Finite Group Databasebeta

← #7644135

Subgroups — #7644135

Order 512.

4220 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42670C214yesmaximal, complemented
2#42667C214yesmaximal, complemented
3#42663C214yesmaximal, complemented
4#42657C214yesmaximal, complemented
5#42470C214yesmaximal, complemented
6#42469C214yesmaximal, complemented
7#42461C214yesmaximal, complemented
8#42455C214yesmaximal, complemented
9#37466C214yesmaximal, complemented
10#37460C214yesmaximal
11#36762C214yesmaximal, complemented
12#36760C214yesmaximal
13#35627C212yesmaximal, complemented
14#35555C212yesmaximal, complemented
15#35544C212yesmaximal
16#35544C212yesmaximal
17#35181C211yesmaximal, characteristic, complemented
18#35173C211yesmaximal, characteristic, complemented
19#34634C211yesmaximal, characteristic
20#34634C211yesmaximal, characteristic
21#34213C211yesmaximal, characteristic, complemented
22#34213C211yesmaximal, characteristic, complemented
23C2×#2314C211yesmaximal, characteristic
24C2×#533C2211yescharacteristic
25C2×#533C2211yescharacteristic
26C22×#117C2211yescharacteristic
27#2857C2214yes—
28#2851C2214yes—
29#2839C2218yescomplemented
30#2836C2218yes—
31#2833C2218yescomplemented
32#2831C2218yes—
33#2802C2218yescomplemented
34#2798C2218yes—
35#2794C2218yescomplemented
36#2789C2218yescomplemented
37#2783C2218yes—
38#2776C2218yescomplemented
39#2772C2218yes—
40#2766C2218yescomplemented
41#2758C2218yescomplemented
42#2754C2218yes—
43#2725C2218yes—
44#2725C2218yes—
45#2721C2218yes—
46#2719C2218yescomplemented
47#2716C2218yes—
48#2713C2218yescomplemented
49#2666C2218yescomplemented
50#2664C2218yes—
51#2659C2214yes—
52#2655C2218yescomplemented
53#2655C2218yescomplemented
54#2654C2218yes—
55#2650C2218yes—
56#2646C2214yes—
57#2637C2218yes—
58#2634C2218yescomplemented
59#2629C2212yes—
60#2629C2212yes—
61#2629C2212yes—
62#2629C2212yes—
63#2628C2212yes—
64#2628C2212yes—
65#2628C2212yes—
66#2628C2212yes—
67#2627C2212yes—
68#2627C2212yes—
69#2627C2212yes—
70#2627C2212yes—
71#2626C2212yes—
72#2626C2212yes—
73#2626C2212yes—
74#2626C2212yes—
75#2584C2214yescomplemented
76#2584C2214yescomplemented
77#2571C2214yescomplemented
78#2571C2214yescomplemented
79#2571C2212yescomplemented
80#2571C2212yescomplemented
81#2570C2214yescomplemented
82#2570C2214yescomplemented
83#2570C2214yescomplemented
84#2570C2214yescomplemented
85#2570C2214yescomplemented
86#2570C2214yescomplemented
87#2567C2212yescomplemented
88#2567C2212yescomplemented
89#2552C2212yescomplemented
90#2552C2212yescomplemented
91#2552C2214yescomplemented
92#2552C2214yescomplemented
93#2546C2212yescomplemented
94#2546C2212yescomplemented
95#2524C2218yescomplemented
