Finite Group Databasebeta

← #7657662

Subgroups — #7657662

Order 512.

7436 conjugacy classes of subgroups.

The subgroup lattice has 1053 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3511C211yesmaximal, characteristic, complemented
2C2×#3517C211yesmaximal, characteristic, complemented
3#42909C214yesmaximal, complemented
4#42646C214yesmaximal, complemented
5#41959C218yesmaximal, complemented
6#41954C218yesmaximal, complemented
7#39747C212yesmaximal, complemented
8#39744C212yesmaximal, complemented
9#37683C214yesmaximal, complemented
10#37680C214yesmaximal, complemented
11#37619C212yesmaximal, complemented
12#37618C211yesmaximal, characteristic, complemented
13#37617C211yesmaximal, characteristic, complemented
14#37544C212yesmaximal, complemented
15#36127C212yesmaximal, complemented
16#36125C212yesmaximal, complemented
17#35701C214yesmaximal, complemented
18#35689C214yesmaximal, complemented
19#35326C212yesmaximal, complemented
20#35317C211yesmaximal, characteristic, complemented
21#34641C212yesmaximal, complemented
22#34624C211yesmaximal, characteristic, complemented
23#34123C211yesmaximal, characteristic, complemented
24#3517—216no—
25#3511—216no—
26C2×#557C2211yescharacteristic
27C2×#556C2212yes—
28C2×#555C2212yes—
29C2×#554C2212yes—
30C2×#553C2212yes—
31C2×#553C2214yes—
32C2×#553C2214yes—
33C2×#550C2211yescharacteristic
34C2×#550C2212yes—
35C2×#550C2211yescharacteristic
36C2×#550C2212yes—
37C2×#548C2214yes—
38C2×#547C2212yes—
39C2×#547C2211yescharacteristic
40C2×#547C2212yes—
41C2×#542C2214yes—
42C2×#540C2212yes—
43C2×#540C2214yes—
44C2×#537C2212yes—
45C2×#536C2214yes—
46C2×#533C2212yes—
47C2×#532C2211yescharacteristic
48C2×#532C2212yes—
49C2×#532C2211yescharacteristic
50C2×#532C2212yes—
51C2×#532C2214yes—
52C2×#532C2214yes—
53C22×C4⋊Q8C2211yescharacteristic
54C2×#529C2211yescharacteristic
55C2×#529C2212yes—
56C2×#520C2212yes—
57C2×#520C2212yes—
58C2×C4×#41C2211yescharacteristic
59#2868C2212yes—
60#2858C2212yes—
61#2857C2214yes—
62#2850C2214yes—
63#2821C2214yes—
64#2816C2218yes—
65#2815C2214yes—
66#2813C2218yes—
67#2721C22116yes—
68#2714C22116yes—
69#2676C22116yes—
70#2673C22116yes—
71#2672C22116yes—
72#2671C22116yes—
73#2662C2214yes—
74#2661C2214yes—
75#2660C2211yescharacteristic
76#2658C2214yes—
77#2658C2212yes—
78#2658C2212yes—
79#2658C2212yes—
80#2657C2214yes—
81#2657C2211yescharacteristic
82#2657C2212yes—
83#2656C2218yes—
84#2656C2218yes—
85#2642C2212yes—
86#2641C2211yescharacteristic
87#2640C2211yescharacteristic
88#2640C2212yes—
89#2636C2218yes—
90#2635C2218yes—
91#2633C2218yes—
92#2631C2214yes—
93#2628C2214yes—
