Finite Group Databasebeta

← #7630724

Subgroups — #7630724

Order 512.

5118 conjugacy classes of subgroups.

The subgroup lattice has 1050 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36073C214yesmaximal, complemented
2#36069C214yesmaximal, complemented
3#36006C214yesmaximal, complemented
4#36000C214yesmaximal, complemented
5#35993C214yesmaximal, complemented
6#35989C214yesmaximal, complemented
7#35984C214yesmaximal, complemented
8#35978C214yesmaximal, complemented
9#35224C211yesmaximal, characteristic, complemented
10#35223C211yesmaximal, characteristic
11#35160C212yesmaximal, complemented
12#35159C211yesmaximal, characteristic, complemented
13#35158C211yesmaximal, characteristic, complemented
14#35098C214yesmaximal, complemented
15#35034C214yesmaximal, complemented
16#35023C214yesmaximal, complemented
17#34635C212yesmaximal, complemented
18#34584C214yesmaximal, complemented
19#34274C211yesmaximal, characteristic, complemented
20#34271C211yesmaximal, characteristic, complemented
21#34252C212yesmaximal, complemented
22#34201C212yesmaximal, complemented
23C2×#2274C211yesmaximal, characteristic, complemented
24C2×#544C2211yescharacteristic
25C2×#537C2211yescharacteristic
26C2×#525C2212yes—
27C2×#520C2212yes—
28C22×#117C2211yescharacteristic
29C22×#117C2211yescharacteristic
30C23×C4⋊C4C2211yescharacteristic
31#2852C2218yes—
32#2851C2214yes—
33#2850C2214yes—
34#2848C2214yes—
35#2847C2214yes—
36#2655C2218yescomplemented
37#2654C2218yescomplemented
38#2651C2218yescomplemented
39#2650C2218yescomplemented
40#2646C2214yes—
41#2643C2218yes—
42#2639C2214yes—
43#2627C2214yes—
44#2625C2212yes—
45#2625C2212yes—
46#2625C2212yes—
47#2625C2212yes—
48#2624C2212yes—
49#2624C2212yes—
50#2624C2212yes—
51#2624C2212yes—
52#2623C2214yes—
53#2623C2214yes—
54#2622C2214yes—
55#2622C2214yes—
56#2618C2214yes—
57#2597C2218yes—
58#2595C2218yes—
59#2578C2218yes—
60#2578C2218yes—
61#2577C2218yes—
62#2576C2218yes—
63#2560C2218yes—
64#2559C2218yes—
65#2531C2218yes—
66#2530C2218yes—
67#2525C2218yescomplemented
68#2524C2218yescomplemented
69#2522C2218yescomplemented
70#2521C2218yescomplemented
71#2520C2218yescomplemented
72#2519C2218yescomplemented
73#2516C2218yescomplemented
74#2515C2218yescomplemented
75#2514C2214yescomplemented
76#2513C2214yescomplemented
77#2512C2214yescomplemented
78#2511C2214yescomplemented
79#2509C2214yescomplemented
80#2508C2214yescomplemented
81#2507C2214yescomplemented
82#2506C2214yescomplemented
83#2497C2214yescomplemented
84#2496C2214yescomplemented
85#2495C2214yes—
86#2495C2214yescomplemented
87#2494C2214yes—
88#2494C2214yescomplemented
89#2492C2214yescomplemented
90#2491C2214yescomplemented
91#2490C2214yes—
92#2490C2214yescomplemented
