Finite Group Databasebeta

← #7647444

Subgroups — #7647444

Order 512.

4606 conjugacy classes of subgroups.

The subgroup lattice has 1047 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42465C214yesmaximal, complemented
2#42463C214yesmaximal, complemented
3#40646C218yesmaximal, complemented
4#39758C212yesmaximal, complemented
5#39735C212yesmaximal, complemented
6#39500C212yesmaximal, complemented
7#39480C212yesmaximal, complemented
8#39187C212yesmaximal, complemented
9#39158C212yesmaximal, complemented
10#38969C212yesmaximal, complemented
11#38941C212yesmaximal, complemented
12#37501C214yesmaximal, complemented
13#37031C214yesmaximal, complemented
14#37022C214yesmaximal, complemented
15#35550C214yesmaximal, complemented
16#35292C211yesmaximal, characteristic, complemented
17#35192C211yesmaximal, characteristic, complemented
18#35164C214yesmaximal, complemented
19#35164C214yesmaximal, 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#2866C2218yes—
29#2864C2212yes—
30#2862C2212yes—
31#2861C2218yes—
32#2857C2212yes—
33#2856C2212yes—
34#2825C2218yes—
35#2824C2218yes—
36#2808C2218yes—
37#2798C2218yes—
38#2797C2218yes—
39#2787C2218yes—
40#2762C2218yes—
41#2759C2218yes—
42#2759C2218yes—
43#2753C2218yes—
44#2751C2218yes—
45#2737C2218yes—
46#2733C2218yes—
47#2703C2218yes—
48#2700C2218yes—
49#2694C2218yes—
50#2690C2218yes—
51#2686C2218yes—
52#2665C2214yes—
53#2653C2218yes—
54#2653C2218yes—
55#2648C2218yes—
56#2648C2218yes—
57#2644C2214yes—
58#2640C2214yes—
59#2631C2218yes—
60#2630C2218yes—
61#2625C2214yes—
62#2624C2212yes—
63#2619C2214yes—
64#2615C2212yes—
65#2610C2214yes—
66#2605C2214yes—
67#2600C2214yes—
68#2599C2212yes—
69#2598C2212yes—
70#2592C2212yes—
71#2581C2211yescharacteristic
72#2580C2211yescharacteristic
73#2580C2212yes—
74#2578C2218yes—
75#2571C2212yes—
76#2570C2214yes—
77#2567C2211yescharacteristic
78#2563C2214yes—
79#2563C2211yescharacteristic
80#2557C2218yes—
81#2551C2212yes—
82#2548C2211yescharacteristic
83#2547C2214yes—
84#2541C2211yescharacteristic
85#2540C2212yes—
86#2536C2211yescharacteristic
87#2535C2212yes—
88#2535C2214yes—
89#2535C2211yescharacteristic
90#2531C2218yes—
91#2531C2218yes—
92#2527C2218yes—
93#2527C2218yes—
94#2523C2218yes—
95#2514C2214yes—
96#2513C2214yes—
97#2513C2214yes—
98#2510C2218yes—
99#2506C2214yes—
100#2506C2214yes—
101#2500C2214yes—
102#2500C2212yes—
103#2495C2214yes—
104#2494C2214yes—
105#2494C2214yes—
106#2494C2214yes—
107#2491C2214yes—
108#2491C2214yes—
109#2491C2214yes—
110#2485C2212yes—
111#2485C2214yes—
112#2460C2218yes—
113#2460C2218yes—
114#2459C2218yes—
115#2459C2218yes—
116#2459C2218yes—
117#2445C2214yes—
118#2439C2214yes—
