Finite Group Databasebeta

← #7644287

Subgroups — #7644287

Order 512.

5610 conjugacy classes of subgroups.

The subgroup lattice has 1085 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42993C214yesmaximal, complemented
2#42991C214yesmaximal, complemented
3#42990C214yesmaximal, complemented
4#42989C214yesmaximal, complemented
5#42945C214yesmaximal, complemented
6#42923C214yesmaximal, complemented
7#42920C214yesmaximal, complemented
8#42919C214yesmaximal, complemented
9#37518C214yesmaximal, complemented
10#37517C214yesmaximal, complemented
11#36758C218yesmaximal, complemented
12#35544C212yesmaximal, complemented
13#35542C212yesmaximal, complemented
14#35518C212yesmaximal, complemented
15#35516C212yesmaximal, complemented
16#35224C211yesmaximal, characteristic, complemented
17#35223C211yesmaximal, characteristic, complemented
18#34632C212yesmaximal, complemented
19#34201C212yesmaximal, complemented
20C2×#2311C211yesmaximal, characteristic, complemented
21C23×#41C2211yescharacteristic
22C2×#544C2211yescharacteristic
23C2×#537C2211yescharacteristic
24C2×#525C2212yes—
25C2×#525C2212yes—
26C2×#525C2212yes—
27C2×#520C2212yes—
28C22×#117C2211yescharacteristic
29C23×C4⋊C4C2211yescharacteristic
30#2848C2214yes—
31#2847C2214yes—
32#2833C2214yescomplemented
33#2832C2214yescomplemented
34#2831C2218yescomplemented
35#2830C2214yescomplemented
36#2829C2218yescomplemented
37#2828C2214yescomplemented
38#2797C2218yescomplemented
39#2781C2218yescomplemented
40#2779C2218yescomplemented
41#2778C2218yescomplemented
42#2778C2218yescomplemented
43#2756C2218yescomplemented
44#2753C2218yescomplemented
45#2749C2218yescomplemented
46#2741C2218yescomplemented
47#2730C2218yescomplemented
48#2714C2218yescomplemented
49#2703C2218yescomplemented
50#2702C2218yescomplemented
51#2696C2218yescomplemented
52#2688C2218yescomplemented
53#2676C2218yescomplemented
54#2666C2218yescomplemented
55#2665C2218yescomplemented
56#2662C2218yescomplemented
57#2661C2218yescomplemented
58#2653C2218yescomplemented
59#2651C2218yescomplemented
60#2650C2218yescomplemented
61#2648C2218yescomplemented
62#2627C2214yes—
63#2618C2214yes—
64#2616C2212yes—
65#2616C2212yes—
66#2616C2212yes—
67#2616C2212yes—
68#2615C2212yes—
69#2615C2212yes—
70#2615C2212yes—
71#2615C2212yes—
72#2614C2214yes—
73#2613C2214yes—
74#2613C2214yes—
75#2613C2214yes—
76#2593C2214yescomplemented
77#2586C2214yescomplemented
78#2574C2218yescomplemented
79#2572C2214yescomplemented
80#2563C2214yescomplemented
81#2562C2214yescomplemented
82#2562C2214yescomplemented
83#2555C2214yescomplemented
84#2554C2218yescomplemented
85#2547C2214yescomplemented
86#2538C2214yescomplemented
87#2537C2214yescomplemented
88#2536C2214yescomplemented
89#2535C2214yescomplemented
90#2497C2214yescomplemented
91#2497C2214yescomplemented
92#2496C2214yescomplemented
93#2496C2214yescomplemented
