Finite Group Databasebeta

← #8429253

Subgroups — #8429253

Order 512.

4814 conjugacy classes of subgroups.

The subgroup lattice has 1021 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59822C211yesmaximal, characteristic, complemented
2#59566C214yesmaximal, complemented
3#59303C211yesmaximal, characteristic, complemented
4#59220C211yesmaximal, characteristic, complemented
5#58355C214yesmaximal, complemented
6#53977C214yesmaximal, complemented
7#53098C214yesmaximal, complemented
8#53063C214yesmaximal, complemented
9#52653C214yesmaximal, complemented
10#42935C214yesmaximal, complemented
11#42688C214yesmaximal, complemented
12#41951C214yesmaximal, complemented
13#39410C214yesmaximal, complemented
14#39055C214yesmaximal, complemented
15#38975C212yesmaximal, complemented
16#38922C212yesmaximal, complemented
17#37638C211yesmaximal, characteristic, complemented
18#37620C211yesmaximal, characteristic, complemented
19#37508C214yesmaximal, complemented
20#36411C212yesmaximal, complemented
21#36181C211yesmaximal, characteristic, complemented
22#34976C211yesmaximal, characteristic, complemented
23#34727C212yesmaximal, complemented
24C2×#555C2212yes—
25C2×#552C2212yes—
26C2×#540C2214yes—
27C2×#529C2212yes—
28C2×C4×#41C2212yes—
29#2859C2211yescharacteristic
30#2857C2211yescharacteristic
31#2857C2211yescharacteristic
32#2854C2214yes—
33#2837C2218yes—
34#2833C2214yes—
35#2828C2218yes—
36#2827C2218yes—
37#2826C2218yes—
38#2825C2218yes—
39#2823C2214yes—
40#2818C2214yes—
41#2813C2214yes—
42#2795C2214yes—
43#2782C2214yes—
44#2780C2218yes—
45#2778C2218yes—
46#2761C2218yes—
47#2757C2218yes—
48#2746C2218yes—
49#2741C2218yes—
50#2740C2218yes—
51#2739C2218yes—
52#2733C2214yes—
53#2715C2218yes—
54#2709C2218yes—
55#2707C2218yes—
56#2707C2218yes—
57#2705C2218yes—
58#2703C2218yes—
59#2699C2218yes—
60#2688C2218yes—
61#2672C2218yes—
62#2664C2214yes—
63#2661C2214yes—
64#2654C2218yes—
65#2651C2218yes—
66#2647C2214yes—
67#2645C2214yes—
68#2644C2214yes—
69#2634C2214yes—
70#2633C2214yes—
71#2630C2218yes—
72#2629C2214yes—
73#2624C2214yes—
74#2620C2214yes—
75#2618C2214yes—
76#2609C2214yes—
77#2598C2214yes—
78#2594C2218yes—
79#2591C2214yes—
80#2585C2218yes—
81#2582C2211yescharacteristic
82#2577C2218yes—
83#2571C2211yescharacteristic
84#2567C2212yes—
85#2565C2212yes—
86#2562C2214yes—
87#2558C2218yes—
88#2548C2214yes—
89#2541C2214yes—
90#2538C2212yes—
91#2538C2212yes—
92#2537C2214yes—
93#2537C2211yescharacteristic
94#2537C2211yescharacteristic
