Finite Group Databasebeta

← #7715267

Subgroups — #7715267

Order 512.

6472 conjugacy classes of subgroups.

The subgroup lattice has 1030 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3550C211yesmaximal, characteristic, complemented
2C2×#3458C211yesmaximal, characteristic, complemented
3#52056C214yesmaximal, complemented
4#52007C214yesmaximal, complemented
5#51750C214yesmaximal, complemented
6#51543C214yesmaximal, complemented
7#47216C214yesmaximal, complemented
8#46816C214yesmaximal, complemented
9#46426C214yesmaximal, complemented
10#46357C214yesmaximal, complemented
11#39719C214yesmaximal, complemented
12#39718C214yesmaximal, complemented
13#39597C214yesmaximal, complemented
14#39596C214yesmaximal, complemented
15#37635C211yesmaximal, characteristic, complemented
16#37619C211yesmaximal, characteristic, complemented
17#37275C214yesmaximal, complemented
18#35325C211yesmaximal, characteristic, complemented
19#35301C211yesmaximal, characteristic
20#35260C214yesmaximal, complemented
21#34375C211yesmaximal, characteristic, complemented
22#3550—216no—
23C2×#563C2214yescomplemented
24C2×#559C2212yescomplemented
25C2×Q82C2212yescomplemented
26C2×#556C2212yescomplemented
27C2×#556C2212yescomplemented
28C2×D4×Q8C2212yescomplemented
29C2×D4×Q8C2212yescomplemented
30#3458—216no—
31C2×#544C2212yes—
32C2×#544C2212yes—
33C2×#544C2212yes—
34C2×#544C2212yes—
35C2×#544C2212yes—
36C2×#544C2212yes—
37C2×#543C2212yes—
38C2×#543C2212yes—
39C2×#542C2214yes—
40C2×#542C2214yes—
41C2×#536C2214yes—
42C2×#533C2211yescharacteristic
43C2×#533C2211yescharacteristic
44C2×#533C2214yes—
45C2×#533C2214yes—
46C2×#533C2212yes—
47C2×#533C2211yescharacteristic
48C2×#532C2211yescharacteristic
49C22×#117C2212yes—
50C22×#117C2211yescharacteristic
51#2857C2214yes—
52#2855C2212yes—
53#2854C2212yes—
54#2850C2214yes—
55#2848C2212yes—
56#2847C2212yes—
57#2817C2214yes—
58#2816C2214yes—
59#2731C2218yescomplemented
60#2730C2218yes—
61#2729C2218yescomplemented
62#2728C2218yes—
63#2723C2218yes—
64#2721C2218yescomplemented
65#2720C2218yescomplemented
66#2720C2218yescomplemented
67#2716C2218yescomplemented
68#2716C2218yescomplemented
69#2713C2218yescomplemented
70#2713C2218yescomplemented
71#2700C2218yes—
72#2696C2218yes—
73#2692C2218yes—
74#2692C2218yes—
75#2690C2218yescomplemented
76#2687C2218yes—
77#2680C2218yes—
78#2677C2218yes—
79#2677C2218yes—
80#2677C2218yescomplemented
81#2674C2218yes—
82#2674C2218yescomplemented
83#2660C2212yescomplemented
84#2658C2212yescomplemented
85#2642C2212yescomplemented
86#2640C2212yescomplemented
87#2634C2214yescomplemented
88#2633C2214yescomplemented
89#2628C2212yes—
90#2628C2214yes—
91#2628C2212yes—
92#2625C2214yes—
93#2624C2214yes—
94#2621C2212yes—
95#2620C2214yes—
96#2619C2212yes—