94#2495C2214yescomplemented
95#2495C2214yescomplemented
96#2494C2214yescomplemented
97#2494C2214yescomplemented
98#2493C2218yes—
99#2492C2214yescomplemented
100#2491C2214yescomplemented
101#2490C2214yescomplemented
102#2489C2214yescomplemented
103#2488C2218yes—
104#2487C2214yescomplemented
105#2486C2214yescomplemented
106#2485C2214yescomplemented
107#2485C2214yescomplemented
108#2480C2218yes—
109#2472C2218yes—
110#2442C2214yescomplemented
111#2442C2214yescomplemented
112#2440C2214yescomplemented
113#2440C2214yescomplemented
114#2425C2218yes—
115#2424C2218yes—
116#2423C2214yescomplemented
117#2422C2214yescomplemented
118#2421C2214yescomplemented
119#2420C2214yescomplemented
120#2419C2218yes—
121#2418C2218yes—
122#2417C2214yescomplemented
123#2417C2214yescomplemented
124#2417C2214yescomplemented
125#2416C2214yescomplemented
126#2416C2214yescomplemented
127#2416C2214yescomplemented
128#2415C2214yescomplemented
129#2414C2214yescomplemented
130#2388C2214yes—
131#2388C2214yes—
132#2388C2214yes—
133#2388C2214yes—
134#2363C2214yescomplemented
135#2363C2214yescomplemented
136#2362C2214yescomplemented
137#2362C2214yescomplemented
138#2354C2214yescomplemented
139#2354C2214yescomplemented
140#2352C2214yescomplemented
141#2352C2214yescomplemented
142#2321C2218yes—
143#2317C2212yes—
144#2317C2212yes—
145#2316C2211yescharacteristic
146#2316C2211yescharacteristic
147#2311C2212yes—
148#2311C2212yes—
149#2311C2214yes—
150#2311C2214yes—
151#2311C2214yes—
152#2311C2214yes—
153C4×#123C2218yes—
154C2×#391C2212yes—
155C2×#390C2212yes—
156C2×#386C2214yes—
157#2280C2212yes—
158#2280C2212yes—
159#2280C2212yes—
160C2×#380C2212yes—
161C2×#380C2212yes—
162#2274C2212yes—
163C22×#41—28no—
164C22×#41—44no—
165C22×#41—44no—
166C22×#41C2312yes—
167C22×#41C2312yes—
168C22×#41C2312yes—
169C22×#41C2312yes—
170C22×#41C2312yes—
171C23×Q8C2311yescharacteristic
172C23×D4C2312yes—
173C23×D4C2311yescharacteristic
174C24×C4C2312yes—
175C24×C4C2311yescharacteristic
176C24×C4C2312yes—
177#544—44no—
178#537—44no—
179C2×C4⋊Q8C2314yes—
180C2×#126C2318yes—
181C2×#125C2314yes—
182C2×#124C2318yes—
183#525—216no—
184#525—48no—
185#525—48no—
186C2×#123C2314yes—
187C2×#123C2314yes—
188C2×#123C2314yes—
189C2×#123C2318yes—
190C2×C22⋊Q8C2312yes—
191C2×C22⋊Q8C2312yes—
192C2×C22⋊Q8C2314yes—
193C2×C22⋊Q8C2312yes—
194C2×C22⋊Q8C2312yes—
195C2×C22⋊Q8C2312yes—
196C2×C22⋊Q8C2312yes—
197C2×C22⋊Q8C2314yes—
198C2×C22⋊Q8C2318yes—
199C2×#121C2312yes—
200C2×#121C2312yes—
201C2×#121C2314yes—
202C2×#121C2312yes—
203C2×#121C2312yes—
204C2×#121C2312yes—
205C2×#121C2312yes—
206C2×#121C2314yes—
207C2×#121C2318yes—
208C2×#121C2318yes—
209C2×#120C2314yes—
210C2×#120C2314yes—
211C2×#120C2314yes—
212#520—48no—
213C2×C4×Q8C2314yes—
214C2×C4×D4C2314yes—
215C2×C4×D4C2314yes—
216C2×C4×D4C2314yes—
217C2×C4×D4C2314yes—
218C2×C4×D4C2318yes—
219C2×C4×D4C2314yes—
220C2×C4×D4C2314yes—
