Finite Group Databasebeta

← #8095658

Subgroups — #8095658

Order 512.

4222 conjugacy classes of subgroups.

The subgroup lattice has 1019 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53093C214yesmaximal, complemented
2#53092C214yesmaximal, complemented
3#53091C214yesmaximal, complemented
4#53086C214yesmaximal, complemented
5#52368C218yesmaximal
6#46117C214yesmaximal, complemented
7#46079C214yesmaximal, complemented
8#46051C214yesmaximal, complemented
9#46011C214yesmaximal, complemented
10#45551C218yesmaximal, complemented
11#35672C211yesmaximal, characteristic
12#35668C211yesmaximal, characteristic, complemented
13#35668C211yesmaximal, characteristic, complemented
14#35644C211yesmaximal, characteristic
15#35627C211yesmaximal, characteristic, complemented
16#35555C211yesmaximal, characteristic, complemented
17#35330C211yesmaximal, characteristic, complemented
18#35313C211yesmaximal, characteristic, complemented
19#35313C211yesmaximal, characteristic, complemented
20#35275C211yesmaximal, characteristic, complemented
21#35151C211yesmaximal, characteristic
22#35151C211yesmaximal, characteristic
23#34814C211yesmaximal, characteristic
24#34814C211yesmaximal, characteristic
25C2×#2499C211yesmaximal, characteristic
26C2×#544C2211yescharacteristic
27C2×#544C2211yescharacteristic
28C2×#544C2211yescharacteristic
29C22×C22⋊Q8C2211yescharacteristic
30C2×#519C2211yescharacteristic
31C22×#117C2211yescharacteristic
32#2868C2212yescomplemented
33#2863C2214yescomplemented
34#2863C2214yescomplemented
35#2862C2212yescomplemented
36#2859C2212yescomplemented
37#2859C2212yescomplemented
38#2855C2214yes—
39#2855C2214yes—
40#2839C2218yescomplemented
41#2838C2218yes—
42#2838C2218yes—
43#2838C2218yes—
44#2836C2218yes—
45#2836C2218yes—
46#2833C2218yescomplemented
47#2831C2218yes—
48#2831C2218yes—
49#2821C2218yes—
50#2805C2218yescomplemented
51#2799C2218yescomplemented
52#2794C2218yescomplemented
53#2793C2218yes—
54#2791C2218yescomplemented
55#2789C2218yescomplemented
56#2777C2218yes—
57#2776C2218yescomplemented
58#2776C2218yescomplemented
59#2775C2218yes—
60#2774C2218yescomplemented
61#2773C2218yes—
62#2766C2218yescomplemented
63#2762C2218yescomplemented
64#2759C2218yes—
65#2758C2218yescomplemented
66#2725C2218yes—
67#2721C2218yes—
68#2716C2218yes—
69#2713C2218yescomplemented
70#2660C2212yescomplemented
71#2660C2212yescomplemented
72#2660C2212yescomplemented
73#2660C2212yescomplemented
74#2645C2214yescomplemented
75#2645C2214yescomplemented
76#2626C2214yes—
77#2626C2214yes—
78#2571C2214yescomplemented
79#2570C2214yescomplemented
80#2570C2214yescomplemented
81#2568C2212yescomplemented
82#2568C2212yescomplemented
83#2567C2212yescomplemented
84#2567C2212yescomplemented
85#2565C2212yescomplemented