94#2624C2218yes—
95#2623C2214yes—
96#2620C2212yes—
97#2619C2212yes—
98#2615C2214yes—
99#2611C2218yes—
100#2604C2218yes—
101#2598C2218yes—
102#2580C2218yes—
103#2564C2218yes—
104#2548C2214yes—
105#2547C2212yes—
106#2547C2212yes—
107#2546C2212yes—
108#2546C2214yes—
109#2545C2214yes—
110#2544C2214yes—
111#2542C2214yes—
112#2542C2214yes—
113#2541C2212yes—
114#2537C2218yes—
115#2535C2214yes—
116#2501C2214yes—
117#2501C2214yes—
118#2498C2218yes—
119#2487C2214yes—
120#2464C22116yes—
121#2463C22116yes—
122#2456C22116yes—
123#2455C22116yes—
124#2449C22116yes—
125#2441C2218yes—
126#2436C2212yes—
127#2434C2212yes—
128#2432C2214yes—
129#2432C2214yes—
130#2432C2214yes—
131#2431C2214yes—
132#2431C2214yes—
133#2428C2218yes—
134#2423C2218yes—
135#2422C22116yes—
136#2414C2218yes—
137#2407C2218yes—
138#2397C2218yes—
139#2397C2218yes—
140#2392C2214yes—
141#2388C2214yes—
142#2361C2218yes—
143#2356C2212yes—
144#2353C2214yes—
145#2349C2212yes—
146D4×C4⋊C4C2218yes—
147#2346C2212yes—
148#2343C2214yes—
149#2339C2212yes—
150#2327C2214yes—
151#2326C2214yes—
152C4×#127C2212yes—
153C4×#124C2212yes—
154#2295C2212yes—
155#2290C2214yes—
156#2283C2212yes—
157#2283C2211yescharacteristic
158C42×D4C2212yes—
159C4×#117C2211yescharacteristic
160C2×#376C2212yes—
161C22×#41C2312yes—
162C22×#41C2312yes—
163C22×#41C2314yes—
164C22×#41C2312yes—
165C22×#41C2312yes—
166C22×#41C2312yes—
167C22×#41C2311yescharacteristic
168C23×Q8C2312yes—
169#557—28no—
170#556—216no—
171#555—216no—
172#554—216no—
173#553—232no—
174#553—216no—
175#553—232no—
176#550—216no—
177#550—28no—
178#550—28no—
179#550—216no—
180#548—232no—
181#547—216no—
182#547—28no—
183#547—216no—
184#542—232no—
185#540—232no—
186#540—216no—
187#537—216no—
188#536—416no—
189#533—216no—
190#532—28no—
191#532—216no—
192#532—28no—
193#532—216no—
194#532—416no—
195#532—416no—
196C2×C4⋊Q8—28no—
197C2×C4⋊Q8C2312yes—
198C2×C4⋊Q8C2314yes—
199C2×C4⋊Q8C2312yes—
200C2×C4⋊Q8C2311yescharacteristic
201C2×C4⋊Q8C2312yes—
202C2×C4⋊Q8C2311yescharacteristic
203C2×C4⋊Q8C2312yes—
204C2×C4⋊Q8C2312yes—
205C2×C4⋊Q8C2314yes—
206C2×C4⋊Q8C2314yes—
207C2×#127C2312yes—
208C2×#127C2311yescharacteristic
209C2×#127C2311yescharacteristic
210C2×#127C2312yes—
211C2×#127C2314yes—
212C2×#127C2312yes—
213C2×#127C2314yes—
214#529—28no—
215#529—216no—
216C2×#126C2312yes—
217C2×#126C2314yes—
218C2×#126C2318yes—
219C2×#125C2314yes—
220C2×#125C2311yescharacteristic
221C2×#125C2312yes—
222C2×#125C2314yes—
223C2×#124C2314yes—
224C2×#124C2312yes—
225C2×#124C2312yes—
226C2×#124C2311yescharacteristic
227C2×#124C2312yes—
228C2×#124C2314yes—
229C2×#124C2318yes—