221C2×C4×D4C2314yes—
222C2×#117—44no—
223C2×#117C2312yes—
224C2×#117C2312yes—
225C2×#117C2312yes—
226C2×#117C2314yes—
227C2×#117C2314yes—
228C2×#117C2314yes—
229C22×C4⋊C4—44no—
230C22×C4⋊C4C2311yescharacteristic
231C22×C4⋊C4C2312yes—
232C22×C4⋊C4C2311yescharacteristic
233C22×C4⋊C4C2314yes—
234C22×C4⋊C4C2314yes—
235C22×C4⋊C4C2314yes—
236C22×C4⋊C4C2312yes—
237C22×C22⋊C4C2312yes—
238C22×C22⋊C4C2314yes—
239C22×C22⋊C4C2314yes—
240C22×C42C2312yes—
241#401C2318yes—
242#400C2318yes—
243#400C2318yes—
244#400C2314yes—
245#400C2314yes—
246#400C2318yes—
247#400C2318yes—
248#400C2318yes—
249#400C2318yes—
250#399C2318yes—
251#398C2318yes—
252#398C2318yes—
253#398C2314yes—
254#398C2318yes—
255#398C2314yes—
256#398C2318yes—
257#397C2318yes—
258#397C2318yes—
259#397C2318yes—
260#397C2318yes—
261#397C2318yes—
262#397C2318yes—
263#397C2318yes—
264#397C2318yes—
265#397C2318yes—
266#396C2318yes—
267#396C2318yes—
268#396C2318yes—
269#396C2318yes—
270#396C2318yes—
271#395C2314yes—
272#395C2314yes—
273#395C2314yes—
274#395C2314yes—
275#395C2314yes—
276#395C2314yes—
277#394C2318yes—
278#394C2318yes—
279#394C2314yes—
280#394C2314yes—
281#394C2318yes—
282#394C2314yes—
283#394C2318yes—
284#394C2318yes—
285#394C2318yes—
286#394C2314yes—
287#394C2318yes—
288#394C2314yes—
289#394C2314yes—
290#394C2314yes—
291#394C2314yes—
292#394C2314yes—
293#394C2314yes—
294#394C2314yes—
295#394C2314yes—
296#394C2314yes—
297#394C2314yes—
298#393C2318yes—
299#393C2318yes—
300#393C2314yes—
301#393C2314yes—
302#393C2314yes—
303#393C2314yes—
304#392C2314yes—
305#392C2318yes—
306#392C2314yes—
307#392C2314yes—
308#392C2314yes—
309#392C2314yes—
310#392C2314yes—
311#392C2314yes—
312#392C2314yes—
313#392C2314yes—
314#392C2314yes—
315#392C2314yes—
316#392C2314yes—
317#391C2314yes—
318#391C2314yes—
319#391C2318yes—
320#391C2314yes—
321#391C2314yes—
322#391C2318yes—
323#390C2318yes—
324#390C2314yes—
325#390C2314yes—
326#390C2318yes—
327#390C2314yes—
328#390C2314yes—
329#390C2318yes—
330#390C2318yes—
331#390C2318yes—
332#389C2314yes—
333#389C2314yes—
334#389C2314yes—
335#389C2314yes—
336#389C2314yes—
337#389C2314yes—
338#389C2314yes—
339#389C2314yes—
340#389C2318yes—
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#388C2318yes—
354#388C2318yes—
355#388C2318yes—
356#388C2318yes—
357#388C2318yes—
358#387C2318yes—
359#387C2318yes—
360#387C2318yes—
361#387C2318yes—
362#387C2318yes—
363#387C2318yes—
364#387C2318yes—
365#386C2318yes—
366#386C2318yes—
367#386C2318yes—
368#386C2318yes—
369#386C2318yes—
370#386C2318yes—
371#386C2318yes—
372#386C2318yes—
373#386C2318yes—
374#386C2318yes—
375#386C2318yes—
376#386C2318yes—
377#386C2318yes—
378#385C2318yes—
379#385C2318yes—
380#385C2318yes—
381#385C2318yes—
382#385C2318yes—
383#384C2314yes—
384#384C2314yes—
385#383C2318yes—
386#382C2318yes—
387#382C2314yes—
388#382C2314yes—
389#381C2318yes—
390#381C2314yes—
