Finite Group Databasebeta

← #7647499

Subgroups — #7647499

Order 512.

4598 conjugacy classes of subgroups.

The subgroup lattice has 1046 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42464C214yesmaximal, complemented
2#42462C214yesmaximal, complemented
3#40648C218yesmaximal, complemented
4#39756C212yesmaximal, complemented
5#39736C212yesmaximal, complemented
6#39502C212yesmaximal, complemented
7#39479C212yesmaximal, complemented
8#39185C212yesmaximal, complemented
9#39157C212yesmaximal, complemented
10#38971C212yesmaximal, complemented
11#38942C212yesmaximal, complemented
12#37498C214yesmaximal, complemented
13#37027C214yesmaximal, complemented
14#37026C214yesmaximal, complemented
15#35552C214yesmaximal, complemented
16#35292C211yesmaximal, characteristic, complemented
17#35202C211yesmaximal, characteristic, complemented
18#35161C214yesmaximal, complemented
19#35161C214yesmaximal, complemented
20#34977C211yesmaximal, characteristic, complemented
21#34909C211yesmaximal, characteristic, complemented
22#34236C211yesmaximal, characteristic, complemented
23#34121C211yesmaximal, characteristic, complemented
24#34060C211yesmaximal, characteristic, complemented
25C2×#532C2211yescharacteristic
26C2×C4×#41C2211yescharacteristic
27C2×C4×#41C2211yescharacteristic
28#2865C2218yes—
29#2864C2212yes—
30#2860C2218yes—
31#2859C2212yes—
32#2857C2212yes—
33#2856C2212yes—
34#2826C2218yes—
35#2825C2218yes—
36#2808C2218yes—
37#2803C2218yes—
38#2796C2218yes—
39#2783C2218yes—
40#2771C2218yes—
41#2762C2218yes—
42#2761C2218yes—
43#2756C2218yes—
44#2754C2218yes—
45#2745C2218yes—
46#2727C2218yes—
47#2714C2218yes—
48#2702C2218yes—
49#2699C2218yes—
50#2691C2218yes—
51#2689C2218yes—
52#2667C2214yes—
53#2649C2218yes—
54#2649C2218yes—
55#2648C2218yes—
56#2648C2218yes—
57#2645C2214yes—
58#2641C2214yes—
59#2636C2218yes—
60#2635C2218yes—
61#2624C2214yes—
62#2624C2212yes—
63#2620C2214yes—
64#2615C2212yes—
65#2610C2214yes—
66#2606C2214yes—
67#2600C2214yes—
68#2599C2212yes—
69#2598C2212yes—
70#2592C2212yes—
71#2581C2211yescharacteristic
72#2580C2212yes—
73#2580C2211yescharacteristic
74#2576C2218yes—
75#2571C2214yes—
76#2567C2211yescharacteristic
77#2566C2214yes—
78#2563C2211yescharacteristic
79#2562C2214yes—
80#2559C2218yes—
81#2552C2212yes—
82#2552C2212yes—
83#2548C2211yescharacteristic
84#2541C2211yescharacteristic
85#2540C2212yes—
86#2537C2214yes—
87#2536C2211yescharacteristic
88#2535C2211yescharacteristic
89#2535C2212yes—
90#2530C2218yes—
91#2530C2218yes—
92#2526C2218yes—
93#2526C2218yes—
94#2518C2218yes—
95#2512C2214yes—
