Finite Group Databasebeta

← #7651186

Subgroups — #7651186

Order 512.

5040 conjugacy classes of subgroups.

The subgroup lattice has 958 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42724C214yesmaximal, complemented
2#42605C214yesmaximal, complemented
3#42592C214yesmaximal, complemented
4#42572C214yesmaximal, complemented
5#40663C214yesmaximal, complemented
6#40658C214yesmaximal, complemented
7#40172C214yesmaximal, complemented
8#40045C214yesmaximal, complemented
9#39536C214yesmaximal, complemented
10#39005C214yesmaximal, complemented
11#38121C218yesmaximal, complemented
12#35629C212yesmaximal, complemented
13#35585C212yesmaximal, complemented
14#35541C212yesmaximal, complemented
15#35255C212yesmaximal, complemented
16#35168C211yesmaximal, characteristic
17#34952C212yesmaximal, complemented
18C2×#2580C211yesmaximal, characteristic, complemented
19#34269C212yesmaximal, complemented
20#34248C211yesmaximal, characteristic, complemented
21C2×#537C2211yescharacteristic
22C2×#535C2212yes—
23C2×#518C2211yescharacteristic
24C2×#518C2211yescharacteristic
25C2×C4×#41C2212yes—
26C22×C4×Q8C2211yescharacteristic
27C22×C4×D4C2211yescharacteristic
28#2855C2214yescomplemented
29#2854C2214yescomplemented
30#2847C2214yes—
31#2835C2214yescomplemented
32#2834C2214yescomplemented
33#2826C2214yescomplemented
34#2824C2214yescomplemented
35#2796C2218yescomplemented
36#2787C2218yescomplemented
37#2782C2218yescomplemented
38#2770C2218yescomplemented
39#2757C2218yescomplemented
40#2746C2218yescomplemented
41#2746C2218yescomplemented
42#2745C2218yescomplemented
43#2738C2218yescomplemented
44#2737C2218yescomplemented
45#2711C2218yescomplemented
46#2708C2218yescomplemented
47#2706C2218yescomplemented
48#2696C2218yescomplemented
49#2694C2218yescomplemented
50#2687C2218yescomplemented
51#2653C2218yescomplemented
52#2649C2218yescomplemented
53#2643C2218yescomplemented
54#2638C2218yescomplemented
55#2633C2218yescomplemented
56#2625C2214yescomplemented
57#2624C2214yescomplemented
58#2623C2218yescomplemented
59#2617C2214yes—
60#2582C2212yescomplemented
61#2582C2212yescomplemented
62#2581C2212yescomplemented
63#2581C2212yescomplemented
64#2580C2214yes—
65#2580C2214yes—
66#2580C2214yes—
67#2580C2214yes—
68#2580C2212yescomplemented
69#2580C2212yescomplemented
70#2579C2214yes—
71#2579C2214yes—
72#2569C2218yes—
73#2538C2212yescomplemented
74#2538C2212yescomplemented
75#2523C2214yescomplemented
76#2517C2214yescomplemented
77#2514C2214yescomplemented
78#2514C2214yescomplemented
79#2513C2214yescomplemented
80#2513C2214yescomplemented
81#2510C2218yes—
82#2510C2218yes—