93#2489C2214yes—
94#2489C2214yescomplemented
95#2477C2218yes—
96#2476C2218yes—
97#2442C2214yes—
98#2442C2214yes—
99#2440C2214yes—
100#2440C2214yes—
101#2427C2214yes—
102#2426C2214yes—
103#2421C2214yes—
104#2420C2214yes—
105#2417C2214yes—
106#2417C2214yes—
107#2416C2214yes—
108#2416C2214yes—
109#2402C2218yescomplemented
110#2401C2218yescomplemented
111#2396C2218yescomplemented
112#2395C2214yes—
113#2395C2214yes—
114#2395C2214yes—
115#2395C2214yes—
116#2395C2218yescomplemented
117#2370C2214yescomplemented
118#2370C2214yescomplemented
119#2369C2214yescomplemented
120#2365C2214yescomplemented
121#2363C2214yes—
122#2363C2214yes—
123#2363C2214yescomplemented
124#2362C2214yes—
125#2362C2214yes—
126#2362C2214yescomplemented
127#2361C2214yescomplemented
128#2360C2214yescomplemented
129#2357C2214yescomplemented
130#2356C2214yescomplemented
131#2355C2214yescomplemented
132#2354C2214yes—
133#2354C2214yes—
134#2354C2214yescomplemented
135#2352C2214yes—
136#2352C2214yes—
137#2347C2214yescomplemented
138#2346C2214yescomplemented
139#2345C2214yescomplemented
140#2344C2214yescomplemented
141#2329C2214yes—
142#2325C2214yes—
143#2321C2218yes—
144#2318C2218yes—
145#2317C2212yes—
146#2317C2212yes—
147#2316C2211yescharacteristic
148#2316C2211yescharacteristic
149#2311C2212yes—
150#2311C2212yes—
151C4×C22⋊Q8C2214yes—
152C4×#123C2218yes—
153C4×#121C2214yes—
154#2297C2212yes—
155#2297C2212yes—
156#2296C2212yes—
157#2296C2212yes—
158#2290C2218yes—
159#2280C2212yes—
160#2274C2214yes—
161#2274C2214yes—
162#2274C2214yes—
163#2274C2212yes—
164#2274C2214yes—
165C2×C4×C4⋊C4C2212yes—
166C2×C4×C4⋊C4C2212yes—
167C2×C4×C4⋊C4C2211yescharacteristic
168C2×C4×C4⋊C4C2211yescharacteristic
169C2×C4×C4⋊C4C2211yescharacteristic
170C2×C4×C4⋊C4C2211yescharacteristic
171C2×C4×C22⋊C4C2212yes—
172C2×C4×C22⋊C4C2212yes—
173C22×#41C2312yes—
174C24×C4C2311yescharacteristic
175C24×C4C2312yes—
176#544—28no—
177#537—28no—
178C2×C4⋊Q8C2314yes—
179C2×#126C2318yes—
180C2×#125C2314yes—
181C2×#125C2314yes—
182C2×#124C2314yes—
183#525—216no—
184C2×#123C2314yes—
185C2×C22⋊Q8C2314yes—
186C2×C22⋊Q8C2314yes—
187C2×C22⋊Q8C2312yes—
188C2×C22⋊Q8C2312yes—
189C2×C22⋊Q8C2314yes—
190C2×C22⋊Q8C2314yes—
191C2×#121C2314yes—
192C2×#121C2314yes—
193C2×#121C2312yes—
194C2×#121C2312yes—
195C2×#121C2314yes—
196C2×#121C2314yes—
197C2×#120C2314yes—
198#520—216no—
199C2×C4×Q8C2314yes—
200C2×C4×Q8C2314yes—
201C2×C4×D4C2318yes—
202C2×C4×D4C2314yes—
203C2×C4×D4C2314yes—
204C2×C4×D4C2314yes—
205C2×C4×D4C2314yes—
206C2×#117—28no—
207C2×#117—28no—
208C2×#117C2312yes—
209C2×#117C2312yes—
210C2×#117C2312yes—
211C2×#117C2314yes—
212C2×#117C2314yes—
213C2×#117C2314yes—
214C2×#117C2312yes—
215C2×#117C2312yes—
216C2×#117C2312yes—
