yescharacteristic
168C2×#389C2211yescharacteristic
169C2×#388C2212yes—
170C2×#388C2212yes—
171#2285C2211yescharacteristic
172#2285C2211yescharacteristic
173#2285C2212yes—
174C2×#381C2212yes—
175C2×#380C2212yes—
176#2274C2212yes—
177C2×C4×C4⋊C4C2211yescharacteristic
178C2×#376C2211yescharacteristic
179C22×#41C2312yes—
180C23×D4C2311yescharacteristic
181C24×C4C2312yes—
182#535—48no—
183#533—28no—
184#533—48no—
185#532—28no—
186C2×C4⋊Q8C2311yescharacteristic
187C2×C4⋊Q8C2311yescharacteristic
188C2×C4⋊Q8C2311yescharacteristic
189C2×C4⋊Q8C2312yes—
190C2×C4⋊Q8C2312yes—
191C2×#127C2311yescharacteristic
192C2×#127C2314yes—
193C2×#126C2318yes—
194C2×#125C2312yes—
195C2×#125C2312yes—
196C2×#125C2312yes—
197C2×#124C2312yes—
198C2×#124C2314yes—
199C2×#124C2318yes—
200C2×#124C2318yes—
201C2×#123C2318yes—
202C2×#123C2318yes—
203C2×C22⋊Q8C2312yes—
204C2×C22⋊Q8C2312yes—
205C2×C22⋊Q8C2314yes—
206C2×C22⋊Q8C2314yes—
207C2×C22⋊Q8C2314yes—
208C2×C22⋊Q8C2314yes—
209C2×C22⋊Q8C2318yes—
210C2×#121C2312yes—
211C2×#121C2312yes—
212C2×#121C2314yes—
213C2×#121C2314yes—
214C2×#121C2314yes—
215C2×#121C2314yes—
216C2×#120C2318yes—
217#520—48no—
218C2×C4×Q8C2312yes—
219C2×C4×Q8C2312yes—
220C2×C4×Q8C2314yes—
221C2×C4×Q8C2314yes—
222C2×C4×Q8C2314yes—
223C2×C4×Q8C2314yes—
224C2×C4×D4—28no—
225C2×C4×D4C2312yes—
226C2×C4×D4C2312yes—
227C2×C4×D4C2312yes—
228C2×C4×D4C2312yes—
229C2×C4×D4C2312yes—
230C2×C4×D4C2312yes—
231C2×C4×D4C2314yes—
232C2×C4×D4C2318yes—
233C2×C4×D4C2314yes—
234C2×#117C2312yes—
235C2×#117C2312yes—
236C2×#117C2312yes—
237C2×#117C2314yes—
238C22×C4⋊C4C2311yescharacteristic
239C22×C4⋊C4C2311yescharacteristic
240C22×C4⋊C4C2311yescharacteristic
241C22×C4⋊C4C2314yes—
242C22×C4⋊C4C2312yes—
243C22×C4⋊C4C2312yes—
244C22×C22⋊C4C2312yes—
245C22×C22⋊C4C2312yes—
246C22×C22⋊C4C2312yes—
247C22×C22⋊C4C2312yes—
248C22×C22⋊C4C2312yes—
249C22×C42C2311yescharacteristic
250C22×C42C2311yescharacteristic
251C22×C42C2312yes—
252C22×C42C2311yescharacteristic
253#401C2318yes—
254#400C2318yes—
255#400C2318yes—
256#400C2318yes—
257#400C2314yes—
258#400C2318yes—
259#400C2314yes—
260#400C2314yes—
261#400C2314yes—
262#399C2318yes—
263#399C2318yes—
264#399C2318yes—
265#399C2318yes—
266#398C2314yes—
267#398C2314yes—
268#398C2318yes—
269#398C2318yes—
270#398C2314yes—
271#398C2314yes—
272#398C2314yes—
273#398C2314yes—
274#398C2314yes—
275#398C2314yes—
276#397C2318yes—