96#2512C2214yes—
97#2512C2214yes—
98#2509C2214yes—
99#2509C2214yes—
100#2500C2214yes—
101#2500C2212yes—
102#2496C2214yes—
103#2496C2214yes—
104#2496C2214yes—
105#2494C2214yes—
106#2493C2218yes—
107#2490C2214yes—
108#2490C2214yes—
109#2489C2214yes—
110#2485C2214yes—
111#2485C2212yes—
112#2467C2218yes—
113#2467C2218yes—
114#2466C2218yes—
115#2466C2218yes—
116#2466C2218yes—
117#2447C2214yes—
118#2444C2218yes—
119#2441C2214yes—
120#2441C2214yes—
121#2441C2214yes—
122#2431C2212yes—
123#2428C2214yes—
124#2420C2214yes—
125#2420C2214yes—
126#2414C2214yes—
127#2414C2214yes—
128#2414C2214yes—
129#2407C2212yes—
130#2407C2214yes—
131#2395C2212yes—
132#2388C2212yes—
133#2388C2214yes—
134#2369C2212yes—
135#2366C2212yes—
136#2361C2214yes—
137#2357C2212yes—
138#2357C2212yes—
139#2356C2212yes—
140#2355C2212yes—
141#2354C2212yes—
142#2353C2214yes—
143#2352C2214yes—
144#2349C2212yes—
145#2339C2214yes—
146#2337C2214yes—
147#2330C2214yes—
148#2330C2214yes—
149#2324C2214yes—
150#2324C2214yes—
151#2320C2212yes—
152#2319C2212yes—
153#2319C2214yes—
154#2319C2212yes—
155#2318C2214yes—
156#2317C2212yes—
157#2314C2212yes—
158#2314C2212yes—
159#2314C2214yes—
160#2311C2212yes—
161C4×#127C2212yes—
162C4×#124C2212yes—
163C4×C22⋊Q8C2212yes—
164C4×#121C2212yes—
165C4×#121C2214yes—
166C4×#121C2214yes—
167#2298C2214yes—
168#2297C2212yes—
169#2295C2212yes—
170#2293C2212yes—
171#2290C2214yes—
172#2290C2214yes—
173#2285C2212yes—
174#2285C2211yescharacteristic
175#2283C2212yes—
176#2283C2212yes—
177#2283C2211yescharacteristic
178#2275C2212yes—
179C4×#117C2211yescharacteristic
180C4×#117C2212yes—
181C4×#117C2212yes—
182C2×C4×C4⋊C4C2211yescharacteristic
183C22×#41C2311yescharacteristic
184C22×#41C2311yescharacteristic
185C22×#41C2312yes—
186#532—28no—
187C2×C4⋊Q8C2311yescharacteristic
188C2×#127C2311yescharacteristic
189C2×#127C2312yes—
190C2×#126C2318yes—
191C2×#126C2318yes—
192C2×#126C2318yes—
193C2×#125C2314yes—
194C2×#125C2314yes—
195C2×#124C2312yes—
196C2×#124C2312yes—
197C2×C22⋊Q8C2312yes—
198C2×C22⋊Q8C2314yes—
199C2×#121C2312yes—
200C2×#121C2312yes—
201C2×#121C2314yes—
202C2×#121C2314yes—
203C2×#121C2312yes—
204C2×#121C2314yes—
205C2×#121C2314yes—
206C2×#121C2318yes—
207C4×#41—28no—
208C4×#41—28no—
209C2×C4×Q8C2311yescharacteristic
210C2×C4×Q8C2311yescharacteristic
211C2×C4×Q8C2311yescharacteristic
212C2×C4×Q8C2311yescharacteristic
213C2×C4×D4C2311yescharacteristic
214C2×C4×D4C2312yes—
215C2×C4×D4C2311yescharacteristic
216C2×C4×D4C2312yes—
217C2×C4×D4C2311yescharacteristic
218C2×C4×D4C2312yes—
219C2×C4×D4C2312yes—
