Finite Group Databasebeta

← #7645840

Subgroups — #7645840

Order 512.

6648 conjugacy classes of subgroups.

The subgroup lattice has 936 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3507C211yesmaximal, characteristic, complemented
2C22×#556C211yesmaximal, characteristic, complemented
3#42175C218yesmaximal, complemented
4#42170C218yesmaximal, complemented
5#39741C214yesmaximal, complemented
6#39740C214yesmaximal, complemented
7#39163C214yesmaximal, complemented
8#39162C214yesmaximal, complemented
9#37617C212yesmaximal, complemented
10#37537C211yesmaximal, characteristic, complemented
11#37536C211yesmaximal, characteristic
12#37186C214yesmaximal, complemented
13#36971C214yesmaximal, complemented
14#35454C214yesmaximal, complemented
15#35249C211yesmaximal, characteristic, complemented
16#35248C211yesmaximal, characteristic, complemented
17#35233C212yesmaximal, complemented
18#35131C212yesmaximal, complemented
19#35094C214yesmaximal, complemented
20#34972C212yesmaximal, complemented
21#34059C211yesmaximal, characteristic, complemented
22#3507—216no—
23C2×#559C2212yescomplemented
24C2×#557C2212yescomplemented
25C2×#556—216no—
26C2×#556C2214yes—
27C2×#556C2214yes—
28C2×#556C2214yes—
29C2×#556C2214yes—
30C2×#556C2212yescomplemented
31C2×#556C2214yescomplemented
32C2×#554C2212yescomplemented
33C2×#552C2214yescomplemented
34C2×#539C2212yes—
35C2×#539C2212yes—
36C2×#536C2212yes—
37C2×#533C2211yescharacteristic
38C2×#532C2211yescharacteristic
39C22×C4⋊Q8C2211yescharacteristic
40C2×#529C2212yes—
41C2×#529C2212yes—
42C22×#126C2212yes—
43C22×#126C2212yes—
44C22×#124C2211yescharacteristic
45C22×#124C2211yescharacteristic
46C22×C22⋊Q8C2212yes—
47C2×#520C2212yes—
48C22×C4×Q8C2211yescharacteristic
49C22×C4×Q8C2211yescharacteristic
50C22×C4×Q8C2211yescharacteristic
51C22×C4×D4C2211yescharacteristic
52C22×#117C2212yes—
53#2861C2214yes—
54#2858C2214yes—
55#2855C2214yes—
56#2854C2214yes—
57#2849C2218yes—
58#2821C2218yescomplemented
59#2820C2214yes—
60#2819C2214yes—
61#2732C22116yescomplemented
62#2730C22116yescomplemented
63#2729C22116yescomplemented
64#2728C22116yescomplemented
65#2727C22116yescomplemented
66#2725C22116yescomplemented
67#2705C22116yescomplemented
68#2702C22116yescomplemented
69#2662C2218yes—
70#2658C2212yes—
71#2658C2214yescomplemented
72#2657C2212yes—
73#2642C2214yescomplemented
74#2640C2212yes—
75#2640C2212yes—
76#2636C2218yes—
77#2634C2214yescomplemented
78#2632C2214yes—
79#2632C2214yescomplemented
80#2631C2214yes—
81#2628C2218yescomplemented
82#2626C2214yes—
