Finite Group Databasebeta

← #6344265

Subgroups — #6344265

Order 512.

2801 conjugacy classes of subgroups.

The subgroup lattice has 1211 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62805C211yesmaximal, characteristic
2#60282C211yesmaximal, characteristic, complemented
3#60263C211yesmaximal, characteristic, complemented
4#17781C212yesmaximal, complemented
5#17780C214yesmaximal, complemented
6#17779C212yesmaximal, complemented
7#17778C212yesmaximal, complemented
8#17775C214yesmaximal, complemented
9#17774C212yesmaximal, complemented
10#17756C212yesmaximal, complemented
11#17753C212yesmaximal, complemented
12#17749C211yesmaximal, characteristic, complemented
13#17747C211yesmaximal, characteristic, complemented
14#17740C211yesmaximal, characteristic, complemented
15#17737C211yesmaximal, characteristic, complemented
16#17734C212yesmaximal, complemented
17C2×#1559C212yesmaximal, complemented
18#3523—21no—
19#3520—21no—
20#3520—22no—
21#3518—21no—
22#3515—21no—
23#3515—22no—
24#3511C2212yes—
25#3511C2211yescharacteristic
26#3509C2211yescharacteristic
27#3509C2212yes—
28#3503C2211yescharacteristic
29#3499C2211yescharacteristic
30#3495C412yes—
31#3495C414yes—
32#3489C412yes—
33#3482—21no—
34#3482—21no—
35#3482—22no—
36Q8×#41—21no—
37#3475—21no—
38#3475—22no—
39#3461C414yes—
40#3461C412yes—
41#3444C2211yescharacteristic
42#3444C2212yes—
43C2×#533C2212yes—
44C2×#533C2211yescharacteristic
45C4×2−1+4C412yes—
46C2×C4×#41C2211yescharacteristic
47#2991C2212yes—
48#2990C2212yes—
49#2990C2214yes—
50#2990C2212yes—
51#2990C2214yes—
52#2990C2212yes—
53#2989—22no—
54#2989—21no—
55#2988—21no—
56#2983—21no—
57#2973—22no—
58#2972—21no—
59#2970—21no—
60#2970—22no—
61#2970—21no—
62Q8×M16—21no—
63D4×M16—21no—
64D4×M16—22no—
65#2920C2212yes—
66#2920C2211yescharacteristic
67#2920C2211yescharacteristic
68#2920C2211yescharacteristic
69C2×#432C2212yes—
70C2×#432C2212yes—
71C2×#423C2212yes—
72C2×#423C2211yescharacteristic
73#1561C2212yescomplemented
74#1560C2212yescomplemented
75#1559C2211yescharacteristic
76#1559C2212yes—
77#1559C2212yes—
78#1559C2212yes—
79#1559C2211yescharacteristic
80#1559C2212yes—
81#1559C2212yes—
82#1559C2214yescomplemented
83#1559C2214yescomplemented
84#1559C2212yescomplemented
85#1558C2214yescomplemented
86#1557C2212yes—
87#1557C2211yescharacteristic
88#1557C2211yescharacteristic
89#1557C2212yescomplemented
90#1556C2214yescomplemented
91#1554C2214yescomplemented
92#1554C2214yescomplemented
93#1553C2214yescomplemented
94#1552C2214yescomplemented
95#1552C2214yescomplemented
96#1551C2214yescomplemented
97#1551C2214yescomplemented
98#1550C2214yescomplemented
99#1550C2214yescomplemented
100#1549C2212yescomplemented
101#1548C2212yescomplemented
102#1548C2212yescomplemented
103#1547C2214yescomplemented
104#1546C2212yescomplemented
105#1544C2212yescomplemented
106#1543C2212yescomplemented
107#1542C2214yescomplemented
108#1542C2214yescomplemented
109#1542C2212yescomplemented
110C2×#333C2214yescomplemented
