Finite Group Databasebeta

← #7674382

Subgroups — #7674382

Order 512.

4684 conjugacy classes of subgroups.

The subgroup lattice has 1038 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45350C212yesmaximal, complemented
2#45347C212yesmaximal, complemented
3#45318C212yesmaximal, complemented
4#45306C212yesmaximal, complemented
5#45231C212yesmaximal, complemented
6#45211C212yesmaximal, complemented
7#45083C212yesmaximal, complemented
8#45056C212yesmaximal, complemented
9#38223C218yesmaximal, complemented
10#38221C218yesmaximal, complemented
11#37939C214yesmaximal, complemented
12#37938C214yesmaximal, complemented
13#37887C214yesmaximal, complemented
14#37884C214yesmaximal, complemented
15#35543C212yesmaximal, complemented
16#35517C212yesmaximal
17#35279C211yesmaximal, characteristic, complemented
18#35279C211yesmaximal, characteristic, complemented
19#35160C212yesmaximal, complemented
20#34638C211yesmaximal, characteristic, complemented
21#34252C212yesmaximal, complemented
22#34189C211yesmaximal, characteristic, complemented
23#34184C211yesmaximal, characteristic, complemented
24C2×#2331C211yesmaximal, characteristic, complemented
25#34070C211yesmaximal, characteristic
26C2×#532C2211yescharacteristic
27C22×C4⋊Q8C2211yescharacteristic
28C2×#520C2212yes—
29C2×C4×#41C2211yescharacteristic
30C2×C4×#41C2211yescharacteristic
31#2857C2214yes—
32#2857C2214yes—
33#2852C2218yes—
34#2773C2218yes—
35#2767C2218yes—
36#2766C2218yes—
37#2764C2218yes—
38#2762C2218yes—
39#2758C2218yes—
40#2754C2218yes—
41#2747C2218yes—
42#2743C2218yes—
43#2741C2218yes—
44#2738C2218yes—
45#2738C2218yes—
46#2702C2218yes—
47#2698C2218yes—
48#2690C2218yes—
49#2687C2218yes—
50#2647C2212yes—
51#2647C2212yes—
52#2647C2212yes—
53#2647C2212yes—
54#2646C2214yes—
55#2646C2214yes—
56#2643C2218yes—
57#2628C2212yes—
58#2628C2212yes—
59#2628C2212yes—
60#2628C2212yes—
61#2612C2218yes—
62#2611C2218yes—
63#2571C2214yes—
64#2570C2214yes—
65#2570C2214yes—
66#2568C2212yes—
67#2568C2212yes—
68#2567C2212yes—
69#2567C2212yes—
70#2563C2212yes—
71#2563C2212yes—
72#2556C2218yes—
73#2553C2218yes—
74#2552C2214yes—
75#2542C2212yes—
76#2542C2212yes—
77#2533C2218yes—
78#2533C2218yes—
79#2532C2218yes—
80#2530C2218yes—
81#2527C2218yes—
82#2520C2218yes—
83#2519C2218yes—
84#2514C2214yes—
85#2513C2214yes—
86#2512C2214yes—
87#2511C2214yes—
88#2509C2214yes—
89#2508C2214yes—
90#2507C2214yes—
91#2506C2214yes—
92#2505C2218yes—
93#2498C2218yes—
94#2497C2214yes—
95#2496C2214yes—
96#2495C2214yes—
97#2494C2214yes—
98#2493C2218yes—
99#2488C2218yes—
100#2487C2214yes—
101#2487C2214yes—