86#2565C2212yescomplemented
87#2565C2212yescomplemented
88#2565C2212yescomplemented
89#2561C2214yes—
90#2552C2214yescomplemented
91#2552C2214yescomplemented
92#2551C2214yescomplemented
93#2550C2214yescomplemented
94#2550C2214yescomplemented
95#2549C2218yes—
96#2514C2214yescomplemented
97#2514C2214yescomplemented
98#2511C2214yescomplemented
99#2511C2214yescomplemented
100#2509C2214yescomplemented
101#2508C2214yescomplemented
102#2507C2214yescomplemented
103#2506C2214yescomplemented
104#2505C2218yes—
105#2503C2214yes—
106#2499C2214yes—
107#2499C2214yes—
108#2499C2214yes—
109#2499C2214yes—
110#2497C2212yes—
111#2497C2212yes—
112#2496C2212yes—
113#2496C2212yes—
114#2495C2212yes—
115#2495C2212yes—
116#2494C2212yes—
117#2494C2212yes—
118#2493C2218yes—
119#2493C2218yes—
120#2493C2214yes—
121#2493C2214yes—
122#2492C2214yes—
123#2492C2214yes—
124#2489C2214yes—
125#2489C2214yes—
126#2484C2214yes—
127#2482C2214yes—
128#2480C2214yes—
129#2480C2214yes—
130#2473C2218yes—
131#2453C2214yescomplemented
132#2453C2214yescomplemented
133#2451C2214yescomplemented
134#2451C2214yescomplemented
135#2441C2214yes—
136#2441C2214yes—
137#2441C2214yes—
138#2441C2214yes—
139#2440C2218yes—
140#2439C2214yes—
141#2439C2214yes—
142#2439C2214yes—
143#2439C2214yes—
144#2438C2218yes—
145#2438C2218yes—
146#2423C2214yes—
147#2423C2214yes—
148#2421C2214yes—
149#2421C2214yes—
150#2401C2214yes—
151#2401C2214yes—
152C2×#397C2214yes—
153#2382C2218yescomplemented
154#2381C2218yescomplemented
155#2317C2211yescharacteristic
156#2317C2211yescharacteristic
157#2317C2211yescharacteristic
158#2317C2211yescharacteristic
159#2317C2211yescharacteristic
160#2317C2211yescharacteristic
161#2316C2211yescharacteristic
162#2316C2211yescharacteristic
163#2310C2211yescharacteristic
164#2310C2211yescharacteristic
165#2310C2211yescharacteristic
166C4×#126C2214yes—
167C4×#126C2214yes—
168#2296C2211yescharacteristic
169#2296C2211yescharacteristic
170#2296C2211yescharacteristic
171#2296C2211yescharacteristic
172C2×#391C2211yescharacteristic
173C2×#391C2211yescharacteristic
174C2×#387C2214yes—
175#2285C2211yescharacteristic
176#2285C2211yescharacteristic
177C2×#384C2211yescharacteristic
178C2×#382C2211yescharacteristic
179#2280C2211yescharacteristic
180#2280C2211yescharacteristic
181#2280C2211yescharacteristic
182#2280C2211yescharacteristic
183#2274C2211yescharacteristic
184C4×#117C2211yescharacteristic
185C4×#117C2211yescharacteristic
186C2×C4×C22⋊C4C2211yescharacteristic
187C23×Q8C2311yescharacteristic
188C24×C4C2311yescharacteristic
189#544—44no—
190#544—44no—
191#544—44no—
192C2×C4⋊Q8C2318yes—
193C2×C4⋊Q8C2312yes—
194C2×C4⋊Q8C2312yes—
195C2×C4⋊Q8C2312yes—
196C2×C4⋊Q8C2312yes—
197C2×C4⋊Q8C2312yes—
198C2×C4⋊Q8C2312yes—
199C2×#126C2314yes—
