Finite Group Databasebeta

← #7681093

Subgroups — #7681093

Order 512.

4798 conjugacy classes of subgroups.

The subgroup lattice has 1057 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59333C214yesmaximal, complemented
2#59321C214yesmaximal, complemented
3#59285C218yesmaximal
4#45328C214yesmaximal, complemented
5#44956C214yesmaximal, complemented
6#43977C218yesmaximal, complemented
7#39077C214yesmaximal, complemented
8#38261C214yesmaximal, complemented
9#38066C214yesmaximal, complemented
10#36280C214yesmaximal, complemented
11#35662C211yesmaximal, characteristic, complemented
12#35630C211yesmaximal, characteristic, complemented
13#35555C211yesmaximal, characteristic, complemented
14#35555C211yesmaximal, characteristic, complemented
15#35313C211yesmaximal, characteristic, complemented
16#35311C211yesmaximal, characteristic
17#35286C211yesmaximal, characteristic, complemented
18C2×#2502C211yesmaximal, characteristic
19#34739C211yesmaximal, characteristic
20#34254C211yesmaximal, characteristic, complemented
21#34214C211yesmaximal, characteristic, complemented
22#34203C211yesmaximal, characteristic
23#34178C211yesmaximal, characteristic
24#34109C211yesmaximal, characteristic
25C2×#2317C211yesmaximal, characteristic
26C2×#533C2211yescharacteristic
27C22×C22⋊Q8C2211yescharacteristic
28C2×#519C2211yescharacteristic
29C22×#117C2211yescharacteristic
30C22×#117C2211yescharacteristic
31C23×C4⋊C4C2211yescharacteristic
32#2863C2214yescomplemented
33#2859C2214yescomplemented
34#2855C2214yes—
35#2791C2218yescomplemented
36#2791C2218yescomplemented
37#2776C2218yescomplemented
38#2771C2218yes—
39#2769C2218yescomplemented
40#2767C2218yescomplemented
41#2766C2218yescomplemented
42#2765C2218yes—
43#2765C2218yes—
44#2764C2218yes—
45#2762C2218yescomplemented
46#2719C2218yescomplemented
47#2647C2214yescomplemented
48#2645C2214yescomplemented
49#2625C2214yes—
50#2612C2218yescomplemented
51#2611C2218yes—
52#2606C2218yescomplemented
53#2599C2218yes—
54#2585C2218yescomplemented
55#2582C2214yescomplemented
56#2581C2214yescomplemented
57#2571C2214yescomplemented
58#2570C2214yescomplemented
59#2570C2214yescomplemented
60#2565C2218yescomplemented
61#2552C2214yescomplemented
62#2552C2214yescomplemented
63#2552C2214yescomplemented
64#2528C2218yescomplemented
65#2524C2218yescomplemented
66#2514C2214yescomplemented
67#2514C2214yescomplemented
68#2514C2214yescomplemented
69#2511C2214yescomplemented
70#2511C2214yescomplemented
71#2511C2214yescomplemented
72#2507C2214yescomplemented
73#2507C2214yescomplemented
74#2506C2214yescomplemented
75#2506C2218yescomplemented
76#2506C2214yescomplemented
77#2503C2212yes—
78#2502C2214yes—
79#2502C2212yes—
80#2502C2212yes—
81#2502C2212yes—
82#2502C2212yes—
83#2502C2212yes—
84#2502C2214yes—
85#2499C2212yes—
86#2499C2212yes—
87#2493C2218yes—
88#2493C2218yes—
89#2493C2218yes—
90#2493C2218yes—