83#2509C2214yescomplemented
84#2509C2214yescomplemented
85#2508C2214yescomplemented
86#2508C2214yescomplemented
87#2507C2214yescomplemented
88#2507C2214yescomplemented
89#2506C2214yescomplemented
90#2506C2214yescomplemented
91#2495C2214yescomplemented
92#2495C2214yescomplemented
93#2494C2214yescomplemented
94#2494C2214yescomplemented
95#2493C2218yescomplemented
96#2487C2214yes—
97#2473C2218yescomplemented
98#2463C2214yescomplemented
99#2455C2214yescomplemented
100#2447C2214yes—
101#2447C2214yes—
102#2445C2214yes—
103#2445C2214yes—
104#2444C2218yes—
105#2443C2218yes—
106#2443C2218yescomplemented
107#2442C2218yes—
108#2428C2214yes—
109#2428C2214yes—
110#2427C2214yes—
111#2427C2214yes—
112#2425C2218yescomplemented
113#2423C2214yescomplemented
114#2422C2214yes—
115#2422C2214yes—
116#2422C2214yescomplemented
117#2421C2214yescomplemented
118#2420C2214yes—
119#2420C2214yes—
120#2420C2214yescomplemented
121#2412C2218yes—
122#2412C2218yes—
123#2409C2214yes—
124#2396C2214yescomplemented
125#2396C2214yescomplemented
126C2×#399C2212yes—
127C2×#393C2212yes—
128#2367C2214yes—
129#2367C2214yes—
130#2366C2214yes—
131#2366C2214yes—
132#2358C2218yes—
133#2358C2218yes—
134#2349C2214yes—
135#2349C2214yes—
136D4×C4⋊C4C2214yes—
137D4×C4⋊C4C2214yes—
138#2324C2214yes—
139#2324C2214yes—
140#2322C2218yescomplemented
141#2318C2218yescomplemented
142#2317C2212yes—
143#2316C2211yescharacteristic
144#2316C2212yes—
145#2315C2214yes—
146#2311C2212yes—
147#2311C2212yes—
148C4×C22⋊Q8C2214yescomplemented
149C4×C22⋊Q8C2214yescomplemented
150C4×#121C2214yes—
151C4×#121C2214yes—
152#2297C2212yes—
153#2297C2212yes—
154#2296C2212yes—
155#2296C2212yes—
156C2×#390C2212yes—
157C2×#389C2212yes—
158C2×#385C2214yes—
159C2×#385C2214yes—
160#2285C2212yes—
161C2×#382C2211yescharacteristic
162#2274C2212yes—
163C22×#41C2312yes—
164C23×Q8C2311yescharacteristic
165C23×D4C2311yescharacteristic
166C24×C4C2312yes—
167#537—44no—
168#535—216no—
169C2×#127C2314yes—
170C2×#125C2318yes—
171C2×#124C2314yes—
172C2×#123C2318yes—
173C2×#123C2318yes—
174C2×#123C2318yes—
175C2×C22⋊Q8C2314yes—
176C2×C22⋊Q8C2314yes—
177C2×C22⋊Q8C2314yes—
178C2×#121C2314yes—
179C2×#121C2314yes—
180C2×#121C2314yes—
181C2×#121C2314yes—
182C2×#121C2318yes—
183C2×#120C2318yes—
184#518—28no—
185#518—44no—
186C4×#41—48no—
187C2×C4×Q8—44no—
188C2×C4×Q8C2312yes—
189C2×C4×Q8C2312yes—
190C2×C4×Q8C2312yes—
191C2×C4×Q8C2312yes—
192C2×C4×Q8C2312yes—
193C2×C4×Q8C2312yes—
194C2×C4×D4—44no—
195C2×C4×D4C2314yes—
196C2×C4×D4C2314yes—
197C2×C4×D4C2318yes—
198C2×C4×D4C2314yes—
199C2×C4×D4C2314yes—
200C2×C4×D4C2314yes—
201C2×C4×D4C2314yes—