277#397C2318yes—
278#397C2318yes—
279#397C2318yes—
280#397C2314yes—
281#397C2318yes—
282#397C2318yes—
283#397C2318yes—
284#397C2318yes—
285#397C2314yes—
286#397C2314yes—
287#397C2314yes—
288#396C2318yes—
289#396C2318yes—
290#396C2318yes—
291#396C2318yes—
292#396C2318yes—
293#395C2314yes—
294#395C2318yes—
295#395C2314yes—
296#395C2314yes—
297#395C2314yes—
298#395C2314yes—
299#395C2314yes—
300#395C2314yes—
301#395C2314yes—
302#394C2314yes—
303#394C2318yes—
304#394C2318yes—
305#394C2318yes—
306#394C2318yes—
307#394C2318yes—
308#394C2318yes—
309#394C2318yes—
310#394C2318yes—
311#394C2318yes—
312#394C2318yes—
313#394C2314yes—
314#394C2314yes—
315#394C2314yes—
316#393C2318yes—
317#393C2314yes—
318#393C2318yes—
319#393C2318yes—
320#393C2318yes—
321#393C2314yes—
322#393C2314yes—
323#393C2314yes—
324#392C2318yes—
325#391C2314yes—
326#391C2314yes—
327#391C2314yes—
328#391C2312yes—
329#391C2312yes—
330#391C2318yes—
331#391C2318yes—
332#391C2312yes—
333#391C2312yes—
334#390C2314yes—
335#390C2314yes—
336#390C2314yes—
337#390C2314yes—
338#390C2314yes—
339#390C2314yes—
340#390C2314yes—
341#390C2314yes—
342#390C2314yes—
343#390C2314yes—
344#390C2314yes—
345#390C2312yes—
346#390C2312yes—
347#390C2312yes—
348#390C2312yes—
349#390C2318yes—
350#390C2318yes—
351#389C2314yes—
352#389C2314yes—
353#389C2314yes—
354#389C2314yes—
355#389C2314yes—
356#389C2314yes—
357#389C2314yes—
358#389C2314yes—
359#389C2314yes—
360#389C2318yes—
361#389C2314yes—
362#389C2318yes—
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#388C2318yes—
378#388C2318yes—
379#388C2318yes—
380#387C2318yes—
381#387C2318yes—
382#387C2318yes—
383#387C2318yes—
384#387C2318yes—
385#387C2318yes—
386#387C2318yes—
387#387C2318yes—
388#387C2318yes—
389#386C2318yes—
390#386C2318yes—
391#386C2318yes—
392#386C2318yes—
393#386C2318yes—
394#386C2318yes—
395#386C2314yes—
396#386C2314yes—
397#386C2314yes—
398#386C2314yes—
399#386C2318yes—
400#385C2318yes—
401#385C2318yes—
402#385C2318yes—
403#385C2318yes—
404#385C2318yes—
405#385C2318yes—
406#385C2318yes—
407#384C2314yes—
408#384C2314yes—
409#384C2311yescharacteristic
410#384C2311yescharacteristic
411#384C2311yescharacteristic
412#384C2311yescharacteristic
413#384C2312yes—
414#384C2312yes—
415#383C2318yes—
416#382C2314yes—
417#382C2314yes—
418#382C2312yes—
419#382C2312yes—
420#382C2312yes—
421#382C2312yes—
422#381C2318yes—
