Finite Group Databasebeta

← #7665667

Subgroups — #7665667

Order 512.

4942 conjugacy classes of subgroups.

The subgroup lattice has 998 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39514C211yesmaximal, characteristic, complemented
2#39507C211yesmaximal, characteristic, complemented
3#39479C212yesmaximal, complemented
4#39030C214yesmaximal, complemented
5#39021C214yesmaximal, complemented
6#38190C218yesmaximal, complemented
7#38181C218yesmaximal, complemented
8#37898C212yesmaximal, complemented
9#37889C212yesmaximal, complemented
10#37857C214yesmaximal, complemented
11#36417C214yesmaximal, complemented
12#36414C214yesmaximal, complemented
13#36192C211yesmaximal, characteristic, complemented
14#36187C211yesmaximal, characteristic, complemented
15#36160C212yesmaximal, complemented
16#35284C211yesmaximal, characteristic, complemented
17#35261C212yesmaximal, complemented
18#35207C212yesmaximal, complemented
19#35161C214yesmaximal, complemented
20C4×#555C212yesmaximal, complemented
21D4×#117C211yesmaximal, characteristic, complemented
22C4×#540C211yesmaximal, characteristic, complemented
23#34048C212yesmaximal, complemented
24C2×#555C2212yes—
25C2×#540C2211yescharacteristic
26C22×C4×D4C2211yescharacteristic
27C22×#117C2212yes—
28#2868C2211yescharacteristic, complemented
29#2865C2218yescomplemented
30#2860C2218yescomplemented
31#2859C2211yescharacteristic, complemented
32#2857C2212yes—
33#2856C2212yescomplemented
34#2854C2214yes—
35#2851C2212yescomplemented
36#2851C2214yescomplemented
37#2847C2214yes—
38#2803C2218yescomplemented
39#2787C2218yescomplemented
40#2779C2218yes—
41#2754C2218yescomplemented
42#2746C2218yescomplemented
43#2740C2218yescomplemented
44#2716C2218yescomplemented
45#2703C2218yes—
46#2702C2218yes—
47#2697C2218yes—
48#2691C2218yescomplemented
49#2685C2218yes—
50#2653C2218yescomplemented
51#2649C2218yescomplemented
52#2648C2218yes—
53#2647C2212yescomplemented
54#2629C2212yes—
55#2629C2212yescomplemented
56#2624C2214yes—
57#2619C2212yescomplemented
58#2597C2218yescomplemented
59#2576C2218yes—
60#2570C2214yescomplemented
61#2563C2212yes—
62#2563C2212yescomplemented
63#2562C2214yes—
64#2554C2218yescomplemented
65#2553C2218yescomplemented
66#2552C2212yescomplemented
67#2537C2212yes—
68#2537C2214yes—
69#2531C2218yescomplemented
70#2530C2218yescomplemented
71#2529C2218yescomplemented
72#2528C2218yescomplemented
73#2526C2218yes—
74#2526C2218yescomplemented
75#2522C2218yescomplemented
76#2512C2214yes—
77#2512C2214yescomplemented
78#2509C2214yescomplemented
79#2507C2214yescomplemented
80#2500C2214yescomplemented
81#2497C2214yes—
82#2496C2214yescomplemented
83#2496C2214yescomplemented
84#2494C2214yescomplemented
85#2494C2214yescomplemented
86#2491C2218yescomplemented
87#2490C2214yes—
88#2490C2214yescomplemented
