Finite Group Databasebeta

← #7681831

Subgroups — #7681831

Order 512.

4542 conjugacy classes of subgroups.

The subgroup lattice has 1025 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59876C214yesmaximal, complemented
2#59443C214yesmaximal, complemented
3#59241C218yesmaximal, complemented
4#45370C214yesmaximal, complemented
5#45152C214yesmaximal, complemented
6#43058C218yesmaximal, complemented
7#39299C214yesmaximal, complemented
8#39294C214yesmaximal, complemented
9#39153C214yesmaximal, complemented
10#36512C214yesmaximal, complemented
11#35629C211yesmaximal, characteristic
12#35628C211yesmaximal, characteristic
13#35628C211yesmaximal, characteristic
14#35557C211yesmaximal, characteristic
15#35333C211yesmaximal, characteristic
16#35313C211yesmaximal, characteristic, complemented
17#35313C211yesmaximal, characteristic, complemented
18#34938C211yesmaximal, characteristic, complemented
19C2×#2565C211yesmaximal, characteristic, complemented
20#34217C211yesmaximal, characteristic, complemented
21#34215C211yesmaximal, characteristic, complemented
22#34214C211yesmaximal, characteristic, complemented
23#34187C211yesmaximal, characteristic, complemented
24#34121C211yesmaximal, characteristic
25C4×#536C211yesmaximal, characteristic
26C2×#536C2211yescharacteristic
27C2×#533C2211yescharacteristic
28C2×#533C2211yescharacteristic
29C22×#125C2211yescharacteristic
30C2×C4×#41C2211yescharacteristic
31C22×C4×Q8C2211yescharacteristic
32#2863C2214yes—
33#2863C2214yes—
34#2851C2214yes—
35#2793C2218yes—
36#2789C2218yes—
37#2789C2218yes—
38#2788C2218yes—
39#2787C2218yes—
40#2783C2218yes—
41#2776C2218yes—
42#2776C2218yes—
43#2775C2218yes—
44#2767C2218yes—
45#2767C2218yes—
46#2716C2218yes—
47#2645C2214yes—
48#2645C2214yes—
49#2629C2214yes—
50#2599C2218yes—
51#2594C2218yes—
52#2594C2218yes—
53#2592C2214yes—
54#2592C2214yes—
55#2588C2218yes—
56#2588C2218yes—
57#2579C2214yes—
58#2579C2214yes—
59#2573C2218yes—
60#2570C2218yes—
61#2568C2214yes—
62#2568C2214yes—
63#2566C2212yes—
64#2566C2212yes—
65#2565C2212yes—
66#2565C2212yes—
67#2565C2214yes—
68#2565C2214yes—
69#2565C2212yes—
70#2565C2212yes—
71#2565C2212yes—
72#2565C2212yes—
73#2552C2212yes—
74#2551C2212yes—
75#2550C2212yes—
76#2550C2212yes—
77#2549C2214yes—
78#2533C2218yes—
79#2533C2218yes—
80#2527C2218yes—
81#2525C2218yes—
82#2524C2218yes—
83#2524C2218yes—
84#2523C2218yes—
85#2514C2214yes—
86#2514C2214yes—
87#2514C2218yes—
88#2514C2214yes—
89#2513C2214yes—
90#2512C2214yes—
91#2511C2214yes—
92#2511C2214yes—
93#2511C2214yes—
94#2510C2218yes—
95#2497C2214yes—
