Finite Group Databasebeta

← #7643082

Subgroups — #7643082

Order 512.

4926 conjugacy classes of subgroups.

The subgroup lattice has 1008 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39510C212yesmaximal, complemented
2#39507C211yesmaximal, characteristic, complemented
3#39506C211yesmaximal, characteristic, complemented
4#39382C212yesmaximal, complemented
5#39379C211yesmaximal, characteristic, complemented
6#39378C211yesmaximal, characteristic, complemented
7#39197C214yesmaximal, complemented
8#39194C212yesmaximal, complemented
9#39193C212yesmaximal, complemented
10#39189C214yesmaximal, complemented
11#38973C214yesmaximal, complemented
12#38126C218yesmaximal, complemented
13#37201C218yesmaximal, complemented
14#36640C211yesmaximal, characteristic, complemented
15#36631C211yesmaximal, characteristic, complemented
16#35614C214yesmaximal, complemented
17#35603C214yesmaximal, complemented
18#35310C212yesmaximal, complemented
19#35261C212yesmaximal, complemented
20#35236C212yesmaximal, complemented
21#35023C214yesmaximal, complemented
22#34243C212yesmaximal, complemented
23C2×#2293C211yesmaximal, characteristic, complemented
24C2×#541C2212yescomplemented
25C2×#540C2212yescomplemented
26C2×#529C2212yes—
27C22×C4×D4C2211yescharacteristic
28C22×#117C2212yes—
29#2864C2214yescomplemented
30#2861C2212yescomplemented
31#2860C2214yescomplemented
32#2859C2211yescharacteristic, complemented
33#2859C2212yescomplemented
34#2859C2211yescharacteristic, complemented
35#2859C2211yescharacteristic, complemented
36#2858C2211yescharacteristic, complemented
37#2857C2211yescharacteristic
38#2856C2211yescharacteristic
39#2854C2214yes—
40#2851C2214yes—
41#2851C2212yes—
42#2851C2212yes—
43#2850C2212yes—
44#2848C2214yes—
45#2847C2214yes—
46#2803C2218yes—
47#2803C2218yescomplemented
48#2801C2218yescomplemented
49#2800C2218yes—
50#2800C2218yescomplemented
51#2797C2218yes—
52#2783C2218yescomplemented
53#2779C2218yescomplemented
54#2776C2218yescomplemented
55#2773C2218yescomplemented
56#2771C2218yescomplemented
57#2757C2218yescomplemented
58#2725C2218yescomplemented
59#2714C2218yes—
60#2701C2218yescomplemented
61#2694C2218yescomplemented
62#2643C2218yes—
63#2636C2218yes—
64#2629C2212yescomplemented
65#2629C2212yescomplemented
66#2625C2214yescomplemented
67#2624C2214yescomplemented
68#2622C2218yes—
69#2621C2212yescomplemented
70#2619C2212yescomplemented
71#2597C2218yescomplemented
72#2597C2218yescomplemented
73#2595C2218yescomplemented
74#2594C2218yescomplemented
75#2593C2218yescomplemented
76#2578C2218yescomplemented
77#2576C2218yescomplemented
78#2562C2214yes—
79#2554C2218yescomplemented
80#2540C2214yes—
81#2538C2212yes—
82#2538C2212yes—
83#2537C2212yes—
84#2537C2212yes—
85#2525C2218yescomplemented
86#2516C2218yescomplemented
87#2513C2214yes—
88#2513C2218yescomplemented