89#2485C2214yes—
90#2485C2214yes—
91#2485C2214yescomplemented
92#2476C2218yes—
93#2472C2218yes—
94#2471C2218yescomplemented
95#2467C2218yes—
96#2466C2218yescomplemented
97#2459C2218yes—
98#2458C2218yescomplemented
99#2454C2214yes—
100#2446C2214yescomplemented
101#2443C2218yescomplemented
102#2441C2214yescomplemented
103#2441C2214yescomplemented
104#2429C2214yes—
105#2424C2218yes—
106#2422C2214yescomplemented
107#2420C2214yes—
108#2414C2214yes—
109#2414C2214yes—
110#2408C2214yes—
111#2372C2218yescomplemented
112#2370C2214yescomplemented
113#2369C2212yescomplemented
114#2363C2214yes—
115#2363C2214yes—
116#2363C2214yescomplemented
117#2354C2212yes—
118#2354C2212yes—
119#2354C2212yescomplemented
120#2354C2214yescomplemented
121#2352C2214yes—
122#2352C2214yes—
123D4×C4⋊C4C2212yes—
124#2346C2214yescomplemented
125#2346C2214yescomplemented
126#2344C2212yes—
127#2342C2214yes—
128D4×C22⋊C4C2212yes—
129#2335C2214yescomplemented
130#2333C2214yes—
131#2330C2211yescharacteristic, complemented
132#2330C2212yescomplemented
133#2328C2211yescharacteristic, complemented
134#2324C2212yes—
135#2324C2214yescomplemented
136#2319C2212yescomplemented
137#2314C2211yescharacteristic
138#2314C2214yes—
139#2314C2212yes—
140#2314C2212yescomplemented
141#2314C2212yescomplemented
142#2314C2214yescomplemented
143#2313C2218yescomplemented
144#2312C2218yes—
145C4×C4⋊Q8C2212yescomplemented
146C4×#127C2211yescharacteristic, complemented
147C4×#125C2211yescharacteristic, complemented
148C4×#124C2218yescomplemented
149C4×#123C2214yescomplemented
150C4×#121C2212yes—
151C4×#121C2214yes—
152C4×#121C2214yes—
153C4×#121C2214yescomplemented
154#2298C2218yes—
155#2298C2218yescomplemented
156#2293C2211yescharacteristic
157#2293C2211yescharacteristic
158#2290C2212yes—
159#2290C2212yes—
160#2285C2211yescharacteristic
161#2285C2212yescomplemented
162#2285C2212yescomplemented
163#2280C2214yes—
164#2280C2212yes—
165C42×D4C2211yescharacteristic
166C42×D4C2211yescharacteristic
167C42×D4C2212yescomplemented
168C4×#117C2211yescharacteristic
169C4×#117C2214yescomplemented
170C4×#117C2214yescomplemented
171C23×D4C2311yescharacteristic
172C24×C4C2312yes—
173#555—216no—
174#540—28no—
175C2×C4⋊Q8C2312yes—
176C2×C4⋊Q8C2314yes—
177C2×#127C2311yescharacteristic
178C2×#126C2318yes—
179C2×#126C2318yes—
180C2×#125C2311yescharacteristic
181C2×#125C2314yes—
182C2×#125C2312yes—
183C2×#124C2318yes—
184C2×#123C2314yes—
185C2×#123C2318yes—
186C2×C22⋊Q8C2314yes—
187C2×#121C2312yes—
188C2×#121C2314yes—
189C2×#121C2314yes—
190C2×#121C2314yes—
191C2×#121C2314yes—
192C2×#121C2314yes—
193C2×#121C2318yes—
194C2×#120C2318yes—
195C2×C4×Q8C2314yes—
196C2×C4×D4—28no—
197C2×C4×D4C2312yes—
198C2×C4×D4C2311yescharacteristic
199C2×C4×D4C2312yes—
200C2×C4×D4C2311yescharacteristic
201C2×C4×D4C2312yes—
202C2×C4×D4C2311yescharacteristic