423#381C2318yes—
424#380C2314yes—
425#380C2314yes—
426#380C2314yes—
427#380C2314yes—
428#380C2314yes—
429#380C2314yes—
430#380C2318yes—
431#380C2318yes—
432#380C2312yes—
433#380C2312yes—
434#380C2314yes—
435#380C2314yes—
436#380C2312yes—
437#380C2312yes—
438#380C2318yes—
439#380C2314yes—
440#380C2314yes—
441#379C2318yes—
442C4×C4⋊C4C2312yes—
443C4×C4⋊C4C2312yes—
444C4×C4⋊C4C2312yes—
445C4×C4⋊C4C2312yes—
446C4×C4⋊C4C2312yes—
447C4×C4⋊C4C2312yes—
448C4×C4⋊C4C2314yes—
449C4×C4⋊C4C2314yes—
450C4×C4⋊C4C2314yes—
451C4×C4⋊C4C2314yes—
452C4×C4⋊C4C2314yes—
453C4×C4⋊C4C2314yes—
454C4×C4⋊C4C2318yes—
455C4×C4⋊C4C2312yes—
456C4×C4⋊C4C2312yes—
457C4×C4⋊C4C2314yes—
458C4×C4⋊C4C2314yes—
459C4×C22⋊C4C2318yes—
460C4×C22⋊C4C2318yes—
461C4×C22⋊C4C2314yes—
462C4×C22⋊C4C2314yes—
463C4×C22⋊C4C2314yes—
464C4×C22⋊C4C2314yes—
465#376C2312yes—
466#376C2312yes—
467#376C2312yes—
468#376C2312yes—
469C2×#95C2312yes—
470C2×#95C2311yescharacteristic
471C2×#95C2311yescharacteristic
472C2×#95C2311yescharacteristic
473C2×#95C2311yescharacteristic
474C2×#95C2312yes—
475C2×#95C2312yes—
476C25C2412yes—
477C2×#41—28no—
478C2×#41—28no—
479C2×#41—28no—
480C22×Q8C2412yes—
481C22×Q8C2412yes—
482C22×Q8C2412yes—
483C22×Q8C2414yes—
484C22×Q8C2414yes—
485C22×D4—24no—
486C22×D4—24no—
487C22×D4—24no—
488C22×D4C2414yes—
489C22×D4C2412yes—
490C22×D4C2412yes—
491C22×D4C2412yes—
492C22×D4C2412yes—
493C22×D4C2412yes—
494C22×D4C2418yes—
495C22×D4C2418yes—
496C23×C4—28no—
497C23×C4—82no—
498C23×C4—82no—
499C23×C4C2414yes—
500C23×C4C2412yes—
501C23×C4C2411yescharacteristic
502C23×C4C2412yes—
503C23×C4C2411yescharacteristic
504C23×C4C2411yescharacteristic
505C23×C4C2411yescharacteristic
506C23×C4C2412yes—
507C23×C4C2414yes—
508C23×C4C2414yes—
509C23×C4C2418yes—
510C23×C4C2411yescharacteristic
511C23×C4C2411yescharacteristic
512C23×C4C2411yescharacteristic
513C4⋊Q8—24no—
514C4⋊Q8—24no—
515C4⋊Q8—24no—
516C4⋊Q8—44no—
517C4⋊Q8—44no—
518#127—24no—
519#127—48no—
520#126—88no—
521#125—28no—
522#125—44no—
523#125—44no—
524#124—28no—
525#124—48no—
526#124—88no—
527#124—88no—
528#123—88no—
529#123—88no—
530C22⋊Q8—28no—
531C22⋊Q8—28no—
532C22⋊Q8—48no—
533C22⋊Q8—48no—
534C22⋊Q8—88no—
535C22⋊Q8—84no—
536C22⋊Q8—84no—
537#121—28no—
538#121—28no—
539#121—48no—
540#121—48no—
541#121—84no—
542#121—84no—
543#120—416no—
544C4×Q8—28no—
545C4×Q8—28no—
546C4×Q8—48no—
547C4×Q8—48no—
548C4×Q8—48no—
