Finite Group Databasebeta

← #8093520

Subgroups — #8093520

Order 512.

5466 conjugacy classes of subgroups.

The subgroup lattice has 1081 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53064C214yesmaximal, complemented
2#53045C214yesmaximal, complemented
3#53045C214yesmaximal, complemented
4#53044C214yesmaximal, complemented
5#53014C214yesmaximal, complemented
6#53007C214yesmaximal, complemented
7#53006C214yesmaximal, complemented
8#52956C214yesmaximal, complemented
9#52913C214yesmaximal, complemented
10#52340C218yesmaximal, complemented
11#52339C214yesmaximal, complemented
12#35672C211yesmaximal, characteristic, complemented
13#35661C212yesmaximal, complemented
14#35634C211yesmaximal, characteristic, complemented
15#35633C212yesmaximal, complemented
16#35544C212yesmaximal, complemented
17#35518C212yesmaximal, complemented
18#35516C212yesmaximal, complemented
19#34632C212yesmaximal, complemented
20C2×#2616C211yesmaximal, characteristic, complemented
21C23×#41C2211yescharacteristic
22C2×#537C2211yescharacteristic
23C2×#536C2212yes—
24C2×#525C2212yes—
25C2×#525C2212yes—
26C2×#525C2212yes—
27C22×C22⋊Q8C2212yes—
28C22×C22⋊Q8C2211yescharacteristic
29C2×#520C2212yes—
30C2×#519C2211yescharacteristic
31#2843C2214yescomplemented
32#2841C2218yescomplemented
33#2838C2218yescomplemented
34#2838C2218yescomplemented
35#2837C2218yescomplemented
36#2837C2218yescomplemented
37#2837C2218yescomplemented
38#2830C2214yescomplemented
39#2829C2218yescomplemented
40#2829C2218yescomplemented
41#2829C2218yescomplemented
42#2829C2218yescomplemented
43#2828C2218yescomplemented
44#2828C2214yescomplemented
45#2826C2218yescomplemented
46#2825C2218yescomplemented
47#2823C2214yescomplemented
48#2813C2218yescomplemented
49#2803C2218yescomplemented
50#2803C2218yescomplemented
51#2801C2218yescomplemented
52#2795C2218yescomplemented
53#2795C2214yescomplemented
54#2792C2218yescomplemented
55#2792C2214yescomplemented
56#2784C2214yescomplemented
57#2756C2218yescomplemented
58#2756C2218yescomplemented
59#2752C2218yescomplemented
60#2742C2218yescomplemented
61#2737C2218yescomplemented
62#2714C2218yescomplemented
63#2705C2218yescomplemented
64#2705C2218yescomplemented
65#2703C2218yescomplemented
66#2699C2214yescomplemented
67#2616C2212yes—
68#2616C2214yes—
69#2616C2212yes—
70#2616C2214yes—
71#2616C2214yes—
72#2616C2214yes—
73#2616C2212yes—
74#2616C2212yes—
75#2615C2212yes—
76#2615C2212yes—
77#2615C2212yes—
78#2615C2212yes—
79#2614C2214yes—
80#2613C2214yes—
81#2613C2214yes—
82#2613C2214yes—
83#2542C2214yescomplemented
84#2542C2214yescomplemented
85#2540C2214yescomplemented
86#2540C2214yescomplemented
87#2539C2214yes—
88#2538C2214yescomplemented
89#2538C2214yescomplemented
90#2538C2214yescomplemented
91#2537C2214yescomplemented