89#2512C2214yes—
90#2508C2214yescomplemented
91#2506C2214yescomplemented
92#2504C2214yes—
93#2500C2214yes—
94#2495C2214yescomplemented
95#2495C2214yescomplemented
96#2494C2214yescomplemented
97#2494C2214yescomplemented
98#2490C2214yes—
99#2490C2214yes—
100#2490C2218yescomplemented
101#2490C2214yescomplemented
102#2489C2214yescomplemented
103#2487C2214yes—
104#2486C2214yescomplemented
105#2485C2214yescomplemented
106#2480C2218yes—
107#2478C2218yescomplemented
108#2476C2218yescomplemented
109#2475C2218yescomplemented
110#2473C2218yes—
111#2471C2218yescomplemented
112#2443C2218yes—
113#2442C2214yescomplemented
114#2441C2214yescomplemented
115#2427C2214yescomplemented
116#2426C2214yescomplemented
117#2424C2218yes—
118#2421C2214yescomplemented
119#2420C2214yescomplemented
120#2416C2214yes—
121#2414C2214yes—
122#2411C2218yes—
123#2408C2214yes—
124#2370C2214yescomplemented
125#2367C2214yescomplemented
126#2359C2218yes—
127#2355C2212yescomplemented
128#2354C2212yescomplemented
129#2352C2214yes—
130Q8×C4⋊C4C2212yescomplemented
131D4×C4⋊C4C2214yes—
132D4×C4⋊C4C2212yescomplemented
133#2334C2218yescomplemented
134#2324C2214yes—
135#2324C2214yes—
136#2324C2214yescomplemented
137#2323C2214yescomplemented
138#2321C2218yes—
139#2318C2218yes—
140#2314C2214yescomplemented
141#2314C2212yescomplemented
142#2314C2212yescomplemented
143C4×C4⋊Q8C2211yescharacteristic, complemented
144C4×#127C2211yescharacteristic, complemented
145C4×#125C2214yescomplemented
146C4×#125C2212yescomplemented
147C4×#125C2212yescomplemented
148C4×#124C2212yescomplemented
149C4×C22⋊Q8C2214yes—
150C4×#121C2214yes—
151C4×#121C2214yes—
152#2296C2214yes—
153#2293C2212yes—
154#2293C2211yescharacteristic
155#2293C2211yescharacteristic
156#2293C2212yes—
157#2293C2212yes—
158#2293C2214yes—
159#2293C2211yescharacteristic
160#2293C2211yescharacteristic
161#2293C2212yes—
162#2293C2214yescomplemented
163C2×#390C2212yes—
164C2×#389C2212yes—
165C2×#388C2214yes—
166#2285C2212yes—
167#2274C2214yescomplemented
168C2×C4×C4⋊C4C2211yescharacteristic
169C2×C4×C22⋊C4C2212yes—
170C2×C43C2211yescharacteristic
171C23×D4C2311yescharacteristic
172C24×C4C2312yes—
173#541—48no—
174#540—48no—
175C2×C4⋊Q8C2311yescharacteristic
176C2×#127C2311yescharacteristic
177#529—216no—
178C2×#126C2314yes—
179C2×#126C2318yes—
180C2×#125C2312yes—
181C2×#125C2312yes—
182C2×#125C2314yes—
183C2×#125C2312yes—
184C2×#125C2318yes—
185C2×#124C2312yes—
186C2×#124C2312yes—
187C2×#123C2314yes—
188C2×#123C2318yes—
189C2×C22⋊Q8C2312yes—
190C2×C22⋊Q8C2314yes—
191C2×C22⋊Q8C2314yes—
192C2×#121C2312yes—
193C2×#121C2314yes—
194C2×#121C2314yes—
195C2×#121C2314yes—
196C2×#121C2314yes—
197C2×#121C2314yes—
198C2×#121C2318yes—
199C2×#120C2318yes—
200C2×C4×Q8C2312yes—
201C2×C4×Q8C2314yes—
202C2×C4×D4—28no—
203C2×C4×D4C2312yes—
204C2×C4×D4C2312yes—
