Finite Group Databasebeta

← #7630384

Subgroups — #7630384

Order 512.

5320 conjugacy classes of subgroups.

The subgroup lattice has 945 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36640C211yesmaximal, characteristic, complemented
2#36635C212yesmaximal, complemented
3#36600C211yesmaximal, characteristic, complemented
4#36565C211yesmaximal, characteristic, complemented
5#36535C212yesmaximal, complemented
6#36478C214yesmaximal, complemented
7#36387C214yesmaximal, complemented
8#36282C218yesmaximal, complemented
9#36261C212yesmaximal, complemented
10#36219C214yesmaximal
11#36191C212yesmaximal, complemented
12#36165C211yesmaximal, characteristic, complemented
13#36131C212yesmaximal, complemented
14D4×#125C211yesmaximal, characteristic, complemented
15#34978C212yesmaximal, complemented
16#34966C214yesmaximal, complemented
17#34920C214yesmaximal, complemented
18#34840C218yesmaximal, complemented
19C4×#554C214yesmaximal, complemented
20#34127C212yesmaximal
21C4×#533C211yesmaximal, characteristic, complemented
22C2×C4×#125C212yesmaximal, complemented
23C42×#41C211yesmaximal, characteristic
24C2×#554C2214yes—
25C2×#533C2211yescharacteristic
26C22×#125C2212yes—
27C2×C4×#41C2212yes—
28C2×C4×#41C2211yescharacteristic
29#2864C2214yes—
30#2864C2214yes—
31#2863C2218yes—
32#2862C2212yes—
33#2859C2211yescharacteristic
34#2859C2212yes—
35#2859C2211yescharacteristic
36#2859C2212yes—
37#2857C2214yes—
38#2855C2218yes—
39#2851C2212yes—
40#2851C2212yes—
41#2851C2212yes—
42#2851C2212yes—
43#2851C2214yes—
44#2612C2218yes—
45#2606C2218yes—
46#2605C2218yes—
47#2590C2218yes—
48#2590C2218yes—
49#2589C2218yes—
50#2588C2218yes—
51#2588C2218yes—
52#2587C2218yes—
53#2586C2218yes—
54#2585C2218yes—
55#2584C2214yes—
56#2583C2218yes—
57#2581C2214yes—
58#2579C2218yes—
59#2574C2218yes—
60#2571C2212yes—
61#2570C2214yes—
62#2570C2214yes—
63#2565C2214yes—
64#2564C2218yes—
65#2556C2218yes—
66#2552C2212yes—
67#2552C2212yes—
68#2551C2212yes—
69#2550C2214yes—
70#2550C2214yes—
71#2550C2214yes—
72#2549C2218yes—
73#2520C2218yes—
74#2508C2214yes—
75#2506C2214yes—
76#2505C2218yes—
77#2473C2218yes—
78#2462C2218yes—
79#2453C2214yes—
80#2451C2214yes—
81#2450C2218yes—
82#2449C2218yes—
83#2442C2214yes—
84#2442C2214yes—
85#2441C2214yes—
86#2441C2214yes—
87#2440C2214yes—
88#2440C2214yes—
89#2439C2214yes—
90#2439C2214yes—
91#2438C2218yes—
92#2438C2218yes—
93#2402C2218yes—
94#2399C2218yes—
95#2396C2218yes—