92#2536C2214yescomplemented
93#2536C2214yescomplemented
94#2536C2214yescomplemented
95#2535C2214yescomplemented
96#2534C2218yes—
97#2501C2214yes—
98#2497C2214yescomplemented
99#2497C2214yescomplemented
100#2496C2214yescomplemented
101#2496C2214yescomplemented
102#2495C2214yescomplemented
103#2495C2214yescomplemented
104#2494C2214yescomplemented
105#2494C2214yescomplemented
106#2493C2218yes—
107#2487C2214yescomplemented
108#2486C2218yes—
109#2486C2214yescomplemented
110#2485C2214yescomplemented
111#2485C2214yescomplemented
112#2484C2214yes—
113#2482C2214yes—
114#2480C2218yes—
115#2429C2214yescomplemented
116#2429C2214yescomplemented
117#2429C2214yescomplemented
118#2429C2214yescomplemented
119#2427C2214yescomplemented
120#2427C2214yescomplemented
121#2426C2214yescomplemented
122#2426C2214yescomplemented
123#2425C2218yes—
124#2424C2218yes—
125#2423C2214yescomplemented
126#2423C2214yescomplemented
127#2423C2214yescomplemented
128#2422C2214yescomplemented
129#2421C2214yescomplemented
130#2421C2214yescomplemented
131#2421C2214yescomplemented
132#2420C2214yescomplemented
133#2419C2218yes—
134#2418C2218yes—
135#2417C2214yescomplemented
136#2417C2214yescomplemented
137#2417C2214yescomplemented
138#2416C2214yescomplemented
139#2415C2214yescomplemented
140#2415C2214yescomplemented
141#2415C2214yescomplemented
142#2414C2214yescomplemented
143#2413C2218yes—
144#2411C2218yes—
145#2388C2214yes—
146#2388C2214yes—
147#2388C2214yes—
148#2388C2214yes—
149C2×#395C2212yes—
150C2×#394C2212yes—
151C2×#394C2214yes—
152#2317C2212yes—
153#2317C2212yes—
154#2316C2212yes—
155#2311C2212yes—
156#2310C2211yescharacteristic
157#2280C2212yes—
158#2280C2212yes—
159#2280C2212yes—
160C2×#380C2211yescharacteristic
161C2×#380C2212yes—
162#2274C2211yescharacteristic
163C22×#41—48no—
164C22×#41—44no—
165C22×#41C2312yes—
166C22×#41C2312yes—
167C22×#41C2312yes—
168C22×#41C2312yes—
169C22×#41C2312yes—
170C23×Q8C2311yescharacteristic
171C23×Q8C2311yescharacteristic
172C23×D4C2311yescharacteristic
173C23×D4C2312yes—
174C24×C4C2312yes—
175C24×C4C2311yescharacteristic
176#537—44no—
177#536—48no—
178C2×C4⋊Q8C2314yes—
179C2×#126C2318yes—
180C2×#124C2314yes—
181#525—48no—
182#525—48no—
183#525—48no—
184C2×#123C2314yes—
185C2×#123C2314yes—
186C2×#123C2314yes—
187C2×#123C2318yes—
188C2×#123C2318yes—
189C2×C22⋊Q8—48no—
190C2×C22⋊Q8—44no—
191C2×C22⋊Q8C2314yes—
192C2×C22⋊Q8C2314yes—
193C2×C22⋊Q8C2314yes—
194C2×C22⋊Q8C2314yes—
195C2×C22⋊Q8C2314yes—
196C2×C22⋊Q8C2314yes—
197C2×C22⋊Q8C2312yes—
198C2×C22⋊Q8C2312yes—
199C2×C22⋊Q8C2312yes—
200C2×C22⋊Q8C2312yes—
201C2×C22⋊Q8C2312yes—
202C2×C22⋊Q8C2312yes—
203C2×C22⋊Q8C2314yes—
204C2×C22⋊Q8C2314yes—
205C2×C22⋊Q8C2314yes—
206C2×#121C2312yes—
207C2×#121C2312yes—
208C2×#121C2312yes—
209C2×#121C2312yes—