217C2×#117C2312yes—
218C2×#117C2318yes—
219C22×C4⋊C4—28no—
220C22×C4⋊C4C2311yescharacteristic
221C22×C4⋊C4C2311yescharacteristic
222C22×C4⋊C4C2314yes—
223C22×C4⋊C4C2312yes—
224C22×C4⋊C4C2311yescharacteristic
225C22×C4⋊C4C2311yescharacteristic
226C22×C4⋊C4C2314yes—
227C22×C4⋊C4C2314yes—
228C22×C4⋊C4C2311yescharacteristic
229C22×C4⋊C4C2311yescharacteristic
230C22×C22⋊C4C2312yes—
231C22×C22⋊C4C2311yescharacteristic
232C22×C22⋊C4C2311yescharacteristic
233C22×C42C2311yescharacteristic
234C22×C42C2311yescharacteristic
235C22×C42C2312yes—
236C22×C42C2312yes—
237C22×C42C2312yes—
238C22×C42C2312yes—
239C22×C42C2312yes—
240#401C2318yes—
241#400C2318yes—
242#400C2318yes—
243#400C2318yes—
244#400C2318yes—
245#400C2318yes—
246#400C2314yes—
247#400C2314yes—
248#400C2314yes—
249#400C2314yes—
250#400C2318yes—
251#400C2318yes—
252#399C2314yes—
253#399C2314yes—
254#399C2314yes—
255#399C2314yes—
256#398C2318yes—
257#398C2318yes—
258#398C2318yes—
259#398C2314yes—
260#398C2314yes—
261#398C2314yes—
262#398C2314yes—
263#398C2318yes—
264#398C2318yes—
265#397C2314yes—
266#397C2314yes—
267#397C2314yes—
268#397C2314yes—
269#397C2314yes—
270#397C2314yes—
271#397C2318yes—
272#397C2318yes—
273#397C2314yes—
274#397C2318yes—
275#397C2314yes—
276#397C2318yes—
277#397C2314yes—
278#397C2314yes—
279#397C2314yes—
280#397C2314yes—
281#396C2318yes—
282#396C2318yes—
283#396C2318yes—
284#395C2318yes—
285#394C2314yes—
286#394C2314yes—
287#394C2314yes—
288#394C2314yes—
289#394C2314yes—
290#394C2314yes—
291#394C2318yes—
292#394C2314yes—
293#394C2314yes—
294#394C2318yes—
295#393C2318yes—
296#391C2318yes—
297#391C2314yes—
298#391C2314yes—
299#391C2314yes—
300#391C2312yes—
301#391C2312yes—
302#391C2312yes—
303#391C2312yes—
304#391C2314yes—
305#390C2318yes—
306#390C2314yes—
307#390C2314yes—
308#390C2318yes—
309#390C2314yes—
310#390C2312yes—
311#390C2312yes—
312#390C2312yes—
313#390C2312yes—
314#390C2314yes—
315#389C2314yes—
316#389C2314yes—
317#389C2314yes—
318#389C2314yes—
319#389C2314yes—
320#389C2314yes—
321#389C2314yes—
322#389C2314yes—
323#389C2318yes—
324#389C2314yes—
325#389C2314yes—
326#389C2312yes—
327#389C2312yes—
328#389C2312yes—
329#389C2312yes—
330#389C2314yes—
331#389C2312yes—
332#389C2312yes—
333#389C2312yes—
334#389C2312yes—
335#389C2314yes—
336#388C2318yes—
337#388C2318yes—
338#388C2318yes—
339#388C2318yes—
340#388C2318yes—
341#388C2318yes—
342#388C2318yes—
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#386C2318yes—
369#386C2318yes—
370#386C2318yes—
371#386C2314yes—
372#386C2318yes—
373#386C2318yes—
374#386C2318yes—
375#386C2314yes—
376#386C2318yes—
377#386C2314yes—
378#386C2314yes—
379#385C2318yes—
380#385C2318yes—
381#385C2314yes—
382#385C2318yes—