91#2484C2214yes—
92#2483C2214yes—
93#2475C2218yes—
94#2475C2218yes—
95#2473C2218yes—
96#2473C2218yes—
97#2473C2218yes—
98#2473C2218yes—
99#2462C2218yescomplemented
100#2453C2214yescomplemented
101#2451C2214yescomplemented
102#2442C2218yes—
103#2442C2218yes—
104#2442C2212yes—
105#2441C2212yes—
106#2440C2212yes—
107#2439C2212yes—
108#2438C2218yes—
109#2438C2218yes—
110#2438C2214yes—
111#2437C2214yes—
112#2396C2214yes—
113C2×#398C2214yes—
114#2362C2214yes—
115#2360C2218yes—
116#2360C2218yes—
117#2360C2214yes—
118#2356C2214yescomplemented
119#2355C2214yescomplemented
120#2355C2214yescomplemented
121Q8×C4⋊C4C2214yescomplemented
122#2347C2212yes—
123#2346C2212yes—
124#2345C2212yes—
125#2345C2214yes—
126#2345C2214yes—
127#2344C2214yes—
128#2344C2212yes—
129#2344C2214yes—
130#2344C2214yes—
131#2343C2214yes—
132#2343C2218yes—
133#2343C2218yes—
134#2342C2214yes—
135#2342C2214yes—
136#2330C2214yescomplemented
137#2323C2214yes—
138#2320C2214yescomplemented
139#2317C2212yes—
140#2317C2211yescharacteristic
141#2317C2211yescharacteristic
142#2317C2214yes—
143#2317C2212yes—
144#2317C2211yescharacteristic
145#2317C2214yes—
146#2317C2211yescharacteristic
147#2317C2211yescharacteristic
148#2317C2211yescharacteristic
149#2316C2211yescharacteristic
150#2316C2211yescharacteristic
151#2316C2211yescharacteristic
152#2313C2214yes—
153#2310C2211yescharacteristic
154#2310C2211yescharacteristic
155#2310C2211yescharacteristic
156C4×C4⋊Q8C2214yescomplemented
157C4×C22⋊Q8C2214yes—
158C4×C22⋊Q8C2214yes—
159#2298C2212yes—
160#2298C2212yes—
161#2296C2211yescharacteristic
162#2296C2211yescharacteristic
163#2296C2211yescharacteristic
164#2296C2211yescharacteristic
165#2295C2214yescomplemented
166C2×#391C2211yescharacteristic
167C2×#391C2211yescharacteristic
168C2×#389C2214yes—
169C2×#385C2214yes—
170C2×#385C2214yes—
171#2285C2211yescharacteristic
172C2×#384C2212yes—
173C2×#384C2211yescharacteristic
174C2×#384C2211yescharacteristic
175#2283C2212yes—
176C2×#382C2212yes—
177#2280C2211yescharacteristic
178#2280C2214yes—
179#2280C2211yescharacteristic
180#2274C2211yescharacteristic
181#2274C2211yescharacteristic
182#2274C2211yescharacteristic
183C4×#117C2211yescharacteristic
184C4×#117C2212yes—
185C4×#117C2211yescharacteristic
186C2×C4×C22⋊C4C2211yescharacteristic
187C23×Q8C2311yescharacteristic
188C24×C4C2311yescharacteristic
189C24×C4C2312yes—
190#533—28no—
191C2×C4⋊Q8C2312yes—
192C2×#125C2312yes—
193C2×#125C2318yes—
194C2×#125C2318yes—
195C2×#125C2318yes—
196C2×C22⋊Q8—28no—
197C2×C22⋊Q8C2312yes—
198C2×C22⋊Q8C2312yes—
199C2×C22⋊Q8C2314yes—
200C2×C22⋊Q8C2314yes—
201C2×C22⋊Q8C2312yes—
202C2×C22⋊Q8C2312yes—
203#519—28no—
204C2×C4×Q8C2314yes—
205C2×C4×Q8C2314yes—
206C2×C4×Q8C2314yes—
207C2×C4×Q8C2318yes—
208C2×#117—28no—
209C2×#117—28no—
210C2×#117C2311yescharacteristic
211C2×#117C2311yescharacteristic
212C2×#117C2311yescharacteristic