96#2519C2218yes—
97#2509C2214yescomplemented
98#2509C2214yescomplemented
99#2508C2214yescomplemented
100#2508C2214yescomplemented
101#2507C2214yescomplemented
102#2507C2214yescomplemented
103#2506C2214yescomplemented
104#2506C2214yescomplemented
105#2505C2218yes—
106#2505C2218yes—
107#2497C2214yes—
108#2497C2214yes—
109#2497C2214yes—
110#2497C2214yes—
111#2496C2214yes—
112#2496C2214yes—
113#2496C2214yes—
114#2496C2214yes—
115#2495C2214yes—
116#2495C2214yes—
117#2495C2214yes—
118#2495C2214yes—
119#2494C2214yes—
120#2494C2214yes—
121#2494C2214yes—
122#2494C2214yes—
123#2493C2218yes—
124#2493C2218yes—
125#2480C2218yes—
126#2480C2218yes—
127#2473C2218yes—
128#2473C2218yes—
129#2469C2218yes—
130#2462C2218yescomplemented
131#2396C2214yes—
132#2396C2214yes—
133#2396C2214yes—
134#2396C2214yes—
135#2370C2214yescomplemented
136#2370C2214yescomplemented
137#2369C2212yescomplemented
138#2369C2212yescomplemented
139#2365C2212yescomplemented
140#2365C2212yescomplemented
141#2355C2212yescomplemented
142#2355C2212yescomplemented
143#2355C2214yescomplemented
144#2355C2214yescomplemented
145Q8×C4⋊C4C2212yescomplemented
146Q8×C4⋊C4C2212yescomplemented
147#2329C2214yes—
148#2329C2214yes—
149#2317C2212yes—
150#2317C2212yes—
151#2317C2212yes—
152#2317C2212yes—
153#2316C2212yes—
154#2316C2212yes—
155#2314C2214yes—
156#2314C2214yes—
157#2314C2214yes—
158#2314C2214yes—
159C4×C22⋊Q8C2214yes—
160C4×C22⋊Q8C2214yes—
161#2296C2212yes—
162#2296C2212yes—
163C2×#388C2212yes—
164C2×#388C2212yes—
165C2×#387C2212yes—
166C2×#387C2212yes—
167#2285C2211yescharacteristic
168#2285C2211yescharacteristic
169C2×#384C2211yescharacteristic
170C2×#382C2211yescharacteristic
171#2280C2212yes—
172#2280C2212yes—
173C2×#380C2211yescharacteristic
174C2×#380C2211yescharacteristic
175#2274C2212yes—
176#2274C2212yes—
177C2×C4×C4⋊C4C2211yescharacteristic
178C2×C4×C4⋊C4C2211yescharacteristic
179C24×C4C2311yescharacteristic
180#533—28no—
181#533—28no—
182C2×C4⋊Q8C2311yescharacteristic
183C2×C4⋊Q8C2311yescharacteristic
184C2×C4⋊Q8C2311yescharacteristic
185C2×C4⋊Q8C2311yescharacteristic
186C2×C4⋊Q8C2314yes—
187C2×#126C2318yes—
188C2×#126C2318yes—
189C2×#125C2312yes—
190C2×#125C2312yes—
191C2×#125C2314yes—
192C2×#125C2318yes—
193C2×#125C2318yes—
194C2×C22⋊Q8C2312yes—
195C2×C22⋊Q8C2312yes—
196C2×C22⋊Q8C2312yes—
197C2×C22⋊Q8C2312yes—
198C2×C4×Q8C2312yes—
199C2×C4×Q8C2312yes—
200C2×C4×Q8C2312yes—
201C2×C4×Q8C2312yes—
202C2×C4×Q8C2314yes—
203C2×C4×Q8C2314yes—
204C2×#117—28no—
205C2×#117C2312yes—
206C2×#117C2312yes—
207C2×#117C2312yes—
208C2×#117C2312yes—
209C2×#117C2312yes—
210C2×#117C2312yes—
211C2×#117C2312yes—
212C2×#117C2312yes—
213C22×C4⋊C4C2311yescharacteristic