210C2×#121C2312yes—
211C2×#121C2312yes—
212C2×#121C2314yes—
213C2×#121C2314yes—
214C2×#121C2318yes—
215C2×#120C2314yes—
216C2×#120C2314yes—
217C2×#120C2314yes—
218#520—48no—
219#519—44no—
220C2×C4×Q8C2314yes—
221C2×C4×Q8C2314yes—
222C2×C4×Q8C2314yes—
223C2×C4×D4C2314yes—
224C2×C4×D4C2314yes—
225C2×C4×D4C2314yes—
226C2×C4×D4C2314yes—
227C2×C4×D4C2314yes—
228C2×C4×D4C2314yes—
229C2×C4×D4C2318yes—
230C2×C4×D4C2314yes—
231C2×#117C2312yes—
232C2×#117C2312yes—
233C2×#117C2312yes—
234C2×#117C2314yes—
235C2×#117C2314yes—
236C22×C4⋊C4C2312yes—
237C22×C4⋊C4C2311yescharacteristic
238C22×C4⋊C4C2314yes—
239C22×C4⋊C4C2312yes—
240C22×C4⋊C4C2314yes—
241C22×C22⋊C4C2314yes—
242C22×C22⋊C4C2312yes—
243C22×C22⋊C4C2312yes—
244C22×C22⋊C4C2314yes—
245#401C2318yes—
246#400C2314yes—
247#400C2318yes—
248#400C2318yes—
249#400C2314yes—
250#400C2318yes—
251#400C2318yes—
252#399C2318yes—
253#399C2318yes—
254#399C2318yes—
255#399C2318yes—
256#399C2318yes—
257#398C2318yes—
258#398C2314yes—
259#398C2314yes—
260#398C2318yes—
261#398C2318yes—
262#398C2318yes—
263#398C2318yes—
264#398C2318yes—
265#397C2318yes—
266#397C2318yes—
267#397C2318yes—
268#397C2318yes—
269#397C2318yes—
270#397C2318yes—
271#397C2318yes—
272#397C2318yes—
273#397C2318yes—
274#397C2318yes—
275#396C2318yes—
276#396C2318yes—
277#396C2318yes—
278#396C2318yes—
279#396C2318yes—
280#396C2318yes—
281#396C2318yes—
282#396C2318yes—
283#396C2318yes—
284#395C2314yes—
285#395C2314yes—
286#395C2314yes—
287#395C2314yes—
288#395C2318yes—
289#395C2314yes—
290#395C2314yes—
291#394C2314yes—
292#394C2314yes—
293#394C2318yes—
294#394C2318yes—
295#394C2318yes—
296#394C2314yes—
297#394C2318yes—
298#394C2318yes—
299#394C2318yes—
300#394C2318yes—
301#394C2318yes—
302#394C2318yes—
303#394C2318yes—
304#394C2314yes—
305#394C2314yes—
306#394C2314yes—
307#394C2314yes—
308#394C2314yes—
309#394C2318yes—
310#394C2318yes—
311#394C2318yes—
312#394C2314yes—
313#394C2314yes—
314#394C2314yes—
315#394C2314yes—
316#394C2314yes—
317#394C2314yes—
318#394C2318yes—
319#393C2314yes—
320#393C2314yes—
321#393C2314yes—
322#393C2314yes—
323#392C2314yes—
324#392C2314yes—
325#392C2318yes—
326#392C2318yes—
327#392C2314yes—
328#392C2314yes—
329#392C2314yes—
330#392C2314yes—
331#392C2314yes—
332#392C2314yes—
333#392C2314yes—
334#392C2314yes—
335#392C2314yes—
336#392C2314yes—
337#391C2314yes—
338#391C2314yes—
339#391C2314yes—
340#390C2314yes—
341#390C2318yes—
342#390C2314yes—
343#390C2318yes—
344#390C2318yes—
345#390C2318yes—
346#390C2318yes—
347#390C2314yes—
348#389C2314yes—
349#389C2314yes—
350#389C2314yes—
351#389C2314yes—
352#389C2314yes—
353#389C2314yes—
354#389C2314yes—
355#389C2314yes—
356#389C2318yes—
357#389C2318yes—
358#389C2318yes—
359#389C2318yes—
360#389C2318yes—
361#388C2318yes—
362#388C2318yes—
363#388C2318yes—