83#2623C2218yes—
84#2617C2214yes—
85#2610C2218yes—
86#2604C2218yescomplemented
87#2598C2218yes—
88#2581C2214yescomplemented
89#2580C2214yescomplemented
90#2568C2212yescomplemented
91#2567C2212yescomplemented
92#2566C2214yes—
93#2565C2214yescomplemented
94#2548C2212yescomplemented
95#2547C2214yescomplemented
96#2546C2212yescomplemented
97#2546C2214yescomplemented
98#2545C2214yes—
99#2545C2214yes—
100#2545C2214yescomplemented
101#2544C2214yes—
102#2544C2214yes—
103#2544C2214yes—
104#2534C2218yes—
105#2503C2212yes—
106#2501C2212yes—
107#2487C2218yes—
108#2484C2214yes—
109#2482C2214yes—
110#2481C22116yescomplemented
111#2479C22116yescomplemented
112#2479C22116yescomplemented
113#2477C22116yescomplemented
114#2475C22116yescomplemented
115#2471C22116yescomplemented
116#2469C22116yescomplemented
117#2467C22116yescomplemented
118#2436C2212yes—
119#2436C2212yes—
120#2435C2212yes—
121#2434C2212yes—
122#2434C2212yes—
123#2433C2212yes—
124#2413C2218yes—
125#2411C2218yes—
126#2406C2214yes—
127#2404C2214yes—
128#2396C2218yescomplemented
129#2328C2214yes—
130#2327C2214yescomplemented
131#2326C2214yes—
132#2326C2214yescomplemented
133#2321C2218yes—
134#2320C2214yescomplemented
135#2320C2214yescomplemented
136#2316C2212yes—
137#2313C2212yes—
138#2313C2212yes—
139#2310C2212yes—
140C4×C4⋊Q8C2214yescomplemented
141C4×#124C2214yescomplemented
142C4×#123C2218yes—
143#2295C2214yescomplemented
144#2295C2214yescomplemented
145#2283C2211yescharacteristic
146#2283C2212yes—
147#2283C2211yescharacteristic
148C4×#117C2212yes—
149C22×#41C2312yes—
150C23×Q8C2311yescharacteristic
151C23×Q8C2311yescharacteristic
152C23×Q8C2311yescharacteristic
153C23×D4C2311yescharacteristic
154C24×C4C2312yes—
155#559—216no—
156#557—216no—
157#556—232no—
158#556—232no—
159#556—232no—
160#556—232no—
161#556—216no—
162#556—232no—
163#554—216no—
164#552—232no—
165#539—216no—
166#539—216no—
167#536—216no—
168#533—28no—
169#532—28no—
170C2×C4⋊Q8—28no—
171C2×C4⋊Q8C2314yes—
172C2×C4⋊Q8C2311yescharacteristic
173C2×C4⋊Q8C2311yescharacteristic
174C2×C4⋊Q8C2314yes—
175C2×C4⋊Q8C2311yescharacteristic
176C2×C4⋊Q8C2314yes—
177C2×C4⋊Q8C2314yes—
178C2×C4⋊Q8C2314yes—
179C2×#127C2311yescharacteristic
180C2×#127C2314yes—
181#529—216no—
182#529—216no—
183C2×#126—216no—
184C2×#126—216no—
185C2×#126C2314yes—
186C2×#126C2314yes—
187C2×#126C2318yes—
188C2×#126C2318yes—
189C2×#126C2318yes—
190C2×#126C2318yes—
191C2×#126C2314yes—
192C2×#126C2314yes—
193C2×#125C2312yes—
194C2×#125C2312yes—
195C2×#125C2312yes—
196C2×#125C2314yes—
197C2×#125C2314yes—
198C2×#124—28no—