119#2439C2214yes—
120#2439C2214yes—
121#2431C2212yes—
122#2427C2214yes—
123#2422C2214yes—
124#2420C2214yes—
125#2419C2218yes—
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#2331C2214yes—
148#2331C2214yes—
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×C4⋊Q8C2314yes—
189C2×C4⋊Q8C2314yes—
190C2×#127C2311yescharacteristic
191C2×#127C2312yes—
192C2×#125C2318yes—
193C2×#124C2312yes—
194C2×#124C2312yes—
195C2×#124C2318yes—
196C2×#124C2318yes—
197C2×#123C2318yes—
198C2×C22⋊Q8C2312yes—
199C2×C22⋊Q8C2314yes—
200C2×#121C2312yes—
201C2×#121C2312yes—
202C2×#121C2314yes—
203C2×#121C2314yes—
204C2×#121C2312yes—
205C2×#121C2314yes—
206C2×#121C2314yes—
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#401C2318yes—
243#400C2318yes—
244#400C2318yes—
245#400C2318yes—
246#400C2312yes—
247#400C2318yes—
248#399C2312yes—
249#399C2314yes—
250#398C2318yes—
251#398C2312yes—
252#398C2318yes—
253#397C2318yes—
254#397C2318yes—
255#397C2318yes—
256#397C2318yes—
257#397C2318yes—
258#397C2314yes—
259#397C2312yes—
260#397C2314yes—
261#397C2318yes—
262#397C2318yes—
263#397C2318yes—
264#397C2318yes—
265#397C2318yes—
266#397C2318yes—
267#396C2318yes—
268#396C2318yes—
269#395C2314yes—
270#395C2312yes—
271#395C2318yes—
272#394C2314yes—
273#394C2318yes—
274#394C2318yes—
275#394C2318yes—
276#394C2318yes—
277#394C2318yes—
278#394C2318yes—
279#394C2312yes—
280#394C2314yes—
281#394C2314yes—
282#394C2318yes—
283#394C2318yes—
284#394C2318yes—
285#393C2318yes—
286#393C2314yes—
287#393C2318yes—
288#393C2318yes—
289#393C2318yes—
290#393C2314yes—
291#393C2312yes—
292#393C2318yes—
293#392C2318yes—
294#392C2314yes—
295#392C2318yes—
296#392C2318yes—
297#392C2312yes—
298#392C2314yes—
299#392C2314yes—
300#392C2318yes—
301#391C2314yes—
302#391C2312yes—
303#391C2312yes—
304#391C2318yes—
305#391C2318yes—
306#391C2318yes—
307#391C2318yes—
308#391C2314yes—
309#391C2318yes—
310#391C2318yes—
311#391C2314yes—
312#390C2312yes—
313#390C2312yes—
314#390C2318yes—
315#390C2314yes—
316#390C2314yes—
317#390C2314yes—
318#390C2314yes—
319#390C2314yes—
320#390C2312yes—
321#390C2318yes—
322#390C2318yes—
323#390C2312yes—
324#390C2314yes—
325#390C2314yes—
326#390C2314yes—
327#389C2314yes—
328#389C2314yes—
329#389C2314yes—
330#389C2314yes—
331#389C2314yes—
332#389C2314yes—
333#389C2312yes—
334#389C2314yes—
335#389C2314yes—
336#389C2314yes—
337#389C2312yes—
338#389C2314yes—
339#389C2314yes—
340#388C2314yes—
341#388C2314yes—
342#388C2314yes—
343#388C2314yes—
344#388C2318yes—
345#388C2318yes—
346#388C2318yes—
347#388C2318yes—
348#388C2318yes—
349#388C2318yes—
350#388C2318yes—
351#388C2318yes—
352#388C2318yes—
353#388C2314yes—