96#2496C2214yes—
97#2495C2214yes—
98#2494C2214yes—
99#2493C2218yes—
100#2493C2218yes—
101#2492C2214yes—
102#2492C2214yes—
103#2489C2214yes—
104#2489C2214yes—
105#2488C2218yes—
106#2488C2218yes—
107#2481C2218yes—
108#2478C2218yes—
109#2469C2218yes—
110#2446C2218yes—
111#2440C2214yes—
112#2399C2214yes—
113C2×#398C2214yes—
114#2373C2218yes—
115#2370C2214yes—
116#2370C2214yes—
117#2368C2218yes—
118#2360C2218yes—
119#2357C2212yes—
120#2356C2212yes—
121#2356C2218yes—
122#2356C2214yes—
123#2356C2214yes—
124#2355C2214yes—
125#2355C2214yes—
126#2355C2212yes—
127#2355C2214yes—
128#2355C2214yes—
129#2355C2214yes—
130#2354C2212yes—
131#2353C2214yes—
132#2352C2214yes—
133Q8×C4⋊C4C2214yes—
134#2345C2214yes—
135#2345C2214yes—
136#2331C2214yes—
137#2330C2214yes—
138#2330C2214yes—
139#2327C2212yes—
140#2326C2212yes—
141#2323C2214yes—
142#2322C2214yes—
143#2317C2211yescharacteristic
144#2317C2211yescharacteristic
145#2317C2211yescharacteristic
146#2316C2211yescharacteristic
147#2316C2211yescharacteristic
148#2313C2214yes—
149#2311C2211yescharacteristic
150#2311C2211yescharacteristic
151#2311C2211yescharacteristic
152#2310C2211yescharacteristic
153#2310C2211yescharacteristic
154#2310C2211yescharacteristic
155C4×C4⋊Q8C2212yes—
156C4×C4⋊Q8C2214yes—
157C4×C4⋊Q8C2214yes—
158C4×#125C2214yes—
159C4×#125C2214yes—
160C4×#124C2212yes—
161C4×C22⋊Q8C2214yes—
162C4×#123C2214yes—
163#2298C2212yes—
164#2298C2212yes—
165#2297C2211yescharacteristic
166#2297C2211yescharacteristic
167#2296C2211yescharacteristic
168#2296C2211yescharacteristic
169C2×#391C2211yescharacteristic
170C2×#391C2211yescharacteristic
171C2×#387C2214yes—
172#2285C2211yescharacteristic
173#2285C2211yescharacteristic
174C2×#384C2211yescharacteristic
175#2283C2212yes—
176#2283C2214yes—
177C2×#382C2211yescharacteristic
178#2274C2211yescharacteristic
179#2274C2211yescharacteristic
180#2274C2211yescharacteristic
181#2274C2211yescharacteristic
182C4×#117C2211yescharacteristic
183C4×#117C2212yes—
184C4×#117C2211yescharacteristic
185C4×#117C2211yescharacteristic
186C2×C4×C4⋊C4C2211yescharacteristic
187C22×#41C2311yescharacteristic
188C23×Q8C2311yescharacteristic
189#536—28no—
190#533—28no—
191#533—28no—
192C2×C4⋊Q8C2312yes—
193C2×C4⋊Q8C2312yes—
194C2×C4⋊Q8C2312yes—
195C2×C4⋊Q8C2314yes—
196C2×#126C2318yes—
197C2×#125—28no—
198C2×#125C2312yes—
199C2×#125C2312yes—
200C2×#125C2312yes—
201C2×#125C2312yes—
202C2×#125C2312yes—
203C2×#125C2312yes—
204C2×#124C2312yes—
205C2×#123C2314yes—
206C2×C22⋊Q8C2314yes—
207C2×C22⋊Q8C2314yes—
208C2×C22⋊Q8C2314yes—
209C4×#41—28no—