111#1540C2212yescomplemented
112C2×#332C2214yescomplemented
113C2×2−1+4C2×C412yes—
114C22×#41C2×C411yescharacteristic
115C22×M16—22no—
116C22×M16—21no—
117Q82—21no—
118#557—21no—
119#557—22no—
120#557—21no—
121#557—21no—
122#557—22no—
123#556—21no—
124#556—22no—
125#556—21no—
126#556—22no—
127#556—22no—
128#556—21no—
129#556—22no—
130#556—24no—
131#555—21no—
132#555—22no—
133#554—22no—
134#554—21no—
135#554—21no—
136#554—22no—
137#554—22no—
138#554—24no—
139#553—22no—
140#553—22no—
141#553—22no—
142#552—22no—
143#552—22no—
144#552—22no—
145#552—22no—
146#552—22no—
147#552—22no—
148#552—24no—
149#552—24no—
150#552—24no—
151#552—22no—
152#552—24no—
153#552—22no—
154#552—24no—
155#551—24no—
156#551—24no—
157#551—24no—
158D4×Q8—22no—
159D4×Q8—21no—
160D4×Q8—21no—
161D4×Q8—21no—
162D4×Q8—22no—
163#548—22no—
164#548—22no—
165#548—22no—
166#548—22no—
167#547—22no—
168#547—24no—
169#547—21no—
170#547—22no—
171#547—21no—
172#547—22no—
173#547—22no—
174#547—21no—
175#546—22no—
176#546—24no—
177#544C2×C414yes—
178#544C2×C412yes—
179#542—22no—
180#542—24no—
181#542C2×C414yes—
182#542C2×C414yes—
183#542C2×C414yes—
184#541—22no—
185#541—24no—
186#541C2×C414yes—
187#541C2×C414yes—
188#541C2×C414yes—
189#539—24no—
190#539—24no—
191#539—24no—
192#537C2×C414yes—
193#537C2×C412yes—
194#536C2×C414yes—
195#536C2×C412yes—
196#536C2×C412yes—
197#536C2×C414yes—
198#533—22no—
199#533—24no—
200#533—21no—
201#533—22no—
202#533—21no—
203#533—22no—
204#533—22no—
205#533—21no—
206#533—22no—
207#533—21no—
208#533C2×C414yes—
209#533C2×C412yes—
210#533C2×C414yes—
211#533C2×C412yes—
212#533C2312yes—
213#533C2312yes—
214#533C2311yescharacteristic
215#533C2312yes—
216#533C2312yes—
217#533C2311yescharacteristic
218#533C2312yes—
219#533C2311yescharacteristic
220#533C2312yes—
221#532C2311yescharacteristic
222#532C2312yes—
223#532C2311yescharacteristic
224#532C2312yes—
225#532C2311yescharacteristic
226C2×C4⋊Q8C2312yes—
227C2×C4⋊Q8C2311yescharacteristic
228C2×C4⋊Q8C2312yes—
229C2×C4⋊Q8C2311yescharacteristic
230#529—24no—
231#529—24no—
232#529—24no—
233#529—22no—
234#529—24no—
235#529—22no—
236#529—21no—
237#529—22no—
238#529—21no—
239#529—22no—
240#529—21no—
241#529—21no—
242#529—22no—
243#529C2×C412yes—
244#529C2×C414yes—
245#529C2×C412yes—
246#529C2×C414yes—
247C2×#125—22no—
248C2×#125—21no—
249#525—22no—
250#525—21no—
251#525—21no—
252#525—22no—
253#525C2×C412yes—
254#525C2×C414yes—
255C2×C22⋊Q8—22no—
256C2×C22⋊Q8—21no—
257C2×C22⋊Q8C2×C414yes—
258C2×C22⋊Q8C2×C412yes—
259#520—24no—
260#520—22no—
261#520C2×C414yes—
262#520C2×C412yes—
263#520C2×C412yes—
264#519—22no—
265#519C2×C412yes—
266#519C2×C414yes—
267C4×#41—24no—
268C4×#41—22no—
269C4×#41—21no—
270C4×#41—22no—
271C4×#41—21no—
272C4×#41—22no—
273C4×#41C2×C412yes—
274C4×#41C2×C414yes—
275C4×#41C2×C411yescharacteristic
276C4×#41C2×C412yes—
277C4×#41C2×C411yescharacteristic
278C4×#41D411yescharacteristic
279C4×#41D412yes—
280C4×#41D411yescharacteristic
281C4×#41D411yescharacteristic
282C4×#41D412yes—