364#388C2318yes—
365#388C2318yes—
366#388C2318yes—
367#388C2318yes—
368#388C2318yes—
369#388C2318yes—
370#388C2318yes—
371#388C2318yes—
372#388C2318yes—
373#388C2318yes—
374#388C2318yes—
375#388C2318yes—
376#387C2318yes—
377#387C2318yes—
378#387C2318yes—
379#387C2318yes—
380#387C2318yes—
381#387C2318yes—
382#387C2318yes—
383#386C2318yes—
384#386C2318yes—
385#386C2318yes—
386#386C2318yes—
387#386C2318yes—
388#386C2318yes—
389#385C2318yes—
390#385C2318yes—
391#385C2318yes—
392#384C2314yes—
393#384C2314yes—
394#384C2314yes—
395#384C2314yes—
396#383C2318yes—
397#382C2314yes—
398#382C2314yes—
399#381C2314yes—
400#381C2318yes—
401#381C2314yes—
402#381C2314yes—
403#381C2314yes—
404#380C2314yes—
405#380C2314yes—
406#380C2318yes—
407#380C2318yes—
408#380C2318yes—
409#380C2312yes—
410#380C2312yes—
411#380C2312yes—
412#380C2312yes—
413#380C2312yes—
414#380C2312yes—
415#380C2312yes—
416#380C2312yes—
417#380C2312yes—
418#380C2312yes—
419#380C2312yes—
420#380C2312yes—
421#380C2314yes—
422#380C2314yes—
423#380C2314yes—
424#380C2314yes—
425#380C2314yes—
426#380C2314yes—
427#380C2318yes—
428#379C2314yes—
429#379C2314yes—
430#379C2314yes—
431C4×C4⋊C4C2314yes—
432C4×C4⋊C4C2314yes—
433C4×C22⋊C4C2314yes—
434C4×C22⋊C4C2314yes—
435C4×C22⋊C4C2314yes—
436C4×C22⋊C4C2314yes—
437C4×C22⋊C4C2314yes—
438C4×C22⋊C4C2314yes—
439C4×C22⋊C4C2314yes—
440C2×#95C2312yes—
441C2×#95C2314yes—
442C25C2412yes—
443C25C2411yescharacteristic
444C2×#41—28no—
445C2×#41—28no—
446C2×#41—28no—
447C2×#41—44no—
448C2×#41—44no—
449C2×#41—44no—
450C2×#41—44no—
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—28no—
462C22×Q8—42no—
463C22×Q8—44no—
464C22×Q8C2414yes—
465C22×Q8C2412yes—
466C22×Q8C2411yescharacteristic
467C22×Q8C2412yes—
468C22×Q8C2411yescharacteristic
469C22×D4—42no—
470C22×D4—44no—
471C22×D4—44no—
472C22×D4—44no—
473C22×D4—44no—
474C22×D4C2414yes—
475C22×D4C2412yes—
476C22×D4C2414yes—
477C22×D4C2414yes—
478C22×D4C2414yes—
479C22×D4C2414yes—
480C22×D4C2414yes—
481C22×D4C2414yes—
482C22×D4C2414yes—
483C22×D4C2412yes—
484C22×D4C2412yes—
485C22×D4C2412yes—
486C22×D4C2411yescharacteristic
487C22×D4C2411yescharacteristic
488C22×D4C2412yes—
489C22×D4C2412yes—
490C23×C4—28no—
491C23×C4—24no—
492C23×C4—28no—
493C23×C4—28no—
494C23×C4—28no—
495C23×C4C2412yes—
496C23×C4C2412yes—
497C23×C4C2411yescharacteristic
498C23×C4C2414yes—
499C23×C4C2412yes—
500C23×C4C2412yes—
501C23×C4C2412yes—
502C23×C4C2412yes—
503C23×C4C2412yes—
504C23×C4C2412yes—
505C23×C4C2414yes—
506C23×C4C2412yes—
507C23×C4C2418yes—
508C23×C4C2411yescharacteristic
509C4⋊Q8—48no—
510#126—88no—
511#124—48no—
512#123—48no—
513#123—48no—
514#123—48no—
515#123—416no—
516#123—88no—
517C22⋊Q8—48no—
518C22⋊Q8—48no—
519C22⋊Q8—48no—
520C22⋊Q8—48no—
521C22⋊Q8—48no—
522C22⋊Q8—48no—