97#2611C2214yes—
98#2610C2214yes—
99#2599C2214yes—
100#2598C2214yes—
101#2592C2214yescomplemented
102#2592C2214yescomplemented
103#2591C2212yes—
104#2583C2212yes—
105#2582C2214yescomplemented
106#2581C2214yescomplemented
107#2581C2214yescomplemented
108#2580C2214yescomplemented
109#2580C2214yescomplemented
110#2568C2212yescomplemented
111#2567C2212yescomplemented
112#2567C2214yescomplemented
113#2561C2212yes—
114#2560C2218yes—
115#2558C2218yescomplemented
116#2551C2218yescomplemented
117#2548C2212yescomplemented
118#2546C2214yescomplemented
119#2546C2212yescomplemented
120#2542C2218yes—
121#2539C2212yes—
122#2538C2214yescomplemented
123#2519C2218yescomplemented
124#2499C2214yes—
125#2492C2218yes—
126#2492C2218yescomplemented
127#2484C2212yes—
128#2482C2212yes—
129#2481C2218yes—
130#2479C2218yes—
131#2477C2218yes—
132#2477C2218yes—
133#2475C2218yescomplemented
134#2474C2218yes—
135#2472C2218yes—
136#2470C2218yes—
137#2463C2218yes—
138#2461C2218yes—
139#2460C2218yescomplemented
140#2449C2218yes—
141#2446C2218yescomplemented
142#2434C2218yescomplemented
143#2432C2214yes—
144#2423C2218yes—
145#2418C2218yes—
146#2409C2218yes—
147#2406C2212yes—
148#2404C2212yes—
149#2381C2212yescomplemented
150#2381C2212yescomplemented
151#2371C2214yescomplemented
152#2355C2214yescomplemented
153#2355C2214yescomplemented
154#2332C2214yes—
155#2332C2214yes—
156#2324C2214yes—
157#2324C2214yes—
158#2323C2214yes—
159#2323C2214yes—
160#2314C2214yes—
161C4×C22⋊Q8C2214yes—
162C4×#121C2214yes—
163#2283C2211yescharacteristic
164#2283C2211yescharacteristic
165C22×#41C2312yes—
166C23×Q8C2314yes—
167C24×C4C2311yescharacteristic
168#563—232no—
169#559—216no—
170Q82—216no—
171#556—216no—
172#556—216no—
173D4×Q8—216no—
174D4×Q8—216no—
175#544—216no—
176#544—216no—
177#544—216no—
178#544—216no—
179#544—216no—
180#544—216no—
181#543—216no—
182#543—216no—
183#542—232no—
184#542—232no—
185#536—232no—
186#533—232no—
187#533—232no—
188#533—216no—
189#533—28no—
190#533—28no—
191#533D4116yescomplemented
192#532—28no—
193C2×C4⋊Q8C2311yescharacteristic
194C2×C4⋊Q8C2314yes—
195C2×C4⋊Q8C2311yescharacteristic
196C2×C4⋊Q8C2311yescharacteristic
197C2×C4⋊Q8C2311yescharacteristic
198C2×C4⋊Q8C2311yescharacteristic
199C2×C4⋊Q8C2314yes—
200C2×C4⋊Q8C2312yes—
201C2×C4⋊Q8C2314yes—
202C2×C4⋊Q8C2314yes—
203C2×C4⋊Q8C2312yes—
204C2×C4⋊Q8C2314yes—
205C2×C4⋊Q8C2314yes—
206C2×C4⋊Q8C2318yes—
207C2×C4⋊Q8C2314yes—
208C2×C4⋊Q8C2318yes—
209C2×C4⋊Q8C2311yescharacteristic
210C2×C4⋊Q8C2311yescharacteristic
211C2×#127C2311yescharacteristic
212C2×#126C2318yes—
213C2×#126C2318yes—
214C2×#125C2312yes—
215C2×#125C2312yes—
216C2×#125C2312yes—
217C2×#125C2314yes—
218C2×#125C2314yes—
219C2×#125C2314yes—
220C2×#125C2314yes—
221C2×#125C2312yes—
222C2×#125C2312yes—
