Finite Group Databasebeta

← #7630722

Subgroups — #7630722

Order 512.

4920 conjugacy classes of subgroups.

The subgroup lattice has 1022 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36050C214yesmaximal, complemented
2#35974C214yesmaximal, complemented
3#35968C214yesmaximal, complemented
4#35945C214yesmaximal, complemented
5#35911C214yesmaximal, complemented
6#35870C214yesmaximal, complemented
7#35869C214yesmaximal, complemented
8#35855C214yesmaximal, complemented
9#35182C212yesmaximal, complemented
10#35179C211yesmaximal, characteristic, complemented
11#35178C211yesmaximal, characteristic
12#35160C212yesmaximal, complemented
13#35099C214yesmaximal, complemented
14#35042C214yesmaximal, complemented
15#35021C214yesmaximal, complemented
16#34638C211yesmaximal, characteristic, complemented
17#34637C211yesmaximal, characteristic
18#34584C214yesmaximal, complemented
19#34266C212yesmaximal, complemented
20#34252C212yesmaximal, complemented
21#34213C211yesmaximal, characteristic, complemented
22#34206C211yesmaximal, characteristic
23C2×#2276C211yesmaximal, characteristic, complemented
24C2×#536C2212yes—
25C2×#533C2211yescharacteristic
26C2×#532C2211yescharacteristic
27C2×#520C2212yes—
28C22×C4×Q8C2211yescharacteristic
29C22×C4×Q8C2211yescharacteristic
30C22×C4×Q8C2211yescharacteristic
31#2855C2214yes—
32#2854C2214yes—
33#2853C2218yes—
34#2852C2218yes—
35#2655C2218yes—
36#2654C2218yes—
37#2651C2218yes—
38#2650C2218yes—
39#2647C2212yes—
40#2647C2212yes—
41#2647C2212yes—
42#2647C2212yes—
43#2646C2212yes—
44#2646C2212yes—
45#2646C2212yes—
46#2646C2212yes—
47#2643C2218yes—
48#2642C2212yes—
49#2641C2212yes—
50#2640C2212yes—
51#2640C2212yes—
52#2639C2212yes—
53#2639C2212yes—
54#2639C2212yes—
55#2639C2212yes—
56#2627C2214yes—
57#2623C2218yes—
58#2618C2214yes—
59#2597C2218yes—
60#2596C2218yes—
61#2593C2218yes—
62#2590C2218yes—
63#2589C2218yes—
64#2585C2218yes—
65#2582C2212yes—
66#2582C2212yes—
67#2581C2214yes—
68#2574C2218yes—
69#2573C2218yes—
70#2568C2212yes—
71#2567C2212yes—
72#2565C2214yes—
73#2548C2212yes—
74#2546C2212yes—
75#2545C2214yes—
76#2538C2212yes—
77#2538C2212yes—
78#2536C2214yes—
79#2533C2218yes—
80#2533C2218yes—
81#2532C2218yes—
82#2532C2218yes—
83#2531C2218yes—
84#2530C2218yes—
85#2529C2218yes—
86#2528C2218yes—
87#2527C2218yes—
88#2526C2218yes—
89#2525C2218yes—
90#2524C2218yes—
91#2514C2214yes—
92#2513C2214yes—
93#2512C2214yes—
94#2511C2214yes—
95#2497C2214yes—
96#2496C2214yes—
97#2495C2214yes—
98#2494C2214yes—
99#2479C2218yes—