213C2×#117C2311yescharacteristic
214C2×#117C2311yescharacteristic
215C2×#117C2311yescharacteristic
216C2×#117C2311yescharacteristic
217C2×#117C2312yes—
218C2×#117C2312yes—
219C2×#117C2312yes—
220C2×#117C2311yescharacteristic
221C2×#117C2311yescharacteristic
222C2×#117C2312yes—
223C2×#117C2312yes—
224C2×#117C2314yes—
225C2×#117C2314yes—
226C2×#117C2318yes—
227C2×#117C2311yescharacteristic
228C22×C4⋊C4—28no—
229C22×C4⋊C4C2312yes—
230C22×C4⋊C4C2311yescharacteristic
231C22×C4⋊C4C2311yescharacteristic
232C22×C4⋊C4C2312yes—
233C22×C4⋊C4C2312yes—
234C22×C4⋊C4C2311yescharacteristic
235C22×C4⋊C4C2312yes—
236C22×C4⋊C4C2311yescharacteristic
237C22×C4⋊C4C2312yes—
238C22×C4⋊C4C2312yes—
239C22×C4⋊C4C2311yescharacteristic
240C22×C4⋊C4C2312yes—
241C22×C4⋊C4C2314yes—
242C22×C4⋊C4C2318yes—
243C22×C4⋊C4C2314yes—
244C22×C22⋊C4C2312yes—
245C22×C22⋊C4C2312yes—
246C22×C22⋊C4C2312yes—
247C22×C22⋊C4C2312yes—
248C22×C42C2312yes—
249C22×C42C2312yes—
250C22×C42C2311yescharacteristic
251C22×C42C2311yescharacteristic
252#401C2318yes—
253#401C2318yes—
254#400C2318yes—
255#400C2318yes—
256#400C2318yes—
257#400C2318yes—
258#400C2318yes—
259#400C2318yes—
260#400C2318yes—
261#400C2318yes—
262#400C2318yes—
263#400C2318yes—
264#400C2318yes—
265#400C2314yes—
266#400C2318yes—
267#399C2314yes—
268#398C2318yes—
269#398C2318yes—
270#398C2318yes—
271#398C2318yes—
272#398C2318yes—
273#398C2318yes—
274#398C2318yes—
275#398C2318yes—
276#398C2314yes—
277#398C2318yes—
278#398C2318yes—
279#398C2318yes—
280#398C2318yes—
281#398C2318yes—
282#398C2314yes—
283#398C2318yes—
284#398C2318yes—
285#397C2318yes—
286#397C2318yes—
287#396C2314yes—
288#396C2314yes—
289#395C2318yes—
290#395C2314yes—
291#393C2314yes—
292#391C2318yes—
293#391C2314yes—
294#391C2318yes—
295#391C2314yes—
296#391C2314yes—
297#391C2312yes—
298#391C2312yes—
299#391C2314yes—
300#391C2314yes—
301#391C2312yes—
302#391C2312yes—
303#391C2312yes—
304#391C2314yes—
305#391C2312yes—
306#391C2314yes—
307#391C2312yes—
308#391C2312yes—
309#389C2314yes—
310#389C2314yes—
311#389C2318yes—
312#389C2312yes—
313#389C2312yes—
314#389C2314yes—
315#389C2314yes—
316#389C2314yes—
317#389C2318yes—
318#389C2314yes—
319#389C2314yes—
320#389C2314yes—
321#389C2318yes—
322#389C2314yes—
323#389C2318yes—
324#389C2314yes—
325#389C2314yes—
326#389C2314yes—
327#389C2312yes—
328#389C2318yes—
329#389C2312yes—
330#389C2318yes—
331#389C2318yes—
332#389C2318yes—
333#389C2318yes—
334#389C2312yes—
335#389C2318yes—
336#389C2312yes—
337#389C2318yes—
338#389C2312yes—
339#389C2314yes—
340#389C2312yes—
341#388C2318yes—
342#388C2318yes—
343#388C2314yes—
344#388C2314yes—
345#388C2314yes—
346#388C2314yes—
347#387C2314yes—
348#387C2318yes—
349#387C2318yes—
350#387C2318yes—
351#387C2318yes—
352#387C2318yes—
353#387C2318yes—
354#387C2318yes—
355#387C2318yes—
356#387C2318yes—
357#387C2318yes—
358#387C2318yes—
359#387C2318yes—
360#387C2318yes—
