Finite Group Databasebeta

← #7720087

Subgroups — #7720087

Order 512.

4543 conjugacy classes of subgroups.

The subgroup lattice has 1064 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#51473C214yesmaximal, complemented
2#51427C214yesmaximal, complemented
3#51231C214yesmaximal, complemented
4#51224C214yesmaximal, complemented
5#45433C214yesmaximal, complemented
6#45251C214yesmaximal, complemented
7#45058C214yesmaximal, complemented
8#44898C214yesmaximal, complemented
9#39608C212yesmaximal, complemented
10#39158C212yesmaximal, complemented
11#38264C214yesmaximal, complemented
12#37975C214yesmaximal, complemented
13#37433C212yesmaximal, complemented
14#37322C212yesmaximal, complemented
15#36301C212yesmaximal, complemented
16#36176C212yesmaximal, complemented
17#35344C212yesmaximal, complemented
18#35296C212yesmaximal, complemented
19#35289C211yesmaximal, characteristic, complemented
20#35279C211yesmaximal, characteristic, complemented
21#35192C211yesmaximal, characteristic, complemented
22#34609C211yesmaximal, characteristic
23#34367C211yesmaximal, characteristic, complemented
24#34365C211yesmaximal, characteristic, complemented
25#34121C211yesmaximal, characteristic, complemented
26C2×#532C2211yescharacteristic
27C22×C4⋊Q8C2211yescharacteristic
28C2×C4×#41C2211yescharacteristic
29#2864C2214yes—
30#2864C2212yes—
31#2862C2212yes—
32#2862C2212yes—
33#2858C2212yes—
34#2857C2212yes—
35#2857C2212yes—
36#2854C2214yes—
37#2793C2218yes—
38#2789C2218yes—
39#2789C2218yes—
40#2763C2218yes—
41#2761C2218yes—
42#2760C2218yes—
43#2759C2218yes—
44#2759C2218yes—
45#2754C2218yes—
46#2754C2218yes—
47#2754C2218yes—
48#2752C2218yes—
49#2751C2218yes—
50#2751C2218yes—
51#2749C2218yes—
52#2730C2218yes—
53#2712C2218yes—
54#2700C2218yes—
55#2700C2218yes—
56#2692C2218yes—
57#2665C2214yes—
58#2644C2214yes—
59#2640C2214yes—
60#2635C2212yes—
61#2635C2212yes—
62#2632C2212yes—
63#2631C2212yes—
64#2628C2211yescharacteristic
65#2628C2214yes—
66#2628C2212yes—
67#2628C2211yescharacteristic
68#2628C2212yes—
69#2624C2212yes—
70#2619C2211yescharacteristic
71#2619C2211yescharacteristic
72#2615C2212yes—
73#2610C2218yes—
74#2609C2218yes—
75#2607C2218yes—
76#2607C2218yes—
77#2605C2218yes—
78#2605C2218yes—
79#2605C2214yes—
80#2595C2218yes—
81#2571C2212yes—
82#2568C2212yes—
83#2567C2212yes—
84#2563C2212yes—
85#2563C2212yes—
86#2563C2214yes—
87#2563C2212yes—
88#2557C2218yes—
89#2557C2218yes—
90#2551C2212yes—
91#2547C2214yes—
92#2547C2214yes—
93#2542C2212yes—
94#2532C2218yes—
95#2527C2218yes—
96#2527C2218yes—
97#2517C2218yes—
98#2513C2214yes—
99#2508C2214yes—
100#2508C2214yes—
101#2504C2214yes—
102#2499C2218yes—