205C2×C4×D4C2311yescharacteristic
206C2×C4×D4C2311yescharacteristic
207C2×C4×D4C2314yes—
208C2×C4×D4C2312yes—
209C2×C4×D4C2311yescharacteristic
210C2×C4×D4C2311yescharacteristic
211C2×C4×D4C2314yes—
212C2×C4×D4C2318yes—
213C2×C4×D4C2314yes—
214C2×#117—48no—
215C2×#117C2314yes—
216C2×#117C2312yes—
217C2×#117C2312yes—
218C2×#117C2312yes—
219C2×#117C2312yes—
220C2×#117C2314yes—
221C2×#117C2314yes—
222C2×#117C2314yes—
223C2×#117C2314yes—
224C22×C4⋊C4C2311yescharacteristic
225C22×C4⋊C4C2312yes—
226C22×C4⋊C4C2314yes—
227C22×C4⋊C4C2314yes—
228C22×C22⋊C4C2312yes—
229C22×C22⋊C4C2314yes—
230C22×C22⋊C4C2314yes—
231C22×C42C2311yescharacteristic
232C22×C42C2311yescharacteristic
233C22×C42C2312yes—
234C22×C42C2312yes—
235C22×C42C2312yes—
236C22×C42C2311yescharacteristic
237#401C2318yes—
238#400C2318yes—
239#400C2318yes—
240#400C2318yes—
241#400C2318yes—
242#400C2318yes—
243#399C2318yes—
244#399C2318yes—
245#398C2318yes—
246#398C2318yes—
247#398C2318yes—
248#398C2318yes—
249#397C2318yes—
250#397C2318yes—
251#397C2318yes—
252#397C2318yes—
253#397C2318yes—
254#397C2318yes—
255#397C2318yes—
256#397C2318yes—
257#397C2318yes—
258#397C2318yes—
259#397C2318yes—
260#396C2318yes—
261#396C2318yes—
262#396C2318yes—
263#396C2318yes—
264#396C2318yes—
265#394C2318yes—
266#394C2318yes—
267#394C2318yes—
268#394C2318yes—
269#394C2318yes—
270#394C2318yes—
271#394C2318yes—
272#394C2318yes—
273#394C2318yes—
274#394C2318yes—
275#392C2318yes—
276#392C2318yes—
277#391C2312yes—
278#391C2312yes—
279#391C2314yes—
280#390C2312yes—
281#390C2314yes—
282#390C2318yes—
283#390C2318yes—
284#390C2318yes—
285#390C2314yes—
286#390C2314yes—
287#390C2318yes—
288#390C2312yes—
289#390C2318yes—
290#390C2314yes—
291#390C2314yes—
292#390C2314yes—
293#390C2314yes—
294#390C2312yes—
295#390C2312yes—
296#390C2314yes—
297#390C2312yes—
298#390C2312yes—
299#390C2314yes—
300#389C2314yes—
301#389C2314yes—
302#389C2314yes—
303#389C2314yes—
304#389C2314yes—
305#389C2318yes—
306#389C2314yes—
307#389C2314yes—
308#389C2318yes—
309#389C2318yes—
310#389C2314yes—
311#389C2314yes—
312#389C2314yes—
313#389C2314yes—
314#389C2314yes—
315#389C2314yes—
316#389C2314yes—
317#389C2314yes—
318#389C2314yes—
319#389C2314yes—
320#389C2312yes—
321#389C2312yes—
322#389C2312yes—
323#389C2312yes—
324#389C2314yes—
325#388C2318yes—
326#388C2318yes—
327#388C2318yes—
328#388C2318yes—
329#388C2318yes—
330#388C2318yes—
331#388C2318yes—
332#388C2318yes—
333#388C2314yes—
334#388C2318yes—
335#388C2318yes—
336#388C2318yes—
337#388C2318yes—
338#388C2314yes—
339#388C2318yes—
340#388C2318yes—
341#388C2318yes—
342#388C2318yes—
343#388C2318yes—
344#388C2314yes—
345#388C2314yes—
346#388C2314yes—
347#388C2314yes—
348#388C2314yes—
349#388C2314yes—
350#388C2314yes—
351#388C2314yes—
352#388C2314yes—
353#388C2314yes—
354#388C2314yes—
355#388C2314yes—
356#388C2314yes—
