Finite Group Databasebeta

← #6344114

Subgroups — #6344114

Order 512.

2820 conjugacy classes of subgroups.

The subgroup lattice has 1236 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62805C211yesmaximal, characteristic
2#60263C211yesmaximal, characteristic, complemented
3#60125C211yesmaximal, characteristic, complemented
4#17769C214yesmaximal, complemented
5#17767C214yesmaximal, complemented
6#17761C212yesmaximal, complemented
7#17759C212yesmaximal, complemented
8#17757C212yesmaximal, complemented
9#17752C211yesmaximal, characteristic, complemented
10#17751C211yesmaximal, characteristic, complemented
11#17751C212yesmaximal, complemented
12#17739C212yesmaximal, complemented
13#17737C211yesmaximal, characteristic, complemented
14#17737C212yesmaximal, complemented
15C2×#1561C211yesmaximal, characteristic, complemented
16#17727C212yesmaximal, complemented
17#17725C212yesmaximal, complemented
18#3523—21no—
19#3520—22no—
20#3520—21no—
21#3518C412yes—
22#3515C414yes—
23#3515C412yes—
24#3511C2211yescharacteristic
25#3511C2212yes—
26#3509C2211yescharacteristic
27#3509C2212yes—
28#3503C2211yescharacteristic
29#3499C2211yescharacteristic
30#3495—21no—
31#3495—22no—
32#3489—21no—
33#3482—21no—
34#3482—22no—
35#3482—21no—
36Q8×#41C412yes—
37#3475C414yes—
38#3475C412yes—
39#3461—21no—
40#3461—22no—
41#3444C2211yescharacteristic
42#3444C2212yes—
43C2×#533C2211yescharacteristic
44C2×#533C2212yes—
45C4×2−1+4—21no—
46C2×C4×#41C2211yescharacteristic
47#2991—21no—
48#2990—22no—
49#2990—21no—
50#2989C2212yes—
51#2989C2214yes—
52#2988C2212yes—
53Q8×M16—21no—
54D4×M16—22no—
55D4×M16—21no—
56#2925—21no—
57#2925—21no—
58#2925—22no—
59#2925C2212yes—
60#2925C2212yes—
61#2925C2214yes—
62#2921—22no—
63#2920C2212yes—
64#2920C2211yescharacteristic
65#2920C2212yes—
66#2920C2212yes—
67C2×#423C2211yescharacteristic
68C2×#423C2211yescharacteristic
69C2×#423C2212yes—
70C2×#423C2211yescharacteristic
71#2879—21no—
72#2873—21no—
73#1561C2212yes—
74#1561C2212yes—
75#1561C2211yescharacteristic
76#1561C2212yes—
77#1561C2211yescharacteristic
78#1561C2212yes—
79#1561C2212yes—
80#1561C2214yescomplemented
81#1560C2211yescharacteristic
82#1560C2212yes—
83#1560C2211yescharacteristic
84#1559C2214yescomplemented
85#1559C2212yescomplemented
86#1557C2214yescomplemented
87#1557C2212yescomplemented
88#1556C2214yescomplemented
89#1556C2214yescomplemented
90#1554C2214yescomplemented
91#1554C2214yescomplemented
92#1553C2214yescomplemented
93#1553C2214yescomplemented
94#1552C2214yescomplemented
95#1552C2214yescomplemented
96#1552C2214yescomplemented
97#1550C2212yescomplemented
98#1550C2212yescomplemented
99#1549C2212yescomplemented
100#1549C2214yescomplemented
101#1547C2212yescomplemented
102#1547C2212yescomplemented
103#1546C2212yescomplemented
104#1546C2214yescomplemented
105#1544C2214yescomplemented
106#1544C2214yescomplemented
107#1542C2212yescomplemented
108#1542C2214yescomplemented
109#1540C2212yescomplemented
110#1540C2214yescomplemented
111C2×#332C2212yescomplemented
112C2×#332C2212yescomplemented
113C2×2−1+4—21no—
114C22×#41D411yescharacteristic
115C22×M16—21no—
116C22×M16—21no—
117C22×M16—21no—
118C22×M16—22no—
119Q82C2×C412yes—
120#557—21no—
