Finite Group Databasebeta

← #7646819

Subgroups — #7646819

Order 512.

5190 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#42632C214yesmaximal, complemented
2#42621C214yesmaximal, complemented
3#42585C214yesmaximal, complemented
4#42571C214yesmaximal, complemented
5#40174C214yesmaximal, complemented
6#40047C214yesmaximal, complemented
7#39411C214yesmaximal, complemented
8#39029C214yesmaximal, complemented
9#37461C214yesmaximal, complemented
10#36765C214yesmaximal, complemented
11#36729C214yesmaximal, complemented
12#35557C212yesmaximal, complemented
13#35556C212yesmaximal, complemented
14#35260C214yesmaximal, complemented
15#35254C212yesmaximal, complemented
16#35174C211yesmaximal, characteristic, complemented
17#35173C211yesmaximal, characteristic, complemented
18#35168C211yesmaximal, characteristic
19#35158C211yesmaximal, characteristic, complemented
20#34745C212yesmaximal, complemented
21#34271C211yesmaximal, characteristic, complemented
22C2×#2354C211yesmaximal, characteristic, complemented
23C4×#537C211yesmaximal, characteristic, complemented
24C2×#544C2211yescharacteristic
25C2×#542C2214yescomplemented
26C2×#537C2211yescharacteristic
27C2×#535C2212yes—
28C2×#533C2212yes—
29C2×C4×#41C2212yes—
30C22×C4×D4C2211yescharacteristic
31C22×#117C2212yes—
32#2857C2214yes—
33#2854C2214yes—
34#2854C2214yes—
35#2850C2214yes—
36#2848C2214yes—
37#2847C2214yes—
38#2837C2218yescomplemented
39#2832C2218yescomplemented
40#2800C2218yescomplemented
41#2798C2218yescomplemented
42#2779C2218yescomplemented
43#2754C2218yescomplemented
44#2747C2218yescomplemented
45#2742C2218yescomplemented
46#2741C2218yescomplemented
47#2731C2218yescomplemented
48#2718C2218yescomplemented
49#2717C2218yescomplemented
50#2712C2218yescomplemented
51#2705C2218yescomplemented
52#2702C2218yescomplemented
53#2692C2218yescomplemented
54#2691C2218yescomplemented
55#2672C2218yescomplemented
56#2662C2218yescomplemented
57#2659C2214yes—
58#2654C2218yescomplemented
59#2650C2218yescomplemented
60#2639C2214yes—
61#2630C2218yescomplemented
62#2628C2214yescomplemented
63#2626C2214yes—
64#2625C2214yescomplemented
65#2624C2214yes—
66#2624C2214yes—
67#2624C2214yescomplemented
68#2620C2214yescomplemented
69#2617C2214yes—
70#2592C2214yes—
71#2592C2214yes—
72#2584C2214yescomplemented
73#2584C2214yescomplemented
74#2567C2214yescomplemented
75#2548C2214yes—
76#2548C2214yes—
77#2546C2214yescomplemented
78#2521C2218yescomplemented
79#2512C2214yescomplemented
80#2512C2214yescomplemented
81#2511C2214yescomplemented
82#2511C2214yescomplemented
83#2497C2214yescomplemented
84#2497C2214yescomplemented
85#2496C2214yescomplemented
86#2496C2214yescomplemented
87#2492C2214yescomplemented
88#2491C2214yes—
89#2491C2214yes—
90#2491C2214yescomplemented
91#2490C2214yes—
92#2490C2214yes—
93#2490C2214yescomplemented
94#2489C2214yescomplemented
95#2481C2218yes—
96#2481C2218yes—