523C22⋊Q8—44no—
524C22⋊Q8—44no—
525C22⋊Q8—44no—
526C22⋊Q8—44no—
527C22⋊Q8—44no—
528C22⋊Q8—44no—
529C22⋊Q8—48no—
530C22⋊Q8—48no—
531C22⋊Q8—48no—
532#121—44no—
533#121—44no—
534#121—44no—
535#121—44no—
536#121—44no—
537#121—44no—
538#121—48no—
539#121—48no—
540#121—88no—
541#120—48no—
542#120—48no—
543#120—48no—
544C4×Q8—48no—
545C4×Q8—48no—
546C4×Q8—48no—
547C4×D4—48no—
548C4×D4—48no—
549C4×D4—48no—
550C4×D4—48no—
551C4×D4—48no—
552C4×D4—48no—
553C4×D4—48no—
554C4×D4—416no—
555#117—28no—
556#117—28no—
557#117—28no—
558#117—48no—
559#117—48no—
560C2×C4⋊C4—28no—
561C2×C4⋊C4—24no—
562C2×C4⋊C4—48no—
563C2×C4⋊C4—44no—
564C2×C4⋊C4—48no—
565C2×C4⋊C4C2412yes—
566C2×C4⋊C4C2414yes—
567C2×C4⋊C4C2414yes—
568C2×C4⋊C4C2414yes—
569C2×C4⋊C4C2412yes—
570C2×C4⋊C4C2412yes—
571C2×C4⋊C4C2412yes—
572C2×C4⋊C4C2412yes—
573C2×C4⋊C4C2412yes—
574C2×C4⋊C4C2418yes—
575C2×C4⋊C4C2418yes—
576C2×C4⋊C4C2418yes—
577C2×C4⋊C4C2414yes—
578C2×C4⋊C4C2414yes—
579C2×C4⋊C4C2414yes—
580C2×C4⋊C4C2414yes—
581C2×C4⋊C4C2414yes—
582C2×C4⋊C4C2414yes—
583C2×C4⋊C4C2414yes—
584C2×C4⋊C4C2414yes—
585C2×C4⋊C4C2414yes—
586C2×C4⋊C4C2414yes—
587C2×C4⋊C4C2414yes—
588C2×C4⋊C4C2418yes—
589C2×C4⋊C4C2418yes—
590C2×C4⋊C4C2418yes—
591C2×C4⋊C4C2418yes—
592C2×C4⋊C4C2418yes—
593C2×C4⋊C4C2418yes—
594C2×C4⋊C4C2418yes—
595C2×C4⋊C4C2418yes—
596C2×C22⋊C4—44no—
597C2×C22⋊C4—48no—
598C2×C22⋊C4—84no—
599C2×C22⋊C4—82no—
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⋊C4C2418yes—
610C2×C22⋊C4C2414yes—
611C2×C22⋊C4C2414yes—
612C2×C22⋊C4C2414yes—
613C2×C22⋊C4C2414yes—
614C2×C22⋊C4C2414yes—
615C2×C22⋊C4C2414yes—
616C2×C22⋊C4C2414yes—
617C2×C22⋊C4C2414yes—
618C2×C22⋊C4C2414yes—
619C2×C22⋊C4C2414yes—
620C2×C22⋊C4C2414yes—
621C2×C22⋊C4C2414yes—
622C2×C22⋊C4C2418yes—
623C2×C22⋊C4C2418yes—
624C2×C22⋊C4C2418yes—
625C2×C22⋊C4C2418yes—
626C2×C22⋊C4C2414yes—
627C2×C22⋊C4C2414yes—
628C2×C22⋊C4C2414yes—
629C2×C22⋊C4C2414yes—
630C2×C22⋊C4C2414yes—
631C2×C22⋊C4C2414yes—
632C2×C22⋊C4C2414yes—
633C2×C22⋊C4C2414yes—
634C2×C22⋊C4C2414yes—
635C2×C22⋊C4C2414yes—
636C2×C22⋊C4C2414yes—
637C2×C22⋊C4C2414yes—
638C2×C22⋊C4C2418yes—
639C2×C42C2414yes—
640C2×C42C2414yes—
641C2×C42C2414yes—
642C2×C42C2418yes—
643C2×C42C2418yes—
644C2×C42C2414yes—
645C2×C42C2414yes—
646#95C2418yes—
647#95C2414yes—
648#95C2414yes—
649#95C2418yes—
650#95C2418yes—
651#95C2414yes—
652#95C2414yes—
653#95C2414yes—
654#95C2414yes—
655#95C2414yes—
656#95C2414yes—
657#95C2414yes—
658#95C2414yes—
659#95C2414yes—
660#95C2414yes—
661#95C2414yes—
662#95C2414yes—
663#95C2414yes—
664#95C2418yes—
665#95C2418yes—
666#95C2418yes—
667#95C2418yes—
668#95C2418yes—
669#95C2418yes—
670#95C2414yes—
671#95C2418yes—
672#95C2418yes—
673#95C2418yes—
674C24—22no—
675C24—24no—
676C24—24no—
677C24—24no—
678C24—24no—
679C24—42no—
680C24—41no—
681C24—42no—
