Finite Group Databasebeta

← #7646176

Subgroups — #7646176

Order 512.

4772 conjugacy classes of subgroups.

The subgroup lattice has 1031 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42766C214yesmaximal, complemented
2#42711C214yesmaximal, complemented
3#42599C214yesmaximal, complemented
4#42554C214yesmaximal, complemented
5#40212C214yesmaximal, complemented
6#40131C214yesmaximal, complemented
7#39781C214yesmaximal, complemented
8#39216C214yesmaximal, complemented
9#37461C214yesmaximal, complemented
10#36980C214yesmaximal, complemented
11#36766C214yesmaximal, complemented
12#35519C212yesmaximal, complemented
13#35516C212yesmaximal, complemented
14#35267C212yesmaximal, complemented
15#35173C211yesmaximal, characteristic, complemented
16#35158C211yesmaximal, characteristic, complemented
17#35151C211yesmaximal, characteristic, complemented
18#35150C211yesmaximal, characteristic
19#35083C214yesmaximal, complemented
20#34813C212yesmaximal, complemented
21#34274C211yesmaximal, characteristic, complemented
22C2×#2347C211yesmaximal, characteristic, complemented
23C4×#544C211yesmaximal, characteristic, complemented
24C2×#544C2211yescharacteristic
25C2×#537C2211yescharacteristic
26C2×#533C2212yes—
27C2×#525C2212yes—
28C2×#520C2212yes—
29C22×#117C2211yescharacteristic
30#2863C2214yescomplemented
31#2860C2214yescomplemented
32#2857C2214yes—
33#2855C2214yes—
34#2854C2214yes—
35#2850C2214yes—
36#2837C2218yes—
37#2832C2218yes—
38#2801C2218yes—
39#2795C2218yes—
40#2775C2218yescomplemented
41#2773C2218yes—
42#2770C2218yescomplemented
43#2766C2218yescomplemented
44#2764C2218yescomplemented
45#2759C2218yes—
46#2759C2218yescomplemented
47#2758C2218yescomplemented
48#2757C2218yes—
49#2757C2218yescomplemented
50#2737C2218yescomplemented
51#2730C2218yes—
52#2710C2218yes—
53#2674C2218yes—
54#2662C2218yes—
55#2659C2214yes—
56#2654C2218yes—
57#2654C2218yescomplemented
58#2650C2218yes—
59#2650C2218yescomplemented
60#2645C2214yescomplemented
61#2644C2214yescomplemented
62#2639C2214yes—
63#2630C2218yes—
64#2626C2214yes—
65#2617C2214yes—
66#2584C2214yescomplemented
67#2584C2214yescomplemented
68#2582C2214yescomplemented
69#2581C2214yescomplemented
70#2580C2214yescomplemented
71#2567C2214yescomplemented
72#2546C2214yescomplemented
73#2538C2214yescomplemented
74#2521C2218yes—
75#2512C2214yescomplemented
76#2511C2214yescomplemented
77#2510C2218yes—
78#2509C2214yescomplemented
79#2508C2214yescomplemented
80#2497C2214yescomplemented
81#2496C2214yescomplemented
82#2495C2214yescomplemented
83#2494C2214yescomplemented
84#2492C2212yes—
85#2492C2212yes—
86#2492C2214yescomplemented
87#2491C2212yes—
88#2491C2212yes—
89#2491C2214yescomplemented
90#2490C2212yes—
91#2490C2212yes—