210C2×C4×Q8—28no—
211C2×C4×Q8C2311yescharacteristic
212C2×C4×Q8C2312yes—
213C2×C4×Q8C2314yes—
214C2×C4×Q8C2314yes—
215C2×C4×Q8C2312yes—
216C2×C4×Q8C2312yes—
217C2×C4×Q8C2311yescharacteristic
218C2×C4×Q8C2312yes—
219C2×C4×Q8C2318yes—
220C2×C4×D4C2311yescharacteristic
221C2×C4×D4C2311yescharacteristic
222C2×C4×D4C2312yes—
223C2×C4×D4C2312yes—
224C2×#117C2311yescharacteristic
225C2×#117C2311yescharacteristic
226C2×#117C2311yescharacteristic
227C2×#117C2311yescharacteristic
228C2×#117C2311yescharacteristic
229C2×#117C2311yescharacteristic
230C2×#117C2312yes—
231C2×#117C2314yes—
232C2×#117C2311yescharacteristic
233C22×C4⋊C4C2311yescharacteristic
234C22×C4⋊C4C2311yescharacteristic
235C22×C4⋊C4C2311yescharacteristic
236C22×C4⋊C4C2312yes—
237C22×C4⋊C4C2312yes—
238C22×C4⋊C4C2312yes—
239C22×C4⋊C4C2312yes—
240C22×C4⋊C4C2314yes—
241C22×C42C2312yes—
242C22×C42C2312yes—
243C22×C42C2311yescharacteristic
244C22×C42C2311yescharacteristic
245C22×C42C2311yescharacteristic
246#401C2318yes—
247#401C2318yes—
248#401C2318yes—
249#400C2318yes—
250#400C2318yes—
251#400C2318yes—
252#400C2318yes—
253#400C2318yes—
254#400C2318yes—
255#400C2318yes—
256#400C2318yes—
257#400C2318yes—
258#400C2318yes—
259#400C2318yes—
260#400C2318yes—
261#400C2318yes—
262#398C2318yes—
263#398C2318yes—
264#398C2318yes—
265#398C2318yes—
266#398C2318yes—
267#398C2318yes—
268#398C2314yes—
269#398C2314yes—
270#398C2314yes—
271#398C2314yes—
272#397C2318yes—
273#397C2318yes—
274#397C2318yes—
275#397C2318yes—
276#397C2318yes—
277#396C2318yes—
278#396C2318yes—
279#396C2318yes—
280#395C2314yes—
281#395C2314yes—
282#395C2314yes—
283#395C2314yes—
284#393C2318yes—
285#393C2318yes—
286#391C2312yes—
287#391C2312yes—
288#391C2318yes—
289#391C2314yes—
290#391C2314yes—
291#391C2312yes—
292#391C2312yes—
293#391C2314yes—
294#391C2314yes—
295#391C2312yes—
296#391C2312yes—
297#391C2312yes—
298#391C2312yes—
299#391C2314yes—
300#391C2314yes—
301#391C2314yes—
302#391C2312yes—
303#391C2314yes—
304#391C2314yes—
305#391C2312yes—
306#391C2312yes—
307#391C2318yes—
308#391C2318yes—
309#391C2318yes—
310#391C2318yes—
311#390C2312yes—
312#390C2312yes—
313#390C2312yes—
314#390C2312yes—
315#390C2312yes—
316#389C2314yes—
317#389C2314yes—
318#389C2314yes—
319#389C2314yes—
320#389C2318yes—
321#389C2314yes—
322#389C2314yes—
323#389C2314yes—
324#389C2318yes—
325#389C2314yes—
326#389C2314yes—
327#389C2318yes—
328#389C2314yes—
329#389C2314yes—
330#389C2318yes—
331#389C2318yes—
332#389C2318yes—
333#389C2312yes—
334#389C2312yes—
335#389C2312yes—
336#389C2312yes—
337#388C2318yes—