283C4×#41D411yescharacteristic
284C4×#41C2311yescharacteristic
285C4×#41C2312yes—
286C4×#41C2311yescharacteristic
287C2×C4×Q8—22no—
288C2×C4×Q8—22no—
289C2×C4×Q8—21no—
290C2×C4×Q8C2×C414yes—
291C2×C4×Q8C2×C412yes—
292C2×C4×Q8D411yescharacteristic
293C2×C4×Q8D411yescharacteristic
294C2×C4×D4D411yescharacteristic
295C2×C4×D4D412yes—
296C2×C4×D4D411yescharacteristic
297C2×C4×D4D412yes—
298C2×#117—22no—
299C2×#117—21no—
300C2×#117C2×C411yescharacteristic
301C2×#117C2×C412yes—
302C22×C42C2312yes—
303C22×C42C2311yescharacteristic
304#446—22no—
305#446—24no—
306#446—22no—
307#446—24no—
308#446—22no—
309C8×Q8—22no—
310#436—22no—
311#436—24no—
312#435—24no—
313#435—24no—
314#435—24no—
315#435—24no—
316#435—24no—
317#435—24no—
318#435—24no—
319C8×D4—22no—
320C8×D4—24no—
321C8×D4—22no—
322C8×D4—24no—
323C8×D4—22no—
324#432—22no—
325#432—22no—
326#432—22no—
327#432—22no—
328#432—21no—
329#432—21no—
330#432—21no—
331#432—22no—
332#432C2314yes—
333#432C2314yes—
334#432C2314yes—
335#432C2312yes—
336#432C2312yes—
337#432C2311yescharacteristic
338#432C2311yescharacteristic
339#431—21no—
340#431—21no—
341#431—22no—
342#431—21no—
343#431C2312yes—
344#431C2314yes—
345#431C2312yes—
346#431C2312yes—
347#423—22no—
348#423—21no—
349#423—21no—
350#423—22no—
351#423C2312yes—
352#423C2314yes—
353#423C2312yes—
354#423C2312yes—
355#423C2312yes—
356#423C2311yescharacteristic
357#423C2311yescharacteristic
358C2×C4⋊C8—22no—
359C2×C4⋊C8—21no—
360C2×C4⋊C8C2314yes—
361C2×C4⋊C8C2314yes—
362C2×C4⋊C8C2312yes—
363C2×C4⋊C8C2314yes—
364#407—22no—
365#407—21no—
366#407—21no—
367#407—21no—
368C2×C22⋊C8—22no—
369C2×C22⋊C8—22no—
370C4×M16—22no—
371C4×M16—21no—
372C4×M16—21no—
373C4×M16—21no—
374C2×#97—22no—
375C2×#97—22no—
376#333C2312yes—
377#333C2314yes—
378#333C2314yes—
379#333C2314yes—
380#333C2312yes—
381#333C2314yes—
382#333C2314yes—
383#332C2312yes—
384#332C2314yes—
385#332C2314yes—
386#332C2314yes—
387#332C2312yes—
388#332C2314yes—
389#332C2314yes—
390#332C2314yes—
391#332C2312yes—
392#332C2312yes—
393#331C2314yes—
394#331C2312yes—
395#331C2312yes—
3962−1+4—48no—
397C2×#41—24no—
398C2×#41—22no—
399C2×#41—21no—
400C2×#41—21no—
401C2×#41—22no—
402C2×#41—44no—
403C2×#41C22⋊C411yescharacteristic
404C2×#41C22⋊C412yes—
405C2×#41C22⋊C411yescharacteristic
406C2×#41C22×C414yes—
407C2×#41C22×C412yes—
408C2×#41C22×C411yescharacteristic
409C2×#41C22×C412yes—
410C2×#41C22×C411yescharacteristic
411C22×Q8—22no—
412C22×Q8—22no—
413C22×Q8—21no—
414C22×Q8C22⋊C411yescharacteristic
415C22×Q8C22×C412yes—
416C22×Q8C22×C414yes—
417C22×D4C22⋊C411yescharacteristic
418C22×D4C22⋊C412yes—
419C23×C4C22×C411yescharacteristic
420C23×C4C22×C412yes—
421C23×C4C2×D412yes—
422C23×C4C2×D411yescharacteristic
423C23×C4C2×D412yes—
424C23×C4C2×D411yescharacteristic
425C2×M16—21no—
426C2×M16—22no—
427C2×M16—21no—
428C2×M16—22no—
429C2×M16—24no—
430C2×M16—22no—
431C2×M16—22no—
432C2×M16—84no—
433C2×M16—82no—
434C22×C8—24no—
435C22×C8—22no—
436C22×C8—24no—
437C22×C8—24no—
438C4⋊Q8—22no—