103#2497C2214yes—
104#2495C2214yes—
105#2494C2214yes—
106#2494C2214yes—
107#2494C2214yes—
108#2494C2214yes—
109#2491C2214yes—
110#2488C2218yes—
111#2487C2212yes—
112#2487C2214yes—
113#2487C2212yes—
114#2486C2214yes—
115#2485C2214yes—
116#2485C2214yes—
117#2477C2218yes—
118#2477C2218yes—
119#2474C2218yes—
120#2471C2218yes—
121#2471C2218yes—
122#2452C2214yes—
123#2440C2214yes—
124#2439C2214yes—
125#2439C2214yes—
126#2439C2214yes—
127#2436C2214yes—
128#2420C2214yes—
129#2409C2212yes—
130#2409C2212yes—
131#2398C2212yes—
132#2397C2212yes—
133#2388C2212yes—
134#2388C2212yes—
135#2381C2214yes—
136#2377C2214yes—
137#2369C2212yes—
138#2369C2212yes—
139#2363C2214yes—
140#2357C2212yes—
141#2356C2212yes—
142#2355C2212yes—
143#2354C2212yes—
144#2354C2212yes—
145#2353C2212yes—
146#2353C2212yes—
147#2352C2214yes—
148#2352C2212yes—
149#2352C2212yes—
150#2352C2214yes—
151#2352C2214yes—
152D4×C4⋊C4C2212yes—
153#2346C2214yes—
154#2344C2214yes—
155#2344C2214yes—
156#2344C2214yes—
157#2337C2214yes—
158#2331C2214yes—
159#2331C2214yes—
160#2331C2212yes—
161#2331C2212yes—
162#2331C2214yes—
163#2331C2212yes—
164#2328C2212yes—
165#2324C2214yes—
166#2317C2212yes—
167#2311C2214yes—
168#2311C2212yes—
169#2311C2214yes—
170#2310C2214yes—
171C4×#121C2212yes—
172C4×#121C2212yes—
173#2298C2212yes—
174#2298C2212yes—
175#2297C2212yes—
176#2293C2214yes—
177#2285C2211yescharacteristic
178#2285C2211yescharacteristic
179#2283C2214yes—
180#2283C2211yescharacteristic
181#2283C2211yescharacteristic
182#2283C2211yescharacteristic
183C4×#117C2212yes—
184C4×#117C2211yescharacteristic
185C4×#117C2211yescharacteristic
186C2×C4×C4⋊C4C2211yescharacteristic
187C22×#41C2311yescharacteristic
188C22×#41C2312yes—
189C23×Q8C2312yes—
190#532—28no—
191C2×C4⋊Q8—28no—
192C2×C4⋊Q8C2312yes—
193C2×C4⋊Q8C2312yes—
194C2×C4⋊Q8C2312yes—
195C2×C4⋊Q8C2312yes—
196C2×C4⋊Q8C2311yescharacteristic
197C2×C4⋊Q8C2314yes—
198C2×C4⋊Q8C2314yes—
199C2×#127C2311yescharacteristic
200C2×#124C2312yes—
201C2×#124C2318yes—
202C2×#124C2318yes—
203C2×#123C2318yes—
204C2×C22⋊Q8C2314yes—
205C2×C22⋊Q8C2314yes—
206C2×C22⋊Q8C2318yes—
207C2×#121C2312yes—
208C2×#121C2312yes—
209C2×#121C2312yes—
210C2×#121C2312yes—
211C4×#41—28no—
212C2×C4×Q8C2311yescharacteristic
213C2×C4×Q8C2311yescharacteristic
214C2×C4×D4C2312yes—
215C2×C4×D4C2311yescharacteristic
216C2×C4×D4C2311yescharacteristic
217C2×C4×D4C2312yes—
218C2×C4×D4C2311yescharacteristic
219C2×C4×D4C2311yescharacteristic
220C2×C4×D4C2311yescharacteristic
221C2×C4×D4C2311yescharacteristic
222C2×C4×D4C2314yes—
223C2×C4×D4C2314yes—
224C2×C4×D4C2314yes—
225C2×#117C2311yescharacteristic
226C2×#117C2311yescharacteristic