200C2×#126C2314yes—
201C2×#125C2312yes—
202C2×#125C2312yes—
203C2×#125C2312yes—
204C2×#125C2312yes—
205C2×#125C2312yes—
206C2×#125C2312yes—
207C2×#125C2318yes—
208C2×C22⋊Q8—44no—
209C2×C22⋊Q8C2314yes—
210C2×C22⋊Q8C2314yes—
211C2×C22⋊Q8C2314yes—
212C2×C22⋊Q8C2314yes—
213C2×C22⋊Q8C2314yes—
214#519—44no—
215C2×C4×Q8C2312yes—
216C2×C4×Q8C2312yes—
217C2×C4×Q8C2312yes—
218C2×C4×Q8C2312yes—
219C2×#117—44no—
220C2×#117C2311yescharacteristic
221C2×#117C2311yescharacteristic
222C2×#117C2311yescharacteristic
223C2×#117C2311yescharacteristic
224C2×#117C2311yescharacteristic
225C2×#117C2311yescharacteristic
226C2×#117C2311yescharacteristic
227C2×#117C2311yescharacteristic
228C2×#117C2314yes—
229C2×#117C2314yes—
230C2×#117C2314yes—
231C22×C4⋊C4C2311yescharacteristic
232C22×C4⋊C4C2311yescharacteristic
233C22×C4⋊C4C2311yescharacteristic
234C22×C4⋊C4C2314yes—
235C22×C4⋊C4C2312yes—
236C22×C22⋊C4C2312yes—
237C22×C22⋊C4C2312yes—
238C22×C22⋊C4C2312yes—
239C22×C42C2311yescharacteristic
240C22×C42C2311yescharacteristic
241C22×C42C2312yes—
242#401C2314yes—
243#401C2318yes—
244#401C2318yes—
245#401C2314yes—
246#400C2318yes—
247#400C2318yes—
248#400C2318yes—
249#400C2318yes—
250#400C2318yes—
251#400C2318yes—
252#400C2318yes—
253#400C2318yes—
254#400C2318yes—
255#400C2318yes—
256#400C2314yes—
257#400C2318yes—
258#400C2318yes—
259#400C2318yes—
260#400C2314yes—
261#400C2314yes—
262#400C2318yes—
263#400C2318yes—
264#400C2314yes—
265#400C2314yes—
266#400C2314yes—
267#399C2318yes—
268#399C2318yes—
269#399C2318yes—
270#398C2318yes—
271#398C2318yes—
272#398C2318yes—
273#398C2318yes—
274#398C2318yes—
275#398C2318yes—
276#398C2318yes—
277#398C2318yes—
278#398C2318yes—
279#398C2318yes—
280#398C2318yes—
281#398C2318yes—
282#398C2318yes—
283#397C2318yes—
284#397C2314yes—
285#397C2318yes—
286#397C2314yes—
287#397C2314yes—
288#397C2318yes—
289#397C2318yes—
290#397C2318yes—
291#397C2314yes—
292#397C2314yes—
293#397C2314yes—
294#397C2318yes—
295#396C2314yes—
296#396C2318yes—
297#396C2318yes—
298#396C2318yes—
299#396C2318yes—
300#396C2314yes—
301#395C2318yes—
302#395C2318yes—
303#395C2318yes—
304#395C2318yes—
305#395C2318yes—
306#395C2318yes—
307#393C2318yes—
308#393C2318yes—
309#393C2318yes—
310#391C2312yes—
311#391C2312yes—
312#391C2312yes—
313#391C2312yes—
314#391C2312yes—
315#391C2312yes—
316#391C2312yes—
317#391C2312yes—
318#391C2314yes—
319#391C2314yes—
320#391C2314yes—
321#391C2314yes—
322#391C2318yes—
323#391C2318yes—
324#391C2318yes—
325#391C2318yes—
326#391C2318yes—
327#391C2318yes—
328#391C2318yes—
329#391C2314yes—
330#391C2314yes—
331#389C2318yes—
332#389C2318yes—
333#389C2312yes—
334#389C2312yes—
335#389C2314yes—
336#389C2314yes—
337#389C2312yes—
338#389C2318yes—
339#389C2314yes—
340#389C2314yes—