95#2535C2214yes—
96#2516C2218yes—
97#2514C2214yes—
98#2507C2214yes—
99#2506C2214yes—
100#2506C2214yes—
101#2503C2212yes—
102#2500C2214yes—
103#2499C2212yes—
104#2497C2214yes—
105#2496C2214yes—
106#2495C2214yes—
107#2487C2214yes—
108#2486C2214yes—
109#2486C2214yes—
110#2485C2214yes—
111#2485C2214yes—
112#2485C2214yes—
113#2485C2214yes—
114#2479C2214yes—
115#2476C2218yes—
116#2474C2218yes—
117#2471C2214yes—
118#2467C2214yes—
119#2461C2218yes—
120#2457C2218yes—
121#2456C2214yes—
122#2454C2212yes—
123#2448C2212yes—
124#2445C2214yes—
125#2441C2214yes—
126#2441C2212yes—
127#2431C2212yes—
128#2428C2212yes—
129#2427C2214yes—
130#2423C2212yes—
131#2422C2214yes—
132#2417C2214yes—
133#2417C2214yes—
134#2416C2214yes—
135#2416C2214yes—
136#2416C2214yes—
137#2415C2214yes—
138#2415C2214yes—
139#2414C2214yes—
140#2414C2214yes—
141#2414C2214yes—
142#2414C2212yes—
143#2407C2214yes—
144#2407C2214yes—
145#2407C2212yes—
146#2397C2214yes—
147#2392C2214yes—
148#2392C2214yes—
149#2362C2214yes—
150#2361C2214yes—
151#2354C2212yes—
152#2354C2214yes—
153#2354C2214yes—
154#2352C2214yes—
155D4×C4⋊C4C2212yes—
156#2347C2214yes—
157#2344C2214yes—
158#2319C2214yes—
159#2316C2214yes—
160C4×C4⋊Q8C2211yescharacteristic
161C4×#127C2212yes—
162C4×C22⋊Q8C2214yes—
163C4×#121C2212yes—
164C4×#121C2212yes—
165C4×#121C2214yes—
166C4×#121C2214yes—
167#2296C2214yes—
168#2295C2212yes—
169#2290C2214yes—
170#2285C2211yescharacteristic
171C2×#384C2211yescharacteristic
172C42×D4C2211yescharacteristic
173C22×#41C2312yes—
174#555—48no—
175#552—48no—
176#540—416no—
177C2×C4⋊Q8C2311yescharacteristic
178C2×#127C2312yes—
179C2×#127C2314yes—
180#529—48no—
181C2×#126C2314yes—
182C2×#126C2314yes—
183C2×#125C2314yes—
184C2×#125C2312yes—
185C2×#125C2312yes—
186C2×#125C2314yes—
187C2×#124C2312yes—
188C2×#124C2318yes—
189C2×#123C2318yes—
190C2×#123C2314yes—
191C2×#123C2314yes—
192C2×#123C2318yes—
193C2×C22⋊Q8C2312yes—
194C2×C22⋊Q8C2312yes—
195C2×C22⋊Q8C2314yes—
196C2×C22⋊Q8C2312yes—
197C2×C22⋊Q8C2314yes—
198C2×#121C2314yes—
199C2×#121C2314yes—
200C2×#121C2314yes—
201C2×#121C2314yes—
202C2×#121C2314yes—
203C2×#121C2314yes—
204C2×#121C2314yes—
205C2×#121C2312yes—
206C2×#121C2312yes—
207C2×#121C2312yes—
208C2×#121C2318yes—
209C4×#41—48no—
210C2×C4×Q8C2312yes—
211C2×C4×Q8C2312yes—
212C2×C4×Q8C2312yes—
213C2×C4×D4C2312yes—
214C2×C4×D4C2312yes—
215C2×C4×D4C2311yescharacteristic
216C2×C4×D4C2314yes—
217C2×C4×D4C2314yes—
218C2×C4×D4C2314yes—
219C2×C4×D4C2314yes—
220C2×C4×D4C2314yes—