230C2×#124C2314yes—
231C2×#124C2314yes—
232C2×#124C2314yes—
233C2×#123C2312yes—
234C2×#123C2314yes—
235C2×#123C2314yes—
236C2×#123C2314yes—
237C2×#123C2318yes—
238C2×#123C2314yes—
239C2×#123C23116yes—
240C2×C22⋊Q8C2314yes—
241C2×C22⋊Q8C2314yes—
242C2×C22⋊Q8C2312yes—
243C2×C22⋊Q8C2311yescharacteristic
244C2×C22⋊Q8C2314yes—
245C2×C22⋊Q8C2318yes—
246C2×C22⋊Q8C23116yes—
247C2×#121C2314yes—
248C2×#121C2312yes—
249C2×#121C2312yes—
250C2×#121C2311yescharacteristic
251C2×#121C2312yes—
252C2×#121C2314yes—
253C2×#121C2314yes—
254C2×#121C2314yes—
255C2×#121C2312yes—
256C2×#121C2312yes—
257C2×#121C2314yes—
258C2×#121C2318yes—
259C2×#121C2312yes—
260C2×#121C2314yes—
261C2×#121C2314yes—
262C2×#121C2312yes—
263C2×#121C2314yes—
264C2×#121C2314yes—
265C2×#121C2314yes—
266C2×#121C2318yes—
267C2×#121C23116yes—
268C2×#121C23116yes—
269#520—216no—
270#520—216no—
271C4×#41D4116yescomplemented
272C2×C4×Q8C2314yes—
273C2×C4×Q8C2314yes—
274C2×C4×Q8C2312yes—
275C2×C4×Q8C2312yes—
276C2×C4×Q8C2311yescharacteristic
277C2×C4×Q8C2311yescharacteristic
278C2×C4×Q8C2311yescharacteristic
279C2×C4×D4C2311yescharacteristic
280C2×C4×D4C2312yes—
281C2×C4×D4C2314yes—
282C2×C4×D4C2314yes—
283C2×C4×D4C2312yes—
284C2×C4×D4C2314yes—
285C2×C4×D4C2312yes—
286C2×C4×D4C2312yes—
287C2×C4×D4C2314yes—
288C2×C4×D4C2314yes—
289C2×C4×D4C2312yes—
290C2×C4×D4C2312yes—
291C2×C4×D4C2312yes—
292C2×C4×D4C2318yes—
293C2×C4×D4C2314yes—
294C2×C4×D4C2318yes—
295C2×C4×D4C2314yes—
296C2×C4×D4C23116yes—
297C2×C4×D4C23116yes—
298C2×C4×D4C2311yescharacteristic
299C2×C4×D4C2312yes—
300C2×C4×D4C2311yescharacteristic
301C2×C4×D4C2312yes—
302C2×#117C2314yes—
303C2×#117C2312yes—
304C2×#117C2314yes—
305C2×#117C2312yes—
306C2×#117C2314yes—
307C2×#117C2312yes—
308C2×#117C2311yescharacteristic
309C22×C4⋊C4C2312yes—
310C22×C4⋊C4C2314yes—
311C22×C4⋊C4C2312yes—
312C22×C4⋊C4C2312yes—
313C22×C4⋊C4C2314yes—
314C22×C42C2314yes—
315C22×C42C2311yescharacteristic
316C22×C42C2312yes—
317#400C2318yes—
318#400C2318yes—
319#399C2318yes—
320#399C2318yes—
321#399C2318yes—
322#399C2318yes—
323#399C2318yes—
324#399C2318yes—
325#399C23116yes—
326#399C23116yes—
327#398C23116yes—
328#398C2318yes—
329#398C2314yes—
330#397C2318yes—
331#397C2318yes—
332#397C2314yes—
333#397C2318yes—
334#396C2318yes—
335#396C23116yes—
336#395C2314yes—
337#395C2318yes—
338#394C23116yes—
339#394C23116yes—
340#394C23116yes—
341#394C2314yes—
342#394C2318yes—
343#394C2318yes—
344#394C2314yes—
345#394C23116yes—
346#394C23116yes—
347#393C2314yes—
348#393C2318yes—
349#393C2318yes—
350#392C2318yes—
351#392C2318yes—
352#392C23116yes—
353#392C2318yes—
354#392C2318yes—