682C24—42no—
683C24—42no—
684C24—42no—
685C24—41no—
686C24C2512yes—
687C24C2512yes—
688C24C2512yes—
689C24C2514yes—
690C24C2511yescharacteristic
691#41—432no—
692#41—432no—
693#41—432no—
694#41—432no—
695#41—432no—
696C2×Q8—28no—
697C2×Q8—24no—
698C2×Q8—28no—
699C2×Q8—24no—
700C2×Q8—28no—
701C2×Q8—24no—
702C2×Q8—42no—
703C2×Q8—41no—
704C2×Q8—42no—
705C2×Q8—42no—
706C2×Q8—42no—
707C2×Q8—42no—
708C2×Q8—41no—
709C2×Q8—416no—
710C2×Q8—416no—
711C2×D4—28no—
712C2×D4—28no—
713C2×D4—28no—
714C2×D4—24no—
715C2×D4—24no—
716C2×D4—24no—
717C2×D4—42no—
718C2×D4—42no—
719C2×D4—42no—
720C2×D4—42no—
721C2×D4—42no—
722C2×D4—42no—
723C2×D4—42no—
724C2×D4—42no—
725C2×D4—42no—
726C2×D4—42no—
727C2×D4—42no—
728C2×D4—42no—
729C2×D4—41no—
730C2×D4—42no—
731C2×D4—42no—
732C2×D4—42no—
733C2×D4—42no—
734C2×D4—42no—
735C2×D4—41no—
736C2×D4—44no—
737C2×D4—44no—
738C2×D4—44no—
739C2×D4—44no—
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—416no—
758C2×D4—432no—
759C22×C4—24no—
760C22×C4—28no—
761C22×C4—22no—
762C22×C4—24no—
763C22×C4—24no—
764C22×C4—24no—
765C22×C4—24no—
766C22×C4—28no—
767C22×C4—24no—
768C22×C4—28no—
769C22×C4—28no—
770C22×C4—28no—
771C22×C4—24no—
772C22×C4—24no—
773C22×C4—24no—
774C22×C4—24no—
775C22×C4—24no—
776C22×C4—24no—
777C22×C4—24no—
778C22×C4—24no—
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—24no—
788C22×C4—24no—
789C22×C4—42no—
790C22×C4—44no—
791C22×C4—42no—
792C22×C4—44no—
793C22×C4—48no—
794C22×C4—48no—
795C22×C4—48no—
796C22×C4—432no—
797C22×C4—416no—
798C22×C4H(5,𝔽2)18yes—
799C22×C4H(5,𝔽2)14yes—
800C22×C4C2514yes—
801C22×C4C2514yes—
802C22×C4C2514yes—
803C22×C4C2514yes—
804C22×C4C2512yes—
805C22×C4C2511yescharacteristic
806C22×C4C2511yescharacteristic
807C22×C4C2512yes—
808C22×C4C2514yes—
809C22×C4C2518yes—
810C22×C4C2514yes—
811C22×C4C2514yes—
812C22×C4C2514yes—
813C22×C4C2514yes—
814C22×C4C2512yes—
815C4⋊C4—28no—
816C4⋊C4—28no—
817C4⋊C4—28no—
818C4⋊C4—24no—
819C4⋊C4—24no—
820C4⋊C4—24no—
821C4⋊C4—24no—
822C4⋊C4—24no—
823C4⋊C4—24no—
824C4⋊C4—48no—
825C4⋊C4—44no—
826C4⋊C4—44no—
827C4⋊C4—48no—
828C4⋊C4—48no—
829C4⋊C4—48no—
830C4⋊C4—48no—
831C4⋊C4—48no—
832C4⋊C4—44no—
833C4⋊C4—44no—
834C4⋊C4—44no—
835C4⋊C4—44no—
836C4⋊C4—44no—
837C4⋊C4—44no—
838C4⋊C4—44no—
839C4⋊C4—44no—
840C4⋊C4—44no—
841C4⋊C4—48no—
842C4⋊C4—48no—
843C4⋊C4—48no—
844C4⋊C4—48no—
845C4⋊C4—48no—
846C22⋊C4—28no—
847C22⋊C4—28no—
848C22⋊C4—28no—
849C22⋊C4—48no—
850C22⋊C4—48no—
851C22⋊C4—48no—
852C22⋊C4—48no—
853C22⋊C4—48no—
854C22⋊C4—48no—
855C22⋊C4—44no—
856C22⋊C4—44no—
857C22⋊C4—44no—
858C22⋊C4—44no—
859C22⋊C4—48no—
860C22⋊C4—44no—
861C22⋊C4—44no—
862C22⋊C4—44no—
863C22⋊C4—44no—
864C22⋊C4—44no—
865C22⋊C4—48no—
866C22⋊C4—44no—
867C22⋊C4—44no—
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—44no—