96#2370C2214yes—
97#2370C2214yes—
98#2369C2214yes—
99#2368C2218yes—
100#2368C2218yes—
101#2360C2218yes—
102#2355C2212yes—
103#2355C2212yes—
104#2355C2214yes—
105#2352C2214yes—
106#2352C2214yes—
107#2349C2214yes—
108#2349C2214yes—
109D4×C4⋊C4C2212yes—
110D4×C4⋊C4C2214yes—
111D4×C4⋊C4C2212yes—
112#2347C2214yes—
113#2345C2218yes—
114#2343C2218yes—
115#2339C2214yes—
116C4×C4⋊Q8C2214yes—
117C4×C4⋊Q8C2214yes—
118C4×C4⋊Q8C2212yes—
119C4×C4⋊Q8C2212yes—
120C4×#125C2211yescharacteristic
121C4×#125C2218yes—
122C4×#125C2211yescharacteristic
123C4×#125C2212yes—
124C4×#125C2214yes—
125C4×#125C2212yes—
126C4×#125C2212yes—
127C4×#125C2214yes—
128C4×#125C2211yescharacteristic
129C4×#125C2212yes—
130C4×#125C2214yes—
131C4×#125C2218yes—
132C4×#125C2214yes—
133C4×#125C2211yescharacteristic
134C4×C22⋊Q8C2214yes—
135C4×C22⋊Q8C2218yes—
136C4×C22⋊Q8C2218yes—
137C4×C22⋊Q8C2218yes—
138C4×C22⋊Q8C2214yes—
139#2296C2214yes—
140#2296C2212yes—
141#2295C2218yes—
142#2295C2214yes—
143#2295C2214yes—
144C2×#389C2214yes—
145#2290C2218yes—
146C2×#387C2218yes—
147#2285C2212yes—
148#2285C2211yescharacteristic
149#2283C2214yes—
150C2×#382C2212yes—
151C42×Q8C2212yes—
152C42×Q8C2214yes—
153C42×Q8C2211yescharacteristic
154C42×Q8C2211yescharacteristic
155C42×D4C2211yescharacteristic
156C42×D4C2214yes—
157C42×D4C2212yes—
158C42×D4C2212yes—
159C42×D4C2214yes—
160C42×D4C2212yes—
161C42×D4C2211yescharacteristic
162C4×#117C2212yes—
163C4×#117C2212yes—
164C4×#117C2212yes—
165C4×#117C2211yescharacteristic
166C4×#117C2214yes—
167C2×C4×C4⋊C4C2218yes—
168C2×C4×C4⋊C4C2214yes—
169C2×C43C2212yes—
170C2×C43C2211yescharacteristic
171C22×#41C2311yescharacteristic
172#554—232no—
173#533—28no—
174C2×C4⋊Q8C2312yes—
175C2×C4⋊Q8C2314yes—
176C2×C4⋊Q8C2314yes—
177C2×#125—216no—
178C2×#125C2312yes—
179C2×#125C2311yescharacteristic
180C2×#125C2314yes—
181C2×#125C2318yes—
182C2×#125C2314yes—
183C2×#125C2314yes—
184C2×#125C2312yes—
185C2×#125C2311yescharacteristic
186C2×C22⋊Q8C2318yes—
187C2×C22⋊Q8C2318yes—
188C2×C22⋊Q8C2318yes—
189C2×C22⋊Q8C2314yes—
190C4×#41—216no—
191C4×#41Q8116yescomplemented
192C2×C4×Q8C2314yes—
193C2×C4×Q8C2312yes—
194C2×C4×Q8C2314yes—
195C2×C4×Q8C2312yes—
196C2×C4×Q8C2318yes—
197C2×C4×Q8C2314yes—
198C2×C4×Q8C2311yescharacteristic
199C2×C4×Q8C2311yescharacteristic
200C2×C4×D4C2314yes—
201C2×C4×D4C2314yes—
202C2×C4×D4C2314yes—
203C2×C4×D4C2312yes—
204C2×C4×D4C2314yes—
205C2×C4×D4C2311yescharacteristic
206C2×C4×D4C2312yes—