121#557—21no—
122#557—22no—
123#557C2×C412yes—
124#557C2×C414yes—
125#556—21no—
126#556—22no—
127#556—21no—
128#556—22no—
129#556—22no—
130#556—24no—
131#556C2×C412yes—
132#556C2×C414yes—
133#555C2×C412yes—
134#555C2×C414yes—
135#554—22no—
136#554—24no—
137#554C2×C412yes—
138#554C2×C414yes—
139#554C2×C414yes—
140#554C2×C412yes—
141#553C2×C414yes—
142#553C2×C414yes—
143#553C2×C414yes—
144#552—22no—
145#552—22no—
146#552—22no—
147#552—24no—
148#552—24no—
149#552—24no—
150#552—22no—
151#552—24no—
152#552—22no—
153#552—24no—
154#552C2×C414yes—
155#552C2×C414yes—
156#552C2×C414yes—
157#551—24no—
158#551—24no—
159#551—24no—
160D4×Q8—22no—
161D4×Q8—21no—
162D4×Q8—22no—
163D4×Q8—21no—
164D4×Q8C2×C412yes—
165#548—22no—
166#548—22no—
167#548—22no—
168#548—22no—
169#547—24no—
170#547—22no—
171#547—22no—
172#547—21no—
173#547—21no—
174#547—22no—
175#547C2×C414yes—
176#547C2×C412yes—
177#546—24no—
178#546—22no—
179#544—21no—
180#544—22no—
181#542—22no—
182#542—24no—
183#542—22no—
184#542—22no—
185#542—22no—
186#541—22no—
187#541—24no—
188#541—22no—
189#541—22no—
190#541—22no—
191#539—24no—
192#539—24no—
193#539—24no—
194#537—21no—
195#537—22no—
196#536—21no—
197#536—22no—
198#536—21no—
199#536—22no—
200#533—22no—
201#533—24no—
202#533—21no—
203#533—22no—
204#533—22no—
205#533—21no—
206#533—22no—
207#533—21no—
208#533—21no—
209#533—22no—
210#533C2×C412yes—
211#533C2×C414yes—
212#533C2×C412yes—
213#533C2×C414yes—
214#533C2311yescharacteristic
215#533C2312yes—
216#533C2311yescharacteristic
217#533C2312yes—
218#533C2312yes—
219#533C2312yes—
220#533C2312yes—
221#533C2312yes—
222#533C2311yescharacteristic
223#532C2311yescharacteristic
224#532C2311yescharacteristic
225#532C2312yes—
226#532C2311yescharacteristic
227#532C2312yes—
228C2×C4⋊Q8C2311yescharacteristic
229C2×C4⋊Q8C2311yescharacteristic
230C2×C4⋊Q8C2312yes—
231C2×C4⋊Q8C2312yes—
232#529—24no—
233#529—24no—
234#529—24no—
235#529—22no—
236#529—24no—
237#529—21no—
238#529—22no—
239#529—21no—
240#529—22no—
241#529—22no—
242#529—21no—
243#529—21no—
244#529—22no—
245#529C2×C412yes—
246#529C2×C414yes—
247#529C2×C412yes—
248#529C2×C414yes—
249C2×#125C2×C412yes—
250C2×#125C2×C414yes—
251#525—21no—
252#525—22no—
253#525—21no—
254#525—22no—
255#525C2×C412yes—
256#525C2×C414yes—
257C2×C22⋊Q8—21no—
258C2×C22⋊Q8—22no—
259C2×C22⋊Q8—21no—
260C2×C22⋊Q8—22no—
261#520—21no—
262#520—22no—
263#520—24no—
264#520—21no—
265#520—22no—
266#519—22no—
267#519—21no—
268#519—22no—
269C4×#41—24no—
270C4×#41—22no—
271C4×#41—21no—
272C4×#41—22no—
273C4×#41—22no—
274C4×#41—21no—
275C4×#41C2×C412yes—
276C4×#41C2×C414yes—
277C4×#41C2×C412yes—
278C4×#41C2×C411yescharacteristic
279C4×#41C2×C411yescharacteristic
280C4×#41D412yes—
281C4×#41D411yescharacteristic
282C4×#41D411yescharacteristic
283C4×#41D411yescharacteristic
284C4×#41D411yescharacteristic
285C4×#41D412yes—
286C4×#41C2311yescharacteristic
287C4×#41C2311yescharacteristic
288C4×#41C2312yes—
289C2×C4×Q8—22no—
290C2×C4×Q8—21no—
291C2×C4×Q8—22no—
292C2×C4×Q8—21no—
293C2×C4×Q8—22no—
294C2×C4×Q8C2×C411yescharacteristic
295C2×C4×Q8D411yescharacteristic
296C2×C4×D4C2×C411yescharacteristic
297C2×C4×D4C2×C412yes—
298C2×C4×D4D412yes—