223C2×#124C2314yes—
224C2×#124C2312yes—
225C2×#124C2318yes—
226C2×#124C2314yes—
227C2×#124C2314yes—
228C2×#123C2318yes—
229C2×#123C2318yes—
230C2×#123C2314yes—
231C2×C22⋊Q8C2314yes—
232C2×C22⋊Q8C2312yes—
233C2×C22⋊Q8C2312yes—
234C2×C22⋊Q8C2312yes—
235C2×C22⋊Q8C2314yes—
236C2×C22⋊Q8C2312yes—
237C2×C22⋊Q8C2314yes—
238C2×C22⋊Q8C2314yes—
239C2×C22⋊Q8C2314yes—
240C2×C22⋊Q8C2314yes—
241C2×C22⋊Q8C2314yes—
242C2×C22⋊Q8C2314yes—
243C2×C22⋊Q8C2314yes—
244C2×C22⋊Q8C2314yes—
245C2×C22⋊Q8C2314yes—
246C2×C22⋊Q8C2318yes—
247C2×C22⋊Q8C2314yes—
248C2×C22⋊Q8C2314yes—
249C2×C22⋊Q8C2318yes—
250C2×C22⋊Q8C2318yes—
251C2×C22⋊Q8C2318yes—
252C2×C22⋊Q8C2312yes—
253C2×C22⋊Q8C2312yes—
254C2×#121C2312yes—
255C2×#121C2314yes—
256C2×#121C2312yes—
257C2×#120C2314yes—
258C2×C4×Q8C2312yes—
259C2×C4×Q8C2314yes—
260C2×C4×Q8C2312yes—
261C2×C4×Q8C2314yes—
262C2×C4×Q8C2312yes—
263C2×C4×Q8C2314yes—
264C2×C4×Q8C2312yes—
265C2×C4×Q8C2314yes—
266C2×C4×Q8C2312yes—
267C2×C4×Q8C2312yes—
268C2×C4×D4C2312yes—
269C2×C4×D4C2314yes—
270C2×C4×D4C2312yes—
271C2×C4×D4C2314yes—
272C2×C4×D4C2318yes—
273C2×#117—216no—
274C2×#117—28no—
275C2×#117C2312yes—
276C2×#117C2314yes—
277C2×#117C2312yes—
278C2×#117C2312yes—
279C2×#117C2312yes—
280C2×#117C2312yes—
281C2×#117C2314yes—
282C2×#117C2312yes—
283C2×#117C2312yes—
284C2×#117C2312yes—
285C2×#117C2314yes—
286C2×#117C2312yes—
287C22×C4⋊C4C2311yescharacteristic
288C22×C4⋊C4C2311yescharacteristic
289C22×C4⋊C4C2312yes—
290C22×C4⋊C4C2312yes—
291C22×C22⋊C4C2311yescharacteristic
292C22×C22⋊C4C2314yes—
293C22×C22⋊C4C2311yescharacteristic
294C22×C42C2314yes—
295C22×C42C2311yescharacteristic
296C22×C42C2311yescharacteristic
297#400C2318yes—
298#400C2318yes—
299#400C2318yes—
300#400C2314yes—
301#400C2314yes—
302#400C2318yes—
303#400C2318yes—
304#399C2318yes—
305#399C2318yes—
306#399C2314yes—
307#399C2314yes—
308#399C2318yes—
309#399C2318yes—
310#398C2318yes—
311#398C2318yes—
312#398C2318yes—
313#398C2314yes—
314#398C2314yes—
315#398C2318yes—
316#398C2318yes—
317#398C2318yes—
318#397C2314yes—
319#397C2314yes—
320#397C2318yes—
321#397C2318yes—
322#397C2318yes—
323#397C2318yes—
324#397C2318yes—
325#396C2318yes—
326#396C2318yes—
327#396C2318yes—
328#396C2318yes—
329#395C2318yes—
330#395C2318yes—
331#395C2318yes—
332#395C2318yes—
333#395C2318yes—
334#395C2314yes—
335#395C2314yes—
336#395C2318yes—
337#394C2318yes—
338#394C2318yes—
339#394C2318yes—
340#394C2318yes—
341#394C2314yes—
342#394C2314yes—
343#394C2318yes—
344#393C2318yes—
345#393C2314yes—
346#393C2318yes—
347#393C2318yes—
348#393C2318yes—
349#393C2314yes—
350#393C2318yes—
351#392C2314yes—
352#392C2314yes—
353#391C2314yes—
354#391C2314yes—
355#391C2318yes—
356#391C2314yes—
357#391C2314yes—
358#391C2314yes—
359#391C2318yes—
360#391C2318yes—
361#391C2318yes—