207C2×C4×D4C2311yescharacteristic
208C2×C4×D4C2312yes—
209C2×C4×D4C2312yes—
210C2×#117C2312yes—
211C2×#117C2314yes—
212C2×#117C2312yes—
213C2×#117C2312yes—
214C2×#117C2314yes—
215C2×#117C2312yes—
216C2×#117C2311yescharacteristic
217C22×C4⋊C4C2318yes—
218C22×C4⋊C4C2314yes—
219C22×C4⋊C4C2318yes—
220C22×C4⋊C4C2314yes—
221C22×C42C2312yes—
222C22×C42C2312yes—
223C22×C42C2311yescharacteristic
224C22×C42C2314yes—
225C22×C42C2311yescharacteristic
226C22×C42C2312yes—
227C22×C42C2314yes—
228C22×C42C2312yes—
229C22×C42C2318yes—
230C22×C42C2312yes—
231C22×C42C2311yescharacteristic
232#400C2318yes—
233#400C2318yes—
234#400C2318yes—
235#400C2318yes—
236#400C2318yes—
237#399C2318yes—
238#398C2318yes—
239#398C2318yes—
240#398C2318yes—
241#398C2318yes—
242#398C2318yes—
243#398C2318yes—
244#398C2318yes—
245#398C2318yes—
246#398C2318yes—
247#398C2318yes—
248#396C2318yes—
249#396C2318yes—
250#395C2318yes—
251#395C2318yes—
252#395C2318yes—
253#395C2318yes—
254#395C2318yes—
255#393C2318yes—
256#391C2314yes—
257#391C2318yes—
258#391C2318yes—
259#391C2314yes—
260#391C2314yes—
261#391C2314yes—
262#391C2318yes—
263#391C2318yes—
264#391C2318yes—
265#391C2318yes—
266#391C2318yes—
267#389C2312yes—
268#389C2314yes—
269#389C2318yes—
270#389C2318yes—
271#389C2314yes—
272#389C2314yes—
273#389C2312yes—
274#389C2312yes—
275#389C2312yes—
276#389C2314yes—
277#389C2314yes—
278#389C2314yes—
279#389C2314yes—
280#389C2314yes—
281#389C2314yes—
282#389C2314yes—
283#389C2314yes—
284#389C2314yes—
285#389C2314yes—
286#389C2318yes—
287#389C2318yes—
288#389C2314yes—
289#389C2314yes—
290#389C2318yes—
291#389C2314yes—
292#389C2314yes—
293#389C2314yes—
294#389C2318yes—
295#389C2318yes—
296#389C2314yes—
297#389C2318yes—
298#389C2314yes—
299#389C2318yes—
300#388C2318yes—
301#388C2318yes—
302#387C2314yes—
303#387C2318yes—
304#387C2318yes—
305#387C2318yes—
306#387C2318yes—
307#387C2318yes—
308#387C2318yes—
309#387C2318yes—
310#387C2314yes—
311#387C2314yes—
312#387C2318yes—
313#387C2318yes—
314#387C2318yes—
315#387C2318yes—
316#387C2318yes—
317#387C2314yes—
318#387C2318yes—
319#387C2318yes—
320#387C2318yes—
321#387C2318yes—
322#387C2318yes—
323#387C2318yes—
324#387C2318yes—
325#387C2318yes—
326#387C2318yes—
327#387C2318yes—
328#387C2318yes—
329#387C2318yes—
330#387C2318yes—
331#387C2318yes—
332#386C2318yes—
333#386C2318yes—
334#385C2314yes—
335#385C2318yes—
336#385C2318yes—
337#385C2314yes—
338#385C2318yes—
339#385C2318yes—