214C22×C4⋊C4C2311yescharacteristic
215C22×C4⋊C4C2311yescharacteristic
216C22×C4⋊C4C2311yescharacteristic
217C22×C4⋊C4C2311yescharacteristic
218C22×C4⋊C4C2311yescharacteristic
219C22×C4⋊C4C2312yes—
220C22×C4⋊C4C2312yes—
221C22×C22⋊C4C2311yescharacteristic
222C22×C22⋊C4C2311yescharacteristic
223C22×C22⋊C4C2312yes—
224C22×C22⋊C4C2312yes—
225C22×C42C2311yescharacteristic
226C22×C42C2312yes—
227C22×C42C2312yes—
228C22×C42C2311yescharacteristic
229#401C2318yes—
230#401C2318yes—
231#400C2318yes—
232#400C2318yes—
233#400C2318yes—
234#400C2318yes—
235#400C2318yes—
236#400C2318yes—
237#400C2318yes—
238#400C2318yes—
239#400C2318yes—
240#400C2318yes—
241#400C2318yes—
242#400C2318yes—
243#400C2314yes—
244#400C2318yes—
245#400C2318yes—
246#400C2318yes—
247#400C2318yes—
248#400C2314yes—
249#400C2314yes—
250#400C2314yes—
251#399C2314yes—
252#399C2314yes—
253#399C2314yes—
254#399C2314yes—
255#398C2318yes—
256#398C2318yes—
257#398C2318yes—
258#398C2318yes—
259#398C2318yes—
260#398C2318yes—
261#398C2318yes—
262#398C2314yes—
263#398C2318yes—
264#398C2318yes—
265#398C2314yes—
266#398C2318yes—
267#398C2318yes—
268#398C2318yes—
269#398C2314yes—
270#398C2314yes—
271#398C2314yes—
272#398C2314yes—
273#398C2314yes—
274#398C2314yes—
275#397C2318yes—
276#397C2318yes—
277#397C2318yes—
278#397C2318yes—
279#397C2318yes—
280#397C2318yes—
281#396C2314yes—
282#396C2318yes—
283#396C2314yes—
284#396C2318yes—
285#396C2314yes—
286#396C2314yes—
287#396C2314yes—
288#396C2314yes—
289#396C2314yes—
290#396C2314yes—
291#395C2318yes—
292#395C2318yes—
293#395C2314yes—
294#395C2314yes—
295#395C2314yes—
296#395C2314yes—
297#393C2314yes—
298#393C2314yes—
299#393C2314yes—
300#393C2314yes—
301#391C2314yes—
302#391C2314yes—
303#391C2314yes—
304#391C2314yes—
305#391C2318yes—
306#391C2318yes—
307#389C2314yes—
308#389C2314yes—
309#389C2314yes—
310#389C2314yes—
311#389C2312yes—
312#389C2312yes—
313#389C2312yes—
314#389C2312yes—
315#389C2314yes—
316#389C2314yes—
317#389C2314yes—
318#389C2314yes—
319#389C2314yes—
320#389C2314yes—
321#389C2312yes—
322#389C2312yes—
323#389C2314yes—
324#389C2314yes—
325#389C2318yes—
326#389C2318yes—
327#389C2314yes—
328#389C2314yes—
329#389C2314yes—
330#389C2314yes—
331#389C2314yes—
332#389C2314yes—
333#389C2314yes—
334#389C2314yes—
335#389C2318yes—
336#389C2318yes—
337#389C2318yes—
338#389C2318yes—
339#389C2312yes—
340#389C2312yes—
341#389C2318yes—
342#389C2318yes—
343#388C2318yes—
344#388C2318yes—
345#388C2318yes—
346#388C2318yes—
347#388C2318yes—
348#388C2318yes—
349#388C2318yes—
350#388C2318yes—
351#388C2318yes—
352#388C2318yes—
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#387C2318yes—
367#387C2318yes—
368#387C2318yes—