92#2490C2214yescomplemented
93#2489C2212yes—
94#2489C2212yes—
95#2489C2214yescomplemented
96#2488C2214yes—
97#2488C2214yes—
98#2487C2214yes—
99#2486C2214yes—
100#2485C2214yes—
101#2485C2214yes—
102#2481C2218yes—
103#2472C2214yes—
104#2472C2214yes—
105#2458C2218yes—
106#2452C2214yescomplemented
107#2451C2214yescomplemented
108#2450C2218yes—
109#2449C2218yes—
110#2448C2214yescomplemented
111#2447C2214yescomplemented
112#2442C2214yescomplemented
113#2441C2214yes—
114#2441C2214yes—
115#2441C2214yescomplemented
116#2440C2214yescomplemented
117#2439C2214yes—
118#2439C2214yes—
119#2439C2214yescomplemented
120#2423C2214yes—
121#2422C2214yes—
122#2421C2214yes—
123#2420C2214yes—
124#2419C2218yes—
125#2418C2218yes—
126#2415C2214yes—
127#2415C2214yes—
128#2414C2214yes—
129#2414C2214yes—
130#2398C2214yes—
131#2398C2214yes—
132#2363C2214yescomplemented
133#2362C2214yescomplemented
134#2361C2214yescomplemented
135#2360C2214yescomplemented
136#2347C2214yes—
137#2347C2214yes—
138#2347C2214yes—
139#2347C2214yes—
140#2334C2218yescomplemented
141#2332C2218yescomplemented
142#2331C2214yescomplemented
143#2330C2214yescomplemented
144#2329C2214yes—
145#2325C2214yes—
146#2317C2212yes—
147#2317C2212yes—
148#2316C2211yescharacteristic
149#2316C2211yescharacteristic
150#2316C2212yes—
151#2311C2212yes—
152#2311C2212yes—
153C4×C4⋊Q8C2214yescomplemented
154C4×#125C2214yescomplemented
155C4×#124C2214yes—
156C4×#124C2214yes—
157C4×C22⋊Q8C2214yes—
158C4×#121C2214yes—
159#2297C2212yes—
160#2297C2212yes—
161C2×#389C2211yescharacteristic
162C2×#389C2211yescharacteristic
163C2×#388C2212yes—
164C2×#388C2212yes—
165C2×#383C2212yes—
166#2280C2212yes—
167C2×#380C2211yescharacteristic
168C4×#117C2212yes—
169C2×C4×C4⋊C4C2212yes—
170C2×C4×C4⋊C4C2211yescharacteristic
171C2×C4×C4⋊C4C2211yescharacteristic
172C2×C4×C22⋊C4C2211yescharacteristic
173C22×#41C2312yes—
174C24×C4C2311yescharacteristic
175#544—28no—
176#537—28no—
177#533—48no—
178C2×C4⋊Q8C2314yes—
179C2×C4⋊Q8C2312yes—
180C2×C4⋊Q8C2312yes—
181C2×C4⋊Q8C2314yes—
182C2×#126C2318yes—
183C2×#125C2314yes—
184C2×#125C2312yes—
185C2×#125C2312yes—
186C2×#124C2314yes—
187C2×#124C2314yes—
188C2×#124C2314yes—
189#525—48no—
190C2×#123C2314yes—
191C2×#123C2318yes—
192C2×C22⋊Q8C2314yes—
193C2×C22⋊Q8C2314yes—
194C2×C22⋊Q8C2318yes—
195C2×C22⋊Q8C2314yes—
196C2×C22⋊Q8C2314yes—
197C2×C22⋊Q8C2312yes—
198C2×C22⋊Q8C2312yes—
199C2×#121C2314yes—
200C2×#121C2314yes—
201C2×#121C2312yes—
202C2×#121C2312yes—
203C2×#120C2314yes—
204#520—48no—
205C2×C4×Q8C2314yes—
206C2×C4×Q8C2314yes—
207C2×C4×Q8C2314yes—
208C2×C4×Q8C2314yes—
209C2×C4×D4C2314yes—
210C2×C4×D4C2318yes—
211C2×C4×D4C2314yes—
212C2×C4×D4C2314yes—
213C2×C4×D4C2314yes—
214C2×#117—28no—
215C2×#117C2312yes—
216C2×#117C2312yes—