355#392C23116yes—
356#392C2314yes—
357#392C2314yes—
358#392C23116yes—
359#392C23116yes—
360#391C2314yes—
361#391C2314yes—
362#391C2314yes—
363#391C2314yes—
364#391C2312yes—
365#390C2312yes—
366#390C2312yes—
367#390C2318yes—
368#390C23116yes—
369#390C2314yes—
370#390C2318yes—
371#390C2318yes—
372#390C2312yes—
373#389C23116yes—
374#389C23116yes—
375#389C2314yes—
376#389C2318yes—
377#388C23116yes—
378#388C23116yes—
379#388C23116yes—
380#388C2318yes—
381#388C2318yes—
382#387C23116yes—
383#387C23116yes—
384#387C2318yes—
385#387C2318yes—
386#386C23116yes—
387#386C2318yes—
388#386C23116yes—
389#386C23116yes—
390#386C2318yes—
391#386C23116yes—
392#385C23116yes—
393#385C23116yes—
394#385C23116yes—
395#385C23116yes—
396#385C2318yes—
397#385C2318yes—
398#384C2312yes—
399#384C2318yes—
400#384C2318yes—
401#383C2312yes—
402#383C2314yes—
403#382C2314yes—
404#382C2312yes—
405#382C2312yes—
406#381C2314yes—
407#381C2312yes—
408#380C23116yes—
409#380C2312yes—
410#380C2318yes—
411#380C2318yes—
412#380C2314yes—
413C4×C4⋊C4C2312yes—
414C4×C4⋊C4C2314yes—
415C4×C4⋊C4C2312yes—
416C4×C4⋊C4C2312yes—
417C4×C4⋊C4C2314yes—
418C4×C22⋊C4C2312yes—
419C4×C22⋊C4C2318yes—
420C4×C22⋊C4C2312yes—
421C4×C22⋊C4C2318yes—
422C4×C22⋊C4C2312yes—
423C4×C22⋊C4C2314yes—
424#376C2314yes—
425#376C2314yes—
426#376C2314yes—
427#376C2311yescharacteristic
428#376C2312yes—
429#376C2311yescharacteristic
430C2×#95C2314yes—
431C2×#95C2314yes—
432C43C2312yes—
433C2×#41—28no—
434C2×#41—28no—
435C2×#41—216no—
436C2×#41—28no—
437C2×#41—28no—
438C2×#41—28no—
439C2×#41—48no—
440C2×#41—44no—
441C2×#41—48no—
442C2×#41—48no—
443C2×#41—48no—
444C2×#41—48no—
445C2×#41—48no—
446C2×#41—48no—
447C2×#41C2×D418yes—
448C22×Q8—28no—
449C22×Q8—48no—
450C22×Q8C2414yes—
451C22×Q8C2411yescharacteristic
452C22×Q8C2412yes—
453C22×Q8C2411yescharacteristic
454C22×Q8C2412yes—
455C22×Q8C2414yes—
456C22×D4C2412yes—
457C22×D4C2412yes—
458C22×D4C2412yes—
459C22×D4C2411yescharacteristic
460C22×D4C2411yescharacteristic
461C22×D4C2412yes—
462C22×D4C2418yes—
463C22×D4C2414yes—
464C22×D4C2412yes—
465C22×D4C2414yes—
466C22×D4C2414yes—
467C22×D4C2412yes—
468C22×D4C2414yes—
469C22×D4C2412yes—
470C22×D4C2418yes—
471C22×D4C2414yes—
472C22×D4C2414yes—
473C22×D4C2414yes—
474C22×D4C24116yes—
475C22×D4C2412yes—
476C23×C4C2412yes—
477C23×C4C2414yes—
478C23×C4C2411yescharacteristic
479C23×C4C2411yescharacteristic
480C23×C4C2412yes—
481C23×C4C2414yes—
482C23×C4C2414yes—
483C23×C4C2414yes—
484C23×C4C2414yes—
485C23×C4C2418yes—
486C23×C4C2414yes—
487C23×C4C2418yes—
488C23×C4C2411yescharacteristic
489C23×C4C2412yes—
490C23×C4C2412yes—
