Finite Group Databasebeta

← #7630913

Subgroups — #7630913

Order 512.

4818 conjugacy classes of subgroups.

The subgroup lattice has 934 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35972C214yesmaximal, complemented
2#35963C214yesmaximal, complemented
3#35962C218yesmaximal, complemented
4#35871C214yesmaximal, complemented
5#35867C214yesmaximal, complemented
6#35862C218yesmaximal, complemented
7#35337C212yesmaximal, complemented
8#35336C212yesmaximal, complemented
9#35330C211yesmaximal, characteristic, complemented
10#35304C214yesmaximal, complemented
11#35284C212yesmaximal, complemented
12#35283C212yesmaximal, complemented
13#35275C211yesmaximal, characteristic, complemented
14#35257C212yesmaximal
15#35257C212yesmaximal
16#34638C211yesmaximal, characteristic, complemented
17#34625C214yesmaximal, complemented
18C2×#2647C211yesmaximal, characteristic, complemented
19#34272C212yesmaximal, complemented
20#34272C212yesmaximal, complemented
21#34189C211yesmaximal, characteristic
22#34188C211yesmaximal, characteristic
23#33999C211yesmaximal, characteristic
24C2×#544C2212yes—
25C2×#544C2212yes—
26C2×C4×#41C2211yescharacteristic
27C2×C4×#41C2211yescharacteristic
28C2×C4×#41C2211yescharacteristic
29#2868C2212yes—
30#2862C2212yes—
31#2859C2212yes—
32#2859C2212yes—
33#2857C2214yes—
34#2857C2214yes—
35#2851C2214yes—
36#2851C2214yes—
37#2667C2218yes—
38#2666C2218yes—
39#2666C2218yes—
40#2665C2218yes—
41#2660C2214yes—
42#2660C2214yes—
43#2647C2211yescharacteristic
44#2647C2212yes—
45#2647C2211yescharacteristic
46#2647C2212yes—
47#2647C2214yes—
48#2647C2214yes—
49#2647C2212yes—
50#2647C2212yes—
51#2647C2212yes—
52#2647C2211yescharacteristic
53#2647C2211yescharacteristic
54#2647C2212yes—
55#2646C2214yes—
56#2646C2214yes—
57#2629C2214yes—
58#2629C2214yes—
59#2628C2214yes—
60#2628C2214yes—
61#2612C2218yes—
62#2612C2218yes—
63#2606C2218yes—
64#2605C2218yes—
65#2590C2218yes—
66#2590C2218yes—
67#2589C2218yes—
68#2589C2218yes—
69#2588C2218yes—
70#2588C2218yes—
71#2587C2218yes—
72#2587C2218yes—
73#2569C2218yes—
74#2552C2214yes—
75#2551C2214yes—
76#2550C2214yes—
77#2550C2214yes—
78#2549C2218yes—
79#2549C2218yes—
80#2511C2218yes—
81#2507C2218yes—
82#2497C2218yes—
83#2492C2218yes—
84#2454C2214yes—
85#2454C2214yes—
86#2453C2214yes—
87#2453C2214yes—
88#2452C2214yes—
89#2452C2214yes—
90#2451C2218yes—
91#2451C2214yes—
92#2451C2214yes—
93#2450C2218yes—
94#2450C2218yes—
95#2449C2218yes—
96#2449C2218yes—
97#2446C2218yes—
98#2440C2218yes—
99#2438C2218yes—
100#2438C2218yes—
101#2429C2218yes—
102#2423C2218yes—
103#2402C2214yes—
104#2402C2214yes—
105#2402C2218yes—
106#2399C2218yes—
107#2396C2218yes—
108#2396C2218yes—
109C2×#400C2214yes—
