Finite Group Databasebeta

← #7888971

Subgroups — #7888971

Order 512.

7019 conjugacy classes of subgroups.

The subgroup lattice has 989 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3503C212yesmaximal, complemented
2#59660C211yesmaximal, characteristic, complemented
3#59136C212yesmaximal, complemented
4#59127C214yesmaximal, complemented
5#52007C218yesmaximal, complemented
6#47799C214yesmaximal, complemented
7#45418C214yesmaximal, complemented
8#45337C214yesmaximal, complemented
9#45109C214yesmaximal, complemented
10#42814C214yesmaximal, complemented
11#39855C214yesmaximal, complemented
12#39617C212yesmaximal, complemented
13#39597C212yesmaximal, complemented
14#37686C214yesmaximal, complemented
15#36492C212yesmaximal, complemented
16D4×C4⋊Q8C211yesmaximal, characteristic, complemented
17#35701C214yesmaximal, complemented
18#35526C214yesmaximal, complemented
19#34720C212yesmaximal, complemented
20#34491C211yesmaximal, characteristic, complemented
21#3503—232no—
22C2×Q82C2212yes—
23C2×Q82C2211yescharacteristic
24C2×#557C2214yes—
25C2×#554C2212yes—
26C2×#554C2214yes—
27C2×#554C2214yes—
28C2×#554C2212yes—
29C2×D4×Q8C2214yes—
30C2×D4×Q8C2218yes—
31C2×D4×Q8C2212yes—
32C2×D4×Q8C2214yes—
33C2×#544C2218yes—
34C2×#544C2214yes—
35C2×#533C2212yes—
36C2×#533C2214yes—
37C22×C4⋊Q8C2212yes—
38C22×C4⋊Q8C2214yes—
39C2×#520C2214yes—
40C2×C4×#41C2212yes—
41#2868C2211yescharacteristic
42#2857C2212yes—
43#2851C2214yes—
44#2822C2214yes—
45#2734C2214yes—
46#2729C2218yes—
47#2729C2218yes—
48#2728C2214yes—
49#2728C2214yes—
50#2728C2218yes—
51#2719C2218yes—
52#2713C2218yes—
53#2713C2218yes—
54#2690C2218yes—
55#2690C2218yes—
56#2690C2218yes—
57#2677C2218yes—
58#2677C2218yes—
59#2677C2218yes—
60#2677C2218yes—
61#2677C2218yes—
62#2677C2218yes—
63#2660C2214yes—
64#2634C2218yes—
65#2633C2218yes—
66#2628C2214yes—
67#2611C2218yes—
68#2609C2214yes—
69#2599C2218yes—
70#2598C2218yes—
71#2582C2211yescharacteristic
72#2581C2214yes—
73#2567C2212yes—
74#2565C2214yes—
75#2563C2212yes—
76#2562C2214yes—
77#2551C2214yes—
78#2551C2214yes—
79#2550C2214yes—
80#2546C2212yes—
81#2546C2214yes—
82#2542C2214yes—
83#2537C2211yescharacteristic
84#2536C2214yes—
85#2536C2214yes—
86#2536C2218yes—
87#2535C2214yes—
88#2492C2214yes—
89#2492C2214yes—
90#2489C2214yes—
91#2477C2214yes—
92#2477C2218yes—
93#2475C2214yes—
94#2473C2218yes—
95#2463C2218yes—