341#389C2314yes—
342#389C2314yes—
343#389C2314yes—
344#389C2314yes—
345#389C2314yes—
346#389C2314yes—
347#389C2318yes—
348#389C2318yes—
349#389C2318yes—
350#389C2318yes—
351#389C2318yes—
352#389C2318yes—
353#389C2318yes—
354#389C2312yes—
355#389C2312yes—
356#389C2312yes—
357#389C2312yes—
358#389C2312yes—
359#388C2314yes—
360#388C2314yes—
361#388C2314yes—
362#388C2314yes—
363#388C2314yes—
364#388C2314yes—
365#388C2318yes—
366#388C2318yes—
367#388C2318yes—
368#388C2318yes—
369#387C2314yes—
370#387C2314yes—
371#387C2314yes—
372#387C2314yes—
373#387C2314yes—
374#387C2314yes—
375#387C2318yes—
376#387C2318yes—
377#387C2318yes—
378#387C2318yes—
379#387C2318yes—
380#387C2318yes—
381#387C2318yes—
382#387C2318yes—
383#387C2318yes—
384#387C2318yes—
385#387C2318yes—
386#387C2318yes—
387#387C2318yes—
388#387C2318yes—
389#387C2318yes—
390#387C2318yes—
391#387C2318yes—
392#387C2318yes—
393#387C2318yes—
394#387C2318yes—
395#387C2318yes—
396#387C2318yes—
397#387C2318yes—
398#387C2318yes—
399#385C2314yes—
400#385C2314yes—
401#385C2314yes—
402#385C2314yes—
403#385C2314yes—
404#385C2314yes—
405#385C2314yes—
406#385C2314yes—
407#385C2314yes—
408#385C2314yes—
409#384C2311yescharacteristic
410#384C2311yescharacteristic
411#384C2312yes—
412#384C2312yes—
413#384C2311yescharacteristic
414#384C2311yescharacteristic
415#384C2312yes—
416#384C2314yes—
417#384C2312yes—
418#384C2312yes—
419#384C2312yes—
420#384C2312yes—
421#384C2318yes—
422#384C2312yes—
423#383C2314yes—
424#383C2314yes—
425#383C2318yes—
426#383C2318yes—
427#382C2311yescharacteristic
428#382C2311yescharacteristic
429#382C2312yes—
430#382C2312yes—
431#382C2311yescharacteristic
432#382C2311yescharacteristic
433#382C2312yes—
434#382C2314yes—
435#382C2312yes—
436#382C2318yes—
437#382C2312yes—
438#382C2312yes—
439#382C2312yes—
440#382C2318yes—
441#382C2312yes—
442#381C2314yes—
443#381C2314yes—
444#381C2314yes—
445#381C2312yes—
446#381C2312yes—
447#381C2312yes—
448#381C2312yes—
449#380C2314yes—
450#380C2314yes—
451#380C2312yes—
452#380C2312yes—
453#380C2312yes—
454#380C2312yes—
455#380C2314yes—
456#380C2314yes—
457#380C2312yes—
458#380C2312yes—
459#380C2312yes—
460#380C2312yes—
461#379C2312yes—
462#379C2312yes—
463#379C2312yes—
464#379C2312yes—
465C4×C4⋊C4C2312yes—
466C4×C4⋊C4C2312yes—
467C4×C4⋊C4C2314yes—
468C4×C4⋊C4C2314yes—
469C4×C4⋊C4C2314yes—
470C4×C4⋊C4C2314yes—
471C4×C4⋊C4C2312yes—
472C4×C4⋊C4C2312yes—
473C4×C4⋊C4C2314yes—
474C4×C4⋊C4C2314yes—
475C4×C4⋊C4C2312yes—
476C4×C4⋊C4C2312yes—
477C4×C4⋊C4C2312yes—
478C4×C4⋊C4C2312yes—
479C4×C22⋊C4C2312yes—
480C4×C22⋊C4C2312yes—
481C4×C22⋊C4C2314yes—
482C4×C22⋊C4C2314yes—
483C4×C22⋊C4C2314yes—
484C4×C22⋊C4C2314yes—
485C4×C22⋊C4C2314yes—
486C4×C22⋊C4C2312yes—
487C4×C22⋊C4C2312yes—
488C4×C22⋊C4C2314yes—