221C2×C4×D4C2314yes—
222C2×C4×D4C2314yes—
223C2×C4×D4C2314yes—
224C2×C4×D4C2314yes—
225C2×C4×D4C2312yes—
226C2×C4×D4C2314yes—
227C2×C4×D4C2312yes—
228C2×#117C2314yes—
229C2×#117C2314yes—
230C2×#117C2314yes—
231C2×#117C2312yes—
232C2×#117C2314yes—
233C2×#117C2314yes—
234C2×#117C2312yes—
235C2×#117C2314yes—
236C22×C4⋊C4C2314yes—
237C22×C4⋊C4C2312yes—
238C22×C4⋊C4C2314yes—
239C22×C42C2311yescharacteristic
240C22×C42C2311yescharacteristic
241C22×C42C2314yes—
242#401C2318yes—
243#400C2314yes—
244#400C2314yes—
245#400C2318yes—
246#400C2318yes—
247#400C2314yes—
248#400C2318yes—
249#400C2318yes—
250#400C2318yes—
251#399C2318yes—
252#399C2314yes—
253#399C2314yes—
254#399C2314yes—
255#399C2314yes—
256#399C2314yes—
257#398C2318yes—
258#398C2318yes—
259#398C2314yes—
260#398C2318yes—
261#398C2318yes—
262#398C2314yes—
263#398C2318yes—
264#398C2314yes—
265#398C2314yes—
266#397C2318yes—
267#397C2318yes—
268#397C2318yes—
269#397C2318yes—
270#397C2318yes—
271#397C2318yes—
272#397C2318yes—
273#397C2318yes—
274#397C2314yes—
275#397C2314yes—
276#396C2318yes—
277#396C2318yes—
278#396C2318yes—
279#396C2314yes—
280#396C2318yes—
281#396C2318yes—
282#396C2318yes—
283#396C2318yes—
284#396C2318yes—
285#396C2314yes—
286#395C2318yes—
287#394C2314yes—
288#394C2314yes—
289#394C2314yes—
290#394C2318yes—
291#394C2318yes—
292#394C2318yes—
293#394C2314yes—
294#394C2314yes—
295#394C2318yes—
296#394C2318yes—
297#394C2318yes—
298#394C2318yes—
299#394C2314yes—
300#394C2314yes—
301#394C2318yes—
302#394C2318yes—
303#394C2314yes—
304#394C2314yes—
305#394C2318yes—
306#394C2318yes—
307#392C2314yes—
308#392C2314yes—
309#392C2318yes—
310#392C2314yes—
311#392C2314yes—
312#392C2318yes—
313#392C2318yes—
314#392C2314yes—
315#392C2314yes—
316#392C2314yes—
317#391C2312yes—
318#391C2312yes—
319#391C2312yes—
320#391C2314yes—
321#391C2314yes—
322#391C2312yes—
323#391C2312yes—
324#390C2312yes—
325#390C2312yes—
326#390C2314yes—
327#390C2314yes—
328#390C2318yes—
329#390C2314yes—
330#390C2312yes—
331#390C2314yes—
332#390C2318yes—
333#390C2312yes—
334#390C2314yes—
335#390C2318yes—
336#390C2314yes—
337#389C2314yes—
338#389C2314yes—
339#389C2314yes—
340#389C2314yes—
341#389C2312yes—
342#389C2314yes—
343#389C2318yes—
344#389C2314yes—
345#389C2318yes—
346#389C2314yes—
347#389C2314yes—
348#389C2314yes—
349#389C2318yes—
350#389C2314yes—
351#389C2314yes—
352#389C2314yes—
353#389C2314yes—
354#389C2312yes—
355#389C2312yes—
356#389C2312yes—
357#388C2314yes—
358#388C2318yes—