202C2×C4×D4C2314yes—
203C2×C4×D4C2312yes—
204C2×C4×D4C2314yes—
205C2×C4×D4C2312yes—
206C2×C4×D4C2318yes—
207C2×#117C2312yes—
208C2×#117C2312yes—
209C2×#117C2312yes—
210C2×#117C2314yes—
211C22×C4⋊C4C2312yes—
212C22×C4⋊C4C2311yescharacteristic
213C22×C4⋊C4C2311yescharacteristic
214C22×C4⋊C4C2312yes—
215C22×C4⋊C4C2318yes—
216C22×C4⋊C4C2314yes—
217C22×C22⋊C4C2314yes—
218C22×C22⋊C4C2312yes—
219C22×C22⋊C4C2314yes—
220C22×C22⋊C4C2314yes—
221C22×C22⋊C4C2314yes—
222C22×C42C2311yescharacteristic
223C22×C42C2312yes—
224C22×C42C2314yes—
225#401C2318yes—
226#401C2318yes—
227#400C2318yes—
228#400C2318yes—
229#400C2318yes—
230#400C2318yes—
231#400C2318yes—
232#400C2314yes—
233#400C2314yes—
234#400C2318yes—
235#400C2318yes—
236#399C2314yes—
237#399C2318yes—
238#399C2314yes—
239#399C2314yes—
240#399C2314yes—
241#399C2318yes—
242#398C2318yes—
243#398C2318yes—
244#398C2314yes—
245#398C2318yes—
246#398C2318yes—
247#398C2314yes—
248#398C2314yes—
249#398C2314yes—
250#398C2318yes—
251#397C2318yes—
252#397C2318yes—
253#397C2314yes—
254#397C2318yes—
255#397C2314yes—
256#397C2318yes—
257#397C2318yes—
258#397C2318yes—
259#397C2318yes—
260#397C2318yes—
261#397C2318yes—
262#397C2318yes—
263#397C2318yes—
264#396C2314yes—
265#396C2314yes—
266#396C2314yes—
267#396C2314yes—
268#395C2314yes—
269#395C2314yes—
270#394C2318yes—
271#394C2318yes—
272#394C2318yes—
273#394C2318yes—
274#394C2318yes—
275#394C2318yes—
276#394C2318yes—
277#394C2318yes—
278#393C2314yes—
279#393C2314yes—
280#393C2318yes—
281#393C2314yes—
282#393C2314yes—
283#392C2314yes—
284#392C2314yes—
285#391C2314yes—
286#391C2314yes—
287#391C2312yes—
288#391C2312yes—
289#391C2312yes—
290#391C2312yes—
291#391C2314yes—
292#391C2314yes—
293#390C2314yes—
294#390C2314yes—
295#390C2314yes—
296#390C2318yes—
297#390C2318yes—
298#390C2314yes—
299#390C2314yes—
300#390C2314yes—
301#390C2312yes—
302#390C2312yes—
303#390C2312yes—
304#390C2312yes—
305#389C2314yes—
306#389C2314yes—
307#389C2314yes—
308#389C2314yes—
309#389C2314yes—
310#389C2314yes—
311#389C2314yes—
312#389C2314yes—
313#389C2314yes—
314#389C2318yes—
315#389C2312yes—
316#389C2312yes—
317#389C2314yes—
318#389C2314yes—
319#389C2314yes—
320#389C2314yes—
321#389C2312yes—
322#389C2312yes—
323#389C2312yes—
324#389C2312yes—
325#389C2312yes—
326#389C2312yes—
327#389C2314yes—
328#389C2318yes—
329#388C2318yes—
330#388C2318yes—
331#388C2318yes—
332#388C2318yes—
333#388C2318yes—
334#388C2318yes—
335#388C2318yes—
336#388C2318yes—
337#388C2318yes—
338#388C2318yes—
339#387C2318yes—
340#387C2318yes—
341#387C2318yes—
342#387C2318yes—
343#387C2314yes—
344#387C2318yes—