357#388C2314yes—
358#387C2318yes—
359#387C2318yes—
360#387C2318yes—
361#387C2318yes—
362#387C2318yes—
363#387C2318yes—
364#387C2318yes—
365#387C2318yes—
366#387C2318yes—
367#387C2318yes—
368#387C2318yes—
369#387C2318yes—
370#387C2318yes—
371#386C2314yes—
372#386C2318yes—
373#386C2318yes—
374#386C2318yes—
375#386C2314yes—
376#386C2318yes—
377#386C2318yes—
378#386C2318yes—
379#386C2318yes—
380#385C2318yes—
381#385C2318yes—
382#385C2318yes—
383#385C2318yes—
384#385C2318yes—
385#385C2318yes—
386#385C2318yes—
387#385C2318yes—
388#385C2318yes—
389#384C2311yescharacteristic
390#384C2311yescharacteristic
391#384C2314yes—
392#384C2312yes—
393#384C2312yes—
394#383C2318yes—
395#382C2312yes—
396#382C2312yes—
397#382C2314yes—
398#382C2314yes—
399#382C2318yes—
400#382C2314yes—
401#382C2312yes—
402#381C2318yes—
403#380C2314yes—
404#380C2314yes—
405#380C2314yes—
406#380C2314yes—
407#380C2314yes—
408#380C2314yes—
409#380C2318yes—
410#380C2314yes—
411#380C2314yes—
412#380C2314yes—
413#380C2314yes—
414#380C2314yes—
415#379C2318yes—
416C4×C4⋊C4C2314yes—
417C4×C4⋊C4C2314yes—
418C4×C4⋊C4C2318yes—
419C4×C4⋊C4C2318yes—
420C4×C4⋊C4C2314yes—
421C4×C4⋊C4C2312yes—
422C4×C4⋊C4C2314yes—
423C4×C4⋊C4C2314yes—
424C4×C4⋊C4C2312yes—
425C4×C4⋊C4C2318yes—
426C4×C4⋊C4C2318yes—
427C4×C4⋊C4C2314yes—
428C4×C4⋊C4C2311yescharacteristic
429C4×C4⋊C4C2311yescharacteristic
430C4×C4⋊C4C2314yes—
431C4×C4⋊C4C2312yes—
432C4×C22⋊C4C2318yes—
433C4×C22⋊C4C2314yes—
434C4×C22⋊C4C2318yes—
435C4×C22⋊C4C2314yes—
436C4×C22⋊C4C2318yes—
437C4×C22⋊C4C2312yes—
438C4×C22⋊C4C2312yes—
439C4×C22⋊C4C2312yes—
440C4×C22⋊C4C2312yes—
441C4×C22⋊C4C2314yes—
442C4×C22⋊C4C2314yes—
443C2×#95C2314yes—
444C2×#95C2312yes—
445C43C2311yescharacteristic
446C43C2311yescharacteristic
447C43C2312yes—
448C43C2311yescharacteristic
449C43C2311yescharacteristic
450C43C2312yes—
451C25C2412yes—
452C22×Q8C2412yes—
453C22×D4—24no—
454C22×D4—44no—
455C22×D4C2414yes—
456C22×D4C2412yes—
457C22×D4C2411yescharacteristic
458C22×D4C2411yescharacteristic
459C22×D4C2412yes—
460C22×D4C2414yes—
461C22×D4C2418yes—
462C22×D4C2418yes—
463C23×C4—28no—
464C23×C4—44no—
465C23×C4—44no—
466C23×C4C2414yes—
467C23×C4C2412yes—
468C23×C4C2412yes—
469C23×C4C2412yes—
470C23×C4C2411yescharacteristic
471C23×C4C2411yescharacteristic
472C23×C4C2411yescharacteristic
473C23×C4C2414yes—
474C23×C4C2412yes—
475C23×C4C2412yes—
476C23×C4C2412yes—
477C23×C4C2412yes—
478C23×C4C2418yes—
479C4⋊Q8—24no—
480#127—24no—
481#126—216no—
482#126—416no—
483#125—28no—
484#125—28no—
485#125—48no—
486#125—44no—
487#125—416no—
488#124—28no—
489#124—44no—
490#123—216no—
491#123—416no—
492C22⋊Q8—28no—
493C22⋊Q8—48no—
494C22⋊Q8—48no—
495#121—28no—
496#121—416no—
497#121—48no—
498#121—48no—
499#121—48no—
500#121—48no—
501#121—48no—
502#120—416no—
503C4×Q8—28no—
504C4×Q8—48no—
505C4×D4—216no—