491C4⋊Q8—28no—
492C4⋊Q8—28no—
493C4⋊Q8—28no—
494C4⋊Q8—28no—
495C4⋊Q8—24no—
496C4⋊Q8—24no—
497C4⋊Q8—28no—
498C4⋊Q8—216no—
499C4⋊Q8—48no—
500C4⋊Q8—48no—
501#127—28no—
502#127—216no—
503#127—24no—
504#127—24no—
505#127—28no—
506#127—28no—
507#127—48no—
508#126—232no—
509#126—216no—
510#126—28no—
511#125—28no—
512#125—216no—
513#125—24no—
514#125—216no—
515#124—232no—
516#124—24no—
517#124—28no—
518#124—28no—
519#124—216no—
520#124—28no—
521#124—216no—
522#124—48no—
523#124—48no—
524#124—48no—
525#123—28no—
526#123—216no—
527#123—216no—
528#123—216no—
529#123—216no—
530#123—232no—
531#123—432no—
532C22⋊Q8—216no—
533C22⋊Q8—24no—
534C22⋊Q8—28no—
535C22⋊Q8—216no—
536C22⋊Q8—216no—
537C22⋊Q8—232no—
538C22⋊Q8—432no—
539#121—216no—
540#121—232no—
541#121—28no—
542#121—216no—
543#121—24no—
544#121—28no—
545#121—216no—
546#121—28no—
547#121—216no—
548#121—28no—
549#121—28no—
550#121—216no—
551#121—28no—
552#121—216no—
553#121—28no—
554#121—216no—
555#121—216no—
556#121—216no—
557#121—216no—
558#121—432no—
559#121—416no—
560#121—432no—
561C4×Q8—28no—
562C4×Q8—216no—
563C4×Q8—24no—
564C4×Q8—28no—
565C4×Q8—216no—
566C4×Q8C2×D418yes—
567C4×Q8C2×D418yes—
568C4×D4—28no—
569C4×D4—216no—
570C4×D4—28no—
571C4×D4—216no—
572C4×D4—232no—
573C4×D4—216no—
574C4×D4—28no—
575C4×D4—216no—
576C4×D4—24no—
577C4×D4—28no—
578C4×D4—28no—
579C4×D4—216no—
580C4×D4—28no—
581C4×D4—216no—
582C4×D4—28no—
583C4×D4—432no—
584C4×D4—48no—
585C4×D4—432no—
586C4×D4—416no—
587C4×D4C2×D4116yes—
588C4×D4C2×D418yes—
589C4×D4C2×D418yes—
590C4×D4C2×D4116yes—
591#117—216no—
592#117—216no—
593#117—216no—
594#117—28no—
595#117—28no—
596#117C2×D418yes—
597#117C2×D4116yes—
598C2×C4⋊C4—28no—
599C2×C4⋊C4—28no—
600C2×C4⋊C4—28no—
601C2×C4⋊C4—216no—
602C2×C4⋊C4—216no—
603C2×C4⋊C4C2414yes—
604C2×C4⋊C4C2414yes—
605C2×C4⋊C4C2412yes—
606C2×C4⋊C4C2414yes—
607C2×C4⋊C4C2412yes—
608C2×C4⋊C4C2414yes—
609C2×C4⋊C4C2414yes—
610C2×C4⋊C4C2418yes—
611C2×C4⋊C4C2414yes—
612C2×C4⋊C4C2412yes—
613C2×C4⋊C4C2412yes—
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2411yescharacteristic
616C2×C4⋊C4C2412yes—
617C2×C4⋊C4C2412yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C24116yes—
620C2×C4⋊C4C2412yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C2412yes—
625C2×C4⋊C4C2418yes—
626C2×C4⋊C4C24116yes—
627C2×C4⋊C4C2418yes—
628C2×C4⋊C4C24116yes—
629C2×C4⋊C4C2418yes—
630C2×C4⋊C4C2411yescharacteristic
631C2×C4⋊C4C2412yes—
632C2×C4⋊C4C2411yescharacteristic
633C2×C4⋊C4C2412yes—
634C2×C22⋊C4C2414yes—
635C2×C22⋊C4C2412yes—
636C2×C22⋊C4C2414yes—
637C2×C22⋊C4C2412yes—
638C2×C22⋊C4C2418yes—
639C2×C22⋊C4C2418yes—