383#385C2318yes—
384#385C2318yes—
385#385C2314yes—
386#385C2314yes—
387#385C2314yes—
388#384C2314yes—
389#384C2314yes—
390#383C2318yes—
391#383C2318yes—
392#382C2314yes—
393#382C2314yes—
394#382C2318yes—
395#382C2314yes—
396#382C2314yes—
397#381C2318yes—
398#381C2314yes—
399#380C2314yes—
400#380C2314yes—
401#380C2314yes—
402#380C2314yes—
403#380C2314yes—
404#380C2314yes—
405#380C2318yes—
406#380C2314yes—
407#380C2314yes—
408#380C2314yes—
409#380C2314yes—
410#380C2312yes—
411#380C2312yes—
412#380C2312yes—
413#380C2312yes—
414#379C2314yes—
415C4×C4⋊C4C2318yes—
416C4×C4⋊C4C2318yes—
417C4×C4⋊C4C2314yes—
418C4×C4⋊C4C2314yes—
419C4×C4⋊C4C2314yes—
420C4×C4⋊C4C2314yes—
421C4×C4⋊C4C2314yes—
422C4×C4⋊C4C2314yes—
423C4×C4⋊C4C2318yes—
424C4×C4⋊C4C2318yes—
425C4×C4⋊C4C2314yes—
426C4×C4⋊C4C2314yes—
427C4×C4⋊C4C2314yes—
428C4×C4⋊C4C2314yes—
429C4×C4⋊C4C2314yes—
430C4×C4⋊C4C2314yes—
431C4×C4⋊C4C2314yes—
432C4×C4⋊C4C2314yes—
433C4×C4⋊C4C2318yes—
434C4×C4⋊C4C2318yes—
435C4×C4⋊C4C2314yes—
436C4×C4⋊C4C2314yes—
437C4×C4⋊C4C2314yes—
438C4×C4⋊C4C2314yes—
439C4×C4⋊C4C2318yes—
440C4×C4⋊C4C2318yes—
441C4×C22⋊C4C2318yes—
442C4×C22⋊C4C2318yes—
443C4×C22⋊C4C2314yes—
444C4×C22⋊C4C2318yes—
445C4×C22⋊C4C2318yes—
446C4×C22⋊C4C2314yes—
447C4×C22⋊C4C2318yes—
448C4×C22⋊C4C2314yes—
449C4×C22⋊C4C2314yes—
450C4×C22⋊C4C2314yes—
451C4×C22⋊C4C2314yes—
452C4×C22⋊C4C2318yes—
453C4×C22⋊C4C2318yes—
454C4×C22⋊C4C2314yes—
455C4×C22⋊C4C2314yes—
456C4×C22⋊C4C2314yes—
457C4×C22⋊C4C2314yes—
458#376C2318yes—
459C2×#95C2312yes—
460C2×#95C2312yes—
461C2×#95C2312yes—
462C2×#95C2312yes—
463C25C2411yescharacteristic
464C2×#41—28no—
465C2×#41—28no—
466C2×#41—28no—
467C22×Q8C2412yes—
468C22×Q8C2414yes—
469C22×D4C2414yes—
470C22×D4C2412yes—
471C22×D4C2414yes—
472C22×D4C2414yes—
473C22×D4C2414yes—
474C23×C4—24no—
475C23×C4—24no—
476C23×C4—28no—
477C23×C4—82no—
478C23×C4—82no—
479C23×C4#4118yes—
480C23×C4C2414yes—
481C23×C4C2411yescharacteristic
482C23×C4C2412yes—
483C23×C4C2412yes—
484C23×C4C2412yes—
485C23×C4C2411yescharacteristic
486C23×C4C2411yescharacteristic
487C23×C4C2411yescharacteristic
488C23×C4C2411yescharacteristic
489C23×C4C2414yes—
490C23×C4C2414yes—
491C23×C4C2412yes—
492C23×C4C2418yes—
493C23×C4C2412yes—
494C23×C4C2412yes—
495C23×C4C2411yescharacteristic
496C4⋊Q8—216no—
497#126—88no—
498#125—216no—
499#125—84no—
500#124—84no—
501#123—216no—
502C22⋊Q8—28no—
503C22⋊Q8—28no—
504C22⋊Q8—216no—
505C22⋊Q8—216no—
506C22⋊Q8—84no—
507C22⋊Q8—84no—
508#121—28no—
509#121—28no—
510#121—216no—
511#121—216no—
512#121—84no—
513#121—84no—
514#120—216no—
515C4×Q8—216no—
516C4×Q8—84no—
517C4×D4—232no—
518C4×D4—216no—
519C4×D4—216no—
520C4×D4—216no—
521C4×D4—84no—
522#117—28no—
523#117—28no—
524#117—28no—