391#381C2314yes—
392#381C2314yes—
393#380C2314yes—
394#380C2312yes—
395#380C2312yes—
396#380C2314yes—
397#380C2314yes—
398#380C2314yes—
399#380C2314yes—
400#380C2312yes—
401#380C2314yes—
402#380C2314yes—
403#380C2314yes—
404#380C2314yes—
405#380C2314yes—
406#380C2314yes—
407#380C2314yes—
408#380C2314yes—
409#380C2314yes—
410#380C2318yes—
411#380C2318yes—
412#380C2318yes—
413#380C2312yes—
414#380C2312yes—
415#380C2312yes—
416#380C2312yes—
417#380C2312yes—
418#380C2312yes—
419#380C2312yes—
420#380C2312yes—
421#380C2312yes—
422#379C2314yes—
423#379C2314yes—
424#379C2314yes—
425C4×C4⋊C4C2314yes—
426C4×C4⋊C4C2314yes—
427C4×C4⋊C4C2318yes—
428C4×C4⋊C4C2318yes—
429C4×C4⋊C4C2314yes—
430C4×C4⋊C4C2314yes—
431C4×C22⋊C4C2318yes—
432C4×C22⋊C4C2318yes—
433C4×C22⋊C4C2318yes—
434C4×C22⋊C4C2314yes—
435C4×C22⋊C4C2314yes—
436C4×C22⋊C4C2314yes—
437C4×C22⋊C4C2314yes—
438C4×C22⋊C4C2314yes—
439C4×C22⋊C4C2314yes—
440C2×#95C2314yes—
441C2×#95C2314yes—
442C25C2412yes—
443C25C2411yescharacteristic
444C2×#41—28no—
445C2×#41—28no—
446C2×#41—28no—
447C2×#41—28no—
448C2×#41—28no—
449C2×#41—28no—
450C2×#41—28no—
451C2×#41—44no—
452C2×#41—44no—
453C2×#41—44no—
454C2×#41—44no—
455C2×#41—44no—
456C2×#41—44no—
457C2×#41—44no—
458C2×#41—44no—
459C2×#41—464no—
460C22×Q8—24no—
461C22×Q8—42no—
462C22×Q8—42no—
463C22×Q8C2412yes—
464C22×Q8C2411yescharacteristic
465C22×Q8C2411yescharacteristic
466C22×Q8C2412yes—
467C22×Q8C2414yes—
468C22×D4—28no—
469C22×D4—24no—
470C22×D4—42no—
471C22×D4—42no—
472C22×D4—44no—
473C22×D4—44no—
474C22×D4C2414yes—
475C22×D4C2412yes—
476C22×D4C2414yes—
477C22×D4C2414yes—
478C22×D4C2412yes—
479C22×D4C2412yes—
480C22×D4C2412yes—
481C22×D4C2412yes—
482C22×D4C2411yescharacteristic
483C22×D4C2411yescharacteristic
484C22×D4C2412yes—
485C22×D4C2414yes—
486C22×D4C2414yes—
487C22×D4C2414yes—
488C22×D4C2414yes—
489C22×D4C2414yes—
490C23×C4—24no—
491C23×C4—24no—
492C23×C4—28no—
493C23×C4—28no—
494C23×C4—28no—
495C23×C4—44no—
496C23×C4—84no—
497C23×C4#4118yes—
498C23×C4C2414yes—
499C23×C4C2412yes—
500C23×C4C2412yes—
501C23×C4C2412yes—
502C23×C4C2412yes—
503C23×C4C2412yes—
504C23×C4C2412yes—
505C23×C4C2412yes—
506C23×C4C2411yescharacteristic
507C23×C4C2414yes—
508C23×C4C2412yes—
509C23×C4C2412yes—
510C23×C4C2418yes—
511C23×C4C2418yes—
512C23×C4C2411yescharacteristic
513C4⋊Q8—48no—
514#126—88no—
515#125—48no—
516#124—88no—
517#123—216no—
518#123—48no—
519#123—48no—
520#123—88no—
521C22⋊Q8—28no—
522C22⋊Q8—28no—
523C22⋊Q8—48no—
524C22⋊Q8—44no—
525C22⋊Q8—44no—
526C22⋊Q8—44no—
527C22⋊Q8—44no—
528C22⋊Q8—48no—
529C22⋊Q8—88no—
530#121—28no—
531#121—28no—
532#121—44no—
533#121—44no—
534#121—44no—
535#121—44no—
536#121—48no—
537#121—48no—
538#121—88no—
539#121—88no—
540#120—216no—
541#120—48no—
542#120—48no—
543C4×Q8—48no—
544C4×D4—216no—
545C4×D4—216no—
546C4×D4—48no—
547C4×D4—48no—
548C4×D4—48no—
549C4×D4—48no—