362#391C2318yes—
363#391C2314yes—
364#391C2318yes—
365#390C2318yes—
366#390C2314yes—
367#390C2314yes—
368#390C2318yes—
369#390C2314yes—
370#390C2314yes—
371#389C2314yes—
372#389C2314yes—
373#389C2314yes—
374#389C2314yes—
375#389C2314yes—
376#389C2318yes—
377#389C2318yes—
378#389C2314yes—
379#389C2318yes—
380#389C2318yes—
381#388C2318yes—
382#388C2318yes—
383#388C2318yes—
384#388C2318yes—
385#388C2318yes—
386#388C2318yes—
387#388C2318yes—
388#388C2318yes—
389#388C2318yes—
390#388C2318yes—
391#388C2318yes—
392#388C2318yes—
393#388C2318yes—
394#388C2318yes—
395#388C2318yes—
396#388C2318yes—
397#387C2318yes—
398#387C2318yes—
399#387C2318yes—
400#387C2318yes—
401#387C2318yes—
402#387C2318yes—
403#387C2318yes—
404#387C2318yes—
405#387C2318yes—
406#387C2318yes—
407#387C2318yes—
408#387C2318yes—
409#387C2318yes—
410#387C2318yes—
411#386C2318yes—
412#386C2318yes—
413#386C2318yes—
414#386C2314yes—
415#386C2314yes—
416#386C2318yes—
417#386C2318yes—
418#386C2318yes—
419#385C2318yes—
420#385C2318yes—
421#385C2318yes—
422#385C2318yes—
423#385C2318yes—
424#385C2318yes—
425#385C2314yes—
426#385C2314yes—
427#385C2318yes—
428#385C2318yes—
429#384C2314yes—
430#384C2318yes—
431#384C2314yes—
432#383C2312yes—
433#383C2312yes—
434#382C2314yes—
435#382C2314yes—
436#382C2312yes—
437#382C2312yes—
438#381C2312yes—
439#381C2314yes—
440#381C2312yes—
441#380C2312yes—
442#380C2312yes—
443#380C2314yes—
444#380C2314yes—
445#380C2318yes—
446#380C2318yes—
447#379C2314yes—
448C4×C4⋊C4C2318yes—
449C4×C4⋊C4C2312yes—
450C4×C4⋊C4C2314yes—
451C4×C4⋊C4C2314yes—
452C4×C4⋊C4C2312yes—
453C4×C4⋊C4C2318yes—
454C4×C4⋊C4C2318yes—
455C4×C22⋊C4C2318yes—
456C4×C22⋊C4C2312yes—
457C4×C22⋊C4C2312yes—
458C4×C22⋊C4C2318yes—
459#376C2312yes—
460#376C2312yes—
461C25C2411yescharacteristic
462C2×#41—28no—
463C2×#41—84no—
464C22×Q8—216no—
465C22×Q8—84no—
466C22×Q8—84no—
467C22×Q8C2412yes—
468C22×Q8C2414yes—
469C22×Q8C2412yes—
470C22×Q8C2412yes—
471C22×Q8C2414yes—
472C22×Q8C2412yes—
473C22×Q8C2418yes—
474C22×Q8C2412yes—
475C22×Q8C2412yes—
476C22×Q8C2412yes—
477C22×D4C2412yes—
478C22×D4C2412yes—
479C22×D4C2418yes—
480C22×D4C2414yes—
481C22×D4C2412yes—
482C23×C4—24no—
483C23×C4—28no—
484C23×C4C2411yescharacteristic
485C23×C4C2412yes—
486C23×C4C2411yescharacteristic
487C23×C4C2412yes—
488C23×C4C2414yes—
489C23×C4C2411yescharacteristic
490C23×C4C2414yes—
491C23×C4C2411yescharacteristic
492C23×C4C2414yes—
493C23×C4C2418yes—
494C23×C4C2411yescharacteristic
495C23×C4C2411yescharacteristic
496C4⋊Q8—216no—
497C4⋊Q8—216no—
498C4⋊Q8—216no—
499C4⋊Q8—216no—
500C4⋊Q8—28no—
501C4⋊Q8—28no—
502C4⋊Q8—232no—
503C4⋊Q8—216no—
504C4⋊Q8—24no—
505C4⋊Q8—24no—
506C4⋊Q8—24no—
507C4⋊Q8—24no—
508C4⋊Q8—24no—
509C4⋊Q8—216no—
510C4⋊Q8—88no—
511C4⋊Q8—84no—
512C4⋊Q8C2×D418yes—