203C2×C4×D4C2312yes—
204C2×C4×D4C2314yes—
205C2×C4×D4C2314yes—
206C2×C4×D4C2312yes—
207C2×C4×D4C2312yes—
208C2×C4×D4C2312yes—
209C2×C4×D4C2318yes—
210C2×C4×D4C2311yescharacteristic
211C2×#117—216no—
212C2×#117C2312yes—
213C2×#117C2312yes—
214C2×#117C2312yes—
215C2×#117C2314yes—
216C2×#117C2314yes—
217C2×#117C2314yes—
218C2×#117C2314yes—
219C2×#117C2311yescharacteristic
220C2×#117C2314yes—
221C2×#117C2314yes—
222C2×#117C2311yescharacteristic
223C22×C4⋊C4C2314yes—
224C22×C4⋊C4C2311yescharacteristic
225C22×C22⋊C4C2314yes—
226C22×C22⋊C4C2312yes—
227C22×C42C2312yes—
228C22×C42C2311yescharacteristic
229C22×C42C2312yes—
230C22×C42C2314yes—
231#401C2318yes—
232#400C2318yes—
233#400C2318yes—
234#400C2318yes—
235#400C2318yes—
236#399C2318yes—
237#399C2318yes—
238#398C2318yes—
239#398C2318yes—
240#398C2318yes—
241#398C2318yes—
242#397C2318yes—
243#397C2318yes—
244#397C2318yes—
245#397C2318yes—
246#397C2318yes—
247#397C2318yes—
248#397C2318yes—
249#396C2318yes—
250#396C2318yes—
251#396C2318yes—
252#396C2318yes—
253#394C2318yes—
254#394C2318yes—
255#394C2318yes—
256#394C2318yes—
257#394C2318yes—
258#394C2318yes—
259#394C2318yes—
260#394C2318yes—
261#394C2318yes—
262#394C2318yes—
263#393C2318yes—
264#393C2318yes—
265#392C2318yes—
266#392C2318yes—
267#391C2314yes—
268#391C2314yes—
269#391C2318yes—
270#390C2312yes—
271#390C2314yes—
272#390C2314yes—
273#390C2314yes—
274#390C2312yes—
275#390C2314yes—
276#390C2318yes—
277#390C2312yes—
278#390C2312yes—
279#390C2318yes—
280#390C2318yes—
281#390C2318yes—
282#390C2314yes—
283#390C2314yes—
284#390C2318yes—
285#389C2312yes—
286#389C2314yes—
287#389C2314yes—
288#389C2312yes—
289#389C2314yes—
290#389C2312yes—
291#389C2314yes—
292#389C2314yes—
293#389C2314yes—
294#389C2318yes—
295#389C2312yes—
296#389C2314yes—
297#389C2314yes—
298#389C2314yes—
299#389C2314yes—
300#389C2314yes—
301#389C2318yes—
302#389C2318yes—
303#388C2318yes—
304#388C2318yes—
305#388C2314yes—
306#388C2318yes—
307#388C2318yes—
308#388C2318yes—
309#388C2318yes—
310#388C2318yes—
311#388C2318yes—
312#388C2314yes—
313#388C2314yes—
314#388C2318yes—
315#388C2314yes—
316#388C2318yes—
317#388C2314yes—
318#388C2318yes—
319#388C2318yes—
320#388C2314yes—
321#388C2314yes—
322#388C2314yes—
323#388C2314yes—
324#388C2318yes—
325#388C2318yes—
326#388C2318yes—
327#388C2318yes—
328#388C2318yes—
329#388C2318yes—
330#388C2318yes—
331#388C2318yes—
332#388C2318yes—
333#387C2314yes—
334#387C2314yes—
335#387C2318yes—
336#387C2318yes—
337#387C2318yes—
338#387C2318yes—
339#387C2318yes—
340#387C2318yes—
341#387C2318yes—
342#387C2318yes—
343#387C2318yes—
344#387C2314yes—
345#387C2318yes—
346#387C2318yes—
347#387C2318yes—
348#387C2314yes—
349#387C2314yes—
350#387C2318yes—
351#387C2318yes—
352#386C2314yes—
353#386C2318yes—
354#386C2318yes—
355#386C2314yes—