340#385C2318yes—
341#385C2318yes—
342#385C2318yes—
343#385C2318yes—
344#385C2318yes—
345#385C2318yes—
346#384C2312yes—
347#384C2314yes—
348#384C2314yes—
349#384C2312yes—
350#384C2312yes—
351#383C2318yes—
352#382C2311yescharacteristic
353#382C2314yes—
354#382C2318yes—
355#382C2312yes—
356#382C2311yescharacteristic
357#382C2314yes—
358#382C2312yes—
359#382C2314yes—
360#382C2314yes—
361#382C2314yes—
362#382C2314yes—
363#381C2318yes—
364#380C2318yes—
365#380C2318yes—
366#380C2314yes—
367#380C2318yes—
368#380C2314yes—
369#380C2314yes—
370#380C2314yes—
371#380C2314yes—
372C4×C4⋊C4C2312yes—
373C4×C4⋊C4C2314yes—
374C4×C4⋊C4C2314yes—
375C4×C4⋊C4C2318yes—
376C4×C4⋊C4C2314yes—
377C4×C4⋊C4C2318yes—
378C4×C4⋊C4C2312yes—
379C4×C4⋊C4C2318yes—
380C4×C4⋊C4C2314yes—
381C4×C4⋊C4C2318yes—
382C4×C4⋊C4C2318yes—
383C4×C4⋊C4C2318yes—
384C4×C4⋊C4C2318yes—
385C4×C4⋊C4C2318yes—
386C4×C4⋊C4C2314yes—
387C4×C4⋊C4C2318yes—
388C4×C4⋊C4C2318yes—
389C4×C4⋊C4C2312yes—
390C4×C4⋊C4C2312yes—
391C4×C4⋊C4C2312yes—
392C4×C4⋊C4C2318yes—
393C4×C4⋊C4C2314yes—
394C4×C4⋊C4C2314yes—
395C4×C4⋊C4C2314yes—
396C4×C4⋊C4C2314yes—
397C4×C4⋊C4C2314yes—
398C4×C4⋊C4C2312yes—
399C4×C4⋊C4C2312yes—
400C4×C4⋊C4C2311yescharacteristic
401C4×C4⋊C4C2312yes—
402C4×C4⋊C4C2314yes—
403C4×C4⋊C4C2314yes—
404C4×C4⋊C4C2314yes—
405C4×C4⋊C4C2314yes—
406C4×C4⋊C4C2314yes—
407C4×C4⋊C4C2314yes—
408C4×C4⋊C4C2314yes—
409C4×C4⋊C4C2312yes—
410C4×C4⋊C4C2314yes—
411C4×C4⋊C4C2312yes—
412C4×C4⋊C4C2314yes—
413C4×C4⋊C4C2314yes—
414C4×C4⋊C4C2312yes—
415C4×C4⋊C4C2311yescharacteristic
416C4×C22⋊C4C2314yes—
417C4×C22⋊C4C2314yes—
418C4×C22⋊C4C2314yes—
419C4×C22⋊C4C2314yes—
420C4×C22⋊C4C2318yes—
421C4×C22⋊C4C2318yes—
422C4×C22⋊C4C2314yes—
423C4×C22⋊C4C2314yes—
424C4×C22⋊C4C2312yes—
425C4×C22⋊C4C2314yes—
426C4×C22⋊C4C2312yes—
427C4×C22⋊C4C2312yes—
428C4×C22⋊C4C2312yes—
429C4×C22⋊C4C2314yes—
430C4×C22⋊C4C2314yes—
431C4×C22⋊C4C2318yes—
432#376C2314yes—
433#376C2314yes—
434#376C2312yes—
435#376C2318yes—
436C2×#95C2318yes—
437C2×#95C2318yes—
438C2×#95C2318yes—
439C43C2311yescharacteristic
440C43C2311yescharacteristic
441C43C2312yes—
442C43C2311yescharacteristic
443C43C2312yes—
444C43C2314yes—
445C43C2312yes—
446C43C2312yes—
447C43C2314yes—
448C43C2314yes—
449C43C2311yescharacteristic
450C43C2312yes—
451C2×#41—28no—
452C2×#41C2×Q818yes—
453C22×Q8C2414yes—
454C22×Q8C2411yescharacteristic
455C22×Q8C2418yes—
456C22×D4C2412yes—
457C22×D4C2411yescharacteristic