513C4⋊Q8C2×D418yes—
514#127—24no—
515#126—232no—
516#126—232no—
517#125—216no—
518#125—216no—
519#125—216no—
520#125—216no—
521#125—28no—
522#125—28no—
523#125—28no—
524#125—28no—
525#125C2×D4116yes—
526#124—216no—
527#124—232no—
528#124—28no—
529#124—216no—
530#124—84no—
531#123—232no—
532#123—232no—
533#123—84no—
534C22⋊Q8—216no—
535C22⋊Q8—216no—
536C22⋊Q8—216no—
537C22⋊Q8—28no—
538C22⋊Q8—28no—
539C22⋊Q8—28no—
540C22⋊Q8—28no—
541C22⋊Q8—216no—
542C22⋊Q8—216no—
543C22⋊Q8—216no—
544C22⋊Q8—216no—
545C22⋊Q8—216no—
546C22⋊Q8—216no—
547C22⋊Q8—216no—
548C22⋊Q8—216no—
549C22⋊Q8—232no—
550C22⋊Q8—232no—
551C22⋊Q8—216no—
552C22⋊Q8—216no—
553C22⋊Q8—88no—
554C22⋊Q8—88no—
555C22⋊Q8C2×D4116yes—
556C22⋊Q8C2×D4116yes—
557#121—28no—
558#121—28no—
559#121—216no—
560#120—84no—
561C4×Q8—216no—
562C4×Q8—216no—
563C4×Q8—216no—
564C4×Q8—28no—
565C4×Q8—28no—
566C4×Q8—28no—
567C4×Q8—28no—
568C4×Q8—216no—
569C4×Q8C2×D4116yes—
570C4×Q8C2×D4116yes—
571C4×D4—216no—
572C4×D4—28no—
573C4×D4—28no—
574C4×D4—216no—
575C4×D4—88no—
576#117—28no—
577#117—28no—
578#117—28no—
579#117—28no—
580#117—216no—
581#117—216no—
582#117—216no—
583#117—28no—
584#117—28no—
585#117—28no—
586#117—28no—
587#117C2×D4116yes—
588C2×C4⋊C4—24no—
589C2×C4⋊C4—24no—
590C2×C4⋊C4—28no—
591C2×C4⋊C4—28no—
592C2×C4⋊C4C2412yes—
593C2×C4⋊C4C2414yes—
594C2×C4⋊C4C2412yes—
595C2×C4⋊C4C2414yes—
596C2×C4⋊C4C2412yes—
597C2×C4⋊C4C2412yes—
598C2×C4⋊C4C2412yes—
599C2×C4⋊C4C2412yes—
600C2×C4⋊C4C2412yes—
601C2×C4⋊C4C2412yes—
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2412yes—
604C2×C4⋊C4C2412yes—
605C2×C4⋊C4C2412yes—
606C2×C4⋊C4C2414yes—
607C2×C4⋊C4C2412yes—
608C2×C4⋊C4C2414yes—
609C2×C4⋊C4C2414yes—
610C2×C4⋊C4C2414yes—
611C2×C4⋊C4C2414yes—
612C2×C4⋊C4C2414yes—
613C2×C4⋊C4C2414yes—
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2412yes—
616C2×C4⋊C4C2414yes—
617C2×C4⋊C4C2418yes—
618C2×C4⋊C4C2418yes—
619C2×C4⋊C4C2414yes—
620C2×C4⋊C4C2414yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2418yes—
623C2×C4⋊C4C2418yes—
624C2×C4⋊C4C2418yes—
625C2×C4⋊C4C2418yes—
626C2×C4⋊C4C2418yes—
627C2×C4⋊C4C2418yes—
628C2×C4⋊C4C2418yes—
629C2×C4⋊C4C2418yes—
630C2×C4⋊C4C2418yes—
631C2×C4⋊C4C2412yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2412yes—
634C2×C4⋊C4C2412yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2414yes—
637C2×C22⋊C4—24no—
638C2×C22⋊C4—24no—
639C2×C22⋊C4—216no—
640C2×C22⋊C4C2412yes—
641C2×C22⋊C4C2414yes—
642C2×C22⋊C4C2412yes—
643C2×C22⋊C4C2412yes—
644C2×C22⋊C4C2414yes—
645C2×C22⋊C4C2412yes—
646C2×C22⋊C4C2414yes—
647C2×C22⋊C4C2414yes—
648C2×C22⋊C4C2418yes—
649C2×C22⋊C4C2414yes—
650C2×C22⋊C4C2414yes—
651C2×C22⋊C4C2418yes—
652C2×C22⋊C4C2418yes—
653C2×C22⋊C4C2418yes—
654C2×C22⋊C4C2418yes—
655C2×C22⋊C4C2418yes—
656C2×C22⋊C4C2418yes—