100#2478C2218yes—
101#2469C2218yes—
102#2468C2218yes—
103#2448C2214yes—
104#2448C2214yes—
105#2446C2214yes—
106#2446C2214yes—
107#2423C2214yes—
108#2423C2214yes—
109#2421C2214yes—
110#2421C2214yes—
111#2402C2218yes—
112#2402C2214yes—
113#2402C2214yes—
114#2401C2218yes—
115#2398C2214yes—
116#2398C2214yes—
117#2396C2218yes—
118#2395C2218yes—
119#2370C2214yes—
120#2369C2212yes—
121#2367C2214yes—
122#2367C2214yes—
123#2367C2214yes—
124#2366C2212yes—
125#2365C2212yes—
126#2365C2214yes—
127#2365C2212yes—
128#2365C2214yes—
129#2362C2214yes—
130#2362C2214yes—
131#2360C2214yes—
132#2360C2214yes—
133#2357C2214yes—
134#2356C2214yes—
135#2355C2212yes—
136#2355C2214yes—
137#2355C2214yes—
138#2354C2214yes—
139#2354C2212yes—
140#2352C2214yes—
141Q8×C4⋊C4C2212yes—
142D4×C4⋊C4C2212yes—
143#2347C2214yes—
144#2346C2214yes—
145#2345C2214yes—
146#2344C2214yes—
147#2329C2214yes—
148#2325C2214yes—
149#2322C2218yes—
150#2318C2218yes—
151#2317C2212yes—
152#2317C2212yes—
153#2311C2212yes—
154#2311C2212yes—
155#2310C2212yes—
156C4×C22⋊Q8C2214yes—
157C4×#123C2218yes—
158C4×#121C2214yes—
159#2297C2212yes—
160#2297C2212yes—
161#2296C2212yes—
162#2296C2212yes—
163#2290C2218yes—
164#2285C2211yescharacteristic
165#2285C2211yescharacteristic
166#2276C2214yes—
167#2276C2214yes—
168#2276C2214yes—
169#2276C2214yes—
170#2274C2212yes—
171C2×C4×C4⋊C4C2212yes—
172C2×C4×C4⋊C4C2211yescharacteristic
173C2×C4×C4⋊C4C2211yescharacteristic
174C2×C4×C4⋊C4C2211yescharacteristic
175C2×C4×C4⋊C4C2212yes—
176C2×C4×C4⋊C4C2212yes—
177C2×#376C2212yes—
178C2×#376C2211yescharacteristic
179C22×#41C2312yes—
180C23×Q8C2311yescharacteristic
181#536—216no—
182#533—28no—
183#532—28no—
184C2×C4⋊Q8C2311yescharacteristic
185C2×C4⋊Q8C2311yescharacteristic
186C2×C4⋊Q8C2311yescharacteristic
187C2×C4⋊Q8C2314yes—
188C2×#127C2311yescharacteristic
189C2×#126C2318yes—
190C2×#125C2312yes—
191C2×#124C2312yes—
192C2×#124C2314yes—
193C2×#123C2318yes—
194C2×C22⋊Q8C2312yes—
195C2×C22⋊Q8C2314yes—
196C2×C22⋊Q8C2314yes—
197C2×C22⋊Q8C2312yes—
198C2×#121C2312yes—
199C2×#121C2312yes—
200#520—216no—
201C2×C4×Q8—28no—
202C2×C4×Q8—28no—
203C2×C4×Q8—28no—
204C2×C4×Q8C2312yes—
205C2×C4×Q8C2312yes—
206C2×C4×Q8C2312yes—
207C2×C4×Q8C2312yes—
208C2×C4×Q8C2312yes—
209C2×C4×Q8C2312yes—
210C2×C4×Q8C2314yes—
211C2×C4×Q8C2314yes—
212C2×C4×Q8C2314yes—
213C2×C4×Q8C2314yes—
214C2×C4×Q8C2314yes—
215C2×C4×Q8C2314yes—
216C2×C4×D4C2318yes—
217C2×C4×D4C2312yes—
218C2×C4×D4C2312yes—
219C2×C4×D4C2314yes—
220C2×C4×D4C2314yes—
221C2×#117C2312yes—