338#388C2318yes—
339#388C2318yes—
340#388C2318yes—
341#388C2318yes—
342#388C2318yes—
343#388C2314yes—
344#388C2314yes—
345#388C2318yes—
346#388C2318yes—
347#388C2318yes—
348#388C2314yes—
349#388C2314yes—
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#387C2314yes—
365#387C2318yes—
366#387C2318yes—
367#387C2318yes—
368#387C2318yes—
369#387C2318yes—
370#387C2318yes—
371#387C2318yes—
372#387C2318yes—
373#387C2318yes—
374#387C2318yes—
375#387C2318yes—
376#387C2314yes—
377#387C2318yes—
378#387C2318yes—
379#387C2318yes—
380#387C2318yes—
381#387C2318yes—
382#387C2318yes—
383#387C2314yes—
384#387C2314yes—
385#386C2314yes—
386#386C2314yes—
387#386C2314yes—
388#386C2314yes—
389#386C2314yes—
390#385C2318yes—
391#385C2318yes—
392#385C2314yes—
393#385C2314yes—
394#385C2314yes—
395#385C2318yes—
396#385C2314yes—
397#385C2314yes—
398#384C2312yes—
399#384C2314yes—
400#384C2312yes—
401#384C2312yes—
402#384C2314yes—
403#384C2312yes—
404#384C2312yes—
405#384C2312yes—
406#384C2312yes—
407#383C2318yes—
408#383C2318yes—
409#383C2318yes—
410#383C2314yes—
411#383C2318yes—
412#382C2312yes—
413#382C2312yes—
414#382C2312yes—
415#382C2314yes—
416#382C2312yes—
417#382C2312yes—
418#382C2318yes—
419#382C2318yes—
420#382C2312yes—
421#382C2312yes—
422#382C2314yes—
423#382C2318yes—
424#381C2314yes—
425#381C2314yes—
426#381C2314yes—
427#381C2314yes—
428#380C2314yes—
429#380C2314yes—
430#380C2314yes—
431#380C2312yes—
432#380C2312yes—
433#380C2314yes—
434#380C2314yes—
435#380C2312yes—
436#380C2312yes—
437#380C2314yes—
438C4×C4⋊C4C2314yes—
439C4×C4⋊C4C2314yes—
440C4×C4⋊C4C2318yes—
441C4×C4⋊C4C2318yes—
442C4×C4⋊C4C2318yes—
443C4×C4⋊C4C2314yes—
444C4×C4⋊C4C2314yes—
445C4×C4⋊C4C2318yes—
446C4×C4⋊C4C2312yes—
447C4×C4⋊C4C2312yes—
448C4×C4⋊C4C2314yes—
449C4×C4⋊C4C2314yes—
450C4×C4⋊C4C2318yes—
451C4×C4⋊C4C2318yes—
452C4×C4⋊C4C2314yes—
453C4×C4⋊C4C2314yes—
454C4×C4⋊C4C2312yes—
455C4×C4⋊C4C2311yescharacteristic
456C4×C4⋊C4C2311yescharacteristic
457C4×C4⋊C4C2311yescharacteristic
458C4×C4⋊C4C2311yescharacteristic
459C4×C4⋊C4C2312yes—
460C4×C4⋊C4C2312yes—
461C4×C4⋊C4C2314yes—
462C4×C4⋊C4C2318yes—
463C4×C4⋊C4C2312yes—
464C4×C4⋊C4C2314yes—
465C4×C4⋊C4C2312yes—
466C4×C4⋊C4C2314yes—
467C4×C4⋊C4C2312yes—
468C4×C4⋊C4C2312yes—
469C4×C4⋊C4C2312yes—
470C4×C4⋊C4C2312yes—
471C4×C4⋊C4C2312yes—
472C4×C22⋊C4C2314yes—
473C4×C22⋊C4C2314yes—
474C4×C22⋊C4C2318yes—
475C4×C22⋊C4C2312yes—
476C4×C22⋊C4C2314yes—
477C4×C22⋊C4C2314yes—
478C4×C22⋊C4C2312yes—
479C4×C22⋊C4C2314yes—
480C4×C22⋊C4C2314yes—
481C4×C22⋊C4C2314yes—
482C4×C22⋊C4C2312yes—