657C2×C22⋊C4C2418yes—
658C2×C22⋊C4C2414yes—
659C2×C22⋊C4C2418yes—
660C2×C22⋊C4C2418yes—
661C2×C22⋊C4C2414yes—
662C2×C22⋊C4C2418yes—
663C2×C22⋊C4C2418yes—
664C2×C22⋊C4C2418yes—
665C2×C22⋊C4C2414yes—
666C2×C42—24no—
667C2×C42—216no—
668C2×C42C2×D418yes—
669C2×C42C2412yes—
670C2×C42C2414yes—
671C2×C42C2414yes—
672C2×C42C2414yes—
673C2×C42C2412yes—
674C2×C42C2414yes—
675C2×C42C2418yes—
676C2×C42C2418yes—
677C2×C42C2414yes—
678C2×C42C2414yes—
679C2×C42C2418yes—
680C2×C42C2411yescharacteristic
681C2×C42C2411yescharacteristic
682C2×C42C2414yes—
683C2×C42C2411yescharacteristic
684C2×C42C2411yescharacteristic
685#95C2414yes—
686#95C2414yes—
687#95C2414yes—
688#95C2414yes—
689#95C2418yes—
690#95C2418yes—
691#95C2414yes—
692#95C2414yes—
693#95C2418yes—
694#95C2418yes—
695#95C2418yes—
696#95C2414yes—
697#95C2414yes—
698#95C2418yes—
699#95C2418yes—
700#95C2418yes—
701#95C2418yes—
702#95C2418yes—
703#95C2418yes—
704#95C2418yes—
705#95C2418yes—
706#95C2418yes—
707#95C2418yes—
708#95C2418yes—
709#95C2418yes—
710#95C2418yes—
711C24—22no—
712C24—24no—
713C24—42no—
714C24—42no—
715C24C2514yes—
716C24C2511yescharacteristic
717C24C2512yes—
718#41—816no—
719C2×Q8—24no—
720C2×Q8—24no—
721C2×Q8—28no—
722C2×Q8—28no—
723C2×Q8—24no—
724C2×Q8—24no—
725C2×Q8—216no—
726C2×Q8—24no—
727C2×Q8—28no—
728C2×Q8—42no—
729C2×Q8—42no—
730C2×Q8—44no—
731C2×Q8—42no—
732C2×Q8—42no—
733C2×Q8—44no—
734C2×Q8—48no—
735C2×Q8—42no—
736C2×Q8—44no—
737C2×Q8—42no—
738C2×Q8—48no—
739C2×Q8—44no—
740C2×Q8—42no—
741C2×Q8—42no—
742C2×Q8—44no—
743C2×Q8—44no—
744C2×Q8—832no—
745C2×Q8C22×D418yes—
746C2×Q8C22×D418yes—
747C2×D4—28no—
748C2×D4—216no—
749C2×D4—24no—
750C2×D4—24no—
751C2×D4—24no—
752C2×D4—28no—
753C2×D4—44no—
754C2×D4—48no—
755C2×D4—44no—
756C2×D4—44no—
757C2×D4—44no—
758C2×D4—48no—
759C22×C4—232no—
760C22×C4—22no—
761C22×C4—24no—
762C22×C4—24no—
763C22×C4—24no—
764C22×C4—24no—
765C22×C4—24no—
766C22×C4—24no—
767C22×C4—24no—
768C22×C4—22no—
769C22×C4—22no—
770C22×C4—28no—
771C22×C4—28no—
772C22×C4—28no—
773C22×C4—216no—
774C22×C4—42no—
775C22×C4—44no—
776C22×C4—44no—
777C22×C4—42no—
778C22×C4—44no—
779C22×C4—48no—
780C22×C4—44no—
781C22×C4—48no—
782C22×C4—42no—
783C22×C4—44no—
784C22×C4—44no—
785C22×C4—42no—
786C22×C4C22×D414yes—
787C22×C4C22×D414yes—
788C22×C4C22×D414yes—
789C22×C42−1+418yes—
790C22×C4C2518yes—
791C22×C4C2518yes—
792C22×C4C2514yes—
793C22×C4C2514yes—
794C22×C4C2512yes—
795C22×C4C2514yes—
796C22×C4C2514yes—
797C22×C4C2514yes—
798C22×C4C2512yes—
799C22×C4C2511yescharacteristic
800C22×C4C2511yescharacteristic
801C22×C4C2511yescharacteristic
802C22×C4C2511yescharacteristic
803C22×C4C2514yes—
804C22×C4C2511yescharacteristic
805C22×C4C2514yes—
806C22×C4C2512yes—
807C22×C4C2511yescharacteristic
808C4⋊C4—24no—
809C4⋊C4—28no—