222C2×#117C2312yes—
223C2×#117C2312yes—
224C2×#117C2314yes—
225C2×#117C2318yes—
226C22×C4⋊C4C2311yescharacteristic
227C22×C4⋊C4C2311yescharacteristic
228C22×C4⋊C4C2312yes—
229C22×C4⋊C4C2314yes—
230C22×C4⋊C4C2312yes—
231C22×C4⋊C4C2312yes—
232C22×C4⋊C4C2311yescharacteristic
233C22×C42C2312yes—
234C22×C42C2312yes—
235C22×C42C2311yescharacteristic
236C22×C42C2311yescharacteristic
237C22×C42C2312yes—
238C22×C42C2312yes—
239C22×C42C2312yes—
240C22×C42C2312yes—
241C22×C42C2311yescharacteristic
242#401C2318yes—
243#400C2318yes—
244#400C2314yes—
245#400C2314yes—
246#400C2318yes—
247#400C2314yes—
248#400C2314yes—
249#400C2314yes—
250#400C2318yes—
251#400C2314yes—
252#400C2314yes—
253#400C2314yes—
254#400C2318yes—
255#400C2318yes—
256#400C2318yes—
257#400C2314yes—
258#400C2314yes—
259#400C2314yes—
260#400C2314yes—
261#399C2318yes—
262#399C2318yes—
263#398C2318yes—
264#398C2318yes—
265#398C2314yes—
266#398C2314yes—
267#398C2318yes—
268#398C2314yes—
269#398C2314yes—
270#398C2318yes—
271#398C2318yes—
272#398C2314yes—
273#398C2314yes—
274#398C2314yes—
275#398C2314yes—
276#397C2314yes—
277#397C2314yes—
278#397C2318yes—
279#397C2318yes—
280#397C2314yes—
281#397C2314yes—
282#397C2318yes—
283#397C2318yes—
284#397C2318yes—
285#396C2318yes—
286#396C2318yes—
287#396C2318yes—
288#395C2318yes—
289#394C2314yes—
290#394C2318yes—
291#394C2314yes—
292#394C2314yes—
293#394C2314yes—
294#393C2314yes—
295#393C2314yes—
296#393C2314yes—
297#393C2314yes—
298#391C2314yes—
299#391C2314yes—
300#391C2314yes—
301#391C2314yes—
302#391C2314yes—
303#391C2314yes—
304#391C2314yes—
305#391C2314yes—
306#391C2314yes—
307#391C2318yes—
308#391C2312yes—
309#391C2312yes—
310#391C2312yes—
311#391C2312yes—
312#390C2314yes—
313#390C2314yes—
314#390C2314yes—
315#390C2314yes—
316#390C2314yes—
317#390C2312yes—
318#390C2312yes—
319#390C2312yes—
320#390C2312yes—
321#389C2314yes—
322#389C2314yes—
323#389C2314yes—
324#389C2314yes—
325#389C2314yes—
326#389C2314yes—
327#389C2314yes—
328#389C2318yes—
329#389C2318yes—
330#389C2318yes—
331#389C2314yes—
332#389C2314yes—
333#389C2314yes—
334#389C2312yes—
335#389C2312yes—
336#389C2312yes—
337#389C2312yes—
338#389C2312yes—
339#389C2312yes—
340#389C2312yes—
341#389C2312yes—
342#388C2318yes—
343#388C2318yes—
344#388C2318yes—
345#388C2318yes—
346#388C2318yes—
347#388C2318yes—
348#388C2318yes—
349#388C2318yes—
350#388C2318yes—
351#388C2318yes—
352#388C2318yes—
353#388C2318yes—
354#388C2318yes—
355#388C2318yes—
356#388C2318yes—
357#388C2318yes—
358#388C2318yes—
359#388C2318yes—