110C2×#398C2214yes—
111#2370C2214yes—
112#2370C2214yes—
113#2370C2214yes—
114#2370C2214yes—
115#2369C2214yes—
116#2369C2214yes—
117#2368C2218yes—
118#2368C2218yes—
119#2365C2214yes—
120#2365C2214yes—
121#2360C2218yes—
122#2360C2218yes—
123#2357C2214yes—
124#2356C2214yes—
125#2355C2214yes—
126#2354C2214yes—
127#2353C2218yes—
128#2352C2218yes—
129#2331C2214yes—
130#2331C2214yes—
131#2330C2214yes—
132#2330C2214yes—
133#2317C2212yes—
134#2317C2212yes—
135#2314C2212yes—
136#2314C2212yes—
137#2314C2212yes—
138#2314C2212yes—
139#2311C2212yes—
140#2311C2212yes—
141C4×C4⋊Q8C2214yes—
142C4×C4⋊Q8C2214yes—
143C4×#125C2214yes—
144C4×#125C2214yes—
145#2296C2212yes—
146#2296C2212yes—
147C2×#389C2212yes—
148C2×#389C2212yes—
149#2285C2211yescharacteristic
150#2285C2214yes—
151#2285C2211yescharacteristic
152C2×#384C2211yescharacteristic
153#2283C2214yes—
154C2×#382C2211yescharacteristic
155#2276C2212yes—
156#2276C2212yes—
157#2275C2214yes—
158#2275C2212yes—
159#2275C2214yes—
160#2275C2212yes—
161#2274C2212yes—
162#2274C2212yes—
163C4×#117C2211yescharacteristic
164C4×#117C2212yes—
165C4×#117C2212yes—
166C4×#117C2212yes—
167C4×#117C2211yescharacteristic
168C4×#117C2211yescharacteristic
169C2×#376C2211yescharacteristic
170C2×#376C2212yes—
171C22×#41C2311yescharacteristic
172#544—216no—
173#544—216no—
174C2×C4⋊Q8C2314yes—
175C2×C4⋊Q8C2314yes—
176C2×C4⋊Q8C2314yes—
177C2×C4⋊Q8C2314yes—
178C2×C4⋊Q8C2318yes—
179C2×#125C2314yes—
180C2×#125C2314yes—
181C2×#125C2314yes—
182C2×#125C2314yes—
183C2×C22⋊Q8C2318yes—
184C2×C22⋊Q8C2318yes—
185C2×C22⋊Q8C2318yes—
186C2×C22⋊Q8C2318yes—
187C4×#41—28no—
188C4×#41—28no—
189C4×#41Q8116yescomplemented
190C2×C4×Q8C2311yescharacteristic
191C2×C4×Q8C2312yes—
192C2×C4×Q8C2311yescharacteristic
193C2×C4×Q8C2318yes—
194C2×C4×Q8C2318yes—
195C2×C4×Q8C2312yes—
196C2×C4×D4C2312yes—
197C2×C4×D4C2314yes—
198C2×C4×D4C2312yes—
199C2×C4×D4C2311yescharacteristic
200C2×C4×D4C2312yes—
201C2×C4×D4C2311yescharacteristic
202C2×C4×D4C2314yes—
203C2×C4×D4C2312yes—
204C2×#117C2312yes—
205C2×#117C2312yes—
206C2×#117C2312yes—
207C2×#117C2312yes—
208C2×#117C2318yes—
209C2×#117C2312yes—
210C2×#117C2311yescharacteristic
211C2×#117C2311yescharacteristic
212C2×#117C2311yescharacteristic
213C22×C4⋊C4C2312yes—
214C22×C4⋊C4C2312yes—
215C22×C4⋊C4C2314yes—
216C22×C4⋊C4C2314yes—
217C22×C4⋊C4C2314yes—
218C22×C42C2312yes—
219C22×C42C2312yes—
220C22×C42C2311yescharacteristic
221C22×C42C2311yescharacteristic
222C22×C42C2311yescharacteristic
223C22×C42C2312yes—
224#400C2314yes—
225#400C2318yes—
226#400C2314yes—
227#400C2318yes—
228#400C2314yes—
229#400C2318yes—
230#400C2318yes—
231#400C2314yes—
232#400C2318yes—
233#400C2314yes—
234#400C2314yes—
235#400C2314yes—