549C4×Q8—84no—
550C4×D4—28no—
551C4×D4—28no—
552C4×D4—28no—
553C4×D4—28no—
554C4×D4—28no—
555C4×D4—28no—
556C4×D4—48no—
557C4×D4—416no—
558C4×D4—84no—
559#117—28no—
560#117—28no—
561#117—28no—
562#117—48no—
563C2×C4⋊C4—24no—
564C2×C4⋊C4—24no—
565C2×C4⋊C4—24no—
566C2×C4⋊C4—48no—
567C2×C4⋊C4—82no—
568C2×C4⋊C4—82no—
569C2×C4⋊C4C2412yes—
570C2×C4⋊C4C2412yes—
571C2×C4⋊C4C2412yes—
572C2×C4⋊C4C2412yes—
573C2×C4⋊C4C2412yes—
574C2×C4⋊C4C2412yes—
575C2×C4⋊C4C2412yes—
576C2×C4⋊C4C2412yes—
577C2×C4⋊C4C2412yes—
578C2×C4⋊C4C2412yes—
579C2×C4⋊C4C2412yes—
580C2×C4⋊C4C2412yes—
581C2×C4⋊C4C2412yes—
582C2×C4⋊C4C2412yes—
583C2×C4⋊C4C2414yes—
584C2×C4⋊C4C2414yes—
585C2×C4⋊C4C2412yes—
586C2×C4⋊C4C2412yes—
587C2×C4⋊C4C2418yes—
588C2×C4⋊C4C2418yes—
589C2×C4⋊C4C2418yes—
590C2×C4⋊C4C2412yes—
591C2×C4⋊C4C2412yes—
592C2×C4⋊C4C2414yes—
593C2×C4⋊C4C2414yes—
594C2×C4⋊C4C2414yes—
595C2×C4⋊C4C2414yes—
596C2×C4⋊C4C2414yes—
597C2×C4⋊C4C2414yes—
598C2×C4⋊C4C2418yes—
599C2×C4⋊C4C2412yes—
600C2×C4⋊C4C2412yes—
601C2×C4⋊C4C2412yes—
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2418yes—
604C2×C4⋊C4C2418yes—
605C2×C4⋊C4C2418yes—
606C2×C4⋊C4C2414yes—
607C2×C4⋊C4C2414yes—
608C2×C4⋊C4C2414yes—
609C2×C4⋊C4C2412yes—
610C2×C4⋊C4C2412yes—
611C2×C4⋊C4C2414yes—
612C2×C22⋊C4—28no—
613C2×C22⋊C4—82no—
614C2×C22⋊C4—82no—
615C2×C22⋊C4—82no—
616C2×C22⋊C4—82no—
617C2×C22⋊C4C2414yes—
618C2×C22⋊C4C2414yes—
619C2×C22⋊C4C2414yes—
620C2×C22⋊C4C2414yes—
621C2×C22⋊C4C2414yes—
622C2×C22⋊C4C2414yes—
623C2×C22⋊C4C2414yes—
624C2×C22⋊C4C2418yes—
625C2×C22⋊C4C2418yes—
626C2×C22⋊C4C2418yes—
627C2×C22⋊C4C2418yes—
628C2×C22⋊C4C2418yes—
629C2×C22⋊C4C2418yes—
630C2×C22⋊C4C2418yes—
631C2×C22⋊C4C2418yes—
632C2×C22⋊C4C2418yes—
633C2×C22⋊C4C2418yes—
634C2×C22⋊C4C2414yes—
635C2×C22⋊C4C2418yes—
636C2×C22⋊C4C2418yes—
637C2×C22⋊C4C2414yes—
638C2×C22⋊C4C2414yes—
639C2×C22⋊C4C2418yes—
640C2×C22⋊C4C2414yes—
641C2×C22⋊C4C2414yes—
642C2×C22⋊C4C2418yes—
643C2×C22⋊C4C2414yes—
644C2×C22⋊C4C2414yes—
645C2×C22⋊C4C2414yes—
646C2×C22⋊C4C2418yes—
647C2×C42—24no—
648C2×C42—24no—
649C2×C42—82no—
650C2×C42#4118yes—
651C2×C42C2414yes—
652C2×C42C2414yes—
653C2×C42C2414yes—
654C2×C42C2412yes—
655C2×C42C2412yes—
656C2×C42C2412yes—
657C2×C42C2412yes—
658C2×C42C2418yes—
659C2×C42C2414yes—
660C2×C42C2418yes—
661C2×C42C2414yes—
662C2×C42C2418yes—
663C2×C42C2411yescharacteristic
664C2×C42C2411yescharacteristic