550C4×D4—48no—
551C4×D4—416no—
552#117—28no—
553#117—28no—
554#117—28no—
555#117—48no—
556#117—48no—
557#117—48no—
558C2×C4⋊C4—24no—
559C2×C4⋊C4—24no—
560C2×C4⋊C4—28no—
561C2×C4⋊C4—48no—
562C2×C4⋊C4—48no—
563C2×C4⋊C4—48no—
564C2×C4⋊C4—44no—
565C2×C4⋊C4C2414yes—
566C2×C4⋊C4C2414yes—
567C2×C4⋊C4C2414yes—
568C2×C4⋊C4C2412yes—
569C2×C4⋊C4C2414yes—
570C2×C4⋊C4C2412yes—
571C2×C4⋊C4C2412yes—
572C2×C4⋊C4C2412yes—
573C2×C4⋊C4C2412yes—
574C2×C4⋊C4C2412yes—
575C2×C4⋊C4C2414yes—
576C2×C4⋊C4C2414yes—
577C2×C4⋊C4C2414yes—
578C2×C4⋊C4C2414yes—
579C2×C4⋊C4C2418yes—
580C2×C4⋊C4C2414yes—
581C2×C4⋊C4C2414yes—
582C2×C4⋊C4C2414yes—
583C2×C4⋊C4C2414yes—
584C2×C4⋊C4C2414yes—
585C2×C4⋊C4C2418yes—
586C2×C4⋊C4C2418yes—
587C2×C4⋊C4C2418yes—
588C2×C4⋊C4C2414yes—
589C2×C4⋊C4C2418yes—
590C2×C4⋊C4C2418yes—
591C2×C4⋊C4C2418yes—
592C2×C4⋊C4C2418yes—
593C2×C22⋊C4—44no—
594C2×C22⋊C4—84no—
595C2×C22⋊C4—84no—
596C2×C22⋊C4C2414yes—
597C2×C22⋊C4C2414yes—
598C2×C22⋊C4C2414yes—
599C2×C22⋊C4C2414yes—
600C2×C22⋊C4C2414yes—
601C2×C22⋊C4C2414yes—
602C2×C22⋊C4C2414yes—
603C2×C22⋊C4C2418yes—
604C2×C22⋊C4C2418yes—
605C2×C22⋊C4C2418yes—
606C2×C22⋊C4C2418yes—
607C2×C22⋊C4C2418yes—
608C2×C22⋊C4C2418yes—
609C2×C22⋊C4C2414yes—
610C2×C22⋊C4C2414yes—
611C2×C22⋊C4C2414yes—
612C2×C22⋊C4C2414yes—
613C2×C22⋊C4C2414yes—
614C2×C22⋊C4C2414yes—
615C2×C22⋊C4C2414yes—
616C2×C22⋊C4C2414yes—
617C2×C22⋊C4C2418yes—
618C2×C22⋊C4C2418yes—
619C2×C22⋊C4C2418yes—
620C2×C22⋊C4C2418yes—
621C2×C22⋊C4C2414yes—
622C2×C22⋊C4C2414yes—
623C2×C22⋊C4C2414yes—
624C2×C22⋊C4C2414yes—
625C2×C22⋊C4C2414yes—
626C2×C22⋊C4C2414yes—
627C2×C22⋊C4C2414yes—
628C2×C22⋊C4C2414yes—
629C2×C22⋊C4C2414yes—
630C2×C22⋊C4C2414yes—
631C2×C22⋊C4C2414yes—
632C2×C22⋊C4C2414yes—
633C2×C22⋊C4C2418yes—
634C2×C42—44no—
635C2×C42C2414yes—
636C2×C42C2414yes—
637C2×C42C2414yes—
638C2×C42C2414yes—
639C2×C42C2414yes—
640C2×C42C2418yes—
641C2×C42C2418yes—
642C2×C42C2418yes—
643#95C2418yes—
644#95C2418yes—
645#95C2418yes—
646#95C2418yes—
647#95C2414yes—
648#95C2414yes—
649#95C2414yes—
650#95C2414yes—
651#95C2418yes—
652#95C2418yes—
653#95C2414yes—
654#95C2414yes—
655#95C2414yes—
656#95C2414yes—
657#95C2414yes—
658#95C2414yes—
659#95C2414yes—
660#95C2414yes—
661#95C2418yes—
662#95C2418yes—
663#95C2418yes—
664#95C2418yes—
665#95C2418yes—
666#95C2418yes—
667#95C2414yes—
668#95C2418yes—
669#95C2418yes—
670#95C2414yes—
671#95C2414yes—
672#95C2414yes—
673C24—22no—
674C24—22no—
675C24—24no—
676C24—24no—
677C24—24no—
678C24—42no—
679C24—42no—
680C24—42no—
681C24—42no—
682C24—42no—
683C24—42no—
684C24C2×#4114yes—
685C24C2512yes—
686C24C2512yes—
687C24C2514yes—
688C24C2512yes—
689C24C2511yescharacteristic
690#41—432no—
691#41—432no—
692#41—432no—
693#41—432no—
694#41—432no—
695C2×Q8—24no—
696C2×Q8—22no—
697C2×Q8—22no—
698C2×Q8—24no—
699C2×Q8—24no—
700C2×Q8—24no—
701C2×Q8—41no—
702C2×Q8—41no—
703C2×Q8—42no—
704C2×Q8—41no—