439C4⋊Q8—24no—
440C4⋊Q8—24no—
441C4⋊Q8—22no—
442C4⋊Q8—21no—
443C4⋊Q8—21no—
444C4⋊Q8—21no—
445C4⋊Q8—22no—
446C4⋊Q8—22no—
447C4⋊Q8—22no—
448C4⋊Q8—21no—
449C4⋊Q8—22no—
450C4⋊Q8C22×C414yes—
451C4⋊Q8C22×C412yes—
452C4⋊Q8C22×C414yes—
453C4⋊Q8C22×C412yes—
454C4⋊Q8C2411yescharacteristic
455C4⋊Q8C2412yes—
456C4⋊Q8C2411yescharacteristic
457C4⋊Q8C2412yes—
458C4⋊Q8C2411yescharacteristic
459#127C2411yescharacteristic
460#126—24no—
461#126—24no—
462#126—24no—
463#126—24no—
464#126—24no—
465#126—24no—
466#126—24no—
467#126—24no—
468#126—24no—
469#126—24no—
470#126—22no—
471#126—24no—
472#126—22no—
473#125—24no—
474#125—24no—
475#125—24no—
476#125—24no—
477#125—22no—
478#125—24no—
479#125—24no—
480#125—24no—
481#125—24no—
482#125—22no—
483#125—22no—
484#125—24no—
485#125—21no—
486#125—22no—
487#125—22no—
488#125—22no—
489#125—22no—
490#125—22no—
491#125—21no—
492#125C22×C412yes—
493#125C22×C414yes—
494#124—22no—
495#124—24no—
496#124—24no—
497#124—24no—
498#124—24no—
499#124—21no—
500#124—22no—
501#124—21no—
502#124C22×C412yes—
503#124C22×C414yes—
504#123—24no—
505#123—24no—
506#123—24no—
507#123—24no—
508#123—22no—
509#123—24no—
510#123—22no—
511#123—24no—
512#123—22no—
513#123—24no—
514#123—24no—
515#123—24no—
516#123—24no—
517#123—24no—
518#123—24no—
519C22⋊Q8—22no—
520C22⋊Q8—24no—
521C22⋊Q8—24no—
522C22⋊Q8—22no—
523C22⋊Q8—22no—
524C22⋊Q8—24no—
525C22⋊Q8—22no—
526C22⋊Q8—24no—
527C22⋊Q8—22no—
528C22⋊Q8—24no—
529C22⋊Q8—21no—
530C22⋊Q8—22no—
531C22⋊Q8—22no—
532C22⋊Q8—22no—
533C22⋊Q8—22no—
534C22⋊Q8—22no—
535C22⋊Q8—21no—
536C22⋊Q8—22no—
537C22⋊Q8—21no—
538C22⋊Q8—22no—
539C22⋊Q8—21no—
540C22⋊Q8—24no—
541C22⋊Q8—22no—
542C22⋊Q8—24no—
543C22⋊Q8—22no—
544C22⋊Q8—24no—
545C22⋊Q8—24no—
546C22⋊Q8—24no—
547C22⋊Q8—24no—
548C22⋊Q8—24no—
549C22⋊Q8—24no—
550C22⋊Q8C22×C412yes—
551C22⋊Q8C22×C414yes—
552C22⋊Q8C22×C414yes—
553C22⋊Q8C22×C414yes—
554C22⋊Q8C22×C414yes—
555C22⋊Q8C22×C412yes—
556C22⋊Q8C22×C414yes—
557#121—24no—
558#121—24no—
559#121—24no—
560#121—22no—
561#121—24no—
562#121—21no—
563#121—22no—
564#121—21no—
565#121—22no—
566#121—21no—
567#121—22no—
568#121—21no—
569#121C22×C412yes—
570#121C22×C412yes—
571#121C22×C414yes—
572#120—24no—
573#120—22no—
574C4×Q8—22no—
575C4×Q8—24no—
576C4×Q8—22no—
577C4×Q8—24no—
578C4×Q8—22no—
579C4×Q8—24no—
580C4×Q8—22no—
581C4×Q8—22no—
582C4×Q8—24no—
583C4×Q8—24no—
584C4×Q8—22no—
585C4×Q8—24no—
586C4×Q8—22no—
587C4×Q8—21no—
588C4×Q8—22no—
589C4×Q8—22no—
590C4×Q8—22no—
591C4×Q8—22no—
592C4×Q8—21no—
593C4×Q8—22no—
594C4×Q8—21no—
595C4×Q8—22no—
596C4×Q8—21no—
597C4×Q8—22no—
598C4×Q8C22⋊C411yescharacteristic
599C4×Q8C22⋊C411yescharacteristic
600C4×Q8C22⋊C411yescharacteristic
601C4×Q8C22⋊C412yes—
602C4×Q8C22⋊C411yescharacteristic
603C4×Q8C22⋊C412yes—
604C4×Q8C22×C412yes—
605C4×Q8C22×C414yes—
606C4×Q8C22×C414yes—
607C4×Q8C22×C414yes—
608C4×Q8C22×C414yes—
609C4×Q8C22×C412yes—
610C4×Q8C22×C414yes—
611C4×Q8C2×D411yescharacteristic
612C4×Q8C2×D411yescharacteristic
613C4×Q8C2×D412yes—
614C4×Q8C2×D411yescharacteristic
