Finite Group Databasebeta

← #7652128

Subgroups — #7652128

Order 512.

5580 conjugacy classes of subgroups.

The subgroup lattice has 1048 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42894C214yesmaximal, complemented
2#42862C214yesmaximal, complemented
3#42855C214yesmaximal, complemented
4#42852C214yesmaximal, complemented
5#42012C218yesmaximal, complemented
6#40221C214yesmaximal, complemented
7#40118C214yesmaximal, complemented
8#39666C214yesmaximal, complemented
9#39244C214yesmaximal, complemented
10#38467C214yesmaximal, complemented
11#38466C214yesmaximal, complemented
12#35659C212yesmaximal, complemented
13#35557C212yesmaximal, complemented
14#35542C212yesmaximal, complemented
15#35263C212yesmaximal, complemented
16#35154C211yesmaximal, characteristic, complemented
17C2×#2538C211yesmaximal, characteristic, complemented
18#34737C212yesmaximal, complemented
19#34257C211yesmaximal, characteristic, complemented
20#34203C212yesmaximal, complemented
21C22×2−1+4C2211yescharacteristic
22C2×#544C2211yescharacteristic
23C2×#525C2212yes—
24C2×#525C2212yes—
25C22×C22⋊Q8C2212yes—
26C2×#519C2211yescharacteristic
27C22×C4×Q8C2211yescharacteristic
28C22×C4×D4C2211yescharacteristic
29C22×#117C2212yes—
30#2855C2214yes—
31#2855C2214yescomplemented
32#2854C2214yescomplemented
33#2831C2218yescomplemented
34#2829C2218yescomplemented
35#2808C2214yes—
36#2808C2214yescomplemented
37#2806C2214yescomplemented
38#2805C2214yescomplemented
39#2804C2214yes—
40#2800C2218yescomplemented
41#2786C2218yescomplemented
42#2784C2218yescomplemented
43#2781C2218yescomplemented
44#2780C2218yescomplemented
45#2779C2218yescomplemented
46#2774C2218yescomplemented
47#2751C2218yes—
48#2750C2218yescomplemented
49#2733C2214yes—
50#2727C2214yescomplemented
51#2715C2218yescomplemented
52#2714C2218yes—
53#2695C2218yescomplemented
54#2682C2214yes—
55#2665C2218yescomplemented
56#2662C2218yescomplemented
57#2652C2218yescomplemented
58#2650C2218yescomplemented
59#2648C2218yes—
60#2648C2218yescomplemented
61#2627C2214yes—
62#2625C2214yescomplemented
63#2624C2214yescomplemented
64#2589C2218yescomplemented
65#2587C2218yescomplemented
66#2574C2218yescomplemented
67#2563C2214yescomplemented
68#2562C2214yescomplemented
69#2562C2214yescomplemented
70#2559C2218yes—
71#2557C2218yes—
72#2554C2218yescomplemented
73#2547C2214yescomplemented
74#2538C2214yes—
75#2538C2214yes—
76#2538C2214yes—
77#2538C2214yes—
78#2512C2214yescomplemented
79#2512C2214yescomplemented
80#2511C2214yescomplemented
81#2511C2214yescomplemented
82#2498C2218yes—
83#2497C2214yescomplemented
84#2497C2214yescomplemented
85#2496C2214yescomplemented
86#2496C2214yescomplemented
87#2492C2214yescomplemented
88#2491C2214yescomplemented
89#2490C2214yescomplemented
90#2489C2214yescomplemented
91#2488C2218yes—
92#2487C2214yescomplemented