360#388C2318yes—
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#387C2318yes—
380#387C2318yes—
381#387C2318yes—
382#386C2318yes—
383#386C2318yes—
384#386C2314yes—
385#386C2314yes—
386#386C2318yes—
387#386C2314yes—
388#386C2314yes—
389#385C2318yes—
390#385C2318yes—
391#385C2318yes—
392#385C2314yes—
393#385C2318yes—
394#385C2314yes—
395#385C2318yes—
396#385C2314yes—
397#385C2314yes—
398#384C2314yes—
399#384C2314yes—
400#384C2311yescharacteristic
401#384C2311yescharacteristic
402#384C2311yescharacteristic
403#384C2311yescharacteristic
404#383C2318yes—
405#383C2318yes—
406#382C2314yes—
407#382C2314yes—
408#382C2318yes—
409#382C2312yes—
410#382C2312yes—
411#381C2318yes—
412#381C2318yes—
413#380C2314yes—
414#380C2314yes—
415#380C2314yes—
416#380C2314yes—
417#380C2318yes—
418#380C2312yes—
419#380C2312yes—
420#380C2312yes—
421#380C2312yes—
422C4×C4⋊C4C2312yes—
423C4×C4⋊C4C2312yes—
424C4×C4⋊C4C2318yes—
425C4×C4⋊C4C2318yes—
426C4×C4⋊C4C2318yes—
427C4×C4⋊C4C2318yes—
428C4×C4⋊C4C2318yes—
429C4×C4⋊C4C2318yes—
430C4×C4⋊C4C2314yes—
431C4×C4⋊C4C2314yes—
432C4×C4⋊C4C2314yes—
433C4×C4⋊C4C2312yes—
434C4×C4⋊C4C2312yes—
435C4×C4⋊C4C2314yes—
436C4×C4⋊C4C2314yes—
437C4×C4⋊C4C2314yes—
438C4×C4⋊C4C2314yes—
439C4×C4⋊C4C2314yes—
440C4×C4⋊C4C2314yes—
441C4×C4⋊C4C2314yes—
442C4×C4⋊C4C2318yes—
443C4×C4⋊C4C2318yes—
444C4×C4⋊C4C2312yes—
445C4×C4⋊C4C2312yes—
446C4×C4⋊C4C2314yes—
447C4×C4⋊C4C2314yes—
448C4×C4⋊C4C2312yes—
449C4×C4⋊C4C2312yes—
450C4×C4⋊C4C2318yes—
451C4×C4⋊C4C2318yes—
452C4×C4⋊C4C2314yes—
453C4×C4⋊C4C2314yes—
454C4×C22⋊C4C2318yes—
455C4×C22⋊C4C2318yes—
456C4×C22⋊C4C2318yes—
457C4×C22⋊C4C2314yes—
458C4×C22⋊C4C2314yes—
459C4×C22⋊C4C2314yes—
460C4×C22⋊C4C2314yes—
461C4×C22⋊C4C2318yes—
462C4×C22⋊C4C2318yes—
463#376C2318yes—
464#376C2312yes—
465#376C2312yes—
466#376C2312yes—
467#376C2312yes—
468#376C2318yes—
469#376C2318yes—
470C2×#95C2312yes—
471C2×#95C2312yes—
472C2×#95C2311yescharacteristic
473C2×#95C2311yescharacteristic
474C2×#95C2311yescharacteristic
475C2×#95C2311yescharacteristic
476C2×#95C2312yes—
477C2×#41—28no—
478C2×#41—28no—
479C2×#41—28no—
480C22×Q8—24no—
481C22×Q8—24no—
482C22×Q8#4118yes—
483C22×Q8C2412yes—
484C22×Q8C2412yes—
485C22×Q8C2412yes—
486C22×Q8C2412yes—
487C22×Q8C2412yes—
488C22×D4C2414yes—
489C22×D4C2412yes—
490C22×D4C2412yes—
491C22×D4C2412yes—
492C23×C4C2414yes—
493C23×C4C2412yes—
494C23×C4C2412yes—
495C23×C4C2412yes—
496C23×C4C2411yescharacteristic
497C23×C4C2411yescharacteristic
498C23×C4C2418yes—
499C23×C4C2411yescharacteristic