199C2×#124—28no—
200C2×#124C2312yes—
201C2×#124C2312yes—
202C2×#124C2312yes—
203C2×#124C2312yes—
204C2×#124C2314yes—
205C2×#124C2314yes—
206C2×#124C2312yes—
207C2×#124C2312yes—
208C2×#124C2312yes—
209C2×#124C2314yes—
210C2×#124C2314yes—
211C2×#124C2314yes—
212C2×#124C2314yes—
213C2×#123C2314yes—
214C2×#123C2314yes—
215C2×#123C2314yes—
216C2×#123C2314yes—
217C2×#123C2318yes—
218C2×C22⋊Q8—216no—
219C2×C22⋊Q8C2312yes—
220C2×C22⋊Q8C2318yes—
221C2×C22⋊Q8C2318yes—
222C2×C22⋊Q8C2312yes—
223C2×C22⋊Q8C2314yes—
224C2×C22⋊Q8C2314yes—
225C2×C22⋊Q8C2314yes—
226C2×C22⋊Q8C2314yes—
227C2×#121C2312yes—
228C2×#121C2312yes—
229C2×#120C2318yes—
230#520—216no—
231C2×C4×Q8—28no—
232C2×C4×Q8—28no—
233C2×C4×Q8D4116yescomplemented
234C2×C4×Q8C2312yes—
235C2×C4×Q8C2314yes—
236C2×C4×Q8C2312yes—
237C2×C4×Q8C2312yes—
238C2×C4×Q8C2312yes—
239C2×C4×Q8C2312yes—
240C2×C4×Q8C2312yes—
241C2×C4×Q8C2312yes—
242C2×C4×Q8C2312yes—
243C2×C4×Q8C2314yes—
244C2×C4×Q8C2314yes—
245C2×C4×Q8C2312yes—
246C2×C4×Q8C2312yes—
247C2×C4×Q8C2312yes—
248C2×C4×Q8C2312yes—
249C2×C4×D4—28no—
250C2×C4×D4C2314yes—
251C2×C4×D4C2314yes—
252C2×C4×D4C2312yes—
253C2×C4×D4C2312yes—
254C2×C4×D4C2312yes—
255C2×C4×D4C2314yes—
256C2×C4×D4C2314yes—
257C2×C4×D4C2314yes—
258C2×C4×D4C2312yes—
259C2×#117—216no—
260C2×#117C2314yes—
261C2×#117C2314yes—
262C2×#117C2318yes—
263C2×#117C2318yes—
264C2×#117C2312yes—
265C2×#117C2314yes—
266C2×#117C2314yes—
267C22×C4⋊C4C2312yes—
268C22×C4⋊C4C2311yescharacteristic
269C22×C4⋊C4C2312yes—
270C22×C4⋊C4C2312yes—
271C22×C4⋊C4C2314yes—
272C22×C4⋊C4C2312yes—
273C22×C4⋊C4C2311yescharacteristic
274C22×C4⋊C4C2311yescharacteristic
275C22×C4⋊C4C2311yescharacteristic
276C22×C22⋊C4C2312yes—
277C22×C22⋊C4C2312yes—
278C22×C22⋊C4C2312yes—
279C22×C22⋊C4C2312yes—
280C22×C22⋊C4C2312yes—
281C22×C42C2312yes—
282C22×C42C2312yes—
283C22×C42C2311yescharacteristic
284C22×C42C2311yescharacteristic
285C22×C42C2311yescharacteristic
286#400C23116yes—
287#400C2318yes—
288#400C2318yes—
289#400C23116yes—
290#399C2318yes—
291#399C23116yes—
292#399C2318yes—
293#399C23116yes—
294#399C2318yes—
295#398C23116yes—
296#398C23116yes—
297#398C2318yes—
298#397C2318yes—
299#397C23116yes—
300#397C2318yes—
301#396C23116yes—
302#396C23116yes—
303#396C23116yes—
304#396C23116yes—
305#395C2318yes—
306#395C2318yes—
307#395C2318yes—
308#394C23116yes—
309#394C2318yes—
310#394C2318yes—
311#394C23116yes—
312#394C23116yes—
313#393C2318yes—
314#393C2318yes—
315#393C2318yes—
316#393C2318yes—
317#392C2318yes—
318#392C2318yes—
319#392C2318yes—
320#391C2314yes—