369#387C2318yes—
370#387C2318yes—
371#387C2318yes—
372#387C2318yes—
373#387C2318yes—
374#387C2318yes—
375#387C2318yes—
376#387C2318yes—
377#387C2318yes—
378#387C2318yes—
379#385C2318yes—
380#385C2318yes—
381#385C2318yes—
382#385C2318yes—
383#385C2314yes—
384#385C2314yes—
385#385C2314yes—
386#385C2314yes—
387#384C2314yes—
388#384C2314yes—
389#384C2314yes—
390#384C2314yes—
391#384C2314yes—
392#384C2314yes—
393#384C2311yescharacteristic
394#384C2311yescharacteristic
395#384C2314yes—
396#384C2311yescharacteristic
397#384C2311yescharacteristic
398#383C2318yes—
399#383C2318yes—
400#382C2314yes—
401#382C2314yes—
402#382C2314yes—
403#382C2314yes—
404#382C2314yes—
405#382C2312yes—
406#382C2312yes—
407#382C2314yes—
408#382C2314yes—
409#382C2318yes—
410#382C2318yes—
411#381C2314yes—
412#381C2314yes—
413#380C2314yes—
414#380C2314yes—
415#380C2314yes—
416#380C2314yes—
417#380C2318yes—
418#380C2318yes—
419#380C2312yes—
420#380C2312yes—
421#380C2312yes—
422#380C2312yes—
423#380C2312yes—
424#380C2312yes—
425#380C2312yes—
426#380C2312yes—
427#380C2312yes—
428#380C2312yes—
429#380C2312yes—
430#380C2312yes—
431#379C2314yes—
432#379C2314yes—
433C4×C4⋊C4C2312yes—
434C4×C4⋊C4C2312yes—
435C4×C4⋊C4C2312yes—
436C4×C4⋊C4C2312yes—
437C4×C4⋊C4C2312yes—
438C4×C4⋊C4C2312yes—
439C4×C4⋊C4C2312yes—
440C4×C4⋊C4C2312yes—
441C4×C4⋊C4C2312yes—
442C4×C4⋊C4C2312yes—
443C4×C4⋊C4C2314yes—
444C4×C4⋊C4C2314yes—
445C4×C4⋊C4C2314yes—
446C4×C4⋊C4C2314yes—
447C4×C4⋊C4C2314yes—
448C4×C4⋊C4C2314yes—
449C4×C4⋊C4C2314yes—
450C4×C4⋊C4C2314yes—
451C4×C4⋊C4C2312yes—
452C4×C4⋊C4C2312yes—
453C4×C4⋊C4C2314yes—
454C4×C4⋊C4C2314yes—
455C4×C4⋊C4C2314yes—
456C4×C4⋊C4C2314yes—
457C4×C4⋊C4C2314yes—
458C4×C4⋊C4C2314yes—
459C4×C4⋊C4C2318yes—
460C4×C4⋊C4C2318yes—
461C4×C22⋊C4C2318yes—
462C4×C22⋊C4C2318yes—
463C4×C22⋊C4C2314yes—
464C4×C22⋊C4C2314yes—
465C4×C22⋊C4C2314yes—
466C4×C22⋊C4C2314yes—
467C2×#95C2312yes—
468C2×#95C2312yes—
469C2×#95C2312yes—
470C2×#95C2312yes—
471C2×#95C2312yes—
472C2×#95C2312yes—
473C25C2411yescharacteristic
474C22×Q8C2412yes—
475C22×Q8C2412yes—
476C22×Q8C2412yes—
477C22×Q8C2412yes—
478C23×C4—24no—
479C23×C4—24no—
480C23×C4—24no—
481C23×C4C2411yescharacteristic
482C23×C4C2412yes—
483C23×C4C2412yes—
484C23×C4C2412yes—
485C23×C4C2412yes—
486C23×C4C2411yescharacteristic
487C23×C4C2411yescharacteristic
488C23×C4C2412yes—
489C23×C4C2412yes—
490C23×C4C2411yescharacteristic
491C23×C4C2411yescharacteristic
492C23×C4C2411yescharacteristic
493C4⋊Q8—24no—
494C4⋊Q8—24no—
495C4⋊Q8—24no—
496C4⋊Q8—24no—
497C4⋊Q8—84no—
498#126—88no—
499#126—88no—
500#125—28no—
501#125—28no—
502#125—84no—
503#125—88no—
504#125—88no—
505C22⋊Q8—28no—
506C22⋊Q8—28no—
507C22⋊Q8—28no—