356#386C2314yes—
357#386C2314yes—
358#386C2318yes—
359#386C2318yes—
360#386C2314yes—
361#386C2314yes—
362#386C2318yes—
363#386C2318yes—
364#385C2318yes—
365#385C2314yes—
366#385C2318yes—
367#385C2318yes—
368#385C2314yes—
369#385C2314yes—
370#384C2311yescharacteristic
371#384C2312yes—
372#384C2312yes—
373#384C2314yes—
374#384C2314yes—
375#384C2312yes—
376#384C2312yes—
377#382C2311yescharacteristic
378#382C2314yes—
379#382C2314yes—
380#382C2312yes—
381#382C2318yes—
382#382C2312yes—
383#381C2318yes—
384#381C2314yes—
385#381C2314yes—
386#380C2312yes—
387#380C2314yes—
388#380C2314yes—
389#380C2314yes—
390#380C2314yes—
391#380C2314yes—
392#380C2314yes—
393#380C2318yes—
394#380C2318yes—
395#380C2312yes—
396#380C2314yes—
397#380C2314yes—
398#380C2314yes—
399#380C2314yes—
400#380C2314yes—
401#380C2312yes—
402#380C2314yes—
403#380C2314yes—
404#379C2318yes—
405#379C2314yes—
406C4×C4⋊C4C2312yes—
407C4×C4⋊C4C2314yes—
408C4×C4⋊C4C2314yes—
409C4×C4⋊C4C2314yes—
410C4×C4⋊C4C2314yes—
411C4×C4⋊C4C2311yescharacteristic
412C4×C4⋊C4C2312yes—
413C4×C4⋊C4C2314yes—
414C4×C4⋊C4C2314yes—
415C4×C4⋊C4C2312yes—
416C4×C4⋊C4C2312yes—
417C4×C4⋊C4C2318yes—
418C4×C4⋊C4C2312yes—
419C4×C4⋊C4C2312yes—
420C4×C4⋊C4C2314yes—
421C4×C4⋊C4C2312yes—
422C4×C4⋊C4C2311yescharacteristic
423C4×C4⋊C4C2318yes—
424C4×C4⋊C4C2312yes—
425C4×C22⋊C4C2318yes—
426C4×C22⋊C4C2318yes—
427C4×C22⋊C4C2318yes—
428C4×C22⋊C4C2318yes—
429C4×C22⋊C4C2312yes—
430C4×C22⋊C4C2314yes—
431C4×C22⋊C4C2314yes—
432C4×C22⋊C4C2312yes—
433C4×C22⋊C4C2314yes—
434C4×C22⋊C4C2314yes—
435C4×C22⋊C4C2312yes—
436C4×C22⋊C4C2314yes—
437C4×C22⋊C4C2314yes—
438C4×C22⋊C4C2318yes—
439C4×C22⋊C4C2312yes—
440C4×C22⋊C4C2312yes—
441C4×C22⋊C4C2318yes—
442C4×C22⋊C4C2312yes—
443#376C2311yescharacteristic
444#376C2311yescharacteristic
445#376C2318yes—
446#376C2318yes—
447C43C2311yescharacteristic
448C43C2311yescharacteristic
449C43C2318yes—
450C25C2412yes—
451C22×Q8C2414yes—
452C22×D4—24no—
453C22×D4—44no—
454C22×D4C2412yes—
455C22×D4C2411yescharacteristic
456C22×D4C2411yescharacteristic
457C22×D4C2412yes—
458C22×D4C2414yes—
459C22×D4C2418yes—
460C22×D4C2414yes—
461C22×D4C2418yes—
462C23×C4—28no—
463C23×C4—28no—
464C23×C4—44no—
465C23×C4C2411yescharacteristic
466C23×C4C2414yes—
467C23×C4C2412yes—
468C23×C4C2412yes—
469C23×C4C2412yes—
470C23×C4C2412yes—
471C23×C4C2412yes—
472C23×C4C2411yescharacteristic
473C23×C4C2411yescharacteristic
474C23×C4C2414yes—
475C23×C4C2414yes—
476C23×C4C2414yes—
477C23×C4C2414yes—
478C4⋊Q8—28no—
479C4⋊Q8—84no—
480#127—24no—
481#126—88no—
482#126—88no—
483#125—24no—
484#125—48no—
485#125—44no—
486#124—232no—
487#123—216no—
488#123—88no—
489C22⋊Q8—84no—
490#121—216no—
491#121—28no—
492#121—216no—
493#121—216no—
494#121—48no—
495#121—48no—
496#121—88no—
497#120—88no—
498C4×Q8—84no—
499C4×D4—24no—
500C4×D4—28no—
501C4×D4—24no—