321#391C2314yes—
322#391C2314yes—
323#391C2318yes—
324#391C2318yes—
325#391C2314yes—
326#391C2318yes—
327#391C2314yes—
328#390C2314yes—
329#390C2314yes—
330#390C23116yes—
331#390C2318yes—
332#390C2314yes—
333#390C23116yes—
334#389C23116yes—
335#389C2318yes—
336#389C2318yes—
337#389C2318yes—
338#389C2318yes—
339#389C23116yes—
340#388C23116yes—
341#388C23116yes—
342#388C23116yes—
343#388C23116yes—
344#388C23116yes—
345#388C23116yes—
346#388C23116yes—
347#388C23116yes—
348#387C23116yes—
349#387C2318yes—
350#387C2318yes—
351#387C2318yes—
352#387C2318yes—
353#387C23116yes—
354#387C23116yes—
355#386C2318yes—
356#386C23116yes—
357#386C23116yes—
358#386C23116yes—
359#386C23116yes—
360#386C2318yes—
361#386C23116yes—
362#385C23116yes—
363#385C2318yes—
364#385C23116yes—
365#385C23116yes—
366#385C2318yes—
367#384C2314yes—
368#383C2314yes—
369#383C2312yes—
370#383C2312yes—
371#382C2312yes—
372#382C2312yes—
373#382C2314yes—
374#382C2314yes—
375#381C2314yes—
376#381C2312yes—
377#381C2312yes—
378#381C2318yes—
379#380C2312yes—
380#380C2312yes—
381#380C2314yes—
382#380C23116yes—
383#379C2318yes—
384C4×C4⋊C4C23116yes—
385C4×C4⋊C4C2314yes—
386C4×C4⋊C4C2314yes—
387C4×C4⋊C4C2312yes—
388C4×C4⋊C4C2312yes—
389C4×C4⋊C4C2314yes—
390C4×C22⋊C4C2314yes—
391C4×C22⋊C4C23116yes—
392C4×C22⋊C4C2312yes—
393C4×C22⋊C4C2312yes—
394#376C2314yes—
395#376C2314yes—
396#376C2312yes—
397#376C2312yes—
398C43C2314yes—
399C25C2412yes—
400C2×#41—28no—
401C2×#41—48no—
402C22×Q8—24no—
403C22×Q8—24no—
404C22×Q8—44no—
405C22×Q8—44no—
406C22×Q8—44no—
407C22×Q8C2×D418yes—
408C22×Q8C2412yes—
409C22×Q8C2412yes—
410C22×Q8C2412yes—
411C22×Q8C2412yes—
412C22×Q8C2412yes—
413C22×Q8C2412yes—
414C22×Q8C2412yes—
415C22×Q8C2412yes—
416C22×Q8C2412yes—
417C22×D4—24no—
418C22×D4—44no—
419C22×D4C2412yes—
420C22×D4C2414yes—
421C22×D4C2412yes—
422C22×D4C2412yes—
423C22×D4C2412yes—
424C22×D4C2412yes—
425C22×D4C24116yes—
426C23×C4—28no—
427C23×C4—48no—
428C23×C4C2412yes—
429C23×C4C2411yescharacteristic
430C23×C4C2411yescharacteristic
431C23×C4C2411yescharacteristic
432C23×C4C2411yescharacteristic
433C23×C4C2412yes—
434C23×C4C2412yes—
435C23×C4C2414yes—
436C23×C4C2414yes—
437C23×C4C2414yes—
438C23×C4C2418yes—
439C23×C4C2411yescharacteristic
440C23×C4C2411yescharacteristic
441C23×C4C2411yescharacteristic
442C4⋊Q8—216no—
443C4⋊Q8—216no—
444C4⋊Q8—216no—
445C4⋊Q8—24no—
446C4⋊Q8—24no—
447C4⋊Q8—24no—
448C4⋊Q8—48no—
449C4⋊Q8—48no—
450#127—24no—
451#127—48no—
452#126—232no—
453#126—232no—
454#126—232no—
455#126—232no—
456#126—216no—
457#126—216no—
458#126—216no—
