Finite Group Databasebeta

← #7646174

Subgroups — #7646174

Order 512.

4932 conjugacy classes of subgroups.

The subgroup lattice has 1033 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42754C214yesmaximal, complemented
2#42729C214yesmaximal, complemented
3#42611C214yesmaximal, complemented
4#42545C214yesmaximal, complemented
5#40226C214yesmaximal, complemented
6#40121C214yesmaximal, complemented
7#39789C214yesmaximal, complemented
8#39224C214yesmaximal, complemented
9#37461C214yesmaximal, complemented
10#36765C214yesmaximal, complemented
11#36730C214yesmaximal, complemented
12#35620C212yesmaximal, complemented
13#35531C212yesmaximal, complemented
14#35264C212yesmaximal, complemented
15#35174C211yesmaximal, characteristic, complemented
16#35168C211yesmaximal, characteristic
17#35167C211yesmaximal, characteristic, complemented
18#35158C211yesmaximal, characteristic, complemented
19#35080C214yesmaximal, complemented
20#34816C212yesmaximal, complemented
21#34274C211yesmaximal, characteristic, complemented
22C2×#2357C211yesmaximal, characteristic, complemented
23C4×#544C211yesmaximal, characteristic, complemented
24C2×#544C2211yescharacteristic
25C2×#544C2212yes—
26C2×#537C2211yescharacteristic
27C2×#535C2212yes—
28C2×#520C2212yes—
29C22×C4×D4C2211yescharacteristic
30#2861C2214yes—
31#2858C2214yes—
32#2857C2214yes—
33#2850C2214yes—
34#2848C2214yes—
35#2847C2214yes—
36#2837C2218yescomplemented
37#2832C2218yescomplemented
38#2800C2218yescomplemented
39#2798C2218yescomplemented
40#2779C2218yescomplemented
41#2754C2218yescomplemented
42#2746C2218yescomplemented
43#2745C2218yescomplemented
44#2738C2218yescomplemented
45#2737C2218yescomplemented
46#2731C2218yescomplemented
47#2718C2218yescomplemented
48#2712C2218yescomplemented
49#2705C2218yescomplemented
50#2701C2218yescomplemented
51#2700C2218yescomplemented
52#2687C2218yescomplemented
53#2686C2218yescomplemented
54#2662C2218yescomplemented
55#2659C2214yes—
56#2654C2218yescomplemented
57#2653C2218yescomplemented
58#2650C2218yescomplemented
59#2649C2218yescomplemented
60#2641C2214yes—
61#2640C2214yes—
62#2639C2214yes—
63#2630C2218yescomplemented
64#2626C2214yes—
65#2617C2214yes—
66#2568C2214yescomplemented
67#2566C2214yescomplemented
68#2565C2214yescomplemented
69#2563C2214yescomplemented
70#2552C2214yescomplemented
71#2551C2214yescomplemented
72#2550C2214yescomplemented
73#2550C2214yescomplemented
74#2521C2218yescomplemented
75#2514C2212yescomplemented
76#2514C2212yescomplemented
77#2513C2212yescomplemented
78#2513C2212yescomplemented
79#2512C2212yescomplemented
80#2512C2212yescomplemented
81#2511C2212yescomplemented
82#2511C2212yescomplemented
83#2510C2214yes—
84#2510C2214yes—
85#2504C2214yes—
86#2501C2214yes—
87#2500C2214yes—
88#2500C2214yes—
89#2495C2214yescomplemented
90#2494C2214yescomplemented