299C2×C4×D4D411yescharacteristic
300C2×#117C2×C412yes—
301C2×#117C2×C414yes—
302C2×#117D411yescharacteristic
303C2×#117D412yes—
304C22×C42C2311yescharacteristic
305C22×C42C2312yes—
306#446—22no—
307#446—24no—
308C8×Q8—22no—
309#436—22no—
310#436—24no—
311#435—24no—
312#435—24no—
313#435—24no—
314C8×D4—22no—
315C8×D4—24no—
316#433—24no—
317#433—24no—
318#433—24no—
319#433—24no—
320#432—22no—
321#432—22no—
322#432—21no—
323#432—22no—
324#432C2314yes—
325#432C2312yes—
326#432C2314yes—
327#432C2314yes—
328#431—22no—
329#431—22no—
330#431—22no—
331#431—21no—
332#431C2314yes—
333#431C2312yes—
334#431C2314yes—
335#431C2314yes—
336#423—21no—
337#423—21no—
338#423—21no—
339#423—21no—
340#423—21no—
341#423—22no—
342#423—22no—
343#423—21no—
344#423C2312yes—
345#423C2314yes—
346#423C2312yes—
347#423C2312yes—
348#423C2311yescharacteristic
349#423C2312yes—
350#423C2311yescharacteristic
351#423C2312yes—
352#423C2311yescharacteristic
353#423C2311yescharacteristic
354C2×C4⋊C8—21no—
355C2×C4⋊C8—21no—
356C2×C4⋊C8—21no—
357C2×C4⋊C8—22no—
358C2×C4⋊C8C2312yes—
359C2×C4⋊C8C2312yes—
360C2×C4⋊C8C2314yes—
361C2×C4⋊C8C2312yes—
362#408—22no—
363#408—22no—
364#408—24no—
365#407—22no—
366#407—22no—
367#407—21no—
368#407—22no—
369#405—22no—
370#405—22no—
371#405—24no—
372C4×M16—22no—
373C4×M16—22no—
374C4×M16—21no—
375C4×M16—22no—
376#333C2312yes—
377#333C2314yes—
378#333C2312yes—
379#332C2314yes—
380#332C2314yes—
381#332C2314yes—
382#332C2314yes—
383#332C2312yes—
384#332C2314yes—
385#332C2312yes—
386#332C2312yes—
387#332C2312yes—
388#332C2314yes—
389#332C2314yes—
390#332C2314yes—
391#332C2314yes—
392#332C2314yes—
393#331C2312yes—
394#331C2314yes—
395#331C2312yes—
3962−1+4—44no—
3972−1+4—44no—
398C2×#41—22no—
399C2×#41—24no—
400C2×#41—22no—
401C2×#41—21no—
402C2×#41—22no—
403C2×#41—21no—
404C2×#41—42no—
405C2×#41—42no—
406C2×#41C22⋊C412yes—
407C2×#41C22⋊C411yescharacteristic
408C2×#41C22⋊C411yescharacteristic
409C2×#41C22×C412yes—
410C2×#41C2×D411yescharacteristic
411C2×#41C2×D411yescharacteristic
412C2×#41C2×D412yes—
413C22×Q8—22no—
414C22×Q8—22no—
415C22×Q8—21no—
416C22×Q8—21no—
417C22×Q8—22no—
418C22×Q8C22⋊C411yescharacteristic
419C22×D4C22⋊C411yescharacteristic
420C22×D4C22⋊C412yes—
421C23×C4C22×C411yescharacteristic
422C23×C4C22×C412yes—
423C23×C4C2×D411yescharacteristic
424C23×C4C2×D412yes—
425C23×C4C2×D411yescharacteristic
426C23×C4C2×D412yes—
427C2×M16—22no—
428C2×M16—21no—
429C2×M16—21no—
430C2×M16—21no—
431C2×M16—22no—
432C2×M16—22no—
433C2×M16—22no—
434C2×M16—21no—
435C2×M16—24no—
436C2×M16—22no—
437C2×M16—44no—
438C2×M16—44no—
439C2×M16—82no—
440C2×M16—84no—
441C22×C8—22no—
442C22×C8—22no—
443C22×C8—22no—
444C22×C8—24no—
445C4⋊Q8—22no—
446C4⋊Q8—24no—
447C4⋊Q8—24no—
448C4⋊Q8—22no—
449C4⋊Q8—22no—
450C4⋊Q8—21no—
451C4⋊Q8—22no—
452C4⋊Q8—21no—
453C4⋊Q8—21no—
454C4⋊Q8—21no—
455C4⋊Q8—22no—
456C4⋊Q8—22no—
457C4⋊Q8C22×C412yes—
458C4⋊Q8C22×C414yes—
459C4⋊Q8C22×C412yes—
460C4⋊Q8C22×C414yes—
461C4⋊Q8C2411yescharacteristic
462C4⋊Q8C2412yes—
463C4⋊Q8C2412yes—
464C4⋊Q8C2411yescharacteristic
465C4⋊Q8C2411yescharacteristic
466#127C2411yescharacteristic
467#126—24no—
468#126—24no—
469#126—24no—
470#126—24no—
471#126—24no—
472#126—24no—
473#126—24no—