500C23×C4C2411yescharacteristic
501C23×C4C2412yes—
502C23×C4C2411yescharacteristic
503C23×C4C2411yescharacteristic
504C23×C4C2411yescharacteristic
505C4⋊Q8—216no—
506C4⋊Q8—24no—
507C4⋊Q8—24no—
508C4⋊Q8—24no—
509#127—24no—
510#126—88no—
511#125—28no—
512#124—216no—
513#124—28no—
514#123—232no—
515C22⋊Q8—216no—
516C22⋊Q8—216no—
517C22⋊Q8—28no—
518C22⋊Q8—28no—
519#121—28no—
520#121—28no—
521C4×Q8—216no—
522C4×Q8—216no—
523C4×Q8—216no—
524C4×Q8—216no—
525C4×Q8—216no—
526C4×Q8—28no—
527C4×Q8—28no—
528C4×Q8—28no—
529C4×Q8—28no—
530C4×Q8—28no—
531C4×Q8—28no—
532C4×Q8—84no—
533C4×D4—232no—
534C4×D4—216no—
535C4×D4—28no—
536C4×D4—28no—
537C4×D4—84no—
538#117—28no—
539#117—28no—
540#117—28no—
541#117—216no—
542#117—88no—
543C2×C4⋊C4—28no—
544C2×C4⋊C4—28no—
545C2×C4⋊C4—28no—
546C2×C4⋊C4—24no—
547C2×C4⋊C4—24no—
548C2×C4⋊C4—216no—
549C2×C4⋊C4#4118yes—
550C2×C4⋊C4C2412yes—
551C2×C4⋊C4C2418yes—
552C2×C4⋊C4C2412yes—
553C2×C4⋊C4C2412yes—
554C2×C4⋊C4C2412yes—
555C2×C4⋊C4C2418yes—
556C2×C4⋊C4C2412yes—
557C2×C4⋊C4C2414yes—
558C2×C4⋊C4C2414yes—
559C2×C4⋊C4C2418yes—
560C2×C4⋊C4C2412yes—
561C2×C4⋊C4C2412yes—
562C2×C4⋊C4C2412yes—
563C2×C4⋊C4C2412yes—
564C2×C4⋊C4C2412yes—
565C2×C4⋊C4C2412yes—
566C2×C4⋊C4C2412yes—
567C2×C4⋊C4C2414yes—
568C2×C4⋊C4C2414yes—
569C2×C4⋊C4C2412yes—
570C2×C4⋊C4C2412yes—
571C2×C4⋊C4C2418yes—
572C2×C4⋊C4C2418yes—
573C2×C4⋊C4C2414yes—
574C2×C4⋊C4C2418yes—
575C2×C4⋊C4C2412yes—
576C2×C4⋊C4C2412yes—
577C2×C4⋊C4C2418yes—
578C2×C4⋊C4C2414yes—
579C2×C4⋊C4C2412yes—
580C2×C4⋊C4C2412yes—
581C2×C4⋊C4C2414yes—
582C2×C4⋊C4C2414yes—
583C2×C4⋊C4C2414yes—
584C2×C4⋊C4C2414yes—
585C2×C4⋊C4C2412yes—
586C2×C4⋊C4C2412yes—
587C2×C4⋊C4C2412yes—
588C2×C4⋊C4C2412yes—
589C2×C4⋊C4C2414yes—
590C2×C4⋊C4C2418yes—
591C2×C4⋊C4C2418yes—
592C2×C4⋊C4C2414yes—
593C2×C4⋊C4C2412yes—
594C2×C4⋊C4C2412yes—
595C2×C22⋊C4C2414yes—
596C2×C22⋊C4C2418yes—
597C2×C22⋊C4C2414yes—
598C2×C22⋊C4C2414yes—
599C2×C22⋊C4C2414yes—
600C2×C22⋊C4C2414yes—
601C2×C22⋊C4C2418yes—
602C2×C22⋊C4C2418yes—
603C2×C22⋊C4C2414yes—
604C2×C22⋊C4C2418yes—
605C2×C22⋊C4C2418yes—
606C2×C22⋊C4C2414yes—
607C2×C22⋊C4C2414yes—
608C2×C22⋊C4C2414yes—
609C2×C22⋊C4C2414yes—
610C2×C22⋊C4C2414yes—
611C2×C22⋊C4C2418yes—
612C2×C22⋊C4C2418yes—
613C2×C22⋊C4C2414yes—
614C2×C22⋊C4C2414yes—
615C2×C42—28no—
616C2×C42—28no—
617C2×C42—28no—
618C2×C42—24no—
619C2×C42—24no—
620C2×C42—82no—
621C2×C42—82no—
622C2×C42—82no—
623C2×C42#4118yes—
624C2×C42C2418yes—
625C2×C42C2414yes—
626C2×C42C2414yes—
627C2×C42C2414yes—
628C2×C42C2412yes—