217C2×#117C2312yes—
218C2×#117C2314yes—
219C2×#117C2314yes—
220C2×#117C2314yes—
221C22×C4⋊C4C2311yescharacteristic
222C22×C4⋊C4C2311yescharacteristic
223C22×C4⋊C4C2311yescharacteristic
224C22×C4⋊C4C2314yes—
225C22×C4⋊C4C2312yes—
226C22×C4⋊C4C2312yes—
227C22×C4⋊C4C2311yescharacteristic
228C22×C22⋊C4C2312yes—
229C22×C22⋊C4C2311yescharacteristic
230C22×C22⋊C4C2311yescharacteristic
231C22×C22⋊C4C2312yes—
232C22×C42C2312yes—
233C22×C42C2311yescharacteristic
234C22×C42C2311yescharacteristic
235C22×C42C2312yes—
236C22×C42C2312yes—
237#401C2318yes—
238#400C2318yes—
239#400C2318yes—
240#400C2318yes—
241#400C2318yes—
242#400C2318yes—
243#400C2314yes—
244#400C2318yes—
245#400C2314yes—
246#400C2314yes—
247#400C2314yes—
248#399C2318yes—
249#399C2318yes—
250#399C2318yes—
251#398C2318yes—
252#398C2318yes—
253#398C2318yes—
254#398C2318yes—
255#398C2318yes—
256#397C2318yes—
257#397C2318yes—
258#397C2314yes—
259#397C2318yes—
260#397C2318yes—
261#397C2318yes—
262#397C2318yes—
263#397C2318yes—
264#397C2314yes—
265#397C2314yes—
266#397C2314yes—
267#397C2318yes—
268#396C2318yes—
269#396C2318yes—
270#396C2318yes—
271#396C2318yes—
272#396C2318yes—
273#395C2318yes—
274#395C2318yes—
275#395C2318yes—
276#394C2314yes—
277#394C2318yes—
278#394C2318yes—
279#394C2314yes—
280#394C2318yes—
281#394C2318yes—
282#394C2318yes—
283#394C2314yes—
284#394C2314yes—
285#393C2314yes—
286#393C2318yes—
287#393C2318yes—
288#393C2318yes—
289#393C2314yes—
290#393C2314yes—
291#393C2314yes—
292#392C2318yes—
293#391C2318yes—
294#391C2314yes—
295#391C2314yes—
296#391C2318yes—
297#391C2314yes—
298#391C2312yes—
299#391C2312yes—
300#391C2318yes—
301#391C2314yes—
302#391C2314yes—
303#391C2314yes—
304#391C2314yes—
305#391C2312yes—
306#391C2312yes—
307#391C2314yes—
308#390C2314yes—
309#390C2314yes—
310#390C2312yes—
311#390C2314yes—
312#390C2314yes—
313#390C2314yes—
314#390C2312yes—
315#390C2312yes—
316#390C2314yes—
317#390C2314yes—
318#390C2314yes—
319#390C2312yes—
320#389C2314yes—
321#389C2314yes—
322#389C2314yes—
323#389C2314yes—
324#389C2318yes—
325#389C2314yes—
326#389C2314yes—
327#389C2314yes—
328#389C2314yes—
329#389C2314yes—
330#389C2314yes—
331#389C2314yes—
332#389C2314yes—
333#389C2314yes—
334#389C2314yes—
335#389C2314yes—
336#389C2318yes—
337#389C2318yes—
338#389C2314yes—
339#389C2314yes—
340#389C2314yes—
341#389C2314yes—
342#389C2314yes—
343#389C2314yes—
344#389C2314yes—
345#389C2314yes—
346#389C2314yes—
347#388C2318yes—
348#388C2318yes—
349#388C2318yes—
350#388C2314yes—
351#388C2318yes—
352#388C2318yes—
353#388C2318yes—
354#388C2314yes—
355#388C2318yes—
356#388C2318yes—
357#388C2318yes—
358#388C2318yes—
359#388C2318yes—
360#388C2318yes—
361#388C2318yes—
362#388C2318yes—
363#388C2318yes—
364#388C2314yes—