93#2486C2214yescomplemented
94#2485C2214yescomplemented
95#2485C2214yescomplemented
96#2481C2218yes—
97#2481C2218yes—
98#2472C2218yes—
99#2453C2214yescomplemented
100#2453C2214yescomplemented
101#2451C2214yescomplemented
102#2451C2214yescomplemented
103#2417C2212yes—
104#2417C2212yes—
105#2416C2212yes—
106#2416C2212yes—
107#2415C2212yes—
108#2415C2212yes—
109#2414C2212yes—
110#2414C2212yes—
111#2413C2214yes—
112#2412C2214yes—
113#2412C2218yes—
114#2411C2214yes—
115#2410C2214yes—
116#2409C2214yescomplemented
117#2409C2214yescomplemented
118#2409C2214yescomplemented
119#2409C2214yescomplemented
120#2407C2214yescomplemented
121#2407C2214yescomplemented
122#2407C2214yescomplemented
123#2407C2214yescomplemented
124#2406C2218yes—
125#2404C2218yes—
126#2392C2214yes—
127#2392C2214yes—
128C2×#396C2214yes—
129#2362C2214yescomplemented
130#2362C2214yescomplemented
131#2360C2214yescomplemented
132#2360C2214yescomplemented
133#2344C2218yes—
134#2342C2218yes—
135#2341C2214yescomplemented
136#2341C2214yescomplemented
137Q8×C22⋊C4C2214yescomplemented
138Q8×C22⋊C4C2214yescomplemented
139#2334C2218yescomplemented
140#2333C2218yes—
141#2323C2214yescomplemented
142#2323C2214yescomplemented
143#2316C2211yescharacteristic
144#2316C2212yes—
145#2311C2214yes—
146#2311C2212yes—
147#2311C2212yes—
148#2311C2212yes—
149#2310C2212yes—
150C4×C22⋊Q8C2214yescomplemented
151C4×C22⋊Q8C2214yescomplemented
152C4×#121C2214yes—
153C4×#121C2214yes—
154#2297C2214yes—
155#2297C2212yes—
156#2296C2212yes—
157C2×#390C2212yes—
158C2×#389C2212yes—
159C2×#384C2211yescharacteristic
160#2280C2212yes—
161C2×#380C2212yes—
162#2274C2212yes—
163C2×2−1+4—28no—
164C2×2−1+4—44no—
165C2×2−1+4—44no—
166C22×#41C2312yes—
167C22×#41C2314yes—
168C22×#41C2314yes—
169C23×Q8C2311yescharacteristic
170C23×Q8C2314yes—
171C23×D4C2311yescharacteristic
172C24×C4C2312yes—
173#544—44no—
174C2×C4⋊Q8C2314yes—
175C2×#126C2318yes—
176C2×#126C2318yes—
177C2×#125C2314yes—
178C2×#124C2318yes—
179#525—48no—
180#525—48no—
181C2×#123C2314yes—
182C2×#123C2314yes—
183C2×#123C2318yes—
184C2×C22⋊Q8—216no—
185C2×C22⋊Q8C2314yes—
186C2×C22⋊Q8C2314yes—
187C2×C22⋊Q8C2314yes—
188C2×C22⋊Q8C2314yes—
189C2×C22⋊Q8C2314yes—
190C2×C22⋊Q8C2312yes—
191C2×C22⋊Q8C2312yes—
192C2×C22⋊Q8C2312yes—
193C2×C22⋊Q8C2312yes—
194C2×#121C2314yes—
195C2×#121C2312yes—
196C2×#121C2312yes—
197C2×#121C2312yes—
198C2×#121C2312yes—
199C2×#121C2314yes—
200C2×#120C2314yes—
201C2×#120C2314yes—
202#519—44no—
203C2×C4×Q8—44no—
204C2×C4×Q8C2314yes—
205C2×C4×Q8C2314yes—
206C2×C4×Q8C2314yes—
207C2×C4×Q8C2314yes—
208C2×C4×D4—44no—
209C2×C4×D4C2314yes—
210C2×C4×D4C2314yes—
211C2×C4×D4C2312yes—
212C2×C4×D4C2312yes—
213C2×C4×D4C2314yes—
214C2×C4×D4C2314yes—
215C2×C4×D4C2312yes—
216C2×C4×D4C2312yes—
217C2×#117—48no—
218C2×#117C2312yes—
219C2×#117C2312yes—
220C2×#117C2312yes—