97#2479C2218yescomplemented
98#2477C2218yescomplemented
99#2474C2218yescomplemented
100#2472C2218yes—
101#2472C2218yes—
102#2470C2218yescomplemented
103#2458C2218yescomplemented
104#2454C2214yes—
105#2454C2214yes—
106#2454C2212yescomplemented
107#2454C2212yescomplemented
108#2453C2212yescomplemented
109#2453C2212yescomplemented
110#2452C2214yes—
111#2452C2214yes—
112#2452C2212yescomplemented
113#2452C2212yescomplemented
114#2451C2212yescomplemented
115#2451C2212yescomplemented
116#2450C2214yes—
117#2450C2214yes—
118#2449C2214yes—
119#2449C2214yes—
120#2448C2214yes—
121#2448C2214yes—
122#2445C2214yes—
123#2445C2214yes—
124#2428C2214yes—
125#2428C2214yes—
126#2427C2214yes—
127#2427C2214yes—
128#2418C2218yes—
129#2418C2218yes—
130#2396C2214yescomplemented
131#2396C2214yescomplemented
132#2370C2214yescomplemented
133#2370C2214yescomplemented
134#2369C2214yescomplemented
135#2365C2214yescomplemented
136#2354C2214yes—
137#2354C2214yes—
138#2354C2214yes—
139#2354C2214yes—
140#2329C2214yes—
141#2325C2214yes—
142#2324C2214yescomplemented
143#2324C2214yescomplemented
144#2323C2214yescomplemented
145#2323C2214yescomplemented
146#2316C2211yescharacteristic
147#2316C2211yescharacteristic
148#2316C2212yes—
149#2314C2214yescomplemented
150#2311C2212yes—
151#2311C2212yes—
152#2309C2212yes—
153C4×C22⋊Q8C2214yes—
154C4×C22⋊Q8C2214yescomplemented
155C4×C22⋊Q8C2214yescomplemented
156C4×C22⋊Q8C2214yescomplemented
157C4×#121C2214yes—
158C4×#121C2214yescomplemented
159#2297C2212yes—
160#2297C2212yes—
161#2296C2212yes—
162#2296C2212yes—
163C2×#390C2211yescharacteristic
164C2×#390C2211yescharacteristic
165C2×#388C2212yes—
166C2×#388C2212yes—
167C2×#384C2211yescharacteristic
168C2×#380C2212yes—
169#2274C2212yes—
170C2×C4×C4⋊C4C2211yescharacteristic
171C2×C4×C4⋊C4C2211yescharacteristic
172C2×C4×C4⋊C4C2211yescharacteristic
173C22×#41C2312yes—
174C23×D4C2311yescharacteristic
175C24×C4C2312yes—
176#544—28no—
177#542—416no—
178#537—28no—
179#535—48no—
180#533—48no—
181C2×C4⋊Q8C2314yes—
182C2×C4⋊Q8C2312yes—
183C2×C4⋊Q8C2314yes—
184C2×C4⋊Q8C2312yes—
185C2×#127C2314yes—
186C2×#126C2318yes—
187C2×#126C2318yes—
188C2×#125C2314yes—
189C2×#125C2312yes—
190C2×#125C2312yes—
191C2×#124C2314yes—
192C2×#124C2314yes—
193C2×#124C2318yes—
194C2×#124C2318yes—
195C2×#123C2318yes—
196C2×#123C2318yes—
197C2×C22⋊Q8C2314yes—
198C2×C22⋊Q8C2314yes—
199C2×C22⋊Q8C2314yes—
200C2×C22⋊Q8C2314yes—
201C2×C22⋊Q8C2314yes—
202C2×C22⋊Q8C2314yes—
203C2×C22⋊Q8C2314yes—
204C2×C22⋊Q8C2314yes—
205C2×#121C2314yes—
206C2×#121C2314yes—
207C2×#121C2314yes—
208C2×#121C2314yes—
209C2×#121C2314yes—
210C2×#121C2314yes—
211C2×#120C2318yes—
212C4×#41—48no—
213C2×C4×Q8C2314yes—
214C2×C4×Q8C2312yes—
215C2×C4×Q8C2314yes—
216C2×C4×Q8C2314yes—
217C2×C4×Q8C2312yes—
218C2×C4×D4—28no—
219C2×C4×D4C2314yes—
220C2×C4×D4C2314yes—
221C2×C4×D4C2312yes—
222C2×C4×D4C2314yes—
223C2×C4×D4C2314yes—
224C2×C4×D4C2314yes—