345#387C2314yes—
346#387C2314yes—
347#387C2314yes—
348#387C2318yes—
349#387C2318yes—
350#387C2318yes—
351#386C2318yes—
352#386C2318yes—
353#386C2318yes—
354#386C2318yes—
355#386C2318yes—
356#386C2318yes—
357#386C2318yes—
358#386C2314yes—
359#386C2314yes—
360#386C2314yes—
361#386C2314yes—
362#386C2318yes—
363#386C2318yes—
364#386C2318yes—
365#386C2318yes—
366#385C2314yes—
367#385C2314yes—
368#385C2318yes—
369#385C2314yes—
370#385C2314yes—
371#385C2314yes—
372#385C2314yes—
373#385C2318yes—
374#385C2318yes—
375#385C2314yes—
376#385C2318yes—
377#385C2318yes—
378#385C2314yes—
379#385C2314yes—
380#385C2314yes—
381#385C2314yes—
382#385C2314yes—
383#385C2318yes—
384#385C2318yes—
385#385C2318yes—
386#385C2318yes—
387#385C2318yes—
388#385C2318yes—
389#385C2318yes—
390#384C2314yes—
391#384C2312yes—
392#384C2312yes—
393#383C2318yes—
394#383C2318yes—
395#382C2314yes—
396#382C2318yes—
397#382C2314yes—
398#382C2314yes—
399#382C2312yes—
400#382C2312yes—
401#381C2318yes—
402#381C2318yes—
403#381C2318yes—
404#380C2314yes—
405#380C2314yes—
406#380C2314yes—
407#380C2314yes—
408#380C2314yes—
409#380C2314yes—
410#380C2318yes—
411#380C2318yes—
412#380C2318yes—
413#380C2314yes—
414#380C2314yes—
415#380C2318yes—
416#380C2314yes—
417C4×C4⋊C4C2314yes—
418C4×C4⋊C4C2314yes—
419C4×C4⋊C4C2314yes—
420C4×C4⋊C4C2314yes—
421C4×C4⋊C4C2314yes—
422C4×C4⋊C4C2314yes—
423C4×C4⋊C4C2314yes—
424C4×C4⋊C4C2314yes—
425C4×C4⋊C4C2314yes—
426C4×C4⋊C4C2314yes—
427C4×C22⋊C4C2318yes—
428C4×C22⋊C4C2318yes—
429C4×C22⋊C4C2318yes—
430C4×C22⋊C4C2314yes—
431C4×C22⋊C4C2314yes—
432C4×C22⋊C4C2314yes—
433C4×C22⋊C4C2314yes—
434C2×#95C2314yes—
435C2×#95C2318yes—
436C2×#95C2312yes—
437C2×#95C2312yes—
438C25C2412yes—
439C2×#41—28no—
440C2×#41—28no—
441C2×#41—28no—
442C22×Q8—42no—
443C22×Q8—44no—
444C22×Q8C2412yes—
445C22×Q8C2411yescharacteristic
446C22×Q8C2412yes—
447C22×Q8C2411yescharacteristic
448C22×D4—24no—
449C22×D4—24no—
450C22×D4#4118yes—
451C22×D4C2414yes—
452C22×D4C2412yes—
453C22×D4C2414yes—
454C22×D4C2418yes—
455C22×D4C2418yes—
456C22×D4C2414yes—
457C23×C4—44no—
458C23×C4—84no—
459C23×C4C2414yes—
460C23×C4C2412yes—
461C23×C4C2412yes—
462C23×C4C2414yes—
463C23×C4C2411yescharacteristic
464C23×C4C2412yes—
465C23×C4C2418yes—
466C23×C4C2411yescharacteristic
467C23×C4C2414yes—
468C23×C4C2414yes—
469C23×C4C2414yes—
470C23×C4C2418yes—
471C23×C4C2414yes—
472C23×C4C2411yescharacteristic
473#127—216no—
474#125—88no—
475#124—216no—
476#123—416no—
477#123—88no—
478#123—88no—
479C22⋊Q8—48no—
480C22⋊Q8—48no—
481C22⋊Q8—48no—
482#121—216no—
483#121—216no—
484#121—48no—
485#121—48no—
486#121—88no—
487#120—232no—