221C2×#117C2314yes—
222C2×#117C2314yes—
223C2×#117C2314yes—
224C2×#117C2312yes—
225C2×#117C2312yes—
226C22×C4⋊C4C2311yescharacteristic
227C22×C4⋊C4C2312yes—
228C22×C4⋊C4C2314yes—
229C22×C4⋊C4C2312yes—
230C22×C4⋊C4C2312yes—
231C22×C4⋊C4C2312yes—
232C22×C4⋊C4C2311yescharacteristic
233C22×C4⋊C4C2312yes—
234C22×C4⋊C4C2312yes—
235C22×C22⋊C4C2314yes—
236C22×C22⋊C4C2314yes—
237C22×C22⋊C4C2312yes—
238C22×C22⋊C4C2314yes—
239C22×C42C2311yescharacteristic
240C22×C42C2314yes—
241C22×C42C2312yes—
242#400C2318yes—
243#400C2318yes—
244#400C2318yes—
245#400C2318yes—
246#400C2318yes—
247#400C2318yes—
248#400C2318yes—
249#400C2318yes—
250#399C2318yes—
251#398C2318yes—
252#398C2318yes—
253#398C2318yes—
254#398C2314yes—
255#398C2314yes—
256#397C2318yes—
257#397C2318yes—
258#397C2314yes—
259#397C2318yes—
260#397C2318yes—
261#397C2318yes—
262#397C2318yes—
263#397C2314yes—
264#397C2318yes—
265#396C2318yes—
266#396C2318yes—
267#396C2318yes—
268#396C2314yes—
269#396C2314yes—
270#396C2318yes—
271#396C2318yes—
272#396C2318yes—
273#396C2314yes—
274#396C2314yes—
275#395C2318yes—
276#395C2318yes—
277#395C2318yes—
278#394C2318yes—
279#394C2318yes—
280#394C2314yes—
281#394C2314yes—
282#394C2318yes—
283#394C2318yes—
284#394C2318yes—
285#394C2314yes—
286#394C2314yes—
287#394C2314yes—
288#394C2314yes—
289#394C2318yes—
290#393C2318yes—
291#393C2318yes—
292#393C2318yes—
293#393C2318yes—
294#392C2318yes—
295#392C2314yes—
296#392C2314yes—
297#392C2318yes—
298#391C2314yes—
299#391C2314yes—
300#391C2314yes—
301#391C2314yes—
302#391C2318yes—
303#391C2314yes—
304#391C2314yes—
305#391C2314yes—
306#391C2314yes—
307#391C2318yes—
308#391C2312yes—
309#391C2312yes—
310#391C2314yes—
311#391C2314yes—
312#391C2314yes—
313#390C2318yes—
314#390C2318yes—
315#390C2314yes—
316#390C2314yes—
317#390C2314yes—
318#390C2314yes—
319#390C2312yes—
320#390C2312yes—
321#390C2314yes—
322#390C2314yes—
323#390C2314yes—
324#390C2314yes—
325#390C2314yes—
326#390C2318yes—
327#389C2314yes—
328#389C2314yes—
329#389C2314yes—
330#389C2314yes—
331#389C2314yes—
332#389C2314yes—
333#389C2318yes—
334#389C2318yes—
335#389C2314yes—
336#389C2314yes—
337#389C2318yes—
338#389C2314yes—
339#389C2314yes—
340#389C2314yes—
341#389C2314yes—
342#389C2312yes—
343#389C2312yes—
344#389C2312yes—
345#389C2312yes—
346#388C2318yes—
347#388C2318yes—
348#388C2318yes—
349#388C2318yes—
350#388C2318yes—
351#388C2314yes—
352#388C2318yes—
353#388C2318yes—
354#388C2318yes—
355#388C2318yes—
356#388C2318yes—
357#388C2314yes—
358#388C2314yes—
359#388C2318yes—
360#388C2318yes—
361#388C2314yes—
362#387C2318yes—
363#387C2318yes—
364#387C2318yes—
365#387C2318yes—
366#387C2318yes—
367#387C2318yes—
368#387C2318yes—
369#387C2318yes—
370#387C2318yes—
371#387C2318yes—
372#387C2318yes—
373#387C2318yes—
374#386C2314yes—
375#386C2318yes—
376#386C2318yes—
377#386C2318yes—