365#388C2314yes—
366#388C2314yes—
367#388C2314yes—
368#388C2314yes—
369#388C2314yes—
370#387C2318yes—
371#387C2318yes—
372#387C2318yes—
373#387C2318yes—
374#387C2318yes—
375#387C2318yes—
376#387C2318yes—
377#387C2318yes—
378#387C2318yes—
379#387C2318yes—
380#387C2318yes—
381#387C2318yes—
382#387C2318yes—
383#386C2318yes—
384#386C2318yes—
385#386C2314yes—
386#386C2318yes—
387#386C2314yes—
388#386C2318yes—
389#386C2314yes—
390#386C2314yes—
391#385C2318yes—
392#385C2318yes—
393#385C2318yes—
394#385C2318yes—
395#385C2318yes—
396#385C2318yes—
397#384C2314yes—
398#384C2314yes—
399#384C2314yes—
400#383C2318yes—
401#383C2318yes—
402#383C2318yes—
403#382C2314yes—
404#382C2314yes—
405#382C2314yes—
406#382C2314yes—
407#382C2314yes—
408#381C2318yes—
409#381C2314yes—
410#380C2314yes—
411#380C2314yes—
412#380C2314yes—
413#380C2314yes—
414#380C2314yes—
415#380C2314yes—
416#380C2318yes—
417#380C2314yes—
418#380C2314yes—
419#380C2318yes—
420#380C2312yes—
421#380C2312yes—
422#380C2312yes—
423#380C2312yes—
424#379C2314yes—
425C4×C4⋊C4C2312yes—
426C4×C4⋊C4C2314yes—
427C4×C4⋊C4C2318yes—
428C4×C4⋊C4C2314yes—
429C4×C4⋊C4C2312yes—
430C4×C4⋊C4C2314yes—
431C4×C4⋊C4C2314yes—
432C4×C4⋊C4C2312yes—
433C4×C4⋊C4C2314yes—
434C4×C4⋊C4C2312yes—
435C4×C4⋊C4C2314yes—
436C4×C4⋊C4C2314yes—
437C4×C4⋊C4C2314yes—
438C4×C4⋊C4C2314yes—
439C4×C4⋊C4C2314yes—
440C4×C22⋊C4C2314yes—
441C4×C22⋊C4C2318yes—
442C4×C22⋊C4C2312yes—
443C4×C22⋊C4C2312yes—
444C4×C22⋊C4C2312yes—
445C4×C22⋊C4C2312yes—
446C4×C22⋊C4C2314yes—
447C4×C22⋊C4C2314yes—
448C4×C22⋊C4C2314yes—
449C4×C22⋊C4C2314yes—
450C4×C22⋊C4C2314yes—
451C4×C22⋊C4C2314yes—
452C4×C22⋊C4C2314yes—
453#376C2314yes—
454C2×#95C2312yes—
455C2×#95C2312yes—
456C2×#95C2312yes—
457C2×#95C2312yes—
458C2×#95C2311yescharacteristic
459C2×#95C2311yescharacteristic
460C2×#95C2312yes—
461C43C2314yes—
462C25C2411yescharacteristic
463C2×#41—28no—
464C2×#41—28no—
465C2×#41—28no—
466C22×Q8C2412yes—
467C22×Q8C2414yes—
468C22×Q8C2414yes—
469C22×Q8C2414yes—
470C22×D4C2414yes—
471C22×D4C2412yes—
472C22×D4C2414yes—
473C22×D4C2414yes—
474C22×D4C2414yes—
475C23×C4—24no—
476C23×C4—24no—
477C23×C4—24no—
478C23×C4C2414yes—
479C23×C4C2412yes—
480C23×C4C2412yes—
481C23×C4C2411yescharacteristic
482C23×C4C2411yescharacteristic
483C23×C4C2411yescharacteristic
484C23×C4C2412yes—
485C23×C4C2412yes—
486C23×C4C2412yes—
487C23×C4C2411yescharacteristic
488C23×C4C2411yescharacteristic
489C23×C4C2418yes—
490C23×C4C2412yes—
491C23×C4C2411yescharacteristic
492C4⋊Q8—216no—
493C4⋊Q8—44no—
494C4⋊Q8—44no—
495C4⋊Q8—84no—
496#126—416no—
497#125—216no—
498#125—44no—
499#125—44no—
500#124—48no—
501#124—48no—
502#124—84no—
503#123—48no—
504#123—88no—
505C22⋊Q8—216no—
506C22⋊Q8—216no—
507C22⋊Q8—48no—
508C22⋊Q8—48no—