96#2463C2218yes—
97#2463C2218yes—
98#2463C2218yes—
99#2463C2214yes—
100#2460C2214yes—
101#2460C2218yes—
102#2452C2214yes—
103#2452C2212yes—
104#2449C2218yes—
105#2449C2218yes—
106#2449C2218yes—
107#2446C2212yes—
108#2446C2214yes—
109#2442C2214yes—
110#2442C2214yes—
111#2440C2214yes—
112#2440C2214yes—
113#2440C2214yes—
114#2440C2214yes—
115#2440C2214yes—
116#2439C2212yes—
117#2434C2214yes—
118#2434C2218yes—
119#2432C2212yes—
120#2429C2218yes—
121#2427C2214yes—
122#2427C2212yes—
123#2423C2214yes—
124#2423C2214yes—
125#2423C2214yes—
126#2421C2212yes—
127#2421C2214yes—
128#2417C2214yes—
129#2415C2212yes—
130#2409C2218yes—
131#2409C2218yes—
132#2409C2218yes—
133#2407C2212yes—
134#2407C2214yes—
135#2398C2214yes—
136#2397C2214yes—
137#2392C2214yes—
138#2381C2214yes—
139#2369C2211yescharacteristic
140#2365C2214yes—
141#2361C2214yes—
142#2361C2214yes—
143#2361C2214yes—
144#2356C2214yes—
145#2355C2212yes—
146#2352C2214yes—
147D4×C4⋊C4C2214yes—
148D4×C4⋊C4C2214yes—
149#2331C2214yes—
150#2327C2214yes—
151#2327C2214yes—
152#2326C2214yes—
153#2323C2214yes—
154#2320C2214yes—
155C4×C4⋊Q8C2211yescharacteristic
156C4×#124C2212yes—
157C4×C22⋊Q8C2212yes—
158C4×C22⋊Q8C2214yes—
159C4×#121C2212yes—
160C4×#121C2214yes—
161#2295C2212yes—
162#2290C2214yes—
163C42×D4C2211yescharacteristic
164C22×#41C2312yes—
165C23×Q8C2318yes—
166C23×Q8C2314yes—
167Q82—216no—
168Q82D4116yescomplemented
169#557—232no—
170#554—216no—
171#554—232no—
172#554—216no—
173#554—232no—
174D4×Q8—232no—
175D4×Q8—264no—
176D4×Q8—48no—
177D4×Q8—416no—
178#544—232no—
179#544—264no—
180#533—216no—
181#533—232no—
182C2×C4⋊Q8—216no—
183C2×C4⋊Q8—232no—
184C2×C4⋊Q8C2312yes—
185C2×C4⋊Q8C2314yes—
186C2×C4⋊Q8C2314yes—
187C2×C4⋊Q8C2312yes—
188C2×C4⋊Q8C2314yes—
189C2×C4⋊Q8C2318yes—
190C2×C4⋊Q8C2318yes—
191C2×C4⋊Q8C2314yes—
192C2×C4⋊Q8C2314yes—
193C2×C4⋊Q8C2312yes—
194C2×C4⋊Q8C2318yes—
195C2×C4⋊Q8C2314yes—
196C2×C4⋊Q8C2312yes—
197C2×C4⋊Q8C2318yes—
198C2×C4⋊Q8C2312yes—
199C2×C4⋊Q8C2311yescharacteristic
200C2×C4⋊Q8C2314yes—
201C2×C4⋊Q8C2314yes—
202C2×#125C2314yes—
203C2×#125C2318yes—
204C2×#125C2314yes—
205C2×#125C2318yes—
206C2×#125C2318yes—
207C2×#125C2314yes—
208C2×#124C2312yes—
209C2×C22⋊Q8C2312yes—
210C2×C22⋊Q8C2312yes—
211C2×C22⋊Q8C2314yes—
212C2×C22⋊Q8C2318yes—
213C2×C22⋊Q8C2318yes—
214C2×C22⋊Q8C2318yes—
215C2×C22⋊Q8C2312yes—
216C2×C22⋊Q8C2314yes—
217C2×C22⋊Q8C2314yes—