502C4×D4—28no—
503C4×D4—24no—
504C4×D4—28no—
505C4×D4—28no—
506C4×D4—44no—
507C4×D4—44no—
508C4×D4—44no—
509C4×D4—48no—
510C4×D4—48no—
511C4×D4—88no—
512C4×D4#4118yes—
513#117—28no—
514#117—216no—
515#117—216no—
516#117—216no—
517#117—216no—
518#117—28no—
519#117—28no—
520#117—42no—
521#117—48no—
522#117—48no—
523#117#4118yes—
524C2×C4⋊C4—216no—
525C2×C4⋊C4—24no—
526C2×C4⋊C4C2414yes—
527C2×C4⋊C4C2414yes—
528C2×C4⋊C4C2414yes—
529C2×C4⋊C4C2411yescharacteristic
530C2×C4⋊C4C2412yes—
531C2×C4⋊C4C2412yes—
532C2×C4⋊C4C2412yes—
533C2×C4⋊C4C2412yes—
534C2×C4⋊C4C2414yes—
535C2×C4⋊C4C2414yes—
536C2×C4⋊C4C2414yes—
537C2×C4⋊C4C2414yes—
538C2×C4⋊C4C2412yes—
539C2×C4⋊C4C2412yes—
540C2×C4⋊C4C2414yes—
541C2×C4⋊C4C2412yes—
542C2×C4⋊C4C2418yes—
543C2×C4⋊C4C2414yes—
544C2×C4⋊C4C2414yes—
545C2×C4⋊C4C2414yes—
546C2×C4⋊C4C2418yes—
547C2×C4⋊C4C2418yes—
548C2×C4⋊C4C2418yes—
549C2×C4⋊C4C2418yes—
550C2×C4⋊C4C2418yes—
551C2×C4⋊C4C2418yes—
552C2×C4⋊C4C2418yes—
553C2×C4⋊C4C2414yes—
554C2×C4⋊C4C2414yes—
555C2×C4⋊C4C2418yes—
556C2×C4⋊C4C2412yes—
557C2×C4⋊C4C2411yescharacteristic
558C2×C22⋊C4—216no—
559C2×C22⋊C4—28no—
560C2×C22⋊C4C2414yes—
561C2×C22⋊C4C2414yes—
562C2×C22⋊C4C2414yes—
563C2×C22⋊C4C2412yes—
564C2×C22⋊C4C2412yes—
565C2×C22⋊C4C2412yes—
566C2×C22⋊C4C2418yes—
567C2×C22⋊C4C2418yes—
568C2×C22⋊C4C2414yes—
569C2×C22⋊C4C2414yes—
570C2×C22⋊C4C2414yes—
571C2×C22⋊C4C2412yes—
572C2×C22⋊C4C2418yes—
573C2×C22⋊C4C2418yes—
574C2×C22⋊C4C2418yes—
575C2×C22⋊C4C2418yes—
576C2×C22⋊C4C2414yes—
577C2×C22⋊C4C2414yes—
578C2×C22⋊C4C2414yes—
579C2×C22⋊C4C2414yes—
580C2×C22⋊C4C2414yes—
581C2×C22⋊C4C2414yes—
582C2×C22⋊C4C2414yes—
583C2×C22⋊C4C2418yes—
584C2×C22⋊C4C2418yes—
585C2×C22⋊C4C2418yes—
586C2×C22⋊C4C2418yes—
587C2×C22⋊C4C2418yes—
588C2×C22⋊C4C2418yes—
589C2×C22⋊C4C2414yes—
590C2×C22⋊C4C2418yes—
591C2×C22⋊C4C2414yes—
592C2×C22⋊C4C2414yes—
593C2×C22⋊C4C2412yes—
594C2×C22⋊C4C2412yes—
595C2×C42—28no—
596C2×C42—28no—
597C2×C42—24no—
598C2×C42—48no—
599C2×C42C2418yes—
600C2×C42C2414yes—
601C2×C42C2412yes—
602C2×C42C2412yes—
603C2×C42C2414yes—
604C2×C42C2411yescharacteristic
605C2×C42C2411yescharacteristic
606C2×C42C2412yes—
607C2×C42C2411yescharacteristic
608C2×C42C2411yescharacteristic
609C2×C42C2411yescharacteristic
610C2×C42C2414yes—
611C2×C42C2412yes—
612C2×C42C2418yes—
613C2×C42C2418yes—
614C2×C42C2418yes—
615C2×C42C2412yes—
616C2×C42C2418yes—
617C2×C42C2412yes—
618C2×C42C2414yes—
619C2×C42C2414yes—
620C2×C42C2411yescharacteristic
621C2×C42C2411yescharacteristic
622C2×C42C2411yescharacteristic
623#95C2414yes—
624#95C2414yes—
625#95C2412yes—
626#95C2418yes—
627#95C2418yes—
628#95C2412yes—
629#95C2412yes—
630#95C2418yes—
631#95C2412yes—
632#95C2418yes—
633#95C2418yes—
634#95C2418yes—
635#95C2414yes—
636#95C2414yes—
637#95C2412yes—
638#95C2412yes—
639#95C2414yes—
640#95C2414yes—