508C22⋊Q8—28no—
509C4×Q8—28no—
510C4×Q8—28no—
511C4×Q8—28no—
512C4×Q8—28no—
513C4×Q8—84no—
514C4×Q8—84no—
515#117—28no—
516#117—28no—
517#117—28no—
518#117—28no—
519#117—28no—
520#117—28no—
521#117—28no—
522#117—28no—
523C2×C4⋊C4—24no—
524C2×C4⋊C4—24no—
525C2×C4⋊C4—24no—
526C2×C4⋊C4—24no—
527C2×C4⋊C4—24no—
528C2×C4⋊C4—24no—
529C2×C4⋊C4—82no—
530C2×C4⋊C4—82no—
531C2×C4⋊C4C2412yes—
532C2×C4⋊C4C2412yes—
533C2×C4⋊C4C2412yes—
534C2×C4⋊C4C2412yes—
535C2×C4⋊C4C2412yes—
536C2×C4⋊C4C2412yes—
537C2×C4⋊C4C2412yes—
538C2×C4⋊C4C2412yes—
539C2×C4⋊C4C2412yes—
540C2×C4⋊C4C2412yes—
541C2×C4⋊C4C2412yes—
542C2×C4⋊C4C2412yes—
543C2×C4⋊C4C2412yes—
544C2×C4⋊C4C2412yes—
545C2×C4⋊C4C2412yes—
546C2×C4⋊C4C2412yes—
547C2×C4⋊C4C2412yes—
548C2×C4⋊C4C2412yes—
549C2×C4⋊C4C2412yes—
550C2×C4⋊C4C2412yes—
551C2×C4⋊C4C2414yes—
552C2×C4⋊C4C2414yes—
553C2×C4⋊C4C2414yes—
554C2×C4⋊C4C2414yes—
555C2×C4⋊C4C2412yes—
556C2×C4⋊C4C2412yes—
557C2×C4⋊C4C2412yes—
558C2×C4⋊C4C2412yes—
559C2×C4⋊C4C2418yes—
560C2×C4⋊C4C2418yes—
561C2×C4⋊C4C2412yes—
562C2×C4⋊C4C2412yes—
563C2×C4⋊C4C2418yes—
564C2×C4⋊C4C2418yes—
565C2×C4⋊C4C2412yes—
566C2×C4⋊C4C2412yes—
567C2×C4⋊C4C2414yes—
568C2×C4⋊C4C2414yes—
569C2×C4⋊C4C2414yes—
570C2×C4⋊C4C2414yes—
571C2×C4⋊C4C2418yes—
572C2×C4⋊C4C2418yes—
573C2×C4⋊C4C2418yes—
574C2×C4⋊C4C2418yes—
575C2×C4⋊C4C2418yes—
576C2×C4⋊C4C2418yes—
577C2×C4⋊C4C2418yes—
578C2×C4⋊C4C2412yes—
579C2×C4⋊C4C2412yes—
580C2×C4⋊C4C2412yes—
581C2×C4⋊C4C2412yes—
582C2×C4⋊C4C2414yes—
583C2×C4⋊C4C2418yes—
584C2×C4⋊C4C2414yes—
585C2×C4⋊C4C2414yes—
586C2×C4⋊C4C2414yes—
587C2×C4⋊C4C2418yes—
588C2×C4⋊C4C2418yes—
589C2×C22⋊C4—24no—
590C2×C22⋊C4—24no—
591C2×C22⋊C4—82no—
592C2×C22⋊C4—82no—
593C2×C22⋊C4C2412yes—
594C2×C22⋊C4C2412yes—
595C2×C22⋊C4C2412yes—
596C2×C22⋊C4C2412yes—
597C2×C22⋊C4C2414yes—
598C2×C22⋊C4C2414yes—
599C2×C22⋊C4C2414yes—
600C2×C22⋊C4C2414yes—
601C2×C22⋊C4C2418yes—
602C2×C22⋊C4C2418yes—
603C2×C22⋊C4C2414yes—
604C2×C22⋊C4C2414yes—
605C2×C22⋊C4C2414yes—
606C2×C22⋊C4C2414yes—
607C2×C22⋊C4C2414yes—
608C2×C22⋊C4C2414yes—
609C2×C22⋊C4C2414yes—
610C2×C22⋊C4C2414yes—
611C2×C42—24no—
612C2×C42—82no—
613C2×C42—82no—
614C2×C42#4118yes—
615C2×C42C2412yes—
616C2×C42C2412yes—
617C2×C42C2414yes—
618C2×C42C2414yes—
619C2×C42C2414yes—
620C2×C42C2414yes—
621C2×C42C2418yes—
622C2×C42C2418yes—
623C2×C42C2414yes—
624C2×C42C2414yes—
625C2×C42C2418yes—
626C2×C42C2414yes—
627C2×C42C2414yes—
628C2×C42C2418yes—
629C2×C42C2411yescharacteristic
630C2×C42C2411yescharacteristic
631C2×C42C2411yescharacteristic
632C2×C42C2411yescharacteristic
633#95C2414yes—
634#95C2414yes—
635#95C2414yes—
636#95C2414yes—
637#95C2418yes—
638#95C2418yes—
639#95C2418yes—
640#95C2418yes—