359#388C2318yes—
360#388C2318yes—
361#388C2318yes—
362#388C2318yes—
363#388C2318yes—
364#388C2318yes—
365#388C2318yes—
366#388C2314yes—
367#388C2318yes—
368#388C2318yes—
369#388C2318yes—
370#388C2314yes—
371#388C2318yes—
372#388C2318yes—
373#388C2318yes—
374#388C2314yes—
375#388C2314yes—
376#388C2314yes—
377#387C2318yes—
378#387C2314yes—
379#387C2318yes—
380#387C2318yes—
381#387C2318yes—
382#387C2314yes—
383#387C2318yes—
384#387C2318yes—
385#387C2318yes—
386#387C2318yes—
387#387C2314yes—
388#387C2314yes—
389#386C2318yes—
390#386C2318yes—
391#386C2318yes—
392#386C2314yes—
393#386C2318yes—
394#386C2314yes—
395#386C2318yes—
396#386C2314yes—
397#386C2318yes—
398#386C2318yes—
399#386C2318yes—
400#386C2314yes—
401#386C2314yes—
402#386C2314yes—
403#385C2318yes—
404#385C2314yes—
405#385C2318yes—
406#385C2318yes—
407#385C2318yes—
408#385C2318yes—
409#385C2314yes—
410#384C2312yes—
411#384C2311yescharacteristic
412#384C2312yes—
413#384C2314yes—
414#384C2311yescharacteristic
415#384C2311yescharacteristic
416#384C2314yes—
417#383C2314yes—
418#383C2314yes—
419#382C2312yes—
420#382C2314yes—
421#382C2312yes—
422#381C2318yes—
423#381C2318yes—
424#380C2318yes—
425#380C2318yes—
426#380C2318yes—
427#380C2314yes—
428#380C2314yes—
429#380C2314yes—
430#380C2314yes—
431#380C2314yes—
432#380C2314yes—
433#380C2312yes—
434#380C2314yes—
435#380C2314yes—
436#380C2314yes—
437#380C2312yes—
438#380C2314yes—
439#380C2314yes—
440C4×C4⋊C4C2314yes—
441C4×C4⋊C4C2314yes—
442C4×C4⋊C4C2311yescharacteristic
443C4×C4⋊C4C2312yes—
444C4×C4⋊C4C2314yes—
445C4×C4⋊C4C2318yes—
446C4×C4⋊C4C2314yes—
447C4×C4⋊C4C2318yes—
448C4×C4⋊C4C2314yes—
449C4×C4⋊C4C2314yes—
450C4×C4⋊C4C2312yes—
451C4×C22⋊C4C2318yes—
452C4×C22⋊C4C2314yes—
453C4×C22⋊C4C2312yes—
454C4×C22⋊C4C2314yes—
455C4×C22⋊C4C2312yes—
456C4×C22⋊C4C2314yes—
457C4×C22⋊C4C2311yescharacteristic
458C4×C22⋊C4C2311yescharacteristic
459#376C2314yes—
460C43C2311yescharacteristic
461C2×#41—44no—
462C2×#41—44no—
463C2×#41—44no—
464C22×Q8C2412yes—
465C22×Q8C2412yes—
466C22×D4C2412yes—
467C22×D4C2412yes—
468C22×D4C2411yescharacteristic
469C22×D4C2414yes—
470C22×D4C2414yes—
471C22×D4C2414yes—
472C22×D4C2414yes—
473C22×D4C2414yes—
474C22×D4C2414yes—
475C22×D4C2414yes—
476C22×D4C2414yes—
477C22×D4C2418yes—
478C23×C4C2412yes—
479C23×C4C2414yes—
480C23×C4C2414yes—
481C23×C4C2412yes—
482C23×C4C2411yescharacteristic
483C23×C4C2411yescharacteristic
484C23×C4C2414yes—
485C23×C4C2414yes—
486C23×C4C2418yes—
487C23×C4C2414yes—