354#388C2314yes—
355#388C2314yes—
356#388C2318yes—
357#388C2318yes—
358#388C2318yes—
359#388C2318yes—
360#388C2318yes—
361#388C2318yes—
362#388C2318yes—
363#388C2318yes—
364#387C2318yes—
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#386C2318yes—
396#385C2314yes—
397#385C2314yes—
398#385C2314yes—
399#385C2318yes—
400#385C2318yes—
401#385C2314yes—
402#385C2318yes—
403#385C2314yes—
404#384C2312yes—
405#384C2312yes—
406#384C2312yes—
407#384C2312yes—
408#383C2314yes—
409#383C2318yes—
410#383C2312yes—
411#383C2314yes—
412#382C2312yes—
413#382C2314yes—
414#382C2312yes—
415#382C2314yes—
416#382C2312yes—
417#382C2314yes—
418#382C2314yes—
419#382C2311yescharacteristic
420#382C2312yes—
421#382C2311yescharacteristic
422#381C2314yes—
423#381C2314yes—
424#381C2318yes—
425#381C2312yes—
426#381C2314yes—
427#380C2318yes—
428#380C2318yes—
429#380C2314yes—
430#380C2312yes—
431#380C2312yes—
432#380C2312yes—
433#380C2312yes—
434#380C2312yes—
435#380C2314yes—
436#380C2314yes—
437#380C2314yes—
438#380C2312yes—
439#380C2314yes—
440#380C2312yes—
441#380C2314yes—
442#380C2312yes—
443#380C2312yes—
444C4×C4⋊C4C2314yes—
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2312yes—
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2314yes—
451C4×C4⋊C4C2314yes—
452C4×C4⋊C4C2314yes—
453C4×C4⋊C4C2312yes—
454C4×C4⋊C4C2312yes—
455C4×C4⋊C4C2312yes—
456C4×C4⋊C4C2314yes—
457C4×C4⋊C4C2312yes—
458C4×C4⋊C4C2312yes—
459C4×C4⋊C4C2314yes—
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×Q8C2418yes—
495C22×D4C2412yes—
496C22×D4C2412yes—
497C22×D4C2411yescharacteristic
498C22×D4C2414yes—
499C22×D4C2412yes—
500C22×D4C2412yes—
501C22×D4C2411yescharacteristic
502C22×D4C2412yes—
503C22×D4C2418yes—
504C22×D4C2414yes—
505C22×D4C2418yes—
506C23×C4C2412yes—
507C23×C4C2412yes—
508C23×C4C2412yes—
509C23×C4C2411yescharacteristic
510C23×C4C2411yescharacteristic
511C23×C4C2412yes—
512C23×C4C2412yes—
513C23×C4C2414yes—
514C23×C4C2412yes—
515C23×C4C2414yes—
516C23×C4C2418yes—
517C23×C4C2411yescharacteristic
518C4⋊Q8—24no—
519C4⋊Q8—48no—
520C4⋊Q8—48no—
521#127—24no—
522#127—44no—
523#125—88no—
524#124—28no—
525#124—44no—
526#124—88no—
527#124—88no—
528#123—88no—
529C22⋊Q8—44no—
530C22⋊Q8—84no—
531#121—28no—
532#121—28no—
533#121—48no—
534#121—48no—
535#121—48no—
536#121—44no—
537#121—84no—
538C4×Q8—24no—
539C4×Q8—24no—
540C4×Q8—24no—
541C4×Q8—24no—
542C4×D4—28no—
543C4×D4—28no—
544C4×D4—28no—
545C4×D4—28no—
546C4×D4—24no—
547C4×D4—24no—
548C4×D4—24no—
549C4×D4—24no—
550C4×D4—28no—
551C4×D4—28no—
552C4×D4—48no—
553C4×D4—48no—
554C4×D4—48no—
555C4×D4—88no—
556C4×D4—88no—
557#117—24no—
558#117—24no—
559#117—28no—