509C22⋊Q8—416no—
510C22⋊Q8—44no—
511C22⋊Q8—44no—
512#121—216no—
513#121—216no—
514#121—44no—
515#121—44no—
516#120—48no—
517C4×Q8—48no—
518C4×Q8—48no—
519C4×Q8—48no—
520C4×Q8—84no—
521C4×D4—48no—
522C4×D4—48no—
523C4×D4—48no—
524C4×D4—416no—
525C4×D4—84no—
526#117—28no—
527#117—28no—
528#117—28no—
529#117—216no—
530#117—216no—
531#117—48no—
532C2×C4⋊C4—24no—
533C2×C4⋊C4—24no—
534C2×C4⋊C4—24no—
535C2×C4⋊C4—44no—
536C2×C4⋊C4—44no—
537C2×C4⋊C4—48no—
538C2×C4⋊C4#4118yes—
539C2×C4⋊C4C2414yes—
540C2×C4⋊C4C2412yes—
541C2×C4⋊C4C2414yes—
542C2×C4⋊C4C2414yes—
543C2×C4⋊C4C2414yes—
544C2×C4⋊C4C2414yes—
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⋊C4C2418yes—
554C2×C4⋊C4C2414yes—
555C2×C4⋊C4C2414yes—
556C2×C4⋊C4C2414yes—
557C2×C4⋊C4C2414yes—
558C2×C4⋊C4C2414yes—
559C2×C4⋊C4C2414yes—
560C2×C4⋊C4C2414yes—
561C2×C4⋊C4C2414yes—
562C2×C4⋊C4C2414yes—
563C2×C4⋊C4C2414yes—
564C2×C4⋊C4C2414yes—
565C2×C4⋊C4C2418yes—
566C2×C4⋊C4C2414yes—
567C2×C4⋊C4C2418yes—
568C2×C4⋊C4C2418yes—
569C2×C4⋊C4C2418yes—
570C2×C4⋊C4C2418yes—
571C2×C4⋊C4C2418yes—
572C2×C4⋊C4C2414yes—
573C2×C4⋊C4C2414yes—
574C2×C4⋊C4C2414yes—
575C2×C22⋊C4—28no—
576C2×C22⋊C4—42no—
577C2×C22⋊C4—42no—
578C2×C22⋊C4—82no—
579C2×C22⋊C4C2418yes—
580C2×C22⋊C4C2412yes—
581C2×C22⋊C4C2412yes—
582C2×C22⋊C4C2414yes—
583C2×C22⋊C4C2414yes—
584C2×C22⋊C4C2414yes—
585C2×C22⋊C4C2418yes—
586C2×C22⋊C4C2414yes—
587C2×C22⋊C4C2414yes—
588C2×C22⋊C4C2418yes—
589C2×C22⋊C4C2412yes—
590C2×C22⋊C4C2412yes—
591C2×C22⋊C4C2418yes—
592C2×C22⋊C4C2414yes—
593C2×C22⋊C4C2414yes—
594C2×C22⋊C4C2414yes—
595C2×C22⋊C4C2414yes—
596C2×C22⋊C4C2414yes—
597C2×C22⋊C4C2418yes—
598C2×C22⋊C4C2414yes—
599C2×C22⋊C4C2418yes—
600C2×C22⋊C4C2414yes—
601C2×C22⋊C4C2414yes—
602C2×C22⋊C4C2414yes—
603C2×C22⋊C4C2414yes—
604C2×C22⋊C4C2414yes—
605C2×C22⋊C4C2418yes—
606C2×C22⋊C4C2418yes—
607C2×C22⋊C4C2414yes—
608C2×C22⋊C4C2414yes—
609C2×C22⋊C4C2414yes—
610C2×C42—28no—
611C2×C42—24no—
612C2×C42—24no—
613C2×C42—82no—
614C2×C42—82no—
615C2×C42C2414yes—
616C2×C42C2414yes—
617C2×C42C2414yes—
618C2×C42C2414yes—
619C2×C42C2414yes—
620C2×C42C2412yes—
621C2×C42C2412yes—
622C2×C42C2414yes—
623C2×C42C2412yes—
624C2×C42C2412yes—
625C2×C42C2418yes—
626C2×C42C2414yes—
627C2×C42C2414yes—
628C2×C42C2414yes—
629C2×C42C2414yes—
630C2×C42C2414yes—
631C2×C42C2414yes—
632C2×C42C2414yes—
633#95C2411yescharacteristic
634#95C2411yescharacteristic
635#95C2411yescharacteristic
636#95C2411yescharacteristic
637#95C2412yes—
638#95C2412yes—
639#95C2414yes—
640#95C2414yes—
641#95C2418yes—
642#95C2418yes—
643#95C2418yes—
644#95C2418yes—
645#95C2414yes—
646#95C2414yes—
647#95C2414yes—
648#95C2414yes—
649#95C2414yes—
650#95C2414yes—
651#95C2414yes—
652#95C2414yes—
653#95C2414yes—
654#95C2414yes—
655#95C2418yes—