102#2487C2214yes—
103#2486C2214yes—
104#2485C2214yes—
105#2485C2214yes—
106#2477C2218yes—
107#2473C2218yes—
108#2448C2214yes—
109#2447C2214yes—
110#2446C2214yes—
111#2445C2214yes—
112#2444C2218yes—
113#2443C2218yes—
114#2438C2218yes—
115#2409C2214yes—
116#2409C2214yes—
117#2402C2212yes—
118#2402C2212yes—
119#2402C2212yes—
120#2402C2212yes—
121#2357C2212yes—
122#2357C2212yes—
123#2357C2214yes—
124#2356C2214yes—
125#2356C2212yes—
126#2356C2212yes—
127#2355C2214yes—
128#2354C2214yes—
129#2353C2214yes—
130#2353C2214yes—
131#2351C2212yes—
132#2351C2212yes—
133#2349C2212yes—
134#2349C2212yes—
135#2349C2214yes—
136#2349C2214yes—
137#2347C2214yes—
138#2346C2214yes—
139#2345C2214yes—
140#2344C2214yes—
141#2331C2212yes—
142#2331C2212yes—
143#2331C2212yes—
144#2331C2212yes—
145#2331C2214yes—
146#2331C2214yes—
147#2328C2211yescharacteristic
148#2328C2211yescharacteristic
149#2327C2211yescharacteristic
150#2327C2211yescharacteristic
151#2326C2211yescharacteristic
152#2326C2211yescharacteristic
153#2326C2211yescharacteristic
154#2326C2211yescharacteristic
155#2325C2214yes—
156#2325C2214yes—
157#2318C2218yes—
158#2317C2214yes—
159#2317C2212yes—
160#2317C2212yes—
161#2317C2212yes—
162#2314C2214yes—
163#2311C2212yes—
164#2311C2212yes—
165#2311C2212yes—
166#2297C2211yescharacteristic
167#2297C2211yescharacteristic
168#2296C2212yes—
169#2296C2212yes—
170C2×#391C2214yes—
171C2×#389C2212yes—
172#2290C2214yes—
173#2290C2214yes—
174#2290C2218yes—
175C2×#387C2214yes—
176#2285C2211yescharacteristic
177#2285C2211yescharacteristic
178#2285C2211yescharacteristic
179#2285C2212yes—
180#2283C2212yes—
181#2283C2212yes—
182C2×#382C2211yescharacteristic
183C2×#382C2212yes—
184#2274C2212yes—
185C2×C4×C4⋊C4C2212yes—
186C2×#376C2211yescharacteristic
187C22×#41C2311yescharacteristic
188C22×#41C2311yescharacteristic
189C23×Q8C2312yes—
190#532—28no—
191C2×C4⋊Q8—28no—
192C2×C4⋊Q8C2312yes—
193C2×C4⋊Q8C2312yes—
194C2×C4⋊Q8C2311yescharacteristic
195C2×C4⋊Q8C2312yes—
196C2×C4⋊Q8C2312yes—
197C2×#127C2311yescharacteristic
198C2×#126C2318yes—
199C2×#125C2318yes—
200C2×#124C2311yescharacteristic
201C2×#124C2311yescharacteristic
202C2×#123C2318yes—
203C2×C22⋊Q8C2318yes—
204C2×C22⋊Q8C2318yes—
205C2×#121C2314yes—
206#520—216no—
207C4×#41—28no—
208C4×#41—28no—
209C2×C4×Q8C2311yescharacteristic
210C2×C4×Q8C2311yescharacteristic
211C2×C4×Q8C2311yescharacteristic
212C2×C4×Q8C2311yescharacteristic
213C2×C4×Q8C2314yes—
214C2×C4×D4C2311yescharacteristic
215C2×C4×D4C2311yescharacteristic
216C2×C4×D4C2318yes—
217C2×C4×D4C2312yes—
218C2×C4×D4C2312yes—
219C2×C4×D4C2312yes—
220C2×C4×D4C2312yes—