361#387C2318yes—
362#387C2318yes—
363#387C2318yes—
364#387C2318yes—
365#387C2318yes—
366#387C2314yes—
367#387C2314yes—
368#387C2314yes—
369#387C2318yes—
370#387C2318yes—
371#387C2318yes—
372#387C2318yes—
373#387C2318yes—
374#387C2318yes—
375#387C2318yes—
376#387C2318yes—
377#387C2314yes—
378#387C2314yes—
379#385C2314yes—
380#385C2318yes—
381#385C2318yes—
382#385C2314yes—
383#385C2314yes—
384#385C2314yes—
385#385C2314yes—
386#385C2314yes—
387#385C2314yes—
388#385C2314yes—
389#385C2318yes—
390#385C2314yes—
391#385C2314yes—
392#385C2318yes—
393#385C2318yes—
394#385C2318yes—
395#385C2318yes—
396#385C2314yes—
397#385C2314yes—
398#385C2318yes—
399#384C2312yes—
400#384C2318yes—
401#384C2314yes—
402#384C2314yes—
403#384C2312yes—
404#384C2312yes—
405#384C2312yes—
406#384C2312yes—
407#384C2312yes—
408#384C2312yes—
409#384C2312yes—
410#384C2312yes—
411#384C2312yes—
412#384C2312yes—
413#383C2318yes—
414#383C2314yes—
415#383C2318yes—
416#383C2318yes—
417#382C2318yes—
418#382C2312yes—
419#382C2312yes—
420#382C2312yes—
421#382C2312yes—
422#382C2312yes—
423#382C2318yes—
424#382C2312yes—
425#382C2318yes—
426#382C2314yes—
427#382C2312yes—
428#381C2314yes—
429#381C2314yes—
430#381C2314yes—
431#381C2312yes—
432#381C2312yes—
433#381C2314yes—
434#381C2318yes—
435#381C2318yes—
436#380C2314yes—
437#380C2314yes—
438#380C2314yes—
439#380C2312yes—
440#380C2314yes—
441#380C2312yes—
442#380C2312yes—
443#380C2312yes—
444#380C2318yes—
445#380C2314yes—
446#380C2314yes—
447#379C2312yes—
448#379C2312yes—
449C4×C4⋊C4C2314yes—
450C4×C4⋊C4C2314yes—
451C4×C4⋊C4C2318yes—
452C4×C4⋊C4C2318yes—
453C4×C4⋊C4C2314yes—
454C4×C4⋊C4C2314yes—
455C4×C4⋊C4C2314yes—
456C4×C4⋊C4C2314yes—
457C4×C4⋊C4C2312yes—
458C4×C4⋊C4C2314yes—
459C4×C4⋊C4C2314yes—
460C4×C4⋊C4C2314yes—
461C4×C4⋊C4C2318yes—
462C4×C4⋊C4C2314yes—
463C4×C4⋊C4C2312yes—
464C4×C4⋊C4C2312yes—
465C4×C4⋊C4C2312yes—
466C4×C4⋊C4C2312yes—
467C4×C4⋊C4C2312yes—
468C4×C4⋊C4C2312yes—
469C4×C4⋊C4C2312yes—
470C4×C22⋊C4C2314yes—
471C4×C22⋊C4C2314yes—
472C4×C22⋊C4C2314yes—
473C4×C22⋊C4C2318yes—
474C4×C22⋊C4C2314yes—
475C4×C22⋊C4C2314yes—
476C4×C22⋊C4C2314yes—
477C4×C22⋊C4C2318yes—
478C4×C22⋊C4C2312yes—
479C4×C22⋊C4C2312yes—
480C4×C22⋊C4C2312yes—
481C4×C22⋊C4C2312yes—
482C4×C22⋊C4C2312yes—
483C4×C22⋊C4C2312yes—
484C4×C22⋊C4C2311yescharacteristic
485C4×C22⋊C4C2311yescharacteristic
486C4×C22⋊C4C2311yescharacteristic
487C4×C22⋊C4C2311yescharacteristic
488#376C2312yes—
489#376C2312yes—
490#376C2318yes—
491#376C2314yes—
492C2×#95C2312yes—
493C2×#95C2314yes—
494C2×#95C2318yes—
495C2×#95C2314yes—
496C43C2312yes—
497C43C2312yes—
498C25C2411yescharacteristic
499C22×Q8—24no—
500C22×Q8—24no—
501C22×Q8—24no—
502C22×Q8C2412yes—
503C22×Q8C2412yes—
504C22×Q8C2414yes—
505C23×C4—24no—
506C23×C4—24no—
507C23×C4—28no—
508C23×C4—84no—
509C23×C4#4118yes—
510C23×C4C2412yes—
511C23×C4C2412yes—
512C23×C4C2414yes—