227C2×#117C2311yescharacteristic
228C2×#117C2312yes—
229C2×#117C2312yes—
230C2×#117C2314yes—
231C2×#117C2312yes—
232C2×#117C2312yes—
233C2×#117C2318yes—
234C2×#117C2318yes—
235C22×C4⋊C4C2312yes—
236C22×C4⋊C4C2312yes—
237C22×C4⋊C4C2314yes—
238C22×C4⋊C4C2312yes—
239C22×C42C2312yes—
240C22×C42C2311yescharacteristic
241C22×C42C2311yescharacteristic
242C22×C42C2311yescharacteristic
243#401C2318yes—
244#401C2318yes—
245#400C2314yes—
246#400C2314yes—
247#400C2318yes—
248#400C2312yes—
249#400C2318yes—
250#400C2312yes—
251#400C2318yes—
252#400C2318yes—
253#399C2312yes—
254#399C2318yes—
255#399C2314yes—
256#399C2314yes—
257#399C2312yes—
258#399C2314yes—
259#398C2318yes—
260#398C2318yes—
261#397C2318yes—
262#397C2318yes—
263#397C2314yes—
264#397C2318yes—
265#397C2318yes—
266#397C2318yes—
267#397C2318yes—
268#397C2318yes—
269#397C2318yes—
270#397C2318yes—
271#397C2318yes—
272#396C2318yes—
273#396C2318yes—
274#396C2318yes—
275#395C2314yes—
276#395C2314yes—
277#395C2312yes—
278#395C2318yes—
279#395C2318yes—
280#395C2312yes—
281#394C2312yes—
282#394C2314yes—
283#394C2318yes—
284#394C2312yes—
285#394C2312yes—
286#394C2312yes—
287#394C2314yes—
288#394C2318yes—
289#393C2314yes—
290#393C2318yes—
291#393C2314yes—
292#393C2318yes—
293#393C2318yes—
294#393C2318yes—
295#393C2312yes—
296#393C2318yes—
297#393C2314yes—
298#393C2312yes—
299#393C2318yes—
300#392C2314yes—
301#392C2314yes—
302#392C2314yes—
303#392C2312yes—
304#392C2312yes—
305#392C2312yes—
306#392C2312yes—
307#391C2318yes—
308#391C2318yes—
309#391C2318yes—
310#391C2318yes—
311#391C2314yes—
312#391C2318yes—
313#391C2318yes—
314#391C2314yes—
315#391C2314yes—
316#391C2318yes—
317#391C2318yes—
318#391C2318yes—
319#391C2318yes—
320#391C2318yes—
321#391C2318yes—
322#391C2314yes—
323#390C2314yes—
324#390C2314yes—
325#390C2318yes—
326#390C2314yes—
327#390C2318yes—
328#390C2318yes—
329#390C2314yes—
330#390C2314yes—
331#390C2312yes—
332#390C2312yes—
333#389C2314yes—
334#389C2314yes—
335#389C2314yes—
336#389C2314yes—
337#389C2314yes—
338#389C2314yes—
339#389C2314yes—
340#389C2312yes—
341#389C2314yes—
342#389C2314yes—
343#389C2314yes—
344#389C2314yes—
345#389C2314yes—
346#389C2314yes—
347#389C2312yes—
348#388C2318yes—
349#388C2318yes—
350#388C2318yes—
351#388C2318yes—
352#388C2318yes—
353#388C2318yes—
354#388C2318yes—
355#388C2314yes—
356#388C2318yes—
357#388C2318yes—
358#388C2314yes—
359#388C2314yes—
360#388C2314yes—
361#388C2318yes—
362#388C2314yes—
363#388C2314yes—
364#388C2318yes—
365#388C2318yes—
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#387C2314yes—
382#387C2314yes—
383#387C2318yes—
384#387C2314yes—
385#387C2314yes—
386#387C2318yes—