705C2×Q8—41no—
706C2×Q8—42no—
707C2×Q8—44no—
708C2×Q8—48no—
709C2×Q8—416no—
710C2×D4—28no—
711C2×D4—24no—
712C2×D4—24no—
713C2×D4—24no—
714C2×D4—24no—
715C2×D4—28no—
716C2×D4—28no—
717C2×D4—28no—
718C2×D4—28no—
719C2×D4—24no—
720C2×D4—22no—
721C2×D4—22no—
722C2×D4—24no—
723C2×D4—24no—
724C2×D4—24no—
725C2×D4—41no—
726C2×D4—41no—
727C2×D4—42no—
728C2×D4—41no—
729C2×D4—42no—
730C2×D4—41no—
731C2×D4—42no—
732C2×D4—42no—
733C2×D4—42no—
734C2×D4—42no—
735C2×D4—42no—
736C2×D4—42no—
737C2×D4—42no—
738C2×D4—42no—
739C2×D4—416no—
740C2×D4—44no—
741C2×D4—44no—
742C2×D4—44no—
743C2×D4—44no—
744C2×D4—44no—
745C2×D4—44no—
746C2×D4—44no—
747C2×D4—44no—
748C2×D4—44no—
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—48no—
758C2×D4—432no—
759C22×C4—22no—
760C22×C4—22no—
761C22×C4—232no—
762C22×C4—24no—
763C22×C4—24no—
764C22×C4—24no—
765C22×C4—24no—
766C22×C4—24no—
767C22×C4—24no—
768C22×C4—24no—
769C22×C4—28no—
770C22×C4—24no—
771C22×C4—24no—
772C22×C4—28no—
773C22×C4—24no—
774C22×C4—24no—
775C22×C4—24no—
776C22×C4—24no—
777C22×C4—28no—
778C22×C4—28no—
779C22×C4—24no—
780C22×C4—24no—
781C22×C4—24no—
782C22×C4—24no—
783C22×C4—24no—
784C22×C4—24no—
785C22×C4—24no—
786C22×C4—24no—
787C22×C4—44no—
788C22×C4—44no—
789C22×C4—44no—
790C22×C4—48no—
791C22×C4—48no—
792C22×C4—48no—
793C22×C4—44no—
794C22×C4—48no—
795C22×C4—48no—
796C22×C4—48no—
797C22×C4—432no—
798C22×C4—816no—
799C22×C4C2×#4118yes—
800C22×C4C2×#4118yes—
801C22×C4C2×#4114yes—
802C22×C4C2×#4114yes—
803C22×C4H(5,𝔽2)14yes—
804C22×C4H(5,𝔽2)14yes—
805C22×C4C2512yes—
806C22×C4C2512yes—
807C22×C4C2514yes—
808C22×C4C2514yes—
809C22×C4C2514yes—
810C22×C4C2514yes—
811C22×C4C2518yes—
812C22×C4C2514yes—
813C22×C4C2514yes—
814C22×C4C2514yes—
815C22×C4C2514yes—
816C22×C4C2514yes—
817C22×C4C2511yescharacteristic
818C22×C4C2511yescharacteristic
819C22×C4C2512yes—
820C4⋊C4—24no—
821C4⋊C4—24no—
822C4⋊C4—28no—
823C4⋊C4—28no—
824C4⋊C4—28no—
825C4⋊C4—28no—
826C4⋊C4—28no—
827C4⋊C4—28no—
828C4⋊C4—24no—
829C4⋊C4—24no—
830C4⋊C4—24no—
831C4⋊C4—24no—
832C4⋊C4—44no—
833C4⋊C4—44no—
834C4⋊C4—48no—
835C4⋊C4—48no—
836C4⋊C4—44no—
837C4⋊C4—44no—
838C4⋊C4—44no—
839C4⋊C4—44no—
840C4⋊C4—44no—
841C4⋊C4—48no—
842C4⋊C4—48no—
843C4⋊C4—44no—
844C4⋊C4—48no—
845C4⋊C4—48no—
846C4⋊C4—48no—
847C4⋊C4—48no—
848C22⋊C4—28no—
849C22⋊C4—28no—
850C22⋊C4—28no—
851C22⋊C4—28no—
852C22⋊C4—28no—
853C22⋊C4—28no—
854C22⋊C4—28no—
855C22⋊C4—48no—
856C22⋊C4—48no—
857C22⋊C4—48no—
858C22⋊C4—48no—
859C22⋊C4—48no—
860C22⋊C4—44no—
861C22⋊C4—44no—
862C22⋊C4—44no—
863C22⋊C4—44no—
864C22⋊C4—48no—
865C22⋊C4—44no—
866C22⋊C4—44no—
867C22⋊C4—48no—
868C22⋊C4—44no—
869C22⋊C4—44no—
870C22⋊C4—44no—
871C22⋊C4—44no—
872C22⋊C4—44no—
873C22⋊C4—44no—
874C22⋊C4—44no—
875C22⋊C4—44no—
876C22⋊C4—48no—
877C22⋊C4—48no—
878C22⋊C4—48no—
879C22⋊C4—48no—
880C22⋊C4—44no—
881C22⋊C4—44no—
882C22⋊C4—44no—
883C22⋊C4—44no—
884C22⋊C4—44no—