513C23×C4C2412yes—
514C23×C4C2412yes—
515C23×C4C2411yescharacteristic
516C23×C4C2411yescharacteristic
517C23×C4C2411yescharacteristic
518C23×C4C2411yescharacteristic
519C23×C4C2411yescharacteristic
520C23×C4C2412yes—
521C23×C4C2412yes—
522C23×C4C2412yes—
523C23×C4C2414yes—
524C23×C4C2412yes—
525C23×C4C2414yes—
526C23×C4C2411yescharacteristic
527C4⋊Q8—28no—
528#125—28no—
529#125—88no—
530#125—88no—
531#125—88no—
532C22⋊Q8—28no—
533C22⋊Q8—28no—
534C22⋊Q8—28no—
535C22⋊Q8—28no—
536C22⋊Q8—216no—
537C22⋊Q8—216no—
538C4×Q8—216no—
539C4×Q8—216no—
540C4×Q8—216no—
541C4×Q8—88no—
542#117—28no—
543#117—24no—
544#117—24no—
545#117—28no—
546#117—24no—
547#117—24no—
548#117—24no—
549#117—24no—
550#117—24no—
551#117—24no—
552#117—24no—
553#117—28no—
554#117—28no—
555#117—216no—
556#117—216no—
557#117—28no—
558#117—88no—
559#117#4118yes—
560C2×C4⋊C4—28no—
561C2×C4⋊C4—28no—
562C2×C4⋊C4—28no—
563C2×C4⋊C4—28no—
564C2×C4⋊C4—28no—
565C2×C4⋊C4—24no—
566C2×C4⋊C4—24no—
567C2×C4⋊C4—24no—
568C2×C4⋊C4—24no—
569C2×C4⋊C4—28no—
570C2×C4⋊C4—24no—
571C2×C4⋊C4—28no—
572C2×C4⋊C4—84no—
573C2×C4⋊C4—88no—
574C2×C4⋊C4—84no—
575C2×C4⋊C4C2412yes—
576C2×C4⋊C4C2412yes—
577C2×C4⋊C4C2412yes—
578C2×C4⋊C4C2414yes—
579C2×C4⋊C4C2412yes—
580C2×C4⋊C4C2414yes—
581C2×C4⋊C4C2411yescharacteristic
582C2×C4⋊C4C2411yescharacteristic
583C2×C4⋊C4C2411yescharacteristic
584C2×C4⋊C4C2412yes—
585C2×C4⋊C4C2412yes—
586C2×C4⋊C4C2411yescharacteristic
587C2×C4⋊C4C2412yes—
588C2×C4⋊C4C2414yes—
589C2×C4⋊C4C2412yes—
590C2×C4⋊C4C2412yes—
591C2×C4⋊C4C2414yes—
592C2×C4⋊C4C2414yes—
593C2×C4⋊C4C2412yes—
594C2×C4⋊C4C2418yes—
595C2×C4⋊C4C2412yes—
596C2×C4⋊C4C2412yes—
597C2×C4⋊C4C2412yes—
598C2×C4⋊C4C2414yes—
599C2×C4⋊C4C2414yes—
600C2×C4⋊C4C2414yes—
601C2×C4⋊C4C2414yes—
602C2×C4⋊C4C2414yes—
603C2×C4⋊C4C2414yes—
604C2×C4⋊C4C2414yes—
605C2×C4⋊C4C2414yes—
606C2×C4⋊C4C2418yes—
607C2×C4⋊C4C2418yes—
608C2×C4⋊C4C2418yes—
609C2×C4⋊C4C2418yes—
610C2×C4⋊C4C2418yes—
611C2×C4⋊C4C2418yes—
612C2×C4⋊C4C2418yes—
613C2×C4⋊C4C2418yes—
614C2×C4⋊C4C2418yes—
615C2×C4⋊C4C2418yes—
616C2×C4⋊C4C2418yes—
617C2×C4⋊C4C2414yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2414yes—
620C2×C4⋊C4C2414yes—
621C2×C4⋊C4C2418yes—
622C2×C4⋊C4C2414yes—
623C2×C4⋊C4C2418yes—
624C2×C4⋊C4C2412yes—
625C2×C22⋊C4—28no—
626C2×C22⋊C4—28no—
627C2×C22⋊C4—28no—
628C2×C22⋊C4—28no—
629C2×C22⋊C4C2412yes—
630C2×C22⋊C4C2412yes—
631C2×C22⋊C4C2412yes—
632C2×C22⋊C4C2414yes—
633C2×C22⋊C4C2412yes—
634C2×C22⋊C4C2412yes—
635C2×C22⋊C4C2414yes—
636C2×C22⋊C4C2414yes—
637C2×C22⋊C4C2412yes—
638C2×C22⋊C4C2412yes—
639C2×C22⋊C4C2412yes—
640C2×C22⋊C4C2412yes—
641C2×C22⋊C4C2412yes—
642C2×C22⋊C4C2414yes—
643C2×C22⋊C4C2412yes—
644C2×C22⋊C4C2412yes—
645C2×C22⋊C4C2414yes—
646C2×C22⋊C4C2414yes—
647C2×C22⋊C4C2414yes—
648C2×C22⋊C4C2412yes—
649C2×C22⋊C4C2412yes—
650C2×C42—28no—
651C2×C42—24no—
652C2×C42—24no—
653C2×C42—28no—
654C2×C42C2412yes—
655C2×C42C2412yes—