221C2×C4×D4C2311yescharacteristic
222C2×C4×D4C2311yescharacteristic
223C2×C4×D4C2314yes—
224C2×C4×D4C2314yes—
225C2×#117C2312yes—
226C2×#117C2312yes—
227C2×#117C2312yes—
228C2×#117C2311yescharacteristic
229C2×#117C2312yes—
230C2×#117C2311yescharacteristic
231C2×#117C2314yes—
232C2×#117C2318yes—
233C22×C4⋊C4C2312yes—
234C22×C4⋊C4C2312yes—
235C22×C4⋊C4C2314yes—
236C22×C4⋊C4C2312yes—
237C22×C4⋊C4C2314yes—
238C22×C42C2312yes—
239C22×C42C2312yes—
240C22×C42C2311yescharacteristic
241C22×C42C2311yescharacteristic
242C22×C42C2314yes—
243C22×C42C2311yescharacteristic
244#401C2318yes—
245#400C2314yes—
246#400C2314yes—
247#400C2314yes—
248#400C2314yes—
249#400C2318yes—
250#400C2318yes—
251#400C2318yes—
252#400C2318yes—
253#400C2318yes—
254#400C2318yes—
255#400C2318yes—
256#400C2314yes—
257#400C2314yes—
258#400C2314yes—
259#400C2314yes—
260#400C2314yes—
261#400C2314yes—
262#400C2314yes—
263#400C2314yes—
264#400C2318yes—
265#399C2314yes—
266#399C2314yes—
267#399C2314yes—
268#399C2314yes—
269#399C2318yes—
270#398C2318yes—
271#398C2318yes—
272#398C2314yes—
273#398C2314yes—
274#398C2318yes—
275#398C2314yes—
276#398C2314yes—
277#398C2314yes—
278#398C2314yes—
279#398C2314yes—
280#398C2314yes—
281#398C2318yes—
282#398C2318yes—
283#397C2318yes—
284#397C2318yes—
285#397C2318yes—
286#397C2318yes—
287#397C2318yes—
288#397C2318yes—
289#396C2318yes—
290#395C2314yes—
291#395C2314yes—
292#395C2314yes—
293#395C2314yes—
294#394C2318yes—
295#394C2318yes—
296#393C2314yes—
297#393C2314yes—
298#393C2314yes—
299#393C2314yes—
300#391C2314yes—
301#391C2314yes—
302#391C2314yes—
303#391C2318yes—
304#391C2318yes—
305#391C2311yescharacteristic
306#391C2311yescharacteristic
307#391C2311yescharacteristic
308#391C2311yescharacteristic
309#391C2318yes—
310#391C2318yes—
311#391C2318yes—
312#391C2318yes—
313#390C2314yes—
314#390C2314yes—
315#390C2314yes—
316#390C2311yescharacteristic
317#390C2311yescharacteristic
318#390C2311yescharacteristic
319#390C2311yescharacteristic
320#389C2318yes—
321#389C2318yes—
322#389C2314yes—
323#389C2314yes—
324#389C2314yes—
325#389C2314yes—
326#389C2318yes—
327#389C2314yes—
328#389C2314yes—
329#389C2314yes—
330#389C2314yes—
331#389C2318yes—
332#389C2318yes—
333#389C2314yes—
334#389C2314yes—
335#389C2312yes—
336#389C2312yes—
337#389C2312yes—
338#389C2312yes—
339#389C2318yes—
340#389C2312yes—
341#389C2312yes—
342#389C2312yes—
343#389C2312yes—
344#388C2318yes—
345#388C2318yes—
346#388C2318yes—
347#388C2318yes—
348#388C2314yes—
349#388C2314yes—
350#388C2314yes—
351#388C2314yes—
352#388C2318yes—
353#388C2318yes—
354#388C2318yes—