488C4⋊Q8—24no—
489#127—44no—
490#127—48no—
491#126—48no—
492#126—48no—
493#125—44no—
494#125—48no—
495#125—48no—
496#125—44no—
497#124—44no—
498#124—416no—
499#123—48no—
500#123—416no—
501#123—48no—
502#123—416no—
503C22⋊Q8—44no—
504C22⋊Q8—44no—
505C22⋊Q8—48no—
506C22⋊Q8—48no—
507C22⋊Q8—44no—
508#121—216no—
509#121—416no—
510#121—44no—
511#121—48no—
512#121—48no—
513#121—44no—
514#121—44no—
515#121—48no—
516#121—48no—
517#121—48no—
518#121—48no—
519C4×Q8—28no—
520C4×Q8—44no—
521C4×Q8—44no—
522C4×D4—24no—
523C4×D4—28no—
524C4×D4—28no—
525C4×D4—48no—
526C4×D4—48no—
527C4×D4—44no—
528C4×D4—44no—
529C4×D4—48no—
530C4×D4—48no—
531C4×D4—48no—
532C4×D4—48no—
533C4×D4—48no—
534C4×D4—48no—
535C4×D4—48no—
536C4×D4—48no—
537#117—216no—
538#117—48no—
539#117—44no—
540#117—48no—
541#117—48no—
542#117—44no—
543#117—48no—
544#117—48no—
545C2×C4⋊C4—48no—
546C2×C4⋊C4—48no—
547C2×C4⋊C4—44no—
548C2×C4⋊C4C2412yes—
549C2×C4⋊C4C2414yes—
550C2×C4⋊C4C2414yes—
551C2×C4⋊C4C2414yes—
552C2×C4⋊C4C2412yes—
553C2×C4⋊C4C2412yes—
554C2×C4⋊C4C2414yes—
555C2×C4⋊C4C2412yes—
556C2×C4⋊C4C2412yes—
557C2×C4⋊C4C2414yes—
558C2×C4⋊C4C2414yes—
559C2×C4⋊C4C2414yes—
560C2×C4⋊C4C2411yescharacteristic
561C2×C4⋊C4C2414yes—
562C2×C4⋊C4C2412yes—
563C2×C4⋊C4C2412yes—
564C2×C4⋊C4C2414yes—
565C2×C4⋊C4C2418yes—
566C2×C4⋊C4C2418yes—
567C2×C4⋊C4C2414yes—
568C2×C4⋊C4C2412yes—
569C2×C4⋊C4C2414yes—
570C2×C4⋊C4C2414yes—
571C2×C4⋊C4C2414yes—
572C2×C4⋊C4C2414yes—
573C2×C4⋊C4C2414yes—
574C2×C4⋊C4C2414yes—
575C2×C4⋊C4C2412yes—
576C2×C4⋊C4C2414yes—
577C2×C4⋊C4C2414yes—
578C2×C4⋊C4C2414yes—
579C2×C4⋊C4C2414yes—
580C2×C4⋊C4C2418yes—
581C2×C4⋊C4C2414yes—
582C2×C4⋊C4C2418yes—
583C2×C4⋊C4C2418yes—
584C2×C4⋊C4C2414yes—
585C2×C4⋊C4C2414yes—
586C2×C4⋊C4C2418yes—
587C2×C22⋊C4C2414yes—
588C2×C22⋊C4C2414yes—
589C2×C22⋊C4C2414yes—
590C2×C22⋊C4C2414yes—
591C2×C22⋊C4C2411yescharacteristic
592C2×C22⋊C4C2414yes—
593C2×C22⋊C4C2414yes—
594C2×C22⋊C4C2418yes—
595C2×C22⋊C4C2418yes—
596C2×C22⋊C4C2414yes—
597C2×C22⋊C4C2414yes—
598C2×C22⋊C4C2414yes—
599C2×C22⋊C4C2418yes—
600C2×C22⋊C4C2418yes—
601C2×C22⋊C4C2414yes—
602C2×C22⋊C4C2414yes—
603C2×C22⋊C4C2414yes—
604C2×C22⋊C4C2412yes—
605C2×C22⋊C4C2412yes—
606C2×C22⋊C4C2414yes—
607C2×C22⋊C4C2418yes—
608C2×C22⋊C4C2414yes—
609C2×C22⋊C4C2414yes—
610C2×C22⋊C4C2414yes—
611C2×C22⋊C4C2414yes—
612C2×C22⋊C4C2414yes—
613C2×C22⋊C4C2414yes—
614C2×C22⋊C4C2418yes—
615C2×C22⋊C4C2418yes—
616C2×C22⋊C4C2418yes—
617C2×C22⋊C4C2414yes—
618C2×C22⋊C4C2414yes—