560#117—28no—
561#117—48no—
562#117—48no—
563#117—44no—
564#117—44no—
565C2×C4⋊C4—44no—
566C2×C4⋊C4C2412yes—
567C2×C4⋊C4C2412yes—
568C2×C4⋊C4C2411yescharacteristic
569C2×C4⋊C4C2411yescharacteristic
570C2×C4⋊C4C2412yes—
571C2×C4⋊C4C2412yes—
572C2×C4⋊C4C2412yes—
573C2×C4⋊C4C2412yes—
574C2×C4⋊C4C2411yescharacteristic
575C2×C4⋊C4C2411yescharacteristic
576C2×C4⋊C4C2412yes—
577C2×C4⋊C4C2414yes—
578C2×C4⋊C4C2414yes—
579C2×C4⋊C4C2412yes—
580C2×C4⋊C4C2412yes—
581C2×C4⋊C4C2412yes—
582C2×C4⋊C4C2412yes—
583C2×C4⋊C4C2412yes—
584C2×C4⋊C4C2414yes—
585C2×C4⋊C4C2414yes—
586C2×C4⋊C4C2414yes—
587C2×C4⋊C4C2418yes—
588C2×C4⋊C4C2418yes—
589C2×C4⋊C4C2414yes—
590C2×C4⋊C4C2414yes—
591C2×C4⋊C4C2418yes—
592C2×C4⋊C4C2414yes—
593C2×C4⋊C4C2414yes—
594C2×C4⋊C4C2418yes—
595C2×C4⋊C4C2414yes—
596C2×C4⋊C4C2414yes—
597C2×C4⋊C4C2418yes—
598C2×C4⋊C4C2418yes—
599C2×C22⋊C4C2412yes—
600C2×C22⋊C4C2412yes—
601C2×C22⋊C4C2412yes—
602C2×C22⋊C4C2412yes—
603C2×C22⋊C4C2412yes—
604C2×C22⋊C4C2412yes—
605C2×C22⋊C4C2414yes—
606C2×C22⋊C4C2414yes—
607C2×C22⋊C4C2414yes—
608C2×C22⋊C4C2414yes—
609C2×C22⋊C4C2418yes—
610C2×C22⋊C4C2414yes—
611C2×C22⋊C4C2414yes—
612C2×C22⋊C4C2414yes—
613C2×C22⋊C4C2418yes—
614C2×C22⋊C4C2418yes—
615C2×C22⋊C4C2418yes—
616C2×C22⋊C4C2418yes—
617C2×C22⋊C4C2418yes—
618C2×C22⋊C4C2414yes—
619C2×C22⋊C4C2414yes—
620C2×C22⋊C4C2418yes—
621C2×C22⋊C4C2418yes—
622C2×C22⋊C4C2414yes—
623C2×C22⋊C4C2418yes—
624C2×C22⋊C4C2418yes—
625C2×C22⋊C4C2418yes—
626C2×C22⋊C4C2414yes—
627C2×C22⋊C4C2414yes—
628C2×C22⋊C4C2418yes—
629C2×C22⋊C4C2414yes—
630C2×C22⋊C4C2414yes—
631C2×C22⋊C4C2414yes—
632C2×C22⋊C4C2418yes—
633C2×C42—28no—
634C2×C42—28no—
635C2×C42—44no—
636C2×C42#4118yes—
637C2×C42C2412yes—
638C2×C42C2412yes—
639C2×C42C2412yes—
640C2×C42C2414yes—
641C2×C42C2414yes—
642C2×C42C2412yes—
643C2×C42C2412yes—
644C2×C42C2412yes—
645C2×C42C2412yes—
646C2×C42C2412yes—
647C2×C42C2414yes—
648C2×C42C2418yes—
649C2×C42C2414yes—
650C2×C42C2414yes—
651C2×C42C2418yes—
652C2×C42C2418yes—
653C2×C42C2412yes—
654C2×C42C2412yes—
655C2×C42C2411yescharacteristic
656C2×C42C2411yescharacteristic
657C2×C42C2411yescharacteristic
658C2×C42C2411yescharacteristic
659#95C2412yes—
660#95C2412yes—
661#95C2412yes—
662#95C2418yes—
663#95C2414yes—
664#95C2414yes—
665#95C2412yes—
666#95C2412yes—
667#95C2418yes—
668#95C2414yes—
669#95C2418yes—
670#95C2412yes—
671#95C2414yes—
672#95C2418yes—
673#95C2414yes—
674#95C2414yes—
675#95C2414yes—
676#95C2414yes—
677#95C2414yes—
678#95C2418yes—
679#95C2418yes—
680#95C2414yes—
681#95C2414yes—
682#95C2412yes—
683#95C2414yes—
684#95C2412yes—
685#95C2414yes—
686#95C2418yes—
687#95C2414yes—
688#95C2414yes—
689#95C2414yes—
690#95C2414yes—