489C4×C22⋊C4C2314yes—
490#376C2312yes—
491#376C2312yes—
492C2×#95C2314yes—
493C2×#95C2314yes—
494C2×#95C2314yes—
495C2×#95C2312yes—
496C43C2312yes—
497C43C2312yes—
498C25C2411yescharacteristic
499C22×Q8—24no—
500C22×Q8—24no—
501C22×Q8—24no—
502C22×Q8C2412yes—
503C22×Q8C2412yes—
504C22×Q8C2414yes—
505C22×Q8C2414yes—
506C22×Q8C2414yes—
507C23×C4—24no—
508C23×C4—24no—
509C23×C4—24no—
510C23×C4C2412yes—
511C23×C4C2411yescharacteristic
512C23×C4C2412yes—
513C23×C4C2412yes—
514C23×C4C2412yes—
515C23×C4C2412yes—
516C23×C4C2412yes—
517C23×C4C2412yes—
518C23×C4C2412yes—
519C23×C4C2411yescharacteristic
520C4⋊Q8—416no—
521C4⋊Q8—44no—
522C4⋊Q8—44no—
523C4⋊Q8—44no—
524C4⋊Q8—44no—
525C4⋊Q8—44no—
526C4⋊Q8—44no—
527#126—48no—
528#126—48no—
529#125—44no—
530#125—44no—
531#125—44no—
532#125—44no—
533#125—44no—
534#125—44no—
535#125—416no—
536C22⋊Q8—48no—
537C22⋊Q8—48no—
538C22⋊Q8—48no—
539C22⋊Q8—48no—
540C22⋊Q8—48no—
541C4×Q8—44no—
542C4×Q8—44no—
543C4×Q8—44no—
544C4×Q8—44no—
545#117—24no—
546#117—24no—
547#117—24no—
548#117—24no—
549#117—24no—
550#117—24no—
551#117—24no—
552#117—24no—
553#117—48no—
554#117—48no—
555#117—48no—
556C2×C4⋊C4—24no—
557C2×C4⋊C4—24no—
558C2×C4⋊C4—24no—
559C2×C4⋊C4—48no—
560C2×C4⋊C4—44no—
561C2×C4⋊C4C2412yes—
562C2×C4⋊C4C2412yes—
563C2×C4⋊C4C2412yes—
564C2×C4⋊C4C2412yes—
565C2×C4⋊C4C2412yes—
566C2×C4⋊C4C2412yes—
567C2×C4⋊C4C2418yes—
568C2×C4⋊C4C2411yescharacteristic
569C2×C4⋊C4C2411yescharacteristic
570C2×C4⋊C4C2411yescharacteristic
571C2×C4⋊C4C2411yescharacteristic
572C2×C4⋊C4C2411yescharacteristic
573C2×C4⋊C4C2411yescharacteristic
574C2×C4⋊C4C2411yescharacteristic
575C2×C4⋊C4C2411yescharacteristic
576C2×C4⋊C4C2412yes—
577C2×C4⋊C4C2412yes—
578C2×C4⋊C4C2412yes—
579C2×C4⋊C4C2412yes—
580C2×C4⋊C4C2414yes—
581C2×C4⋊C4C2414yes—
582C2×C4⋊C4C2414yes—
583C2×C4⋊C4C2418yes—
584C2×C4⋊C4C2418yes—
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⋊C4C2414yes—
594C2×C4⋊C4C2414yes—
595C2×C4⋊C4C2414yes—
596C2×C4⋊C4C2418yes—
597C2×C4⋊C4C2418yes—
598C2×C4⋊C4C2418yes—
599C2×C4⋊C4C2414yes—
600C2×C4⋊C4C2414yes—
601C2×C4⋊C4C2414yes—
602C2×C4⋊C4C2418yes—
603C2×C4⋊C4C2418yes—
604C2×C4⋊C4C2414yes—
605C2×C4⋊C4C2414yes—
606C2×C4⋊C4C2414yes—
607C2×C4⋊C4C2414yes—
608C2×C4⋊C4C2414yes—
609C2×C4⋊C4C2414yes—
610C2×C4⋊C4C2418yes—
611C2×C4⋊C4C2418yes—
612C2×C4⋊C4C2418yes—
613C2×C22⋊C4—44no—
614C2×C22⋊C4—44no—
615C2×C22⋊C4—44no—
616C2×C22⋊C4C2412yes—
617C2×C22⋊C4C2412yes—
618C2×C22⋊C4C2412yes—
619C2×C22⋊C4C2412yes—
620C2×C22⋊C4C2412yes—
621C2×C22⋊C4C2412yes—
622C2×C22⋊C4C2412yes—
623C2×C22⋊C4C2412yes—
624C2×C22⋊C4C2412yes—
625C2×C22⋊C4C2412yes—
626C2×C22⋊C4C2418yes—
627C2×C22⋊C4C2418yes—
628C2×C22⋊C4C2412yes—
629C2×C22⋊C4C2412yes—
630C2×C22⋊C4C2414yes—
631C2×C22⋊C4C2414yes—
632C2×C22⋊C4C2414yes—