459#126—216no—
460#125—216no—
461#125—216no—
462#125—28no—
463#125—28no—
464#125—28no—
465#124—216no—
466#124—216no—
467#124—28no—
468#124—28no—
469#124—216no—
470#124—28no—
471#124—28no—
472#124—28no—
473#124—28no—
474#124—28no—
475#124—48no—
476#124—48no—
477#124—48no—
478#123—216no—
479#123—216no—
480#123—216no—
481#123—216no—
482#123—416no—
483C22⋊Q8—232no—
484C22⋊Q8—232no—
485C22⋊Q8—216no—
486C22⋊Q8—216no—
487C22⋊Q8—28no—
488C22⋊Q8—28no—
489C22⋊Q8—216no—
490C22⋊Q8—216no—
491#121—28no—
492#121—28no—
493#120—416no—
494C4×Q8—216no—
495C4×Q8—216no—
496C4×Q8—28no—
497C4×Q8—28no—
498C4×Q8—216no—
499C4×Q8—28no—
500C4×Q8—28no—
501C4×Q8—28no—
502C4×Q8—28no—
503C4×Q8—28no—
504C4×Q8—28no—
505C4×Q8C2×D4116yes—
506C4×Q8C2×D4116yes—
507C4×Q8C2×D4116yes—
508C4×Q8C2×D4116yes—
509C4×D4—216no—
510C4×D4—216no—
511C4×D4—216no—
512C4×D4—216no—
513C4×D4—216no—
514C4×D4—28no—
515C4×D4—28no—
516C4×D4—28no—
517C4×D4—28no—
518#117—28no—
519#117—232no—
520#117—232no—
521#117—216no—
522#117—216no—
523#117—216no—
524#117—48no—
525C2×C4⋊C4—28no—
526C2×C4⋊C4—24no—
527C2×C4⋊C4—28no—
528C2×C4⋊C4—28no—
529C2×C4⋊C4—28no—
530C2×C4⋊C4—216no—
531C2×C4⋊C4C2×D418yes—
532C2×C4⋊C4C2×D418yes—
533C2×C4⋊C4C2×D418yes—
534C2×C4⋊C4C2412yes—
535C2×C4⋊C4C2418yes—
536C2×C4⋊C4C2412yes—
537C2×C4⋊C4C2412yes—
538C2×C4⋊C4C2414yes—
539C2×C4⋊C4C2414yes—
540C2×C4⋊C4C2414yes—
541C2×C4⋊C4C2414yes—
542C2×C4⋊C4C2418yes—
543C2×C4⋊C4C2418yes—
544C2×C4⋊C4C2412yes—
545C2×C4⋊C4C2414yes—
546C2×C4⋊C4C2414yes—
547C2×C4⋊C4C2414yes—
548C2×C4⋊C4C2412yes—
549C2×C4⋊C4C2412yes—
550C2×C4⋊C4C2412yes—
551C2×C4⋊C4C2414yes—
552C2×C4⋊C4C2414yes—
553C2×C4⋊C4C2414yes—
554C2×C4⋊C4C2412yes—
555C2×C4⋊C4C2418yes—
556C2×C4⋊C4C24116yes—
557C2×C4⋊C4C24116yes—
558C2×C4⋊C4C24116yes—
559C2×C4⋊C4C2418yes—
560C2×C4⋊C4C2414yes—
561C2×C4⋊C4C2414yes—
562C2×C4⋊C4C2412yes—
563C2×C4⋊C4C2412yes—
564C2×C4⋊C4C2412yes—
565C2×C4⋊C4C2412yes—
566C2×C4⋊C4C2412yes—
567C2×C4⋊C4C2412yes—
568C2×C22⋊C4—28no—
569C2×C22⋊C4—28no—
570C2×C22⋊C4—28no—
571C2×C22⋊C4—28no—
572C2×C22⋊C4—28no—
573C2×C22⋊C4C2418yes—
574C2×C22⋊C4C2414yes—
575C2×C22⋊C4C2414yes—
576C2×C22⋊C4C2418yes—
577C2×C22⋊C4C2414yes—
578C2×C22⋊C4C2414yes—
579C2×C22⋊C4C2418yes—
580C2×C22⋊C4C2414yes—
581C2×C22⋊C4C2414yes—
582C2×C22⋊C4C2414yes—
583C2×C22⋊C4C2414yes—
584C2×C22⋊C4C2414yes—
585C2×C22⋊C4C2414yes—
586C2×C22⋊C4C2414yes—
587C2×C22⋊C4C2414yes—
588C2×C22⋊C4C2414yes—
589C2×C22⋊C4C2414yes—
590C2×C22⋊C4C2414yes—
591C2×C22⋊C4C24116yes—
592C2×C22⋊C4C24116yes—
593C2×C22⋊C4C24116yes—
594C2×C22⋊C4C24116yes—
595C2×C22⋊C4C24116yes—