474#126—24no—
475#126—24no—
476#126—22no—
477#126—24no—
478#126—24no—
479#126—22no—
480#125—24no—
481#125—24no—
482#125—24no—
483#125—24no—
484#125—22no—
485#125—24no—
486#125—24no—
487#125—24no—
488#125—22no—
489#125—24no—
490#125—24no—
491#125—22no—
492#125—22no—
493#125—21no—
494#125—22no—
495#125—21no—
496#125C22×C414yes—
497#125C22×C412yes—
498#125C22×C414yes—
499#125C22×C414yes—
500#125C22×C414yes—
501#124—22no—
502#124—24no—
503#124—24no—
504#124—24no—
505#124—24no—
506#124—22no—
507#124—21no—
508#124—22no—
509#124—21no—
510#124C22×C412yes—
511#123—24no—
512#123—24no—
513#123—24no—
514#123—22no—
515#123—24no—
516#123—22no—
517#123—24no—
518#123—24no—
519#123—22no—
520#123—24no—
521#123—24no—
522#123—24no—
523#123—24no—
524#123—24no—
525#123—24no—
526C22⋊Q8—22no—
527C22⋊Q8—24no—
528C22⋊Q8—22no—
529C22⋊Q8—24no—
530C22⋊Q8—22no—
531C22⋊Q8—24no—
532C22⋊Q8—22no—
533C22⋊Q8—24no—
534C22⋊Q8—24no—
535C22⋊Q8—22no—
536C22⋊Q8—22no—
537C22⋊Q8—21no—
538C22⋊Q8—22no—
539C22⋊Q8—21no—
540C22⋊Q8—22no—
541C22⋊Q8—22no—
542C22⋊Q8—22no—
543C22⋊Q8—22no—
544C22⋊Q8—22no—
545C22⋊Q8—22no—
546C22⋊Q8—22no—
547C22⋊Q8—21no—
548C22⋊Q8—21no—
549C22⋊Q8—22no—
550C22⋊Q8—24no—
551C22⋊Q8—22no—
552C22⋊Q8—24no—
553C22⋊Q8—22no—
554C22⋊Q8—24no—
555C22⋊Q8—24no—
556C22⋊Q8—24no—
557C22⋊Q8—24no—
558C22⋊Q8—24no—
559C22⋊Q8—24no—
560C22⋊Q8C22×C412yes—
561C22⋊Q8C22×C414yes—
562C22⋊Q8C22×C414yes—
563C22⋊Q8C22×C412yes—
564#121—24no—
565#121—24no—
566#121—24no—
567#121—22no—
568#121—24no—
569#121—21no—
570#121—21no—
571#121—22no—
572#121—21no—
573#121—21no—
574#121—22no—
575#121C22×C412yes—
576#121C22×C414yes—
577#121C22×C414yes—
578#121C22×C412yes—
579#120—22no—
580#120—24no—
581C4×Q8—22no—
582C4×Q8—24no—
583C4×Q8—22no—
584C4×Q8—24no—
585C4×Q8—22no—
586C4×Q8—24no—
587C4×Q8—22no—
588C4×Q8—24no—
589C4×Q8—22no—
590C4×Q8—22no—
591C4×Q8—24no—
592C4×Q8—24no—
593C4×Q8—22no—
594C4×Q8—22no—
595C4×Q8—21no—
596C4×Q8—22no—
597C4×Q8—21no—
598C4×Q8—22no—
599C4×Q8—22no—
600C4×Q8—22no—
601C4×Q8—22no—
602C4×Q8—22no—
603C4×Q8—22no—
604C4×Q8—22no—
605C4×Q8—21no—
606C4×Q8—21no—
607C4×Q8—22no—
608C4×Q8C22⋊C411yescharacteristic
609C4×Q8C22⋊C411yescharacteristic
610C4×Q8C22⋊C412yes—
611C4×Q8C22⋊C411yescharacteristic
612C4×Q8C22⋊C411yescharacteristic
613C4×Q8C22⋊C412yes—
614C4×Q8C22×C414yes—
615C4×Q8C22×C412yes—
616C4×Q8C22×C412yes—
617C4×Q8C22×C414yes—
618C4×Q8C22×C411yescharacteristic
619C4×Q8C22×C411yescharacteristic
620C4×Q8C22×C412yes—
621C4×Q8C2×D411yescharacteristic
622C4×Q8C2×D411yescharacteristic
623C4×Q8C2×D412yes—
624C4×D4—24no—
625C4×D4—22no—
626C4×D4—24no—
627C4×D4—22no—
628C4×D4—24no—
629C4×D4—22no—
630C4×D4—22no—
631C4×D4—24no—
632C4×D4—24no—
633C4×D4—22no—
634C4×D4—22no—
635C4×D4—24no—
636C4×D4—24no—
637C4×D4—22no—
638C4×D4—24no—
639C4×D4—24no—
640C4×D4—24no—
641C4×D4—21no—
642C4×D4—21no—
643C4×D4—22no—
644C4×D4—21no—
645C4×D4—21no—
646C4×D4—22no—
647C4×D4C22⋊C412yes—
648C4×D4C22⋊C411yescharacteristic
649C4×D4C22⋊C411yescharacteristic
650C4×D4C22⋊C412yes—
651C4×D4C22⋊C412yes—
652C4×D4C22⋊C412yes—
653C4×D4C22⋊C412yes—
654C4×D4C22⋊C412yes—
655C4×D4C22⋊C411yescharacteristic
656C4×D4C22⋊C412yes—
657C4×D4C22⋊C412yes—
658C4×D4C22⋊C412yes—
659C4×D4C22⋊C411yescharacteristic