225C2×C4×D4C2312yes—
226C2×#117—48no—
227C2×#117C2312yes—
228C2×#117C2312yes—
229C2×#117C2314yes—
230C2×#117C2312yes—
231C2×#117C2314yes—
232C2×#117C2314yes—
233C2×#117C2314yes—
234C2×#117C2314yes—
235C22×C4⋊C4C2311yescharacteristic
236C22×C4⋊C4C2311yescharacteristic
237C22×C4⋊C4C2311yescharacteristic
238C22×C4⋊C4C2312yes—
239C22×C4⋊C4C2311yescharacteristic
240C22×C4⋊C4C2312yes—
241C22×C4⋊C4C2311yescharacteristic
242C22×C22⋊C4C2312yes—
243C22×C22⋊C4C2312yes—
244C22×C22⋊C4C2312yes—
245C22×C22⋊C4C2312yes—
246C22×C22⋊C4C2312yes—
247C22×C42C2311yescharacteristic
248C22×C42C2311yescharacteristic
249C22×C42C2311yescharacteristic
250C22×C42C2312yes—
251C22×C42C2314yes—
252C22×C42C2312yes—
253#400C2314yes—
254#400C2318yes—
255#400C2318yes—
256#400C2318yes—
257#400C2318yes—
258#400C2318yes—
259#400C2314yes—
260#399C2318yes—
261#399C2318yes—
262#399C2318yes—
263#399C2314yes—
264#399C2314yes—
265#398C2314yes—
266#398C2318yes—
267#398C2318yes—
268#398C2314yes—
269#398C2314yes—
270#398C2314yes—
271#397C2318yes—
272#397C2318yes—
273#397C2318yes—
274#397C2318yes—
275#397C2318yes—
276#397C2318yes—
277#397C2318yes—
278#397C2318yes—
279#396C2314yes—
280#396C2318yes—
281#396C2314yes—
282#396C2318yes—
283#396C2318yes—
284#396C2318yes—
285#396C2314yes—
286#396C2314yes—
287#395C2318yes—
288#395C2318yes—
289#395C2314yes—
290#395C2314yes—
291#394C2318yes—
292#394C2318yes—
293#394C2318yes—
294#394C2318yes—
295#394C2318yes—
296#394C2318yes—
297#394C2318yes—
298#394C2318yes—
299#394C2318yes—
300#394C2318yes—
301#394C2318yes—
302#393C2314yes—
303#393C2318yes—
304#393C2318yes—
305#393C2318yes—
306#393C2318yes—
307#393C2314yes—
308#392C2318yes—
309#391C2314yes—
310#391C2314yes—
311#391C2318yes—
312#391C2314yes—
313#391C2314yes—
314#391C2318yes—
315#391C2312yes—
316#391C2312yes—
317#391C2314yes—
318#391C2312yes—
319#391C2312yes—
320#391C2314yes—
321#390C2314yes—
322#390C2314yes—
323#390C2314yes—
324#390C2314yes—
325#390C2314yes—
326#390C2314yes—
327#390C2314yes—
328#390C2314yes—
329#390C2318yes—
330#390C2314yes—
331#390C2314yes—
332#390C2314yes—
333#390C2314yes—
334#390C2318yes—
335#390C2312yes—
336#390C2312yes—
337#390C2312yes—
338#390C2312yes—
339#389C2314yes—
340#389C2314yes—
341#389C2314yes—
342#389C2314yes—
343#389C2314yes—
344#389C2314yes—
345#389C2314yes—
346#389C2314yes—
347#389C2314yes—
348#389C2314yes—
349#389C2314yes—
350#389C2314yes—
351#389C2314yes—
352#389C2318yes—
353#389C2318yes—
354#389C2312yes—
355#389C2312yes—
356#389C2312yes—
357#389C2312yes—
358#389C2314yes—
359#389C2312yes—
360#389C2312yes—
361#389C2312yes—
362#389C2312yes—
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#388C2318yes—
381#387C2314yes—
382#387C2318yes—
383#387C2318yes—
384#387C2318yes—
385#387C2318yes—
386#387C2318yes—
387#387C2318yes—
388#387C2314yes—
389#387C2318yes—
390#387C2318yes—
391#387C2314yes—
392#387C2314yes—
393#386C2318yes—