355#388C2318yes—
356#388C2318yes—
357#388C2318yes—
358#388C2318yes—
359#387C2318yes—
360#387C2318yes—
361#387C2318yes—
362#387C2318yes—
363#387C2318yes—
364#387C2318yes—
365#387C2318yes—
366#387C2318yes—
367#387C2314yes—
368#387C2314yes—
369#387C2314yes—
370#387C2314yes—
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#386C2318yes—
385#386C2314yes—
386#386C2314yes—
387#386C2314yes—
388#386C2314yes—
389#386C2314yes—
390#386C2314yes—
391#386C2318yes—
392#385C2318yes—
393#385C2318yes—
394#385C2318yes—
395#385C2318yes—
396#385C2318yes—
397#385C2314yes—
398#385C2314yes—
399#385C2314yes—
400#385C2314yes—
401#385C2314yes—
402#385C2318yes—
403#385C2314yes—
404#385C2314yes—
405#385C2314yes—
406#384C2314yes—
407#384C2314yes—
408#384C2312yes—
409#384C2311yescharacteristic
410#384C2312yes—
411#384C2314yes—
412#384C2311yescharacteristic
413#383C2318yes—
414#383C2318yes—
415#383C2314yes—
416#383C2314yes—
417#382C2314yes—
418#382C2314yes—
419#382C2312yes—
420#382C2311yescharacteristic
421#382C2311yescharacteristic
422#382C2318yes—
423#382C2312yes—
424#382C2314yes—
425#382C2318yes—
426#382C2312yes—
427#382C2312yes—
428#382C2314yes—
429#382C2314yes—
430#382C2311yescharacteristic
431#382C2311yescharacteristic
432#382C2311yescharacteristic
433#382C2311yescharacteristic
434#381C2318yes—
435#381C2314yes—
436#381C2314yes—
437#381C2318yes—
438#380C2318yes—
439#380C2318yes—
440#380C2314yes—
441#380C2314yes—
442#380C2314yes—
443#380C2314yes—
444#380C2314yes—
445#380C2314yes—
446#380C2318yes—
447#380C2314yes—
448#380C2312yes—
449#380C2312yes—
450#380C2314yes—
451#380C2314yes—
452#380C2312yes—
453#380C2312yes—
454C4×C4⋊C4C2312yes—
455C4×C4⋊C4C2312yes—
456C4×C4⋊C4C2312yes—
457C4×C4⋊C4C2312yes—
458C4×C4⋊C4C2314yes—
459C4×C4⋊C4C2314yes—
460C4×C4⋊C4C2314yes—
461C4×C4⋊C4C2314yes—
462C4×C4⋊C4C2314yes—
463C4×C4⋊C4C2314yes—
464C4×C4⋊C4C2314yes—
465C4×C4⋊C4C2314yes—
466C4×C4⋊C4C2314yes—
467C4×C4⋊C4C2314yes—
468C4×C4⋊C4C2318yes—
469C4×C4⋊C4C2314yes—
470C4×C4⋊C4C2314yes—
471C4×C4⋊C4C2314yes—
472C4×C4⋊C4C2314yes—
473C4×C4⋊C4C2314yes—
474C4×C22⋊C4C2318yes—
475C4×C22⋊C4C2314yes—
476C4×C22⋊C4C2318yes—
477C4×C22⋊C4C2314yes—
478C4×C22⋊C4C2314yes—
479C4×C22⋊C4C2314yes—
480#376C2311yescharacteristic
481#376C2311yescharacteristic
482#376C2311yescharacteristic
483#376C2311yescharacteristic
484#376C2312yes—
485#376C2312yes—
486#376C2318yes—
487#376C2314yes—
488#376C2314yes—
489C2×#95C2314yes—
490C2×#95C2312yes—
491C2×#95C2312yes—
492C2×#95C2312yes—
493C2×#95C2312yes—
494C2×#95C2314yes—
495C2×#95C2314yes—
496C2×#95C2314yes—
497C2×#41—24no—
498C2×#41—24no—
499C2×#41—24no—