810C4⋊C4—28no—
811C4⋊C4—24no—
812C4⋊C4—24no—
813C4⋊C4—24no—
814C4⋊C4—24no—
815C4⋊C4—24no—
816C4⋊C4—24no—
817C4⋊C4—24no—
818C4⋊C4—24no—
819C4⋊C4—24no—
820C4⋊C4—24no—
821C4⋊C4—24no—
822C4⋊C4—28no—
823C4⋊C4—28no—
824C4⋊C4—28no—
825C4⋊C4—28no—
826C4⋊C4—28no—
827C4⋊C4—28no—
828C4⋊C4—28no—
829C4⋊C4—24no—
830C4⋊C4—24no—
831C4⋊C4—28no—
832C4⋊C4—28no—
833C4⋊C4—216no—
834C4⋊C4—216no—
835C4⋊C4—28no—
836C4⋊C4—28no—
837C4⋊C4—28no—
838C4⋊C4—216no—
839C4⋊C4—48no—
840C4⋊C4—48no—
841C4⋊C4—48no—
842C4⋊C4—48no—
843C4⋊C4—48no—
844C4⋊C4—48no—
845C4⋊C4—48no—
846C4⋊C4—48no—
847C4⋊C4C22×D418yes—
848C4⋊C4C22×D418yes—
849C4⋊C4C22×D418yes—
850C4⋊C4C22×D418yes—
851C4⋊C4C22×D4116yes—
852C4⋊C4C22×D4116yes—
853C22⋊C4—28no—
854C22⋊C4—28no—
855C22⋊C4—216no—
856C22⋊C4—24no—
857C22⋊C4—28no—
858C22⋊C4—28no—
859C22⋊C4—24no—
860C22⋊C4—24no—
861C22⋊C4—24no—
862C22⋊C4—216no—
863C22⋊C4—28no—
864C22⋊C4—28no—
865C22⋊C4—216no—
866C22⋊C4—216no—
867C22⋊C4—216no—
868C22⋊C4—48no—
869C22⋊C4—44no—
870C22⋊C4—48no—
871C22⋊C4—48no—
872C22⋊C4—48no—
873C22⋊C4—48no—
874C22⋊C4—48no—
875C22⋊C4—44no—
876C22⋊C4—48no—
877C22⋊C4—48no—
878C22⋊C4C22×D4116yes—
879C42—24no—
880C42—28no—
881C42—28no—
882C42—28no—
883C42—24no—
884C42—28no—
885C42—216no—
886C42—44no—
887C42—48no—
888C42—48no—
889C42—44no—
890C42C22×D4116yes—
891C42C22×D414yes—
892C42C22×D414yes—
893C42C22×D414yes—
894C42C22×D414yes—
895C23—28no—
896C23—22no—
897C23—22no—
898C23—22no—
899C23—24no—
900C23—22no—
901C23—22no—
902C23—24no—
903C23—24no—
904C23—28no—
905C23—24no—
906C23—24no—
907C23—28no—
908C23—82no—
909C23—82no—
910C23—88no—
911C23C23×D412yes—
912C23C2×2−1+414yes—
913C23C2611yescharacteristic
914Q8—48no—
915Q8—48no—
916Q8—48no—
917Q8—48no—
918Q8—84no—
919Q8—88no—
920Q8—84no—
921Q8—88no—
922Q8—816no—
923Q8—84no—
924D4—48no—
925D4—48no—
926D4—84no—
927D4—816no—
928D4—88no—
929C2×C4—216no—
930C2×C4—28no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—22no—
934C2×C4—24no—
935C2×C4—22no—
936C2×C4—24no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—24no—
940C2×C4—24no—
941C2×C4—22no—
942C2×C4—28no—
943C2×C4—216no—
944C2×C4—24no—
945C2×C4—24no—
946C2×C4—22no—
947C2×C4—24no—
948C2×C4—22no—
949C2×C4—24no—
950C2×C4—24no—
951C2×C4—28no—
952C2×C4—28no—
953C2×C4—28no—
954C2×C4—28no—
955C2×C4—28no—
956C2×C4—24no—
957C2×C4—24no—
958C2×C4—24no—
959C2×C4—28no—
960C2×C4—24no—
961C2×C4—24no—
962C2×C4—28no—
963C2×C4—28no—
964C2×C4—24no—
965C2×C4—24no—
966C2×C4—24no—
967C2×C4—44no—
968C2×C4—44no—
969C2×C4—416no—
970C2×C4—88no—
971C2×C4—88no—
972C2×C4—816no—
973C2×C4—82no—
974C2×C4—82no—
975C2×C4C23×D412yes—
976C2×C4C23×D418yes—
977C2×C4C23×D412yes—
978C2×C4C23×D418yes—
979C2×C4C23×D412yes—
980C2×C4C23×D412yes—
981C2×C4C23×D412yes—
982C2×C4C23×D412yes—
983C2×C4C2×2−1+414yes—