641#95C2418yes—
642#95C2418yes—
643#95C2418yes—
644#95C2418yes—
645#95C2414yes—
646#95C2414yes—
647#95C2414yes—
648#95C2414yes—
649#95C2414yes—
650#95C2414yes—
651#95C2414yes—
652#95C2414yes—
653#95C2414yes—
654#95C2414yes—
655#95C2414yes—
656#95C2414yes—
657#95C2418yes—
658#95C2418yes—
659#95C2414yes—
660#95C2414yes—
661#95C2418yes—
662#95C2418yes—
663#95C2414yes—
664#95C2414yes—
665#95C2414yes—
666#95C2414yes—
667#95C2414yes—
668#95C2414yes—
669#95C2418yes—
670#95C2418yes—
671#95C2418yes—
672#95C2418yes—
673#95C2418yes—
674#95C2418yes—
675#95C2418yes—
676#95C2418yes—
677C24—22no—
678C24—22no—
679C24—22no—
680C24—41no—
681C24—41no—
682C24—41no—
683C24—41no—
684C24C2512yes—
685C24C2511yescharacteristic
686C2×Q8—24no—
687C2×Q8—24no—
688C2×Q8—24no—
689C2×Q8—24no—
690C2×Q8—42no—
691C2×Q8—42no—
692C2×Q8—42no—
693C2×Q8—42no—
694C2×Q8—42no—
695C2×Q8—42no—
696C2×Q8—42no—
697C2×Q8—42no—
698C22×C4—22no—
699C22×C4—22no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—22no—
703C22×C4—24no—
704C22×C4—24no—
705C22×C4—24no—
706C22×C4—24no—
707C22×C4—24no—
708C22×C4—24no—
709C22×C4—24no—
710C22×C4—24no—
711C22×C4—24no—
712C22×C4—24no—
713C22×C4—41no—
714C22×C4—41no—
715C22×C4—41no—
716C22×C4—41no—
717C22×C4—41no—
718C22×C4—41no—
719C22×C4—41no—
720C22×C4—41no—
721C22×C4—42no—
722C22×C4—42no—
723C22×C4—42no—
724C22×C4—42no—
725C22×C4—42no—
726C22×C4—42no—
727C22×C4—42no—
728C22×C4—42no—
729C22×C4—416no—
730C22×C4C2×#4114yes—
731C22×C4C2×#4114yes—
732C22×C4C2×#4114yes—
733C22×C42−1+414yes—
734C22×C42−1+414yes—
735C22×C4C2512yes—
736C22×C4C2514yes—
737C22×C4C2514yes—
738C22×C4C2514yes—
739C22×C4C2514yes—
740C22×C4C2514yes—
741C22×C4C2514yes—
742C22×C4C2514yes—
743C22×C4C2514yes—
744C22×C4C2514yes—
745C22×C4C2514yes—
746C22×C4C2512yes—
747C22×C4C2512yes—
748C22×C4C2514yes—
749C22×C4C2514yes—
750C22×C4C2511yescharacteristic
751C22×C4C2511yescharacteristic
752C22×C4C2511yescharacteristic
753C22×C4C2511yescharacteristic
754C22×C4C2511yescharacteristic
755C22×C4C2511yescharacteristic
756C4⋊C4—24no—
757C4⋊C4—24no—
758C4⋊C4—24no—
759C4⋊C4—24no—
760C4⋊C4—24no—
761C4⋊C4—24no—
762C4⋊C4—24no—
763C4⋊C4—24no—
764C4⋊C4—28no—
765C4⋊C4—28no—
766C4⋊C4—28no—
767C4⋊C4—28no—
768C4⋊C4—24no—
769C4⋊C4—24no—
770C4⋊C4—24no—
771C4⋊C4—24no—
772C4⋊C4—24no—
773C4⋊C4—24no—
774C4⋊C4—24no—
775C4⋊C4—24no—
776C4⋊C4—24no—
777C4⋊C4—24no—
778C4⋊C4—24no—
779C4⋊C4—24no—
780C4⋊C4—24no—
781C4⋊C4—24no—
782C4⋊C4—24no—
783C4⋊C4—24no—
784C4⋊C4—48no—
785C4⋊C4—48no—
786C4⋊C4—42no—
787C4⋊C4—42no—
788C4⋊C4—42no—
789C4⋊C4—42no—
790C4⋊C4—44no—
791C4⋊C4—44no—
792C4⋊C4—48no—
793C4⋊C4—48no—
794C4⋊C4—44no—
795C4⋊C4—44no—
796C4⋊C4—48no—
797C4⋊C4—42no—
798C4⋊C4—42no—