500C2×#41—24no—
501C2×#41—24no—
502C2×#41#4118yes—
503C22×Q8—28no—
504C22×Q8—84no—
505C22×Q8C2411yescharacteristic
506C22×Q8C2411yescharacteristic
507C22×Q8C2414yes—
508C22×Q8C2414yes—
509C22×D4C2412yes—
510C22×D4C2411yescharacteristic
511C22×D4C2412yes—
512C22×D4C2411yescharacteristic
513C22×D4C2414yes—
514C23×C4C2412yes—
515C23×C4C2412yes—
516C23×C4C2414yes—
517C23×C4C2414yes—
518C23×C4C2412yes—
519C23×C4C2418yes—
520C23×C4C2412yes—
521C23×C4C2412yes—
522C23×C4C2412yes—
523C23×C4C2412yes—
524C23×C4C2412yes—
525C23×C4C2411yescharacteristic
526C23×C4C2411yescharacteristic
527C23×C4C2411yescharacteristic
528C4⋊Q8—24no—
529C4⋊Q8—28no—
530C4⋊Q8—28no—
531C4⋊Q8—28no—
532C4⋊Q8—28no—
533#127—24no—
534#126—88no—
535#125—88no—
536#124—24no—
537#124—24no—
538#123—88no—
539C22⋊Q8—88no—
540C22⋊Q8—88no—
541#121—216no—
542C4×Q8—216no—
543C4×Q8—24no—
544C4×Q8—24no—
545C4×Q8—24no—
546C4×Q8—24no—
547C4×D4—232no—
548C4×D4—216no—
549C4×D4—28no—
550C4×D4—28no—
551C4×D4—28no—
552C4×D4—28no—
553C4×D4—216no—
554C4×D4—24no—
555C4×D4—24no—
556C4×D4—24no—
557C4×D4—24no—
558#117—24no—
559#117—24no—
560#117—216no—
561#117—28no—
562#117—28no—
563#117—28no—
564#117—28no—
565#117—88no—
566C2×C4⋊C4—216no—
567C2×C4⋊C4—28no—
568C2×C4⋊C4—28no—
569C2×C4⋊C4—28no—
570C2×C4⋊C4—84no—
571C2×C4⋊C4C2414yes—
572C2×C4⋊C4C2412yes—
573C2×C4⋊C4C2414yes—
574C2×C4⋊C4C2418yes—
575C2×C4⋊C4C2414yes—
576C2×C4⋊C4C2414yes—
577C2×C4⋊C4C2414yes—
578C2×C4⋊C4C2414yes—
579C2×C4⋊C4C2412yes—
580C2×C4⋊C4C2411yescharacteristic
581C2×C4⋊C4C2411yescharacteristic
582C2×C4⋊C4C2411yescharacteristic
583C2×C4⋊C4C2411yescharacteristic
584C2×C4⋊C4C2412yes—
585C2×C4⋊C4C2412yes—
586C2×C4⋊C4C2412yes—
587C2×C4⋊C4C2412yes—
588C2×C4⋊C4C2412yes—
589C2×C4⋊C4C2412yes—
590C2×C4⋊C4C2414yes—
591C2×C4⋊C4C2418yes—
592C2×C4⋊C4C2418yes—
593C2×C4⋊C4C2414yes—
594C2×C4⋊C4C2418yes—
595C2×C4⋊C4C2414yes—
596C2×C4⋊C4C2414yes—
597C2×C4⋊C4C2418yes—
598C2×C4⋊C4C2418yes—
599C2×C4⋊C4C2418yes—
600C2×C4⋊C4C2414yes—
601C2×C4⋊C4C2414yes—
602C2×C4⋊C4C2414yes—
603C2×C4⋊C4C2418yes—
604C2×C4⋊C4C2414yes—
605C2×C4⋊C4C2414yes—
606C2×C4⋊C4C2414yes—
607C2×C4⋊C4C2414yes—
608C2×C4⋊C4C2414yes—
609C2×C4⋊C4C2414yes—
610C2×C4⋊C4C2418yes—
611C2×C4⋊C4C2414yes—
612C2×C4⋊C4C2414yes—
613C2×C22⋊C4C2412yes—
614C2×C22⋊C4C2412yes—
615C2×C22⋊C4C2414yes—
616C2×C22⋊C4C2418yes—
617C2×C22⋊C4C2412yes—
618C2×C22⋊C4C2412yes—
619C2×C22⋊C4C2412yes—
620C2×C22⋊C4C2412yes—
621C2×C22⋊C4C2414yes—
622C2×C22⋊C4C2414yes—
623C2×C22⋊C4C2414yes—
624C2×C22⋊C4C2414yes—
625C2×C22⋊C4C2418yes—
626C2×C22⋊C4C2418yes—
627C2×C22⋊C4C2418yes—
628C2×C22⋊C4C2418yes—