506C4×D4—24no—
507C4×D4—24no—
508C4×D4—24no—
509C4×D4—24no—
510C4×D4—28no—
511C4×D4—28no—
512C4×D4—28no—
513C4×D4—48no—
514C4×D4—48no—
515C4×D4—416no—
516#117—216no—
517#117—28no—
518#117—28no—
519#117—44no—
520#117—44no—
521#117—48no—
522#117—48no—
523#117—48no—
524#117—48no—
525C2×C4⋊C4—24no—
526C2×C4⋊C4—44no—
527C2×C4⋊C4—48no—
528C2×C4⋊C4—48no—
529C2×C4⋊C4C2412yes—
530C2×C4⋊C4C2414yes—
531C2×C4⋊C4C2414yes—
532C2×C4⋊C4C2412yes—
533C2×C4⋊C4C2411yescharacteristic
534C2×C4⋊C4C2411yescharacteristic
535C2×C4⋊C4C2412yes—
536C2×C4⋊C4C2414yes—
537C2×C4⋊C4C2414yes—
538C2×C4⋊C4C2414yes—
539C2×C4⋊C4C2414yes—
540C2×C4⋊C4C2414yes—
541C2×C4⋊C4C2412yes—
542C2×C4⋊C4C2414yes—
543C2×C4⋊C4C2412yes—
544C2×C4⋊C4C2414yes—
545C2×C4⋊C4C2414yes—
546C2×C4⋊C4C2418yes—
547C2×C4⋊C4C2414yes—
548C2×C4⋊C4C2414yes—
549C2×C4⋊C4C2414yes—
550C2×C4⋊C4C2414yes—
551C2×C4⋊C4C2418yes—
552C2×C4⋊C4C2414yes—
553C2×C4⋊C4C2414yes—
554C2×C4⋊C4C2414yes—
555C2×C4⋊C4C2418yes—
556C2×C4⋊C4C2418yes—
557C2×C4⋊C4C2414yes—
558C2×C4⋊C4C2418yes—
559C2×C4⋊C4C2418yes—
560C2×C4⋊C4C2418yes—
561C2×C4⋊C4C2418yes—
562C2×C4⋊C4C2418yes—
563C2×C22⋊C4—28no—
564C2×C22⋊C4—48no—
565C2×C22⋊C4—48no—
566C2×C22⋊C4C2414yes—
567C2×C22⋊C4C2414yes—
568C2×C22⋊C4C2412yes—
569C2×C22⋊C4C2412yes—
570C2×C22⋊C4C2412yes—
571C2×C22⋊C4C2412yes—
572C2×C22⋊C4C2418yes—
573C2×C22⋊C4C2414yes—
574C2×C22⋊C4C2414yes—
575C2×C22⋊C4C2414yes—
576C2×C22⋊C4C2414yes—
577C2×C22⋊C4C2414yes—
578C2×C22⋊C4C2414yes—
579C2×C22⋊C4C2414yes—
580C2×C22⋊C4C2414yes—
581C2×C22⋊C4C2414yes—
582C2×C22⋊C4C2414yes—
583C2×C22⋊C4C2414yes—
584C2×C22⋊C4C2418yes—
585C2×C22⋊C4C2418yes—
586C2×C22⋊C4C2418yes—
587C2×C22⋊C4C2414yes—
588C2×C22⋊C4C2414yes—
589C2×C22⋊C4C2418yes—
590C2×C22⋊C4C2418yes—
591C2×C22⋊C4C2418yes—
592C2×C22⋊C4C2414yes—
593C2×C22⋊C4C2414yes—
594C2×C22⋊C4C2418yes—
595C2×C22⋊C4C2418yes—
596C2×C22⋊C4C2418yes—
597C2×C22⋊C4C2418yes—
598C2×C22⋊C4C2418yes—
599C2×C22⋊C4C2414yes—
600C2×C22⋊C4C2414yes—
601C2×C42—24no—
602C2×C42—44no—
603C2×C42—44no—
604C2×C42—42no—
605C2×C42—44no—
606C2×C42#4118yes—
607C2×C42C2412yes—
608C2×C42C2411yescharacteristic
609C2×C42C2412yes—
610C2×C42C2412yes—
611C2×C42C2414yes—
612C2×C42C2412yes—
613C2×C42C2411yescharacteristic
614C2×C42C2412yes—
615C2×C42C2411yescharacteristic
616C2×C42C2414yes—
617C2×C42C2418yes—
618C2×C42C2418yes—
619C2×C42C2418yes—
620C2×C42C2418yes—
621C2×C42C2412yes—
622C2×C42C2412yes—
623C2×C42C2412yes—
624C2×C42C2412yes—
625C2×C42C2412yes—
626C2×C42C2412yes—
627C2×C42C2412yes—
628C2×C42C2411yescharacteristic
629C2×C42C2411yescharacteristic
630C2×C42C2411yescharacteristic
631C2×C42C2411yescharacteristic
632C2×C42C2411yescharacteristic
633#95C2414yes—
634#95C2414yes—
635#95C2414yes—
636#95C2414yes—
637#95C2414yes—
638#95C2412yes—
639#95C2412yes—
640#95C2418yes—
641#95C2418yes—
642#95C2418yes—
643#95C2418yes—
644#95C2418yes—