525#117—28no—
526#117—28no—
527#117—28no—
528#117—28no—
529#117—216no—
530#117—216no—
531#117—216no—
532#117—88no—
533C2×C4⋊C4—28no—
534C2×C4⋊C4—24no—
535C2×C4⋊C4—24no—
536C2×C4⋊C4—24no—
537C2×C4⋊C4—24no—
538C2×C4⋊C4—216no—
539C2×C4⋊C4—216no—
540C2×C4⋊C4—216no—
541C2×C4⋊C4#4118yes—
542C2×C4⋊C4#4118yes—
543C2×C4⋊C4C2414yes—
544C2×C4⋊C4C2418yes—
545C2×C4⋊C4C2412yes—
546C2×C4⋊C4C2414yes—
547C2×C4⋊C4C2412yes—
548C2×C4⋊C4C2412yes—
549C2×C4⋊C4C2412yes—
550C2×C4⋊C4C2412yes—
551C2×C4⋊C4C2418yes—
552C2×C4⋊C4C2412yes—
553C2×C4⋊C4C2412yes—
554C2×C4⋊C4C2412yes—
555C2×C4⋊C4C2412yes—
556C2×C4⋊C4C2412yes—
557C2×C4⋊C4C2414yes—
558C2×C4⋊C4C2414yes—
559C2×C4⋊C4C2414yes—
560C2×C4⋊C4C2414yes—
561C2×C4⋊C4C2418yes—
562C2×C4⋊C4C2414yes—
563C2×C4⋊C4C2418yes—
564C2×C4⋊C4C2414yes—
565C2×C4⋊C4C2414yes—
566C2×C4⋊C4C2414yes—
567C2×C4⋊C4C2414yes—
568C2×C4⋊C4C2414yes—
569C2×C4⋊C4C2418yes—
570C2×C4⋊C4C2414yes—
571C2×C4⋊C4C2418yes—
572C2×C4⋊C4C2414yes—
573C2×C4⋊C4C2414yes—
574C2×C4⋊C4C2414yes—
575C2×C4⋊C4C2414yes—
576C2×C4⋊C4C2418yes—
577C2×C4⋊C4C2414yes—
578C2×C4⋊C4C2414yes—
579C2×C4⋊C4C2414yes—
580C2×C22⋊C4—24no—
581C2×C22⋊C4—24no—
582C2×C22⋊C4—28no—
583C2×C22⋊C4C2414yes—
584C2×C22⋊C4C2414yes—
585C2×C22⋊C4C2412yes—
586C2×C22⋊C4C2411yescharacteristic
587C2×C22⋊C4C2412yes—
588C2×C22⋊C4C2411yescharacteristic
589C2×C22⋊C4C2411yescharacteristic
590C2×C22⋊C4C2411yescharacteristic
591C2×C22⋊C4C2414yes—
592C2×C22⋊C4C2418yes—
593C2×C22⋊C4C2414yes—
594C2×C22⋊C4C2414yes—
595C2×C22⋊C4C2414yes—
596C2×C22⋊C4C2414yes—
597C2×C22⋊C4C2414yes—
598C2×C22⋊C4C2414yes—
599C2×C22⋊C4C2418yes—
600C2×C22⋊C4C2414yes—
601C2×C22⋊C4C2418yes—
602C2×C22⋊C4C2414yes—
603C2×C22⋊C4C2418yes—
604C2×C22⋊C4C2414yes—
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×C42—28no—
617C2×C42—24no—
618C2×C42—24no—
619C2×C42—82no—
620C2×C42—82no—
621C2×C42—82no—
622C2×C42—82no—
623C2×C42C2418yes—
624C2×C42C2412yes—
625C2×C42C2412yes—
626C2×C42C2412yes—
627C2×C42C2412yes—
628C2×C42C2414yes—
629C2×C42C2418yes—
630C2×C42C2414yes—
631C2×C42C2414yes—
632C2×C42C2418yes—
633C2×C42C2418yes—
634C2×C42C2414yes—
635C2×C42C2414yes—
636C2×C42C2414yes—
637C2×C42C2414yes—
638C2×C42C2418yes—
639C2×C42C2418yes—
640#95C2414yes—
641#95C2414yes—
642#95C2418yes—
643#95C2418yes—
644#95C2414yes—
645#95C2414yes—
646#95C2414yes—
647#95C2414yes—
648#95C2418yes—
649#95C2418yes—
650#95C2414yes—
651#95C2414yes—
652#95C2414yes—
653#95C2414yes—
654#95C2414yes—
655#95C2414yes—
656#95C2418yes—
657#95C2418yes—
658#95C2414yes—
659#95C2414yes—
660#95C2418yes—
661#95C2418yes—
662#95C2414yes—
663#95C2418yes—
664#95C2414yes—
665#95C2418yes—
666#95C2414yes—
667#95C2414yes—
668#95C2414yes—
669#95C2414yes—
670#95C2418yes—
671#95C2418yes—
672#95C2418yes—