629C2×C22⋊C4C2418yes—
630C2×C22⋊C4C2414yes—
631C2×C22⋊C4C2414yes—
632C2×C22⋊C4C2418yes—
633C2×C22⋊C4C2414yes—
634C2×C42—24no—
635C2×C42—24no—
636C2×C42—28no—
637C2×C42—28no—
638C2×C42—84no—
639C2×C42#4118yes—
640C2×C42C2412yes—
641C2×C42C2412yes—
642C2×C42C2418yes—
643C2×C42C2414yes—
644C2×C42C2414yes—
645C2×C42C2412yes—
646C2×C42C2412yes—
647C2×C42C2412yes—
648C2×C42C2412yes—
649C2×C42C2412yes—
650C2×C42C2411yescharacteristic
651C2×C42C2411yescharacteristic
652C2×C42C2412yes—
653C2×C42C2411yescharacteristic
654C2×C42C2411yescharacteristic
655C2×C42C2418yes—
656C2×C42C2418yes—
657C2×C42C2418yes—
658C2×C42C2418yes—
659C2×C42C2411yescharacteristic
660C2×C42C2411yescharacteristic
661C2×C42C2411yescharacteristic
662C2×C42C2411yescharacteristic
663#95C2414yes—
664#95C2414yes—
665#95C2412yes—
666#95C2412yes—
667#95C2412yes—
668#95C2412yes—
669#95C2412yes—
670#95C2412yes—
671#95C2412yes—
672#95C2412yes—
673#95C2412yes—
674#95C2412yes—
675#95C2414yes—
676#95C2414yes—
677#95C2418yes—
678#95C2418yes—
679#95C2418yes—
680#95C2418yes—
681#95C2418yes—
682#95C2418yes—
683#95C2414yes—
684#95C2412yes—
685#95C2412yes—
686#95C2414yes—
687#95C2418yes—
688#95C2418yes—
689#95C2418yes—
690#95C2418yes—
691#95C2412yes—
692#95C2412yes—
693#95C2414yes—
694#95C2418yes—
695#95C2418yes—
696#95C2414yes—
697#95C2418yes—
698#95C2414yes—
699#95C2414yes—
700#95C2412yes—
701#95C2412yes—
702#95C2414yes—
703#95C2414yes—
704#95C2418yes—
705#95C2414yes—
706#95C2414yes—
707#95C2414yes—
708#95C2414yes—
709#95C2414yes—
710#95C2414yes—
711#95C2418yes—
712#95C2418yes—
713#95C2418yes—
714#95C2418yes—
715C24C2512yes—
716C24C2512yes—
717C24C2511yescharacteristic
718#41—232no—
719#41—416no—
720C2×Q8—22no—
721C2×Q8—22no—
722C2×Q8—22no—
723C2×Q8—28no—
724C2×Q8—28no—
725C2×Q8—22no—
726C2×Q8—22no—
727C2×Q8—48no—
728C2×Q8—48no—
729C2×Q8—816no—
730C2×Q8C2×#4114yes—
731C2×D4—24no—
732C2×D4—24no—
733C2×D4—24no—
734C2×D4—24no—
735C2×D4—24no—
736C2×D4—28no—
737C2×D4—22no—
738C2×D4—22no—
739C2×D4—22no—
740C2×D4—22no—
741C2×D4—22no—
742C2×D4—44no—
743C2×D4—44no—
744C2×D4C2×#4118yes—
745C2×D4C2×#4114yes—
746C22×C4—24no—
747C22×C4—24no—
748C22×C4—28no—
749C22×C4—24no—
750C22×C4—24no—
751C22×C4—216no—
752C22×C4—28no—
753C22×C4—24no—
754C22×C4—24no—
755C22×C4—24no—
756C22×C4—24no—
757C22×C4—24no—
758C22×C4—24no—
759C22×C4—24no—
760C22×C4—42no—
761C22×C4—44no—
762C22×C4—44no—
763C22×C4—42no—
764C22×C4—42no—
765C22×C4—42no—
766C22×C4—44no—
767C22×C4—42no—
768C22×C4—48no—
769C22×C4—44no—
770C22×C4—44no—
771C22×C4—44no—
772C22×C4—44no—
773C22×C4—44no—
774C22×C4—48no—
775C22×C4—42no—