236#400C2314yes—
237#400C2318yes—
238#399C2318yes—
239#399C2318yes—
240#398C2318yes—
241#398C2318yes—
242#398C2314yes—
243#398C2318yes—
244#398C2314yes—
245#398C2318yes—
246#398C2318yes—
247#398C2318yes—
248#398C2314yes—
249#398C2318yes—
250#398C2314yes—
251#398C2318yes—
252#398C2318yes—
253#398C2318yes—
254#398C2318yes—
255#398C2314yes—
256#398C2314yes—
257#398C2314yes—
258#398C2314yes—
259#398C2318yes—
260#396C2318yes—
261#396C2318yes—
262#396C2318yes—
263#396C2318yes—
264#395C2318yes—
265#395C2318yes—
266#395C2318yes—
267#395C2318yes—
268#395C2318yes—
269#395C2318yes—
270#393C2318yes—
271#393C2318yes—
272#391C2318yes—
273#391C2318yes—
274#391C2314yes—
275#391C2314yes—
276#391C2318yes—
277#391C2318yes—
278#391C2318yes—
279#391C2318yes—
280#391C2318yes—
281#391C2318yes—
282#391C2318yes—
283#391C2318yes—
284#390C2314yes—
285#390C2314yes—
286#389C2312yes—
287#389C2312yes—
288#389C2314yes—
289#389C2314yes—
290#389C2312yes—
291#389C2312yes—
292#389C2318yes—
293#389C2318yes—
294#389C2314yes—
295#389C2314yes—
296#389C2314yes—
297#389C2314yes—
298#389C2312yes—
299#389C2312yes—
300#389C2314yes—
301#389C2314yes—
302#389C2318yes—
303#389C2318yes—
304#389C2318yes—
305#389C2318yes—
306#389C2312yes—
307#389C2312yes—
308#389C2318yes—
309#389C2318yes—
310#389C2318yes—
311#389C2318yes—
312#389C2318yes—
313#389C2318yes—
314#389C2314yes—
315#389C2314yes—
316#389C2314yes—
317#389C2314yes—
318#388C2318yes—
319#388C2318yes—
320#388C2318yes—
321#388C2318yes—
322#387C2318yes—
323#387C2318yes—
324#387C2318yes—
325#387C2318yes—
326#387C2318yes—
327#387C2318yes—
328#387C2318yes—
329#387C2318yes—
330#387C2318yes—
331#387C2318yes—
332#387C2318yes—
333#387C2318yes—
334#387C2318yes—
335#387C2318yes—
336#387C2318yes—
337#387C2318yes—
338#387C2318yes—
339#387C2318yes—
340#387C2318yes—
341#387C2318yes—
342#386C2318yes—
343#386C2318yes—
344#385C2318yes—
345#385C2318yes—
346#385C2318yes—
347#385C2318yes—
348#385C2318yes—
349#385C2318yes—
350#385C2314yes—
351#385C2314yes—
352#385C2314yes—
353#385C2314yes—
354#384C2314yes—
355#384C2314yes—
356#384C2311yescharacteristic
357#384C2312yes—
358#384C2311yescharacteristic
359#384C2314yes—
360#384C2318yes—
361#384C2312yes—
362#384C2312yes—
363#383C2318yes—
364#382C2314yes—
365#382C2314yes—
366#382C2311yescharacteristic
367#382C2312yes—
368#382C2311yescharacteristic
369#382C2318yes—
370#382C2314yes—
371#382C2312yes—
372#382C2312yes—
373#381C2318yes—
374#380C2314yes—
375#380C2314yes—
376#380C2314yes—
377#380C2314yes—
378#380C2318yes—
379#380C2318yes—
380#380C2318yes—
381#380C2314yes—
382#380C2314yes—
383C4×C4⋊C4C2314yes—
384C4×C4⋊C4C2314yes—
385C4×C4⋊C4C2314yes—
386C4×C4⋊C4C2318yes—
387C4×C4⋊C4C2318yes—
388C4×C4⋊C4C2318yes—