488C4×Q8—44no—
489C4×Q8—44no—
490C4×Q8—44no—
491C4×Q8—44no—
492C4×Q8—44no—
493C4×Q8—44no—
494C4×D4—216no—
495C4×D4—216no—
496C4×D4—48no—
497C4×D4—48no—
498C4×D4—44no—
499C4×D4—44no—
500C4×D4—48no—
501C4×D4—48no—
502C4×D4—416no—
503C4×D4—48no—
504C4×D4—48no—
505C4×D4—88no—
506#117—28no—
507#117—28no—
508#117—28no—
509#117—48no—
510C2×C4⋊C4—24no—
511C2×C4⋊C4—28no—
512C2×C4⋊C4—42no—
513C2×C4⋊C4—44no—
514C2×C4⋊C4—88no—
515C2×C4⋊C4—84no—
516C2×C4⋊C4C2414yes—
517C2×C4⋊C4C2414yes—
518C2×C4⋊C4C2414yes—
519C2×C4⋊C4C2412yes—
520C2×C4⋊C4C2412yes—
521C2×C4⋊C4C2412yes—
522C2×C4⋊C4C2412yes—
523C2×C4⋊C4C2412yes—
524C2×C4⋊C4C2412yes—
525C2×C4⋊C4C2414yes—
526C2×C4⋊C4C2414yes—
527C2×C4⋊C4C2414yes—
528C2×C4⋊C4C2414yes—
529C2×C4⋊C4C2412yes—
530C2×C4⋊C4C2412yes—
531C2×C4⋊C4C2412yes—
532C2×C4⋊C4C2411yescharacteristic
533C2×C4⋊C4C2412yes—
534C2×C4⋊C4C2412yes—
535C2×C4⋊C4C2411yescharacteristic
536C2×C4⋊C4C2418yes—
537C2×C4⋊C4C2418yes—
538C2×C4⋊C4C2418yes—
539C2×C4⋊C4C2418yes—
540C2×C4⋊C4C2414yes—
541C2×C4⋊C4C2414yes—
542C2×C4⋊C4C2414yes—
543C2×C4⋊C4C2414yes—
544C2×C4⋊C4C2418yes—
545C2×C4⋊C4C2414yes—
546C2×C4⋊C4C2414yes—
547C2×C4⋊C4C2414yes—
548C2×C4⋊C4C2414yes—
549C2×C4⋊C4C2414yes—
550C2×C4⋊C4C2418yes—
551C2×C4⋊C4C2418yes—
552C2×C4⋊C4C2414yes—
553C2×C4⋊C4C2414yes—
554C2×C22⋊C4—216no—
555C2×C22⋊C4—48no—
556C2×C22⋊C4—48no—
557C2×C22⋊C4—44no—
558C2×C22⋊C4—84no—
559C2×C22⋊C4C2414yes—
560C2×C22⋊C4C2414yes—
561C2×C22⋊C4C2414yes—
562C2×C22⋊C4C2414yes—
563C2×C22⋊C4C2418yes—
564C2×C22⋊C4C2414yes—
565C2×C22⋊C4C2418yes—
566C2×C22⋊C4C2418yes—
567C2×C22⋊C4C2414yes—
568C2×C22⋊C4C2418yes—
569C2×C22⋊C4C2414yes—
570C2×C22⋊C4C2414yes—
571C2×C22⋊C4C2418yes—
572C2×C22⋊C4C2418yes—
573C2×C22⋊C4C2418yes—
574C2×C22⋊C4C2414yes—
575C2×C22⋊C4C2414yes—
576C2×C22⋊C4C2418yes—
577C2×C22⋊C4C2418yes—
578C2×C22⋊C4C2418yes—
579C2×C22⋊C4C2414yes—
580C2×C22⋊C4C2414yes—
581C2×C22⋊C4C2414yes—
582C2×C22⋊C4C2414yes—
583C2×C22⋊C4C2414yes—
584C2×C22⋊C4C2414yes—
585C2×C22⋊C4C2414yes—
586C2×C22⋊C4C2418yes—
587C2×C22⋊C4C2418yes—
588C2×C42—24no—
589C2×C42—28no—
590C2×C42—48no—
591C2×C42C2414yes—
592C2×C42C2412yes—
593C2×C42C2414yes—
594C2×C42C2414yes—
595C2×C42C2412yes—
596C2×C42C2412yes—
597C2×C42C2412yes—
598C2×C42C2412yes—
599C2×C42C2412yes—
600C2×C42C2414yes—
601C2×C42C2414yes—
602C2×C42C2418yes—
603C2×C42C2418yes—
604#95C2414yes—
605#95C2414yes—
606#95C2418yes—
607#95C2418yes—
608#95C2418yes—
609#95C2414yes—
610#95C2418yes—
611#95C2414yes—
612#95C2418yes—
613#95C2414yes—
614#95C2414yes—
615#95C2418yes—
616#95C2418yes—
617#95C2414yes—
618#95C2414yes—
619#95C2418yes—
620#95C2418yes—
621#95C2414yes—