629C2×C42C2412yes—
630C2×C42C2418yes—
631C2×C42C2412yes—
632C2×C42C2412yes—
633C2×C42C2418yes—
634C2×C42C2414yes—
635C2×C42C2414yes—
636C2×C42C2418yes—
637C2×C42C2418yes—
638C2×C42C2414yes—
639C2×C42C2414yes—
640C2×C42C2418yes—
641C2×C42C2418yes—
642C2×C42C2411yescharacteristic
643C2×C42C2411yescharacteristic
644C2×C42C2411yescharacteristic
645C2×C42C2411yescharacteristic
646#95C2412yes—
647#95C2412yes—
648#95C2418yes—
649#95C2414yes—
650#95C2414yes—
651#95C2412yes—
652#95C2412yes—
653#95C2412yes—
654#95C2412yes—
655#95C2412yes—
656#95C2412yes—
657#95C2418yes—
658#95C2414yes—
659#95C2414yes—
660#95C2418yes—
661#95C2418yes—
662#95C2414yes—
663#95C2414yes—
664#95C2414yes—
665#95C2414yes—
666#95C2418yes—
667#95C2418yes—
668#95C2414yes—
669#95C2414yes—
670#95C2414yes—
671#95C2418yes—
672#95C2418yes—
673#95C2418yes—
674#95C2418yes—
675#95C2414yes—
676#95C2414yes—
677#95C2414yes—
678#95C2414yes—
679#95C2414yes—
680#95C2414yes—
681#95C2414yes—
682#95C2418yes—
683#95C2418yes—
684#95C2414yes—
685#95C2418yes—
686#95C2418yes—
687#95C2418yes—
688#95C2418yes—
689#95C2414yes—
690#95C2414yes—
691#95C2414yes—
692C24C2514yes—
693C24C2511yescharacteristic
694#41—432no—
695C2×Q8—232no—
696C2×Q8—24no—
697C2×Q8—24no—
698C2×Q8—24no—
699C2×Q8—24no—
700C2×Q8—24no—
701C2×Q8—24no—
702C2×Q8—24no—
703C2×Q8—24no—
704C2×Q8—24no—
705C2×Q8—42no—
706C2×Q8—42no—
707C2×Q8—42no—
708C2×Q8—42no—
709C2×Q8C2×#4118yes—
710C2×Q8C2×#4118yes—
711C2×D4—28no—
712C2×D4—28no—
713C2×D4—28no—
714C2×D4—24no—
715C2×D4—24no—
716C2×D4—24no—
717C2×D4—24no—
718C2×D4—24no—
719C2×D4—42no—
720C2×D4—42no—
721C2×D4—42no—
722C2×D4—42no—
723C22×C4—24no—
724C22×C4—24no—
725C22×C4—22no—
726C22×C4—22no—
727C22×C4—24no—
728C22×C4—22no—
729C22×C4—24no—
730C22×C4—22no—
731C22×C4—28no—
732C22×C4—28no—
733C22×C4—28no—
734C22×C4—216no—
735C22×C4—42no—
736C22×C4—41no—
737C22×C4—42no—
738C22×C4—41no—
739C22×C4—41no—
740C22×C4—42no—
741C22×C4—42no—
742C22×C4—41no—
743C22×C4—41no—
744C22×C4—41no—
745C22×C4—42no—
746C22×C4—41no—
747C22×C4—42no—
748C22×C4—41no—
749C22×C4—41no—
750C22×C4—41no—
751C22×C4—41no—
752C22×C4—41no—
753C22×C4—48no—
754C22×C4—48no—
755C22×C4C2×#4118yes—
756C22×C4C2×#4114yes—
757C22×C4C2×#4118yes—
758C22×C4C2×#4114yes—
759C22×C4C2×#4114yes—
760C22×C4C2×#4114yes—
761C22×C4C2×#4114yes—
762C22×C4C2512yes—
763C22×C4C2512yes—
764C22×C4C2514yes—
765C22×C4C2514yes—
766C22×C4C2514yes—
767C22×C4C2514yes—
768C22×C4C2514yes—
769C22×C4C2514yes—
770C22×C4C2514yes—
771C22×C4C2512yes—
772C22×C4C2512yes—