387#387C2318yes—
388#386C2318yes—
389#386C2318yes—
390#386C2318yes—
391#386C2314yes—
392#386C2314yes—
393#386C2318yes—
394#386C2318yes—
395#386C2318yes—
396#386C2318yes—
397#386C2314yes—
398#386C2314yes—
399#386C2318yes—
400#386C2314yes—
401#386C2314yes—
402#385C2314yes—
403#385C2314yes—
404#385C2318yes—
405#385C2318yes—
406#385C2318yes—
407#384C2314yes—
408#384C2312yes—
409#384C2312yes—
410#383C2312yes—
411#383C2312yes—
412#383C2318yes—
413#383C2312yes—
414#382C2314yes—
415#382C2314yes—
416#382C2314yes—
417#382C2318yes—
418#382C2314yes—
419#382C2314yes—
420#382C2312yes—
421#382C2311yescharacteristic
422#382C2312yes—
423#382C2311yescharacteristic
424#382C2318yes—
425#382C2312yes—
426#382C2312yes—
427#381C2312yes—
428#381C2312yes—
429#381C2318yes—
430#381C2318yes—
431#381C2318yes—
432#381C2312yes—
433#380C2314yes—
434#380C2314yes—
435#380C2312yes—
436#380C2314yes—
437#380C2314yes—
438#380C2314yes—
439#380C2314yes—
440#380C2314yes—
441#380C2312yes—
442#380C2312yes—
443#380C2314yes—
444#380C2314yes—
445#380C2314yes—
446#380C2312yes—
447#380C2312yes—
448#380C2312yes—
449#380C2312yes—
450#380C2312yes—
451#380C2312yes—
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2311yescharacteristic
454C4×C4⋊C4C2312yes—
455C4×C4⋊C4C2314yes—
456C4×C4⋊C4C2312yes—
457C4×C4⋊C4C2312yes—
458C4×C4⋊C4C2314yes—
459C4×C4⋊C4C2314yes—
460C4×C4⋊C4C2312yes—
461C4×C4⋊C4C2314yes—
462C4×C4⋊C4C2314yes—
463C4×C4⋊C4C2314yes—
464C4×C4⋊C4C2312yes—
465C4×C4⋊C4C2312yes—
466C4×C4⋊C4C2311yescharacteristic
467C4×C4⋊C4C2314yes—
468C4×C4⋊C4C2311yescharacteristic
469C4×C4⋊C4C2312yes—
470C4×C4⋊C4C2312yes—
471C4×C4⋊C4C2312yes—
472C4×C22⋊C4C2318yes—
473C4×C22⋊C4C2318yes—
474C4×C22⋊C4C2312yes—
475C4×C22⋊C4C2312yes—
476C4×C22⋊C4C2314yes—
477C4×C22⋊C4C2314yes—
478C4×C22⋊C4C2314yes—
479C4×C22⋊C4C2314yes—
480C4×C22⋊C4C2318yes—
481C4×C22⋊C4C2312yes—
482C4×C22⋊C4C2312yes—
483C4×C22⋊C4C2312yes—
484C4×C22⋊C4C2312yes—
485C4×C22⋊C4C2312yes—
486#376C2312yes—
487#376C2312yes—
488#376C2312yes—
489#376C2318yes—
490#376C2312yes—
491#376C2312yes—
492C2×#95C2312yes—
493C43C2312yes—
494C43C2312yes—
495C2×#41—24no—
496C2×#41—28no—
497C2×#41—24no—
498C2×#41—42no—
499C2×#41—48no—
500C22×Q8—28no—
501C22×Q8—84no—
502C22×Q8C2411yescharacteristic
503C22×Q8C2414yes—
504C22×Q8C2414yes—
505C22×Q8C2412yes—
506C22×Q8C2418yes—
507C22×D4C2412yes—
508C22×D4C2411yescharacteristic
509C22×D4C2411yescharacteristic
510C22×D4C2411yescharacteristic
511C22×D4C2414yes—
512C22×D4C2412yes—
513C22×D4C2414yes—
514C22×D4C2412yes—
515C22×D4C2414yes—
516C23×C4C2411yescharacteristic
517C23×C4C2414yes—
518C23×C4C2411yescharacteristic
519C23×C4C2411yescharacteristic