877C22⋊C4—44no—
878C22⋊C4—48no—
879C22⋊C4—48no—
880C22⋊C4—48no—
881C22⋊C4—48no—
882C22⋊C4—44no—
883C22⋊C4—44no—
884C22⋊C4—44no—
885C42—28no—
886C42—28no—
887C42—28no—
888C42—44no—
889C42—48no—
890C42—48no—
891C42—44no—
892C23—21no—
893C23—21no—
894C23—22no—
895C23—24no—
896C23—22no—
897C23—22no—
898C23—22no—
899C23—24no—
900C23—24no—
901C23—22no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—24no—
911C23—22no—
912C23—22no—
913C23—24no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—24no—
920C23—24no—
921C23—22no—
922C23—22no—
923C23—48no—
924C23—44no—
925C23—44no—
926C23—48no—
927C23—48no—
928C23—44no—
929C23—84no—
930C23—84no—
931C23—84no—
932C23—84no—
933C23—84no—
934C23—84no—
935C23C2×H(5,𝔽2)12yes—
936C23C2×H(5,𝔽2)14yes—
937C23C2611yescharacteristic
938Q8—44no—
939Q8—48no—
940Q8—44no—
941Q8—416no—
942Q8—48no—
943D4—44no—
944D4—48no—
945D4—48no—
946D4—48no—
947D4—48no—
948D4—48no—
949D4—44no—
950D4—416no—
951D4—48no—
952D4—88no—
953D4—88no—
954D4—88no—
955D4—88no—
956D4—88no—
957D4—88no—
958D4—164no—
959C2×C4—24no—
960C2×C4—24no—
961C2×C4—24no—
962C2×C4—24no—
963C2×C4—24no—
964C2×C4—24no—
965C2×C4—24no—
966C2×C4—24no—
967C2×C4—28no—
968C2×C4—24no—
969C2×C4—24no—
970C2×C4—28no—
971C2×C4—24no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—21no—
981C2×C4—21no—
982C2×C4—24no—
983C2×C4—24no—
984C2×C4—28no—
985C2×C4—24no—
986C2×C4—24no—
987C2×C4—24no—
988C2×C4—24no—
989C2×C4—24no—
990C2×C4—24no—
991C2×C4—24no—
992C2×C4—24no—
993C2×C4—24no—
994C2×C4—24no—
995C2×C4—24no—
996C2×C4—24no—
997C2×C4—28no—
998C2×C4—44no—
999C2×C4—48no—
1000C2×C4—48no—
1001C2×C4—48no—
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—168no—
1011C2×C4#560116yes—
1012C2×C4C2×H(5,𝔽2)14yes—
1013C2×C4C2×H(5,𝔽2)14yes—
1014C2×C4C2×H(5,𝔽2)14yes—
1015C22—24no—
1016C22—22no—
1017C22—22no—
1018C22—24no—
1019C22—44no—
1020C22—42no—
1021C22—42no—
1022C22—42no—
1023C22—44no—
1024C22—44no—
1025C22—42no—
1026C22—42no—
1027C22—42no—
1028C22—42no—
1029C22—42no—
1030C22—42no—
1031C22—42no—
1032C22—42no—
1033C22—42no—
1034C22—44no—
1035C22—44no—
1036C22—44no—
1037C22—42no—
1038C22—42no—
1039C22—42no—
1040C22—42no—
1041C22—42no—
1042C22—42no—
1043C22—42no—
1044C22—42no—
1045C22—42no—
1046C22—44no—
1047C22—816no—
1048C22—88no—
1049C22C2×#56014yes—
1050C22C22×H(5,𝔽2)12yes—
1051C22C22×H(5,𝔽2)11yescharacteristic
1052C22H(7,𝔽2)11yescharacteristic
1053C222−1+611yescharacteristic
1054C222−1+612yes—
1055C4—48no—
1056C4—44no—
1057C4—44no—
1058C4—44no—
1059C4—44no—
1060C4—44no—
1061C4—44no—
1062C4—44no—
1063C4—42no—
1064C4—41no—
1065C4—41no—
1066C4—42no—
1067C4—44no—
1068C4—44no—
1069C4C2×#56018yes—
1070C2—24no—
1071C2—84no—
1072C2—82no—
1073C2—82no—
1074C2—82no—
1075C2C22×#56011yescharacteristic
1076C2#6287512yes—
1077C2#6287511yescharacteristic