91#2492C2214yescomplemented
92#2492C2214yescomplemented
93#2491C2214yes—
94#2491C2214yes—
95#2491C2214yescomplemented
96#2491C2214yescomplemented
97#2490C2214yes—
98#2490C2214yes—
99#2490C2214yescomplemented
100#2489C2214yescomplemented
101#2481C2214yes—
102#2481C2214yes—
103#2472C2218yes—
104#2472C2218yes—
105#2458C2218yescomplemented
106#2454C2214yes—
107#2454C2214yes—
108#2452C2214yes—
109#2452C2214yes—
110#2450C2218yes—
111#2450C2218yes—
112#2448C2214yes—
113#2448C2214yes—
114#2445C2214yes—
115#2445C2214yes—
116#2442C2214yescomplemented
117#2442C2214yescomplemented
118#2439C2214yescomplemented
119#2439C2214yescomplemented
120#2428C2214yes—
121#2428C2214yes—
122#2427C2214yes—
123#2427C2214yes—
124#2427C2214yescomplemented
125#2426C2214yescomplemented
126#2423C2214yescomplemented
127#2422C2214yescomplemented
128#2418C2218yes—
129#2418C2218yes—
130#2401C2214yescomplemented
131#2401C2214yescomplemented
132#2363C2214yescomplemented
133#2362C2214yescomplemented
134#2361C2214yescomplemented
135#2360C2214yescomplemented
136#2357C2214yes—
137#2357C2214yes—
138#2357C2214yes—
139#2357C2214yes—
140#2337C2218yescomplemented
141#2335C2218yescomplemented
142#2331C2214yescomplemented
143#2330C2214yescomplemented
144#2329C2214yes—
145#2325C2214yes—
146#2317C2212yes—
147#2316C2211yescharacteristic
148#2316C2211yescharacteristic
149#2311C2212yes—
150#2309C2212yes—
151C4×C4⋊Q8C2214yescomplemented
152C4×#125C2214yescomplemented
153C4×#126C2214yescomplemented
154C4×#126C2214yescomplemented
155C4×C22⋊Q8C2214yes—
156C4×#121C2214yes—
157#2297C2212yes—
158#2297C2212yes—
159#2297C2212yes—
160#2296C2212yes—
161C2×#390C2211yescharacteristic
162C2×#390C2211yescharacteristic
163C2×#388C2212yes—
164C2×#388C2212yes—
165#2285C2212yes—
166C2×#382C2211yescharacteristic
167C2×#381C2212yes—
168C4×#117C2212yes—
169C2×C4×C4⋊C4C2211yescharacteristic
170C2×C4×C4⋊C4C2211yescharacteristic
171C2×C4×C4⋊C4C2211yescharacteristic
172C2×C4×C22⋊C4C2212yes—
173C22×#41C2312yes—
174C23×D4C2311yescharacteristic
175C24×C4C2312yes—
176#544—28no—
177#544—48no—
178#537—28no—
179#535—48no—
180C2×C4⋊Q8C2314yes—
181C2×C4⋊Q8C2314yes—
182C2×C4⋊Q8C2314yes—
183C2×C4⋊Q8C2314yes—
184C2×#127C2314yes—
185C2×#126C2314yes—
186C2×#126C2314yes—
187C2×#125C2314yes—
188C2×#125C2314yes—
189C2×#125C2314yes—
190C2×#124C2318yes—
191C2×#124C2314yes—
192C2×#124C2314yes—
193C2×#124C2318yes—
194C2×#123C2318yes—
195C2×#123C2318yes—
196C2×C22⋊Q8C2314yes—
197C2×C22⋊Q8C2314yes—
198C2×C22⋊Q8C2318yes—
199C2×C22⋊Q8C2314yes—
200C2×C22⋊Q8C2314yes—
201C2×#121C2314yes—
202C2×#121C2314yes—
203C2×#121C2314yes—
204C2×#121C2314yes—
205C2×#121C2314yes—
206C2×#121C2314yes—
207C2×#120C2318yes—
208#520—48no—
209C2×C4×Q8C2314yes—
210C2×C4×Q8C2314yes—
211C2×C4×D4—28no—
212C2×C4×D4C2314yes—
213C2×C4×D4C2314yes—
214C2×C4×D4C2314yes—
215C2×C4×D4C2318yes—
216C2×C4×D4C2314yes—