640C2×C22⋊C4C2414yes—
641C2×C22⋊C4C2414yes—
642C2×C22⋊C4C2412yes—
643C2×C22⋊C4C2418yes—
644C2×C22⋊C4C2418yes—
645C2×C22⋊C4C2414yes—
646C2×C22⋊C4C2412yes—
647C2×C22⋊C4C2414yes—
648C2×C22⋊C4C2412yes—
649C2×C22⋊C4C2414yes—
650C2×C22⋊C4C24116yes—
651C2×C22⋊C4C2414yes—
652C2×C22⋊C4C24116yes—
653C2×C22⋊C4C24116yes—
654C2×C22⋊C4C2418yes—
655C2×C22⋊C4C2418yes—
656C2×C22⋊C4C2418yes—
657C2×C22⋊C4C24116yes—
658C2×C22⋊C4C24116yes—
659C2×C22⋊C4C2414yes—
660C2×C22⋊C4C2418yes—
661C2×C22⋊C4C2412yes—
662C2×C22⋊C4C2412yes—
663C2×C22⋊C4C2412yes—
664C2×C42—216no—
665C2×C42C2×D418yes—
666C2×C42C2×D4116yes—
667C2×C42C2418yes—
668C2×C42C2412yes—
669C2×C42C2414yes—
670C2×C42C2412yes—
671C2×C42C2418yes—
672C2×C42C2414yes—
673C2×C42C2414yes—
674C2×C42C2414yes—
675C2×C42C2412yes—
676C2×C42C2411yescharacteristic
677C2×C42C2412yes—
678C2×C42C2411yescharacteristic
679C2×C42C2411yescharacteristic
680C2×C42C2412yes—
681C2×C42C2411yescharacteristic
682C2×C42C2412yes—
683#95C2412yes—
684#95C2412yes—
685#95C2414yes—
686#95C2414yes—
687#95C2418yes—
688#95C2418yes—
689#95C2412yes—
690#95C2412yes—
691#95C2414yes—
692#95C2418yes—
693#95C2414yes—
694#95C2418yes—
695#95C2418yes—
696#95C2418yes—
697#95C24116yes—
698#95C24116yes—
699#95C24116yes—
700C24C2514yes—
701C24C2514yes—
702C24C2512yes—
703C24C2511yescharacteristic
704C24C2512yes—
705#41—416no—
706#41—432no—
707#41—432no—
708#41—816no—
709#41—832no—
710#41—816no—
711#41—816no—
712C2×Q8—24no—
713C2×Q8—28no—
714C2×Q8—22no—
715C2×Q8—24no—
716C2×Q8—28no—
717C2×Q8—28no—
718C2×Q8—24no—
719C2×Q8—28no—
720C2×Q8—28no—
721C2×Q8—24no—
722C2×Q8—44no—
723C2×Q8—48no—
724C2×Q8—816no—
725C2×Q8C22×D414yes—
726C2×D4—28no—
727C2×D4—28no—
728C2×D4—24no—
729C2×D4—216no—
730C2×D4—28no—
731C2×D4—28no—
732C2×D4—28no—
733C2×D4—24no—
734C2×D4—24no—
735C2×D4—28no—
736C2×D4—24no—
737C2×D4—24no—
738C2×D4—24no—
739C2×D4—22no—
740C2×D4—28no—
741C2×D4—24no—
742C2×D4—216no—
743C2×D4—28no—
744C2×D4—24no—
745C2×D4—24no—
746C2×D4—24no—
747C2×D4—24no—
748C2×D4—28no—
749C2×D4—48no—
750C2×D4—48no—
751C2×D4—44no—
752C2×D4—44no—
753C2×D4—44no—
754C2×D4—48no—
755C2×D4—48no—
756C2×D4—416no—
757C2×D4—48no—
758C2×D4—48no—
759C2×D4—48no—
760C2×D4—48no—
761C2×D4—416no—
762C2×D4—48no—
763C2×D4—44no—
764C2×D4—48no—
765C2×D4—44no—
766C2×D4—48no—
767C2×D4—416no—
768C2×D4C22×D414yes—
769C2×D4C22×D418yes—
770C22×C4—28no—
771C22×C4—24no—
772C22×C4—24no—
773C22×C4—28no—
774C22×C4—28no—
775C22×C4—24no—
776C22×C4—28no—
777C22×C4—28no—
778C22×C4—216no—
779C22×C4—28no—
780C22×C4—28no—
781C22×C4—28no—
782C22×C4—216no—
783C22×C4—216no—
784C22×C4—42no—
785C22×C4—44no—