656#95C2414yes—
657#95C2414yes—
658#95C2414yes—
659#95C2414yes—
660#95C2414yes—
661#95C2414yes—
662#95C2418yes—
663#95C2418yes—
664#95C2418yes—
665#95C2418yes—
666#95C2418yes—
667#95C2418yes—
668#95C2418yes—
669#95C2418yes—
670#95C2418yes—
671#95C2418yes—
672#95C2418yes—
673C24—22no—
674C24—22no—
675C24—22no—
676C24—41no—
677C24—41no—
678C24—41no—
679C24—41no—
680C24C2512yes—
681C24C2514yes—
682C24C2511yescharacteristic
683#41—432no—
684C2×Q8—24no—
685C2×Q8—28no—
686C2×Q8—24no—
687C2×Q8—24no—
688C2×Q8—28no—
689C2×Q8—44no—
690C2×Q8—44no—
691C2×Q8—44no—
692C2×Q8—44no—
693C2×Q8—44no—
694C2×Q8—44no—
695C2×Q8—44no—
696C2×D4—28no—
697C2×D4—28no—
698C2×D4—28no—
699C2×D4—24no—
700C2×D4—28no—
701C2×D4—24no—
702C2×D4—24no—
703C2×D4—44no—
704C2×D4—44no—
705C2×D4—44no—
706C2×D4—44no—
707C2×D4—44no—
708C2×D4—44no—
709C2×D4—44no—
710C2×D4—44no—
711C22×C4—22no—
712C22×C4—24no—
713C22×C4—22no—
714C22×C4—22no—
715C22×C4—22no—
716C22×C4—22no—
717C22×C4—22no—
718C22×C4—24no—
719C22×C4—22no—
720C22×C4—24no—
721C22×C4—24no—
722C22×C4—24no—
723C22×C4—28no—
724C22×C4—28no—
725C22×C4—24no—
726C22×C4—24no—
727C22×C4—24no—
728C22×C4—24no—
729C22×C4—28no—
730C22×C4—22no—
731C22×C4—22no—
732C22×C4—41no—
733C22×C4—42no—
734C22×C4—41no—
735C22×C4—42no—
736C22×C4—42no—
737C22×C4—42no—
738C22×C4—42no—
739C22×C4—42no—
740C22×C4—41no—
741C22×C4—41no—
742C22×C4—42no—
743C22×C4—42no—
744C22×C4—41no—
745C22×C4—41no—
746C22×C4—48no—
747C22×C4—48no—
748C22×C4—48no—
749C22×C4—416no—
750C22×C4C2×#4118yes—
751C22×C4C2×#4114yes—
752C22×C4H(5,𝔽2)14yes—
753C22×C42−1+414yes—
754C22×C4C2512yes—
755C22×C4C2511yescharacteristic
756C22×C4C2511yescharacteristic
757C22×C4C2514yes—
758C22×C4C2511yescharacteristic
759C22×C4C2514yes—
760C22×C4C2514yes—
761C22×C4C2512yes—
762C22×C4C2514yes—
763C22×C4C2514yes—
764C22×C4C2514yes—
765C22×C4C2514yes—
766C22×C4C2514yes—
767C22×C4C2514yes—
768C22×C4C2514yes—
769C22×C4C2511yescharacteristic
770C22×C4C2514yes—
771C22×C4C2511yescharacteristic
772C22×C4C2511yescharacteristic
773C22×C4C2512yes—
774C4⋊C4—28no—
775C4⋊C4—24no—
776C4⋊C4—24no—
777C4⋊C4—28no—
778C4⋊C4—28no—
779C4⋊C4—216no—
780C4⋊C4—28no—
781C4⋊C4—24no—
782C4⋊C4—24no—
783C4⋊C4—24no—
784C4⋊C4—24no—
785C4⋊C4—28no—
786C4⋊C4—28no—
787C4⋊C4—28no—
788C4⋊C4—44no—
789C4⋊C4—44no—
790C4⋊C4—48no—
791C4⋊C4—44no—
792C4⋊C4—44no—
793C4⋊C4—44no—
794C4⋊C4—44no—
795C4⋊C4—44no—
796C4⋊C4—44no—
797C4⋊C4—44no—
798C4⋊C4—44no—
799C4⋊C4—44no—
800C4⋊C4—44no—
801C4⋊C4—44no—
802C4⋊C4—48no—
803C4⋊C4—44no—
804C4⋊C4—48no—
805C4⋊C4—48no—
806C4⋊C4—48no—
807C4⋊C4—48no—
808C4⋊C4—48no—
809C4⋊C4C2×#41116yes—
810C22⋊C4—28no—
811C22⋊C4—28no—
812C22⋊C4—28no—
813C22⋊C4—216no—
814C22⋊C4—216no—
815C22⋊C4—24no—
816C22⋊C4—24no—
817C22⋊C4—28no—
818C22⋊C4—28no—