378#386C2314yes—
379#386C2318yes—
380#386C2318yes—
381#386C2318yes—
382#386C2318yes—
383#386C2318yes—
384#386C2314yes—
385#386C2314yes—
386#386C2314yes—
387#386C2314yes—
388#385C2318yes—
389#385C2318yes—
390#385C2318yes—
391#385C2318yes—
392#385C2318yes—
393#385C2318yes—
394#385C2318yes—
395#385C2314yes—
396#385C2314yes—
397#384C2314yes—
398#384C2314yes—
399#382C2318yes—
400#381C2318yes—
401#381C2318yes—
402#381C2314yes—
403#380C2314yes—
404#380C2312yes—
405#380C2312yes—
406#380C2314yes—
407#380C2314yes—
408#380C2314yes—
409#380C2314yes—
410#380C2312yes—
411#380C2314yes—
412#380C2318yes—
413#380C2318yes—
414#380C2314yes—
415#380C2314yes—
416#380C2318yes—
417#380C2314yes—
418#380C2314yes—
419#380C2312yes—
420#380C2314yes—
421#380C2314yes—
422#380C2314yes—
423#379C2314yes—
424C4×C4⋊C4C2314yes—
425C4×C4⋊C4C2314yes—
426C4×C4⋊C4C2318yes—
427C4×C4⋊C4C2314yes—
428C4×C4⋊C4C2314yes—
429C4×C4⋊C4C2318yes—
430C4×C4⋊C4C2314yes—
431C4×C4⋊C4C2314yes—
432C4×C22⋊C4C2318yes—
433C4×C22⋊C4C2318yes—
434C4×C22⋊C4C2318yes—
435C4×C22⋊C4C2318yes—
436C4×C22⋊C4C2314yes—
437C4×C22⋊C4C2314yes—
438C4×C22⋊C4C2318yes—
439C4×C22⋊C4C2314yes—
440C4×C22⋊C4C2314yes—
441C2×#95C2314yes—
442C25C2412yes—
4432−1+4—464no—
444C2×#41—216no—
445C2×#41—216no—
446C2×#41—28no—
447C2×#41—28no—
448C2×#41—28no—
449C2×#41—48no—
450C2×#41—48no—
451C2×#41—48no—
452C2×#41—48no—
453C22×Q8—216no—
454C22×Q8—24no—
455C22×Q8—24no—
456C22×Q8—48no—
457C22×Q8—48no—
458C22×Q8#4118yes—
459C22×Q8C2412yes—
460C22×Q8C2414yes—
461C22×Q8C2414yes—
462C22×Q8C2414yes—
463C22×D4—24no—
464C22×D4—42no—
465C22×D4—42no—
466C22×D4C2414yes—
467C22×D4C2412yes—
468C22×D4C2412yes—
469C22×D4C2411yescharacteristic
470C22×D4C2414yes—
471C22×D4C2414yes—
472C22×D4C2414yes—
473C22×D4C2414yes—
474C22×D4C2414yes—
475C22×D4C2411yescharacteristic
476C23×C4—28no—
477C23×C4—28no—
478C23×C4—28no—
479C23×C4C2412yes—
480C23×C4C2411yescharacteristic
481C23×C4C2412yes—
482C23×C4C2412yes—
483C23×C4C2412yes—
484C23×C4C2412yes—
485C23×C4C2414yes—
486C23×C4C2412yes—
487C23×C4C2414yes—
488C23×C4C2411yescharacteristic
489C23×C4C2412yes—
490C23×C4C2414yes—
491C23×C4C2418yes—
492C23×C4C2414yes—
493C23×C4C2411yescharacteristic
494C4⋊Q8—48no—
495#126—416no—
496#126—88no—
497#125—48no—
498#124—88no—
499#123—48no—
500#123—48no—
501#123—88no—
502C22⋊Q8—216no—
503C22⋊Q8—216no—
504C22⋊Q8—216no—
505C22⋊Q8—216no—
506C22⋊Q8—48no—
507C22⋊Q8—44no—
508C22⋊Q8—44no—
509C22⋊Q8—44no—
510C22⋊Q8—44no—
511#121—216no—
512#121—48no—
513#121—44no—
514#121—44no—
515#121—44no—
516#121—44no—
517#120—48no—
518#120—48no—
519C4×Q8—48no—
520C4×Q8—48no—
521C4×Q8—48no—
522C4×Q8—48no—
523C4×D4—44no—
524C4×D4—44no—
525C4×D4—44no—
526C4×D4—44no—
527C4×D4—48no—
528C4×D4—48no—
529C4×D4—48no—
530C4×D4—48no—
531#117—28no—
532#117—28no—
533#117—28no—
534#117—48no—
535#117—48no—
536#117—48no—