520C23×C4C2411yescharacteristic
521C23×C4C2411yescharacteristic
522C23×C4C2411yescharacteristic
523C23×C4C2414yes—
524C23×C4C2414yes—
525C23×C4C2411yescharacteristic
526C23×C4C2411yescharacteristic
527C23×C4C2418yes—
528C23×C4C2411yescharacteristic
529C4⋊Q8—28no—
530C4⋊Q8—28no—
531C4⋊Q8—28no—
532C4⋊Q8—28no—
533C4⋊Q8—24no—
534C4⋊Q8—48no—
535C4⋊Q8—48no—
536#127—24no—
537#124—28no—
538#124—88no—
539#124—88no—
540#123—88no—
541C22⋊Q8—88no—
542C22⋊Q8—84no—
543C22⋊Q8—84no—
544#121—28no—
545#121—28no—
546#121—28no—
547#121—44no—
548C4×Q8—24no—
549C4×Q8—24no—
550C4×D4—24no—
551C4×D4—24no—
552C4×D4—24no—
553C4×D4—24no—
554C4×D4—24no—
555C4×D4—24no—
556C4×D4—28no—
557C4×D4—28no—
558C4×D4—48no—
559C4×D4—48no—
560C4×D4—48no—
561#117—24no—
562#117—24no—
563#117—24no—
564#117—44no—
565#117—44no—
566#117—48no—
567#117—44no—
568#117—44no—
569#117—88no—
570#117—88no—
571C2×C4⋊C4—28no—
572C2×C4⋊C4—28no—
573C2×C4⋊C4—48no—
574C2×C4⋊C4—44no—
575C2×C4⋊C4C2412yes—
576C2×C4⋊C4C2412yes—
577C2×C4⋊C4C2412yes—
578C2×C4⋊C4C2414yes—
579C2×C4⋊C4C2414yes—
580C2×C4⋊C4C2414yes—
581C2×C4⋊C4C2414yes—
582C2×C4⋊C4C2414yes—
583C2×C4⋊C4C2411yescharacteristic
584C2×C4⋊C4C2411yescharacteristic
585C2×C4⋊C4C2411yescharacteristic
586C2×C4⋊C4C2411yescharacteristic
587C2×C4⋊C4C2411yescharacteristic
588C2×C4⋊C4C2411yescharacteristic
589C2×C4⋊C4C2414yes—
590C2×C4⋊C4C2412yes—
591C2×C4⋊C4C2412yes—
592C2×C4⋊C4C2412yes—
593C2×C4⋊C4C2412yes—
594C2×C4⋊C4C2412yes—
595C2×C4⋊C4C2414yes—
596C2×C4⋊C4C2418yes—
597C2×C4⋊C4C2418yes—
598C2×C4⋊C4C2418yes—
599C2×C4⋊C4C2418yes—
600C2×C4⋊C4C2418yes—
601C2×C4⋊C4C2414yes—
602C2×C4⋊C4C2414yes—
603C2×C4⋊C4C2414yes—
604C2×C4⋊C4C2414yes—
605C2×C4⋊C4C2414yes—
606C2×C4⋊C4C2418yes—
607C2×C4⋊C4C2418yes—
608C2×C4⋊C4C2418yes—
609C2×C22⋊C4C2411yescharacteristic
610C2×C22⋊C4C2411yescharacteristic
611C2×C22⋊C4C2411yescharacteristic
612C2×C22⋊C4C2411yescharacteristic
613C2×C22⋊C4C2411yescharacteristic
614C2×C22⋊C4C2411yescharacteristic
615C2×C22⋊C4C2414yes—
616C2×C22⋊C4C2414yes—
617C2×C22⋊C4C2414yes—
618C2×C22⋊C4C2414yes—
619C2×C22⋊C4C2414yes—
620C2×C22⋊C4C2414yes—
621C2×C22⋊C4C2418yes—
622C2×C22⋊C4C2414yes—
623C2×C22⋊C4C2414yes—
624C2×C22⋊C4C2414yes—
625C2×C22⋊C4C2414yes—
626C2×C22⋊C4C2418yes—
627C2×C22⋊C4C2414yes—
628C2×C22⋊C4C2414yes—
629C2×C22⋊C4C2418yes—
630C2×C22⋊C4C2414yes—
631C2×C22⋊C4C2414yes—
632C2×C22⋊C4C2414yes—
633C2×C22⋊C4C2414yes—
634C2×C22⋊C4C2418yes—
635C2×C22⋊C4C2418yes—
636C2×C22⋊C4C2418yes—
637C2×C22⋊C4C2418yes—
638C2×C22⋊C4C2418yes—
639C2×C22⋊C4C2414yes—
640C2×C22⋊C4C2418yes—
641C2×C42—28no—
642C2×C42—24no—
643C2×C42—24no—
644C2×C42#4118yes—
645C2×C42C2411yescharacteristic
646C2×C42C2411yescharacteristic