394#386C2318yes—
395#386C2318yes—
396#386C2318yes—
397#386C2314yes—
398#386C2318yes—
399#386C2318yes—
400#386C2314yes—
401#386C2318yes—
402#386C2314yes—
403#386C2314yes—
404#385C2314yes—
405#385C2318yes—
406#385C2314yes—
407#385C2314yes—
408#385C2318yes—
409#385C2318yes—
410#385C2314yes—
411#385C2314yes—
412#385C2314yes—
413#385C2314yes—
414#385C2314yes—
415#384C2314yes—
416#384C2314yes—
417#384C2314yes—
418#382C2314yes—
419#380C2314yes—
420#380C2314yes—
421#380C2314yes—
422#380C2314yes—
423#380C2314yes—
424#380C2314yes—
425#380C2314yes—
426#380C2314yes—
427#380C2318yes—
428#380C2314yes—
429#380C2314yes—
430#380C2318yes—
431#380C2318yes—
432#380C2314yes—
433#380C2314yes—
434#379C2318yes—
435C4×C4⋊C4C2314yes—
436C4×C4⋊C4C2314yes—
437C4×C4⋊C4C2314yes—
438C4×C4⋊C4C2314yes—
439C4×C4⋊C4C2314yes—
440C4×C4⋊C4C2314yes—
441C4×C4⋊C4C2314yes—
442C4×C4⋊C4C2314yes—
443C4×C4⋊C4C2312yes—
444C4×C4⋊C4C2312yes—
445C4×C4⋊C4C2312yes—
446C4×C4⋊C4C2312yes—
447C4×C4⋊C4C2314yes—
448C4×C4⋊C4C2314yes—
449C4×C4⋊C4C2314yes—
450C4×C4⋊C4C2318yes—
451C4×C4⋊C4C2314yes—
452C4×C4⋊C4C2314yes—
453C4×C4⋊C4C2314yes—
454C4×C22⋊C4C2318yes—
455C4×C22⋊C4C2314yes—
456C4×C22⋊C4C2314yes—
457C4×C22⋊C4C2314yes—
458C4×C22⋊C4C2314yes—
459C4×C22⋊C4C2318yes—
460C2×#95C2312yes—
461C2×#95C2312yes—
462C2×#95C2311yescharacteristic
463C2×#95C2311yescharacteristic
464C25C2412yes—
465C2×#41—28no—
466C2×#41—28no—
467C2×#41—28no—
468C22×Q8C2412yes—
469C22×Q8C2414yes—
470C22×Q8C2414yes—
471C22×Q8C2414yes—
472C22×D4—24no—
473C22×D4—24no—
474C22×D4—24no—
475C22×D4C2414yes—
476C22×D4C2414yes—
477C22×D4C2412yes—
478C22×D4C2414yes—
479C22×D4C2418yes—
480C22×D4C2418yes—
481C23×C4—28no—
482C23×C4—44no—
483C23×C4—44no—
484C23×C4C2411yescharacteristic
485C23×C4C2414yes—
486C23×C4C2411yescharacteristic
487C23×C4C2411yescharacteristic
488C23×C4C2414yes—
489C23×C4C2414yes—
490C23×C4C2412yes—
491C23×C4C2412yes—
492C23×C4C2411yescharacteristic
493C23×C4C2411yescharacteristic
494C23×C4C2411yescharacteristic
495C23×C4C2414yes—
496C23×C4C2414yes—
497C23×C4C2412yes—
498C23×C4C2411yescharacteristic
499C4⋊Q8—216no—
500C4⋊Q8—44no—
501C4⋊Q8—44no—
502C4⋊Q8—48no—
503#127—48no—
504#126—416no—
505#126—88no—
506#125—216no—
507#125—44no—
508#125—44no—
509#124—48no—
510#124—48no—
511#124—416no—
512#124—88no—
513#123—416no—
514#123—88no—
515C22⋊Q8—216no—
516C22⋊Q8—216no—
517C22⋊Q8—216no—
518C22⋊Q8—48no—
519C22⋊Q8—48no—
520C22⋊Q8—48no—
521C22⋊Q8—48no—
522C22⋊Q8—48no—
523#121—216no—
524#121—216no—
525#121—48no—
526#121—48no—
527#121—48no—
528#121—48no—
529#120—416no—
530C4×Q8—48no—
531C4×Q8—48no—
532C4×Q8—48no—
533C4×Q8—44no—
534C4×Q8—44no—
535C4×D4—216no—
536C4×D4—216no—
537C4×D4—44no—
538C4×D4—44no—
539C4×D4—48no—
540C4×D4—48no—
541C4×D4—48no—
542#117—28no—
543#117—28no—
544#117—28no—
545#117—216no—
546#117—48no—
547#117—48no—
548#117—48no—
549#117—48no—
550C2×C4⋊C4—24no—
551C2×C4⋊C4—24no—
552C2×C4⋊C4—24no—