665C2×C42C2411yescharacteristic
666C2×C42C2411yescharacteristic
667#95C2412yes—
668#95C2412yes—
669#95C2412yes—
670#95C2412yes—
671#95C2412yes—
672#95C2412yes—
673#95C2412yes—
674#95C2412yes—
675#95C2414yes—
676#95C2414yes—
677#95C2418yes—
678#95C2418yes—
679#95C2414yes—
680#95C2418yes—
681#95C2418yes—
682#95C2418yes—
683#95C2414yes—
684#95C2414yes—
685#95C2414yes—
686#95C2414yes—
687#95C2414yes—
688#95C2414yes—
689#95C2414yes—
690#95C2414yes—
691#95C2414yes—
692#95C2414yes—
693#95C2414yes—
694#95C2418yes—
695#95C2414yes—
696#95C2414yes—
697#95C2414yes—
698#95C2414yes—
699#95C2418yes—
700#95C2418yes—
701#95C2418yes—
702#95C2418yes—
703#95C2418yes—
704#95C2418yes—
705C24—24no—
706C24—24no—
707C24—24no—
708C24—42no—
709C24—42no—
710C24—42no—
711C24—42no—
712C24C2514yes—
713C24C2514yes—
714C24C2511yescharacteristic
715#41—432no—
716C2×Q8—24no—
717C2×Q8—24no—
718C2×Q8—24no—
719C2×Q8—24no—
720C2×Q8—24no—
721C2×Q8—42no—
722C2×Q8—42no—
723C2×Q8—44no—
724C2×Q8—44no—
725C2×Q8—42no—
726C2×Q8—42no—
727C2×Q8—44no—
728C2×Q8—44no—
729C2×Q8—44no—
730C2×Q8—44no—
731C2×D4—28no—
732C2×D4—28no—
733C2×D4—28no—
734C2×D4—24no—
735C2×D4—24no—
736C2×D4—24no—
737C2×D4—24no—
738C2×D4—24no—
739C2×D4—24no—
740C2×D4—24no—
741C2×D4—24no—
742C2×D4—24no—
743C2×D4—24no—
744C2×D4—24no—
745C2×D4—42no—
746C2×D4—42no—
747C2×D4—42no—
748C2×D4—42no—
749C2×D4—48no—
750C2×D4—48no—
751C2×D4—48no—
752C2×D4—48no—
753C2×D4—48no—
754C2×D4—48no—
755C2×D4—416no—
756C22×C4—24no—
757C22×C4—22no—
758C22×C4—22no—
759C22×C4—24no—
760C22×C4—22no—
761C22×C4—22no—
762C22×C4—24no—
763C22×C4—28no—
764C22×C4—28no—
765C22×C4—28no—
766C22×C4—28no—
767C22×C4—28no—
768C22×C4—41no—
769C22×C4—42no—
770C22×C4—42no—
771C22×C4—41no—
772C22×C4—41no—
773C22×C4—41no—
774C22×C4—42no—
775C22×C4—42no—
776C22×C4—41no—
777C22×C4—41no—
778C22×C4—41no—
779C22×C4—41no—
780C22×C4—42no—
781C22×C4—42no—
782C22×C4—41no—
783C22×C4—41no—
784C22×C4—44no—
785C22×C4—44no—
786C22×C4—44no—
787C22×C4—44no—
788C22×C4—41no—
789C22×C4—41no—
790C22×C4—48no—
791C22×C4—48no—
792C22×C4—48no—
793C22×C4—816no—
794C22×C4C2×#4114yes—
795C22×C4C2×#4114yes—
796C22×C4C2×#4114yes—
797C22×C4H(5,𝔽2)14yes—
798C22×C42−1+414yes—
799C22×C4C2512yes—
800C22×C4C2514yes—
801C22×C4C2514yes—
802C22×C4C2514yes—
803C22×C4C2514yes—
804C22×C4C2512yes—
805C22×C4C2512yes—
806C22×C4C2514yes—
807C22×C4C2514yes—
808C22×C4C2514yes—
809C22×C4C2514yes—