615C4×Q8C2×D411yescharacteristic
616C4×Q8C2×D412yes—
617C4×D4—24no—
618C4×D4—22no—
619C4×D4—22no—
620C4×D4—24no—
621C4×D4—22no—
622C4×D4—24no—
623C4×D4—22no—
624C4×D4—24no—
625C4×D4—22no—
626C4×D4—24no—
627C4×D4—22no—
628C4×D4—24no—
629C4×D4—22no—
630C4×D4—24no—
631C4×D4—24no—
632C4×D4—24no—
633C4×D4—24no—
634C4×D4—21no—
635C4×D4—21no—
636C4×D4—22no—
637C4×D4—21no—
638C4×D4—22no—
639C4×D4—21no—
640C4×D4—22no—
641C4×D4C22⋊C412yes—
642C4×D4C22⋊C411yescharacteristic
643C4×D4C22⋊C412yes—
644C4×D4C22⋊C411yescharacteristic
645C4×D4C22⋊C411yescharacteristic
646C4×D4C22⋊C412yes—
647C4×D4C22⋊C412yes—
648C4×D4C22⋊C412yes—
649C4×D4C22⋊C412yes—
650C4×D4C22⋊C412yes—
651C4×D4C22⋊C412yes—
652C4×D4C22⋊C412yes—
653C4×D4C22⋊C411yescharacteristic
654C4×D4C22⋊C412yes—
655C4×D4C22×C412yes—
656C4×D4C22×C412yes—
657C4×D4C22×C414yes—
658C4×D4C2×D411yescharacteristic
659C4×D4C2×D412yes—
660C4×D4C2×D411yescharacteristic
661C4×D4C2×D412yes—
662C4×D4C2×D412yes—
663C4×D4C2×D411yescharacteristic
664C4×D4C2×D412yes—
665C4×D4C2×D412yes—
666C4×D4C2×D412yes—
667C4×D4C2×D412yes—
668C4×D4C2×D412yes—
669C4×D4C2×D412yes—
670C4×D4C2×D411yescharacteristic
671C4×D4C2×D412yes—
672#117—22no—
673#117—24no—
674#117—24no—
675#117—22no—
676#117—21no—
677#117—22no—
678#117—22no—
679#117—22no—
680#117—22no—
681#117—21no—
682#117—22no—
683#117—24no—
684#117—22no—
685#117—24no—
686#117—24no—
687#117—24no—
688#117—22no—
689#117—24no—
690#117—22no—
691#117—24no—
692#117—24no—
693#117—22no—
694#117C22⋊C411yescharacteristic
695#117C22⋊C412yes—
696#117C22⋊C412yes—
697#117C22⋊C412yes—
698#117C22⋊C412yes—
699#117C22⋊C411yescharacteristic
700#117C22⋊C412yes—
701#117C22×C412yes—
702#117C22×C414yes—
703#117C22×C412yes—
704#117C22×C411yescharacteristic
705#117C22×C411yescharacteristic
706#117C22×C412yes—
707#117C22×C412yes—
708#117C22×C412yes—
709#117C22×C412yes—
710C2×C4⋊C4—24no—
711C2×C4⋊C4—22no—
712C2×C4⋊C4—22no—
713C2×C4⋊C4—24no—
714C2×C4⋊C4—22no—
715C2×C4⋊C4—21no—
716C2×C4⋊C4—22no—
717C2×C4⋊C4—21no—
718C2×C4⋊C4—22no—
719C2×C4⋊C4—21no—
720C2×C4⋊C4—24no—
721C2×C4⋊C4—22no—
722C2×C4⋊C4C22⋊C411yescharacteristic
723C2×C4⋊C4C22⋊C412yes—
724C2×C4⋊C4C22⋊C411yescharacteristic
725C2×C4⋊C4C22⋊C412yes—
726C2×C4⋊C4C22×C414yes—
727C2×C4⋊C4C22×C412yes—
728C2×C22⋊C4—24no—
729C2×C22⋊C4—22no—
730C2×C22⋊C4C22⋊C412yes—
731C2×C22⋊C4C22⋊C412yes—
732C2×C22⋊C4C22⋊C412yes—
733C2×C42—22no—
734C2×C42—24no—
735C2×C42—24no—
736C2×C42—22no—
737C2×C42C22×C412yes—
738C2×C42C22×C411yescharacteristic
739C2×C42C22×C412yes—
740C2×C42C22×C411yescharacteristic
741C2×C42C22×C412yes—
742C2×C42C22×C411yescharacteristic
743C2×C42C2×D411yescharacteristic
744C2×C42C2×D412yes—
745C2×C42C2×D411yescharacteristic
746C2×C42C2×D412yes—
747C2×C42C2×D412yes—
748C2×C42C2×D411yescharacteristic
749C2×C42C2×D411yescharacteristic
750C2×C42C2×D412yes—
751C2×C42C2×D412yes—
752C2×C42C2×D411yescharacteristic
753C2×C42C2×D412yes—
754C2×C42C2×D411yescharacteristic
755C2×C42C2412yes—
756C2×C42C2411yescharacteristic