483C4×C22⋊C4C2312yes—
484C4×C22⋊C4C2312yes—
485C4×C22⋊C4C2312yes—
486#376C2312yes—
487#376C2312yes—
488#376C2312yes—
489#376C2314yes—
490#376C2318yes—
491C2×#95C2312yes—
492C2×#95C2314yes—
493C2×#95C2314yes—
494C2×#95C2314yes—
495C43C2312yes—
496C43C2312yes—
497C43C2312yes—
498C2×#41—24no—
499C2×#41—24no—
500C2×#41—24no—
501C22×Q8—24no—
502C22×Q8—24no—
503C22×Q8—24no—
504C22×Q8C2412yes—
505C22×Q8C2412yes—
506C22×Q8C2411yescharacteristic
507C22×Q8C2414yes—
508C22×Q8C2414yes—
509C22×D4C2412yes—
510C22×D4C2411yescharacteristic
511C23×C4C2412yes—
512C23×C4C2412yes—
513C23×C4C2412yes—
514C23×C4C2412yes—
515C23×C4C2412yes—
516C23×C4C2412yes—
517C23×C4C2412yes—
518C23×C4C2412yes—
519C23×C4C2412yes—
520C23×C4C2411yescharacteristic
521C23×C4C2411yescharacteristic
522C23×C4C2411yescharacteristic
523C4⋊Q8—28no—
524C4⋊Q8—28no—
525C4⋊Q8—28no—
526C4⋊Q8—48no—
527#126—416no—
528#125—28no—
529#125—28no—
530#125—28no—
531#125—28no—
532#125—28no—
533#125—28no—
534#124—28no—
535#123—216no—
536C22⋊Q8—216no—
537C22⋊Q8—216no—
538C22⋊Q8—216no—
539C4×Q8—28no—
540C4×Q8—28no—
541C4×Q8—28no—
542C4×Q8—28no—
543C4×Q8—24no—
544C4×Q8—24no—
545C4×Q8—216no—
546C4×Q8—216no—
547C4×Q8—416no—
548C4×D4—28no—
549C4×D4—28no—
550C4×D4—24no—
551C4×D4—24no—
552#117—24no—
553#117—24no—
554#117—24no—
555#117—24no—
556#117—24no—
557#117—24no—
558#117—28no—
559#117—48no—
560#117#4118yes—
561C2×C4⋊C4—28no—
562C2×C4⋊C4—24no—
563C2×C4⋊C4—28no—
564C2×C4⋊C4—28no—
565C2×C4⋊C4—24no—
566C2×C4⋊C4—24no—
567C2×C4⋊C4—44no—
568C2×C4⋊C4—48no—
569C2×C4⋊C4C2412yes—
570C2×C4⋊C4C2412yes—
571C2×C4⋊C4C2412yes—
572C2×C4⋊C4C2414yes—
573C2×C4⋊C4C2414yes—
574C2×C4⋊C4C2418yes—
575C2×C4⋊C4C2412yes—
576C2×C4⋊C4C2412yes—
577C2×C4⋊C4C2412yes—
578C2×C4⋊C4C2412yes—
579C2×C4⋊C4C2414yes—
580C2×C4⋊C4C2414yes—
581C2×C4⋊C4C2414yes—
582C2×C4⋊C4C2414yes—
583C2×C4⋊C4C2412yes—
584C2×C4⋊C4C2411yescharacteristic
585C2×C4⋊C4C2411yescharacteristic
586C2×C4⋊C4C2412yes—
587C2×C4⋊C4C2412yes—
588C2×C4⋊C4C2412yes—
589C2×C4⋊C4C2412yes—
590C2×C4⋊C4C2412yes—
591C2×C4⋊C4C2412yes—
592C2×C4⋊C4C2412yes—
593C2×C4⋊C4C2414yes—
594C2×C4⋊C4C2414yes—
595C2×C4⋊C4C2414yes—
596C2×C4⋊C4C2414yes—
597C2×C4⋊C4C2414yes—
598C2×C4⋊C4C2414yes—
599C2×C4⋊C4C2418yes—
600C2×C4⋊C4C2414yes—
601C2×C4⋊C4C2412yes—
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2418yes—
604C2×C4⋊C4C2414yes—
605C2×C4⋊C4C2418yes—
606C2×C4⋊C4C2418yes—
607C2×C4⋊C4C2418yes—
608C2×C4⋊C4C2414yes—
609C2×C4⋊C4C2414yes—
610C2×C4⋊C4C2414yes—
611C2×C4⋊C4C2414yes—
612C2×C4⋊C4C2418yes—
613C2×C4⋊C4C2418yes—
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2414yes—