799C4⋊C4—48no—
800C4⋊C4—48no—
801C4⋊C4—42no—
802C4⋊C4—42no—
803C4⋊C4—44no—
804C4⋊C4—44no—
805C4⋊C4—48no—
806C4⋊C4—44no—
807C4⋊C4—44no—
808C4⋊C4—48no—
809C4⋊C4—48no—
810C4⋊C4—48no—
811C4⋊C4—48no—
812C4⋊C4—48no—
813C4⋊C4—48no—
814C22⋊C4—28no—
815C22⋊C4—28no—
816C22⋊C4—28no—
817C22⋊C4—28no—
818C22⋊C4—24no—
819C22⋊C4—24no—
820C22⋊C4—24no—
821C22⋊C4—24no—
822C22⋊C4—48no—
823C22⋊C4—48no—
824C22⋊C4—44no—
825C22⋊C4—44no—
826C22⋊C4—44no—
827C22⋊C4—44no—
828C22⋊C4—44no—
829C22⋊C4—44no—
830C22⋊C4—44no—
831C22⋊C4—44no—
832C42—24no—
833C42—24no—
834C42—28no—
835C42—28no—
836C42—28no—
837C42—28no—
838C42—44no—
839C42—44no—
840C42—44no—
841C42—44no—
842C42—48no—
843C42—48no—
844C42—48no—
845C42—48no—
846C42C2×#4114yes—
847C42C2×#4114yes—
848C42C2×#4114yes—
849C42C2×#4114yes—
850C23—21no—
851C23—21no—
852C23—21no—
853C23—21no—
854C23—22no—
855C23—22no—
856C23—22no—
857C23—22no—
858C23—22no—
859C23—22no—
860C23—22no—
861C23—44no—
862C23—44no—
863C23—44no—
864C23—82no—
865C23—82no—
866C23—82no—
867C23—82no—
868C23C22×#4112yes—
869C23C2×2−1+412yes—
870C23C2×2−1+412yes—
871C23C2611yescharacteristic
872Q8—48no—
873Q8—48no—
874Q8—84no—
875Q8—84no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—21no—
880C2×C4—21no—
881C2×C4—21no—
882C2×C4—21no—
883C2×C4—21no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—24no—
887C2×C4—24no—
888C2×C4—24no—
889C2×C4—24no—
890C2×C4—22no—
891C2×C4—24no—
892C2×C4—24no—
893C2×C4—24no—
894C2×C4—24no—
895C2×C4—24no—
896C2×C4—24no—
897C2×C4—24no—
898C2×C4—24no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—24no—
902C2×C4—24no—
903C2×C4—24no—
904C2×C4—24no—
905C2×C4—24no—
906C2×C4—24no—
907C2×C4—24no—
908C2×C4—24no—
909C2×C4—24no—
910C2×C4—24no—
911C2×C4—24no—
912C2×C4—24no—
913C2×C4—24no—
914C2×C4—24no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—24no—
918C2×C4—24no—
919C2×C4—24no—
920C2×C4—24no—
921C2×C4—24no—
922C2×C4—24no—
923C2×C4—24no—
924C2×C4—24no—
925C2×C4—24no—
926C2×C4—22no—
927C2×C4—22no—
928C2×C4—24no—
929C2×C4—44no—
930C2×C4—44no—
931C2×C4—44no—
932C2×C4—44no—
933C2×C4—44no—
934C2×C4—48no—
935C2×C4—48no—
936C2×C4—84no—
937C2×C4—84no—
938C2×C4—84no—
939C2×C4—84no—
940C2×C4#541116yes—
941C2×C4C22×#4112yes—
942C2×C4C22×#4112yes—
943C2×C4C22×#4112yes—
944C2×C4C22×#4112yes—
945C2×C4C22×#4112yes—
946C2×C4C22×#4112yes—
947C2×C4C2×2−1+412yes—
948C2×C4C2×2−1+412yes—
949C2×C4C2×2−1+412yes—
950C2×C4C2×2−1+412yes—
951C22—22no—
952C22—22no—
953C22—22no—
954C22—22no—
955C22—22no—
956C22—22no—
957C22—42no—
958C22—42no—
959C22—42no—
960C22—42no—
961C22—42no—
962C22—42no—
963C22—42no—
964C22—88no—
965C22C2×#54114yes—
966C22C23×#4111yescharacteristic
967C22C22×2−1+411yescharacteristic