220C2×C4×D4C2312yes—
221C2×C4×D4C2312yes—
222C2×C4×D4C2311yescharacteristic
223C2×C4×D4C2314yes—
224C2×C4×D4C2314yes—
225C2×C4×D4C2314yes—
226C2×C4×D4C2318yes—
227C2×C4×D4C2318yes—
228C2×#117C2312yes—
229C2×#117C2311yescharacteristic
230C2×#117C2312yes—
231C2×#117C2311yescharacteristic
232C2×#117C2312yes—
233C2×#117C2314yes—
234C2×#117C2314yes—
235C2×#117C2312yes—
236C22×C4⋊C4C2312yes—
237C22×C42C2312yes—
238C22×C42C2312yes—
239C22×C42C2312yes—
240C22×C42C2311yescharacteristic
241#401C2318yes—
242#400C2318yes—
243#400C2318yes—
244#400C2318yes—
245#400C2318yes—
246#400C2312yes—
247#400C2318yes—
248#400C2318yes—
249#400C2318yes—
250#399C2318yes—
251#399C2312yes—
252#399C2314yes—
253#399C2318yes—
254#398C2312yes—
255#398C2318yes—
256#398C2318yes—
257#397C2318yes—
258#397C2318yes—
259#397C2318yes—
260#397C2318yes—
261#397C2318yes—
262#397C2314yes—
263#397C2312yes—
264#397C2314yes—
265#397C2318yes—
266#397C2318yes—
267#397C2318yes—
268#396C2318yes—
269#396C2318yes—
270#396C2318yes—
271#396C2318yes—
272#396C2318yes—
273#395C2314yes—
274#395C2312yes—
275#394C2318yes—
276#394C2318yes—
277#394C2318yes—
278#394C2314yes—
279#394C2318yes—
280#394C2318yes—
281#394C2318yes—
282#394C2312yes—
283#394C2314yes—
284#394C2314yes—
285#394C2318yes—
286#394C2318yes—
287#394C2318yes—
288#394C2318yes—
289#394C2318yes—
290#394C2318yes—
291#393C2314yes—
292#393C2314yes—
293#393C2312yes—
294#392C2314yes—
295#392C2318yes—
296#392C2318yes—
297#392C2318yes—
298#392C2312yes—
299#392C2314yes—
300#392C2314yes—
301#391C2314yes—
302#391C2312yes—
303#391C2312yes—
304#391C2314yes—
305#391C2318yes—
306#391C2314yes—
307#390C2312yes—
308#390C2312yes—
309#390C2318yes—
310#390C2314yes—
311#390C2314yes—
312#390C2314yes—
313#390C2312yes—
314#390C2314yes—
315#390C2314yes—
316#390C2318yes—
317#390C2318yes—
318#390C2312yes—
319#390C2314yes—
320#390C2318yes—
321#390C2314yes—
322#390C2314yes—
323#389C2314yes—
324#389C2314yes—
325#389C2318yes—
326#389C2314yes—
327#389C2314yes—
328#389C2312yes—
329#389C2314yes—
330#389C2314yes—
331#389C2314yes—
332#389C2312yes—
333#389C2314yes—
334#389C2318yes—
335#389C2318yes—
336#389C2318yes—
337#389C2314yes—
338#389C2314yes—
339#389C2318yes—
340#389C2318yes—
341#389C2314yes—
342#388C2318yes—
343#388C2318yes—
344#388C2314yes—
345#388C2314yes—
346#388C2314yes—
347#388C2314yes—
348#388C2318yes—
349#388C2318yes—
350#388C2318yes—
351#388C2318yes—
352#388C2318yes—
353#388C2318yes—
354#388C2318yes—
355#388C2314yes—
356#388C2314yes—
357#388C2314yes—
358#388C2318yes—
359#388C2318yes—
360#388C2318yes—
361#388C2318yes—