596C2×C22⋊C4C24116yes—
597C2×C42—28no—
598C2×C42—28no—
599C2×C42C2×D418yes—
600C2×C42C2×D418yes—
601C2×C42C2×D418yes—
602C2×C42C2414yes—
603C2×C42C2414yes—
604C2×C42C2418yes—
605C2×C42C2414yes—
606C2×C42C2414yes—
607C2×C42C2414yes—
608C2×C42C2414yes—
609C2×C42C2414yes—
610C2×C42C2418yes—
611C2×C42C2418yes—
612C2×C42C2412yes—
613C2×C42C2412yes—
614C2×C42C2412yes—
615C2×C42C2411yescharacteristic
616C2×C42C2411yescharacteristic
617C2×C42C2412yes—
618C2×C42C2411yescharacteristic
619C2×C42C2411yescharacteristic
620#95C2414yes—
621#95C2414yes—
622#95C2418yes—
623#95C2418yes—
624#95C2414yes—
625#95C2414yes—
626#95C2414yes—
627#95C2418yes—
628#95C2414yes—
629#95C24116yes—
630#95C24116yes—
631#95C2418yes—
632#95C2414yes—
633#95C2414yes—
634#95C24116yes—
635#95C24116yes—
636#95C24116yes—
637#95C24116yes—
638C24—24no—
639C24—28no—
640C24—44no—
641C24—44no—
642C24C2514yes—
643C24C2514yes—
644C24C2511yescharacteristic
645#41—432no—
646C2×Q8—24no—
647C2×Q8—24no—
648C2×Q8—24no—
649C2×Q8—24no—
650C2×Q8—24no—
651C2×Q8—24no—
652C2×Q8—24no—
653C2×Q8—24no—
654C2×Q8—28no—
655C2×Q8—28no—
656C2×Q8—24no—
657C2×Q8—416no—
658C2×Q8—44no—
659C2×Q8—44no—
660C2×Q8—44no—
661C2×Q8—44no—
662C2×Q8—44no—
663C2×Q8—44no—
664C2×Q8—416no—
665C2×Q8—416no—
666C2×Q8C22×D418yes—
667C2×Q8C22×D418yes—
668C2×D4—28no—
669C2×D4—216no—
670C2×D4—24no—
671C2×D4—24no—
672C2×D4—24no—
673C2×D4—24no—
674C2×D4—24no—
675C2×D4—28no—
676C2×D4—28no—
677C2×D4—44no—
678C2×D4—44no—
679C2×D4—416no—
680C2×D4—44no—
681C2×D4—416no—
682C2×D4—416no—
683C2×D4—416no—
684C22×C4—24no—
685C22×C4—24no—
686C22×C4—24no—
687C22×C4—24no—
688C22×C4—24no—
689C22×C4—24no—
690C22×C4—24no—
691C22×C4—28no—
692C22×C4—28no—
693C22×C4—216no—
694C22×C4—28no—
695C22×C4—28no—
696C22×C4—416no—
697C22×C4—42no—
698C22×C4—42no—
699C22×C4—42no—
700C22×C4—44no—
701C22×C4—44no—
702C22×C4—48no—
703C22×C4—48no—
704C22×C4—48no—
705C22×C4—432no—
706C22×C4C22×D414yes—
707C22×C4C22×D414yes—
708C22×C4C22×D414yes—
709C22×C4C22×D414yes—
710C22×C4C22×D414yes—
711C22×C4C22×D414yes—
712C22×C4C22×D414yes—
713C22×C4C2518yes—
714C22×C4C2518yes—
715C22×C4C2514yes—
716C22×C4C2514yes—
717C22×C4C2514yes—
718C22×C4C2514yes—
719C22×C4C2514yes—
720C22×C4C2514yes—
721C22×C4C2511yescharacteristic
722C22×C4C2511yescharacteristic
723C22×C4C2511yescharacteristic
724C22×C4C2512yes—
725C22×C4C2512yes—
726C22×C4C2511yescharacteristic
727C22×C4C2511yescharacteristic
728C22×C4C2512yes—
729C22×C4C2512yes—
730C22×C4C2511yescharacteristic
731C4⋊C4—24no—
732C4⋊C4—216no—
733C4⋊C4—24no—
734C4⋊C4—24no—
735C4⋊C4—28no—