645#95C2414yes—
646#95C2414yes—
647#95C2414yes—
648#95C2414yes—
649#95C2418yes—
650#95C2418yes—
651#95C2418yes—
652#95C2414yes—
653#95C2418yes—
654#95C2418yes—
655#95C2418yes—
656#95C2418yes—
657#95C2414yes—
658#95C2418yes—
659#95C2418yes—
660#95C2418yes—
661#95C2418yes—
662C24—24no—
663C24—28no—
664C24—42no—
665C24—42no—
666C24—44no—
667C24C2512yes—
668C24C2512yes—
669C24C2514yes—
670C24C2511yescharacteristic
671C2×Q8—24no—
672C2×Q8—24no—
673C2×Q8—24no—
674C2×D4—28no—
675C2×D4—28no—
676C2×D4—28no—
677C2×D4—24no—
678C2×D4—22no—
679C2×D4—22no—
680C2×D4—24no—
681C2×D4—24no—
682C2×D4—28no—
683C2×D4—24no—
684C2×D4—24no—
685C2×D4—24no—
686C2×D4—44no—
687C2×D4—416no—
688C2×D4—44no—
689C2×D4—44no—
690C2×D4—48no—
691C2×D4—48no—
692C2×D4—48no—
693C2×D4—48no—
694C2×D4—48no—
695C2×D4—48no—
696C22×C4—24no—
697C22×C4—22no—
698C22×C4—24no—
699C22×C4—22no—
700C22×C4—24no—
701C22×C4—24no—
702C22×C4—24no—
703C22×C4—28no—
704C22×C4—28no—
705C22×C4—24no—
706C22×C4—24no—
707C22×C4—24no—
708C22×C4—24no—
709C22×C4—24no—
710C22×C4—24no—
711C22×C4—24no—
712C22×C4—28no—
713C22×C4—28no—
714C22×C4—24no—
715C22×C4—24no—
716C22×C4—42no—
717C22×C4—42no—
718C22×C4—42no—
719C22×C4—42no—
720C22×C4—42no—
721C22×C4—42no—
722C22×C4—42no—
723C22×C4—42no—
724C22×C4—42no—
725C22×C4—44no—
726C22×C4—44no—
727C22×C4—48no—
728C22×C4—48no—
729C22×C4—48no—
730C22×C4—432no—
731C22×C4C2×#4114yes—
732C22×C4C2×#4114yes—
733C22×C4C2×#4114yes—
734C22×C4C2512yes—
735C22×C4C2512yes—
736C22×C4C2514yes—
737C22×C4C2514yes—
738C22×C4C2518yes—
739C22×C4C2514yes—
740C22×C4C2512yes—
741C22×C4C2512yes—
742C22×C4C2518yes—
743C22×C4C2512yes—
744C22×C4C2514yes—
745C22×C4C2514yes—
746C22×C4C2511yescharacteristic
747C22×C4C2511yescharacteristic
748C22×C4C2511yescharacteristic
749C22×C4C2511yescharacteristic
750C22×C4C2512yes—
751C22×C4C2511yescharacteristic
752C22×C4C2511yescharacteristic
753C4⋊C4—24no—
754C4⋊C4—22no—
755C4⋊C4—22no—
756C4⋊C4—28no—
757C4⋊C4—28no—
758C4⋊C4—24no—
759C4⋊C4—28no—
760C4⋊C4—24no—
761C4⋊C4—28no—
762C4⋊C4—28no—
763C4⋊C4—28no—
764C4⋊C4—28no—
765C4⋊C4—216no—
766C4⋊C4—28no—
767C4⋊C4—24no—
768C4⋊C4—24no—
769C4⋊C4—28no—
770C4⋊C4—28no—
771C4⋊C4—28no—
772C4⋊C4—44no—
773C4⋊C4—48no—
774C4⋊C4—44no—
775C4⋊C4—44no—
776C4⋊C4—44no—
777C4⋊C4—44no—
778C4⋊C4—44no—
779C4⋊C4—48no—
780C4⋊C4—48no—
781C4⋊C4—44no—
782C4⋊C4—48no—
783C4⋊C4—48no—
784C4⋊C4—48no—
785C4⋊C4—48no—
786C4⋊C4—48no—
787C22⋊C4—28no—
788C22⋊C4—216no—
789C22⋊C4—24no—
790C22⋊C4—24no—
791C22⋊C4—24no—
792C22⋊C4—24no—
793C22⋊C4—28no—
794C22⋊C4—28no—
795C22⋊C4—28no—
796C22⋊C4—28no—
797C22⋊C4—28no—
798C22⋊C4—28no—
799C22⋊C4—44no—
800C22⋊C4—44no—
801C22⋊C4—44no—
802C22⋊C4—44no—
803C22⋊C4—44no—
804C22⋊C4—44no—
805C22⋊C4—48no—
806C22⋊C4—44no—
807C22⋊C4—44no—
808C22⋊C4—48no—
809C22⋊C4—48no—
810C22⋊C4—48no—
811C22⋊C4—48no—
812C22⋊C4—44no—