691#95C2414yes—
692#95C2414yes—
693#95C2418yes—
694#95C2414yes—
695#95C2418yes—
696#95C2418yes—
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×Q8—48no—
716C2×Q8—48no—
717C2×Q8—48no—
718C2×D4—24no—
719C2×D4—24no—
720C2×D4—28no—
721C2×D4—22no—
722C2×D4—22no—
723C2×D4—24no—
724C2×D4—24no—
725C2×D4—24no—
726C2×D4—24no—
727C2×D4—28no—
728C2×D4—24no—
729C2×D4—22no—
730C2×D4—22no—
731C2×D4—48no—
732C2×D4—42no—
733C2×D4—42no—
734C2×D4—42no—
735C2×D4—42no—
736C2×D4—42no—
737C2×D4—44no—
738C2×D4—48no—
739C2×D4—48no—
740C2×D4—44no—
741C2×D4—44no—
742C2×D4—44no—
743C2×D4—48no—
744C2×D4—48no—
745C2×D4—48no—
746C2×D4—48no—
747C22×C4—22no—
748C22×C4—24no—
749C22×C4—22no—
750C22×C4—24no—
751C22×C4—24no—
752C22×C4—24no—
753C22×C4—24no—
754C22×C4—24no—
755C22×C4—28no—
756C22×C4—24no—
757C22×C4—24no—
758C22×C4—24no—
759C22×C4—24no—
760C22×C4—24no—
761C22×C4—28no—
762C22×C4—42no—
763C22×C4—42no—
764C22×C4—42no—
765C22×C4—44no—
766C22×C4—44no—
767C22×C4—44no—
768C22×C4—44no—
769C22×C4—48no—
770C22×C4—42no—
771C22×C4—42no—
772C22×C4—48no—
773C22×C4—48no—
774C22×C4—48no—
775C22×C4C2×#4114yes—
776C22×C4C2×#4114yes—
777C22×C4C2×#4114yes—
778C22×C4C2512yes—
779C22×C4C2512yes—
780C22×C4C2514yes—
781C22×C4C2514yes—
782C22×C4C2512yes—
783C22×C4C2514yes—
784C22×C4C2518yes—
785C22×C4C2514yes—
786C22×C4C2512yes—
787C22×C4C2514yes—
788C22×C4C2514yes—
789C22×C4C2514yes—
790C22×C4C2512yes—
791C22×C4C2512yes—
792C22×C4C2511yescharacteristic
793C22×C4C2511yescharacteristic
794C22×C4C2511yescharacteristic
795C22×C4C2511yescharacteristic
796C22×C4C2511yescharacteristic
797C22×C4C2511yescharacteristic
798C4⋊C4—22no—
799C4⋊C4—22no—
800C4⋊C4—22no—
801C4⋊C4—22no—
802C4⋊C4—24no—
803C4⋊C4—24no—
804C4⋊C4—24no—
805C4⋊C4—24no—
806C4⋊C4—24no—
807C4⋊C4—24no—
808C4⋊C4—24no—
809C4⋊C4—24no—
810C4⋊C4—24no—
811C4⋊C4—28no—
812C4⋊C4—28no—
813C4⋊C4—24no—
814C4⋊C4—24no—
815C4⋊C4—24no—
816C4⋊C4—44no—
817C4⋊C4—44no—
818C4⋊C4—44no—
819C4⋊C4—44no—
820C4⋊C4—48no—
821C4⋊C4—48no—
822C4⋊C4—44no—
823C4⋊C4—44no—
824C4⋊C4—48no—
825C4⋊C4—44no—
826C4⋊C4—48no—
827C4⋊C4—44no—
828C4⋊C4—44no—
829C4⋊C4—48no—
830C4⋊C4—48no—
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—44no—
847C22⋊C4—48no—
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—48no—
857C22⋊C4—44no—
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—24no—
900C23—22no—
901C23—22no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—24no—
906C23—22no—
907C23—28no—
908C23C22×#4112yes—
909C23C2611yescharacteristic
910Q8—44no—
911Q8—44no—
912Q8—84no—
913Q8—168no—
914D4—44no—
915D4—48no—
916D4—48no—
917D4—416no—
918D4—48no—
919D4—48no—
920D4—44no—
921D4—84no—