622#95C2414yes—
623#95C2414yes—
624#95C2414yes—
625#95C2414yes—
626#95C2414yes—
627#95C2414yes—
628#95C2414yes—
629#95C2414yes—
630#95C2414yes—
631#95C2414yes—
632#95C2414yes—
633#95C2414yes—
634#95C2414yes—
635#95C2418yes—
636#95C2418yes—
637#95C2418yes—
638#95C2418yes—
639#95C2414yes—
640#95C2414yes—
641C24—24no—
642C24—24no—
643C24—44no—
644C24—44no—
645C24C2×#4118yes—
646C24C2514yes—
647C24C2514yes—
648C24C2511yescharacteristic
649#41—432no—
650C2×Q8—24no—
651C2×Q8—24no—
652C2×Q8—24no—
653C2×Q8—24no—
654C2×Q8—24no—
655C2×Q8—41no—
656C2×Q8—42no—
657C2×Q8—41no—
658C2×Q8—42no—
659C2×Q8—42no—
660C2×Q8—416no—
661C2×D4—28no—
662C2×D4—28no—
663C2×D4—28no—
664C2×D4—216no—
665C2×D4—216no—
666C2×D4—232no—
667C2×D4—24no—
668C2×D4—28no—
669C2×D4—24no—
670C2×D4—28no—
671C2×D4—24no—
672C2×D4—48no—
673C2×D4—48no—
674C2×D4—48no—
675C2×D4—48no—
676C2×D4—44no—
677C2×D4—48no—
678C2×D4C2×#41116yes—
679C22×C4—22no—
680C22×C4—22no—
681C22×C4—24no—
682C22×C4—216no—
683C22×C4—24no—
684C22×C4—24no—
685C22×C4—28no—
686C22×C4—28no—
687C22×C4—28no—
688C22×C4—28no—
689C22×C4—24no—
690C22×C4—28no—
691C22×C4—42no—
692C22×C4—42no—
693C22×C4—42no—
694C22×C4—44no—
695C22×C4—44no—
696C22×C4—44no—
697C22×C4—42no—
698C22×C4—44no—
699C22×C4—42no—
700C22×C4—48no—
701C22×C4—44no—
702C22×C4—48no—
703C22×C4—48no—
704C22×C4—44no—
705C22×C4—48no—
706C22×C4—44no—
707C22×C4—48no—
708C22×C4—44no—
709C22×C4—44no—
710C22×C4—44no—
711C22×C4—48no—
712C22×C4—48no—
713C22×C4—816no—
714C22×C4C2×#4114yes—
715C22×C4H(5,𝔽2)14yes—
716C22×C42−1+414yes—
717C22×C4C2514yes—
718C22×C4C2518yes—
719C22×C4C2514yes—
720C22×C4C2514yes—
721C22×C4C2514yes—
722C22×C4C2511yescharacteristic
723C22×C4C2511yescharacteristic
724C22×C4C2512yes—
725C22×C4C2512yes—
726C22×C4C2514yes—
727C22×C4C2514yes—
728C22×C4C2514yes—
729C22×C4C2512yes—
730C22×C4C2514yes—
731C22×C4C2512yes—
732C22×C4C2512yes—
733C22×C4C2512yes—
734C4⋊C4—24no—
735C4⋊C4—24no—
736C4⋊C4—24no—
737C4⋊C4—24no—
738C4⋊C4—28no—
739C4⋊C4—24no—
740C4⋊C4—24no—
741C4⋊C4—28no—
742C4⋊C4—28no—
743C4⋊C4—28no—
744C4⋊C4—28no—
745C4⋊C4—42no—
746C4⋊C4—42no—
747C4⋊C4—41no—
748C4⋊C4—42no—
749C4⋊C4—42no—
750C4⋊C4—41no—
751C4⋊C4—42no—
752C4⋊C4—44no—
753C4⋊C4—44no—
754C4⋊C4—48no—
755C4⋊C4—48no—
756C4⋊C4—48no—
757C4⋊C4—48no—
758C4⋊C4—44no—
759C4⋊C4—44no—
760C4⋊C4—44no—
761C4⋊C4—44no—
762C4⋊C4—48no—
763C4⋊C4—44no—
764C4⋊C4—44no—
765C4⋊C4—44no—
766C4⋊C4—44no—
767C4⋊C4—48no—
768C4⋊C4—44no—
769C4⋊C4—48no—
770C4⋊C4—44no—
771C4⋊C4—44no—
772C22⋊C4—28no—
773C22⋊C4—28no—
774C22⋊C4—28no—
775C22⋊C4—28no—
776C22⋊C4—216no—
777C22⋊C4—216no—
778C22⋊C4—28no—
779C22⋊C4—216no—