362#388C2318yes—
363#388C2318yes—
364#388C2318yes—
365#387C2314yes—
366#387C2314yes—
367#387C2314yes—
368#387C2314yes—
369#387C2318yes—
370#387C2318yes—
371#387C2318yes—
372#387C2314yes—
373#387C2318yes—
374#387C2318yes—
375#387C2318yes—
376#387C2314yes—
377#387C2314yes—
378#387C2318yes—
379#387C2318yes—
380#387C2318yes—
381#387C2318yes—
382#387C2318yes—
383#386C2314yes—
384#386C2314yes—
385#386C2318yes—
386#386C2318yes—
387#386C2318yes—
388#386C2318yes—
389#386C2318yes—
390#386C2318yes—
391#386C2318yes—
392#386C2314yes—
393#386C2314yes—
394#386C2314yes—
395#385C2318yes—
396#385C2318yes—
397#385C2314yes—
398#385C2314yes—
399#385C2314yes—
400#385C2318yes—
401#385C2314yes—
402#385C2318yes—
403#385C2314yes—
404#384C2312yes—
405#384C2312yes—
406#384C2312yes—
407#384C2314yes—
408#384C2314yes—
409#384C2312yes—
410#383C2314yes—
411#383C2312yes—
412#383C2314yes—
413#382C2312yes—
414#382C2314yes—
415#382C2312yes—
416#382C2312yes—
417#382C2318yes—
418#382C2314yes—
419#382C2311yescharacteristic
420#382C2312yes—
421#382C2311yescharacteristic
422#381C2314yes—
423#381C2314yes—
424#381C2318yes—
425#381C2318yes—
426#381C2312yes—
427#381C2314yes—
428#380C2312yes—
429#380C2314yes—
430#380C2314yes—
431#380C2314yes—
432#380C2312yes—
433#380C2312yes—
434#380C2312yes—
435#380C2312yes—
436#380C2314yes—
437#380C2314yes—
438#380C2314yes—
439#380C2318yes—
440#380C2312yes—
441#380C2312yes—
442#380C2312yes—
443#380C2312yes—
444C4×C4⋊C4C2314yes—
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2314yes—
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2312yes—
450C4×C4⋊C4C2311yescharacteristic
451C4×C4⋊C4C2314yes—
452C4×C4⋊C4C2314yes—
453C4×C4⋊C4C2312yes—
454C4×C4⋊C4C2312yes—
455C4×C4⋊C4C2314yes—
456C4×C4⋊C4C2312yes—
457C4×C4⋊C4C2312yes—
458C4×C4⋊C4C2314yes—
459C4×C4⋊C4C2312yes—
460C4×C4⋊C4C2312yes—
461C4×C4⋊C4C2314yes—
462C4×C22⋊C4C2312yes—
463C4×C22⋊C4C2314yes—
464C4×C22⋊C4C2318yes—
465C4×C22⋊C4C2314yes—
466C4×C22⋊C4C2318yes—
467C4×C22⋊C4C2314yes—
468C4×C22⋊C4C2312yes—
469C4×C22⋊C4C2314yes—
470C4×C22⋊C4C2318yes—
471C4×C22⋊C4C2314yes—
472C4×C22⋊C4C2314yes—
473C4×C22⋊C4C2314yes—
474C4×C22⋊C4C2312yes—
475#376C2312yes—
476#376C2312yes—
477#376C2314yes—
478#376C2314yes—
479#376C2314yes—
480C2×#95C2312yes—
481C2×#95C2314yes—
482C43C2312yes—
483C43C2314yes—
484C2×#41—24no—
485C2×#41—24no—
486C2×#41—28no—
487C2×#41—44no—
488C2×#41—42no—
489C2×#41—42no—
490C2×#41—84no—
491C22×Q8C2411yescharacteristic
492C22×Q8C2411yescharacteristic
493C22×Q8C2412yes—
494C22×D4C2412yes—
495C22×D4C2412yes—
496C22×D4C2411yescharacteristic