218C2×C22⋊Q8C2318yes—
219C2×C22⋊Q8C2318yes—
220C2×C22⋊Q8C2314yes—
221C2×C22⋊Q8C2318yes—
222C2×C22⋊Q8C2318yes—
223C2×C22⋊Q8C2314yes—
224C2×C22⋊Q8C2318yes—
225C2×C22⋊Q8C2318yes—
226C2×C22⋊Q8C2318yes—
227C2×C22⋊Q8C2318yes—
228C2×#121C2312yes—
229C2×#121C2314yes—
230#520—232no—
231C4×#41—216no—
232C2×C4×Q8C2314yes—
233C2×C4×Q8C2312yes—
234C2×C4×Q8C2314yes—
235C2×C4×Q8C2318yes—
236C2×C4×Q8C2312yes—
237C2×C4×Q8C2314yes—
238C2×C4×Q8C2312yes—
239C2×C4×Q8C2314yes—
240C2×C4×Q8C2314yes—
241C2×C4×Q8C2312yes—
242C2×C4×D4C2314yes—
243C2×C4×D4C2312yes—
244C2×C4×D4C2314yes—
245C2×C4×D4C2318yes—
246C2×C4×D4C2312yes—
247C2×C4×D4C2314yes—
248C2×C4×D4C2312yes—
249C2×C4×D4C2314yes—
250C2×C4×D4C2314yes—
251C2×C4×D4C2318yes—
252C2×C4×D4C2311yescharacteristic
253C2×C4×D4C2314yes—
254C2×C4×D4C2314yes—
255C2×C4×D4C2318yes—
256C2×C4×D4C2318yes—
257C2×#117C2314yes—
258C2×#117C2318yes—
259C2×#117C2312yes—
260C2×#117C2314yes—
261C22×C4⋊C4C2314yes—
262C22×C4⋊C4C2314yes—
263C22×C4⋊C4C2314yes—
264C22×C4⋊C4C2314yes—
265C22×C4⋊C4C2318yes—
266C22×C42C2314yes—
267C22×C42C2312yes—
268#400C2318yes—
269#400C2314yes—
270#400C2318yes—
271#400C2318yes—
272#400C2314yes—
273#400C2318yes—
274#400C2318yes—
275#399C2318yes—
276#399C2318yes—
277#399C2318yes—
278#398C2318yes—
279#398C2318yes—
280#398C2318yes—
281#398C2318yes—
282#398C2314yes—
283#398C2318yes—
284#398C2314yes—
285#398C2314yes—
286#398C2318yes—
287#398C2314yes—
288#398C2314yes—
289#398C2318yes—
290#398C2318yes—
291#397C2318yes—
292#397C2318yes—
293#397C2314yes—
294#397C2314yes—
295#397C2314yes—
296#396C2318yes—
297#396C2314yes—
298#396C2314yes—
299#395C2318yes—
300#395C2318yes—
301#395C2318yes—
302#395C2318yes—
303#395C2318yes—
304#395C2318yes—
305#395C2318yes—
306#395C2318yes—
307#394C2318yes—
308#394C2314yes—
309#394C2314yes—
310#394C2314yes—
311#394C2314yes—
312#394C2314yes—
313#394C2314yes—
314#394C2314yes—
315#393C2318yes—
316#393C2318yes—
317#393C2318yes—
318#393C2314yes—
319#393C2314yes—
320#392C2318yes—
321#392C2314yes—
322#391C2312yes—
323#391C2312yes—
324#391C2314yes—
325#391C2312yes—
326#391C2314yes—
327#391C2314yes—
328#391C2312yes—
329#391C2314yes—
330#391C2314yes—
331#391C2318yes—
332#391C2318yes—
333#391C2314yes—
334#391C2312yes—
335#391C2318yes—
336#391C2314yes—
337#390C2314yes—
338#390C2312yes—
339#390C2312yes—
340#389C2314yes—
341#389C2314yes—
342#389C2314yes—
343#389C2314yes—