656C2×C42C2412yes—
657C2×C42C2412yes—
658C2×C42C2414yes—
659C2×C42C2412yes—
660C2×C42C2412yes—
661C2×C42C2418yes—
662C2×C42C2412yes—
663C2×C42C2414yes—
664C2×C42C2412yes—
665C2×C42C2414yes—
666C2×C42C2412yes—
667C2×C42C2412yes—
668C2×C42C2411yescharacteristic
669C2×C42C2411yescharacteristic
670C2×C42C2411yescharacteristic
671C2×C42C2411yescharacteristic
672C2×C42C2412yes—
673C2×C42C2418yes—
674C2×C42C2418yes—
675C2×C42C2414yes—
676C2×C42C2418yes—
677C2×C42C2414yes—
678C2×C42C2412yes—
679#95C2412yes—
680#95C2418yes—
681#95C2418yes—
682#95C2412yes—
683#95C2412yes—
684#95C2412yes—
685#95C2418yes—
686#95C2418yes—
687#95C2418yes—
688#95C2418yes—
689#95C2418yes—
690#95C2418yes—
691#95C2414yes—
692#95C2414yes—
693#95C2414yes—
694#95C2414yes—
695#95C2414yes—
696#95C2414yes—
697#95C2414yes—
698#95C2414yes—
699#95C2418yes—
700#95C2418yes—
701#95C2414yes—
702#95C2418yes—
703#95C2418yes—
704#95C2418yes—
705#95C2418yes—
706#95C2414yes—
707#95C2414yes—
708#95C2418yes—
709#95C2418yes—
710#95C2414yes—
711#95C2414yes—
712#95C2414yes—
713#95C2418yes—
714#95C2418yes—
715#95C2414yes—
716#95C2414yes—
717#95C2418yes—
718#95C2414yes—
719#95C2414yes—
720#95C2418yes—
721#95C2418yes—
722#95C2418yes—
723C24—22no—
724C24—24no—
725C24—22no—
726C24—42no—
727C24C2×#4114yes—
728C24C2511yescharacteristic
729C24C2511yescharacteristic
730C24C2511yescharacteristic
731C2×Q8—24no—
732C2×Q8—24no—
733C2×Q8—28no—
734C2×Q8—24no—
735C2×Q8—24no—
736C2×Q8—28no—
737C2×Q8—24no—
738C2×Q8—24no—
739C2×Q8—44no—
740C2×Q8—416no—
741C22×C4—22no—
742C22×C4—22no—
743C22×C4—232no—
744C22×C4—22no—
745C22×C4—22no—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—22no—
750C22×C4—22no—
751C22×C4—22no—
752C22×C4—24no—
753C22×C4—24no—
754C22×C4—24no—
755C22×C4—28no—
756C22×C4—24no—
757C22×C4—24no—
758C22×C4—28no—
759C22×C4—28no—
760C22×C4—24no—
761C22×C4—24no—
762C22×C4—24no—
763C22×C4—24no—
764C22×C4—24no—
765C22×C4—28no—
766C22×C4—28no—
767C22×C4—24no—
768C22×C4—24no—
769C22×C4—42no—
770C22×C4—44no—
771C22×C4—42no—
772C22×C4—48no—
773C22×C4—44no—
774C22×C4—44no—
775C22×C4—44no—
776C22×C4—48no—
777C22×C4—44no—
778C22×C4—816no—
779C22×C4C2×#4114yes—
780C22×C4C2×#4114yes—
781C22×C4C2×#4114yes—
782C22×C4C2×#4114yes—
783C22×C4C2×#4114yes—
784C22×C4C2×#4114yes—
785C22×C4C2×#4114yes—
786C22×C42−1+414yes—
787C22×C4C2512yes—
788C22×C4C2512yes—
789C22×C4C2514yes—
790C22×C4C2512yes—
791C22×C4C2514yes—
792C22×C4C2514yes—
793C22×C4C2514yes—
794C22×C4C2514yes—
795C22×C4C2512yes—
796C22×C4C2514yes—
797C22×C4C2514yes—
798C22×C4C2514yes—
799C22×C4C2512yes—
800C22×C4C2512yes—
801C22×C4C2514yes—
802C22×C4C2511yescharacteristic
803C22×C4C2511yescharacteristic
804C22×C4C2514yes—
805C22×C4C2512yes—
806C22×C4C2512yes—
807C22×C4C2511yescharacteristic
808C22×C4C2511yescharacteristic
809C4⋊C4—28no—
810C4⋊C4—28no—
811C4⋊C4—24no—
812C4⋊C4—24no—
813C4⋊C4—24no—
814C4⋊C4—24no—