776C22×C4C2×#4118yes—
777C22×C4C2×#4114yes—
778C22×C4C2×#4114yes—
779C22×C4C2×#4114yes—
780C22×C4C2×#4114yes—
781C22×C42−1+414yes—
782C22×C4C2512yes—
783C22×C4C2512yes—
784C22×C4C2512yes—
785C22×C4C2512yes—
786C22×C4C2512yes—
787C22×C4C2512yes—
788C22×C4C2518yes—
789C22×C4C2514yes—
790C22×C4C2514yes—
791C22×C4C2514yes—
792C22×C4C2512yes—
793C22×C4C2518yes—
794C22×C4C2514yes—
795C22×C4C2512yes—
796C22×C4C2512yes—
797C22×C4C2512yes—
798C22×C4C2511yescharacteristic
799C22×C4C2511yescharacteristic
800C22×C4C2511yescharacteristic
801C22×C4C2511yescharacteristic
802C22×C4C2511yescharacteristic
803C22×C4C2511yescharacteristic
804C4⋊C4—28no—
805C4⋊C4—24no—
806C4⋊C4—216no—
807C4⋊C4—28no—
808C4⋊C4—28no—
809C4⋊C4—28no—
810C4⋊C4—28no—
811C4⋊C4—28no—
812C4⋊C4—24no—
813C4⋊C4—24no—
814C4⋊C4—24no—
815C4⋊C4—22no—
816C4⋊C4—22no—
817C4⋊C4—22no—
818C4⋊C4—22no—
819C4⋊C4—24no—
820C4⋊C4—24no—
821C4⋊C4—28no—
822C4⋊C4—24no—
823C4⋊C4—24no—
824C4⋊C4—48no—
825C4⋊C4—48no—
826C4⋊C4—44no—
827C4⋊C4—44no—
828C4⋊C4—44no—
829C4⋊C4—44no—
830C4⋊C4—44no—
831C4⋊C4—48no—
832C4⋊C4—44no—
833C4⋊C4—44no—
834C4⋊C4—44no—
835C4⋊C4—48no—
836C4⋊C4—44no—
837C4⋊C4—44no—
838C4⋊C4—48no—
839C4⋊C4—48no—
840C4⋊C4—48no—
841C4⋊C4—44no—
842C4⋊C4—44no—
843C4⋊C4—44no—
844C4⋊C4—48no—
845C4⋊C4—44no—
846C22⋊C4—216no—
847C22⋊C4—28no—
848C22⋊C4—24no—
849C22⋊C4—24no—
850C22⋊C4—28no—
851C22⋊C4—28no—
852C22⋊C4—24no—
853C22⋊C4—24no—
854C22⋊C4—24no—
855C22⋊C4—24no—
856C22⋊C4—28no—
857C22⋊C4—44no—
858C22⋊C4—48no—
859C22⋊C4—44no—
860C22⋊C4—44no—
861C22⋊C4—48no—
862C22⋊C4—48no—
863C22⋊C4—48no—
864C22⋊C4—48no—
865C22⋊C4—48no—
866C22⋊C4—44no—
867C42—24no—
868C42—24no—
869C42—24no—
870C42—24no—
871C42—24no—
872C42—24no—
873C42—24no—
874C42—22no—
875C42—22no—
876C42—216no—
877C42—28no—
878C42—22no—
879C42—22no—
880C42—24no—
881C42—28no—
882C42—48no—
883C42—48no—
884C42—48no—
885C42—48no—
886C42C2×#4114yes—
887C42C2×#4114yes—
888C42C2×#4114yes—
889C42C2×#4114yes—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—22no—
894C23—24no—
895C23—24no—
896C23—22no—
897C23—22no—
898C23—22no—
899C23—24no—
900C23—24no—
901C23C22×#4114yes—
902C23C22×#4112yes—
903C23C22×#4112yes—
904C23C2×2−1+412yes—
905C23C2611yescharacteristic
906Q8—28no—
907Q8—44no—
908Q8—88no—
909Q8—88no—
910D4—216no—
911D4—28no—
912D4—48no—
913D4—44no—
914D4—88no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—216no—
922C2×C4—24no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—22no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—22no—
930C2×C4—28no—
931C2×C4—24no—
932C2×C4—22no—
933C2×C4—28no—
934C2×C4—22no—
935C2×C4—22no—