647C2×C42C2412yes—
648C2×C42C2412yes—
649C2×C42C2414yes—
650C2×C42C2411yescharacteristic
651C2×C42C2411yescharacteristic
652C2×C42C2411yescharacteristic
653C2×C42C2411yescharacteristic
654C2×C42C2412yes—
655C2×C42C2412yes—
656C2×C42C2414yes—
657C2×C42C2414yes—
658C2×C42C2418yes—
659C2×C42C2418yes—
660C2×C42C2414yes—
661C2×C42C2414yes—
662C2×C42C2418yes—
663C2×C42C2414yes—
664C2×C42C2414yes—
665C2×C42C2411yescharacteristic
666C2×C42C2411yescharacteristic
667C2×C42C2411yescharacteristic
668C2×C42C2411yescharacteristic
669#95C2412yes—
670#95C2412yes—
671#95C2414yes—
672#95C2414yes—
673#95C2412yes—
674#95C2412yes—
675#95C2414yes—
676#95C2414yes—
677#95C2414yes—
678#95C2414yes—
679#95C2414yes—
680#95C2414yes—
681#95C2418yes—
682#95C2418yes—
683#95C2414yes—
684#95C2418yes—
685#95C2412yes—
686#95C2412yes—
687#95C2414yes—
688#95C2418yes—
689#95C2418yes—
690#95C2418yes—
691#95C2414yes—
692#95C2418yes—
693#95C2414yes—
694#95C2414yes—
695#95C2412yes—
696#95C2412yes—
697#95C2418yes—
698#95C2414yes—
699#95C2418yes—
700#95C2414yes—
701#95C2414yes—
702#95C2414yes—
703#95C2418yes—
704#95C2418yes—
705#95C2418yes—
706#95C2414yes—
707#95C2418yes—
708#95C2418yes—
709#95C2418yes—
710#95C2418yes—
711#95C2418yes—
712#95C2418yes—
713C24C2511yescharacteristic
714C24C2514yes—
715C24C2511yescharacteristic
716C24C2511yescharacteristic
717#41—416no—
718#41—816no—
719C2×Q8—22no—
720C2×Q8—24no—
721C2×Q8—28no—
722C2×Q8—28no—
723C2×Q8—22no—
724C2×Q8—41no—
725C2×Q8—44no—
726C2×Q8—44no—
727C2×Q8—48no—
728C2×Q8—44no—
729C2×Q8—48no—
730C2×Q8—48no—
731C2×Q8—48no—
732C2×Q8—816no—
733C2×D4—22no—
734C2×D4—22no—
735C2×D4—22no—
736C2×D4—22no—
737C2×D4—28no—
738C2×D4—28no—
739C2×D4—22no—
740C2×D4—24no—
741C2×D4—24no—
742C2×D4—24no—
743C2×D4—24no—
744C2×D4—22no—
745C2×D4—24no—
746C2×D4—41no—
747C2×D4—41no—
748C2×D4—41no—
749C2×D4—44no—
750C2×D4—44no—
751C2×D4—44no—
752C2×D4—44no—
753C2×D4—44no—
754C2×D4—44no—
755C2×D4—44no—
756C2×D4—44no—
757C2×D4—44no—
758C22×C4—22no—
759C22×C4—22no—
760C22×C4—22no—
761C22×C4—22no—
762C22×C4—24no—
763C22×C4—28no—
764C22×C4—28no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—22no—
768C22×C4—28no—
769C22×C4—22no—
770C22×C4—24no—
771C22×C4—28no—
772C22×C4—24no—
773C22×C4—28no—
774C22×C4—22no—
775C22×C4—22no—
776C22×C4—22no—
777C22×C4—48no—
778C22×C4—42no—
779C22×C4—44no—
780C22×C4—48no—
781C22×C4—48no—
782C22×C4—48no—
783C22×C4—42no—
784C22×C4—42no—
785C22×C4—44no—
786C22×C4C2×#4114yes—
787C22×C4C2×#4114yes—
788C22×C4C2×#4114yes—
789C22×C42−1+414yes—
790C22×C4C2511yescharacteristic
791C22×C4C2514yes—
792C22×C4C2514yes—
793C22×C4C2514yes—
794C22×C4C2514yes—
795C22×C4C2514yes—