217C2×#117C2312yes—
218C2×#117C2312yes—
219C2×#117C2312yes—
220C2×#117C2314yes—
221C22×C4⋊C4C2311yescharacteristic
222C22×C4⋊C4C2311yescharacteristic
223C22×C4⋊C4C2314yes—
224C22×C4⋊C4C2311yescharacteristic
225C22×C4⋊C4C2311yescharacteristic
226C22×C4⋊C4C2311yescharacteristic
227C22×C22⋊C4C2312yes—
228C22×C22⋊C4C2312yes—
229C22×C22⋊C4C2312yes—
230C22×C22⋊C4C2312yes—
231C22×C22⋊C4C2312yes—
232C22×C42C2311yescharacteristic
233C22×C42C2311yescharacteristic
234C22×C42C2311yescharacteristic
235C22×C42C2312yes—
236C22×C42C2312yes—
237#401C2314yes—
238#401C2314yes—
239#400C2318yes—
240#400C2318yes—
241#400C2314yes—
242#400C2314yes—
243#400C2318yes—
244#400C2314yes—
245#400C2314yes—
246#400C2314yes—
247#400C2314yes—
248#399C2318yes—
249#399C2318yes—
250#399C2318yes—
251#398C2318yes—
252#398C2318yes—
253#398C2318yes—
254#398C2318yes—
255#397C2314yes—
256#397C2318yes—
257#397C2318yes—
258#397C2318yes—
259#397C2318yes—
260#397C2318yes—
261#397C2314yes—
262#397C2314yes—
263#397C2318yes—
264#397C2314yes—
265#397C2314yes—
266#397C2314yes—
267#396C2318yes—
268#396C2318yes—
269#396C2314yes—
270#396C2318yes—
271#396C2318yes—
272#396C2314yes—
273#395C2318yes—
274#395C2318yes—
275#394C2318yes—
276#394C2318yes—
277#394C2318yes—
278#394C2318yes—
279#394C2318yes—
280#394C2318yes—
281#394C2318yes—
282#394C2318yes—
283#394C2318yes—
284#394C2318yes—
285#394C2318yes—
286#393C2318yes—
287#393C2318yes—
288#393C2318yes—
289#393C2318yes—
290#393C2318yes—
291#393C2318yes—
292#392C2318yes—
293#391C2318yes—
294#391C2312yes—
295#391C2314yes—
296#391C2312yes—
297#391C2318yes—
298#391C2318yes—
299#391C2314yes—
300#391C2318yes—
301#391C2314yes—
302#391C2312yes—
303#391C2312yes—
304#391C2312yes—
305#391C2312yes—
306#390C2312yes—
307#390C2314yes—
308#390C2314yes—
309#390C2314yes—
310#390C2314yes—
311#390C2314yes—
312#390C2312yes—
313#390C2318yes—
314#390C2314yes—
315#390C2312yes—
316#390C2314yes—
317#390C2318yes—
318#390C2314yes—
319#390C2314yes—
320#390C2314yes—
321#390C2312yes—
322#390C2314yes—
323#390C2312yes—
324#390C2312yes—
325#389C2314yes—
326#389C2314yes—
327#389C2314yes—
328#389C2314yes—
329#389C2318yes—
330#389C2314yes—
331#389C2314yes—
332#389C2314yes—
333#389C2318yes—
334#389C2314yes—
335#389C2314yes—
336#389C2314yes—
337#389C2312yes—
338#389C2312yes—
339#389C2312yes—
340#389C2312yes—
341#388C2314yes—
342#388C2314yes—
343#388C2314yes—
344#388C2314yes—
345#388C2314yes—
346#388C2314yes—
347#388C2318yes—
348#388C2318yes—
349#388C2318yes—
350#388C2318yes—
351#388C2318yes—
352#388C2318yes—
353#388C2318yes—
354#388C2318yes—
355#388C2318yes—
356#388C2318yes—
357#388C2318yes—
358#388C2318yes—
359#388C2318yes—
360#388C2318yes—
361#388C2318yes—
362#388C2318yes—
363#387C2314yes—
364#387C2314yes—
365#387C2314yes—
366#387C2314yes—
367#387C2314yes—
368#387C2314yes—
369#387C2318yes—
370#387C2318yes—