673#95C2418yes—
674#95C2414yes—
675#95C2414yes—
676#95C2414yes—
677#95C2414yes—
678C24—22no—
679C24—22no—
680C24—41no—
681C24—41no—
682C24—41no—
683C24—41no—
684C24C2×#4114yes—
685C24C2514yes—
686C24C2511yescharacteristic
687C24C2511yescharacteristic
688C24C2511yescharacteristic
689#41—432no—
690C2×Q8—24no—
691C2×Q8—24no—
692C2×Q8—24no—
693C2×Q8—28no—
694C2×Q8—44no—
695C2×Q8—44no—
696C2×D4—28no—
697C2×D4—28no—
698C2×D4—28no—
699C2×D4—28no—
700C2×D4—28no—
701C2×D4—24no—
702C2×D4—24no—
703C2×D4—24no—
704C2×D4—28no—
705C2×D4—44no—
706C2×D4—44no—
707C2×D4—44no—
708C2×D4—44no—
709C2×D4—44no—
710C2×D4—44no—
711C22×C4—22no—
712C22×C4—22no—
713C22×C4—232no—
714C22×C4—24no—
715C22×C4—24no—
716C22×C4—24no—
717C22×C4—24no—
718C22×C4—22no—
719C22×C4—22no—
720C22×C4—22no—
721C22×C4—22no—
722C22×C4—24no—
723C22×C4—24no—
724C22×C4—28no—
725C22×C4—28no—
726C22×C4—28no—
727C22×C4—28no—
728C22×C4—28no—
729C22×C4—216no—
730C22×C4—42no—
731C22×C4—41no—
732C22×C4—41no—
733C22×C4—42no—
734C22×C4—41no—
735C22×C4—41no—
736C22×C4—42no—
737C22×C4—42no—
738C22×C4—42no—
739C22×C4—42no—
740C22×C4—42no—
741C22×C4—41no—
742C22×C4—41no—
743C22×C4—42no—
744C22×C4—41no—
745C22×C4—41no—
746C22×C4—48no—
747C22×C4—44no—
748C22×C4—44no—
749C22×C4—44no—
750C22×C4—44no—
751C22×C4—48no—
752C22×C4—816no—
753C22×C4C2×#4114yes—
754C22×C4C2×#4118yes—
755C22×C4C2×#4118yes—
756C22×C4C2×#4118yes—
757C22×C4C2×#4118yes—
758C22×C4C2×#4114yes—
759C22×C4C2×#4114yes—
760C22×C4C2×#4114yes—
761C22×C4C2514yes—
762C22×C4C2514yes—
763C22×C4C2514yes—
764C22×C4C2511yescharacteristic
765C22×C4C2511yescharacteristic
766C22×C4C2512yes—
767C22×C4C2512yes—
768C22×C4C2514yes—
769C22×C4C2511yescharacteristic
770C22×C4C2511yescharacteristic
771C22×C4C2514yes—
772C22×C4C2514yes—
773C22×C4C2514yes—
774C22×C4C2514yes—
775C22×C4C2514yes—
776C22×C4C2514yes—
777C22×C4C2512yes—
778C22×C4C2514yes—
779C22×C4C2512yes—
780C4⋊C4—216no—
781C4⋊C4—28no—
782C4⋊C4—24no—
783C4⋊C4—24no—
784C4⋊C4—24no—
785C4⋊C4—24no—
786C4⋊C4—24no—
787C4⋊C4—28no—
788C4⋊C4—216no—
789C4⋊C4—24no—
790C4⋊C4—24no—
791C4⋊C4—24no—
792C4⋊C4—24no—
793C4⋊C4—24no—
794C4⋊C4—28no—
795C4⋊C4—28no—
796C4⋊C4—28no—
797C4⋊C4—28no—
798C4⋊C4—216no—
799C4⋊C4—44no—
800C4⋊C4—44no—
801C4⋊C4—44no—
802C4⋊C4—44no—
803C4⋊C4—48no—
804C4⋊C4—44no—
805C4⋊C4—48no—
806C4⋊C4—44no—
807C4⋊C4—44no—
808C4⋊C4—44no—
809C4⋊C4—44no—
810C4⋊C4—44no—
811C4⋊C4—48no—
812C4⋊C4—44no—
813C4⋊C4—48no—
814C4⋊C4—44no—
815C4⋊C4C2×#41116yes—
816C4⋊C4C2×#41116yes—
817C22⋊C4—24no—
818C22⋊C4—22no—
819C22⋊C4—24no—
820C22⋊C4—22no—
821C22⋊C4—22no—
822C22⋊C4—22no—
823C22⋊C4—28no—
824C22⋊C4—28no—
825C22⋊C4—28no—
826C22⋊C4—28no—
827C22⋊C4—28no—
828C22⋊C4—28no—
829C22⋊C4—28no—
830C22⋊C4—216no—
831C22⋊C4—28no—