922D4—816no—
923D4—88no—
924D4—168no—
925C2×C4—21no—
926C2×C4—21no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—22no—
930C2×C4—28no—
931C2×C4—28no—
932C2×C4—22no—
933C2×C4—22no—
934C2×C4—22no—
935C2×C4—22no—
936C2×C4—22no—
937C2×C4—22no—
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—24no—
948C2×C4—28no—
949C2×C4—28no—
950C2×C4—24no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—24no—
955C2×C4—24no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—24no—
959C2×C4—22no—
960C2×C4—24no—
961C2×C4—24no—
962C2×C4—24no—
963C2×C4—24no—
964C2×C4—24no—
965C2×C4—28no—
966C2×C4—28no—
967C2×C4—24no—
968C2×C4—22no—
969C2×C4—24no—
970C2×C4—22no—
971C2×C4—44no—
972C2×C4—48no—
973C2×C4—48no—
974C2×C4—48no—
975C2×C4—48no—
976C2×C4—84no—
977C2×C4—84no—
978C2×C4—88no—
979C2×C4—88no—
980C2×C4—168no—
981C2×C4C22×#4112yes—
982C2×C4C22×#4112yes—
983C2×C4C22×#4112yes—
984C2×C4C22×#4112yes—
985C2×C4C22×#4112yes—
986C2×C4C22×#4112yes—
987C2×C4#58514yes—
988C2×C4#58512yes—
989C2×C4#58512yes—
990C22—22no—
991C22—22no—
992C22—22no—
993C22—42no—
994C22—42no—
995C22—42no—
996C22—42no—
997C22—44no—
998C22—44no—
999C22—42no—
1000C22—42no—
1001C22—48no—
1002C22—44no—
1003C22—42no—
1004C22—42no—
1005C22—42no—
1006C22—42no—
1007C22—44no—
1008C22—42no—
1009C22—44no—
1010C22—42no—
1011C22—48no—
1012C22C23×#4111yescharacteristic
1013C22C2×#58511yescharacteristic
1014C22C2×#58511yescharacteristic
1015C22C2×#58512yes—
1016C22H(7,𝔽2)12yes—
1017C4—22no—
1018C4—22no—
1019C4—22no—
1020C4—22no—
1021C4—42no—
1022C4—42no—
1023C4—42no—
1024C4—42no—
1025C4—44no—
1026C4—44no—
1027C4—44no—
1028C4—44no—
1029C4—44no—
1030C4—42no—
1031C4—42no—
1032C4—44no—
1033C4—48no—
1034C4—44no—
1035C4#345514yes—
1036C4#349314yes—
1037C2—42no—
1038C2—82no—
1039C2—82no—
1040C2—84no—
1041C2C2×#345511yescharacteristic
1042C2C2×#349311yescharacteristic
1043C2#6285511yescharacteristic
1044C2#6293812yes—
1045C2#6296612yes—
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. #42465C2semidirect
2. #42463C2semidirect
3. #40646C2semidirect
4. #39758C2semidirect
5. #39735C2semidirect
6. #39500C2semidirect
7. #39480C2semidirect
8. #39187C2semidirect
9. #39158C2semidirect
10. #38969C2semidirect
11. #38941C2semidirect
12. #37501C2semidirect
13. #37031C2semidirect
14. #37022C2semidirect
15. #35550C2semidirect
16. #35292C2semidirect
17. #35192C2semidirect
18. #35164C2semidirect
19. #35164C2semidirect
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
#424652
#424632
#406462
#397582
#397352
#395002
#394802
#391872
#391582
#389692
#389412
#375012
#370312
#370222
#355502
#352922
#351922
#351642
#349772
#349092
#342362
#341212
#340602