371#387C2318yes—
372#387C2318yes—
373#387C2318yes—
374#387C2318yes—
375#386C2318yes—
376#386C2314yes—
377#386C2318yes—
378#386C2318yes—
379#386C2314yes—
380#386C2318yes—
381#386C2318yes—
382#386C2314yes—
383#386C2314yes—
384#386C2318yes—
385#386C2314yes—
386#386C2314yes—
387#385C2318yes—
388#385C2318yes—
389#385C2318yes—
390#385C2318yes—
391#385C2318yes—
392#385C2314yes—
393#385C2318yes—
394#385C2314yes—
395#384C2314yes—
396#384C2314yes—
397#384C2312yes—
398#384C2312yes—
399#383C2314yes—
400#383C2314yes—
401#382C2314yes—
402#382C2314yes—
403#382C2314yes—
404#382C2314yes—
405#382C2312yes—
406#382C2312yes—
407#381C2318yes—
408#381C2318yes—
409#380C2318yes—
410#380C2318yes—
411#380C2314yes—
412#380C2314yes—
413#380C2314yes—
414#380C2314yes—
415#380C2314yes—
416#380C2314yes—
417#380C2314yes—
418#380C2314yes—
419#380C2314yes—
420#380C2314yes—
421#379C2318yes—
422C4×C4⋊C4C2312yes—
423C4×C4⋊C4C2312yes—
424C4×C4⋊C4C2314yes—
425C4×C4⋊C4C2314yes—
426C4×C4⋊C4C2314yes—
427C4×C4⋊C4C2314yes—
428C4×C4⋊C4C2312yes—
429C4×C4⋊C4C2314yes—
430C4×C4⋊C4C2318yes—
431C4×C4⋊C4C2314yes—
432C4×C4⋊C4C2312yes—
433C4×C4⋊C4C2312yes—
434C4×C4⋊C4C2314yes—
435C4×C4⋊C4C2312yes—
436C4×C4⋊C4C2312yes—
437C4×C4⋊C4C2312yes—
438C4×C4⋊C4C2314yes—
439C4×C4⋊C4C2314yes—
440C4×C4⋊C4C2314yes—
441C4×C22⋊C4C2314yes—
442C4×C22⋊C4C2314yes—
443C4×C22⋊C4C2314yes—
444C4×C22⋊C4C2314yes—
445C4×C22⋊C4C2314yes—
446C4×C22⋊C4C2314yes—
447C4×C22⋊C4C2314yes—
448C4×C22⋊C4C2318yes—
449C4×C22⋊C4C2314yes—
450C4×C22⋊C4C2314yes—
451C4×C22⋊C4C2314yes—
452C4×C22⋊C4C2314yes—
453C4×C22⋊C4C2314yes—
454#376C2314yes—
455C2×#95C2312yes—
456C2×#95C2312yes—
457C2×#95C2312yes—
458C2×#95C2312yes—
459C2×#95C2311yescharacteristic
460C2×#95C2311yescharacteristic
461C43C2314yes—
462C25C2412yes—
463C2×#41—28no—
464C2×#41—28no—
465C2×#41—28no—
466C22×Q8C2412yes—
467C22×Q8C2414yes—
468C22×Q8C2418yes—
469C22×D4—24no—
470C22×D4—24no—
471C22×D4—24no—
472C22×D4C2414yes—
473C22×D4C2414yes—
474C22×D4C2412yes—
475C22×D4C2414yes—
476C22×D4C2418yes—
477C22×D4C2418yes—
478C23×C4—28no—
479C23×C4—82no—
480C23×C4—82no—
481C23×C4C2414yes—
482C23×C4C2411yescharacteristic
483C23×C4C2411yescharacteristic
484C23×C4C2411yescharacteristic
485C23×C4C2412yes—
486C23×C4C2412yes—
487C23×C4C2411yescharacteristic
488C23×C4C2411yescharacteristic
489C23×C4C2414yes—
490C23×C4C2414yes—
491C23×C4C2411yescharacteristic
492C23×C4C2418yes—
493C23×C4C2412yes—
494C23×C4C2411yescharacteristic
495C4⋊Q8—216no—
496C4⋊Q8—48no—
497C4⋊Q8—48no—
498C4⋊Q8—84no—
499#127—48no—
500#126—48no—
501#126—48no—
502#125—216no—
503#125—48no—
504#125—48no—
505#124—416no—
506#124—48no—
507#124—84no—
508#124—88no—
509#123—416no—
510#123—88no—
511C22⋊Q8—216no—
512C22⋊Q8—216no—
513C22⋊Q8—416no—
514C22⋊Q8—84no—
515C22⋊Q8—84no—
516#121—216no—
517#121—216no—
518#121—48no—
519#121—48no—
520#121—84no—
521#121—84no—