344#389C2318yes—
345#389C2314yes—
346#389C2314yes—
347#389C2312yes—
348#389C2312yes—
349#389C2314yes—
350#389C2318yes—
351#389C2318yes—
352#389C2312yes—
353#389C2314yes—
354#389C2312yes—
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#387C2318yes—
370#387C2318yes—
371#387C2318yes—
372#387C2318yes—
373#387C2318yes—
374#387C2318yes—
375#387C2318yes—
376#387C2314yes—
377#387C2314yes—
378#387C2318yes—
379#387C2318yes—
380#387C2318yes—
381#387C2318yes—
382#387C2318yes—
383#387C2314yes—
384#387C2314yes—
385#387C2314yes—
386#387C2314yes—
387#387C2314yes—
388#386C2314yes—
389#386C2318yes—
390#386C2318yes—
391#386C2318yes—
392#386C2318yes—
393#386C2318yes—
394#386C2314yes—
395#386C2314yes—
396#385C2318yes—
397#385C2318yes—
398#385C2318yes—
399#385C2318yes—
400#385C2318yes—
401#385C2318yes—
402#385C2314yes—
403#385C2318yes—
404#385C2318yes—
405#385C2314yes—
406#385C2314yes—
407#385C2318yes—
408#385C2318yes—
409#385C2314yes—
410#385C2314yes—
411#384C2311yescharacteristic
412#384C2314yes—
413#384C2314yes—
414#384C2314yes—
415#383C2318yes—
416#382C2314yes—
417#382C2314yes—
418#382C2314yes—
419#382C2314yes—
420#382C2312yes—
421#380C2312yes—
422#380C2314yes—
423#380C2314yes—
424#380C2314yes—
425#380C2314yes—
426#380C2314yes—
427#380C2312yes—
428#380C2314yes—
429#380C2318yes—
430#380C2318yes—
431C4×C4⋊C4C2314yes—
432C4×C4⋊C4C2314yes—
433C4×C4⋊C4C2312yes—
434C4×C4⋊C4C2314yes—
435C4×C4⋊C4C2314yes—
436C4×C4⋊C4C2314yes—
437C4×C4⋊C4C2312yes—
438C4×C4⋊C4C2314yes—
439C4×C4⋊C4C2311yescharacteristic
440C4×C22⋊C4C2318yes—
441C4×C22⋊C4C2314yes—
442C4×C22⋊C4C2314yes—
443C4×C22⋊C4C2314yes—
444C4×C22⋊C4C2312yes—
445C4×C22⋊C4C2314yes—
446C4×C22⋊C4C2312yes—
447C4×C22⋊C4C2312yes—
448#376C2314yes—
449#376C2314yes—
450C43C2311yescharacteristic
451C2×#41—28no—
452C2×#41—28no—
453C2×#41—28no—
454C22×Q8—216no—
455C22×Q8—232no—
456C22×Q8—48no—
457C22×Q8—416no—
458C22×Q8—84no—
459C22×Q8—88no—
460C22×Q8C2412yes—
461C22×Q8C2418yes—
462C22×Q8C2414yes—
463C22×Q8C2412yes—
464C22×Q8C2418yes—
465C22×Q8C2414yes—
466C22×Q8C2412yes—
467C22×Q8C2414yes—
468C22×D4C2411yescharacteristic
469C22×D4C2414yes—
470C22×D4C2414yes—
471C22×D4C2414yes—
472C22×D4C2412yes—
473C23×C4C2414yes—
474C23×C4C2412yes—
475C23×C4C2414yes—
476C23×C4C2414yes—
477C23×C4C2412yes—
478C23×C4C2412yes—
479C23×C4C2418yes—
480C23×C4C2418yes—
481C23×C4C2418yes—
482C4⋊Q8—232no—