619C2×C22⋊C4C2418yes—
620C2×C22⋊C4C2414yes—
621C2×C22⋊C4C2418yes—
622C2×C22⋊C4C2418yes—
623C2×C22⋊C4C2414yes—
624C2×C22⋊C4C2411yescharacteristic
625C2×C42—24no—
626C2×C42—24no—
627C2×C42—48no—
628C2×C42C2411yescharacteristic
629C2×C42C2414yes—
630C2×C42C2412yes—
631C2×C42C2414yes—
632C2×C42C2414yes—
633C2×C42C2412yes—
634C2×C42C2414yes—
635C2×C42C2412yes—
636C2×C42C2411yescharacteristic
637C2×C42C2412yes—
638C2×C42C2411yescharacteristic
639C2×C42C2418yes—
640C2×C42C2414yes—
641C2×C42C2418yes—
642C2×C42C2414yes—
643C2×C42C2411yescharacteristic
644C2×C42C2411yescharacteristic
645#95C2414yes—
646#95C2414yes—
647#95C2414yes—
648#95C2414yes—
649#95C2412yes—
650#95C2412yes—
651#95C2412yes—
652#95C2414yes—
653#95C2414yes—
654#95C2418yes—
655#95C2414yes—
656#95C2414yes—
657#95C2414yes—
658#95C2414yes—
659#95C2418yes—
660#95C2414yes—
661#95C2418yes—
662#95C2418yes—
663#95C2418yes—
664#95C2414yes—
665#95C2418yes—
666#95C2418yes—
667#95C2414yes—
668#95C2418yes—
669#95C2414yes—
670#95C2414yes—
671#95C2418yes—
672#95C2418yes—
673#95C2418yes—
674#95C2418yes—
675#95C2418yes—
676C24C2511yescharacteristic
677C24C2514yes—
678C24C2514yes—
679C24C2511yescharacteristic
680#41—432no—
681C2×Q8—24no—
682C2×Q8—24no—
683C2×Q8—24no—
684C2×Q8—24no—
685C2×Q8—42no—
686C2×Q8—42no—
687C2×D4—22no—
688C2×D4—28no—
689C2×D4—28no—
690C2×D4—24no—
691C2×D4—24no—
692C2×D4—28no—
693C2×D4—24no—
694C2×D4—24no—
695C2×D4—24no—
696C2×D4—24no—
697C2×D4—44no—
698C2×D4—42no—
699C2×D4—44no—
700C2×D4—44no—
701C2×D4—44no—
702C2×D4—44no—
703C2×D4—44no—
704C2×D4—44no—
705C2×D4—44no—
706C2×D4—44no—
707C2×D4—44no—
708C2×D4—44no—
709C2×D4—48no—
710C2×D4—48no—
711C2×D4—44no—
712C2×D4—44no—
713C2×D4—44no—
714C2×D4—44no—
715C2×D4—44no—
716C2×D4—44no—
717C2×D4—48no—
718C2×D4—48no—
719C2×D4—48no—
720C22×C4—22no—
721C22×C4—28no—
722C22×C4—24no—
723C22×C4—22no—
724C22×C4—24no—
725C22×C4—22no—
726C22×C4—28no—
727C22×C4—28no—
728C22×C4—22no—
729C22×C4—24no—
730C22×C4—28no—
731C22×C4—28no—
732C22×C4—24no—
733C22×C4—28no—
734C22×C4—24no—
735C22×C4—28no—
736C22×C4—24no—
737C22×C4—28no—
738C22×C4—44no—
739C22×C4—41no—
740C22×C4—41no—
741C22×C4—44no—
742C22×C4—44no—
743C22×C4—44no—
744C22×C4—48no—
745C22×C4—44no—
746C22×C4—48no—
747C22×C4—48no—
748C22×C4—48no—
749C22×C4C2512yes—
750C22×C4C2514yes—
751C22×C4C2512yes—
752C22×C4C2514yes—
753C22×C4C2514yes—
754C22×C4C2514yes—
755C22×C4C2514yes—
756C22×C4C2514yes—
757C22×C4C2514yes—
758C22×C4C2511yescharacteristic
759C22×C4C2512yes—