641#95C2418yes—
642#95C2418yes—
643#95C2414yes—
644#95C2414yes—
645#95C2418yes—
646#95C2414yes—
647#95C2414yes—
648#95C2418yes—
649#95C2418yes—
650#95C2418yes—
651#95C2414yes—
652#95C2414yes—
653#95C2418yes—
654#95C2418yes—
655#95C2418yes—
656C24—24no—
657C24—24no—
658C24—42no—
659C24—44no—
660C24—44no—
661C24C2512yes—
662C24C2514yes—
663C24C2511yescharacteristic
664C24C2512yes—
665C2×Q8—28no—
666C2×Q8—44no—
667C2×Q8—44no—
668C2×D4—24no—
669C2×D4—28no—
670C2×D4—216no—
671C2×D4—22no—
672C2×D4—24no—
673C2×D4—24no—
674C2×D4—28no—
675C2×D4—24no—
676C2×D4—24no—
677C2×D4—24no—
678C2×D4—44no—
679C2×D4—44no—
680C2×D4—44no—
681C2×D4—48no—
682C2×D4—44no—
683C2×D4—48no—
684C2×D4—44no—
685C2×D4—48no—
686C2×D4—48no—
687C2×D4—48no—
688C2×D4—416no—
689C2×D4C2×#4114yes—
690C22×C4—24no—
691C22×C4—22no—
692C22×C4—24no—
693C22×C4—22no—
694C22×C4—24no—
695C22×C4—24no—
696C22×C4—22no—
697C22×C4—24no—
698C22×C4—24no—
699C22×C4—24no—
700C22×C4—24no—
701C22×C4—28no—
702C22×C4—24no—
703C22×C4—24no—
704C22×C4—28no—
705C22×C4—28no—
706C22×C4—24no—
707C22×C4—24no—
708C22×C4—22no—
709C22×C4—28no—
710C22×C4—28no—
711C22×C4—28no—
712C22×C4—42no—
713C22×C4—42no—
714C22×C4—42no—
715C22×C4—432no—
716C22×C4—44no—
717C22×C4—44no—
718C22×C4—44no—
719C22×C4—44no—
720C22×C4—44no—
721C22×C4—44no—
722C22×C4—44no—
723C22×C4—44no—
724C22×C4—42no—
725C22×C4—44no—
726C22×C4C2×#4114yes—
727C22×C4C2×#4118yes—
728C22×C4C2511yescharacteristic
729C22×C4C2512yes—
730C22×C4C2514yes—
731C22×C4C2512yes—
732C22×C4C2514yes—
733C22×C4C2514yes—
734C22×C4C2514yes—
735C22×C4C2518yes—
736C22×C4C2518yes—
737C22×C4C2514yes—
738C22×C4C2512yes—
739C22×C4C2511yescharacteristic
740C22×C4C2511yescharacteristic
741C22×C4C2512yes—
742C22×C4C2512yes—
743C22×C4C2511yescharacteristic
744C22×C4C2512yes—
745C22×C4C2511yescharacteristic
746C22×C4C2511yescharacteristic
747C4⋊C4—28no—
748C4⋊C4—28no—
749C4⋊C4—28no—
750C4⋊C4—24no—
751C4⋊C4—22no—
752C4⋊C4—24no—
753C4⋊C4—28no—
754C4⋊C4—28no—
755C4⋊C4—24no—
756C4⋊C4—28no—
757C4⋊C4—24no—
758C4⋊C4—24no—
759C4⋊C4—28no—
760C4⋊C4—28no—
761C4⋊C4—24no—
762C4⋊C4—42no—
763C4⋊C4—44no—
764C4⋊C4—44no—
765C4⋊C4—48no—
766C4⋊C4—44no—
767C4⋊C4—48no—
768C4⋊C4—48no—
769C4⋊C4—48no—
770C4⋊C4—48no—
771C4⋊C4—48no—
772C4⋊C4—48no—
773C4⋊C4—48no—
774C4⋊C4—44no—
775C4⋊C4—44no—
776C4⋊C4—48no—
777C4⋊C4C2×#4118yes—
778C4⋊C4C2×#4114yes—
779C22⋊C4—28no—
780C22⋊C4—24no—
781C22⋊C4—216no—
782C22⋊C4—28no—
783C22⋊C4—28no—
784C22⋊C4—24no—
785C22⋊C4—24no—
786C22⋊C4—216no—
787C22⋊C4—28no—
788C22⋊C4—28no—
789C22⋊C4—28no—
790C22⋊C4—42no—
791C22⋊C4—48no—
792C22⋊C4—48no—
793C22⋊C4—44no—
794C22⋊C4—44no—
795C22⋊C4—44no—
796C22⋊C4—44no—
797C22⋊C4—44no—
798C22⋊C4—44no—
799C22⋊C4—44no—
800C22⋊C4—48no—
801C22⋊C4—48no—
802C22⋊C4—48no—
803C22⋊C4—48no—
804C22⋊C4—48no—
805C22⋊C4—48no—
806C22⋊C4—48no—