968C22C22×2−1+411yescharacteristic
969C22H(7,𝔽2)11yescharacteristic
970C22H(7,𝔽2)11yescharacteristic
971C222−1+611yescharacteristic
972C222−1+611yescharacteristic
973C4—22no—
974C4—22no—
975C4—22no—
976C4—22no—
977C4—42no—
978C4—44no—
979C4—44no—
980C4—42no—
981C4—44no—
982C4—44no—
983C4—44no—
984C4—44no—
985C4—44no—
986C4—44no—
987C4—44no—
988C4—44no—
989C4—44no—
990C4—44no—
991C4—42no—
992C4C2×#54114yes—
993C4C2×#54114yes—
994C2—24no—
995C2—82no—
996C2C22×#54111yescharacteristic
997C2#6284511yescharacteristic
998C2#6285611yescharacteristic
999C2#6287911yescharacteristic
1000C2#6287911yescharacteristic
1001C2#6288111yescharacteristic
1002C2#6288911yescharacteristic
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. #42670C2semidirect
2. #42667C2semidirect
3. #42663C2semidirect
4. #42657C2semidirect
5. #42470C2semidirect
6. #42469C2semidirect
7. #42461C2semidirect
8. #42455C2semidirect
9. #37466C2semidirect
11. #36762C2semidirect
13. #35627C2semidirect
14. #35555C2semidirect
17. #35181C2semidirect
18. #35173C2semidirect
21. #34213C2semidirect
22. #34213C2semidirect
29. #2839C22semidirect
31. #2833C22semidirect
33. #2802C22semidirect
35. #2794C22semidirect
36. #2789C22semidirect
38. #2776C22semidirect
40. #2766C22semidirect
41. #2758C22semidirect
46. #2719C22semidirect
48. #2713C22semidirect
49. #2666C22semidirect
52. #2655C22semidirect
53. #2655C22semidirect
58. #2634C22semidirect
75. #2584C22semidirect
76. #2584C22semidirect
77. #2571C22semidirect
78. #2571C22semidirect
79. #2571C22semidirect
80. #2571C22semidirect
81. #2570C22semidirect
82. #2570C22semidirect
83. #2570C22semidirect
84. #2570C22semidirect
85. #2570C22semidirect
86. #2570C22semidirect
87. #2567C22semidirect
88. #2567C22semidirect
89. #2552C22semidirect
90. #2552C22semidirect
91. #2552C22semidirect
92. #2552C22semidirect
93. #2546C22semidirect
94. #2546C22semidirect
95. #2524C22semidirect
97. #2509C22semidirect
98. #2509C22semidirect
99. #2508C22semidirect
100. #2508C22semidirect
101. #2507C22semidirect
102. #2507C22semidirect
103. #2506C22semidirect
104. #2506C22semidirect
130. #2462C22semidirect
135. #2370C22semidirect
136. #2370C22semidirect
137. #2369C22semidirect
138. #2369C22semidirect
139. #2365C22semidirect
140. #2365C22semidirect
141. #2355C22semidirect
142. #2355C22semidirect
143. #2355C22semidirect
144. #2355C22semidirect
145. Q8×C4⋊C4C22semidirect
146. Q8×C4⋊C4C22semidirect

Maximal subgroups

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

subgroupindex
#426702
#426672
#426632
#426572
#424702
#424692
#424612
#424552
#374662
#374602
#367622
#367602
#356272
#355552
#355442
#351812
#351732
#346342
#342132
C2×#23142