757C2×C42C2411yescharacteristic
758C2×C42C2412yes—
759C2×C42C2411yescharacteristic
760C4⋊C8—21no—
761C4⋊C8—22no—
762C4⋊C8—22no—
763C4⋊C8—24no—
764C4⋊C8—24no—
765C4⋊C8—22no—
766C4⋊C8—24no—
767C4⋊C8—24no—
768C4⋊C8—21no—
769C4⋊C8—22no—
770C4⋊C8—22no—
771C4⋊C8C2414yes—
772C4⋊C8C2412yes—
773C4⋊C8C2414yes—
774C4⋊C8C2412yes—
775C4⋊C8C2412yes—
776C4⋊C8C2412yes—
777C22⋊C8—21no—
778C22⋊C8—22no—
779C22⋊C8—21no—
780C22⋊C8—24no—
781C22⋊C8—24no—
782C22⋊C8—24no—
783C22⋊C8—22no—
784C22⋊C8—22no—
785C22⋊C8—22no—
786C22⋊C8—22no—
787C22⋊C8—24no—
788#97—21no—
789#97—22no—
790#97—21no—
791#97—24no—
792#97—24no—
793#97—24no—
794#97—22no—
795C4×C8—22no—
796C4×C8—22no—
797C4×C8—22no—
798C4×C8—24no—
799C24C2×C22⋊C412yes—
800C24C2×C22⋊C411yescharacteristic
801#41—24no—
802#41—24no—
803#41—44no—
804#41—44no—
805#41—42no—
806#41—42no—
807#41—44no—
808#41—48no—
809#41—44no—
810#41—416no—
811#41—48no—
812#41—81no—
813#41—82no—
814#41—81no—
815#41—82no—
816C2×Q8—24no—
817C2×Q8—22no—
818C2×Q8—22no—
819C2×Q8—24no—
820C2×Q8—21no—
821C2×Q8—21no—
822C2×Q8—22no—
823C2×Q8—42no—
824C2×Q8—44no—
825C2×Q8—48no—
826C2×Q8—48no—
827C2×Q8—82no—
828C2×Q8—81no—
829C2×Q8—82no—
830C2×Q8—81no—
831C2×Q8C2×C22⋊C411yescharacteristic
832C2×Q8C2×C22⋊C411yescharacteristic
833C2×Q8C2×C22⋊C412yes—
834C2×Q8C23×C414yes—
835C2×Q8C23×C412yes—
836C2×D4—24no—
837C2×D4—22no—
838C2×D4—22no—
839C2×D4—24no—
840C2×D4—22no—
841C2×D4—24no—
842C2×D4—21no—
843C2×D4—21no—
844C2×D4—44no—
845C2×D4C2×C22⋊C412yes—
846C2×D4C2×C22⋊C412yes—
847C2×D4C2×C22⋊C412yes—
848C2×D4C2×C22⋊C411yescharacteristic
849C2×D4C2×C22⋊C412yes—
850C2×D4C2×C22⋊C412yes—
851C2×D4C2×C22⋊C411yescharacteristic
852C2×D4C23×C412yes—
853C22×C4—22no—
854C22×C4—24no—
855C22×C4—22no—
856C22×C4—24no—
857C22×C4—22no—
858C22×C4—24no—
859C22×C4—22no—
860C22×C4—22no—
861C22×C4—24no—
862C22×C4—42no—
863C22×C4—41no—
864C22×C4—42no—
865C22×C4—44no—
866C22×C4—42no—
867C22×C4—41no—
868C22×C4—42no—
869C22×C4—44no—
870C22×C4C2×C22⋊C412yes—
871C22×C4C2×C22⋊C411yescharacteristic
872C22×C4C2×C22⋊C411yescharacteristic
873C22×C4C2×C22⋊C411yescharacteristic
874C22×C4C2×C22⋊C412yes—
875C22×C4C2×C22⋊C412yes—
876C22×C4C2×C22⋊C411yescharacteristic
877C22×C4C2×C22⋊C411yescharacteristic
878C22×C4C2×C22⋊C412yes—
879C22×C4C2×C22⋊C411yescharacteristic
880C22×C4C2×C22⋊C412yes—
881C22×C4C2×C22⋊C411yescharacteristic
882C22×C4C2×C22⋊C412yes—
883C22×C4C2×C22⋊C412yes—
884C22×C4C2×C22⋊C411yescharacteristic
885C22×C4C2×C22⋊C411yescharacteristic
886C22×C4C2×C22⋊C412yes—
887C22×C4C2×C22⋊C412yes—
888C22×C4C23×C412yes—
889C22×C4C23×C411yescharacteristic
890C22×C4C23×C411yescharacteristic
891C22×C4C23×C411yescharacteristic
892C22×C4C23×C412yes—
893C22×C4C22×D411yescharacteristic
894C22×C4C22×D412yes—
895C22×C4C22×D411yescharacteristic
896C22×C4C22×D412yes—
897C22×C4C22×D411yescharacteristic
898C22×C4C22×D412yes—
899C22×C4C22×D411yescharacteristic
900C22×C4C22×D411yescharacteristic
901C22×C4C22×D412yes—
902C22×C4C22×D411yescharacteristic
903M16—42no—
904M16—42no—