537#117—44no—
538#117—44no—
539C2×C4⋊C4—216no—
540C2×C4⋊C4—28no—
541C2×C4⋊C4—24no—
542C2×C4⋊C4—44no—
543C2×C4⋊C4—44no—
544C2×C4⋊C4—44no—
545C2×C4⋊C4—42no—
546C2×C4⋊C4—44no—
547C2×C4⋊C4—82no—
548C2×C4⋊C4C2412yes—
549C2×C4⋊C4C2412yes—
550C2×C4⋊C4C2412yes—
551C2×C4⋊C4C2412yes—
552C2×C4⋊C4C2414yes—
553C2×C4⋊C4C2414yes—
554C2×C4⋊C4C2414yes—
555C2×C4⋊C4C2418yes—
556C2×C4⋊C4C2418yes—
557C2×C4⋊C4C2414yes—
558C2×C4⋊C4C2412yes—
559C2×C4⋊C4C2412yes—
560C2×C4⋊C4C2414yes—
561C2×C4⋊C4C2414yes—
562C2×C4⋊C4C2414yes—
563C2×C4⋊C4C2414yes—
564C2×C4⋊C4C2411yescharacteristic
565C2×C4⋊C4C2412yes—
566C2×C4⋊C4C2411yescharacteristic
567C2×C4⋊C4C2418yes—
568C2×C4⋊C4C2418yes—
569C2×C4⋊C4C2414yes—
570C2×C4⋊C4C2414yes—
571C2×C4⋊C4C2414yes—
572C2×C4⋊C4C2414yes—
573C2×C4⋊C4C2414yes—
574C2×C4⋊C4C2414yes—
575C2×C4⋊C4C2414yes—
576C2×C4⋊C4C2414yes—
577C2×C4⋊C4C2418yes—
578C2×C4⋊C4C2414yes—
579C2×C4⋊C4C2418yes—
580C2×C4⋊C4C2414yes—
581C2×C4⋊C4C2418yes—
582C2×C4⋊C4C2414yes—
583C2×C4⋊C4C2414yes—
584C2×C22⋊C4—216no—
585C2×C22⋊C4—48no—
586C2×C22⋊C4—44no—
587C2×C22⋊C4—84no—
588C2×C22⋊C4C2414yes—
589C2×C22⋊C4C2414yes—
590C2×C22⋊C4C2418yes—
591C2×C22⋊C4C2418yes—
592C2×C22⋊C4C2414yes—
593C2×C22⋊C4C2414yes—
594C2×C22⋊C4C2414yes—
595C2×C22⋊C4C2414yes—
596C2×C22⋊C4C2414yes—
597C2×C22⋊C4C2414yes—
598C2×C22⋊C4C2412yes—
599C2×C22⋊C4C2412yes—
600C2×C22⋊C4C2412yes—
601C2×C22⋊C4C2412yes—
602C2×C22⋊C4C2418yes—
603C2×C22⋊C4C2418yes—
604C2×C22⋊C4C2414yes—
605C2×C22⋊C4C2414yes—
606C2×C22⋊C4C2414yes—
607C2×C22⋊C4C2414yes—
608C2×C22⋊C4C2414yes—
609C2×C22⋊C4C2414yes—
610C2×C22⋊C4C2414yes—
611C2×C22⋊C4C2414yes—
612C2×C22⋊C4C2414yes—
613C2×C22⋊C4C2418yes—
614C2×C22⋊C4C2418yes—
615C2×C22⋊C4C2414yes—
616C2×C22⋊C4C2418yes—
617C2×C22⋊C4C2414yes—
618C2×C22⋊C4C2418yes—
619C2×C22⋊C4C2418yes—
620C2×C22⋊C4C2414yes—
621C2×C22⋊C4C2418yes—
622C2×C22⋊C4C2414yes—
623C2×C42—24no—
624C2×C42—48no—
625C2×C42—44no—
626C2×C42C2414yes—
627C2×C42C2414yes—
628C2×C42C2414yes—
629C2×C42C2412yes—
630C2×C42C2412yes—
631C2×C42C2414yes—
632C2×C42C2414yes—
633C2×C42C2418yes—
634C2×C42C2414yes—
635C2×C42C2414yes—
636C2×C42C2418yes—
637C2×C42C2418yes—
638#95C2418yes—
639#95C2418yes—
640#95C2414yes—
641#95C2414yes—
642#95C2414yes—
643#95C2414yes—
644#95C2418yes—
645#95C2418yes—
646#95C2414yes—
647#95C2414yes—
648#95C2418yes—
649#95C2414yes—
650#95C2418yes—
651#95C2414yes—
652#95C2418yes—
653#95C2418yes—
654#95C2418yes—
655#95C2418yes—
656#95C2418yes—
657#95C2418yes—
658#95C2414yes—
659#95C2414yes—
660#95C2414yes—
661#95C2414yes—
662#95C2418yes—
663#95C2418yes—
664#95C2418yes—
665#95C2418yes—
666#95C2418yes—
667C24—24no—
668C24—24no—
669C24—24no—
670C24—24no—
671C24—42no—
672C24—42no—
673C24—42no—
674C24C2512yes—
675C24C2514yes—
676C24C2512yes—
677C24C2511yescharacteristic
678#41—464no—
679#41—464no—
680#41—432no—
681C2×Q8—232no—
682C2×Q8—28no—