483C4⋊Q8—216no—
484C4⋊Q8—28no—
485C4⋊Q8—216no—
486C4⋊Q8—28no—
487C4⋊Q8—216no—
488C4⋊Q8—232no—
489C4⋊Q8—216no—
490C4⋊Q8—232no—
491C4⋊Q8—216no—
492C4⋊Q8—28no—
493C4⋊Q8—216no—
494C4⋊Q8—44no—
495C4⋊Q8—416no—
496C4⋊Q8—82no—
497C4⋊Q8C2×D418yes—
498C4⋊Q8C2×D4132yes—
499C4⋊Q8C2×D4132yes—
500#125—232no—
501#125—216no—
502#125—216no—
503#125—232no—
504#125—216no—
505#125—232no—
506#124—28no—
507C22⋊Q8—28no—
508C22⋊Q8—216no—
509C22⋊Q8—232no—
510C22⋊Q8—232no—
511C22⋊Q8—232no—
512C22⋊Q8—28no—
513C22⋊Q8—232no—
514C22⋊Q8—216no—
515C22⋊Q8—216no—
516C22⋊Q8—28no—
517C22⋊Q8—232no—
518C22⋊Q8—232no—
519C22⋊Q8—232no—
520C22⋊Q8—216no—
521C22⋊Q8—416no—
522C22⋊Q8—416no—
523C22⋊Q8—416no—
524C22⋊Q8—48no—
525C22⋊Q8—88no—
526#121—28no—
527#121—216no—
528C4×Q8—28no—
529C4×Q8—216no—
530C4×Q8—216no—
531C4×Q8—232no—
532C4×Q8—28no—
533C4×Q8—216no—
534C4×Q8—44no—
535C4×Q8—48no—
536C4×Q8C2×D4116yes—
537C4×Q8C2×D4132yes—
538C4×D4—28no—
539C4×D4—216no—
540C4×D4—28no—
541C4×D4—216no—
542C4×D4—216no—
543C4×D4—232no—
544C4×D4—24no—
545C4×D4—28no—
546C4×D4—216no—
547C4×D4—216no—
548C4×D4—232no—
549C4×D4—48no—
550C4×D4—48no—
551C4×D4—416no—
552C4×D4—88no—
553#117—28no—
554#117—216no—
555#117—216no—
556#117—232no—
557C2×C4⋊C4—216no—
558C2×C4⋊C4—232no—
559C2×C4⋊C4—216no—
560C2×C4⋊C4—216no—
561C2×C4⋊C4—216no—
562C2×C4⋊C4C2418yes—
563C2×C4⋊C4C2414yes—
564C2×C4⋊C4C2412yes—
565C2×C4⋊C4C2414yes—
566C2×C4⋊C4C2414yes—
567C2×C4⋊C4C2418yes—
568C2×C4⋊C4C2418yes—
569C2×C4⋊C4C2418yes—
570C2×C4⋊C4C2418yes—
571C2×C4⋊C4C2414yes—
572C2×C4⋊C4C2412yes—
573C2×C4⋊C4C2414yes—
574C2×C4⋊C4C2414yes—
575C2×C4⋊C4C2418yes—
576C2×C4⋊C4C2412yes—
577C2×C4⋊C4C2414yes—
578C2×C4⋊C4C2414yes—
579C2×C4⋊C4C2414yes—
580C2×C4⋊C4C2418yes—
581C2×C4⋊C4C2414yes—
582C2×C4⋊C4C2414yes—
583C2×C4⋊C4C2418yes—
584C2×C4⋊C4C2418yes—
585C2×C4⋊C4C2414yes—
586C2×C4⋊C4C2412yes—
587C2×C4⋊C4C2414yes—
588C2×C4⋊C4C2414yes—
589C2×C4⋊C4C2412yes—
590C2×C4⋊C4C2414yes—
591C2×C4⋊C4C2418yes—
592C2×C4⋊C4C2414yes—
593C2×C4⋊C4C2414yes—
594C2×C4⋊C4C2414yes—
595C2×C4⋊C4C2412yes—
596C2×C4⋊C4C2414yes—
597C2×C4⋊C4C2418yes—
598C2×C4⋊C4C2414yes—
599C2×C4⋊C4C2418yes—
600C2×C4⋊C4C2414yes—
601C2×C4⋊C4C2412yes—
602C2×C4⋊C4C2418yes—
603C2×C4⋊C4C2414yes—
604C2×C4⋊C4C2411yescharacteristic
605C2×C22⋊C4C2418yes—
606C2×C22⋊C4C2414yes—
607C2×C22⋊C4C2414yes—
608C2×C22⋊C4C2414yes—
609C2×C22⋊C4C2418yes—
610C2×C22⋊C4C2414yes—
611C2×C22⋊C4C2414yes—