885C22⋊C4—44no—
886C42—28no—
887C42—28no—
888C42—28no—
889C42—44no—
890C42—44no—
891C42—48no—
892C42—48no—
893C42—48no—
894C23—22no—
895C23—22no—
896C23—22no—
897C23—22no—
898C23—22no—
899C23—22no—
900C23—22no—
901C23—22no—
902C23—28no—
903C23—24no—
904C23—22no—
905C23—22no—
906C23—24no—
907C23—24no—
908C23—22no—
909C23—22no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—24no—
916C23—22no—
917C23—24no—
918C23—22no—
919C23—24no—
920C23—22no—
921C23—22no—
922C23—24no—
923C23—22no—
924C23—48no—
925C23—44no—
926C23—48no—
927C23—44no—
928C23—48no—
929C23—48no—
930C23—48no—
931C23—84no—
932C23—84no—
933C23—84no—
934C23—84no—
935C23C22×#4114yes—
936C23C22×#4112yes—
937C23C2×H(5,𝔽2)12yes—
938C23C2×H(5,𝔽2)12yes—
939C23C2611yescharacteristic
940Q8—44no—
941Q8—44no—
942Q8—48no—
943Q8—48no—
944Q8—164no—
945D4—44no—
946D4—48no—
947D4—44no—
948D4—48no—
949D4—48no—
950D4—48no—
951D4—48no—
952D4—416no—
953D4—48no—
954D4—88no—
955D4—88no—
956D4—88no—
957D4—88no—
958D4—88no—
959D4—88no—
960D4—164no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—28no—
966C2×C4—216no—
967C2×C4—216no—
968C2×C4—24no—
969C2×C4—24no—
970C2×C4—24no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—24no—
974C2×C4—24no—
975C2×C4—24no—
976C2×C4—24no—
977C2×C4—28no—
978C2×C4—24no—
979C2×C4—24no—
980C2×C4—24no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—24no—
986C2×C4—24no—
987C2×C4—24no—
988C2×C4—28no—
989C2×C4—24no—
990C2×C4—24no—
991C2×C4—28no—
992C2×C4—24no—
993C2×C4—24no—
994C2×C4—28no—
995C2×C4—24no—
996C2×C4—24no—
997C2×C4—28no—
998C2×C4—24no—
999C2×C4—24no—
1000C2×C4—24no—
1001C2×C4—24no—
1002C2×C4—48no—
1003C2×C4—48no—
1004C2×C4—48no—
1005C2×C4—48no—
1006C2×C4—48no—
1007C2×C4—416no—
1008C2×C4—88no—
1009C2×C4—84no—
1010C2×C4—84no—
1011C2×C4—816no—
1012C2×C4—168no—
1013C2×C4#538116yes—
1014C2×C4C22×#4112yes—
1015C2×C4C22×#4112yes—
1016C2×C4C22×#4114yes—
1017C2×C4C2×H(5,𝔽2)14yes—
1018C2×C4C2×H(5,𝔽2)14yes—
1019C22—24no—
1020C22—22no—
1021C22—24no—
1022C22—22no—
1023C22—24no—
1024C22—24no—
1025C22—24no—
1026C22—416no—
1027C22—42no—
1028C22—42no—
1029C22—42no—
1030C22—42no—
1031C22—44no—
1032C22—44no—
1033C22—42no—
1034C22—42no—
1035C22—42no—
1036C22—42no—
1037C22—42no—
1038C22—44no—
1039C22—42no—
1040C22—44no—
1041C22—42no—
1042C22—42no—
1043C22—44no—
1044C22—42no—
1045C22—42no—
1046C22—42no—
1047C22—44no—
1048C22—42no—
1049C22—42no—
1050C22—42no—
1051C22—44no—
1052C22—816no—
1053C22C2×#53814yes—
1054C22C23×#4111yescharacteristic
1055C22C22×H(5,𝔽2)11yescharacteristic
1056C22C22×H(5,𝔽2)11yescharacteristic
1057C22H(7,𝔽2)12yes—
1058C222−1+612yes—
1059C4—22no—
1060C4—22no—
1061C4—44no—
1062C4—44no—
1063C4—44no—
1064C4—44no—
1065C4—44no—
1066C4—48no—
1067C4—44no—
1068C4—44no—
1069C4—44no—
1070C4—42no—
1071C4—42no—
1072C4—44no—
1073C4C2×#53818yes—
1074C2—24no—
1075C2—44no—
1076C2—84no—
1077C2—82no—
1078C2—82no—