522#120—416no—
523C4×Q8—48no—
524C4×Q8—84no—
525C4×D4—216no—
526C4×D4—216no—
527C4×D4—48no—
528C4×D4—416no—
529C4×D4—84no—
530#117—28no—
531#117—28no—
532#117—28no—
533#117—48no—
534C2×C4⋊C4—24no—
535C2×C4⋊C4—24no—
536C2×C4⋊C4—42no—
537C2×C4⋊C4—42no—
538C2×C4⋊C4—48no—
539C2×C4⋊C4#4118yes—
540C2×C4⋊C4C2414yes—
541C2×C4⋊C4C2412yes—
542C2×C4⋊C4C2414yes—
543C2×C4⋊C4C2412yes—
544C2×C4⋊C4C2412yes—
545C2×C4⋊C4C2412yes—
546C2×C4⋊C4C2412yes—
547C2×C4⋊C4C2412yes—
548C2×C4⋊C4C2412yes—
549C2×C4⋊C4C2412yes—
550C2×C4⋊C4C2414yes—
551C2×C4⋊C4C2414yes—
552C2×C4⋊C4C2418yes—
553C2×C4⋊C4C2414yes—
554C2×C4⋊C4C2418yes—
555C2×C4⋊C4C2412yes—
556C2×C4⋊C4C2412yes—
557C2×C4⋊C4C2414yes—
558C2×C4⋊C4C2414yes—
559C2×C4⋊C4C2418yes—
560C2×C4⋊C4C2414yes—
561C2×C4⋊C4C2414yes—
562C2×C4⋊C4C2414yes—
563C2×C4⋊C4C2418yes—
564C2×C4⋊C4C2418yes—
565C2×C4⋊C4C2418yes—
566C2×C4⋊C4C2414yes—
567C2×C4⋊C4C2414yes—
568C2×C4⋊C4C2418yes—
569C2×C4⋊C4C2414yes—
570C2×C4⋊C4C2414yes—
571C2×C4⋊C4C2414yes—
572C2×C4⋊C4C2414yes—
573C2×C4⋊C4C2414yes—
574C2×C22⋊C4—28no—
575C2×C22⋊C4—44no—
576C2×C22⋊C4—44no—
577C2×C22⋊C4—82no—
578C2×C22⋊C4—82no—
579C2×C22⋊C4C2418yes—
580C2×C22⋊C4C2414yes—
581C2×C22⋊C4C2414yes—
582C2×C22⋊C4C2414yes—
583C2×C22⋊C4C2414yes—
584C2×C22⋊C4C2414yes—
585C2×C22⋊C4C2418yes—
586C2×C22⋊C4C2414yes—
587C2×C22⋊C4C2414yes—
588C2×C22⋊C4C2418yes—
589C2×C22⋊C4C2418yes—
590C2×C22⋊C4C2414yes—
591C2×C22⋊C4C2414yes—
592C2×C22⋊C4C2418yes—
593C2×C22⋊C4C2414yes—
594C2×C22⋊C4C2418yes—
595C2×C22⋊C4C2418yes—
596C2×C22⋊C4C2414yes—
597C2×C22⋊C4C2414yes—
598C2×C22⋊C4C2418yes—
599C2×C22⋊C4C2418yes—
600C2×C22⋊C4C2414yes—
601C2×C22⋊C4C2418yes—
602C2×C22⋊C4C2414yes—
603C2×C22⋊C4C2414yes—
604C2×C22⋊C4C2418yes—
605C2×C22⋊C4C2418yes—
606C2×C22⋊C4C2418yes—
607C2×C22⋊C4C2414yes—
608C2×C22⋊C4C2414yes—
609C2×C22⋊C4C2414yes—
610C2×C22⋊C4C2414yes—
611C2×C42—24no—
612C2×C42—24no—
613C2×C42—24no—
614C2×C42—82no—
615C2×C42—82no—
616C2×C42C2414yes—
617C2×C42C2414yes—
618C2×C42C2414yes—
619C2×C42C2412yes—
620C2×C42C2412yes—
621C2×C42C2414yes—
622C2×C42C2412yes—
623C2×C42C2412yes—
624C2×C42C2412yes—
625C2×C42C2412yes—
626C2×C42C2418yes—
627C2×C42C2414yes—
628C2×C42C2414yes—
629C2×C42C2414yes—
630C2×C42C2414yes—
631C2×C42C2414yes—
632C2×C42C2414yes—
633C2×C42C2414yes—
634#95C2411yescharacteristic
635#95C2411yescharacteristic
636#95C2411yescharacteristic
637#95C2411yescharacteristic
638#95C2414yes—
639#95C2414yes—
640#95C2412yes—
641#95C2412yes—
642#95C2418yes—
643#95C2418yes—
644#95C2418yes—
645#95C2414yes—
646#95C2414yes—
647#95C2414yes—
648#95C2414yes—
649#95C2414yes—
650#95C2414yes—
651#95C2414yes—
652#95C2414yes—
653#95C2418yes—
654#95C2414yes—
655#95C2414yes—
656#95C2414yes—
657#95C2414yes—
658#95C2414yes—
659#95C2414yes—
660#95C2414yes—
661#95C2414yes—
662#95C2414yes—
663#95C2414yes—
664#95C2414yes—
665#95C2414yes—
666#95C2418yes—
667#95C2418yes—