612C2×C22⋊C4C2414yes—
613C2×C22⋊C4C2414yes—
614C2×C22⋊C4C2412yes—
615C2×C22⋊C4C2412yes—
616C2×C22⋊C4C2414yes—
617C2×C22⋊C4C2412yes—
618C2×C22⋊C4C2414yes—
619C2×C22⋊C4C2418yes—
620C2×C22⋊C4C2414yes—
621C2×C22⋊C4C2414yes—
622C2×C22⋊C4C2414yes—
623C2×C22⋊C4C2414yes—
624C2×C22⋊C4C2414yes—
625C2×C22⋊C4C2418yes—
626C2×C22⋊C4C2418yes—
627C2×C22⋊C4C2418yes—
628C2×C22⋊C4C2414yes—
629C2×C42—28no—
630C2×C42—216no—
631C2×C42C2414yes—
632C2×C42C2412yes—
633C2×C42C2414yes—
634C2×C42C2418yes—
635C2×C42C2414yes—
636C2×C42C2412yes—
637C2×C42C2414yes—
638C2×C42C2411yescharacteristic
639C2×C42C2412yes—
640C2×C42C2414yes—
641C2×C42C2412yes—
642C2×C42C2412yes—
643C2×C42C2414yes—
644C2×C42C2418yes—
645C2×C42C2411yescharacteristic
646C2×C42C2414yes—
647C2×C42C2414yes—
648C2×C42C2411yescharacteristic
649#95C2414yes—
650#95C2414yes—
651#95C2418yes—
652#95C2414yes—
653#95C2414yes—
654#95C2414yes—
655#95C2412yes—
656#95C2411yescharacteristic
657#95C2412yes—
658#95C2411yescharacteristic
659#95C2418yes—
660#95C2414yes—
661#95C2418yes—
662#95C2414yes—
663#95C2414yes—
664#95C2414yes—
665#95C2414yes—
666#95C2414yes—
667#95C2414yes—
668#95C2414yes—
669#95C2414yes—
670#95C2414yes—
671#95C2418yes—
672#95C2418yes—
673#95C2414yes—
674#95C2418yes—
675#95C2418yes—
676#95C2414yes—
677#95C2414yes—
678#95C2418yes—
679#95C2418yes—
680#95C2418yes—
681#95C2418yes—
682#95C2414yes—
683#95C2418yes—
684C24C2514yes—
685C24C2512yes—
686#41—264no—
687C2×Q8—24no—
688C2×Q8—28no—
689C2×Q8—216no—
690C2×Q8—28no—
691C2×Q8—216no—
692C2×Q8—28no—
693C2×Q8—216no—
694C2×Q8—24no—
695C2×Q8—24no—
696C2×Q8—24no—
697C2×Q8—24no—
698C2×Q8—42no—
699C2×Q8—44no—
700C2×Q8—42no—
701C2×Q8—44no—
702C2×Q8—48no—
703C2×Q8—44no—
704C2×Q8—44no—
705C2×Q8—48no—
706C2×Q8—48no—
707C2×Q8—44no—
708C2×Q8—832no—
709C2×Q8—864no—
710C2×Q8C22×D418yes—
711C2×Q8C22×D418yes—
712C2×Q8C22×D4116yes—
713C2×D4—24no—
714C2×D4—28no—
715C2×D4—28no—
716C2×D4—28no—
717C2×D4—216no—
718C2×D4—28no—
719C2×D4—28no—
720C2×D4—24no—
721C2×D4—22no—
722C2×D4—24no—
723C2×D4—44no—
724C2×D4—44no—
725C2×D42−1+418yes—
726C22×C4—28no—
727C22×C4—28no—
728C22×C4—24no—
729C22×C4—28no—
730C22×C4—24no—
731C22×C4—24no—
732C22×C4—28no—
733C22×C4—24no—
734C22×C4—28no—
735C22×C4—24no—
736C22×C4—28no—
737C22×C4—24no—
738C22×C4—28no—
739C22×C4—28no—
740C22×C4—24no—
741C22×C4—216no—
742C22×C4—216no—
743C22×C4—216no—
744C22×C4—42no—