616C2×C4⋊C4C2412yes—
617C2×C22⋊C4C2412yes—
618C2×C22⋊C4C2412yes—
619C2×C22⋊C4C2412yes—
620C2×C22⋊C4C2412yes—
621C2×C22⋊C4C2412yes—
622C2×C22⋊C4C2414yes—
623C2×C22⋊C4C2412yes—
624C2×C22⋊C4C2412yes—
625C2×C22⋊C4C2412yes—
626C2×C22⋊C4C2418yes—
627C2×C22⋊C4C2414yes—
628C2×C22⋊C4C2418yes—
629C2×C22⋊C4C2418yes—
630C2×C22⋊C4C2414yes—
631C2×C22⋊C4C2414yes—
632C2×C22⋊C4C2418yes—
633C2×C22⋊C4C2412yes—
634C2×C42—28no—
635C2×C42—24no—
636C2×C42—24no—
637C2×C42—28no—
638C2×C42#4118yes—
639C2×C42C2412yes—
640C2×C42C2414yes—
641C2×C42C2412yes—
642C2×C42C2412yes—
643C2×C42C2412yes—
644C2×C42C2412yes—
645C2×C42C2412yes—
646C2×C42C2412yes—
647C2×C42C2412yes—
648C2×C42C2414yes—
649C2×C42C2412yes—
650C2×C42C2412yes—
651C2×C42C2414yes—
652C2×C42C2411yescharacteristic
653C2×C42C2411yescharacteristic
654C2×C42C2411yescharacteristic
655C2×C42C2411yescharacteristic
656C2×C42C2414yes—
657C2×C42C2418yes—
658C2×C42C2418yes—
659C2×C42C2418yes—
660C2×C42C2414yes—
661C2×C42C2414yes—
662C2×C42C2414yes—
663C2×C42C2414yes—
664C2×C42C2418yes—
665C2×C42C2411yescharacteristic
666C2×C42C2412yes—
667C2×C42C2411yescharacteristic
668C2×C42C2411yescharacteristic
669C2×C42C2411yescharacteristic
670#95C2412yes—
671#95C2412yes—
672#95C2418yes—
673#95C2412yes—
674#95C2412yes—
675#95C2418yes—
676#95C2418yes—
677#95C2418yes—
678#95C2418yes—
679#95C2418yes—
680#95C2414yes—
681#95C2414yes—
682#95C2414yes—
683#95C2414yes—
684#95C2414yes—
685#95C2414yes—
686#95C2414yes—
687#95C2414yes—
688#95C2414yes—
689#95C2414yes—
690#95C2418yes—
691#95C2418yes—
692#95C2418yes—
693#95C2418yes—
694#95C2418yes—
695#95C2418yes—
696#95C2418yes—
697#95C2418yes—
698#95C2414yes—
699#95C2414yes—
700#95C2414yes—
701#95C2414yes—
702#95C2418yes—
703#95C2418yes—
704#95C2418yes—
705#95C2418yes—
706#95C2418yes—
707#95C2418yes—
708#95C2418yes—
709#95C2418yes—
710#95C2414yes—
711#95C2414yes—
712#95C2414yes—
713#95C2414yes—
714#95C2418yes—
715#95C2418yes—
716C24C2512yes—
717C24C2511yescharacteristic
718#41—416no—
719C2×Q8—24no—
720C2×Q8—24no—
721C2×Q8—22no—
722C2×Q8—28no—
723C2×Q8—24no—
724C2×Q8—24no—
725C2×Q8—22no—
726C2×Q8—28no—
727C2×Q8—24no—
728C2×Q8—24no—
729C2×Q8—22no—
730C2×Q8—28no—
731C2×Q8—44no—
732C2×Q8—44no—
733C2×Q8—44no—
734C2×Q8—416no—
735C2×D4—24no—
736C2×D4—24no—
737C2×D4—24no—
738C2×D4—22no—
739C2×D4—22no—
740C2×D4—22no—
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—24no—
751C22×C4—24no—
752C22×C4—24no—
753C22×C4—24no—
754C22×C4—24no—
755C22×C4—42no—
756C22×C4—44no—
757C22×C4—42no—
758C22×C4—42no—
759C22×C4—42no—