819C22⋊C4—42no—
820C22⋊C4—42no—
821C22⋊C4—48no—
822C22⋊C4—44no—
823C22⋊C4—44no—
824C22⋊C4—44no—
825C22⋊C4—48no—
826C22⋊C4—44no—
827C22⋊C4—44no—
828C22⋊C4—44no—
829C22⋊C4—44no—
830C22⋊C4—44no—
831C22⋊C4—48no—
832C22⋊C4—44no—
833C22⋊C4—48no—
834C22⋊C4—44no—
835C22⋊C4—44no—
836C22⋊C4—44no—
837C22⋊C4—44no—
838C22⋊C4—44no—
839C22⋊C4—48no—
840C22⋊C4—48no—
841C42—28no—
842C42—28no—
843C42—28no—
844C42—24no—
845C42—24no—
846C42—28no—
847C42—28no—
848C42—24no—
849C42—24no—
850C42—28no—
851C42—44no—
852C42—44no—
853C42—44no—
854C42—44no—
855C42—44no—
856C42—48no—
857C42—44no—
858C42—44no—
859C23—21no—
860C23—21no—
861C23—21no—
862C23—21no—
863C23—22no—
864C23—24no—
865C23—22no—
866C23—24no—
867C23—22no—
868C23—24no—
869C23—24no—
870C23—24no—
871C23—22no—
872C23—22no—
873C23—22no—
874C23—24no—
875C23—24no—
876C23—22no—
877C23—44no—
878C23—44no—
879C23—44no—
880C23—82no—
881C23—82no—
882C23—82no—
883C23—82no—
884C23C22×#4112yes—
885C23C2×H(5,𝔽2)12yes—
886C23C2×2−1+412yes—
887C23C2611yescharacteristic
888Q8—48no—
889Q8—88no—
890Q8—88no—
891Q8—88no—
892D4—416no—
893D4—48no—
894D4—88no—
895D4—88no—
896D4—88no—
897C2×C4—21no—
898C2×C4—21no—
899C2×C4—21no—
900C2×C4—24no—
901C2×C4—21no—
902C2×C4—24no—
903C2×C4—21no—
904C2×C4—21no—
905C2×C4—24no—
906C2×C4—24no—
907C2×C4—24no—
908C2×C4—24no—
909C2×C4—21no—
910C2×C4—22no—
911C2×C4—24no—
912C2×C4—24no—
913C2×C4—24no—
914C2×C4—24no—
915C2×C4—24no—
916C2×C4—24no—
917C2×C4—21no—
918C2×C4—21no—
919C2×C4—21no—
920C2×C4—22no—
921C2×C4—24no—
922C2×C4—21no—
923C2×C4—21no—
924C2×C4—24no—
925C2×C4—24no—
926C2×C4—24no—
927C2×C4—22no—
928C2×C4—24no—
929C2×C4—24no—
930C2×C4—22no—
931C2×C4—24no—
932C2×C4—24no—
933C2×C4—24no—
934C2×C4—24no—
935C2×C4—21no—
936C2×C4—21no—
937C2×C4—24no—
938C2×C4—24no—
939C2×C4—21no—
940C2×C4—21no—
941C2×C4—24no—
942C2×C4—24no—
943C2×C4—24no—
944C2×C4—24no—
945C2×C4—24no—
946C2×C4—22no—
947C2×C4—24no—
948C2×C4—24no—
949C2×C4—24no—
950C2×C4—22no—
951C2×C4—48no—
952C2×C4—44no—
953C2×C4—44no—
954C2×C4—48no—
955C2×C4—44no—
956C2×C4—48no—
957C2×C4—48no—
958C2×C4—416no—
959C2×C4—84no—
960C2×C4—84no—
961C2×C4—82no—
962C2×C4—82no—
963C2×C4—168no—
964C2×C4#542116yes—
965C2×C4C22×#4118yes—
966C2×C4C22×#4114yes—
967C2×C4C2×H(5,𝔽2)14yes—
968C2×C4C2×2−1+414yes—
969C2×C4#58512yes—
970C2×C4#58512yes—
971C22—22no—
972C22—22no—
973C22—22no—
974C22—22no—
975C22—22no—
976C22—22no—
977C22—44no—
978C22—42no—
979C22—44no—
980C22—42no—
981C22—42no—
982C22—44no—
983C22—44no—
984C22—42no—
985C22—44no—
986C22—42no—
987C22—44no—
988C22—42no—
989C22—42no—
990C22—44no—
991C22—88no—
992C22C2×#54214yes—
993C22C23×#4111yescharacteristic
994C22C22×H(5,𝔽2)11yescharacteristic
995C22C22×2−1+411yescharacteristic
996C22C2×#58511yescharacteristic