553C2×C4⋊C4—42no—
554C2×C4⋊C4—44no—
555C2×C4⋊C4—82no—
556C2×C4⋊C4#4118yes—
557C2×C4⋊C4C2411yescharacteristic
558C2×C4⋊C4C2411yescharacteristic
559C2×C4⋊C4C2411yescharacteristic
560C2×C4⋊C4C2414yes—
561C2×C4⋊C4C2412yes—
562C2×C4⋊C4C2414yes—
563C2×C4⋊C4C2414yes—
564C2×C4⋊C4C2412yes—
565C2×C4⋊C4C2412yes—
566C2×C4⋊C4C2412yes—
567C2×C4⋊C4C2412yes—
568C2×C4⋊C4C2412yes—
569C2×C4⋊C4C2412yes—
570C2×C4⋊C4C2414yes—
571C2×C4⋊C4C2414yes—
572C2×C4⋊C4C2414yes—
573C2×C4⋊C4C2414yes—
574C2×C4⋊C4C2414yes—
575C2×C4⋊C4C2418yes—
576C2×C4⋊C4C2414yes—
577C2×C4⋊C4C2418yes—
578C2×C4⋊C4C2412yes—
579C2×C4⋊C4C2414yes—
580C2×C4⋊C4C2414yes—
581C2×C4⋊C4C2414yes—
582C2×C4⋊C4C2414yes—
583C2×C4⋊C4C2414yes—
584C2×C4⋊C4C2414yes—
585C2×C4⋊C4C2414yes—
586C2×C4⋊C4C2414yes—
587C2×C4⋊C4C2414yes—
588C2×C4⋊C4C2414yes—
589C2×C4⋊C4C2414yes—
590C2×C4⋊C4C2414yes—
591C2×C4⋊C4C2414yes—
592C2×C4⋊C4C2414yes—
593C2×C4⋊C4C2418yes—
594C2×C4⋊C4C2418yes—
595C2×C4⋊C4C2414yes—
596C2×C4⋊C4C2414yes—
597C2×C4⋊C4C2414yes—
598C2×C4⋊C4C2414yes—
599C2×C4⋊C4C2411yescharacteristic
600C2×C22⋊C4—28no—
601C2×C22⋊C4—44no—
602C2×C22⋊C4—44no—
603C2×C22⋊C4—82no—
604C2×C22⋊C4—82no—
605C2×C22⋊C4C2414yes—
606C2×C22⋊C4C2414yes—
607C2×C22⋊C4C2418yes—
608C2×C22⋊C4C2414yes—
609C2×C22⋊C4C2414yes—
610C2×C22⋊C4C2414yes—
611C2×C22⋊C4C2414yes—
612C2×C22⋊C4C2414yes—
613C2×C22⋊C4C2418yes—
614C2×C22⋊C4C2414yes—
615C2×C22⋊C4C2414yes—
616C2×C22⋊C4C2414yes—
617C2×C22⋊C4C2418yes—
618C2×C22⋊C4C2418yes—
619C2×C22⋊C4C2414yes—
620C2×C22⋊C4C2414yes—
621C2×C22⋊C4C2418yes—
622C2×C22⋊C4C2418yes—
623C2×C22⋊C4C2418yes—
624C2×C22⋊C4C2418yes—
625C2×C22⋊C4C2414yes—
626C2×C22⋊C4C2418yes—
627C2×C22⋊C4C2418yes—
628C2×C22⋊C4C2418yes—
629C2×C22⋊C4C2418yes—
630C2×C22⋊C4C2414yes—
631C2×C22⋊C4C2418yes—
632C2×C22⋊C4C2414yes—
633C2×C22⋊C4C2414yes—
634C2×C22⋊C4C2414yes—
635C2×C22⋊C4C2418yes—
636C2×C42—24no—
637C2×C42—24no—
638C2×C42—24no—
639C2×C42—44no—
640C2×C42—44no—
641C2×C42—48no—
642C2×C42C2414yes—
643C2×C42C2412yes—
644C2×C42C2414yes—
645C2×C42C2414yes—
646C2×C42C2414yes—
647C2×C42C2414yes—
648C2×C42C2412yes—
649C2×C42C2412yes—
650C2×C42C2412yes—
651C2×C42C2412yes—
652C2×C42C2412yes—
653C2×C42C2414yes—
654C2×C42C2414yes—
655C2×C42C2414yes—
656C2×C42C2414yes—
657C2×C42C2418yes—
658C2×C42C2418yes—
659#95C2412yes—
660#95C2418yes—
661#95C2412yes—
662#95C2418yes—
663#95C2412yes—
664#95C2412yes—
665#95C2418yes—
666#95C2418yes—
667#95C2414yes—
668#95C2414yes—
669#95C2418yes—
670#95C2418yes—
671#95C2414yes—
672#95C2414yes—
673#95C2414yes—
674#95C2414yes—
675#95C2414yes—
676#95C2414yes—
677#95C2414yes—
678#95C2414yes—
679#95C2414yes—
680#95C2414yes—
681#95C2414yes—
682#95C2418yes—
683#95C2418yes—
684#95C2414yes—
685#95C2414yes—
686#95C2414yes—
687#95C2418yes—
688#95C2418yes—
689#95C2418yes—
690#95C2418yes—
691C24—24no—
692C24—24no—
693C24—24no—
694C24—42no—
695C24—42no—
696C24—42no—
697C24—42no—
698C24C2514yes—
699C24C2514yes—