633C2×C22⋊C4C2414yes—
634C2×C22⋊C4C2414yes—
635C2×C22⋊C4C2414yes—
636C2×C22⋊C4C2414yes—
637C2×C22⋊C4C2414yes—
638C2×C42—24no—
639C2×C42—24no—
640C2×C42—44no—
641C2×C42C2412yes—
642C2×C42C2412yes—
643C2×C42C2412yes—
644C2×C42C2412yes—
645C2×C42C2412yes—
646C2×C42C2412yes—
647C2×C42C2412yes—
648C2×C42C2412yes—
649C2×C42C2414yes—
650C2×C42C2411yescharacteristic
651C2×C42C2411yescharacteristic
652C2×C42C2411yescharacteristic
653C2×C42C2411yescharacteristic
654C2×C42C2412yes—
655C2×C42C2412yes—
656C2×C42C2418yes—
657C2×C42C2414yes—
658C2×C42C2414yes—
659C2×C42C2418yes—
660C2×C42C2414yes—
661C2×C42C2414yes—
662C2×C42C2414yes—
663#95C2412yes—
664#95C2412yes—
665#95C2412yes—
666#95C2412yes—
667#95C2418yes—
668#95C2418yes—
669#95C2418yes—
670#95C2418yes—
671#95C2418yes—
672#95C2418yes—
673#95C2414yes—
674#95C2414yes—
675#95C2414yes—
676#95C2414yes—
677#95C2418yes—
678#95C2414yes—
679#95C2414yes—
680#95C2414yes—
681#95C2414yes—
682#95C2414yes—
683#95C2414yes—
684#95C2414yes—
685#95C2414yes—
686#95C2414yes—
687#95C2414yes—
688#95C2414yes—
689#95C2414yes—
690#95C2414yes—
691#95C2414yes—
692#95C2414yes—
693#95C2414yes—
694#95C2414yes—
695#95C2414yes—
696#95C2414yes—
697#95C2414yes—
698#95C2418yes—
699#95C2418yes—
700#95C2418yes—
701#95C2418yes—
702#95C2418yes—
703#95C2418yes—
704#95C2418yes—
705#95C2418yes—
706#95C2418yes—
707#95C2418yes—
708#95C2418yes—
709#95C2418yes—
710#95C2418yes—
711#95C2418yes—
712C24—22no—
713C24—22no—
714C24—22no—
715C24—42no—
716C24—42no—
717C24C2512yes—
718C24C2511yescharacteristic
719C2×Q8—24no—
720C2×Q8—24no—
721C2×Q8—24no—
722C2×Q8—24no—
723C2×Q8—24no—
724C2×Q8—24no—
725C2×Q8—44no—
726C2×Q8—44no—
727C2×Q8—44no—
728C2×Q8—48no—
729C2×Q8—48no—
730C2×Q8—48no—
731C2×Q8—416no—
732C22×C4—22no—
733C22×C4—24no—
734C22×C4—24no—
735C22×C4—22no—
736C22×C4—22no—
737C22×C4—24no—
738C22×C4—24no—
739C22×C4—24no—
740C22×C4—24no—
741C22×C4—24no—
742C22×C4—24no—
743C22×C4—24no—
744C22×C4—24no—
745C22×C4—24no—
746C22×C4—24no—
747C22×C4—24no—
748C22×C4—24no—
749C22×C4—24no—
750C22×C4—42no—
751C22×C4—42no—
752C22×C4—44no—
753C22×C4—44no—
754C22×C4—42no—
755C22×C4—44no—
756C22×C4—416no—
757C22×C4H(5,𝔽2)14yes—
758C22×C42−1+414yes—
759C22×C42−1+414yes—
760C22×C4C2512yes—
761C22×C4C2514yes—
762C22×C4C2512yes—
763C22×C4C2512yes—
764C22×C4C2512yes—
765C22×C4C2514yes—
766C22×C4C2514yes—
767C22×C4C2514yes—
768C22×C4C2514yes—
769C22×C4C2512yes—
770C22×C4C2512yes—
771C22×C4C2512yes—
772C22×C4C2514yes—
773C22×C4C2512yes—
774C22×C4C2512yes—
775C22×C4C2512yes—
776C22×C4C2512yes—
777C22×C4C2514yes—
778C22×C4C2514yes—
779C22×C4C2512yes—
780C22×C4C2512yes—
781C22×C4C2511yescharacteristic
782C22×C4C2511yescharacteristic
783C4⋊C4—24no—
784C4⋊C4—24no—
785C4⋊C4—24no—
786C4⋊C4—24no—
787C4⋊C4—24no—