815C4⋊C4—28no—
816C4⋊C4—24no—
817C4⋊C4—24no—
818C4⋊C4—24no—
819C4⋊C4—22no—
820C4⋊C4—22no—
821C4⋊C4—22no—
822C4⋊C4—22no—
823C4⋊C4—24no—
824C4⋊C4—24no—
825C4⋊C4—28no—
826C4⋊C4—28no—
827C4⋊C4—24no—
828C4⋊C4—216no—
829C4⋊C4—24no—
830C4⋊C4—28no—
831C4⋊C4—28no—
832C4⋊C4—28no—
833C4⋊C4—24no—
834C4⋊C4—24no—
835C4⋊C4—28no—
836C4⋊C4—28no—
837C4⋊C4—28no—
838C4⋊C4—28no—
839C4⋊C4—28no—
840C4⋊C4—48no—
841C4⋊C4—48no—
842C4⋊C4—48no—
843C4⋊C4—48no—
844C4⋊C4—48no—
845C4⋊C4—48no—
846C4⋊C4—48no—
847C4⋊C4—48no—
848C4⋊C4—48no—
849C4⋊C4—48no—
850C4⋊C4—48no—
851C4⋊C4—44no—
852C4⋊C4—44no—
853C4⋊C4—44no—
854C4⋊C4—48no—
855C4⋊C4—44no—
856C4⋊C4—48no—
857C4⋊C4—44no—
858C4⋊C4C2×#4118yes—
859C22⋊C4—24no—
860C22⋊C4—24no—
861C22⋊C4—24no—
862C22⋊C4—24no—
863C22⋊C4—24no—
864C22⋊C4—28no—
865C22⋊C4—28no—
866C22⋊C4—24no—
867C22⋊C4—24no—
868C22⋊C4—24no—
869C22⋊C4—24no—
870C22⋊C4—24no—
871C22⋊C4—28no—
872C22⋊C4—28no—
873C22⋊C4—28no—
874C22⋊C4—24no—
875C22⋊C4—24no—
876C22⋊C4—44no—
877C22⋊C4—44no—
878C22⋊C4C2×#4118yes—
879C22⋊C42−1+418yes—
880C42—28no—
881C42—24no—
882C42—24no—
883C42—24no—
884C42—24no—
885C42—24no—
886C42—24no—
887C42—22no—
888C42—22no—
889C42—24no—
890C42—216no—
891C42—24no—
892C42—22no—
893C42—24no—
894C42—22no—
895C42—28no—
896C42—28no—
897C42—24no—
898C42—24no—
899C42—48no—
900C42—48no—
901C42—44no—
902C42—48no—
903C42—44no—
904C42C2×#4118yes—
905C23—21no—
906C23—22no—
907C23—21no—
908C23—22no—
909C23—22no—
910C23—21no—
911C23—22no—
912C23—21no—
913C23—22no—
914C23—28no—
915C23—28no—
916C23—44no—
917C23—48no—
918C23—48no—
919C23C22×#4112yes—
920C23C22×#4112yes—
921C23C22×#4112yes—
922C23C22×#4112yes—
923C23C2×2−1+412yes—
924C23C2×2−1+414yes—
925C23C2611yescharacteristic
926Q8—416no—
927Q8—48no—
928Q8—48no—
929C2×C4—21no—
930C2×C4—22no—
931C2×C4—21no—
932C2×C4—22no—
933C2×C4—24no—
934C2×C4—21no—
935C2×C4—21no—
936C2×C4—22no—
937C2×C4—24no—
938C2×C4—22no—
939C2×C4—28no—
940C2×C4—28no—
941C2×C4—28no—
942C2×C4—28no—
943C2×C4—28no—
944C2×C4—24no—
945C2×C4—24no—
946C2×C4—22no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—24no—
952C2×C4—24no—
953C2×C4—24no—
954C2×C4—24no—
955C2×C4—24no—
956C2×C4—24no—
957C2×C4—24no—
958C2×C4—22no—
959C2×C4—24no—
960C2×C4—24no—
961C2×C4—24no—
962C2×C4—24no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—24no—
966C2×C4—24no—
967C2×C4—24no—
968C2×C4—24no—
969C2×C4—24no—
970C2×C4—24no—
971C2×C4—24no—
972C2×C4—24no—
973C2×C4—24no—
974C2×C4—24no—
975C2×C4—28no—
976C2×C4—28no—
977C2×C4—24no—
978C2×C4—22no—
979C2×C4—24no—
980C2×C4—22no—
981C2×C4—28no—
982C2×C4—416no—
983C2×C4—48no—
984C2×C4—48no—
985C2×C4—416no—
986C2×C4—48no—
987C2×C4—48no—
988C2×C4—84no—
989C2×C4—84no—
990C2×C4—84no—
991C2×C4—88no—
992C2×C4—84no—
993C2×C4#552116yes—
994C2×C4C22×#4112yes—
995C2×C4C22×#4118yes—
996C2×C4C22×#4112yes—
997C2×C4C22×#4112yes—
998C2×C4C22×#4112yes—
999C2×C4C22×#4112yes—
1000C2×C4C22×#4112yes—