700C24C2511yescharacteristic
701#41—432no—
702C2×Q8—24no—
703C2×Q8—28no—
704C2×Q8—24no—
705C2×Q8—28no—
706C2×Q8—24no—
707C2×Q8—44no—
708C2×Q8—44no—
709C2×Q8—44no—
710C2×Q8—44no—
711C2×Q8—44no—
712C2×Q8—44no—
713C2×Q8—44no—
714C2×D4—28no—
715C2×D4—28no—
716C2×D4—28no—
717C2×D4—28no—
718C2×D4—24no—
719C2×D4—28no—
720C2×D4—24no—
721C2×D4—28no—
722C2×D4—28no—
723C2×D4—24no—
724C2×D4—44no—
725C2×D4—44no—
726C2×D4—48no—
727C2×D4—48no—
728C2×D4—48no—
729C2×D4—48no—
730C2×D4—48no—
731C2×D4—48no—
732C2×D4—416no—
733C22×C4—22no—
734C22×C4—22no—
735C22×C4—22no—
736C22×C4—22no—
737C22×C4—22no—
738C22×C4—22no—
739C22×C4—22no—
740C22×C4—22no—
741C22×C4—24no—
742C22×C4—24no—
743C22×C4—28no—
744C22×C4—28no—
745C22×C4—28no—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—28no—
749C22×C4—28no—
750C22×C4—28no—
751C22×C4—28no—
752C22×C4—28no—
753C22×C4—42no—
754C22×C4—41no—
755C22×C4—44no—
756C22×C4—44no—
757C22×C4—42no—
758C22×C4—41no—
759C22×C4—41no—
760C22×C4—41no—
761C22×C4—42no—
762C22×C4—42no—
763C22×C4—44no—
764C22×C4—44no—
765C22×C4—41no—
766C22×C4—41no—
767C22×C4—42no—
768C22×C4—42no—
769C22×C4—41no—
770C22×C4—41no—
771C22×C4—44no—
772C22×C4—44no—
773C22×C4—44no—
774C22×C4—432no—
775C22×C4C2×#4118yes—
776C22×C4C2×#4114yes—
777C22×C4H(5,𝔽2)14yes—
778C22×C42−1+414yes—
779C22×C4C2514yes—
780C22×C4C2512yes—
781C22×C4C2514yes—
782C22×C4C2512yes—
783C22×C4C2514yes—
784C22×C4C2514yes—
785C22×C4C2514yes—
786C22×C4C2514yes—
787C22×C4C2514yes—
788C22×C4C2512yes—
789C22×C4C2514yes—
790C22×C4C2514yes—
791C22×C4C2511yescharacteristic
792C22×C4C2511yescharacteristic
793C22×C4C2514yes—
794C22×C4C2511yescharacteristic
795C22×C4C2511yescharacteristic
796C22×C4C2511yescharacteristic
797C22×C4C2511yescharacteristic
798C22×C4C2512yes—
799C4⋊C4—24no—
800C4⋊C4—24no—
801C4⋊C4—28no—
802C4⋊C4—28no—
803C4⋊C4—216no—
804C4⋊C4—22no—
805C4⋊C4—22no—
806C4⋊C4—22no—
807C4⋊C4—28no—
808C4⋊C4—24no—
809C4⋊C4—24no—
810C4⋊C4—24no—
811C4⋊C4—24no—
812C4⋊C4—28no—
813C4⋊C4—28no—
814C4⋊C4—28no—
815C4⋊C4—28no—
816C4⋊C4—24no—
817C4⋊C4—28no—
818C4⋊C4—42no—
819C4⋊C4—44no—
820C4⋊C4—48no—
821C4⋊C4—44no—
822C4⋊C4—44no—
823C4⋊C4—44no—
824C4⋊C4—44no—
825C4⋊C4—44no—
826C4⋊C4—44no—
827C4⋊C4—44no—
828C4⋊C4—44no—
829C4⋊C4—44no—
830C4⋊C4—44no—
831C4⋊C4—44no—
832C4⋊C4—44no—
833C4⋊C4—44no—
834C4⋊C4—44no—
835C4⋊C4—44no—
836C4⋊C4—48no—
837C4⋊C4—44no—
838C4⋊C4—48no—
839C4⋊C4—44no—
840C4⋊C4C2×#41116yes—
841C4⋊C4H(5,𝔽2)14yes—
842C22⋊C4—28no—
843C22⋊C4—28no—
844C22⋊C4—28no—
845C22⋊C4—216no—
846C22⋊C4—216no—
847C22⋊C4—28no—
848C22⋊C4—28no—
849C22⋊C4—28no—
850C22⋊C4—28no—
851C22⋊C4—28no—
852C22⋊C4—44no—
853C22⋊C4—44no—
854C22⋊C4—48no—
855C22⋊C4—48no—
856C22⋊C4—44no—
857C22⋊C4—48no—
858C22⋊C4—44no—
859C22⋊C4—44no—
860C22⋊C4—44no—
861C22⋊C4—48no—
862C22⋊C4—48no—
863C22⋊C4—48no—
864C22⋊C4—48no—
865C22⋊C4—44no—
866C22⋊C4—48no—
867C22⋊C4—48no—
868C22⋊C4—48no—
869C22⋊C4—48no—
870C22⋊C4—44no—