905M16—44no—
906M16—82no—
907M16—82no—
908M16—82no—
909M16—84no—
910C2×C8—22no—
911C2×C8—24no—
912C2×C8—22no—
913C2×C8—22no—
914C2×C8—22no—
915C2×C8—24no—
916C2×C8—84no—
917C2×C8—84no—
918C2×C8—84no—
919C2×C8—82no—
920C4⋊C4—22no—
921C4⋊C4—24no—
922C4⋊C4—24no—
923C4⋊C4—24no—
924C4⋊C4—24no—
925C4⋊C4—24no—
926C4⋊C4—22no—
927C4⋊C4—24no—
928C4⋊C4—22no—
929C4⋊C4—22no—
930C4⋊C4—24no—
931C4⋊C4—22no—
932C4⋊C4—24no—
933C4⋊C4—24no—
934C4⋊C4—24no—
935C4⋊C4—24no—
936C4⋊C4—22no—
937C4⋊C4—24no—
938C4⋊C4—24no—
939C4⋊C4—22no—
940C4⋊C4—22no—
941C4⋊C4—24no—
942C4⋊C4—22no—
943C4⋊C4—24no—
944C4⋊C4—22no—
945C4⋊C4—24no—
946C4⋊C4—21no—
947C4⋊C4—22no—
948C4⋊C4—21no—
949C4⋊C4—22no—
950C4⋊C4—21no—
951C4⋊C4—22no—
952C4⋊C4—21no—
953C4⋊C4C2×C22⋊C412yes—
954C4⋊C4C2×C22⋊C411yescharacteristic
955C4⋊C4C2×C22⋊C412yes—
956C4⋊C4C2×C22⋊C411yescharacteristic
957C4⋊C4C2×C22⋊C412yes—
958C4⋊C4C2×C22⋊C412yes—
959C4⋊C4C2×C22⋊C412yes—
960C4⋊C4C2×C22⋊C412yes—
961C4⋊C4C2×C22⋊C411yescharacteristic
962C4⋊C4C2×C22⋊C412yes—
963C4⋊C4C2×C22⋊C411yescharacteristic
964C4⋊C4C2×C22⋊C412yes—
965C4⋊C4C2×C22⋊C412yes—
966C4⋊C4C2×C22⋊C412yes—
967C4⋊C4C23×C412yes—
968C4⋊C4C23×C414yes—
969C4⋊C4C23×C412yes—
970C22⋊C4—22no—
971C22⋊C4—24no—
972C22⋊C4—24no—
973C22⋊C4—24no—
974C22⋊C4—24no—
975C22⋊C4—22no—
976C22⋊C4—24no—
977C22⋊C4—22no—
978C22⋊C4—24no—
979C22⋊C4—22no—
980C22⋊C4—22no—
981C22⋊C4—24no—
982C22⋊C4—22no—
983C22⋊C4—22no—
984C22⋊C4—24no—
985C22⋊C4—22no—
986C22⋊C4—24no—
987C22⋊C4—22no—
988C22⋊C4—24no—
989C22⋊C4C2×C22⋊C412yes—
990C22⋊C4C2×C22⋊C412yes—
991C22⋊C4C2×C22⋊C412yes—
992C22⋊C4C2×C22⋊C412yes—
993C22⋊C4C2×C22⋊C412yes—
994C22⋊C4C2×C22⋊C412yes—
995C22⋊C4C2×C22⋊C412yes—
996C22⋊C4C2×C22⋊C412yes—
997C22⋊C4C2×C22⋊C412yes—
998C22⋊C4C2×C22⋊C412yes—
999C22⋊C4C2×C22⋊C412yes—
1000C22⋊C4C2×C22⋊C412yes—
1001C42—24no—
1002C42—22no—
1003C42—22no—
1004C42—24no—
1005C42—24no—
1006C42—24no—
1007C42—24no—
1008C42—24no—
1009C42—22no—
1010C42C2×C22⋊C412yes—
1011C42C2×C22⋊C411yescharacteristic
1012C42C2×C22⋊C411yescharacteristic
1013C42C2×C22⋊C412yes—
1014C42C2×C22⋊C411yescharacteristic
1015C42C2×C22⋊C412yes—
1016C42C2×C22⋊C412yes—
1017C42C2×C22⋊C411yescharacteristic
1018C42C2×C22⋊C412yes—
1019C42C2×C22⋊C411yescharacteristic
1020C42C2×C22⋊C412yes—
1021C42C2×C22⋊C411yescharacteristic
1022C42C23×C411yescharacteristic
1023C42C23×C412yes—
1024C42C23×C411yescharacteristic
1025C42C23×C412yes—
1026C42C23×C411yescharacteristic
1027C42C22×D411yescharacteristic
1028C42C22×D411yescharacteristic
1029C42C22×D411yescharacteristic
1030C42C22×D412yes—
1031C42C22×D411yescharacteristic
1032C42C22×D412yes—
1033C42C22×D412yes—
1034C42C22×D412yes—
1035C42C22×D411yescharacteristic
1036C42C22×D411yescharacteristic
1037C42C2511yescharacteristic
1038C23—24no—
1039C23—22no—
1040C23—41no—
1041C23—42no—
1042C23—42no—
1043C23—41no—
1044C23—41no—
1045C23C22×C22⋊C411yescharacteristic
1046C23C22×C22⋊C412yes—
1047C23C22×C22⋊C411yescharacteristic
1048C23C22×C22⋊C411yescharacteristic
1049C23C22×C22⋊C412yes—