389C4×C4⋊C4C2318yes—
390C4×C4⋊C4C2314yes—
391C4×C4⋊C4C2318yes—
392C4×C4⋊C4C2318yes—
393C4×C4⋊C4C2314yes—
394C4×C4⋊C4C2314yes—
395C4×C4⋊C4C2314yes—
396C4×C4⋊C4C2314yes—
397C4×C4⋊C4C2318yes—
398C4×C4⋊C4C2314yes—
399C4×C4⋊C4C2314yes—
400C4×C4⋊C4C2314yes—
401C4×C4⋊C4C2314yes—
402C4×C4⋊C4C2314yes—
403C4×C4⋊C4C2314yes—
404C4×C4⋊C4C2312yes—
405C4×C4⋊C4C2312yes—
406C4×C4⋊C4C2314yes—
407C4×C4⋊C4C2314yes—
408C4×C4⋊C4C2312yes—
409C4×C4⋊C4C2314yes—
410C4×C4⋊C4C2314yes—
411C4×C4⋊C4C2312yes—
412C4×C4⋊C4C2314yes—
413C4×C4⋊C4C2314yes—
414C4×C4⋊C4C2312yes—
415C4×C4⋊C4C2312yes—
416C4×C22⋊C4C2318yes—
417C4×C22⋊C4C2314yes—
418C4×C22⋊C4C2314yes—
419C4×C22⋊C4C2314yes—
420C4×C22⋊C4C2314yes—
421C4×C22⋊C4C2318yes—
422C4×C22⋊C4C2318yes—
423C4×C22⋊C4C2312yes—
424C4×C22⋊C4C2314yes—
425C4×C22⋊C4C2312yes—
426C4×C22⋊C4C2314yes—
427C4×C22⋊C4C2314yes—
428C4×C22⋊C4C2314yes—
429#376C2312yes—
430#376C2312yes—
431#376C2314yes—
432#376C2314yes—
433#376C2318yes—
434#376C2311yescharacteristic
435#376C2311yescharacteristic
436#376C2311yescharacteristic
437#376C2311yescharacteristic
438#376C2312yes—
439#376C2312yes—
440#376C2312yes—
441C2×#95C2314yes—
442C2×#95C2314yes—
443C2×#95C2314yes—
444C2×#95C2314yes—
445C2×#95C2312yes—
446C2×#95C2312yes—
447C2×#95C2314yes—
448C43C2312yes—
449C43C2312yes—
450C43C2312yes—
451C2×#41—24no—
452C2×#41—24no—
453C2×#41C2×Q818yes—
454C22×Q8C2411yescharacteristic
455C22×Q8C2418yes—
456C22×Q8C2418yes—
457C22×D4C2412yes—
458C22×D4C2411yescharacteristic
459C23×C4C2412yes—
460C23×C4C2414yes—
461C23×C4C2411yescharacteristic
462C23×C4C2414yes—
463C23×C4C2412yes—
464C23×C4C2412yes—
465C23×C4C2414yes—
466C23×C4C2411yescharacteristic
467C23×C4C2412yes—
468C23×C4C2412yes—
469C23×C4C2414yes—
470C23×C4C2411yescharacteristic
471C4⋊Q8—216no—
472C4⋊Q8—216no—
473C4⋊Q8—216no—
474C4⋊Q8—216no—
475C4⋊Q8—88no—
476#125—216no—
477#125—216no—
478#125—216no—
479#125—216no—
480C22⋊Q8—232no—
481C22⋊Q8—232no—
482C22⋊Q8—88no—
483C22⋊Q8—88no—
484C4×Q8—24no—
485C4×Q8—28no—
486C4×Q8—24no—
487C4×Q8—88no—
488C4×Q8—88no—
489C4×Q8C2×Q8116yes—
490C4×D4—24no—
491C4×D4—28no—
492C4×D4—24no—
493C4×D4—28no—
494C4×D4—216no—
495C4×D4—28no—
496C4×D4C2×Q8132yes—
497C4×D4C2×Q8116yes—
498#117—28no—
499#117—28no—
500#117—28no—
501#117—28no—
502#117—88no—
503#117C2×Q8116yes—
504#117C2×Q818yes—
505#117#4118yes—
506#117#4118yes—
507C2×C4⋊C4—28no—
508C2×C4⋊C4—28no—
509C2×C4⋊C4—84no—
510C2×C4⋊C4—84no—
511C2×C4⋊C4—84no—
512C2×C4⋊C4C2414yes—
513C2×C4⋊C4C2414yes—
514C2×C4⋊C4C2414yes—
515C2×C4⋊C4C2414yes—
516C2×C4⋊C4C2412yes—
517C2×C4⋊C4C2414yes—
518C2×C4⋊C4C2412yes—
519C2×C4⋊C4C2412yes—
520C2×C4⋊C4C2412yes—
521C2×C4⋊C4C2412yes—
522C2×C4⋊C4C2412yes—
523C2×C4⋊C4C2418yes—