660C4×D4C22⋊C412yes—
661C4×D4C22×C412yes—
662C4×D4C22×C414yes—
663C4×D4C22×C414yes—
664C4×D4C22×C412yes—
665C4×D4C22×C412yes—
666C4×D4C22×C411yescharacteristic
667C4×D4C22×C412yes—
668C4×D4C22×C412yes—
669C4×D4C22×C412yes—
670C4×D4C22×C411yescharacteristic
671C4×D4C22×C412yes—
672C4×D4C2×D412yes—
673C4×D4C2×D411yescharacteristic
674C4×D4C2×D411yescharacteristic
675C4×D4C2×D412yes—
676C4×D4C2×D412yes—
677C4×D4C2×D412yes—
678C4×D4C2×D412yes—
679#117—24no—
680#117—22no—
681#117—24no—
682#117—22no—
683#117—22no—
684#117—21no—
685#117—22no—
686#117—21no—
687#117—24no—
688#117—22no—
689#117—24no—
690#117—24no—
691#117—24no—
692#117—24no—
693#117—22no—
694#117—24no—
695#117—22no—
696#117—22no—
697#117—24no—
698#117C22⋊C411yescharacteristic
699#117C22⋊C412yes—
700#117C22⋊C412yes—
701#117C22⋊C412yes—
702#117C22⋊C412yes—
703#117C22⋊C411yescharacteristic
704#117C22⋊C412yes—
705#117C22×C414yes—
706#117C22×C412yes—
707#117C22×C414yes—
708#117C22×C414yes—
709#117C22×C414yes—
710#117C2×D411yescharacteristic
711#117C2×D412yes—
712#117C2×D411yescharacteristic
713#117C2×D412yes—
714#117C2×D412yes—
715#117C2×D412yes—
716#117C2×D412yes—
717C2×C4⋊C4—24no—
718C2×C4⋊C4—22no—
719C2×C4⋊C4—22no—
720C2×C4⋊C4—24no—
721C2×C4⋊C4—22no—
722C2×C4⋊C4—21no—
723C2×C4⋊C4—21no—
724C2×C4⋊C4—22no—
725C2×C4⋊C4—24no—
726C2×C4⋊C4—22no—
727C2×C4⋊C4C22⋊C411yescharacteristic
728C2×C4⋊C4C22⋊C412yes—
729C2×C4⋊C4C22⋊C411yescharacteristic
730C2×C4⋊C4C22⋊C412yes—
731C2×C4⋊C4C22×C412yes—
732C2×C4⋊C4C22×C414yes—
733C2×C4⋊C4C22×C412yes—
734C2×C4⋊C4C22×C414yes—
735C2×C22⋊C4—22no—
736C2×C22⋊C4—24no—
737C2×C22⋊C4C22⋊C412yes—
738C2×C22⋊C4C22⋊C412yes—
739C2×C22⋊C4C22⋊C412yes—
740C2×C42—24no—
741C2×C42—22no—
742C2×C42—24no—
743C2×C42—22no—
744C2×C42C22×C411yescharacteristic
745C2×C42C22×C412yes—
746C2×C42C22×C411yescharacteristic
747C2×C42C22×C412yes—
748C2×C42C22×C411yescharacteristic
749C2×C42C22×C412yes—
750C2×C42C2×D412yes—
751C2×C42C2×D411yescharacteristic
752C2×C42C2×D411yescharacteristic
753C2×C42C2×D412yes—
754C2×C42C2×D411yescharacteristic
755C2×C42C2×D412yes—
756C2×C42C2×D411yescharacteristic
757C2×C42C2×D412yes—
758C2×C42C2×D412yes—
759C2×C42C2×D411yescharacteristic
760C2×C42C2×D411yescharacteristic
761C2×C42C2×D412yes—
762C2×C42C2411yescharacteristic
763C2×C42C2412yes—
764C2×C42C2411yescharacteristic
765C2×C42C2412yes—
766C2×C42C2411yescharacteristic
767C4⋊C8—22no—
768C4⋊C8—21no—
769C4⋊C8—21no—
770C4⋊C8—21no—
771C4⋊C8—22no—
772C4⋊C8—22no—
773C4⋊C8—22no—
774C4⋊C8—24no—
775C4⋊C8—22no—
776C4⋊C8—22no—
777C4⋊C8—22no—
778C4⋊C8—22no—
779C4⋊C8—24no—
780C4⋊C8—21no—
781C4⋊C8C2412yes—
782C4⋊C8C2414yes—
783C4⋊C8C2412yes—
784C4⋊C8C2414yes—
785C4⋊C8C2412yes—
786C4⋊C8C2412yes—
787C22⋊C8—24no—
788C22⋊C8—24no—
789C22⋊C8—24no—
790C22⋊C8—24no—
791C22⋊C8—24no—
792C22⋊C8—22no—
793C22⋊C8—22no—
794C22⋊C8—24no—
795#97—24no—
796#97—24no—
797#97—24no—
798#97—22no—
799C4×C8—24no—
800C4×C8—24no—
801C4×C8—22no—
802C4×C8—24no—
803C24C2×C22⋊C411yescharacteristic
804C24C2×C22⋊C412yes—
805#41—22no—
806#41—22no—
807#41—22no—
808#41—22no—
809#41—42no—
810#41—42no—
811#41—44no—
812#41—42no—
813#41—42no—
814#41—44no—
815#41—44no—
816#41—44no—
817#41—416no—
818#41—48no—
819#41—42no—