786C22×C4—44no—
787C22×C4—48no—
788C22×C4—48no—
789C22×C4—48no—
790C22×C4—48no—
791C22×C4—48no—
792C22×C4—48no—
793C22×C4—48no—
794C22×C4—48no—
795C22×C4—48no—
796C22×C4C22×D414yes—
797C22×C4C22×D414yes—
798C22×C4C22×D418yes—
799C22×C4C22×D414yes—
800C22×C4C22×D418yes—
801C22×C4C22×D418yes—
802C22×C4C2518yes—
803C22×C4C2512yes—
804C22×C4C2514yes—
805C22×C4C2514yes—
806C22×C4C2512yes—
807C22×C4C2518yes—
808C22×C4C2512yes—
809C22×C4C2514yes—
810C22×C4C2511yescharacteristic
811C22×C4C2511yescharacteristic
812C22×C4C2512yes—
813C22×C4C2511yescharacteristic
814C22×C4C2512yes—
815C22×C4C2512yes—
816C22×C4C2511yescharacteristic
817C22×C4C2514yes—
818C22×C4C2511yescharacteristic
819C22×C4C2511yescharacteristic
820C4⋊C4—28no—
821C4⋊C4—24no—
822C4⋊C4—28no—
823C4⋊C4—28no—
824C4⋊C4—28no—
825C4⋊C4—24no—
826C4⋊C4—28no—
827C4⋊C4—216no—
828C4⋊C4—28no—
829C4⋊C4—24no—
830C4⋊C4—24no—
831C4⋊C4—22no—
832C4⋊C4—24no—
833C4⋊C4—24no—
834C4⋊C4—28no—
835C4⋊C4—24no—
836C4⋊C4—22no—
837C4⋊C4—28no—
838C4⋊C4—24no—
839C4⋊C4—216no—
840C4⋊C4—28no—
841C4⋊C4—232no—
842C4⋊C4—28no—
843C4⋊C4—48no—
844C4⋊C4—48no—
845C4⋊C4—416no—
846C4⋊C4—416no—
847C4⋊C4C22×D414yes—
848C4⋊C4C22×D418yes—
849C4⋊C4C22×D414yes—
850C4⋊C4C22×D418yes—
851C22⋊C4—216no—
852C22⋊C4—28no—
853C22⋊C4—24no—
854C22⋊C4—24no—
855C22⋊C4—28no—
856C22⋊C4—28no—
857C22⋊C4—24no—
858C22⋊C4—216no—
859C22⋊C4—28no—
860C22⋊C4—24no—
861C22⋊C4—216no—
862C22⋊C4—28no—
863C22⋊C4—24no—
864C22⋊C4—28no—
865C22⋊C4—28no—
866C22⋊C4—28no—
867C22⋊C4—216no—
868C22⋊C4—232no—
869C22⋊C4—48no—
870C22⋊C4—44no—
871C22⋊C4—48no—
872C22⋊C4—48no—
873C22⋊C4—48no—
874C22⋊C4—416no—
875C22⋊C4—416no—
876C22⋊C4—416no—
877C22⋊C4—416no—
878C22⋊C4C22×D418yes—
879C22⋊C4C22×D418yes—
880C22⋊C4C22×D418yes—
881C42—216no—
882C42—28no—
883C42—24no—
884C42—216no—
885C42—28no—
886C42—24no—
887C42—28no—
888C42—44no—
889C42C22×D414yes—
890C42C22×D418yes—
891C42C22×D414yes—
892C42C22×D418yes—
893C42C22×D414yes—
894C42C22×D414yes—
895C42C22×D418yes—
896C42H(5,𝔽2)18yes—
897C23—22no—
898C23—24no—
899C23—24no—
900C23—22no—
901C23—22no—
902C23—24no—
903C23—24no—
904C23—24no—
905C23—22no—
906C23—28no—
907C23—24no—
908C23—24no—
909C23—24no—
910C23—24no—
911C23—28no—
912C23—28no—
913C23—28no—
914C23—24no—
915C23—28no—
916C23C23×D414yes—
917C23C23×D412yes—
918C23C2611yescharacteristic
919Q8—28no—
920Q8—48no—
921Q8—416no—
922Q8—44no—
923Q8—48no—
924Q8—88no—
925D4—28no—
926D4—48no—
927D4—48no—
928D4—432no—
929D4—48no—
930D4—416no—
931D4—416no—
932D4—48no—
933D4—48no—
934D4—48no—
935D4—44no—
936D4—84no—
937D4—88no—
938D4—84no—
939D4—88no—
940D4—88no—
941D4—88no—
942D4—88no—