807C22⋊C4—48no—
808C22⋊C4—44no—
809C22⋊C4—48no—
810C22⋊C4—44no—
811C22⋊C4—44no—
812C22⋊C4C2×#4118yes—
813C22⋊C4C2×#4118yes—
814C42—28no—
815C42—28no—
816C42—24no—
817C42—24no—
818C42—22no—
819C42—22no—
820C42—22no—
821C42—216no—
822C42—24no—
823C42—28no—
824C42—22no—
825C42—22no—
826C42—24no—
827C42—44no—
828C42—44no—
829C42—48no—
830C42—48no—
831C42—48no—
832C42—42no—
833C42—48no—
834C42—42no—
835C42C2×#4114yes—
836C42C2×#4114yes—
837C42C2×#4114yes—
838C23—22no—
839C23—21no—
840C23—22no—
841C23—21no—
842C23—22no—
843C23—24no—
844C23—22no—
845C23—24no—
846C23—22no—
847C23—24no—
848C23—22no—
849C23—24no—
850C23—24no—
851C23—24no—
852C23—24no—
853C23—24no—
854C23—22no—
855C23—24no—
856C23—24no—
857C23—24no—
858C23—48no—
859C23—48no—
860C23—88no—
861C23—84no—
862C23—88no—
863C23C22×#4114yes—
864C23C22×#4112yes—
865C23C2611yescharacteristic
866Q8—88no—
867D4—28no—
868D4—48no—
869D4—44no—
870D4—48no—
871D4—88no—
872D4—88no—
873D4—816no—
874D4—168no—
875C2×C4—22no—
876C2×C4—21no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—21no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—28no—
885C2×C4—216no—
886C2×C4—21no—
887C2×C4—24no—
888C2×C4—24no—
889C2×C4—24no—
890C2×C4—21no—
891C2×C4—28no—
892C2×C4—24no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
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—24no—
905C2×C4—28no—
906C2×C4—28no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—24no—
910C2×C4—24no—
911C2×C4—24no—
912C2×C4—28no—
913C2×C4—28no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—28no—
917C2×C4—24no—
918C2×C4—24no—
919C2×C4—22no—
920C2×C4—48no—
921C2×C4—48no—
922C2×C4—48no—
923C2×C4—416no—
924C2×C4—44no—
925C2×C4—48no—
926C2×C4—88no—
927C2×C4—88no—
928C2×C4—88no—
929C2×C4—82no—
930C2×C4—88no—
931C2×C4C22×#4114yes—
932C2×C4C22×#4114yes—
933C2×C4C22×#4114yes—
934C2×C4C22×#4112yes—
935C2×C4C22×#4112yes—
936C2×C4C22×#4112yes—
937C2×C4C22×#4112yes—
938C2×C4C22×#4112yes—
939C2×C4#58514yes—
940C2×C4#58512yes—
941C22—24no—
942C22—24no—
943C22—24no—
944C22—22no—
945C22—24no—
946C22—44no—
947C22—41no—
948C22—44no—
949C22—42no—
950C22—41no—
951C22—44no—
952C22—44no—
953C22—44no—
954C22—44no—
955C22—42no—
956C22—44no—
957C22—44no—
958C22—44no—
959C22—44no—
960C22—42no—
961C22—42no—
962C22—44no—
963C22—816no—
964C22C23×#4111yescharacteristic
965C22C23×#4111yescharacteristic
966C22C2×#58512yes—
967C22C2×#58511yescharacteristic
968C22H(7,𝔽2)12yes—
969C4—24no—
970C4—24no—
971C4—22no—
972C4—22no—
973C4—24no—
974C4—44no—
975C4—44no—
976C4—44no—
977C4—41no—
978C4—48no—
979C4—42no—
980C4—44no—
981C4—42no—
982C4—48no—
983C4—44no—
984C4—41no—
985C4—42no—
986C4#345514yes—
987C4#347514yes—
988C2—44no—
989C2—42no—
990C2—84no—
991C2—82no—
992C2C2×#345511yescharacteristic
993C2C2×#347511yescharacteristic
994C2#6285811yescharacteristic