810C22×C4C2514yes—
811C22×C4C2512yes—
812C22×C4C2514yes—
813C22×C4C2511yescharacteristic
814C22×C4C2511yescharacteristic
815C22×C4C2511yescharacteristic
816C22×C4C2511yescharacteristic
817C22×C4C2511yescharacteristic
818C22×C4C2511yescharacteristic
819C4⋊C4—24no—
820C4⋊C4—24no—
821C4⋊C4—24no—
822C4⋊C4—24no—
823C4⋊C4—24no—
824C4⋊C4—24no—
825C4⋊C4—28no—
826C4⋊C4—28no—
827C4⋊C4—24no—
828C4⋊C4—24no—
829C4⋊C4—24no—
830C4⋊C4—24no—
831C4⋊C4—24no—
832C4⋊C4—24no—
833C4⋊C4—24no—
834C4⋊C4—24no—
835C4⋊C4—24no—
836C4⋊C4—24no—
837C4⋊C4—48no—
838C4⋊C4—48no—
839C4⋊C4—48no—
840C4⋊C4—42no—
841C4⋊C4—42no—
842C4⋊C4—44no—
843C4⋊C4—42no—
844C4⋊C4—44no—
845C4⋊C4—44no—
846C4⋊C4—44no—
847C4⋊C4—44no—
848C4⋊C4—44no—
849C4⋊C4—44no—
850C4⋊C4—42no—
851C4⋊C4—48no—
852C4⋊C4—42no—
853C4⋊C4—42no—
854C4⋊C4—42no—
855C4⋊C4—42no—
856C4⋊C4—48no—
857C4⋊C4—48no—
858C4⋊C4—48no—
859C4⋊C4—44no—
860C4⋊C4—44no—
861C4⋊C4—44no—
862C22⋊C4—28no—
863C22⋊C4—28no—
864C22⋊C4—28no—
865C22⋊C4—28no—
866C22⋊C4—28no—
867C22⋊C4—28no—
868C22⋊C4—28no—
869C22⋊C4—48no—
870C22⋊C4—48no—
871C22⋊C4—48no—
872C22⋊C4—48no—
873C22⋊C4—44no—
874C22⋊C4—48no—
875C22⋊C4—44no—
876C22⋊C4—48no—
877C22⋊C4—48no—
878C22⋊C4—48no—
879C22⋊C4—48no—
880C22⋊C4—48no—
881C22⋊C4—48no—
882C22⋊C4—44no—
883C22⋊C4—48no—
884C22⋊C4—48no—
885C22⋊C4—44no—
886C22⋊C4—44no—
887C22⋊C4—48no—
888C22⋊C4—44no—
889C22⋊C4—44no—
890C22⋊C4—48no—
891C22⋊C4—44no—
892C42—28no—
893C42—24no—
894C42—24no—
895C42—28no—
896C42—28no—
897C42—24no—
898C42—24no—
899C42—44no—
900C42—44no—
901C42—48no—
902C42—48no—
903C42—48no—
904C42C2×#4114yes—
905C42C2×#4114yes—
906C42C2×#4114yes—
907C42C2×#4114yes—
908C23—21no—
909C23—21no—
910C23—21no—
911C23—21no—
912C23—24no—
913C23—24no—
914C23—24no—
915C23—24no—
916C23—24no—
917C23—24no—
918C23—24no—
919C23—24no—
920C23—24no—
921C23—24no—
922C23—24no—
923C23—24no—
924C23—24no—
925C23—24no—
926C23—48no—
927C23—48no—
928C23—48no—
929C23—84no—
930C23—84no—
931C23—84no—
932C23—84no—
933C23C22×#4112yes—
934C23C2×H(5,𝔽2)12yes—
935C23C2×2−1+412yes—
936C23C2611yescharacteristic
937Q8—48no—
938Q8—48no—
939Q8—84no—
940Q8—88no—
941Q8—88no—
942D4—48no—
943D4—416no—
944D4—48no—
945D4—48no—
946D4—48no—
947D4—84no—
948D4—168no—
949D4—168no—
950C2×C4—21no—
951C2×C4—21no—
952C2×C4—21no—
953C2×C4—21no—
954C2×C4—21no—
955C2×C4—21no—
956C2×C4—21no—
957C2×C4—21no—
958C2×C4—24no—
959C2×C4—24no—
960C2×C4—24no—