524C2×C4⋊C4C2418yes—
525C2×C4⋊C4C2418yes—
526C2×C4⋊C4C2418yes—
527C2×C4⋊C4C2418yes—
528C2×C4⋊C4C2418yes—
529C2×C4⋊C4C2418yes—
530C2×C4⋊C4C2418yes—
531C2×C4⋊C4C2418yes—
532C2×C4⋊C4C2418yes—
533C2×C4⋊C4C2418yes—
534C2×C4⋊C4C2418yes—
535C2×C4⋊C4C2414yes—
536C2×C4⋊C4C2414yes—
537C2×C4⋊C4C2414yes—
538C2×C4⋊C4C2418yes—
539C2×C4⋊C4C2418yes—
540C2×C4⋊C4C2414yes—
541C2×C4⋊C4C2414yes—
542C2×C4⋊C4C2418yes—
543C2×C4⋊C4C2414yes—
544C2×C4⋊C4C2414yes—
545C2×C4⋊C4C2414yes—
546C2×C4⋊C4C2414yes—
547C2×C4⋊C4C2418yes—
548C2×C4⋊C4C2414yes—
549C2×C4⋊C4C2414yes—
550C2×C4⋊C4C2414yes—
551C2×C4⋊C4C2412yes—
552C2×C4⋊C4C2414yes—
553C2×C4⋊C4C2411yescharacteristic
554C2×C4⋊C4C2412yes—
555C2×C4⋊C4C2411yescharacteristic
556C2×C22⋊C4C2412yes—
557C2×C22⋊C4C2414yes—
558C2×C22⋊C4C2412yes—
559C2×C22⋊C4C2414yes—
560C2×C22⋊C4C2414yes—
561C2×C22⋊C4C2418yes—
562C2×C22⋊C4C2418yes—
563C2×C22⋊C4C2418yes—
564C2×C22⋊C4C2418yes—
565C2×C22⋊C4C2412yes—
566C2×C22⋊C4C2414yes—
567C2×C22⋊C4C2412yes—
568C2×C22⋊C4C2412yes—
569C2×C42—24no—
570C2×C42—24no—
571C2×C42—28no—
572C2×C42—28no—
573C2×C42C2×Q8116yes—
574C2×C42C2×Q818yes—
575C2×C42C2411yescharacteristic
576C2×C42C2411yescharacteristic
577C2×C42C2414yes—
578C2×C42C2414yes—
579C2×C42C2411yescharacteristic
580C2×C42C2411yescharacteristic
581C2×C42C2412yes—
582C2×C42C2412yes—
583C2×C42C2414yes—
584C2×C42C2412yes—
585C2×C42C2411yescharacteristic
586C2×C42C2411yescharacteristic
587C2×C42C2418yes—
588C2×C42C2418yes—
589C2×C42C2414yes—
590C2×C42C2414yes—
591C2×C42C2418yes—
592C2×C42C2414yes—
593C2×C42C2414yes—
594C2×C42C2414yes—
595C2×C42C2414yes—
596C2×C42C2418yes—
597C2×C42C2412yes—
598C2×C42C2411yescharacteristic
599C2×C42C2414yes—
600C2×C42C2412yes—
601C2×C42C2411yescharacteristic
602C2×C42C2412yes—
603C2×C42C2412yes—
604#95C2412yes—
605#95C2412yes—
606#95C2414yes—
607#95C2414yes—
608#95C2414yes—
609#95C2414yes—
610#95C2414yes—
611#95C2414yes—
612#95C2412yes—
613#95C2412yes—
614#95C2412yes—
615#95C2412yes—
616#95C2412yes—
617#95C2412yes—
618#95C2418yes—
619#95C2418yes—
620#95C2418yes—
621#95C2418yes—
622#95C2418yes—
623#95C2418yes—
624#95C2414yes—
625#95C2418yes—
626#95C2418yes—
627#95C2414yes—
628#95C2418yes—
629#95C2418yes—
630#95C2418yes—
631#95C2418yes—
632#95C2414yes—
633#95C2414yes—
634#95C2414yes—
635#95C2414yes—
636#95C2414yes—
637#95C2414yes—
638#95C2418yes—
639#95C2418yes—
640#95C2414yes—
641#95C2414yes—
642#95C2418yes—
643#95C2418yes—
644#95C2418yes—
645#95C2418yes—
646#95C2414yes—
647#95C2414yes—
648C24C2512yes—
649C24C2511yescharacteristic
650#41—232no—
651C2×Q8—22no—
652C2×Q8—22no—
653C2×Q8—216no—
654C2×Q8—216no—
655C2×Q8—48no—
656C2×Q8—48no—
657C2×Q8—48no—
658C2×Q8—48no—
659C2×Q8C22×Q814yes—
660C2×D4—24no—
661C2×D4—24no—