943D4—816no—
944D4—832no—
945C2×C4—24no—
946C2×C4—22no—
947C2×C4—24no—
948C2×C4—22no—
949C2×C4—24no—
950C2×C4—22no—
951C2×C4—24no—
952C2×C4—24no—
953C2×C4—22no—
954C2×C4—28no—
955C2×C4—28no—
956C2×C4—216no—
957C2×C4—22no—
958C2×C4—24no—
959C2×C4—22no—
960C2×C4—24no—
961C2×C4—28no—
962C2×C4—22no—
963C2×C4—28no—
964C2×C4—24no—
965C2×C4—24no—
966C2×C4—28no—
967C2×C4—28no—
968C2×C4—28no—
969C2×C4—24no—
970C2×C4—28no—
971C2×C4—28no—
972C2×C4—24no—
973C2×C4—24no—
974C2×C4—24no—
975C2×C4—28no—
976C2×C4—44no—
977C2×C4—48no—
978C2×C4—48no—
979C2×C4—416no—
980C2×C4—48no—
981C2×C4—416no—
982C2×C4—816no—
983C2×C4—88no—
984C2×C4—88no—
985C2×C4—816no—
986C2×C4—88no—
987C2×C4—88no—
988C2×C4C23×D414yes—
989C2×C4C23×D414yes—
990C2×C4C23×D412yes—
991C2×C4C23×D412yes—
992C2×C4C23×D412yes—
993C2×C4C23×D412yes—
994C2×C4C23×D414yes—
995C2×C4C23×D412yes—
996C2×C4C23×D412yes—
997C2×C4C2×H(5,𝔽2)18yes—
998C2×C4C2×H(5,𝔽2)14yes—
999C2×C4#58514yes—
1000C22—22no—
1001C22—24no—
1002C22—22no—
1003C22—24no—
1004C22—22no—
1005C22—24no—
1006C22—48no—
1007C22—44no—
1008C22—44no—
1009C22—44no—
1010C22—42no—
1011C22—44no—
1012C22—42no—
1013C22—44no—
1014C22—48no—
1015C22—48no—
1016C22—48no—
1017C22—416no—
1018C22—44no—
1019C22—42no—
1020C22—44no—
1021C22C24×D411yescharacteristic
1022C22C22×H(5,𝔽2)12yes—
1023C22C2×#58512yes—
1024C222−1+612yes—
1025C4—24no—
1026C4—22no—
1027C4—22no—
1028C4—22no—
1029C4—24no—
1030C4—28no—
1031C4—22no—
1032C4—24no—
1033C4—42no—
1034C4—44no—
1035C4—48no—
1036C4—42no—
1037C4—44no—
1038C4—48no—
1039C4—42no—
1040C4—44no—
1041C4#344914yes—
1042C4#349814yes—
1043C2—42no—
1044C2—44no—
1045C2—84no—
1046C2—82no—
1047C2—84no—
1048C2C2×#344911yescharacteristic
1049C2C2×#349811yescharacteristic
1050C2#6285911yescharacteristic
1051C2#6292514yes—
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. C2×#3511C2semidirect
2. C2×#3517C2semidirect
3. #42909C2semidirect
4. #42646C2semidirect
5. #41959C2semidirect
6. #41954C2semidirect
7. #39747C2semidirect
8. #39744C2semidirect
9. #37683C2semidirect
10. #37680C2semidirect
11. #37619C2semidirect
12. #37618C2semidirect
13. #37617C2semidirect
14. #37544C2semidirect
15. #36127C2semidirect
16. #36125C2semidirect
17. #35701C2semidirect
18. #35689C2semidirect
19. #35326C2semidirect
20. #35317C2semidirect
21. #34641C2semidirect
22. #34624C2semidirect
23. #34123C2semidirect
271. C4×#41D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35112
C2×#35172
#429092
#426462
#419592
#419542
#397472
#397442
#376832
#376802
#376192
#376182
#376172
#375442
#361272
#361252
#357012
#356892
#353262
#353172
#346412
#346242
#341232