745C22×C4—44no—
746C22×C4—48no—
747C22×C4—48no—
748C22×C4—48no—
749C22×C4—48no—
750C22×C4—48no—
751C22×C4—48no—
752C22×C42−1+418yes—
753C22×C4C2514yes—
754C22×C4C2512yes—
755C22×C4C2514yes—
756C22×C4C2511yescharacteristic
757C22×C4C2514yes—
758C22×C4C2514yes—
759C22×C4C2512yes—
760C22×C4C2514yes—
761C22×C4C2514yes—
762C22×C4C2518yes—
763C22×C4C2514yes—
764C22×C4C2511yescharacteristic
765C22×C4C2514yes—
766C22×C4C2514yes—
767C22×C4C2511yescharacteristic
768C22×C4C2512yes—
769C22×C4C2512yes—
770C22×C4C2512yes—
771C4⋊C4—28no—
772C4⋊C4—216no—
773C4⋊C4—24no—
774C4⋊C4—28no—
775C4⋊C4—216no—
776C4⋊C4—28no—
777C4⋊C4—216no—
778C4⋊C4—216no—
779C4⋊C4—216no—
780C4⋊C4—28no—
781C4⋊C4—28no—
782C4⋊C4—24no—
783C4⋊C4—28no—
784C4⋊C4—28no—
785C4⋊C4—216no—
786C4⋊C4—28no—
787C4⋊C4—216no—
788C4⋊C4—28no—
789C4⋊C4—216no—
790C4⋊C4—216no—
791C4⋊C4—28no—
792C4⋊C4—28no—
793C4⋊C4—28no—
794C4⋊C4—24no—
795C4⋊C4—28no—
796C4⋊C4—24no—
797C4⋊C4—28no—
798C4⋊C4—24no—
799C4⋊C4—28no—
800C4⋊C4—44no—
801C4⋊C4—48no—
802C4⋊C4—42no—
803C4⋊C4—44no—
804C4⋊C4—44no—
805C4⋊C4—44no—
806C4⋊C4—48no—
807C4⋊C4—44no—
808C4⋊C4—48no—
809C4⋊C4C22×D4116yes—
810C4⋊C4C22×D418yes—
811C4⋊C4C22×D4132yes—
812C4⋊C4C22×D4116yes—
813C4⋊C4H(5,𝔽2)14yes—
814C22⋊C4—24no—
815C22⋊C4—28no—
816C22⋊C4—216no—
817C22⋊C4—28no—
818C22⋊C4—28no—
819C22⋊C4—28no—
820C22⋊C4—28no—
821C22⋊C4—28no—
822C22⋊C4—216no—
823C22⋊C4—28no—
824C22⋊C4—28no—
825C22⋊C4—28no—
826C22⋊C4—28no—
827C22⋊C4—216no—
828C22⋊C4—24no—
829C22⋊C4—28no—
830C22⋊C4—28no—
831C22⋊C4—24no—
832C22⋊C4—28no—
833C22⋊C4—48no—
834C22⋊C4—48no—
835C22⋊C4—44no—
836C22⋊C4—48no—
837C22⋊C4—44no—
838C42—24no—
839C42—24no—
840C42—28no—
841C42—28no—
842C42—24no—
843C42—216no—
844C42—28no—
845C42—22no—
846C42—28no—
847C42—24no—
848C42—28no—
849C42—24no—
850C42—48no—
851C42—44no—
852C42—41no—
853C42C22×D414yes—
854C42C22×D4116yes—
855C42C22×D4116yes—
856C23—24no—
857C23—22no—
858C23—24no—
859C23—22no—
860C23—22no—
861C23—24no—
862C23—24no—
863C23—22no—
864C23—24no—
865C23—22no—
866C23—24no—
867C23—22no—
868C23C2×2−1+418yes—
869C23C2×2−1+414yes—
870C23C2611yescharacteristic
871Q8—216no—
872Q8—48no—
873Q8—416no—
874Q8—416no—
875Q8—432no—
876Q8—48no—
877Q8—88no—
878Q8—816no—
879D4—28no—
880D4—232no—
881D4—216no—
882D4—416no—
883D4—416no—
884C2×C4—232no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—21no—
888C2×C4—24no—