662C2×D4—22no—
663C2×D4—22no—
664C2×D4C22×Q818yes—
665C2×D4C22×Q814yes—
666C22×C4—24no—
667C22×C4—24no—
668C22×C4—22no—
669C22×C4—24no—
670C22×C4—22no—
671C22×C4—28no—
672C22×C4—28no—
673C22×C4—24no—
674C22×C4—28no—
675C22×C4—24no—
676C22×C4—42no—
677C22×C4—44no—
678C22×C4—44no—
679C22×C4—42no—
680C22×C4—42no—
681C22×C4—42no—
682C22×C4—44no—
683C22×C4—44no—
684C22×C4—44no—
685C22×C4—44no—
686C22×C4—44no—
687C22×C4—44no—
688C22×C4—44no—
689C22×C4—42no—
690C22×C4—42no—
691C22×C4—44no—
692C22×C4C22×Q818yes—
693C22×C4C22×Q8116yes—
694C22×C4C22×Q818yes—
695C22×C4C22×Q814yes—
696C22×C4C2×#4114yes—
697C22×C4C2×#4114yes—
698C22×C4C2511yescharacteristic
699C22×C4C2511yescharacteristic
700C22×C4C2512yes—
701C22×C4C2514yes—
702C22×C4C2514yes—
703C22×C4C2518yes—
704C22×C4C2512yes—
705C22×C4C2511yescharacteristic
706C22×C4C2514yes—
707C22×C4C2514yes—
708C22×C4C2518yes—
709C22×C4C2511yescharacteristic
710C22×C4C2512yes—
711C22×C4C2512yes—
712C22×C4C2514yes—
713C22×C4C2512yes—
714C22×C4C2512yes—
715C22×C4C2514yes—
716C22×C4C2512yes—
717C22×C4C2511yescharacteristic
718C22×C4C2511yescharacteristic
719C4⋊C4—28no—
720C4⋊C4—28no—
721C4⋊C4—28no—
722C4⋊C4—28no—
723C4⋊C4—24no—
724C4⋊C4—28no—
725C4⋊C4—24no—
726C4⋊C4—24no—
727C4⋊C4—24no—
728C4⋊C4—24no—
729C4⋊C4—24no—
730C4⋊C4—216no—
731C4⋊C4—216no—
732C4⋊C4—216no—
733C4⋊C4—216no—
734C4⋊C4—216no—
735C4⋊C4—216no—
736C4⋊C4—48no—
737C4⋊C4—48no—
738C4⋊C4—48no—
739C4⋊C4—48no—
740C4⋊C4—48no—
741C4⋊C4—48no—
742C4⋊C4—44no—
743C4⋊C4—48no—
744C4⋊C4—44no—
745C4⋊C4—44no—
746C4⋊C4—44no—
747C4⋊C4—44no—
748C4⋊C4—44no—
749C4⋊C4—44no—
750C4⋊C4—44no—
751C4⋊C4—44no—
752C4⋊C4—48no—
753C4⋊C4—48no—
754C4⋊C4—44no—
755C4⋊C4—44no—
756C4⋊C4—48no—
757C4⋊C4—44no—
758C4⋊C4C22×Q8116yes—
759C4⋊C4C22×Q818yes—
760C4⋊C4C2×#4114yes—
761C4⋊C4C2×#4118yes—
762C4⋊C4C2×#4114yes—
763C22⋊C4—28no—
764C22⋊C4—28no—
765C22⋊C4—24no—
766C22⋊C4—28no—
767C22⋊C4—24no—
768C22⋊C4—48no—
769C22⋊C4—48no—
770C22⋊C4—48no—
771C22⋊C4—48no—
772C22⋊C4C22×Q8116yes—
773C22⋊C4C22×Q818yes—
774C22⋊C4C2×#4118yes—
775C22⋊C4C2×#4118yes—
776C42—22no—
777C42—22no—
778C42—22no—
779C42—22no—
780C42—24no—
781C42—28no—
782C42—24no—
783C42—24no—
784C42—22no—
785C42—22no—
786C42—28no—
787C42—28no—
788C42—44no—
789C42—44no—
790C42—48no—
791C42—44no—
792C42—48no—
793C42—48no—
794C42—44no—
795C42—44no—
796C42—48no—
797C42—44no—
798C42C22×Q814yes—
799C42C22×Q818yes—
800C42C22×Q814yes—
801C42C22×Q8116yes—
802C42C22×Q818yes—
803C42C2×#4118yes—
804C42C2×#4118yes—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—24no—
810C23—24no—
811C23C23×Q814yes—
812C23C23×Q812yes—
813C23C22×#4112yes—
814C23C22×#4112yes—
815C23C2611yescharacteristic
816Q8—28no—
817Q8—816no—
818Q8—816no—