780C22⋊C4—28no—
781C22⋊C4—48no—
782C22⋊C4—44no—
783C22⋊C4—44no—
784C22⋊C4—48no—
785C22⋊C4—48no—
786C22⋊C4—48no—
787C22⋊C4—44no—
788C22⋊C4—44no—
789C22⋊C4—48no—
790C22⋊C4—48no—
791C22⋊C4—48no—
792C22⋊C4—44no—
793C22⋊C4—44no—
794C22⋊C4—44no—
795C22⋊C4—44no—
796C22⋊C4—44no—
797C22⋊C4—48no—
798C22⋊C4—48no—
799C22⋊C4—44no—
800C22⋊C4—44no—
801C42—28no—
802C42—28no—
803C42—24no—
804C42—24no—
805C42—24no—
806C42—24no—
807C42—24no—
808C42—24no—
809C42—28no—
810C42—44no—
811C42—44no—
812C42—48no—
813C42—48no—
814C23—22no—
815C23—22no—
816C23—24no—
817C23—24no—
818C23—28no—
819C23—28no—
820C23—216no—
821C23—24no—
822C23—24no—
823C23—24no—
824C23—24no—
825C23—24no—
826C23—24no—
827C23—24no—
828C23—416no—
829C23—84no—
830C23—84no—
831C23—88no—
832C23C22×#4118yes—
833C23C22×#4112yes—
834C23C2×H(5,𝔽2)12yes—
835C23C2×2−1+412yes—
836C23C2611yescharacteristic
837Q8—44no—
838Q8—48no—
839Q8—44no—
840Q8—48no—
841D4—232no—
842D4—416no—
843D4—48no—
844D4—816no—
845D4—816no—
846D4—164no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—24no—
850C2×C4—24no—
851C2×C4—24no—
852C2×C4—24no—
853C2×C4—24no—
854C2×C4—22no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—24no—
861C2×C4—24no—
862C2×C4—24no—
863C2×C4—24no—
864C2×C4—28no—
865C2×C4—24no—
866C2×C4—24no—
867C2×C4—24no—
868C2×C4—28no—
869C2×C4—24no—
870C2×C4—22no—
871C2×C4—24no—
872C2×C4—24no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—24no—
877C2×C4—24no—
878C2×C4—24no—
879C2×C4—28no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—24no—
884C2×C4—22no—
885C2×C4—24no—
886C2×C4—24no—
887C2×C4—24no—
888C2×C4—22no—
889C2×C4—28no—
890C2×C4—22no—
891C2×C4—48no—
892C2×C4—44no—
893C2×C4—44no—
894C2×C4—416no—
895C2×C4—88no—
896C2×C4—816no—
897C2×C4—84no—
898C2×C4—88no—
899C2×C4—84no—
900C2×C4—88no—
901C2×C4—816no—
902C2×C4—164no—
903C2×C4—164no—
904C2×C4#539116yes—
905C2×C4C22×#4114yes—
906C2×C4C2×H(5,𝔽2)14yes—
907C2×C4C2×2−1+414yes—
908C2×C4#58514yes—
909C22—24no—
910C22—22no—
911C22—22no—
912C22—24no—
913C22—216no—
914C22—28no—
915C22—44no—
916C22—44no—
917C22—48no—
918C22—44no—
919C22—44no—
920C22—44no—
921C22—44no—
922C22—44no—
923C22—44no—
924C22—44no—
925C22—816no—
926C22C2×#53914yes—
927C22C23×#4111yescharacteristic
928C22C22×H(5,𝔽2)11yescharacteristic
929C22C22×2−1+411yescharacteristic
930C22C2×#58512yes—
931C22H(7,𝔽2)12yes—
932C4—24no—
933C4—44no—
934C4—44no—
935C4—44no—
936C4—44no—
937C4—41no—
938C4—41no—
939C4—42no—
940C4—44no—
941C4—42no—
942C4—42no—
943C4—42no—
944C4—44no—
945C4—44no—
946C4—44no—
947C4—48no—
948C4C2×#53918yes—
949C2—24no—
950C2—48no—
951C2—84no—