760C22×C4—44no—
761C22×C4—44no—
762C22×C4—44no—
763C22×C4—42no—
764C22×C4—44no—
765C22×C4C2×#4114yes—
766C22×C4C2×#4114yes—
767C22×C4C2×#4114yes—
768C22×C4C2×#4114yes—
769C22×C42−1+414yes—
770C22×C4C2514yes—
771C22×C4C2512yes—
772C22×C4C2512yes—
773C22×C4C2514yes—
774C22×C4C2514yes—
775C22×C4C2512yes—
776C22×C4C2514yes—
777C22×C4C2514yes—
778C22×C4C2512yes—
779C22×C4C2514yes—
780C22×C4C2514yes—
781C22×C4C2512yes—
782C22×C4C2512yes—
783C22×C4C2514yes—
784C22×C4C2514yes—
785C22×C4C2511yescharacteristic
786C22×C4C2514yes—
787C22×C4C2511yescharacteristic
788C22×C4C2511yescharacteristic
789C22×C4C2511yescharacteristic
790C22×C4C2512yes—
791C22×C4C2511yescharacteristic
792C22×C4C2511yescharacteristic
793C4⋊C4—24no—
794C4⋊C4—24no—
795C4⋊C4—28no—
796C4⋊C4—28no—
797C4⋊C4—28no—
798C4⋊C4—28no—
799C4⋊C4—28no—
800C4⋊C4—28no—
801C4⋊C4—24no—
802C4⋊C4—24no—
803C4⋊C4—24no—
804C4⋊C4—24no—
805C4⋊C4—22no—
806C4⋊C4—22no—
807C4⋊C4—24no—
808C4⋊C4—24no—
809C4⋊C4—24no—
810C4⋊C4—24no—
811C4⋊C4—28no—
812C4⋊C4—28no—
813C4⋊C4—28no—
814C4⋊C4—28no—
815C4⋊C4—28no—
816C4⋊C4—28no—
817C4⋊C4—216no—
818C4⋊C4—24no—
819C4⋊C4—24no—
820C4⋊C4—24no—
821C4⋊C4—24no—
822C4⋊C4—216no—
823C4⋊C4—24no—
824C4⋊C4—28no—
825C4⋊C4—42no—
826C4⋊C4—42no—
827C4⋊C4—48no—
828C4⋊C4—44no—
829C4⋊C4—44no—
830C4⋊C4—48no—
831C4⋊C4—44no—
832C4⋊C4—48no—
833C4⋊C4—44no—
834C4⋊C4—44no—
835C4⋊C4—48no—
836C4⋊C4—48no—
837C4⋊C4—48no—
838C4⋊C4—44no—
839C4⋊C4—44no—
840C4⋊C4C2×#4118yes—
841C22⋊C4—24no—
842C22⋊C4—24no—
843C22⋊C4—24no—
844C22⋊C4—24no—
845C22⋊C4—24no—
846C22⋊C4—24no—
847C22⋊C4—24no—
848C22⋊C4—24no—
849C22⋊C4—216no—
850C22⋊C4—28no—
851C22⋊C4—44no—
852C22⋊C4—44no—
853C22⋊C4—48no—
854C22⋊C4—44no—
855C22⋊C4—48no—
856C22⋊C4—48no—
857C22⋊C4C2×#4118yes—
858C42—24no—
859C42—24no—
860C42—24no—
861C42—24no—
862C42—28no—
863C42—28no—
864C42—24no—
865C42—22no—
866C42—22no—
867C42—22no—
868C42—22no—
869C42—24no—
870C42—24no—
871C42—24no—
872C42—24no—
873C42—24no—
874C42—28no—
875C42—44no—
876C42—48no—
877C42—44no—
878C42—44no—
879C42—44no—
880C42—48no—
881C42—48no—
882C42—48no—
883C42—44no—
884C42C2×#4114yes—
885C42C2×#4114yes—
886C42C2×#4114yes—
887C42C2×#4114yes—
888C42C2×#4118yes—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—22no—
894C23—24no—
895C23—24no—
896C23C22×#4112yes—
897C23C22×#4112yes—
898C23C2×2−1+412yes—
899C23C2611yescharacteristic
900Q8—416no—
901Q8—48no—
902Q8—48no—
903Q8—44no—
904Q8—88no—
905D4—48no—
906D4—44no—
907C2×C4—22no—
908C2×C4—24no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—24no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—24no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—24no—