773C22×C4C2514yes—
774C22×C4C2514yes—
775C22×C4C2511yescharacteristic
776C22×C4C2511yescharacteristic
777C22×C4C2514yes—
778C22×C4C2514yes—
779C22×C4C2511yescharacteristic
780C22×C4C2511yescharacteristic
781C22×C4C2511yescharacteristic
782C22×C4C2511yescharacteristic
783C4⋊C4—24no—
784C4⋊C4—216no—
785C4⋊C4—216no—
786C4⋊C4—28no—
787C4⋊C4—28no—
788C4⋊C4—216no—
789C4⋊C4—24no—
790C4⋊C4—24no—
791C4⋊C4—24no—
792C4⋊C4—24no—
793C4⋊C4—24no—
794C4⋊C4—24no—
795C4⋊C4—24no—
796C4⋊C4—24no—
797C4⋊C4—24no—
798C4⋊C4—24no—
799C4⋊C4—24no—
800C4⋊C4—28no—
801C4⋊C4—28no—
802C4⋊C4—24no—
803C4⋊C4—24no—
804C4⋊C4—216no—
805C4⋊C4—216no—
806C4⋊C4—42no—
807C4⋊C4—42no—
808C4⋊C4—42no—
809C4⋊C4—42no—
810C4⋊C4—42no—
811C4⋊C4—42no—
812C4⋊C4—44no—
813C4⋊C4—44no—
814C4⋊C4—44no—
815C4⋊C4—44no—
816C4⋊C4—44no—
817C4⋊C4—44no—
818C4⋊C4—48no—
819C4⋊C4—48no—
820C4⋊C4—44no—
821C4⋊C4—48no—
822C4⋊C4—42no—
823C4⋊C4—42no—
824C4⋊C4—48no—
825C4⋊C4—44no—
826C4⋊C4C2×#4118yes—
827C4⋊C4C2×#4118yes—
828C22⋊C4—28no—
829C22⋊C4—28no—
830C22⋊C4—28no—
831C22⋊C4—216no—
832C22⋊C4—28no—
833C22⋊C4—28no—
834C22⋊C4—216no—
835C22⋊C4—216no—
836C22⋊C4—44no—
837C22⋊C4—44no—
838C22⋊C4—48no—
839C22⋊C4—48no—
840C22⋊C4—44no—
841C22⋊C4—44no—
842C22⋊C4—44no—
843C22⋊C4—44no—
844C22⋊C4—44no—
845C22⋊C4—48no—
846C22⋊C4—48no—
847C22⋊C4—44no—
848C42—216no—
849C42—28no—
850C42—28no—
851C42—216no—
852C42—24no—
853C42—24no—
854C42—24no—
855C42—24no—
856C42—216no—
857C42—28no—
858C42—28no—
859C42—28no—
860C42—48no—
861C42—44no—
862C42—44no—
863C42—48no—
864C42—48no—
865C42—48no—
866C42C2×#4114yes—
867C42C2×#4114yes—
868C42C2×#4114yes—
869C42C2×#4114yes—
870C23—21no—
871C23—21no—
872C23—21no—
873C23—21no—
874C23—24no—
875C23—24no—
876C23—24no—
877C23—24no—
878C23—24no—
879C23—24no—
880C23—24no—
881C23C22×#4112yes—
882C23C22×#4112yes—
883C23C22×#4112yes—
884C23C2611yescharacteristic
885Q8—216no—
886Q8—216no—
887Q8—48no—
888Q8—48no—
889Q8—84no—
890D4—48no—
891D4—416no—
892D4—48no—
893D4—84no—
894C2×C4—24no—
895C2×C4—24no—
896C2×C4—24no—
897C2×C4—21no—
898C2×C4—21no—
899C2×C4—24no—
900C2×C4—21no—
901C2×C4—21no—
902C2×C4—21no—
903C2×C4—21no—
904C2×C4—21no—
905C2×C4—21no—
906C2×C4—216no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—24no—
910C2×C4—24no—
911C2×C4—22no—
912C2×C4—24no—
913C2×C4—22no—
914C2×C4—24no—
915C2×C4—24no—
916C2×C4—24no—
917C2×C4—24no—
918C2×C4—24no—
919C2×C4—24no—
920C2×C4—24no—
921C2×C4—24no—
922C2×C4—24no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—24no—
926C2×C4—24no—
927C2×C4—24no—
928C2×C4—24no—