961C2×C4—24no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—24no—
965C2×C4—24no—
966C2×C4—24no—
967C2×C4—24no—
968C2×C4—24no—
969C2×C4—24no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—24no—
973C2×C4—24no—
974C2×C4—24no—
975C2×C4—24no—
976C2×C4—24no—
977C2×C4—24no—
978C2×C4—24no—
979C2×C4—24no—
980C2×C4—24no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—24no—
986C2×C4—24no—
987C2×C4—24no—
988C2×C4—22no—
989C2×C4—24no—
990C2×C4—24no—
991C2×C4—24no—
992C2×C4—24no—
993C2×C4—22no—
994C2×C4—24no—
995C2×C4—24no—
996C2×C4—22no—
997C2×C4—24no—
998C2×C4—22no—
999C2×C4—24no—
1000C2×C4—44no—
1001C2×C4—44no—
1002C2×C4—48no—
1003C2×C4—416no—
1004C2×C4—88no—
1005C2×C4—88no—
1006C2×C4—82no—
1007C2×C4—82no—
1008C2×C4—84no—
1009C2×C4—82no—
1010C2×C4—82no—
1011C2×C4—84no—
1012C2×C4—168no—
1013C2×C4#542116yes—
1014C2×C4C22×#4112yes—
1015C2×C4C22×#4112yes—
1016C2×C4C22×#4112yes—
1017C2×C4C22×#4112yes—
1018C2×C4C22×#4112yes—
1019C2×C4C22×#4112yes—
1020C2×C4C2×H(5,𝔽2)12yes—
1021C2×C4C2×H(5,𝔽2)12yes—
1022C2×C4C2×2−1+412yes—
1023C2×C4C2×2−1+412yes—
1024C22—22no—
1025C22—22no—
1026C22—22no—
1027C22—22no—
1028C22—22no—
1029C22—22no—
1030C22—44no—
1031C22—44no—
1032C22—44no—
1033C22—44no—
1034C22—44no—
1035C22—44no—
1036C22—44no—
1037C22—44no—
1038C22—44no—
1039C22—44no—
1040C22—44no—
1041C22—44no—
1042C22—44no—
1043C22—44no—
1044C22—816no—
1045C22C2×#54214yes—
1046C22C23×#4111yescharacteristic
1047C22C22×H(5,𝔽2)11yescharacteristic
1048C22C22×2−1+411yescharacteristic
1049C22H(7,𝔽2)11yescharacteristic
1050C22H(7,𝔽2)11yescharacteristic
1051C22H(7,𝔽2)11yescharacteristic
1052C222−1+611yescharacteristic
1053C4—22no—
1054C4—22no—
1055C4—22no—
1056C4—22no—
1057C4—44no—
1058C4—44no—
1059C4—44no—
1060C4—42no—
1061C4—44no—
1062C4—44no—
1063C4—42no—
1064C4—44no—
1065C4—42no—
1066C4—44no—
1067C4—44no—
1068C4—42no—
1069C4—44no—
1070C4—44no—
1071C4C2×#54214yes—
1072C4C2×#54214yes—
1073C2—24no—
1074C2—84no—
1075C2—84no—
1076C2C22×#54211yescharacteristic
1077C2#6284511yescharacteristic
1078C2#6285511yescharacteristic
1079C2#6287811yescharacteristic
1080C2#6287911yescharacteristic
1081C2#6288011yescharacteristic
1082C2#6288111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35165C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42699C2semidirect
2. #42698C2semidirect
3. #42694C2semidirect
4. #42693C2semidirect
5. #42524C2semidirect