458C23×C4C2418yes—
459C23×C4C2414yes—
460C23×C4C2412yes—
461C23×C4C2412yes—
462C23×C4C2411yescharacteristic
463C23×C4C2412yes—
464C23×C4C2411yescharacteristic
465C23×C4C2411yescharacteristic
466C23×C4C2412yes—
467C23×C4C2418yes—
468C23×C4C2412yes—
469C23×C4C2414yes—
470C4⋊Q8—28no—
471C4⋊Q8—216no—
472C4⋊Q8—48no—
473#125—216no—
474#125—232no—
475#125—216no—
476#125—28no—
477#125—24no—
478#125—216no—
479#125—44no—
480#125#4118yescomplemented
481C22⋊Q8—232no—
482C22⋊Q8—216no—
483C22⋊Q8—232no—
484C22⋊Q8—232no—
485C4×Q8—28no—
486C4×Q8—216no—
487C4×Q8—28no—
488C4×Q8—216no—
489C4×Q8—48no—
490C4×Q8—416no—
491C4×Q8C2×Q818yes—
492C4×Q8C2×Q818yes—
493C4×D4—28no—
494C4×D4—216no—
495C4×D4—216no—
496C4×D4—216no—
497C4×D4—216no—
498C4×D4C2×Q8116yes—
499C4×D4C2×Q8116yes—
500C4×D4C2×Q818yes—
501C4×D4C2×Q818yes—
502C4×D4#41116yes—
503#117—28no—
504#117—28no—
505#117—216no—
506#117—48no—
507#117—44no—
508#117C2×Q8116yes—
509#117C2×Q818yes—
510C2×C4⋊C4—232no—
511C2×C4⋊C4—216no—
512C2×C4⋊C4—232no—
513C2×C4⋊C4—48no—
514C2×C4⋊C4C2412yes—
515C2×C4⋊C4C2414yes—
516C2×C4⋊C4C2418yes—
517C2×C4⋊C4C2418yes—
518C2×C4⋊C4C2418yes—
519C2×C4⋊C4C2414yes—
520C2×C4⋊C4C2418yes—
521C2×C4⋊C4C2418yes—
522C2×C4⋊C4C2418yes—
523C2×C4⋊C4C2418yes—
524C2×C4⋊C4C2414yes—
525C2×C4⋊C4C2412yes—
526C2×C4⋊C4C2414yes—
527C2×C4⋊C4C2414yes—
528C2×C4⋊C4C2412yes—
529C2×C4⋊C4C2412yes—
530C2×C4⋊C4C2414yes—
531C2×C4⋊C4C2414yes—
532C2×C4⋊C4C2414yes—
533C2×C4⋊C4C2414yes—
534C2×C4⋊C4C2414yes—
535C2×C4⋊C4C2414yes—
536C2×C4⋊C4C2418yes—
537C2×C4⋊C4C2418yes—
538C2×C4⋊C4C2418yes—
539C2×C4⋊C4C2414yes—
540C2×C4⋊C4C2414yes—
541C2×C4⋊C4C2414yes—
542C2×C4⋊C4C2414yes—
543C2×C4⋊C4C2414yes—
544C2×C4⋊C4C2418yes—
545C2×C4⋊C4C2418yes—
546C2×C4⋊C4C2418yes—
547C2×C4⋊C4C2418yes—
548C2×C4⋊C4C2418yes—
549C2×C4⋊C4C2411yescharacteristic
550C2×C4⋊C4C2412yes—
551C2×C4⋊C4C2412yes—
552C2×C4⋊C4C2411yescharacteristic
553C2×C4⋊C4C2412yes—
554C2×C4⋊C4C2414yes—
555C2×C4⋊C4C2412yes—
556C2×C22⋊C4C2414yes—
557C2×C22⋊C4C2414yes—
558C2×C22⋊C4C2414yes—
559C2×C22⋊C4C2418yes—
560C2×C22⋊C4C2418yes—
561C2×C22⋊C4C2414yes—
562C2×C22⋊C4C2418yes—
563C2×C22⋊C4C2412yes—
564C2×C22⋊C4C2412yes—
565C2×C22⋊C4C2412yes—
566C2×C22⋊C4C2414yes—
567C2×C42—216no—
568C2×C42—28no—
569C2×C42—28no—
570C2×C42—24no—
571C2×C42—48no—
572C2×C42—44no—
573C2×C42—42no—
574C2×C42—44no—
575C2×C42—416no—
576C2×C42C2×Q8116yes—
577C2×C42C2×Q818yes—
578C2×C42C2412yes—
579C2×C42C2414yes—
580C2×C42C2414yes—
581C2×C42C2414yes—