683C2×Q8—24no—
684C2×Q8—28no—
685C2×Q8—28no—
686C2×Q8—24no—
687C2×Q8—24no—
688C2×Q8—44no—
689C2×Q8—44no—
690C2×Q8—44no—
691C2×Q8—44no—
692C2×Q8—44no—
693C2×Q8—464no—
694C2×Q8C2×#41116yes—
695C2×D4—28no—
696C2×D4—28no—
697C2×D4—28no—
698C2×D4—24no—
699C2×D4—28no—
700C2×D4—28no—
701C2×D4—28no—
702C2×D4—24no—
703C2×D4—24no—
704C2×D4—24no—
705C2×D4—22no—
706C2×D4—24no—
707C2×D4—41no—
708C2×D4—42no—
709C2×D4—41no—
710C2×D4—41no—
711C2×D4—41no—
712C2×D4—44no—
713C2×D4—44no—
714C2×D4—416no—
715C2×D4—44no—
716C2×D4—44no—
717C2×D4—44no—
718C2×D4—44no—
719C2×D4—44no—
720C2×D4—44no—
721C2×D4—44no—
722C2×D4—44no—
723C2×D4—44no—
724C2×D4—44no—
725C2×D42−1+414yescomplemented
726C22×C4—22no—
727C22×C4—24no—
728C22×C4—24no—
729C22×C4—22no—
730C22×C4—22no—
731C22×C4—24no—
732C22×C4—22no—
733C22×C4—24no—
734C22×C4—24no—
735C22×C4—28no—
736C22×C4—24no—
737C22×C4—28no—
738C22×C4—24no—
739C22×C4—24no—
740C22×C4—24no—
741C22×C4—24no—
742C22×C4—216no—
743C22×C4—28no—
744C22×C4—24no—
745C22×C4—24no—
746C22×C4—24no—
747C22×C4—24no—
748C22×C4—24no—
749C22×C4—24no—
750C22×C4—24no—
751C22×C4—24no—
752C22×C4—28no—
753C22×C4—28no—
754C22×C4—41no—
755C22×C4—41no—
756C22×C4—48no—
757C22×C4—48no—
758C22×C4—44no—
759C22×C4—44no—
760C22×C4—42no—
761C22×C4—44no—
762C22×C4—44no—
763C22×C4—44no—
764C22×C4—44no—
765C22×C4—44no—
766C22×C4—42no—
767C22×C4—432no—
768C22×C4C2×#4118yes—
769C22×C4C2×#4114yes—
770C22×C4H(5,𝔽2)14yes—
771C22×C4H(5,𝔽2)14yes—
772C22×C4C2514yes—
773C22×C4C2514yes—
774C22×C4C2514yes—
775C22×C4C2514yes—
776C22×C4C2514yes—
777C22×C4C2514yes—
778C22×C4C2514yes—
779C22×C4C2518yes—
780C22×C4C2514yes—
781C22×C4C2512yes—
782C22×C4C2512yes—
783C22×C4C2512yes—
784C22×C4C2514yes—
785C22×C4C2511yescharacteristic
786C22×C4C2511yescharacteristic
787C22×C4C2512yes—
788C4⋊C4—28no—
789C4⋊C4—28no—
790C4⋊C4—216no—
791C4⋊C4—216no—
792C4⋊C4—28no—
793C4⋊C4—24no—
794C4⋊C4—24no—
795C4⋊C4—24no—
796C4⋊C4—24no—
797C4⋊C4—24no—
798C4⋊C4—24no—
799C4⋊C4—28no—
800C4⋊C4—28no—
801C4⋊C4—28no—
802C4⋊C4—44no—
803C4⋊C4—44no—
804C4⋊C4—44no—
805C4⋊C4—41no—
806C4⋊C4—42no—
807C4⋊C4—41no—
808C4⋊C4—48no—
809C4⋊C4—48no—
810C4⋊C4—44no—
811C4⋊C4—44no—
812C4⋊C4—44no—
813C4⋊C4—44no—
814C4⋊C4—44no—
815C4⋊C4—44no—
816C4⋊C4—44no—
817C4⋊C4—44no—
818C4⋊C4—44no—
819C4⋊C4—48no—
820C4⋊C4—44no—
821C4⋊C4—48no—
822C4⋊C4—48no—
823C4⋊C4—44no—
824C22⋊C4—28no—
825C22⋊C4—28no—
826C22⋊C4—28no—
827C22⋊C4—28no—
828C22⋊C4—216no—
829C22⋊C4—216no—
830C22⋊C4—28no—
831C22⋊C4—28no—
832C22⋊C4—44no—
833C22⋊C4—44no—
834C22⋊C4—42no—
835C22⋊C4—42no—
836C22⋊C4—42no—
837C22⋊C4—42no—
838C22⋊C4—48no—
839C22⋊C4—48no—
840C22⋊C4—44no—
841C22⋊C4—48no—
842C22⋊C4—44no—
843C22⋊C4—44no—
844C22⋊C4—44no—
845C22⋊C4—44no—
846C22⋊C4—44no—
847C22⋊C4—44no—
848C22⋊C4—44no—
849C22⋊C4—44no—
850C22⋊C4—44no—
851C22⋊C4—44no—
852C22⋊C4—48no—
853C22⋊C4—48no—