760C22×C4C2514yes—
761C22×C4C2514yes—
762C22×C4C2514yes—
763C22×C4C2511yescharacteristic
764C22×C4C2511yescharacteristic
765C22×C4C2511yescharacteristic
766C22×C4C2511yescharacteristic
767C22×C4C2512yes—
768C4⋊C4—28no—
769C4⋊C4—28no—
770C4⋊C4—24no—
771C4⋊C4—24no—
772C4⋊C4—28no—
773C4⋊C4—24no—
774C4⋊C4—28no—
775C4⋊C4—22no—
776C4⋊C4—28no—
777C4⋊C4—24no—
778C4⋊C4—28no—
779C4⋊C4—28no—
780C4⋊C4—28no—
781C4⋊C4—24no—
782C4⋊C4—48no—
783C4⋊C4—48no—
784C4⋊C4—42no—
785C4⋊C4—42no—
786C4⋊C4—44no—
787C4⋊C4—44no—
788C4⋊C4—48no—
789C4⋊C4—44no—
790C4⋊C4—42no—
791C4⋊C4—44no—
792C4⋊C4—44no—
793C4⋊C4—44no—
794C4⋊C4—42no—
795C4⋊C4—44no—
796C4⋊C4—44no—
797C4⋊C4—44no—
798C4⋊C4—44no—
799C4⋊C4—44no—
800C4⋊C4—44no—
801C4⋊C4—44no—
802C4⋊C4—48no—
803C4⋊C4—48no—
804C4⋊C4—48no—
805C4⋊C4—44no—
806C4⋊C4—44no—
807C22⋊C4—28no—
808C22⋊C4—28no—
809C22⋊C4—28no—
810C22⋊C4—22no—
811C22⋊C4—28no—
812C22⋊C4—44no—
813C22⋊C4—48no—
814C22⋊C4—44no—
815C22⋊C4—44no—
816C22⋊C4—48no—
817C22⋊C4—48no—
818C22⋊C4—44no—
819C22⋊C4—44no—
820C22⋊C4—44no—
821C22⋊C4—44no—
822C22⋊C4—44no—
823C22⋊C4—44no—
824C22⋊C4—48no—
825C22⋊C4—44no—
826C22⋊C4—44no—
827C22⋊C4—44no—
828C22⋊C4—42no—
829C22⋊C4—42no—
830C22⋊C4—44no—
831C22⋊C4—44no—
832C22⋊C4—48no—
833C22⋊C4—44no—
834C22⋊C4—44no—
835C22⋊C4—44no—
836C22⋊C4—48no—
837C22⋊C4—44no—
838C22⋊C4—48no—
839C22⋊C4—48no—
840C22⋊C4—48no—
841C22⋊C4—48no—
842C22⋊C4—48no—
843C22⋊C4—44no—
844C22⋊C4H(5,𝔽2)14yes—
845C42—24no—
846C42—22no—
847C42—24no—
848C42—22no—
849C42—28no—
850C42—28no—
851C42—28no—
852C42—22no—
853C42—24no—
854C42—28no—
855C42—24no—
856C42—44no—
857C42—44no—
858C42—41no—
859C42—48no—
860C42—48no—
861C42H(5,𝔽2)14yes—
862C23—21no—
863C23—22no—
864C23—22no—
865C23—21no—
866C23—21no—
867C23—24no—
868C23—24no—
869C23—24no—
870C23—21no—
871C23—24no—
872C23—24no—
873C23—24no—
874C23—24no—
875C23—24no—
876C23—24no—
877C23—22no—
878C23—24no—
879C23—24no—
880C23—22no—
881C23—24no—
882C23—24no—
883C23—21no—
884C23—24no—
885C23C2×H(5,𝔽2)12yes—
886C23C2611yescharacteristic
887Q8—48no—
888Q8—84no—
889D4—44no—
890D4—416no—
891D4—48no—
892D4—48no—
893D4—88no—
894D4—88no—
895D4—88no—
896D4—88no—
897D4—88no—
898D4—88no—
899D4—88no—
900D4—168no—
901C2×C4—21no—
902C2×C4—21no—
903C2×C4—22no—
904C2×C4—21no—
905C2×C4—21no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—21no—
909C2×C4—24no—
910C2×C4—24no—
911C2×C4—24no—
912C2×C4—24no—
913C2×C4—24no—
914C2×C4—21no—
915C2×C4—24no—
916C2×C4—24no—
917C2×C4—24no—
918C2×C4—24no—
919C2×C4—21no—