497C22×D4C2414yes—
498C22×D4C2412yes—
499C22×D4C2412yes—
500C22×D4C2411yescharacteristic
501C22×D4C2412yes—
502C22×D4C2414yes—
503C22×D4C2418yes—
504C22×D4C2418yes—
505C23×C4C2412yes—
506C23×C4C2412yes—
507C23×C4C2412yes—
508C23×C4C2411yescharacteristic
509C23×C4C2411yescharacteristic
510C23×C4C2412yes—
511C23×C4C2412yes—
512C23×C4C2414yes—
513C23×C4C2412yes—
514C23×C4C2414yes—
515C23×C4C2418yes—
516C23×C4C2411yescharacteristic
517C4⋊Q8—24no—
518#127—24no—
519#127—44no—
520#126—88no—
521#126—88no—
522#126—88no—
523#125—48no—
524#125—48no—
525#124—28no—
526#124—44no—
527C22⋊Q8—44no—
528C22⋊Q8—84no—
529#121—28no—
530#121—28no—
531#121—48no—
532#121—48no—
533#121—48no—
534#121—44no—
535#121—88no—
536#121—84no—
537C4×Q8—24no—
538C4×Q8—24no—
539C4×Q8—24no—
540C4×Q8—24no—
541C4×D4—28no—
542C4×D4—28no—
543C4×D4—28no—
544C4×D4—28no—
545C4×D4—24no—
546C4×D4—24no—
547C4×D4—24no—
548C4×D4—24no—
549C4×D4—28no—
550C4×D4—28no—
551C4×D4—48no—
552C4×D4—48no—
553C4×D4—48no—
554C4×D4—88no—
555C4×D4—88no—
556#117—24no—
557#117—24no—
558#117—28no—
559#117—28no—
560#117—48no—
561#117—48no—
562#117—44no—
563#117—44no—
564C2×C4⋊C4—44no—
565C2×C4⋊C4C2412yes—
566C2×C4⋊C4C2412yes—
567C2×C4⋊C4C2411yescharacteristic
568C2×C4⋊C4C2411yescharacteristic
569C2×C4⋊C4C2412yes—
570C2×C4⋊C4C2412yes—
571C2×C4⋊C4C2412yes—
572C2×C4⋊C4C2412yes—
573C2×C4⋊C4C2411yescharacteristic
574C2×C4⋊C4C2411yescharacteristic
575C2×C4⋊C4C2412yes—
576C2×C4⋊C4C2414yes—
577C2×C4⋊C4C2414yes—
578C2×C4⋊C4C2412yes—
579C2×C4⋊C4C2412yes—
580C2×C4⋊C4C2412yes—
581C2×C4⋊C4C2412yes—
582C2×C4⋊C4C2412yes—
583C2×C4⋊C4C2414yes—
584C2×C4⋊C4C2414yes—
585C2×C4⋊C4C2414yes—
586C2×C4⋊C4C2418yes—
587C2×C4⋊C4C2418yes—
588C2×C4⋊C4C2414yes—
589C2×C4⋊C4C2414yes—
590C2×C4⋊C4C2418yes—
591C2×C4⋊C4C2418yes—
592C2×C4⋊C4C2414yes—
593C2×C4⋊C4C2418yes—
594C2×C4⋊C4C2418yes—
595C2×C4⋊C4C2418yes—
596C2×C4⋊C4C2418yes—
597C2×C4⋊C4C2414yes—
598C2×C4⋊C4C2414yes—
599C2×C4⋊C4C2414yes—
600C2×C4⋊C4C2418yes—
601C2×C22⋊C4C2412yes—
602C2×C22⋊C4C2412yes—
603C2×C22⋊C4C2412yes—
604C2×C22⋊C4C2412yes—
605C2×C22⋊C4C2412yes—
606C2×C22⋊C4C2412yes—
607C2×C22⋊C4C2414yes—
608C2×C22⋊C4C2414yes—
609C2×C22⋊C4C2414yes—
610C2×C22⋊C4C2414yes—
611C2×C22⋊C4C2418yes—
612C2×C22⋊C4C2414yes—
613C2×C22⋊C4C2414yes—
614C2×C22⋊C4C2414yes—
615C2×C22⋊C4C2418yes—
616C2×C22⋊C4C2418yes—
617C2×C22⋊C4C2418yes—
618C2×C22⋊C4C2418yes—
619C2×C22⋊C4C2418yes—
620C2×C22⋊C4C2414yes—
621C2×C22⋊C4C2414yes—
622C2×C22⋊C4C2414yes—
623C2×C22⋊C4C2418yes—
624C2×C22⋊C4C2418yes—
625C2×C22⋊C4C2418yes—
626C2×C22⋊C4C2414yes—
627C2×C22⋊C4C2418yes—