582C2×C42C2414yes—
583C2×C42C2412yes—
584C2×C42C2414yes—
585C2×C42C2414yes—
586C2×C42C2412yes—
587C2×C42C2414yes—
588C2×C42C2412yes—
589C2×C42C2411yescharacteristic
590C2×C42C2411yescharacteristic
591C2×C42C2412yes—
592C2×C42C2412yes—
593C2×C42C2411yescharacteristic
594C2×C42C2418yes—
595C2×C42C2414yes—
596C2×C42C2414yes—
597C2×C42C2412yes—
598C2×C42C2414yes—
599C2×C42C2412yes—
600C2×C42C2414yes—
601C2×C42C2414yes—
602C2×C42C2412yes—
603C2×C42C2414yes—
604C2×C42C2412yes—
605C2×C42C2414yes—
606C2×C42C2412yes—
607C2×C42C2418yes—
608C2×C42C2418yes—
609C2×C42C2411yescharacteristic
610C2×C42C2412yes—
611C2×C42C2412yes—
612C2×C42C2411yescharacteristic
613C2×C42C2411yescharacteristic
614C2×C42C2412yes—
615C2×C42C2411yescharacteristic
616C2×C42C2412yes—
617C2×C42C2411yescharacteristic
618#95C2414yes—
619#95C2414yes—
620#95C2414yes—
621#95C2418yes—
622#95C2418yes—
623#95C2418yes—
624#95C2418yes—
625#95C2418yes—
626#95C2418yes—
627#95C2418yes—
628#95C2418yes—
629#95C2418yes—
630#95C2414yes—
631#95C2414yes—
632#95C2414yes—
633#95C2414yes—
634#95C2412yes—
635#95C2414yes—
636#95C2412yes—
637#95C2414yes—
638#95C2414yes—
639#95C2414yes—
640#95C2418yes—
641#95C2418yes—
642#95C2418yes—
643#95C2418yes—
644#95C2418yes—
645#95C2418yes—
646#95C2418yes—
647#95C2414yes—
648#95C2414yes—
649#95C2414yes—
650#95C2414yes—
651#95C2418yes—
652#95C2418yes—
653#95C2418yes—
654#95C2418yes—
655C24C2511yescharacteristic
656C24C2512yes—
657#41—232no—
658C2×Q8—24no—
659C2×Q8—28no—
660C2×Q8—28no—
661C2×Q8—216no—
662C2×Q8—44no—
663C2×Q8—48no—
664C2×Q8—48no—
665C2×Q8C22×Q814yes—
666C2×D4—28no—
667C2×D4C22×Q818yes—
668C2×D4C22×Q814yes—
669C2×D4C2×#4118yes—
670C22×C4—28no—
671C22×C4—24no—
672C22×C4—22no—
673C22×C4—24no—
674C22×C4—28no—
675C22×C4—24no—
676C22×C4—22no—
677C22×C4—24no—
678C22×C4—28no—
679C22×C4—216no—
680C22×C4—216no—
681C22×C4—28no—
682C22×C4—24no—
683C22×C4—24no—
684C22×C4—24no—
685C22×C4—216no—
686C22×C4—44no—
687C22×C4—44no—
688C22×C4—42no—
689C22×C4—44no—
690C22×C4—42no—
691C22×C4—42no—
692C22×C4—48no—
693C22×C4—48no—
694C22×C4—48no—
695C22×C4C22×Q818yes—
696C22×C4C22×Q814yes—
697C22×C4C22×Q814yes—
698C22×C4C22×Q818yes—
699C22×C4C22×Q814yes—
700C22×C4C22×Q818yes—
701C22×C4C2×#41116yes—
702C22×C4C2514yes—
703C22×C4C2514yes—
704C22×C4C2518yes—
705C22×C4C2514yes—
706C22×C4C2512yes—
707C22×C4C2514yes—
708C22×C4C2518yes—
709C22×C4C2511yescharacteristic
710C22×C4C2512yes—
711C22×C4C2511yescharacteristic