936C2×C4—24no—
937C2×C4—24no—
938C2×C4—22no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—28no—
942C2×C4—24no—
943C2×C4—28no—
944C2×C4—24no—
945C2×C4—24no—
946C2×C4—24no—
947C2×C4—24no—
948C2×C4—28no—
949C2×C4—24no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—24no—
953C2×C4—24no—
954C2×C4—28no—
955C2×C4—24no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—24no—
959C2×C4—24no—
960C2×C4—22no—
961C2×C4—24no—
962C2×C4—22no—
963C2×C4—44no—
964C2×C4—44no—
965C2×C4—48no—
966C2×C4—416no—
967C2×C4—48no—
968C2×C4—84no—
969C2×C4—84no—
970C2×C4—84no—
971C2×C4—84no—
972C2×C4—84no—
973C2×C4—88no—
974C2×C4—816no—
975C2×C4#552116yes—
976C2×C4C22×#4114yes—
977C2×C4C22×#4112yes—
978C2×C4C22×#4112yes—
979C2×C4C22×#4112yes—
980C2×C4C22×#4112yes—
981C2×C4C22×#4112yes—
982C2×C4C22×#4112yes—
983C2×C4C22×#4112yes—
984C2×C4C22×#4112yes—
985C2×C4C2×2−1+412yes—
986C2×C4C2×2−1+412yes—
987C22—22no—
988C22—24no—
989C22—22no—
990C22—24no—
991C22—28no—
992C22—24no—
993C22—42no—
994C22—42no—
995C22—44no—
996C22—42no—
997C22—44no—
998C22—42no—
999C22—44no—
1000C22—42no—
1001C22C2×#55214yes—
1002C22C23×#4111yescharacteristic
1003C22C23×#4111yescharacteristic
1004C22C22×2−1+411yescharacteristic
1005C22H(7,𝔽2)12yes—
1006C222−1+612yes—
1007C4—22no—
1008C4—22no—
1009C4—22no—
1010C4—22no—
1011C4—24no—
1012C4—48no—
1013C4—42no—
1014C4—42no—
1015C4—44no—
1016C4—42no—
1017C4—48no—
1018C4—44no—
1019C4—42no—
1020C4—42no—
1021C4—42no—
1022C4—44no—
1023C4—44no—
1024C4—42no—
1025C4—42no—
1026C4—42no—
1027C4C2×#55214yes—
1028C4C2×#55214yes—
1029C2—24no—
1030C2—44no—
1031C2—82no—
1032C2C22×#55211yescharacteristic
1033C2#6285511yescharacteristic
1034C2#6285712yes—
1035C2#6286011yescharacteristic
1036C2#6287712yes—
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. #45350C2semidirect
2. #45347C2semidirect
3. #45318C2semidirect
4. #45306C2semidirect
5. #45231C2semidirect
6. #45211C2semidirect
7. #45083C2semidirect
8. #45056C2semidirect
9. #38223C2semidirect
10. #38221C2semidirect
11. #37939C2semidirect
12. #37938C2semidirect
13. #37887C2semidirect
14. #37884C2semidirect
15. #35543C2semidirect
17. #35279C2semidirect
18. #35279C2semidirect
19. #35160C2semidirect
20. #34638C2semidirect
21. #34252C2semidirect
22. #34189C2semidirect
23. #34184C2semidirect
24. C2×#2331C2semidirect

Maximal subgroups

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

subgroupindex
#453502
#453472
#453182
#453062
#452312
#452112
#450832
#450562
#382232
#382212
#379392
#379382
#378872
#378842
#355432
#355172
#352792
#351602
#346382
#342522
#341892
#341842
C2×#23312
#340702