796C22×C4C2511yescharacteristic
797C22×C4C2514yes—
798C22×C4C2514yes—
799C22×C4C2511yescharacteristic
800C22×C4C2518yes—
801C22×C4C2518yes—
802C22×C4C2511yescharacteristic
803C22×C4C2511yescharacteristic
804C22×C4C2511yescharacteristic
805C22×C4C2511yescharacteristic
806C22×C4C2511yescharacteristic
807C22×C4C2511yescharacteristic
808C22×C4C2511yescharacteristic
809C22×C4C2511yescharacteristic
810C22×C4C2511yescharacteristic
811C4⋊C4—28no—
812C4⋊C4—28no—
813C4⋊C4—28no—
814C4⋊C4—28no—
815C4⋊C4—22no—
816C4⋊C4—22no—
817C4⋊C4—22no—
818C4⋊C4—22no—
819C4⋊C4—22no—
820C4⋊C4—22no—
821C4⋊C4—24no—
822C4⋊C4—24no—
823C4⋊C4—24no—
824C4⋊C4—24no—
825C4⋊C4—24no—
826C4⋊C4—24no—
827C4⋊C4—28no—
828C4⋊C4—28no—
829C4⋊C4—24no—
830C4⋊C4—24no—
831C4⋊C4—44no—
832C4⋊C4—48no—
833C4⋊C4—44no—
834C4⋊C4—48no—
835C4⋊C4—48no—
836C4⋊C4—48no—
837C4⋊C4—48no—
838C4⋊C4—44no—
839C4⋊C4—44no—
840C4⋊C4—44no—
841C4⋊C4—44no—
842C4⋊C4—48no—
843C4⋊C4—48no—
844C4⋊C4—48no—
845C22⋊C4—22no—
846C22⋊C4—22no—
847C22⋊C4—22no—
848C22⋊C4—22no—
849C22⋊C4—22no—
850C22⋊C4—22no—
851C22⋊C4—28no—
852C22⋊C4—28no—
853C22⋊C4—28no—
854C22⋊C4—44no—
855C22⋊C4—44no—
856C22⋊C4—48no—
857C22⋊C4—44no—
858C22⋊C4—44no—
859C22⋊C4—44no—
860C22⋊C4—44no—
861C22⋊C4—44no—
862C22⋊C4—48no—
863C22⋊C4—48no—
864C22⋊C4—44no—
865C22⋊C4—44no—
866C22⋊C4—44no—
867C22⋊C4—44no—
868C22⋊C4—44no—
869C22⋊C4—44no—
870C22⋊C4—48no—
871C22⋊C4—48no—
872C22⋊C4—48no—
873C22⋊C4—48no—
874C22⋊C4—48no—
875C22⋊C4—44no—
876C22⋊C4—48no—
877C42—22no—
878C42—22no—
879C42—22no—
880C42—22no—
881C42—22no—
882C42—22no—
883C42—28no—
884C42—24no—
885C42—24no—
886C42—24no—
887C42—24no—
888C42—28no—
889C42—44no—
890C42—44no—
891C42—44no—
892C42—48no—
893C42—44no—
894C42—48no—
895C42—48no—
896C42—44no—
897C42C2×#4114yes—
898C42C2×#4114yes—
899C42C2×#4114yes—
900C42C2×#4114yes—
901C23—21no—
902C23—21no—
903C23—21no—
904C23—21no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—21no—
910C23—24no—
911C23—24no—
912C23—21no—
913C23—22no—
914C23—24no—
915C23—24no—
916C23—24no—
917C23—21no—
918C23—24no—
919C23—22no—
920C23—24no—
921C23C22×#4112yes—
922C23C2×2−1+412yes—
923C23C2611yescharacteristic
924Q8—44no—
925Q8—88no—
926Q8—88no—
927Q8—84no—
928Q8—168no—
929D4—44no—
930D4—44no—
931D4—44no—
932D4—48no—
933D4—84no—
934D4—84no—
935D4—88no—
936D4—88no—
937D4—88no—
938C2×C4—21no—
939C2×C4—21no—
940C2×C4—21no—
941C2×C4—22no—
942C2×C4—21no—
943C2×C4—22no—
944C2×C4—22no—
945C2×C4—28no—
946C2×C4—28no—
947C2×C4—28no—
948C2×C4—21no—
949C2×C4—21no—
950C2×C4—21no—
951C2×C4—21no—
952C2×C4—21no—
953C2×C4—24no—
954C2×C4—28no—
955C2×C4—24no—
956C2×C4—24no—
957C2×C4—24no—
958C2×C4—21no—
959C2×C4—24no—
960C2×C4—24no—