813C22⋊C4—44no—
814C22⋊C4—48no—
815C22⋊C4—48no—
816C22⋊C4—48no—
817C22⋊C4—48no—
818C22⋊C4—48no—
819C22⋊C4—48no—
820C22⋊C4—44no—
821C22⋊C4—44no—
822C42—28no—
823C42—24no—
824C42—22no—
825C42—24no—
826C42—24no—
827C42—24no—
828C42—22no—
829C42—24no—
830C42—22no—
831C42—42no—
832C42—42no—
833C42—42no—
834C42—42no—
835C42—42no—
836C42—42no—
837C42—42no—
838C42—44no—
839C42—48no—
840C42—48no—
841C42—48no—
842C42—48no—
843C42C2×#4114yes—
844C42C2×#4114yes—
845C42C2×#4114yes—
846C42C2×#4114yes—
847C42H(5,𝔽2)14yes—
848C23—21no—
849C23—21no—
850C23—22no—
851C23—24no—
852C23—22no—
853C23—22no—
854C23—22no—
855C23—22no—
856C23—24no—
857C23—22no—
858C23—24no—
859C23—24no—
860C23—24no—
861C23—24no—
862C23—24no—
863C23—24no—
864C23—24no—
865C23—24no—
866C23—24no—
867C23—22no—
868C23—48no—
869C23—48no—
870C23—48no—
871C23—88no—
872C23—88no—
873C23C22×#4112yes—
874C23#58514yes—
875C23C2611yescharacteristic
876Q8—48no—
877D4—48no—
878D4—416no—
879D4—44no—
880D4—44no—
881D4—48no—
882D4—88no—
883D4—168no—
884D4—168no—
885C2×C4—21no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—21no—
892C2×C4—28no—
893C2×C4—28no—
894C2×C4—28no—
895C2×C4—24no—
896C2×C4—24no—
897C2×C4—24no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—24no—
902C2×C4—24no—
903C2×C4—24no—
904C2×C4—28no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—28no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—24no—
917C2×C4—24no—
918C2×C4—24no—
919C2×C4—24no—
920C2×C4—28no—
921C2×C4—28no—
922C2×C4—24no—
923C2×C4—24no—
924C2×C4—24no—
925C2×C4—22no—
926C2×C4—24no—
927C2×C4—28no—
928C2×C4—28no—
929C2×C4—24no—
930C2×C4—22no—
931C2×C4—48no—
932C2×C4—48no—
933C2×C4—48no—
934C2×C4—48no—
935C2×C4—48no—
936C2×C4—416no—
937C2×C4—48no—
938C2×C4—48no—
939C2×C4—88no—
940C2×C4—168no—
941C2×C4C22×#4112yes—
942C2×C4C22×#4112yes—
943C2×C4C22×#4112yes—
944C2×C4C22×#4112yes—
945C2×C4C22×#4112yes—
946C2×C4C22×#4112yes—
947C2×C4C2×H(5,𝔽2)14yes—
948C2×C4C2×H(5,𝔽2)12yes—
949C2×C4#58514yes—
950C2×C4#58512yes—
951C22—22no—
952C22—24no—
953C22—24no—
954C22—22no—
955C22—42no—
956C22—42no—
957C22—44no—
958C22—44no—
959C22—42no—
960C22—42no—
961C22—44no—
962C22—44no—
963C22—44no—
964C22—44no—
965C22—44no—
966C22—44no—
967C22—44no—
968C22—44no—
969C22—44no—
970C22—42no—
971C22—42no—
972C22—816no—
973C22#351214yes—
974C22C23×#4111yescharacteristic
975C22C22×H(5,𝔽2)11yescharacteristic
976C22C2×#58511yescharacteristic
977C22C2×#58512yes—
978C22C2×#58512yes—
979C4—22no—
980C4—22no—
981C4—22no—
982C4—24no—
983C4—22no—
984C4—42no—
985C4—42no—
986C4—44no—
987C4—44no—
988C4—42no—
989C4—42no—
990C4—48no—
991C4—42no—
992C4—44no—
993C4—44no—
994C4—48no—
995C4—44no—
996C4#345514yes—
997C4#350614yes—
998C2—24no—
999C2—84no—
1000C2—82no—
1001C2—82no—
1002C2C2×#345511yescharacteristic
1003C2C2×#350611yescharacteristic
1004C2C2×#351211yescharacteristic