984C2×C4C2×2−1+414yes—
985C22—22no—
986C22—24no—
987C22—22no—
988C22—22no—
989C22—28no—
990C22—42no—
991C22—42no—
992C22—44no—
993C22—44no—
994C22—44no—
995C22—44no—
996C22—44no—
997C22—48no—
998C22—48no—
999C22—88no—
1000C22C24×D411yescharacteristic
1001C22C22×2−1+412yes—
1002C22H(7,𝔽2)12yes—
1003C222−1+612yes—
1004C4—22no—
1005C4—24no—
1006C4—22no—
1007C4—22no—
1008C4—28no—
1009C4—22no—
1010C4—22no—
1011C4—28no—
1012C4—44no—
1013C4—44no—
1014C4—44no—
1015C4—44no—
1016C4—42no—
1017C4—44no—
1018C4—42no—
1019C4—48no—
1020C4—48no—
1021C4#348614yes—
1022C2—42no—
1023C2—44no—
1024C2—84no—
1025C2C2×#348611yescharacteristic
1026C2#6285211yescharacteristic
1027C2#6285911yescharacteristic
1028C2#6287914yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35301C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3550C2semidirect
2. C2×#3458C2semidirect
3. #52056C2semidirect
4. #52007C2semidirect
5. #51750C2semidirect
6. #51543C2semidirect
7. #47216C2semidirect
8. #46816C2semidirect
9. #46426C2semidirect
10. #46357C2semidirect
11. #39719C2semidirect
12. #39718C2semidirect
13. #39597C2semidirect
14. #39596C2semidirect
15. #37635C2semidirect
16. #37619C2semidirect
17. #37275C2semidirect
18. #35325C2semidirect
20. #35260C2semidirect
21. #34375C2semidirect
23. C2×#563C22semidirect
24. C2×#559C22semidirect
25. C2×Q82C22semidirect
26. C2×#556C22semidirect
27. C2×#556C22semidirect
28. C2×D4×Q8C22semidirect
29. C2×D4×Q8C22semidirect
59. #2731C22semidirect
61. #2729C22semidirect
64. #2721C22semidirect
65. #2720C22semidirect
66. #2720C22semidirect
67. #2716C22semidirect
68. #2716C22semidirect
69. #2713C22semidirect
70. #2713C22semidirect
75. #2690C22semidirect
80. #2677C22semidirect
82. #2674C22semidirect
83. #2660C22semidirect
84. #2658C22semidirect
85. #2642C22semidirect
86. #2640C22semidirect
87. #2634C22semidirect
88. #2633C22semidirect
101. #2592C22semidirect
102. #2592C22semidirect
105. #2582C22semidirect
106. #2581C22semidirect
107. #2581C22semidirect
108. #2580C22semidirect
109. #2580C22semidirect
110. #2568C22semidirect
111. #2567C22semidirect
112. #2567C22semidirect
115. #2558C22semidirect
116. #2551C22semidirect
117. #2548C22semidirect
118. #2546C22semidirect
119. #2546C22semidirect
122. #2538C22semidirect
123. #2519C22semidirect
126. #2492C22semidirect
133. #2475C22semidirect
139. #2460C22semidirect
141. #2446C22semidirect
142. #2434C22semidirect
149. #2381C22semidirect
150. #2381C22semidirect
151. #2371C22semidirect
152. #2355C22semidirect
153. #2355C22semidirect
191. #533D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35502
C2×#34582
#520562
#520072
#517502
#515432
#472162
#468162
#464262
#463572
#397192
#397182
#395972
#395962
#376352
#376192
#372752
#353252
#353012
#352602
#343752