923C2×C4—24no—
924C2×C4—24no—
925C2×C4—24no—
926C2×C4—24no—
927C2×C4—24no—
928C2×C4—22no—
929C2×C4—24no—
930C2×C4—24no—
931C2×C4—24no—
932C2×C4—22no—
933C2×C4—24no—
934C2×C4—24no—
935C2×C4—24no—
936C2×C4—24no—
937C2×C4—22no—
938C2×C4—24no—
939C2×C4—28no—
940C2×C4—24no—
941C2×C4—24no—
942C2×C4—28no—
943C2×C4—22no—
944C2×C4—22no—
945C2×C4—24no—
946C2×C4—22no—
947C2×C4—24no—
948C2×C4—24no—
949C2×C4—28no—
950C2×C4—24no—
951C2×C4—22no—
952C2×C4—24no—
953C2×C4—22no—
954C2×C4—24no—
955C2×C4—44no—
956C2×C4—44no—
957C2×C4—48no—
958C2×C4—48no—
959C2×C4—48no—
960C2×C4—48no—
961C2×C4—84no—
962C2×C4—84no—
963C2×C4—84no—
964C2×C4—84no—
965C2×C4—84no—
966C2×C4#556116yes—
967C2×C4C22×#4112yes—
968C2×C4C22×#4112yes—
969C2×C4C22×#4112yes—
970C2×C4C22×#4112yes—
971C2×C4C22×#4118yes—
972C2×C4C22×#4112yes—
973C2×C4C22×#4112yes—
974C2×C4C22×#4112yes—
975C2×C4C22×#4112yes—
976C2×C4C2×2−1+412yes—
977C2×C4C2×2−1+412yes—
978C2×C4#58514yes—
979C22—24no—
980C22—22no—
981C22—22no—
982C22—24no—
983C22—44no—
984C22—42no—
985C22—42no—
986C22—44no—
987C22—42no—
988C22C2×#55614yes—
989C22C23×#4111yescharacteristic
990C22C23×#4111yescharacteristic
991C22C22×2−1+411yescharacteristic
992C22C2×#58512yes—
993C222−1+612yes—
994C4—24no—
995C4—28no—
996C4—22no—
997C4—22no—
998C4—22no—
999C4—22no—
1000C4—42no—
1001C4—42no—
1002C4—42no—
1003C4—44no—
1004C4—44no—
1005C4—42no—
1006C4—44no—
1007C4—44no—
1008C4—42no—
1009C4—44no—
1010C4—44no—
1011C4—44no—
1012C4—44no—
1013C4—42no—
1014C4—44no—
1015C4C2×#55614yes—
1016C4C2×#55614yes—
1017C2—24no—
1018C2—82no—
1019C2C22×#55611yescharacteristic
1020C2#6281511yescharacteristic
1021C2#6286011yescharacteristic
1022C2#6295612yes—
1023C2#6299312yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC22×#41C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59876C2semidirect
2. #59443C2semidirect
3. #59241C2semidirect
4. #45370C2semidirect
5. #45152C2semidirect
6. #43058C2semidirect
7. #39299C2semidirect
8. #39294C2semidirect
9. #39153C2semidirect
10. #36512C2semidirect
16. #35313C2semidirect
17. #35313C2semidirect
18. #34938C2semidirect
19. C2×#2565C2semidirect
20. #34217C2semidirect
21. #34215C2semidirect
22. #34214C2semidirect
23. #34187C2semidirect

Maximal subgroups

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

subgroupindex
#598762
#594432
#592412
#453702
#451522
#430582
#392992
#392942
#391532
#365122
#356292
#356282
#355572
#353332
#353132
#349382
C2×#25652
#342172
#342152
#342142
#341872
#341212
C4×#5362