628C2×C22⋊C4C2418yes—
629C2×C22⋊C4C2418yes—
630C2×C22⋊C4C2414yes—
631C2×C22⋊C4C2418yes—
632C2×C22⋊C4C2414yes—
633C2×C22⋊C4C2414yes—
634C2×C22⋊C4C2414yes—
635C2×C42—28no—
636C2×C42—28no—
637C2×C42—44no—
638C2×C42#4118yes—
639C2×C42C2412yes—
640C2×C42C2412yes—
641C2×C42C2412yes—
642C2×C42C2414yes—
643C2×C42C2414yes—
644C2×C42C2412yes—
645C2×C42C2412yes—
646C2×C42C2412yes—
647C2×C42C2412yes—
648C2×C42C2412yes—
649C2×C42C2414yes—
650C2×C42C2418yes—
651C2×C42C2414yes—
652C2×C42C2414yes—
653C2×C42C2418yes—
654C2×C42C2418yes—
655C2×C42C2412yes—
656C2×C42C2412yes—
657C2×C42C2411yescharacteristic
658C2×C42C2411yescharacteristic
659C2×C42C2411yescharacteristic
660C2×C42C2411yescharacteristic
661#95C2412yes—
662#95C2412yes—
663#95C2412yes—
664#95C2418yes—
665#95C2414yes—
666#95C2414yes—
667#95C2412yes—
668#95C2418yes—
669#95C2412yes—
670#95C2414yes—
671#95C2412yes—
672#95C2418yes—
673#95C2414yes—
674#95C2418yes—
675#95C2414yes—
676#95C2414yes—
677#95C2414yes—
678#95C2414yes—
679#95C2418yes—
680#95C2414yes—
681#95C2414yes—
682#95C2414yes—
683#95C2418yes—
684#95C2414yes—
685#95C2412yes—
686#95C2414yes—
687#95C2412yes—
688#95C2418yes—
689#95C2414yes—
690#95C2414yes—
691#95C2414yes—
692#95C2414yes—
693#95C2414yes—
694#95C2414yes—
695#95C2418yes—
696#95C2414yes—
697#95C2418yes—
698#95C2418yes—
699#95C2418yes—
700#95C2418yes—
701C24C2512yes—
702C24C2512yes—
703C24C2514yes—
704C24C2511yescharacteristic
705#41—416no—
706#41—416no—
707#41—816no—
708C2×Q8—22no—
709C2×Q8—22no—
710C2×Q8—24no—
711C2×Q8—22no—
712C2×Q8—22no—
713C2×Q8—42no—
714C2×Q8—44no—
715C2×D4—24no—
716C2×D4—24no—
717C2×D4—28no—
718C2×D4—22no—
719C2×D4—22no—
720C2×D4—24no—
721C2×D4—24no—
722C2×D4—24no—
723C2×D4—24no—
724C2×D4—28no—
725C2×D4—24no—
726C2×D4—22no—
727C2×D4—22no—
728C2×D4—48no—
729C2×D4—42no—
730C2×D4—42no—
731C2×D4—42no—
732C2×D4—42no—
733C2×D4—42no—
734C2×D4—44no—
735C2×D4—48no—
736C2×D4—48no—
737C2×D4—44no—
738C2×D4—44no—
739C2×D4—44no—
740C2×D4—48no—
741C2×D4—48no—
742C2×D4—48no—
743C2×D4—48no—
744C22×C4—22no—
745C22×C4—24no—
746C22×C4—22no—
747C22×C4—24no—
748C22×C4—24no—
749C22×C4—24no—
750C22×C4—24no—
751C22×C4—24no—
752C22×C4—28no—
753C22×C4—24no—
754C22×C4—24no—
755C22×C4—24no—
756C22×C4—24no—
757C22×C4—24no—
758C22×C4—28no—
759C22×C4—42no—
760C22×C4—42no—
761C22×C4—42no—
762C22×C4—44no—
763C22×C4—44no—
764C22×C4—44no—
765C22×C4—44no—
766C22×C4—48no—
767C22×C4—42no—
768C22×C4—42no—
769C22×C4—48no—
770C22×C4—48no—
771C22×C4—48no—
772C22×C4C2×#4114yes—
773C22×C4C2×#4114yes—
774C22×C4C2×#4114yes—
775C22×C4C2512yes—
776C22×C4C2512yes—