668#95C2414yes—
669#95C2414yes—
670#95C2418yes—
671#95C2414yes—
672#95C2414yes—
673#95C2418yes—
674#95C2418yes—
675C24—24no—
676C24—24no—
677C24—24no—
678C24—42no—
679C24—42no—
680C24—42no—
681C24—42no—
682C24C2514yes—
683C24C2514yes—
684C24C2511yescharacteristic
685#41—432no—
686C2×Q8—24no—
687C2×Q8—28no—
688C2×Q8—24no—
689C2×Q8—24no—
690C2×Q8—44no—
691C2×Q8—44no—
692C2×Q8—48no—
693C2×Q8—48no—
694C2×Q8—48no—
695C2×D4—28no—
696C2×D4—28no—
697C2×D4—28no—
698C2×D4—28no—
699C2×D4—24no—
700C2×D4—28no—
701C2×D4—24no—
702C2×D4—28no—
703C2×D4—28no—
704C2×D4—24no—
705C2×D4—44no—
706C2×D4—44no—
707C2×D4—48no—
708C2×D4—48no—
709C2×D4—48no—
710C2×D4—48no—
711C2×D4—48no—
712C2×D4—48no—
713C2×D4—416no—
714C22×C4—22no—
715C22×C4—22no—
716C22×C4—22no—
717C22×C4—22no—
718C22×C4—24no—
719C22×C4—24no—
720C22×C4—22no—
721C22×C4—22no—
722C22×C4—28no—
723C22×C4—28no—
724C22×C4—28no—
725C22×C4—22no—
726C22×C4—22no—
727C22×C4—28no—
728C22×C4—28no—
729C22×C4—41no—
730C22×C4—41no—
731C22×C4—42no—
732C22×C4—42no—
733C22×C4—41no—
734C22×C4—41no—
735C22×C4—41no—
736C22×C4—41no—
737C22×C4—42no—
738C22×C4—42no—
739C22×C4—42no—
740C22×C4—42no—
741C22×C4—41no—
742C22×C4—41no—
743C22×C4—41no—
744C22×C4—41no—
745C22×C4—44no—
746C22×C4—44no—
747C22×C4—44no—
748C22×C4—44no—
749C22×C4—48no—
750C22×C4—48no—
751C22×C4—48no—
752C22×C4—816no—
753C22×C4C2×#4118yes—
754C22×C4C2×#4114yes—
755C22×C4H(5,𝔽2)14yes—
756C22×C42−1+414yes—
757C22×C4C2514yes—
758C22×C4C2511yescharacteristic
759C22×C4C2511yescharacteristic
760C22×C4C2512yes—
761C22×C4C2511yescharacteristic
762C22×C4C2511yescharacteristic
763C22×C4C2512yes—
764C22×C4C2514yes—
765C22×C4C2512yes—
766C22×C4C2514yes—
767C22×C4C2514yes—
768C22×C4C2514yes—
769C22×C4C2514yes—
770C22×C4C2514yes—
771C22×C4C2514yes—
772C22×C4C2514yes—
773C22×C4C2514yes—
774C22×C4C2511yescharacteristic
775C22×C4C2511yescharacteristic
776C22×C4C2512yes—
777C4⋊C4—24no—
778C4⋊C4—24no—
779C4⋊C4—28no—
780C4⋊C4—28no—
781C4⋊C4—216no—
782C4⋊C4—28no—
783C4⋊C4—28no—
784C4⋊C4—24no—
785C4⋊C4—24no—
786C4⋊C4—24no—
787C4⋊C4—24no—
788C4⋊C4—24no—
789C4⋊C4—24no—
790C4⋊C4—28no—
791C4⋊C4—42no—
792C4⋊C4—42no—
793C4⋊C4—48no—
794C4⋊C4—44no—
795C4⋊C4—44no—
796C4⋊C4—48no—
797C4⋊C4—44no—
798C4⋊C4—48no—
799C4⋊C4—48no—
800C4⋊C4—48no—
801C4⋊C4—44no—
802C4⋊C4—44no—
803C4⋊C4—44no—
804C4⋊C4—48no—
805C4⋊C4—44no—
806C4⋊C4—44no—
807C4⋊C4—44no—
808C4⋊C4—44no—
809C4⋊C4—44no—
810C4⋊C4C2×#41116yes—
811C22⋊C4—28no—
812C22⋊C4—28no—
813C22⋊C4—28no—
814C22⋊C4—216no—
815C22⋊C4—216no—
816C22⋊C4—28no—
817C22⋊C4—28no—
818C22⋊C4—28no—
819C22⋊C4—28no—
820C22⋊C4—44no—
821C22⋊C4—44no—
822C22⋊C4—48no—
823C22⋊C4—48no—
824C22⋊C4—48no—
825C22⋊C4—44no—
826C22⋊C4—48no—
827C22⋊C4—48no—
828C22⋊C4—44no—
829C22⋊C4—44no—
830C22⋊C4—48no—
831C22⋊C4—48no—
832C22⋊C4—48no—
833C22⋊C4—44no—
834C22⋊C4—48no—
835C22⋊C4—48no—
836C22⋊C4—44no—