952C2C22×#53911yescharacteristic
953C2#6282111yescharacteristic
954C2#6287411yescharacteristic
955C2#6296212yes—
956C2#6299212yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35168C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #42724C2semidirect
2. #42605C2semidirect
3. #42592C2semidirect
4. #42572C2semidirect
5. #40663C2semidirect
6. #40658C2semidirect
7. #40172C2semidirect
8. #40045C2semidirect
9. #39536C2semidirect
10. #39005C2semidirect
11. #38121C2semidirect
12. #35629C2semidirect
13. #35585C2semidirect
14. #35541C2semidirect
15. #35255C2semidirect
17. #34952C2semidirect
18. C2×#2580C2semidirect
19. #34269C2semidirect
20. #34248C2semidirect
28. #2855C22semidirect
29. #2854C22semidirect
31. #2835C22semidirect
32. #2834C22semidirect
33. #2826C22semidirect
34. #2824C22semidirect
35. #2796C22semidirect
36. #2787C22semidirect
37. #2782C22semidirect
38. #2770C22semidirect
39. #2757C22semidirect
40. #2746C22semidirect
41. #2746C22semidirect
42. #2745C22semidirect
43. #2738C22semidirect
44. #2737C22semidirect
45. #2711C22semidirect
46. #2708C22semidirect
47. #2706C22semidirect
48. #2696C22semidirect
49. #2694C22semidirect
50. #2687C22semidirect
51. #2653C22semidirect
52. #2649C22semidirect
53. #2643C22semidirect
54. #2638C22semidirect
55. #2633C22semidirect
56. #2625C22semidirect
57. #2624C22semidirect
58. #2623C22semidirect
60. #2582C22semidirect
61. #2582C22semidirect
62. #2581C22semidirect
63. #2581C22semidirect
68. #2580C22semidirect
69. #2580C22semidirect
73. #2538C22semidirect
74. #2538C22semidirect
75. #2523C22semidirect
76. #2517C22semidirect
77. #2514C22semidirect
78. #2514C22semidirect
79. #2513C22semidirect
80. #2513C22semidirect
83. #2509C22semidirect
84. #2509C22semidirect
85. #2508C22semidirect
86. #2508C22semidirect
87. #2507C22semidirect
88. #2507C22semidirect
89. #2506C22semidirect
90. #2506C22semidirect
91. #2495C22semidirect
92. #2495C22semidirect
93. #2494C22semidirect
94. #2494C22semidirect
95. #2493C22semidirect
97. #2473C22semidirect
98. #2463C22semidirect
99. #2455C22semidirect
106. #2443C22semidirect
112. #2425C22semidirect
113. #2423C22semidirect
116. #2422C22semidirect
117. #2421C22semidirect
120. #2420C22semidirect
124. #2396C22semidirect
125. #2396C22semidirect
140. #2322C22semidirect
141. #2318C22semidirect
148. C4×C22⋊Q8C22semidirect
149. C4×C22⋊Q8C22semidirect

Maximal subgroups

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

subgroupindex
#427242
#426052
#425922
#425722
#406632
#406582
#401722
#400452
#395362
#390052
#381212
#356292
#355852
#355412
#352552
#351682
#349522
C2×#25802
#342692
#342482