777C22×C4C2514yes—
778C22×C4C2514yes—
779C22×C4C2512yes—
780C22×C4C2514yes—
781C22×C4C2512yes—
782C22×C4C2514yes—
783C22×C4C2514yes—
784C22×C4C2518yes—
785C22×C4C2512yes—
786C22×C4C2514yes—
787C22×C4C2514yes—
788C22×C4C2512yes—
789C22×C4C2511yescharacteristic
790C22×C4C2511yescharacteristic
791C22×C4C2511yescharacteristic
792C22×C4C2511yescharacteristic
793C22×C4C2511yescharacteristic
794C22×C4C2511yescharacteristic
795C4⋊C4—22no—
796C4⋊C4—22no—
797C4⋊C4—22no—
798C4⋊C4—22no—
799C4⋊C4—24no—
800C4⋊C4—24no—
801C4⋊C4—24no—
802C4⋊C4—24no—
803C4⋊C4—24no—
804C4⋊C4—24no—
805C4⋊C4—24no—
806C4⋊C4—24no—
807C4⋊C4—24no—
808C4⋊C4—28no—
809C4⋊C4—28no—
810C4⋊C4—24no—
811C4⋊C4—24no—
812C4⋊C4—24no—
813C4⋊C4—44no—
814C4⋊C4—44no—
815C4⋊C4—44no—
816C4⋊C4—44no—
817C4⋊C4—48no—
818C4⋊C4—48no—
819C4⋊C4—44no—
820C4⋊C4—48no—
821C4⋊C4—44no—
822C4⋊C4—48no—
823C4⋊C4—48no—
824C4⋊C4—48no—
825C4⋊C4—48no—
826C4⋊C4—48no—
827C4⋊C4—44no—
828C4⋊C4—48no—
829C4⋊C4—44no—
830C4⋊C4—44no—
831C22⋊C4—24no—
832C22⋊C4—24no—
833C22⋊C4—24no—
834C22⋊C4—24no—
835C22⋊C4—24no—
836C22⋊C4—24no—
837C22⋊C4—28no—
838C22⋊C4—28no—
839C22⋊C4—44no—
840C22⋊C4—44no—
841C22⋊C4—48no—
842C22⋊C4—44no—
843C22⋊C4—44no—
844C22⋊C4—48no—
845C22⋊C4—44no—
846C22⋊C4—48no—
847C22⋊C4—44no—
848C22⋊C4—44no—
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—48no—
858C22⋊C4—48no—
859C22⋊C4—44no—
860C22⋊C4—48no—
861C22⋊C4—48no—
862C22⋊C4—44no—
863C22⋊C4—44no—
864C22⋊C4—44no—
865C42—24no—
866C42—24no—
867C42—24no—
868C42—24no—
869C42—24no—
870C42—24no—
871C42—28no—
872C42—24no—
873C42—28no—
874C42—24no—
875C42—42no—
876C42—42no—
877C42—44no—
878C42—44no—
879C42—48no—
880C42—44no—
881C42—48no—
882C42—48no—
883C42C2×#4114yes—
884C42C2×#4114yes—
885C42C2×#4114yes—
886C42C2×#4114yes—
887C23—21no—
888C23—22no—
889C23—21no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—24no—
894C23—22no—
895C23—24no—
896C23—24no—
897C23—28no—
898C23—22no—
899C23—22no—
900C23—22no—
901C23—24no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—24no—
906C23—28no—
907C23—22no—
908C23C22×#4112yes—
909C23C2611yescharacteristic
910Q8—44no—
911Q8—44no—
912Q8—84no—
913D4—44no—
914D4—48no—
915D4—48no—
916D4—416no—
917D4—48no—
918D4—48no—
919D4—44no—
920D4—84no—
921D4—88no—
922D4—816no—
923D4—168no—
924C2×C4—21no—
925C2×C4—21no—
926C2×C4—22no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—28no—
930C2×C4—28no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—22no—
934C2×C4—22no—
935C2×C4—22no—
936C2×C4—22no—
937C2×C4—24no—
938C2×C4—24no—
939C2×C4—24no—
940C2×C4—24no—
941C2×C4—24no—