832C22⋊C4—28no—
833C22⋊C4—216no—
834C22⋊C4—44no—
835C22⋊C4—44no—
836C22⋊C4—44no—
837C22⋊C4—44no—
838C22⋊C4—48no—
839C22⋊C4—44no—
840C22⋊C4—44no—
841C22⋊C4—44no—
842C22⋊C4—48no—
843C22⋊C4—44no—
844C22⋊C4—48no—
845C22⋊C4—44no—
846C22⋊C4—44no—
847C22⋊C4—44no—
848C22⋊C4—48no—
849C22⋊C4—44no—
850C42—216no—
851C42—24no—
852C42—24no—
853C42—24no—
854C42—24no—
855C42—28no—
856C42—216no—
857C42—28no—
858C42—28no—
859C42—48no—
860C42—44no—
861C42—44no—
862C42—44no—
863C42—44no—
864C42—48no—
865C42—48no—
866C42—48no—
867C23—21no—
868C23—21no—
869C23—21no—
870C23—21no—
871C23—21no—
872C23—21no—
873C23—21no—
874C23—21no—
875C23—21no—
876C23—21no—
877C23—21no—
878C23—21no—
879C23—21no—
880C23—21no—
881C23—21no—
882C23—21no—
883C23—28no—
884C23—24no—
885C23—24no—
886C23—24no—
887C23—24no—
888C23—24no—
889C23—24no—
890C23—24no—
891C23—44no—
892C23—44no—
893C23—44no—
894C23—44no—
895C23—44no—
896C23—44no—
897C23C22×#4112yes—
898C23C22×#4112yes—
899C23C22×#4112yes—
900C23C22×#4112yes—
901C23C22×#4112yes—
902C23C2611yescharacteristic
903Q8—48no—
904Q8—88no—
905D4—416no—
906D4—48no—
907D4—88no—
908D4—88no—
909D4—88no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—24no—
913C2×C4—24no—
914C2×C4—24no—
915C2×C4—24no—
916C2×C4—28no—
917C2×C4—216no—
918C2×C4—216no—
919C2×C4—24no—
920C2×C4—24no—
921C2×C4—21no—
922C2×C4—21no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—21no—
926C2×C4—21no—
927C2×C4—24no—
928C2×C4—24no—
929C2×C4—24no—
930C2×C4—24no—
931C2×C4—24no—
932C2×C4—24no—
933C2×C4—24no—
934C2×C4—24no—
935C2×C4—24no—
936C2×C4—21no—
937C2×C4—21no—
938C2×C4—24no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—21no—
942C2×C4—21no—
943C2×C4—24no—
944C2×C4—24no—
945C2×C4—24no—
946C2×C4—24no—
947C2×C4—24no—
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—22no—
959C2×C4—22no—
960C2×C4—24no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—24no—
964C2×C4—48no—
965C2×C4—48no—
966C2×C4—48no—
967C2×C4—44no—
968C2×C4—44no—
969C2×C4—44no—
970C2×C4—44no—
971C2×C4—48no—
972C2×C4—416no—
973C2×C4—816no—
974C2×C4—88no—
975C2×C4—88no—
976C2×C4#529116yes—
977C2×C4C22×#4118yes—
978C2×C4C22×#4114yes—
979C2×C4C22×#4118yes—
980C2×C4C22×#4114yes—
981C2×C4C22×#4114yes—
982C2×C4C22×#4114yes—
983C22—22no—
984C22—22no—
985C22—22no—
986C22—22no—
987C22—22no—
988C22—22no—
989C22—22no—
990C22—22no—
991C22—22no—
992C22—22no—
993C22—22no—
994C22—22no—
995C22—416no—
996C22—41no—
997C22—41no—
998C22—41no—
999C22—41no—
1000C22—41no—
1001C22—41no—
1002C22—41no—
1003C22—41no—
1004C22—44no—
1005C22—44no—
1006C22—44no—
1007C22—44no—
1008C22—44no—
1009C22—44no—
1010C22—44no—
1011C22C2×#52914yes—
1012C22C23×#4111yescharacteristic
1013C22C23×#4111yescharacteristic