712C22×C4C2512yes—
713C22×C4C2512yes—
714C22×C4C2511yescharacteristic
715C22×C4C2512yes—
716C22×C4C2512yes—
717C22×C4C2512yes—
718C22×C4C2514yes—
719C22×C4C2514yes—
720C22×C4C2511yescharacteristic
721C22×C4C2511yescharacteristic
722C22×C4C2511yescharacteristic
723C4⋊C4—28no—
724C4⋊C4—216no—
725C4⋊C4—216no—
726C4⋊C4—216no—
727C4⋊C4—216no—
728C4⋊C4—216no—
729C4⋊C4—216no—
730C4⋊C4—216no—
731C4⋊C4—28no—
732C4⋊C4—28no—
733C4⋊C4—28no—
734C4⋊C4—24no—
735C4⋊C4—24no—
736C4⋊C4—28no—
737C4⋊C4—28no—
738C4⋊C4—28no—
739C4⋊C4—28no—
740C4⋊C4—28no—
741C4⋊C4—28no—
742C4⋊C4—216no—
743C4⋊C4—216no—
744C4⋊C4—24no—
745C4⋊C4—28no—
746C4⋊C4—24no—
747C4⋊C4—48no—
748C4⋊C4—44no—
749C4⋊C4—44no—
750C4⋊C4—44no—
751C4⋊C4—44no—
752C4⋊C4—48no—
753C4⋊C4—44no—
754C4⋊C4—48no—
755C4⋊C4—48no—
756C4⋊C4—48no—
757C4⋊C4—48no—
758C4⋊C4C22×Q818yes—
759C4⋊C4C22×Q818yes—
760C4⋊C4C22×Q814yes—
761C4⋊C4C22×Q814yes—
762C4⋊C4C2×#4118yes—
763C4⋊C4C2×#41116yes—
764C4⋊C4C2×#4118yes—
765C22⋊C4—28no—
766C22⋊C4—216no—
767C22⋊C4—216no—
768C22⋊C4—28no—
769C22⋊C4—28no—
770C22⋊C4—48no—
771C22⋊C4—44no—
772C22⋊C4C22×Q818yes—
773C22⋊C4C22×Q818yes—
774C22⋊C4C22×Q818yes—
775C22⋊C4C2×#41116yes—
776C42—24no—
777C42—28no—
778C42—24no—
779C42—28no—
780C42—24no—
781C42—28no—
782C42—24no—
783C42—28no—
784C42—24no—
785C42—22no—
786C42—28no—
787C42—28no—
788C42—28no—
789C42—22no—
790C42—24no—
791C42—28no—
792C42—216no—
793C42—28no—
794C42—24no—
795C42—22no—
796C42—24no—
797C42—28no—
798C42—44no—
799C42—44no—
800C42—42no—
801C42—42no—
802C42—44no—
803C42—42no—
804C42—48no—
805C42—48no—
806C42—44no—
807C42C22×Q814yes—
808C42C22×Q814yes—
809C42C22×Q818yes—
810C42C22×Q818yes—
811C42C22×Q818yes—
812C42C22×Q814yes—
813C42C22×Q814yes—
814C42C2×#4114yes—
815C42C2×#4118yes—
816C23—22no—
817C23—22no—
818C23—24no—
819C23—21no—
820C23—22no—
821C23—22no—
822C23—21no—
823C23C23×Q812yes—
824C23C23×Q814yes—
825C23C22×#4118yes—
826C23C2611yescharacteristic
827Q8—28no—
828Q8—416no—
829Q8—816no—
830D4—216no—
831D4#533116yescomplemented
832C2×C4—21no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—24no—
837C2×C4—22no—
838C2×C4—24no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—24no—
843C2×C4—24no—
844C2×C4—24no—
845C2×C4—22no—
846C2×C4—24no—
847C2×C4—21no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—216no—
851C2×C4—28no—
852C2×C4—216no—
853C2×C4—28no—
854C2×C4—216no—
855C2×C4—28no—
856C2×C4—22no—
857C2×C4—24no—
858C2×C4—24no—