942C2×C4—24no—
943C2×C4—24no—
944C2×C4—24no—
945C2×C4—24no—
946C2×C4—24no—
947C2×C4—28no—
948C2×C4—28no—
949C2×C4—24no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—24no—
954C2×C4—24no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—24no—
959C2×C4—24no—
960C2×C4—24no—
961C2×C4—24no—
962C2×C4—24no—
963C2×C4—24no—
964C2×C4—28no—
965C2×C4—24no—
966C2×C4—28no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—24no—
970C2×C4—44no—
971C2×C4—48no—
972C2×C4—48no—
973C2×C4—48no—
974C2×C4—48no—
975C2×C4—84no—
976C2×C4—84no—
977C2×C4—88no—
978C2×C4—88no—
979C2×C4—168no—
980C2×C4C22×#4112yes—
981C2×C4C22×#4112yes—
982C2×C4C22×#4112yes—
983C2×C4C22×#4112yes—
984C2×C4C22×#4112yes—
985C2×C4C22×#4112yes—
986C2×C4#58514yes—
987C2×C4#58512yes—
988C2×C4#58512yes—
989C22—22no—
990C22—22no—
991C22—22no—
992C22—42no—
993C22—42no—
994C22—42no—
995C22—42no—
996C22—44no—
997C22—44no—
998C22—42no—
999C22—42no—
1000C22—48no—
1001C22—42no—
1002C22—44no—
1003C22—42no—
1004C22—42no—
1005C22—42no—
1006C22—44no—
1007C22—44no—
1008C22—48no—
1009C22—42no—
1010C22—42no—
1011C22C23×#4111yescharacteristic
1012C22C2×#58511yescharacteristic
1013C22C2×#58511yescharacteristic
1014C22C2×#58512yes—
1015C22H(7,𝔽2)12yes—
1016C4—22no—
1017C4—22no—
1018C4—22no—
1019C4—22no—
1020C4—42no—
1021C4—42no—
1022C4—42no—
1023C4—42no—
1024C4—44no—
1025C4—44no—
1026C4—44no—
1027C4—44no—
1028C4—44no—
1029C4—42no—
1030C4—42no—
1031C4—44no—
1032C4—44no—
1033C4—48no—
1034C4#345514yes—
1035C4#349314yes—
1036C2—42no—
1037C2—82no—
1038C2—82no—
1039C2—84no—
1040C2C2×#345511yescharacteristic
1041C2C2×#349311yescharacteristic
1042C2#6285511yescharacteristic
1043C2#6293712yes—
1044C2#6296912yes—
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. #42464C2semidirect
2. #42462C2semidirect
3. #40648C2semidirect
4. #39756C2semidirect
5. #39736C2semidirect
6. #39502C2semidirect
7. #39479C2semidirect
8. #39185C2semidirect
9. #39157C2semidirect
10. #38971C2semidirect
11. #38942C2semidirect
12. #37498C2semidirect
13. #37027C2semidirect
14. #37026C2semidirect
15. #35552C2semidirect
16. #35292C2semidirect
17. #35202C2semidirect
18. #35161C2semidirect
19. #35161C2semidirect
20. #34977C2semidirect
21. #34909C2semidirect
22. #34236C2semidirect
23. #34121C2semidirect
24. #34060C2semidirect

Maximal subgroups

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

subgroupindex
#424642
#424622
#406482
#397562
#397362
#395022
#394792
#391852
#391572
#389712
#389422
#374982
#370272
#370262
#355522
#352922
#352022
#351612
#349772
#349092
#342362
#341212
#340602