995C2#6293712yes—
996C2#6299412yes—
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. #39514C2semidirect
2. #39507C2semidirect
3. #39479C2semidirect
4. #39030C2semidirect
5. #39021C2semidirect
6. #38190C2semidirect
7. #38181C2semidirect
8. #37898C2semidirect
9. #37889C2semidirect
10. #37857C2semidirect
11. #36417C2semidirect
12. #36414C2semidirect
13. #36192C2semidirect
14. #36187C2semidirect
15. #36160C2semidirect
16. #35284C2semidirect
17. #35261C2semidirect
18. #35207C2semidirect
19. #35161C2semidirect
20. C4×#555C2semidirect
21. D4×#117C2semidirect
22. C4×#540C2semidirect
23. #34048C2semidirect
28. #2868C22semidirect
29. #2865C22semidirect
30. #2860C22semidirect
31. #2859C22semidirect
33. #2856C22semidirect
35. #2851C22semidirect
36. #2851C22semidirect
38. #2803C22semidirect
39. #2787C22semidirect
41. #2754C22semidirect
42. #2746C22semidirect
43. #2740C22semidirect
44. #2716C22semidirect
48. #2691C22semidirect
50. #2653C22semidirect
51. #2649C22semidirect
53. #2647C22semidirect
55. #2629C22semidirect
57. #2619C22semidirect
58. #2597C22semidirect
60. #2570C22semidirect
62. #2563C22semidirect
64. #2554C22semidirect
65. #2553C22semidirect
66. #2552C22semidirect
69. #2531C22semidirect
70. #2530C22semidirect
71. #2529C22semidirect
72. #2528C22semidirect
74. #2526C22semidirect
75. #2522C22semidirect
77. #2512C22semidirect
78. #2509C22semidirect
79. #2507C22semidirect
80. #2500C22semidirect
82. #2496C22semidirect
83. #2496C22semidirect
84. #2494C22semidirect
85. #2494C22semidirect
86. #2491C22semidirect
88. #2490C22semidirect
91. #2485C22semidirect
94. #2471C22semidirect
96. #2466C22semidirect
98. #2458C22semidirect
100. #2446C22semidirect
101. #2443C22semidirect
102. #2441C22semidirect
103. #2441C22semidirect
106. #2422C22semidirect
111. #2372C22semidirect
112. #2370C22semidirect
113. #2369C22semidirect
116. #2363C22semidirect
119. #2354C22semidirect
120. #2354C22semidirect
124. #2346C22semidirect
125. #2346C22semidirect
129. #2335C22semidirect
131. #2330C22semidirect
132. #2330C22semidirect
133. #2328C22semidirect
135. #2324C22semidirect
136. #2319C22semidirect
140. #2314C22semidirect
141. #2314C22semidirect
142. #2314C22semidirect
143. #2313C22semidirect
145. C4×C4⋊Q8C22semidirect
146. C4×#127C22semidirect
147. C4×#125C22semidirect
148. C4×#124C22semidirect
149. C4×#123C22semidirect
153. C4×#121C22semidirect
155. #2298C22semidirect
161. #2285C22semidirect
162. #2285C22semidirect
167. C42×D4C22semidirect
169. C4×#117C22semidirect
170. C4×#117C22semidirect

Maximal subgroups

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

subgroupindex
#395142
#395072
#394792
#390302
#390212
#381902
#381812
#378982
#378892
#378572
#364172
#364142
#361922
#361872
#361602
#352842
#352612
#352072
#351612
C4×#5552
D4×#1172
C4×#5402
#340482