854C22⋊C4—44no—
855C22⋊C4—48no—
856C22⋊C4—48no—
857C22⋊C4—48no—
858C22⋊C4—44no—
859C42—24no—
860C42—24no—
861C42—28no—
862C42—28no—
863C42—28no—
864C42—44no—
865C42—44no—
866C42—44no—
867C42—44no—
868C42—48no—
869C42—48no—
870C42—48no—
871C23—21no—
872C23—21no—
873C23—21no—
874C23—21no—
875C23—22no—
876C23—22no—
877C23—22no—
878C23—22no—
879C23—22no—
880C23—22no—
881C23—22no—
882C23—24no—
883C23—22no—
884C23—22no—
885C23—24no—
886C23—24no—
887C23—24no—
888C23—22no—
889C23—24no—
890C23—22no—
891C23—24no—
892C23—22no—
893C23—24no—
894C23—22no—
895C23—48no—
896C23—48no—
897C23—48no—
898C23—48no—
899C23—84no—
900C23—84no—
901C23—84no—
902C23C22×#4112yes—
903C23C2×H(5,𝔽2)12yes—
904C23C2×H(5,𝔽2)12yes—
905C23C2×2−1+414yes—
906C23C2611yescharacteristic
907Q8—232no—
908Q8—416no—
909Q8—48no—
910Q8—164no—
911D4—44no—
912D4—48no—
913D4—44no—
914D4—416no—
915D4—416no—
916D4—48no—
917D4—88no—
918D4—88no—
919D4—88no—
920D4—88no—
921C2×C4—28no—
922C2×C4—21no—
923C2×C4—21no—
924C2×C4—24no—
925C2×C4—24no—
926C2×C4—21no—
927C2×C4—21no—
928C2×C4—216no—
929C2×C4—28no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—24no—
933C2×C4—22no—
934C2×C4—24no—
935C2×C4—24no—
936C2×C4—24no—
937C2×C4—24no—
938C2×C4—24no—
939C2×C4—24no—
940C2×C4—22no—
941C2×C4—24no—
942C2×C4—22no—
943C2×C4—22no—
944C2×C4—22no—
945C2×C4—24no—
946C2×C4—24no—
947C2×C4—24no—
948C2×C4—24no—
949C2×C4—24no—
950C2×C4—24no—
951C2×C4—24no—
952C2×C4—28no—
953C2×C4—24no—
954C2×C4—24no—
955C2×C4—24no—
956C2×C4—28no—
957C2×C4—24no—
958C2×C4—22no—
959C2×C4—24no—
960C2×C4—24no—
961C2×C4—22no—
962C2×C4—24no—
963C2×C4—24no—
964C2×C4—24no—
965C2×C4—432no—
966C2×C4—44no—
967C2×C4—48no—
968C2×C4—48no—
969C2×C4—48no—
970C2×C4—48no—
971C2×C4—48no—
972C2×C4—416no—
973C2×C4—88no—
974C2×C4—84no—
975C2×C4—88no—
976C2×C4—88no—
977C2×C4#538116yes—
978C2×C4C22×#4118yes—
979C2×C4C22×#4114yes—
980C2×C4C2×H(5,𝔽2)14yes—
981C2×C4C2×H(5,𝔽2)14yes—
982C2×C4C2×2−1+412yes—
983C2×C4#58512yes—
984C22—22no—
985C22—22no—
986C22—22no—
987C22—22no—
988C22—22no—
989C22—22no—
990C22—24no—
991C22—24no—
992C22—24no—
993C22—42no—
994C22—42no—
995C22—42no—
996C22—42no—
997C22—44no—
998C22—42no—
999C22—44no—
1000C22—42no—
1001C22—42no—
1002C22—44no—
1003C22—42no—
1004C22—44no—
1005C22—44no—
1006C22—42no—
1007C22—44no—
1008C22—42no—
1009C22—42no—
1010C22—44no—
1011C22—816no—
1012C22C2×#53814yes—
1013C22C23×#4111yescharacteristic
1014C22C22×H(5,𝔽2)11yescharacteristic
1015C22C22×H(5,𝔽2)11yescharacteristic
1016C22C22×2−1+411yescharacteristic
1017C22C2×#58511yescharacteristic
1018C22H(7,𝔽2)11yescharacteristic
1019C222−1+611yescharacteristic
1020C4—22no—
1021C4—22no—
1022C4—28no—
1023C4—48no—
1024C4—44no—
1025C4—42no—
1026C4—44no—
1027C4—44no—
1028C4—42no—
1029C4—42no—
1030C4—44no—
1031C4—44no—
1032C4—44no—
1033C4—44no—
1034C4—44no—
1035C4C2×#53818yes—