819D4—216no—
820D4—28no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—24no—
824C2×C4—22no—
825C2×C4—24no—
826C2×C4—24no—
827C2×C4—22no—
828C2×C4—24no—
829C2×C4—22no—
830C2×C4—24no—
831C2×C4—24no—
832C2×C4—22no—
833C2×C4—216no—
834C2×C4—22no—
835C2×C4—21no—
836C2×C4—21no—
837C2×C4—22no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—24no—
841C2×C4—24no—
842C2×C4—24no—
843C2×C4—24no—
844C2×C4—28no—
845C2×C4—28no—
846C2×C4—24no—
847C2×C4—24no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—24no—
851C2×C4—28no—
852C2×C4—28no—
853C2×C4—28no—
854C2×C4—24no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—24no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—28no—
861C2×C4—24no—
862C2×C4—24no—
863C2×C4—24no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—48no—
867C2×C4—416no—
868C2×C4—88no—
869C2×C4—84no—
870C2×C4—84no—
871C2×C4—84no—
872C2×C4—88no—
873C2×C4—82no—
874C2×C4—88no—
875C2×C4—82no—
876C2×C4#533116yes—
877C2×C4C23×Q814yes—
878C2×C4C23×Q818yes—
879C2×C4C23×Q814yes—
880C2×C4C23×Q814yes—
881C2×C4C23×Q812yes—
882C2×C4C23×Q812yes—
883C2×C4C22×#4114yes—
884C2×C4C22×#4118yes—
885C2×C4C22×#4114yes—
886C2×C4C22×#4112yes—
887C2×C4C22×#4112yes—
888C2×C4C22×#4112yes—
889C2×C4C22×#4112yes—
890C22—24no—
891C22—24no—
892C22—22no—
893C22—22no—
894C22—28no—
895C22—24no—
896C22—44no—
897C22—42no—
898C22—42no—
899C22C2×#53314yes—
900C22C24×Q811yescharacteristic
901C22C23×#4111yescharacteristic
902C22C23×#4111yescharacteristic
903C22H(7,𝔽2)12yes—
904C222−1+612yes—
905C4—24no—
906C4—28no—
907C4—24no—
908C4—28no—
909C4—24no—
910C4—24no—
911C4—24no—
912C4—44no—
913C4—42no—
914C4—42no—
915C4—48no—
916C4—44no—
917C4—41no—
918C4—41no—
919C4—48no—
920C4—44no—
921C4—44no—
922C4—41no—
923C4—41no—
924C4C2×#53314yes—
925C4C2×#53314yes—
926C2—24no—
927C2—44no—
928C2C22×#53311yescharacteristic
929C2#6285412yes—
930C2#6285712yes—
931C2#6285811yescharacteristic
932C2#6286111yescharacteristic
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. #35972C2semidirect
2. #35963C2semidirect
3. #35962C2semidirect
4. #35871C2semidirect
5. #35867C2semidirect
6. #35862C2semidirect
7. #35337C2semidirect
8. #35336C2semidirect
9. #35330C2semidirect
10. #35304C2semidirect
11. #35284C2semidirect
12. #35283C2semidirect
13. #35275C2semidirect
16. #34638C2semidirect
17. #34625C2semidirect
18. C2×#2647C2semidirect
19. #34272C2semidirect
20. #34272C2semidirect
189. C4×#41Q8semidirect

Maximal subgroups

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

subgroupindex
#359722
#359632
#359622
#358712
#358672
#358622
#353372
#353362
#353302
#353042
#352842
#352832
#352752
#352572
#346382
#346252
C2×#26472
#342722
#341892
#341882
#339992