1005C2#6282712yes—
1006C2#6283012yes—
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. #39510C2semidirect
2. #39507C2semidirect
3. #39506C2semidirect
4. #39382C2semidirect
5. #39379C2semidirect
6. #39378C2semidirect
7. #39197C2semidirect
8. #39194C2semidirect
9. #39193C2semidirect
10. #39189C2semidirect
11. #38973C2semidirect
12. #38126C2semidirect
13. #37201C2semidirect
14. #36640C2semidirect
15. #36631C2semidirect
16. #35614C2semidirect
17. #35603C2semidirect
18. #35310C2semidirect
19. #35261C2semidirect
20. #35236C2semidirect
21. #35023C2semidirect
22. #34243C2semidirect
23. C2×#2293C2semidirect
24. C2×#541C22semidirect
25. C2×#540C22semidirect
29. #2864C22semidirect
30. #2861C22semidirect
31. #2860C22semidirect
32. #2859C22semidirect
33. #2859C22semidirect
34. #2859C22semidirect
35. #2859C22semidirect
36. #2858C22semidirect
47. #2803C22semidirect
48. #2801C22semidirect
50. #2800C22semidirect
52. #2783C22semidirect
53. #2779C22semidirect
54. #2776C22semidirect
55. #2773C22semidirect
56. #2771C22semidirect
57. #2757C22semidirect
58. #2725C22semidirect
60. #2701C22semidirect
61. #2694C22semidirect
64. #2629C22semidirect
65. #2629C22semidirect
66. #2625C22semidirect
67. #2624C22semidirect
69. #2621C22semidirect
70. #2619C22semidirect
71. #2597C22semidirect
72. #2597C22semidirect
73. #2595C22semidirect
74. #2594C22semidirect
75. #2593C22semidirect
76. #2578C22semidirect
77. #2576C22semidirect
79. #2554C22semidirect
85. #2525C22semidirect
86. #2516C22semidirect
88. #2513C22semidirect
90. #2508C22semidirect
91. #2506C22semidirect
94. #2495C22semidirect
95. #2495C22semidirect
96. #2494C22semidirect
97. #2494C22semidirect
100. #2490C22semidirect
101. #2490C22semidirect
102. #2489C22semidirect
104. #2486C22semidirect
105. #2485C22semidirect
107. #2478C22semidirect
108. #2476C22semidirect
109. #2475C22semidirect
111. #2471C22semidirect
113. #2442C22semidirect
114. #2441C22semidirect
115. #2427C22semidirect
116. #2426C22semidirect
118. #2421C22semidirect
119. #2420C22semidirect
124. #2370C22semidirect
125. #2367C22semidirect
127. #2355C22semidirect
128. #2354C22semidirect
130. Q8×C4⋊C4C22semidirect
132. D4×C4⋊C4C22semidirect
133. #2334C22semidirect
136. #2324C22semidirect
137. #2323C22semidirect
140. #2314C22semidirect
141. #2314C22semidirect
142. #2314C22semidirect
143. C4×C4⋊Q8C22semidirect
144. C4×#127C22semidirect
145. C4×#125C22semidirect
146. C4×#125C22semidirect
147. C4×#125C22semidirect
148. C4×#124C22semidirect
162. #2293C22semidirect
167. #2274C22semidirect

Maximal subgroups

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

subgroupindex
#395102
#395072
#395062
#393822
#393792
#393782
#391972
#391942
#391932
#391892
#389732
#381262
#372012
#366402
#366312
#356142
#356032
#353102
#352612
#352362
#350232
#342432
C2×#22932