961C2×C4—24no—
962C2×C4—24no—
963C2×C4—24no—
964C2×C4—24no—
965C2×C4—22no—
966C2×C4—24no—
967C2×C4—28no—
968C2×C4—24no—
969C2×C4—28no—
970C2×C4—24no—
971C2×C4—21no—
972C2×C4—22no—
973C2×C4—24no—
974C2×C4—24no—
975C2×C4—24no—
976C2×C4—24no—
977C2×C4—24no—
978C2×C4—28no—
979C2×C4—22no—
980C2×C4—24no—
981C2×C4—24no—
982C2×C4—24no—
983C2×C4—28no—
984C2×C4—28no—
985C2×C4—22no—
986C2×C4—44no—
987C2×C4—416no—
988C2×C4—44no—
989C2×C4—44no—
990C2×C4—44no—
991C2×C4—416no—
992C2×C4—82no—
993C2×C4—82no—
994C2×C4—88no—
995C2×C4—816no—
996C2×C4C22×#4112yes—
997C2×C4C22×#4112yes—
998C2×C4C22×#4112yes—
999C2×C4C22×#4112yes—
1000C2×C4C22×#4112yes—
1001C2×C4C22×#4112yes—
1002C2×C4C2×2−1+412yes—
1003C2×C4C2×2−1+412yes—
1004C2×C4#58512yes—
1005C2×C4#58514yes—
1006C22—22no—
1007C22—22no—
1008C22—22no—
1009C22—22no—
1010C22—24no—
1011C22—41no—
1012C22—41no—
1013C22—42no—
1014C22—42no—
1015C22—42no—
1016C22—41no—
1017C22—44no—
1018C22—44no—
1019C22—41no—
1020C22—41no—
1021C22—44no—
1022C22—44no—
1023C22—44no—
1024C22—42no—
1025C22—44no—
1026C22—42no—
1027C22—44no—
1028C22C23×#4111yescharacteristic
1029C22C22×2−1+411yescharacteristic
1030C22C2×#58511yescharacteristic
1031C22C2×#58512yes—
1032C22H(7,𝔽2)12yes—
1033C4—22no—
1034C4—22no—
1035C4—22no—
1036C4—22no—
1037C4—22no—
1038C4—41no—
1039C4—41no—
1040C4—41no—
1041C4—44no—
1042C4—48no—
1043C4—41no—
1044C4—41no—
1045C4—44no—
1046C4—44no—
1047C4—44no—
1048C4—44no—
1049C4—48no—
1050C4—44no—
1051C4—44no—
1052C4#349514yes—
1053C4#351014yes—
1054C2—42no—
1055C2—42no—
1056C2—81no—
1057C2—84no—
1058C2C2×#349511yescharacteristic
1059C2C2×#351011yescharacteristic
1060C2#6285511yescharacteristic
1061C2#6292912yes—
1062C2#6293812yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#34609C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #51473C2semidirect
2. #51427C2semidirect
3. #51231C2semidirect
4. #51224C2semidirect
5. #45433C2semidirect
6. #45251C2semidirect
7. #45058C2semidirect
8. #44898C2semidirect
9. #39608C2semidirect
10. #39158C2semidirect
11. #38264C2semidirect
12. #37975C2semidirect
13. #37433C2semidirect
14. #37322C2semidirect
15. #36301C2semidirect
16. #36176C2semidirect
17. #35344C2semidirect
18. #35296C2semidirect
19. #35289C2semidirect
20. #35279C2semidirect
21. #35192C2semidirect
23. #34367C2semidirect
24. #34365C2semidirect
25. #34121C2semidirect

Maximal subgroups

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

subgroupindex
#514732
#514272
#512312
#512242
#454332
#452512
#450582
#448982
#396082
#391582
#382642
#379752
#374332
#373222
#363012
#361762
#353442
#352962
#352892
#352792
#351922
#346092
#343672
#343652
#341212