889C2×C4—24no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—24no—
893C2×C4—24no—
894C2×C4—24no—
895C2×C4—21no—
896C2×C4—24no—
897C2×C4—22no—
898C2×C4—216no—
899C2×C4—24no—
900C2×C4—22no—
901C2×C4—24no—
902C2×C4—24no—
903C2×C4—28no—
904C2×C4—24no—
905C2×C4—21no—
906C2×C4—24no—
907C2×C4—24no—
908C2×C4—28no—
909C2×C4—22no—
910C2×C4—24no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—24no—
914C2×C4—24no—
915C2×C4—22no—
916C2×C4—24no—
917C2×C4—24no—
918C2×C4—22no—
919C2×C4—24no—
920C2×C4—28no—
921C2×C4—24no—
922C2×C4—24no—
923C2×C4—24no—
924C2×C4—22no—
925C2×C4—24no—
926C2×C4—28no—
927C2×C4—48no—
928C2×C4—416no—
929C2×C4—416no—
930C2×C4—48no—
931C2×C4—816no—
932C2×C4—816no—
933C2×C4—816no—
934C2×C4C23×D418yes—
935C2×C4C23×D412yes—
936C2×C4C23×D418yes—
937C2×C4C23×D418yes—
938C2×C4C23×D414yes—
939C2×C4C2×H(5,𝔽2)12yes—
940C2×C4C2×H(5,𝔽2)14yes—
941C2×C4C2×2−1+414yes—
942C2×C4C2×2−1+414yes—
943C2×C4C2×2−1+414yes—
944C22—28no—
945C22—28no—
946C22—24no—
947C22—24no—
948C22—24no—
949C22—28no—
950C22—44no—
951C22—42no—
952C22—42no—
953C22—44no—
954C22—42no—
955C22—44no—
956C22—42no—
957C22—44no—
958C22C24×D411yescharacteristic
959C22C22×H(5,𝔽2)11yescharacteristic
960C22C22×2−1+412yes—
961C22C22×2−1+412yes—
962C22H(7,𝔽2)11yescharacteristic
963C4—24no—
964C4—22no—
965C4—28no—
966C4—28no—
967C4—24no—
968C4—28no—
969C4—22no—
970C4—44no—
971C4—48no—
972C4—41no—
973C4—44no—
974C4—42no—
975C4—44no—
976C4—44no—
977C4—44no—
978C4—42no—
979C4—44no—
980C4#348618yes—
981C2—48no—
982C2—44no—
983C2C2×#348612yes—
984C2#6283311yescharacteristic
985C2#6294512yes—
986C2D4×H(5,𝔽2)11yescharacteristic
987C2#6301611yescharacteristic
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×#3503C2semidirect
2. #59660C2semidirect
3. #59136C2semidirect
4. #59127C2semidirect
5. #52007C2semidirect
6. #47799C2semidirect
7. #45418C2semidirect
8. #45337C2semidirect
9. #45109C2semidirect
10. #42814C2semidirect
11. #39855C2semidirect
12. #39617C2semidirect
13. #39597C2semidirect
14. #37686C2semidirect
15. #36492C2semidirect
16. D4×C4⋊Q8C2semidirect
17. #35701C2semidirect
18. #35526C2semidirect
19. #34720C2semidirect
20. #34491C2semidirect
168. Q82D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35032
#596602
#591362
#591272
#520072
#477992
#454182
#453372
#451092
#428142
#398552
#396172
#395972
#376862
#364922
D4×C4⋊Q82
#357012
#355262
#347202
#344912