1001C2×C4C2×2−1+414yes—
1002C2×C4C2×2−1+414yes—
1003C2×C4C2×2−1+412yes—
1004C2×C4C2×2−1+412yes—
1005C22—24no—
1006C22—24no—
1007C22—22no—
1008C22—22no—
1009C22—22no—
1010C22—24no—
1011C22—24no—
1012C22—22no—
1013C22—22no—
1014C22—22no—
1015C22—22no—
1016C22—416no—
1017C22—42no—
1018C22—42no—
1019C22C2×#55214yes—
1020C22#350914yes—
1021C22C23×#4111yescharacteristic
1022C22C23×#4111yescharacteristic
1023C22C22×2−1+412yes—
1024C22C22×2−1+411yescharacteristic
1025C22H(7,𝔽2)12yes—
1026C4—28no—
1027C4—24no—
1028C4—24no—
1029C4—22no—
1030C4—22no—
1031C4—44no—
1032C4—44no—
1033C4—42no—
1034C4—44no—
1035C4—42no—
1036C4—42no—
1037C4—44no—
1038C4—44no—
1039C4—42no—
1040C4—42no—
1041C4—44no—
1042C4—44no—
1043C4—44no—
1044C4—42no—
1045C4—44no—
1046C4C2×#55214yes—
1047C4C2×#55214yes—
1048C2—24no—
1049C2—24no—
1050C2—42no—
1051C2C22×#55211yescharacteristic
1052C2C2×#350911yescharacteristic
1053C2#6285511yescharacteristic
1054C2#6294512yes—
1055C2#6300012yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC25C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59333C2semidirect
2. #59321C2semidirect
4. #45328C2semidirect
5. #44956C2semidirect
6. #43977C2semidirect
7. #39077C2semidirect
8. #38261C2semidirect
9. #38066C2semidirect
10. #36280C2semidirect
11. #35662C2semidirect
12. #35630C2semidirect
13. #35555C2semidirect
14. #35555C2semidirect
15. #35313C2semidirect
17. #35286C2semidirect
20. #34254C2semidirect
21. #34214C2semidirect
32. #2863C22semidirect
33. #2859C22semidirect
35. #2791C22semidirect
36. #2791C22semidirect
37. #2776C22semidirect
39. #2769C22semidirect
40. #2767C22semidirect
41. #2766C22semidirect
45. #2762C22semidirect
46. #2719C22semidirect
47. #2647C22semidirect
48. #2645C22semidirect
50. #2612C22semidirect
52. #2606C22semidirect
54. #2585C22semidirect
55. #2582C22semidirect
56. #2581C22semidirect
57. #2571C22semidirect
58. #2570C22semidirect
59. #2570C22semidirect
60. #2565C22semidirect
61. #2552C22semidirect
62. #2552C22semidirect
63. #2552C22semidirect
64. #2528C22semidirect
65. #2524C22semidirect
66. #2514C22semidirect
67. #2514C22semidirect
68. #2514C22semidirect
69. #2511C22semidirect
70. #2511C22semidirect
71. #2511C22semidirect
72. #2507C22semidirect
73. #2507C22semidirect
74. #2506C22semidirect
75. #2506C22semidirect
76. #2506C22semidirect
99. #2462C22semidirect
100. #2453C22semidirect
101. #2451C22semidirect
118. #2356C22semidirect
119. #2355C22semidirect
120. #2355C22semidirect
121. Q8×C4⋊C4C22semidirect
136. #2330C22semidirect
138. #2320C22semidirect
156. C4×C4⋊Q8C22semidirect
165. #2295C22semidirect

Maximal subgroups

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

subgroupindex
#593332
#593212
#592852
#453282
#449562
#439772
#390772
#382612
#380662
#362802
#356622
#356302
#355552
#353132
#353112
#352862
C2×#25022
#347392
#342542
#342142
#342032
#341782
#341092
C2×#23172