1079C2C22×#53811yescharacteristic
1080C2#6285612yes—
1081C2#6287411yescharacteristic
1082C2#6287512yes—
1083C2#6288611yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42993C2semidirect
2. #42991C2semidirect
3. #42990C2semidirect
4. #42989C2semidirect
5. #42945C2semidirect
6. #42923C2semidirect
7. #42920C2semidirect
8. #42919C2semidirect
9. #37518C2semidirect
10. #37517C2semidirect
11. #36758C2semidirect
12. #35544C2semidirect
13. #35542C2semidirect
14. #35518C2semidirect
15. #35516C2semidirect
16. #35224C2semidirect
17. #35223C2semidirect
18. #34632C2semidirect
19. #34201C2semidirect
20. C2×#2311C2semidirect
32. #2833C22semidirect
33. #2832C22semidirect
34. #2831C22semidirect
35. #2830C22semidirect
36. #2829C22semidirect
37. #2828C22semidirect
38. #2797C22semidirect
39. #2781C22semidirect
40. #2779C22semidirect
41. #2778C22semidirect
42. #2778C22semidirect
43. #2756C22semidirect
44. #2753C22semidirect
45. #2749C22semidirect
46. #2741C22semidirect
47. #2730C22semidirect
48. #2714C22semidirect
49. #2703C22semidirect
50. #2702C22semidirect
51. #2696C22semidirect
52. #2688C22semidirect
53. #2676C22semidirect
54. #2666C22semidirect
55. #2665C22semidirect
56. #2662C22semidirect
57. #2661C22semidirect
58. #2653C22semidirect
59. #2651C22semidirect
60. #2650C22semidirect
61. #2648C22semidirect
76. #2593C22semidirect
77. #2586C22semidirect
78. #2574C22semidirect
79. #2572C22semidirect
80. #2563C22semidirect
81. #2562C22semidirect
82. #2562C22semidirect
83. #2555C22semidirect
84. #2554C22semidirect
85. #2547C22semidirect
86. #2538C22semidirect
87. #2537C22semidirect
88. #2536C22semidirect
89. #2535C22semidirect
90. #2497C22semidirect
91. #2497C22semidirect
92. #2496C22semidirect
93. #2496C22semidirect
94. #2495C22semidirect
95. #2495C22semidirect
96. #2494C22semidirect
97. #2494C22semidirect
99. #2492C22semidirect
100. #2491C22semidirect
101. #2490C22semidirect
102. #2489C22semidirect
104. #2487C22semidirect
105. #2486C22semidirect
106. #2485C22semidirect
107. #2485C22semidirect
110. #2442C22semidirect
111. #2442C22semidirect
112. #2440C22semidirect
113. #2440C22semidirect
116. #2423C22semidirect
117. #2422C22semidirect
118. #2421C22semidirect
119. #2420C22semidirect
122. #2417C22semidirect
123. #2417C22semidirect
124. #2417C22semidirect
125. #2416C22semidirect
126. #2416C22semidirect
127. #2416C22semidirect
128. #2415C22semidirect
129. #2414C22semidirect
134. #2363C22semidirect
135. #2363C22semidirect
136. #2362C22semidirect
137. #2362C22semidirect
138. #2354C22semidirect
139. #2354C22semidirect
140. #2352C22semidirect
141. #2352C22semidirect

Maximal subgroups

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

subgroupindex
#429932
#429912
#429902
#429892
#429452
#429232
#429202
#429192
#375182
#375172
#367582
#355442
#355422
#355182
#355162
#352242
#352232
#346322
#342012
C2×#23112