871C22⋊C4—48no—
872C22⋊C4—44no—
873C42—24no—
874C42—24no—
875C42—28no—
876C42—24no—
877C42—24no—
878C42—24no—
879C42—24no—
880C42—28no—
881C42—28no—
882C42—28no—
883C42—28no—
884C42—44no—
885C42—44no—
886C42—44no—
887C42—44no—
888C42—48no—
889C42—48no—
890C23—21no—
891C23—21no—
892C23—21no—
893C23—21no—
894C23—24no—
895C23—24no—
896C23—24no—
897C23—24no—
898C23—24no—
899C23—24no—
900C23—24no—
901C23—24no—
902C23—24no—
903C23—24no—
904C23—24no—
905C23—24no—
906C23—24no—
907C23—24no—
908C23—48no—
909C23—48no—
910C23—48no—
911C23—84no—
912C23—84no—
913C23—84no—
914C23—84no—
915C23C22×#4112yes—
916C23C2×H(5,𝔽2)12yes—
917C23C2×2−1+412yes—
918C23C2611yescharacteristic
919Q8—48no—
920Q8—88no—
921Q8—88no—
922Q8—88no—
923D4—416no—
924D4—416no—
925D4—48no—
926D4—88no—
927D4—168no—
928D4—168no—
929C2×C4—28no—
930C2×C4—21no—
931C2×C4—21no—
932C2×C4—21no—
933C2×C4—24no—
934C2×C4—21no—
935C2×C4—21no—
936C2×C4—21no—
937C2×C4—24no—
938C2×C4—21no—
939C2×C4—21no—
940C2×C4—22no—
941C2×C4—24no—
942C2×C4—24no—
943C2×C4—24no—
944C2×C4—22no—
945C2×C4—21no—
946C2×C4—21no—
947C2×C4—22no—
948C2×C4—24no—
949C2×C4—24no—
950C2×C4—24no—
951C2×C4—24no—
952C2×C4—24no—
953C2×C4—24no—
954C2×C4—21no—
955C2×C4—21no—
956C2×C4—24no—
957C2×C4—24no—
958C2×C4—24no—
959C2×C4—24no—
960C2×C4—24no—
961C2×C4—24no—
962C2×C4—24no—
963C2×C4—24no—
964C2×C4—24no—
965C2×C4—24no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—24no—
969C2×C4—24no—
970C2×C4—24no—
971C2×C4—22no—
972C2×C4—24no—
973C2×C4—24no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—21no—
977C2×C4—24no—
978C2×C4—22no—
979C2×C4—24no—
980C2×C4—24no—
981C2×C4—21no—
982C2×C4—48no—
983C2×C4—416no—
984C2×C4—416no—
985C2×C4—44no—
986C2×C4—44no—
987C2×C4—44no—
988C2×C4—416no—
989C2×C4—88no—
990C2×C4—84no—
991C2×C4—84no—
992C2×C4—82no—
993C2×C4—82no—
994C2×C4—88no—
995C2×C4#542116yescomplemented
996C2×C4C22×#4118yes—
997C2×C4C22×#4114yes—
998C2×C4C2×H(5,𝔽2)12yes—
999C2×C4C2×H(5,𝔽2)12yes—
1000C2×C4C2×H(5,𝔽2)12yes—
1001C2×C4C2×H(5,𝔽2)14yes—
1002C2×C4C2×2−1+414yes—
1003C2×C4#58512yes—
1004C22—22no—
1005C22—22no—
1006C22—22no—
1007C22—22no—
1008C22—22no—
1009C22—22no—
1010C22—44no—
1011C22—44no—
1012C22—44no—
1013C22—44no—
1014C22—44no—
1015C22—44no—
1016C22—44no—
1017C22—44no—
1018C22—44no—
1019C22—44no—
1020C22—44no—
1021C22—44no—
1022C22—44no—
1023C22—44no—
1024C22—816no—
1025C22C2×#54214yes—
1026C22C23×#4111yescharacteristic
1027C22C22×H(5,𝔽2)11yescharacteristic
1028C22C22×H(5,𝔽2)11yescharacteristic
1029C22C22×2−1+411yescharacteristic
1030C22C2×#58511yescharacteristic
1031C22H(7,𝔽2)11yescharacteristic
1032C222−1+611yescharacteristic
1033C4—22no—
1034C4—22no—
1035C4—28no—
1036C4—22no—
1037C4—22no—
1038C4—44no—
1039C4—44no—
1040C4—42no—
1041C4—41no—
1042C4—41no—
1043C4—44no—
1044C4—44no—
1045C4—44no—
1046C4—44no—
1047C4—42no—
1048C4—44no—
1049C4—42no—
1050C4—44no—
1051C4—44no—
1052C4C2×#54218yes—