6. #42523C2semidirect
7. #42515C2semidirect
8. #42514C2semidirect
9. #37462C2semidirect
10. #37461C2semidirect
11. #36730C2semidirect
12. #36729C2semidirect
13. #35556C2semidirect
14. #35545C2semidirect
15. #35531C2semidirect
16. #35519C2semidirect
17. #35172C2semidirect
19. #34642C2semidirect
20. #34637C2semidirect
21. #34213C2semidirect
22. #34206C2semidirect
23. C2×#2319C2semidirect
32. #2838C22semidirect
33. #2837C22semidirect
34. #2832C22semidirect
35. #2829C22semidirect
36. #2747C22semidirect
37. #2746C22semidirect
38. #2745C22semidirect
39. #2742C22semidirect
40. #2741C22semidirect
41. #2738C22semidirect
42. #2737C22semidirect
43. #2717C22semidirect
44. #2702C22semidirect
45. #2701C22semidirect
46. #2700C22semidirect
47. #2692C22semidirect
48. #2691C22semidirect
49. #2687C22semidirect
50. #2686C22semidirect
51. #2672C22semidirect
52. #2663C22semidirect
53. #2662C22semidirect
54. #2660C22semidirect
55. #2660C22semidirect
56. #2660C22semidirect
57. #2660C22semidirect
62. #2654C22semidirect
63. #2653C22semidirect
64. #2651C22semidirect
65. #2650C22semidirect
66. #2642C22semidirect
67. #2641C22semidirect
68. #2640C22semidirect
69. #2640C22semidirect
74. #2632C22semidirect
75. #2630C22semidirect
80. #2582C22semidirect
81. #2581C22semidirect
83. #2580C22semidirect
94. #2538C22semidirect
98. #2525C22semidirect
99. #2521C22semidirect
100. #2514C22semidirect
101. #2513C22semidirect
102. #2512C22semidirect
103. #2511C22semidirect
109. #2497C22semidirect
110. #2496C22semidirect
111. #2495C22semidirect
112. #2494C22semidirect
120. #2461C22semidirect
121. #2458C22semidirect
128. #2442C22semidirect
129. #2441C22semidirect
130. #2440C22semidirect
131. #2439C22semidirect
134. #2399C22semidirect
135. #2399C22semidirect
136. #2398C22semidirect
137. #2398C22semidirect
138. #2370C22semidirect
139. #2369C22semidirect
140. #2367C22semidirect
141. #2366C22semidirect
142. #2365C22semidirect
143. #2365C22semidirect
144. #2355C22semidirect
145. #2355C22semidirect
146. #2354C22semidirect
147. #2352C22semidirect
148. Q8×C4⋊C4C22semidirect
149. D4×C4⋊C4C22semidirect

Maximal subgroups

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

subgroupindex
#426992
#426982
#426942
#426932
#425242
#425232
#425152
#425142
#374622
#374612
#367302
#367292
#355562
#355452
#355312
#355192
#351722
#351652
#346422
#346372
#342132
#342062
C2×#23192