788C4⋊C4—24no—
789C4⋊C4—22no—
790C4⋊C4—22no—
791C4⋊C4—22no—
792C4⋊C4—22no—
793C4⋊C4—22no—
794C4⋊C4—22no—
795C4⋊C4—22no—
796C4⋊C4—22no—
797C4⋊C4—24no—
798C4⋊C4—24no—
799C4⋊C4—24no—
800C4⋊C4—24no—
801C4⋊C4—216no—
802C4⋊C4—28no—
803C4⋊C4—28no—
804C4⋊C4—28no—
805C4⋊C4—48no—
806C4⋊C4—48no—
807C4⋊C4—44no—
808C4⋊C4—44no—
809C4⋊C4—48no—
810C4⋊C4—44no—
811C4⋊C4—48no—
812C4⋊C4—44no—
813C4⋊C4—44no—
814C4⋊C4—48no—
815C4⋊C4—44no—
816C4⋊C4—44no—
817C4⋊C4—44no—
818C4⋊C4—44no—
819C4⋊C4—44no—
820C4⋊C4—44no—
821C4⋊C4—44no—
822C4⋊C4—44no—
823C4⋊C4—44no—
824C4⋊C4—44no—
825C4⋊C4—44no—
826C4⋊C4—44no—
827C4⋊C4—48no—
828C4⋊C4—48no—
829C4⋊C4—48no—
830C4⋊C4—44no—
831C4⋊C4—44no—
832C4⋊C4—44no—
833C4⋊C4—48no—
834C4⋊C4—48no—
835C22⋊C4—24no—
836C22⋊C4—24no—
837C22⋊C4—24no—
838C22⋊C4—24no—
839C22⋊C4—24no—
840C22⋊C4—24no—
841C22⋊C4—24no—
842C22⋊C4—24no—
843C22⋊C4—24no—
844C22⋊C4—24no—
845C22⋊C4—42no—
846C22⋊C4—42no—
847C22⋊C4—48no—
848C22⋊C4—48no—
849C22⋊C4—44no—
850C22⋊C4—44no—
851C22⋊C4—44no—
852C22⋊C4—44no—
853C22⋊C4—44no—
854C22⋊C4—44no—
855C22⋊C4—44no—
856C22⋊C4—44no—
857C42—24no—
858C42—24no—
859C42—24no—
860C42—24no—
861C42—22no—
862C42—24no—
863C42—22no—
864C42—22no—
865C42—22no—
866C42—24no—
867C42—24no—
868C42—24no—
869C42—24no—
870C42—24no—
871C42—28no—
872C42—48no—
873C42—44no—
874C42—44no—
875C42—44no—
876C42—44no—
877C42—48no—
878C42—44no—
879C23—22no—
880C23—22no—
881C23—22no—
882C23—22no—
883C23—22no—
884C23—22no—
885C23—22no—
886C23—22no—
887C23—22no—
888C23—44no—
889C23—44no—
890C23—44no—
891C23—84no—
892C23—84no—
893C23C2×H(5,𝔽2)12yes—
894C23C2×2−1+412yes—
895C23C2×2−1+412yes—
896C23C2611yescharacteristic
897Q8—48no—
898Q8—48no—
899Q8—164no—
900Q8—164no—
901Q8—164no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—24no—
914C2×C4—24no—
915C2×C4—24no—
916C2×C4—24no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—24no—
921C2×C4—24no—
922C2×C4—24no—
923C2×C4—24no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—24no—
927C2×C4—24no—
928C2×C4—24no—
929C2×C4—24no—
930C2×C4—22no—
931C2×C4—24no—
932C2×C4—24no—
933C2×C4—24no—
934C2×C4—24no—
935C2×C4—28no—
936C2×C4—22no—
937C2×C4—22no—
938C2×C4—24no—
939C2×C4—24no—
940C2×C4—28no—
941C2×C4—22no—
942C2×C4—24no—
943C2×C4—24no—
944C2×C4—24no—
945C2×C4—24no—
946C2×C4—24no—
947C2×C4—24no—
948C2×C4—24no—
949C2×C4—24no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—28no—
953C2×C4—48no—
954C2×C4—44no—
955C2×C4—48no—
956C2×C4—48no—
957C2×C4—48no—
958C2×C4—84no—
959C2×C4—84no—
960C2×C4—84no—
961C2×C4—84no—
962C2×C4#563116yes—
963C2×C4C2×H(5,𝔽2)12yes—
964C2×C4C2×H(5,𝔽2)12yes—
965C2×C4C2×2−1+412yes—
966C2×C4C2×2−1+412yes—
967C2×C4C2×2−1+412yes—
968C2×C4C2×2−1+412yes—
969C2×C4#58514yes—
970C22—22no—
971C22—22no—
972C22—24no—
973C22—24no—