837C22⋊C4—44no—
838C22⋊C4—48no—
839C22⋊C4—44no—
840C22⋊C4—44no—
841C22⋊C4—44no—
842C22⋊C4—44no—
843C42—24no—
844C42—24no—
845C42—28no—
846C42—28no—
847C42—28no—
848C42—24no—
849C42—24no—
850C42—24no—
851C42—24no—
852C42—28no—
853C42—44no—
854C42—44no—
855C42—44no—
856C42—44no—
857C42—48no—
858C42—44no—
859C42—44no—
860C42—44no—
861C23—21no—
862C23—21no—
863C23—21no—
864C23—21no—
865C23—24no—
866C23—24no—
867C23—24no—
868C23—24no—
869C23—24no—
870C23—24no—
871C23—24no—
872C23—24no—
873C23—24no—
874C23—24no—
875C23—24no—
876C23—24no—
877C23—24no—
878C23—24no—
879C23—48no—
880C23—48no—
881C23—48no—
882C23—84no—
883C23—84no—
884C23—84no—
885C23—84no—
886C23C22×#4112yes—
887C23C2×H(5,𝔽2)12yes—
888C23C2×2−1+412yes—
889C23C2611yescharacteristic
890Q8—48no—
891Q8—88no—
892Q8—168no—
893D4—416no—
894D4—416no—
895D4—48no—
896D4—88no—
897D4—168no—
898D4—168no—
899C2×C4—21no—
900C2×C4—21no—
901C2×C4—21no—
902C2×C4—21no—
903C2×C4—24no—
904C2×C4—24no—
905C2×C4—22no—
906C2×C4—21no—
907C2×C4—21no—
908C2×C4—24no—
909C2×C4—24no—
910C2×C4—24no—
911C2×C4—24no—
912C2×C4—24no—
913C2×C4—24no—
914C2×C4—24no—
915C2×C4—24no—
916C2×C4—24no—
917C2×C4—24no—
918C2×C4—21no—
919C2×C4—21no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—24no—
923C2×C4—24no—
924C2×C4—24no—
925C2×C4—22no—
926C2×C4—24no—
927C2×C4—24no—
928C2×C4—24no—
929C2×C4—24no—
930C2×C4—24no—
931C2×C4—21no—
932C2×C4—21no—
933C2×C4—24no—
934C2×C4—22no—
935C2×C4—22no—
936C2×C4—22no—
937C2×C4—21no—
938C2×C4—21no—
939C2×C4—22no—
940C2×C4—24no—
941C2×C4—24no—
942C2×C4—24no—
943C2×C4—24no—
944C2×C4—24no—
945C2×C4—24no—
946C2×C4—22no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—24no—
950C2×C4—24no—
951C2×C4—21no—
952C2×C4—21no—
953C2×C4—48no—
954C2×C4—44no—
955C2×C4—44no—
956C2×C4—44no—
957C2×C4—44no—
958C2×C4—416no—
959C2×C4—88no—
960C2×C4—88no—
961C2×C4—82no—
962C2×C4—82no—
963C2×C4—84no—
964C2×C4—84no—
965C2×C4—168no—
966C2×C4#542116yes—
967C2×C4C22×#4118yes—
968C2×C4C22×#4114yes—
969C2×C4C2×H(5,𝔽2)14yes—
970C2×C4C2×2−1+414yes—
971C2×C4#58512yes—
972C2×C4#58512yes—
973C22—22no—
974C22—22no—
975C22—22no—
976C22—22no—
977C22—22no—
978C22—22no—
979C22—44no—
980C22—44no—
981C22—44no—
982C22—44no—
983C22—44no—
984C22—44no—
985C22—44no—
986C22—44no—
987C22—44no—
988C22—44no—
989C22—44no—
990C22—44no—
991C22—44no—
992C22—44no—
993C22—816no—
994C22C2×#54214yes—
995C22C23×#4111yescharacteristic
996C22C22×H(5,𝔽2)11yescharacteristic
997C22C22×2−1+411yescharacteristic
998C22C2×#58511yescharacteristic
999C22C2×#58511yescharacteristic
1000C22H(7,𝔽2)11yescharacteristic
1001C22H(7,𝔽2)11yescharacteristic
1002C4—28no—
1003C4—22no—
1004C4—22no—
1005C4—44no—
1006C4—42no—
1007C4—41no—
1008C4—41no—
1009C4—44no—
1010C4—44no—
1011C4—41no—
1012C4—41no—
1013C4—42no—
1014C4—42no—
1015C4—44no—
1016C4—44no—
1017C4—44no—
1018C4—44no—
1019C4—44no—