820#41—42no—
821#41—82no—
822#41—81no—
823#41—82no—
824#41—81no—
825C2×Q8—24no—
826C2×Q8—22no—
827C2×Q8—24no—
828C2×Q8—22no—
829C2×Q8—21no—
830C2×Q8—22no—
831C2×Q8—21no—
832C2×Q8—22no—
833C2×Q8—42no—
834C2×Q8—44no—
835C2×Q8—44no—
836C2×Q8—48no—
837C2×Q8—42no—
838C2×Q8—42no—
839C2×Q8—81no—
840C2×Q8—82no—
841C2×Q8—81no—
842C2×Q8—82no—
843C2×Q8C2×C22⋊C411yescharacteristic
844C2×Q8C2×C22⋊C411yescharacteristic
845C2×Q8C2×C22⋊C412yes—
846C2×Q8C23×C412yes—
847C2×D4—22no—
848C2×D4—24no—
849C2×D4—22no—
850C2×D4—22no—
851C2×D4—24no—
852C2×D4—21no—
853C2×D4—21no—
854C2×D4—42no—
855C2×D4—44no—
856C2×D4C2×C22⋊C412yes—
857C2×D4C2×C22⋊C411yescharacteristic
858C2×D4C2×C22⋊C412yes—
859C2×D4C2×C22⋊C411yescharacteristic
860C2×D4C2×C22⋊C412yes—
861C2×D4C2×C22⋊C412yes—
862C2×D4C2×C22⋊C412yes—
863C2×D4C23×C412yes—
864C22×C4—22no—
865C22×C4—22no—
866C22×C4—24no—
867C22×C4—22no—
868C22×C4—24no—
869C22×C4—22no—
870C22×C4—22no—
871C22×C4—24no—
872C22×C4—22no—
873C22×C4—24no—
874C22×C4—22no—
875C22×C4—41no—
876C22×C4—42no—
877C22×C4—42no—
878C22×C4—44no—
879C22×C4—41no—
880C22×C4—42no—
881C22×C4—42no—
882C22×C4—42no—
883C22×C4C2×C22⋊C412yes—
884C22×C4C2×C22⋊C411yescharacteristic
885C22×C4C2×C22⋊C411yescharacteristic
886C22×C4C2×C22⋊C411yescharacteristic
887C22×C4C2×C22⋊C411yescharacteristic
888C22×C4C2×C22⋊C412yes—
889C22×C4C2×C22⋊C411yescharacteristic
890C22×C4C2×C22⋊C412yes—
891C22×C4C2×C22⋊C411yescharacteristic
892C22×C4C2×C22⋊C412yes—
893C22×C4C2×C22⋊C412yes—
894C22×C4C2×C22⋊C411yescharacteristic
895C22×C4C2×C22⋊C412yes—
896C22×C4C2×C22⋊C412yes—
897C22×C4C2×C22⋊C411yescharacteristic
898C22×C4C2×C22⋊C412yes—
899C22×C4C2×C22⋊C412yes—
900C22×C4C2×C22⋊C411yescharacteristic
901C22×C4C23×C411yescharacteristic
902C22×C4C23×C412yes—
903C22×C4C23×C411yescharacteristic
904C22×C4C23×C411yescharacteristic
905C22×C4C23×C412yes—
906C22×C4C22×D412yes—
907C22×C4C22×D412yes—
908C22×C4C22×D411yescharacteristic
909C22×C4C22×D412yes—
910C22×C4C22×D412yes—
911C22×C4C22×D411yescharacteristic
912C22×C4C22×D411yescharacteristic
913C22×C4C22×D411yescharacteristic
914C22×C4C22×D411yescharacteristic
915C22×C4C22×D411yescharacteristic
916M16—42no—
917M16—44no—
918M16—42no—
919M16—42no—
920M16—44no—
921M16—44no—
922M16—42no—
923M16—44no—
924M16—84no—
925M16—82no—
926C2×C8—22no—
927C2×C8—24no—
928C2×C8—22no—
929C2×C8—22no—
930C2×C8—22no—
931C2×C8—24no—
932C2×C8—44no—
933C2×C8—44no—
934C2×C8—82no—
935C2×C8—84no—
936C4⋊C4—24no—
937C4⋊C4—22no—
938C4⋊C4—24no—
939C4⋊C4—24no—
940C4⋊C4—24no—
941C4⋊C4—24no—
942C4⋊C4—22no—
943C4⋊C4—24no—
944C4⋊C4—22no—
945C4⋊C4—24no—
946C4⋊C4—24no—
947C4⋊C4—24no—
948C4⋊C4—24no—
949C4⋊C4—22no—
950C4⋊C4—24no—
951C4⋊C4—22no—
952C4⋊C4—24no—
953C4⋊C4—22no—
954C4⋊C4—24no—
955C4⋊C4—22no—
956C4⋊C4—24no—
957C4⋊C4—22no—
958C4⋊C4—24no—
959C4⋊C4—22no—
960C4⋊C4—22no—
961C4⋊C4—24no—
962C4⋊C4—22no—
963C4⋊C4—21no—
964C4⋊C4—21no—
965C4⋊C4—22no—
966C4⋊C4—21no—
967C4⋊C4—21no—
968C4⋊C4C2×C22⋊C412yes—
969C4⋊C4C2×C22⋊C411yescharacteristic
970C4⋊C4C2×C22⋊C412yes—
971C4⋊C4C2×C22⋊C411yescharacteristic
972C4⋊C4C2×C22⋊C412yes—
973C4⋊C4C2×C22⋊C411yescharacteristic
974C4⋊C4C2×C22⋊C412yes—
975C4⋊C4C2×C22⋊C412yes—
976C4⋊C4C2×C22⋊C412yes—
977C4⋊C4C2×C22⋊C412yes—