997C22C2×#58511yescharacteristic
998C22H(7,𝔽2)11yescharacteristic
999C222−1+611yescharacteristic
1000C4—28no—
1001C4—22no—
1002C4—22no—
1003C4—44no—
1004C4—44no—
1005C4—44no—
1006C4—41no—
1007C4—41no—
1008C4—44no—
1009C4—41no—
1010C4—44no—
1011C4—44no—
1012C4—44no—
1013C4—41no—
1014C4—44no—
1015C4—42no—
1016C4—42no—
1017C4—44no—
1018C4—44no—
1019C4C2×#54218yes—
1020C2—24no—
1021C2—84no—
1022C2—82no—
1023C2C22×#54211yescharacteristic
1024C2#6279311yescharacteristic
1025C2#6284711yescharacteristic
1026C2#6295711yescharacteristic
1027C2#6295811yescharacteristic
1028C2#6295911yescharacteristic
1029C2#6296011yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35150C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42766C2semidirect
2. #42711C2semidirect
3. #42599C2semidirect
4. #42554C2semidirect
5. #40212C2semidirect
6. #40131C2semidirect
7. #39781C2semidirect
8. #39216C2semidirect
9. #37461C2semidirect
10. #36980C2semidirect
11. #36766C2semidirect
12. #35519C2semidirect
13. #35516C2semidirect
14. #35267C2semidirect
15. #35173C2semidirect
16. #35158C2semidirect
17. #35151C2semidirect
19. #35083C2semidirect
20. #34813C2semidirect
21. #34274C2semidirect
22. C2×#2347C2semidirect
23. C4×#544C2semidirect
30. #2863C22semidirect
31. #2860C22semidirect
40. #2775C22semidirect
42. #2770C22semidirect
43. #2766C22semidirect
44. #2764C22semidirect
46. #2759C22semidirect
47. #2758C22semidirect
49. #2757C22semidirect
50. #2737C22semidirect
57. #2654C22semidirect
59. #2650C22semidirect
60. #2645C22semidirect
61. #2644C22semidirect
66. #2584C22semidirect
67. #2584C22semidirect
68. #2582C22semidirect
69. #2581C22semidirect
70. #2580C22semidirect
71. #2567C22semidirect
72. #2546C22semidirect
73. #2538C22semidirect
75. #2512C22semidirect
76. #2511C22semidirect
78. #2509C22semidirect
79. #2508C22semidirect
80. #2497C22semidirect
81. #2496C22semidirect
82. #2495C22semidirect
83. #2494C22semidirect
86. #2492C22semidirect
89. #2491C22semidirect
92. #2490C22semidirect
95. #2489C22semidirect
106. #2452C22semidirect
107. #2451C22semidirect
110. #2448C22semidirect
111. #2447C22semidirect
112. #2442C22semidirect
115. #2441C22semidirect
116. #2440C22semidirect
119. #2439C22semidirect
132. #2363C22semidirect
133. #2362C22semidirect
134. #2361C22semidirect
135. #2360C22semidirect
140. #2334C22semidirect
141. #2332C22semidirect
142. #2331C22semidirect
143. #2330C22semidirect
153. C4×C4⋊Q8C22semidirect
154. C4×#125C22semidirect

Maximal subgroups

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

subgroupindex
#427662
#427112
#425992
#425542
#402122
#401312
#397812
#392162
#374612
#369802
#367662
#355192
#355162
#352672
#351732
#351582
#351512
#351502
#350832
#348132
#342742
C2×#23472
C4×#5442