1036C2—24no—
1037C2—44no—
1038C2—84no—
1039C2—82no—
1040C2C22×#53811yescharacteristic
1041C2#6281911yescharacteristic
1042C2#6287511yescharacteristic
1043C2#6294411yescharacteristic
1044C2#6296011yescharacteristic
1045C2#6299811yescharacteristic
1046C2#6300611yescharacteristic
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. #42894C2semidirect
2. #42862C2semidirect
3. #42855C2semidirect
4. #42852C2semidirect
5. #42012C2semidirect
6. #40221C2semidirect
7. #40118C2semidirect
8. #39666C2semidirect
9. #39244C2semidirect
10. #38467C2semidirect
11. #38466C2semidirect
12. #35659C2semidirect
13. #35557C2semidirect
14. #35542C2semidirect
15. #35263C2semidirect
16. #35154C2semidirect
17. C2×#2538C2semidirect
18. #34737C2semidirect
19. #34257C2semidirect
20. #34203C2semidirect
31. #2855C22semidirect
32. #2854C22semidirect
33. #2831C22semidirect
34. #2829C22semidirect
36. #2808C22semidirect
37. #2806C22semidirect
38. #2805C22semidirect
40. #2800C22semidirect
41. #2786C22semidirect
42. #2784C22semidirect
43. #2781C22semidirect
44. #2780C22semidirect
45. #2779C22semidirect
46. #2774C22semidirect
48. #2750C22semidirect
50. #2727C22semidirect
51. #2715C22semidirect
53. #2695C22semidirect
55. #2665C22semidirect
56. #2662C22semidirect
57. #2652C22semidirect
58. #2650C22semidirect
60. #2648C22semidirect
62. #2625C22semidirect
63. #2624C22semidirect
64. #2589C22semidirect
65. #2587C22semidirect
66. #2574C22semidirect
67. #2563C22semidirect
68. #2562C22semidirect
69. #2562C22semidirect
72. #2554C22semidirect
73. #2547C22semidirect
78. #2512C22semidirect
79. #2512C22semidirect
80. #2511C22semidirect
81. #2511C22semidirect
83. #2497C22semidirect
84. #2497C22semidirect
85. #2496C22semidirect
86. #2496C22semidirect
87. #2492C22semidirect
88. #2491C22semidirect
89. #2490C22semidirect
90. #2489C22semidirect
92. #2487C22semidirect
93. #2486C22semidirect
94. #2485C22semidirect
95. #2485C22semidirect
99. #2453C22semidirect
100. #2453C22semidirect
101. #2451C22semidirect
102. #2451C22semidirect
116. #2409C22semidirect
117. #2409C22semidirect
118. #2409C22semidirect
119. #2409C22semidirect
120. #2407C22semidirect
121. #2407C22semidirect
122. #2407C22semidirect
123. #2407C22semidirect
129. #2362C22semidirect
130. #2362C22semidirect
131. #2360C22semidirect
132. #2360C22semidirect
135. #2341C22semidirect
136. #2341C22semidirect
137. Q8×C22⋊C4C22semidirect
138. Q8×C22⋊C4C22semidirect
139. #2334C22semidirect
141. #2323C22semidirect
142. #2323C22semidirect
150. C4×C22⋊Q8C22semidirect
151. C4×C22⋊Q8C22semidirect
725. C2×D42−1+4semidirect

Maximal subgroups

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

subgroupindex
#428942
#428622
#428552
#428522
#420122
#402212
#401182
#396662
#392442
#384672
#384662
#356592
#355572
#355422
#352632
#351542
C2×#25382
#347372
#342572
#342032