978C4⋊C4C2×C22⋊C412yes—
979C4⋊C4C2×C22⋊C412yes—
980C4⋊C4C2×C22⋊C412yes—
981C4⋊C4C2×C22⋊C411yescharacteristic
982C4⋊C4C23×C414yes—
983C4⋊C4C23×C412yes—
984C4⋊C4C23×C414yes—
985C4⋊C4C23×C412yes—
986C22⋊C4—24no—
987C22⋊C4—22no—
988C22⋊C4—24no—
989C22⋊C4—24no—
990C22⋊C4—24no—
991C22⋊C4—24no—
992C22⋊C4—22no—
993C22⋊C4—22no—
994C22⋊C4—24no—
995C22⋊C4—22no—
996C22⋊C4—22no—
997C22⋊C4—24no—
998C22⋊C4—22no—
999C22⋊C4—24no—
1000C22⋊C4—22no—
1001C22⋊C4—22no—
1002C22⋊C4—24no—
1003C22⋊C4—24no—
1004C22⋊C4—22no—
1005C22⋊C4C2×C22⋊C412yes—
1006C22⋊C4C2×C22⋊C412yes—
1007C22⋊C4C2×C22⋊C412yes—
1008C22⋊C4C2×C22⋊C412yes—
1009C22⋊C4C2×C22⋊C412yes—
1010C22⋊C4C2×C22⋊C412yes—
1011C22⋊C4C2×C22⋊C412yes—
1012C22⋊C4C2×C22⋊C412yes—
1013C22⋊C4C2×C22⋊C412yes—
1014C22⋊C4C2×C22⋊C412yes—
1015C22⋊C4C2×C22⋊C412yes—
1016C22⋊C4C2×C22⋊C412yes—
1017C42—24no—
1018C42—22no—
1019C42—24no—
1020C42—22no—
1021C42—24no—
1022C42—24no—
1023C42—24no—
1024C42—24no—
1025C42—22no—
1026C42C2×C22⋊C412yes—
1027C42C2×C22⋊C411yescharacteristic
1028C42C2×C22⋊C412yes—
1029C42C2×C22⋊C411yescharacteristic
1030C42C2×C22⋊C412yes—
1031C42C2×C22⋊C411yescharacteristic
1032C42C2×C22⋊C411yescharacteristic
1033C42C2×C22⋊C412yes—
1034C42C2×C22⋊C412yes—
1035C42C2×C22⋊C411yescharacteristic
1036C42C2×C22⋊C411yescharacteristic
1037C42C2×C22⋊C412yes—
1038C42C23×C411yescharacteristic
1039C42C23×C411yescharacteristic
1040C42C23×C412yes—
1041C42C23×C412yes—
1042C42C23×C411yescharacteristic
1043C42C22×D412yes—
1044C42C22×D412yes—
1045C42C22×D411yescharacteristic
1046C42C22×D412yes—
1047C42C22×D412yes—
1048C42C22×D411yescharacteristic
1049C42C22×D411yescharacteristic
1050C42C22×D411yescharacteristic
1051C42C22×D411yescharacteristic
1052C42C22×D411yescharacteristic
1053C42C2511yescharacteristic
1054C23—22no—
1055C23—22no—
1056C23—42no—
1057C23—41no—
1058C23—41no—
1059C23—42no—
1060C23—42no—
1061C23C22×C22⋊C411yescharacteristic
1062C23C22×C22⋊C412yes—
1063C23C22×C22⋊C411yescharacteristic
1064C23C22×C22⋊C412yes—
1065C23C22×C22⋊C411yescharacteristic
1066Q8—22no—
1067Q8—22no—
1068Q8—42no—
1069Q8—42no—
1070Q8—48no—
1071Q8—42no—
1072Q8—41no—
1073Q8—42no—
1074Q8—41no—
1075Q8—44no—
1076Q8—41no—
1077Q8—41no—
1078Q8—42no—
1079Q8—42no—
1080Q8—82no—
1081Q8—84no—
1082D4—24no—
1083D4—24no—
1084D4—22no—
1085D4—22no—
1086D4—42no—
1087D4—42no—
1088D4—42no—
1089D4—42no—
1090D4—44no—
1091D4—48no—
1092D4—44no—
1093D4—41no—
1094D4—41no—
1095D4—41no—
1096D4—41no—
1097D4—84no—
1098D4—82no—
1099C2×C4—22no—
1100C2×C4—21no—
1101C2×C4—22no—
1102C2×C4—21no—
1103C2×C4—22no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—22no—
1108C2×C4—22no—
1109C2×C4—21no—
1110C2×C4—22no—
1111C2×C4—22no—
1112C2×C4—24no—
1113C2×C4—24no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—24no—
1127C2×C4—22no—
1128C2×C4—24no—
1129C2×C4—22no—
1130C2×C4—42no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—42no—
1134C2×C4—41no—
1135C2×C4—42no—
1136C2×C4—42no—
1137C2×C4—41no—
1138C2×C4—42no—
1139C2×C4—42no—
1140C2×C4—42no—
1141C2×C4—41no—
1142C2×C4—42no—
1143C2×C4—41no—
1144C2×C4—42no—
1145C2×C4—48no—
1146C2×C4—48no—
1147C2×C4—44no—
1148C2×C4—44no—
1149C2×C4—44no—
1150C2×C4—84no—
1151C2×C4—82no—
1152C2×C4—82no—
1153C2×C4—84no—