920C2×C4—24no—
921C2×C4—24no—
922C2×C4—22no—
923C2×C4—24no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—24no—
927C2×C4—24no—
928C2×C4—24no—
929C2×C4—28no—
930C2×C4—22no—
931C2×C4—24no—
932C2×C4—22no—
933C2×C4—28no—
934C2×C4—28no—
935C2×C4—24no—
936C2×C4—24no—
937C2×C4—22no—
938C2×C4—24no—
939C2×C4—24no—
940C2×C4—24no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—21no—
944C2×C4—24no—
945C2×C4—24no—
946C2×C4—24no—
947C2×C4—44no—
948C2×C4—44no—
949C2×C4—416no—
950C2×C4—48no—
951C2×C4—416no—
952C2×C4—416no—
953C2×C4—48no—
954C2×C4—88no—
955C2×C4—88no—
956C2×C4—168no—
957C2×C4C2×H(5,𝔽2)12yes—
958C2×C4C2×H(5,𝔽2)12yes—
959C2×C4C2×H(5,𝔽2)12yes—
960C2×C4C2×H(5,𝔽2)14yes—
961C2×C4#58514yes—
962C2×C4#58514yes—
963C22—22no—
964C22—22no—
965C22—22no—
966C22—42no—
967C22—42no—
968C22—44no—
969C22—42no—
970C22—44no—
971C22—44no—
972C22—44no—
973C22—41no—
974C22—44no—
975C22—44no—
976C22—44no—
977C22—44no—
978C22—41no—
979C22—41no—
980C22—44no—
981C22—44no—
982C22—42no—
983C22—44no—
984C22—44no—
985C22—44no—
986C22—44no—
987C22C22×H(5,𝔽2)11yescharacteristic
988C22C22×H(5,𝔽2)11yescharacteristic
989C22C2×#58512yes—
990C22C2×#58512yes—
991C222−1+611yescharacteristic
992C4—22no—
993C4—22no—
994C4—22no—
995C4—42no—
996C4—44no—
997C4—44no—
998C4—42no—
999C4—44no—
1000C4—44no—
1001C4—44no—
1002C4—41no—
1003C4—44no—
1004C4—44no—
1005C4—41no—
1006C4—44no—
1007C4—44no—
1008C4—44no—
1009C4—42no—
1010C4#353918yes—
1011C2—42no—
1012C2—81no—
1013C2—84no—
1014C2—84no—
1015C2C2×#353912yes—
1016C2#6275911yescharacteristic
1017C2#6291411yescharacteristic
1018C2#6293612yes—
1019C2#6302411yescharacteristic
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. #59822C2semidirect
2. #59566C2semidirect
3. #59303C2semidirect
4. #59220C2semidirect
5. #58355C2semidirect
6. #53977C2semidirect
7. #53098C2semidirect
8. #53063C2semidirect
9. #52653C2semidirect
10. #42935C2semidirect
11. #42688C2semidirect
12. #41951C2semidirect
13. #39410C2semidirect
14. #39055C2semidirect
15. #38975C2semidirect
16. #38922C2semidirect
17. #37638C2semidirect
18. #37620C2semidirect
19. #37508C2semidirect
20. #36411C2semidirect
21. #36181C2semidirect
22. #34976C2semidirect
23. #34727C2semidirect

Maximal subgroups

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

subgroupindex
#598222
#595662
#593032
#592202
#583552
#539772
#530982
#530632
#526532
#429352
#426882
#419512
#394102
#390552
#389752
#389222
#376382
#376202
#375082
#364112
#361812
#349762
#347272