1053C2—24no—
1054C2—84no—
1055C2—84no—
1056C2C22×#54211yescharacteristic
1057C2#6277311yescharacteristic
1058C2#6285111yescharacteristic
1059C2#6291411yescharacteristic
1060C2#6291711yescharacteristic
1061C2#6293011yescharacteristic
1062C2#6293211yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35168C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42632C2semidirect
2. #42621C2semidirect
3. #42585C2semidirect
4. #42571C2semidirect
5. #40174C2semidirect
6. #40047C2semidirect
7. #39411C2semidirect
8. #39029C2semidirect
9. #37461C2semidirect
10. #36765C2semidirect
11. #36729C2semidirect
12. #35557C2semidirect
13. #35556C2semidirect
14. #35260C2semidirect
15. #35254C2semidirect
16. #35174C2semidirect
17. #35173C2semidirect
19. #35158C2semidirect
20. #34745C2semidirect
21. #34271C2semidirect
22. C2×#2354C2semidirect
23. C4×#537C2semidirect
25. C2×#542C22semidirect
38. #2837C22semidirect
39. #2832C22semidirect
40. #2800C22semidirect
41. #2798C22semidirect
42. #2779C22semidirect
43. #2754C22semidirect
44. #2747C22semidirect
45. #2742C22semidirect
46. #2741C22semidirect
47. #2731C22semidirect
48. #2718C22semidirect
49. #2717C22semidirect
50. #2712C22semidirect
51. #2705C22semidirect
52. #2702C22semidirect
53. #2692C22semidirect
54. #2691C22semidirect
55. #2672C22semidirect
56. #2662C22semidirect
58. #2654C22semidirect
59. #2650C22semidirect
61. #2630C22semidirect
62. #2628C22semidirect
64. #2625C22semidirect
67. #2624C22semidirect
68. #2620C22semidirect
72. #2584C22semidirect
73. #2584C22semidirect
74. #2567C22semidirect
77. #2546C22semidirect
78. #2521C22semidirect
79. #2512C22semidirect
80. #2512C22semidirect
81. #2511C22semidirect
82. #2511C22semidirect
83. #2497C22semidirect
84. #2497C22semidirect
85. #2496C22semidirect
86. #2496C22semidirect
87. #2492C22semidirect
90. #2491C22semidirect
93. #2490C22semidirect
94. #2489C22semidirect
97. #2479C22semidirect
98. #2477C22semidirect
99. #2474C22semidirect
102. #2470C22semidirect
103. #2458C22semidirect
106. #2454C22semidirect
107. #2454C22semidirect
108. #2453C22semidirect
109. #2453C22semidirect
112. #2452C22semidirect
113. #2452C22semidirect
114. #2451C22semidirect
115. #2451C22semidirect
130. #2396C22semidirect
131. #2396C22semidirect
132. #2370C22semidirect
133. #2370C22semidirect
134. #2369C22semidirect
135. #2365C22semidirect
142. #2324C22semidirect
143. #2324C22semidirect
144. #2323C22semidirect
145. #2323C22semidirect
149. #2314C22semidirect
154. C4×C22⋊Q8C22semidirect
155. C4×C22⋊Q8C22semidirect
156. C4×C22⋊Q8C22semidirect
158. C4×#121C22semidirect
995. C2×C4#542semidirect

Maximal subgroups

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

subgroupindex
#426322
#426212
#425852
#425712
#401742
#400472
#394112
#390292
#374612
#367652
#367292
#355572
#355562
#352602
#352542
#351742
#351732
#351682
#351582
#347452
#342712
C2×#23542
C4×#5372