974C22—42no—
975C22—42no—
976C22—42no—
977C22—42no—
978C22—42no—
979C22—42no—
980C22—42no—
981C22—88no—
982C22C2×#56314yes—
983C22C22×H(5,𝔽2)11yescharacteristic
984C22C22×2−1+411yescharacteristic
985C22C22×2−1+411yescharacteristic
986C22C2×#58512yes—
987C222−1+612yes—
988C4—24no—
989C4—42no—
990C4—44no—
991C4—44no—
992C4—42no—
993C4—42no—
994C4—42no—
995C4—42no—
996C4—42no—
997C4—44no—
998C4—42no—
999C4—42no—
1000C4—44no—
1001C4—44no—
1002C4—42no—
1003C4—42no—
1004C4—44no—
1005C4—44no—
1006C4—44no—
1007C4—42no—
1008C4—42no—
1009C4C2×#56314yes—
1010C4C2×#56314yes—
1011C2—24no—
1012C2—82no—
1013C2C22×#56311yescharacteristic
1014C2#6283611yescharacteristic
1015C2#6288711yescharacteristic
1016C2#6292812yes—
1017C2#6295912yes—
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. #53093C2semidirect
2. #53092C2semidirect
3. #53091C2semidirect
4. #53086C2semidirect
6. #46117C2semidirect
7. #46079C2semidirect
8. #46051C2semidirect
9. #46011C2semidirect
10. #45551C2semidirect
12. #35668C2semidirect
13. #35668C2semidirect
15. #35627C2semidirect
16. #35555C2semidirect
17. #35330C2semidirect
18. #35313C2semidirect
19. #35313C2semidirect
20. #35275C2semidirect
32. #2868C22semidirect
33. #2863C22semidirect
34. #2863C22semidirect
35. #2862C22semidirect
36. #2859C22semidirect
37. #2859C22semidirect
40. #2839C22semidirect
46. #2833C22semidirect
50. #2805C22semidirect
51. #2799C22semidirect
52. #2794C22semidirect
54. #2791C22semidirect
55. #2789C22semidirect
57. #2776C22semidirect
58. #2776C22semidirect
60. #2774C22semidirect
62. #2766C22semidirect
63. #2762C22semidirect
65. #2758C22semidirect
69. #2713C22semidirect
70. #2660C22semidirect
71. #2660C22semidirect
72. #2660C22semidirect
73. #2660C22semidirect
74. #2645C22semidirect
75. #2645C22semidirect
78. #2571C22semidirect
79. #2570C22semidirect
80. #2570C22semidirect
81. #2568C22semidirect
82. #2568C22semidirect
83. #2567C22semidirect
84. #2567C22semidirect
85. #2565C22semidirect
86. #2565C22semidirect
87. #2565C22semidirect
88. #2565C22semidirect
90. #2552C22semidirect
91. #2552C22semidirect
92. #2551C22semidirect
93. #2550C22semidirect
94. #2550C22semidirect
96. #2514C22semidirect
97. #2514C22semidirect
98. #2511C22semidirect
99. #2511C22semidirect
100. #2509C22semidirect
101. #2508C22semidirect
102. #2507C22semidirect
103. #2506C22semidirect
131. #2453C22semidirect
132. #2453C22semidirect
133. #2451C22semidirect
134. #2451C22semidirect
153. #2382C22semidirect
154. #2381C22semidirect

Maximal subgroups

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

subgroupindex
#530932
#530922
#530912
#530862
#523682
#461172
#460792
#460512
#460112
#455512
#356722
#356682
#356442
#356272
#355552
#353302
#353132
#352752
#351512
#348142
C2×#24992