1154C2×C4C22×C22⋊C412yes—
1155C2×C4C22×C22⋊C411yescharacteristic
1156C2×C4C22×C22⋊C412yes—
1157C2×C4C22×C22⋊C411yescharacteristic
1158C2×C4C22×C22⋊C412yes—
1159C2×C4C22×C22⋊C411yescharacteristic
1160C2×C4C22×C22⋊C411yescharacteristic
1161C2×C4C22×C22⋊C412yes—
1162C2×C4C22×C22⋊C411yescharacteristic
1163C2×C4C22×C22⋊C411yescharacteristic
1164C2×C4C22×C22⋊C412yes—
1165C2×C4C22×C22⋊C412yes—
1166C2×C4C22×C22⋊C411yescharacteristic
1167C2×C4C22×C22⋊C411yescharacteristic
1168C2×C4C22×C22⋊C411yescharacteristic
1169C2×C4#57512yes—
1170C2×C4#57512yes—
1171C2×C4C24×C411yescharacteristic
1172C2×C4C23×D411yescharacteristic
1173C2×C4C23×D411yescharacteristic
1174C8—44no—
1175C8—42no—
1176C8—42no—
1177C8—44no—
1178C8—42no—
1179C8—42no—
1180C22—21no—
1181C22—21no—
1182C22—21no—
1183C22—21no—
1184C22—22no—
1185C22—22no—
1186C22—21no—
1187C22—21no—
1188C22—22no—
1189C22—22no—
1190C22—21no—
1191C22—22no—
1192C22—22no—
1193C22—21no—
1194C22—42no—
1195C22—42no—
1196C22—42no—
1197C22—82no—
1198C22—84no—
1199C22#289612yes—
1200C22C23×C22⋊C411yescharacteristic
1201C4—21no—
1202C4—21no—
1203C4—22no—
1204C4—21no—
1205C4—22no—
1206C4—21no—
1207C4—21no—
1208C4—22no—
1209C4—22no—
1210C4—21no—
1211C4—22no—
1212C4—21no—
1213C4—21no—
1214C4—22no—
1215C4—42no—
1216C4—44no—
1217C4—42no—
1218C4—44no—
1219C4—42no—
1220C4#288912yes—
1221C4#289612yes—
1222C4C2×#57511yescharacteristic
1223C4C2×#57511yescharacteristic
1224C4#358511yescharacteristic
1225C4#358611yescharacteristic
1226C2—22no—
1227C2—41no—
1228C2—42no—
1229C2—42no—
1230C2—41no—
1231C2—82no—
1232C2C2×#288911yescharacteristic
1233C2C2×#289611yescharacteristic
1234C2#6008911yescharacteristic
subgroupG/H
center, socleC22C23×C22⋊C4
commutatorC2×C4C24×C4
Frattini, cosocleC42C25
prime radical#62805C2
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C2×C4×#41 ◁ G
LECSG ▷ C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #60263C2semidirect
3. #60125C2semidirect
4. #17769C2semidirect
5. #17767C2semidirect
6. #17761C2semidirect
7. #17759C2semidirect
8. #17757C2semidirect
9. #17752C2semidirect
10. #17751C2semidirect
11. #17751C2semidirect
12. #17739C2semidirect
13. #17737C2semidirect
14. #17737C2semidirect
15. C2×#1561C2semidirect
16. #17727C2semidirect
17. #17725C2semidirect
80. #1561C22semidirect
84. #1559C22semidirect
85. #1559C22semidirect
86. #1557C22semidirect
87. #1557C22semidirect
88. #1556C22semidirect
89. #1556C22semidirect
90. #1554C22semidirect
91. #1554C22semidirect
92. #1553C22semidirect
93. #1553C22semidirect
94. #1552C22semidirect
95. #1552C22semidirect
96. #1552C22semidirect
97. #1550C22semidirect
98. #1550C22semidirect
99. #1549C22semidirect
100. #1549C22semidirect
101. #1547C22semidirect
102. #1547C22semidirect
103. #1546C22semidirect
104. #1546C22semidirect
105. #1544C22semidirect
106. #1544C22semidirect
107. #1542C22semidirect
108. #1542C22semidirect
109. #1540C22semidirect
110. #1540C22semidirect
111. C2×#332C22semidirect
112. C2×#332C22semidirect

Maximal subgroups

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

subgroupindex
#628052
#602632
#601252
#177692
#177672
#177612
#177592
#177572
#177522
#177512
#177392
#177372
C2×#15612
#177272
#177252