859C2×C4—24no—
860C2×C4—24no—
861C2×C4—24no—
862C2×C4—24no—
863C2×C4—28no—
864C2×C4—28no—
865C2×C4—28no—
866C2×C4—24no—
867C2×C4—28no—
868C2×C4—28no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—24no—
872C2×C4—24no—
873C2×C4—24no—
874C2×C4—24no—
875C2×C4—24no—
876C2×C4—28no—
877C2×C4—416no—
878C2×C4—48no—
879C2×C4—416no—
880C2×C4—432no—
881C2×C4—48no—
882C2×C4—816no—
883C2×C4C23×Q812yes—
884C2×C4C23×Q814yes—
885C2×C4C23×Q812yes—
886C2×C4C23×Q812yes—
887C2×C4C23×Q814yes—
888C2×C4C23×Q814yes—
889C2×C4C23×Q812yes—
890C2×C4C23×Q812yes—
891C2×C4C23×Q812yes—
892C2×C4C22×#4114yes—
893C2×C4C22×#4114yes—
894C2×C4C22×#4118yes—
895C2×C4C22×#4114yes—
896C2×C4C22×#4118yes—
897C2×C4C22×#4114yes—
898C2×C4C22×#4112yes—
899C2×C4#58512yes—
900C2×C4#58514yes—
901C22—28no—
902C22—24no—
903C22—24no—
904C22—28no—
905C22—22no—
906C22—22no—
907C22—22no—
908C22—42no—
909C22—42no—
910C22C2×#53318yes—
911C22C24×Q811yescharacteristic
912C22C23×#4112yes—
913C22C23×#4111yescharacteristic
914C22C2×#58511yescharacteristic
915C22C2×#58512yes—
916C4—24no—
917C4—28no—
918C4—24no—
919C4—22no—
920C4—22no—
921C4—24no—
922C4—22no—
923C4—24no—
924C4—24no—
925C4—28no—
926C4—24no—
927C4—42no—
928C4—44no—
929C4—48no—
930C4—44no—
931C4—44no—
932C4—48no—
933C4—44no—
934C4C2×#53314yes—
935C4Q8×#4114yes—
936C4#350414yes—
937C2—28no—
938C2—42no—
939C2C22×#53311yescharacteristic
940C2C2×Q8×#4111yescharacteristic
941C2#41212yes—
942C2#6278112yes—
943C2C2×#350411yescharacteristic
subgroupG/H
centerC22×C4C25
commutator, Frattini, socle, cosocleC23C26
prime radicalC22×#41C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #36640C2semidirect
2. #36635C2semidirect
3. #36600C2semidirect
4. #36565C2semidirect
5. #36535C2semidirect
6. #36478C2semidirect
7. #36387C2semidirect
8. #36282C2semidirect
9. #36261C2semidirect
11. #36191C2semidirect
12. #36165C2semidirect
13. #36131C2semidirect
14. D4×#125C2semidirect
15. #34978C2semidirect
16. #34966C2semidirect
17. #34920C2semidirect
18. #34840C2semidirect
19. C4×#554C2semidirect
21. C4×#533C2semidirect
22. C2×C4×#125C2semidirect
191. C4×#41Q8semidirect
480. #125#41semidirect
831. D4#533semidirect

Maximal subgroups

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

subgroupindex
#366402
#366352
#366002
#365652
#365352
#364782
#363872
#362822
#362612
#362192
#361912
#361652
#361312
D4×#1252
#349782
#349662
#349202
#348402
C4×#5542
#341272
C4×#5332
C2×C4×#1252
C42×#412