736C4⋊C4—28no—
737C4⋊C4—28no—
738C4⋊C4—216no—
739C4⋊C4—28no—
740C4⋊C4—216no—
741C4⋊C4—24no—
742C4⋊C4—28no—
743C4⋊C4—28no—
744C4⋊C4—28no—
745C4⋊C4—24no—
746C4⋊C4—24no—
747C4⋊C4—24no—
748C4⋊C4—28no—
749C4⋊C4—28no—
750C4⋊C4—28no—
751C4⋊C4—24no—
752C4⋊C4—48no—
753C4⋊C4—44no—
754C4⋊C4—44no—
755C4⋊C4—48no—
756C4⋊C4—416no—
757C4⋊C4—416no—
758C4⋊C4—416no—
759C4⋊C4C22×D418yes—
760C4⋊C4C22×D418yes—
761C4⋊C4C22×D418yes—
762C4⋊C4C22×D418yes—
763C4⋊C4C22×D418yes—
764C4⋊C4C22×D418yes—
765C22⋊C4—28no—
766C22⋊C4—28no—
767C22⋊C4—28no—
768C22⋊C4—216no—
769C22⋊C4—28no—
770C22⋊C4—28no—
771C22⋊C4—216no—
772C22⋊C4—28no—
773C22⋊C4—216no—
774C22⋊C4—28no—
775C22⋊C4—28no—
776C22⋊C4—28no—
777C22⋊C4—28no—
778C22⋊C4—28no—
779C22⋊C4—28no—
780C22⋊C4—28no—
781C22⋊C4—28no—
782C22⋊C4—28no—
783C22⋊C4—416no—
784C22⋊C4—416no—
785C22⋊C4—416no—
786C22⋊C4—416no—
787C22⋊C4—416no—
788C22⋊C4—416no—
789C42—216no—
790C42—28no—
791C42—28no—
792C42—28no—
793C42—28no—
794C42—28no—
795C42—28no—
796C42—28no—
797C42—48no—
798C42—48no—
799C42C22×D418yes—
800C42C22×D418yes—
801C42C22×D418yes—
802C42C22×D414yes—
803C42C22×D414yes—
804C42C22×D418yes—
805C42C22×D414yes—
806C42C22×D414yes—
807C23—22no—
808C23—22no—
809C23—24no—
810C23—24no—
811C23—28no—
812C23—28no—
813C23—28no—
814C23—28no—
815C23—28no—
816C23—28no—
817C23—48no—
818C23—48no—
819C23—48no—
820C23—816no—
821C23C23×D412yes—
822C23#58514yes—
823C23C2611yescharacteristic
824Q8—48no—
825Q8—48no—
826Q8—48no—
827Q8—48no—
828Q8—48no—
829Q8—48no—
830Q8—48no—
831Q8—48no—
832Q8—84no—
833D4—48no—
834D4—48no—
835D4—416no—
836D4—48no—
837D4—48no—
838D4—84no—
839D4—1616no—
840C2×C4—24no—
841C2×C4—24no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—24no—
846C2×C4—24no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—28no—
850C2×C4—28no—
851C2×C4—28no—
852C2×C4—28no—
853C2×C4—24no—
854C2×C4—24no—
855C2×C4—24no—
856C2×C4—24no—
857C2×C4—24no—
858C2×C4—24no—
859C2×C4—28no—
860C2×C4—28no—
861C2×C4—28no—
862C2×C4—28no—
863C2×C4—24no—
864C2×C4—28no—
865C2×C4—28no—
866C2×C4—28no—
867C2×C4—28no—
868C2×C4—24no—
869C2×C4—28no—
870C2×C4—28no—
871C2×C4—28no—
872C2×C4—44no—
873C2×C4—44no—
874C2×C4—44no—
875C2×C4—432no—
876C2×C4—416no—
877C2×C4—48no—
878C2×C4—48no—
879C2×C4—48no—
880C2×C4—88no—
881C2×C4—88no—
882C2×C4C23×D414yes—
883C2×C4C23×D412yes—
884C2×C4C23×D412yes—
885C2×C4C23×D412yes—
886C2×C4C23×D414yes—
887C2×C4C23×D412yes—
888C2×C4C23×D414yes—
889C2×C4C23×D414yes—
890C2×C4C23×D412yes—
891C2×C4C23×D412yes—
892C2×C4#58514yes—
893C22—22no—
894C22—22no—
895C22—28no—
896C22—44no—