1020C4—44no—
1021C4C2×#54218yes—
1022C2—24no—
1023C2—84no—
1024C2—84no—
1025C2C22×#54211yescharacteristic
1026C2#6279311yescharacteristic
1027C2#6284611yescharacteristic
1028C2#6295811yescharacteristic
1029C2#6295811yescharacteristic
1030C2#6296111yescharacteristic
1031C2#6296111yescharacteristic
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. #42754C2semidirect
2. #42729C2semidirect
3. #42611C2semidirect
4. #42545C2semidirect
5. #40226C2semidirect
6. #40121C2semidirect
7. #39789C2semidirect
8. #39224C2semidirect
9. #37461C2semidirect
10. #36765C2semidirect
11. #36730C2semidirect
12. #35620C2semidirect
13. #35531C2semidirect
14. #35264C2semidirect
15. #35174C2semidirect
17. #35167C2semidirect
18. #35158C2semidirect
19. #35080C2semidirect
20. #34816C2semidirect
21. #34274C2semidirect
22. C2×#2357C2semidirect
23. C4×#544C2semidirect
36. #2837C22semidirect
37. #2832C22semidirect
38. #2800C22semidirect
39. #2798C22semidirect
40. #2779C22semidirect
41. #2754C22semidirect
42. #2746C22semidirect
43. #2745C22semidirect
44. #2738C22semidirect
45. #2737C22semidirect
46. #2731C22semidirect
47. #2718C22semidirect
48. #2712C22semidirect
49. #2705C22semidirect
50. #2701C22semidirect
51. #2700C22semidirect
52. #2687C22semidirect
53. #2686C22semidirect
54. #2662C22semidirect
56. #2654C22semidirect
57. #2653C22semidirect
58. #2650C22semidirect
59. #2649C22semidirect
63. #2630C22semidirect
66. #2568C22semidirect
67. #2566C22semidirect
68. #2565C22semidirect
69. #2563C22semidirect
70. #2552C22semidirect
71. #2551C22semidirect
72. #2550C22semidirect
73. #2550C22semidirect
74. #2521C22semidirect
75. #2514C22semidirect
76. #2514C22semidirect
77. #2513C22semidirect
78. #2513C22semidirect
79. #2512C22semidirect
80. #2512C22semidirect
81. #2511C22semidirect
82. #2511C22semidirect
89. #2495C22semidirect
90. #2494C22semidirect
91. #2492C22semidirect
92. #2492C22semidirect
95. #2491C22semidirect
96. #2491C22semidirect
99. #2490C22semidirect
100. #2489C22semidirect
105. #2458C22semidirect
116. #2442C22semidirect
117. #2442C22semidirect
118. #2439C22semidirect
119. #2439C22semidirect
124. #2427C22semidirect
125. #2426C22semidirect
126. #2423C22semidirect
127. #2422C22semidirect
130. #2401C22semidirect
131. #2401C22semidirect
132. #2363C22semidirect
133. #2362C22semidirect
134. #2361C22semidirect
135. #2360C22semidirect
140. #2337C22semidirect
141. #2335C22semidirect
142. #2331C22semidirect
143. #2330C22semidirect
151. C4×C4⋊Q8C22semidirect
152. C4×#125C22semidirect
153. C4×#126C22semidirect
154. C4×#126C22semidirect

Maximal subgroups

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

subgroupindex
#427542
#427292
#426112
#425452
#402262
#401212
#397892
#392242
#374612
#367652
#367302
#356202
#355312
#352642
#351742
#351682
#351672
#351582
#350802
#348162
#342742
C2×#23572
C4×#5442