1014C22C23×#4111yescharacteristic
1015C22H(7,𝔽2)11yescharacteristic
1016C22H(7,𝔽2)11yescharacteristic
1017C222−1+611yescharacteristic
1018C222−1+611yescharacteristic
1019C4—28no—
1020C4—28no—
1021C4—24no—
1022C4—44no—
1023C4—44no—
1024C4—44no—
1025C4—44no—
1026C4—44no—
1027C4—44no—
1028C4—41no—
1029C4—41no—
1030C4—42no—
1031C4—42no—
1032C4—41no—
1033C4—41no—
1034C4—44no—
1035C4—44no—
1036C4—44no—
1037C4C2×#52918yes—
1038C2—24no—
1039C2—42no—
1040C2—42no—
1041C2—84no—
1042C2C22×#52911yescharacteristic
1043C2#6284611yescharacteristic
1044C2#6284711yescharacteristic
1045C2#6285011yescharacteristic
1046C2#6285111yescharacteristic
1047C2#6285611yescharacteristic
1048C2#6285611yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35223C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #36073C2semidirect
2. #36069C2semidirect
3. #36006C2semidirect
4. #36000C2semidirect
5. #35993C2semidirect
6. #35989C2semidirect
7. #35984C2semidirect
8. #35978C2semidirect
9. #35224C2semidirect
11. #35160C2semidirect
12. #35159C2semidirect
13. #35158C2semidirect
14. #35098C2semidirect
15. #35034C2semidirect
16. #35023C2semidirect
17. #34635C2semidirect
18. #34584C2semidirect
19. #34274C2semidirect
20. #34271C2semidirect
21. #34252C2semidirect
22. #34201C2semidirect
23. C2×#2274C2semidirect
36. #2655C22semidirect
37. #2654C22semidirect
38. #2651C22semidirect
39. #2650C22semidirect
67. #2525C22semidirect
68. #2524C22semidirect
69. #2522C22semidirect
70. #2521C22semidirect
71. #2520C22semidirect
72. #2519C22semidirect
73. #2516C22semidirect
74. #2515C22semidirect
75. #2514C22semidirect
76. #2513C22semidirect
77. #2512C22semidirect
78. #2511C22semidirect
79. #2509C22semidirect
80. #2508C22semidirect
81. #2507C22semidirect
82. #2506C22semidirect
83. #2497C22semidirect
84. #2496C22semidirect
86. #2495C22semidirect
88. #2494C22semidirect
89. #2492C22semidirect
90. #2491C22semidirect
92. #2490C22semidirect
94. #2489C22semidirect
109. #2402C22semidirect
110. #2401C22semidirect
111. #2396C22semidirect
116. #2395C22semidirect
117. #2370C22semidirect
118. #2370C22semidirect
119. #2369C22semidirect
120. #2365C22semidirect
123. #2363C22semidirect
126. #2362C22semidirect
127. #2361C22semidirect
128. #2360C22semidirect
129. #2357C22semidirect
130. #2356C22semidirect
131. #2355C22semidirect
134. #2354C22semidirect
137. #2347C22semidirect
138. #2346C22semidirect
139. #2345C22semidirect
140. #2344C22semidirect

Maximal subgroups

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

subgroupindex
#360732
#360692
#360062
#360002
#359932
#359892
#359842
#359782
#352242
#352232
#351602
#351592
#351582
#350982
#350342
#350232
#346352
#345842
#342742
#342712
#342522
#342012
C2×#22742