929C2×C4—24no—
930C2×C4—24no—
931C2×C4—24no—
932C2×C4—24no—
933C2×C4—24no—
934C2×C4—22no—
935C2×C4—22no—
936C2×C4—22no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—24no—
940C2×C4—22no—
941C2×C4—24no—
942C2×C4—24no—
943C2×C4—24no—
944C2×C4—24no—
945C2×C4—24no—
946C2×C4—44no—
947C2×C4—48no—
948C2×C4—44no—
949C2×C4—48no—
950C2×C4—44no—
951C2×C4—44no—
952C2×C4—44no—
953C2×C4—44no—
954C2×C4—48no—
955C2×C4—416no—
956C2×C4—816no—
957C2×C4#529116yes—
958C2×C4C22×#4112yes—
959C2×C4C22×#4112yes—
960C2×C4C22×#4118yes—
961C2×C4C22×#4118yes—
962C2×C4C22×#4112yes—
963C2×C4C22×#4112yes—
964C2×C4C22×#4112yes—
965C2×C4C22×#4112yes—
966C2×C4C22×#4112yes—
967C2×C4C22×#4112yes—
968C2×C4C22×#4112yes—
969C2×C4C22×#4112yes—
970C22—22no—
971C22—22no—
972C22—22no—
973C22—22no—
974C22—22no—
975C22—22no—
976C22—44no—
977C22—44no—
978C22—44no—
979C22—44no—
980C22—44no—
981C22—44no—
982C22—44no—
983C22C2×#52914yes—
984C22C23×#4111yescharacteristic
985C22C23×#4111yescharacteristic
986C22C23×#4111yescharacteristic
987C22H(7,𝔽2)11yescharacteristic
988C222−1+611yescharacteristic
989C222−1+611yescharacteristic
990C222−1+611yescharacteristic
991C4—22no—
992C4—22no—
993C4—28no—
994C4—22no—
995C4—22no—
996C4—28no—
997C4—44no—
998C4—44no—
999C4—42no—
1000C4—44no—
1001C4—44no—
1002C4—44no—
1003C4—42no—
1004C4—42no—
1005C4—44no—
1006C4—42no—
1007C4—44no—
1008C4—44no—
1009C4—44no—
1010C4C2×#52914yes—
1011C4C2×#52914yes—
1012C2—24no—
1013C2—84no—
1014C2C22×#52911yescharacteristic
1015C2#6284511yescharacteristic
1016C2#6284711yescharacteristic
1017C2#6285011yescharacteristic
1018C2#6285011yescharacteristic
1019C2#6285111yescharacteristic
1020C2#6286011yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#532C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #36050C2semidirect
2. #35974C2semidirect
3. #35968C2semidirect
4. #35945C2semidirect
5. #35911C2semidirect
6. #35870C2semidirect
7. #35869C2semidirect
8. #35855C2semidirect
9. #35182C2semidirect
10. #35179C2semidirect
12. #35160C2semidirect
13. #35099C2semidirect
14. #35042C2semidirect
15. #35021C2semidirect
16. #34638C2semidirect
18. #34584C2semidirect
19. #34266C2semidirect
20. #34252C2semidirect
21. #34213C2semidirect
23. C2×#2276C2semidirect

Maximal subgroups

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

subgroupindex
#360502
#359742
#359682
#359452
#359112
#358702
#358692
#358552
#351822
#351792
#351782
#351602
#350992
#350422
#350212
#346382
#346372
#345842
#342662
#342522
#342132
#342062
C2×#22762