897C22—44no—
898C22—44no—
899C22—44no—
900C22—44no—
901C22—44no—
902C22—416no—
903C22—416no—
904C22—816no—
905C22#344914yes—
906C22C24×D411yescharacteristic
907C22C2×#58512yes—
908C22C2×#58512yes—
909C222−1+612yes—
910C4—22no—
911C4—24no—
912C4—24no—
913C4—22no—
914C4—22no—
915C4—24no—
916C4—22no—
917C4—22no—
918C4—24no—
919C4—44no—
920C4—44no—
921C4—44no—
922C4—44no—
923C4—44no—
924C4—44no—
925C4—48no—
926C4—48no—
927C4#348714yes—
928C2—24no—
929C2—84no—
930C2—84no—
931C2C2×#344911yescharacteristic
932C2C2×#348711yescharacteristic
933C2#6285911yescharacteristic
934C2#6296414yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#37536C2
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×#3507C2semidirect
2. C22×#556C2semidirect
3. #42175C2semidirect
4. #42170C2semidirect
5. #39741C2semidirect
6. #39740C2semidirect
7. #39163C2semidirect
8. #39162C2semidirect
9. #37617C2semidirect
10. #37537C2semidirect
12. #37186C2semidirect
13. #36971C2semidirect
14. #35454C2semidirect
15. #35249C2semidirect
16. #35248C2semidirect
17. #35233C2semidirect
18. #35131C2semidirect
19. #35094C2semidirect
20. #34972C2semidirect
21. #34059C2semidirect
23. C2×#559C22semidirect
24. C2×#557C22semidirect
30. C2×#556C22semidirect
31. C2×#556C22semidirect
32. C2×#554C22semidirect
33. C2×#552C22semidirect
58. #2821C22semidirect
61. #2732C22semidirect
62. #2730C22semidirect
63. #2729C22semidirect
64. #2728C22semidirect
65. #2727C22semidirect
66. #2725C22semidirect
67. #2705C22semidirect
68. #2702C22semidirect
71. #2658C22semidirect
73. #2642C22semidirect
77. #2634C22semidirect
79. #2632C22semidirect
81. #2628C22semidirect
86. #2604C22semidirect
88. #2581C22semidirect
89. #2580C22semidirect
90. #2568C22semidirect
91. #2567C22semidirect
93. #2565C22semidirect
94. #2548C22semidirect
95. #2547C22semidirect
96. #2546C22semidirect
97. #2546C22semidirect
100. #2545C22semidirect
110. #2481C22semidirect
111. #2479C22semidirect
112. #2479C22semidirect
113. #2477C22semidirect
114. #2475C22semidirect
115. #2471C22semidirect
116. #2469C22semidirect
117. #2467C22semidirect
128. #2396C22semidirect
130. #2327C22semidirect
132. #2326C22semidirect
134. #2320C22semidirect
135. #2320C22semidirect
140. C4×C4⋊Q8C22semidirect
141. C4×#124C22semidirect
143. #2295C22semidirect
144. #2295C22semidirect
233. C2×C4×Q8D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35072
C22×#5562
#421752
#421702
#397412
#397402
#391632
#391622
#376172
#375372
#375362
#371862
#369712
#354542
#352492
#352482
#352332
#351312
#350942
#349722
#340592