1078C2#6288612yes—
1079C2#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. #53064C2semidirect
2. #53045C2semidirect
3. #53045C2semidirect
4. #53044C2semidirect
5. #53014C2semidirect
6. #53007C2semidirect
7. #53006C2semidirect
8. #52956C2semidirect
9. #52913C2semidirect
10. #52340C2semidirect
11. #52339C2semidirect
12. #35672C2semidirect
13. #35661C2semidirect
14. #35634C2semidirect
15. #35633C2semidirect
16. #35544C2semidirect
17. #35518C2semidirect
18. #35516C2semidirect
19. #34632C2semidirect
20. C2×#2616C2semidirect
31. #2843C22semidirect
32. #2841C22semidirect
33. #2838C22semidirect
34. #2838C22semidirect
35. #2837C22semidirect
36. #2837C22semidirect
37. #2837C22semidirect
38. #2830C22semidirect
39. #2829C22semidirect
40. #2829C22semidirect
41. #2829C22semidirect
42. #2829C22semidirect
43. #2828C22semidirect
44. #2828C22semidirect
45. #2826C22semidirect
46. #2825C22semidirect
47. #2823C22semidirect
48. #2813C22semidirect
49. #2803C22semidirect
50. #2803C22semidirect
51. #2801C22semidirect
52. #2795C22semidirect
53. #2795C22semidirect
54. #2792C22semidirect
55. #2792C22semidirect
56. #2784C22semidirect
57. #2756C22semidirect
58. #2756C22semidirect
59. #2752C22semidirect
60. #2742C22semidirect
61. #2737C22semidirect
62. #2714C22semidirect
63. #2705C22semidirect
64. #2705C22semidirect
65. #2703C22semidirect
66. #2699C22semidirect
83. #2542C22semidirect
84. #2542C22semidirect
85. #2540C22semidirect
86. #2540C22semidirect
88. #2538C22semidirect
89. #2538C22semidirect
90. #2538C22semidirect
91. #2537C22semidirect
92. #2536C22semidirect
93. #2536C22semidirect
94. #2536C22semidirect
95. #2535C22semidirect
98. #2497C22semidirect
99. #2497C22semidirect
100. #2496C22semidirect
101. #2496C22semidirect
102. #2495C22semidirect
103. #2495C22semidirect
104. #2494C22semidirect
105. #2494C22semidirect
107. #2487C22semidirect
109. #2486C22semidirect
110. #2485C22semidirect
111. #2485C22semidirect
115. #2429C22semidirect
116. #2429C22semidirect
117. #2429C22semidirect
118. #2429C22semidirect
119. #2427C22semidirect
120. #2427C22semidirect
121. #2426C22semidirect
122. #2426C22semidirect
125. #2423C22semidirect
126. #2423C22semidirect
127. #2423C22semidirect
128. #2422C22semidirect
129. #2421C22semidirect
130. #2421C22semidirect
131. #2421C22semidirect
132. #2420C22semidirect
135. #2417C22semidirect
136. #2417C22semidirect
137. #2417C22semidirect
138. #2416C22semidirect
139. #2415C22semidirect
140. #2415C22semidirect
141. #2415C22semidirect
142. #2414C22semidirect

Maximal subgroups

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

subgroupindex
#530642
#530452
#530442
#530142
#530072
#530062
#529562
#529132
#523402
#523392
#356722
#356612
#356342
#356332
#355442
#355182
#355162
#346322
C2×#26162