1050Q8—22no—
1051Q8—22no—
1052Q8—42no—
1053Q8—44no—
1054Q8—42no—
1055Q8—48no—
1056Q8—41no—
1057Q8—42no—
1058Q8—41no—
1059Q8—42no—
1060Q8—42no—
1061Q8—44no—
1062Q8—84no—
1063Q8—82no—
1064D4—24no—
1065D4—24no—
1066D4—24no—
1067D4—22no—
1068D4—42no—
1069D4—42no—
1070D4—42no—
1071D4—44no—
1072D4—44no—
1073D4—48no—
1074D4—41no—
1075D4—42no—
1076D4—41no—
1077D4—82no—
1078D4—84no—
1079D4#41314yes—
1080C2×C4—24no—
1081C2×C4—24no—
1082C2×C4—22no—
1083C2×C4—21no—
1084C2×C4—21no—
1085C2×C4—21no—
1086C2×C4—22no—
1087C2×C4—24no—
1088C2×C4—24no—
1089C2×C4—21no—
1090C2×C4—22no—
1091C2×C4—22no—
1092C2×C4—22no—
1093C2×C4—22no—
1094C2×C4—21no—
1095C2×C4—21no—
1096C2×C4—22no—
1097C2×C4—22no—
1098C2×C4—22no—
1099C2×C4—22no—
1100C2×C4—22no—
1101C2×C4—24no—
1102C2×C4—22no—
1103C2×C4—24no—
1104C2×C4—22no—
1105C2×C4—41no—
1106C2×C4—42no—
1107C2×C4—41no—
1108C2×C4—42no—
1109C2×C4—41no—
1110C2×C4—42no—
1111C2×C4—41no—
1112C2×C4—42no—
1113C2×C4—41no—
1114C2×C4—42no—
1115C2×C4—41no—
1116C2×C4—41no—
1117C2×C4—42no—
1118C2×C4—42no—
1119C2×C4—42no—
1120C2×C4—41no—
1121C2×C4—41no—
1122C2×C4—42no—
1123C2×C4—48no—
1124C2×C4—44no—
1125C2×C4—44no—
1126C2×C4—48no—
1127C2×C4—44no—
1128C2×C4—82no—
1129C2×C4—84no—
1130C2×C4—84no—
1131C2×C4—82no—
1132C2×C4C22×C22⋊C411yescharacteristic
1133C2×C4C22×C22⋊C412yes—
1134C2×C4C22×C22⋊C411yescharacteristic
1135C2×C4C22×C22⋊C411yescharacteristic
1136C2×C4C22×C22⋊C412yes—
1137C2×C4C22×C22⋊C412yes—
1138C2×C4C22×C22⋊C411yescharacteristic
1139C2×C4C22×C22⋊C411yescharacteristic
1140C2×C4C22×C22⋊C411yescharacteristic
1141C2×C4C22×C22⋊C412yes—
1142C2×C4C22×C22⋊C411yescharacteristic
1143C2×C4C22×C22⋊C412yes—
1144C2×C4C22×C22⋊C411yescharacteristic
1145C2×C4C22×C22⋊C412yes—
1146C2×C4C22×C22⋊C411yescharacteristic
1147C2×C4C24×C411yescharacteristic
1148C2×C4C23×D411yescharacteristic
1149C2×C4C23×D411yescharacteristic
1150C8—42no—
1151C8—44no—
1152C8—44no—
1153C8—42no—
1154C8—42no—
1155C8—42no—
1156C22—22no—
1157C22—22no—
1158C22—21no—
1159C22—21no—
1160C22—21no—
1161C22—22no—
1162C22—21no—
1163C22—22no—
1164C22—21no—
1165C22—21no—
1166C22—21no—
1167C22—21no—
1168C22—21no—
1169C22—22no—
1170C22—42no—
1171C22—42no—
1172C22—42no—
1173C22—84no—
1174C22—82no—
1175C22C2×#41314yes—
1176C22C23×C22⋊C411yescharacteristic
1177C4—21no—
1178C4—21no—
1179C4—22no—
1180C4—21no—
1181C4—22no—
1182C4—21no—
1183C4—22no—
1184C4—22no—
1185C4—21no—
1186C4—21no—
1187C4—21no—
1188C4—21no—
1189C4—22no—
1190C4—22no—
1191C4—21no—
1192C4—44no—
1193C4—42no—
1194C4—42no—
1195C4—42no—
1196C4—44no—
1197C4C2×#41312yes—
1198C4#358511yescharacteristic
1199C4#358612yes—
1200C4#358611yescharacteristic
1201C2—24no—
1202C2—41no—
1203C2—41no—
1204C2—42no—
1205C2—41no—
1206C2—82no—
1207C2C22×#41311yescharacteristic
1208C2#6008811yescharacteristic
1209C2#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. #60282C2semidirect
3. #60263C2semidirect
4. #17781C2semidirect
5. #17780C2semidirect
6. #17779C2semidirect
7. #17778C2semidirect
8. #17775C2semidirect
9. #17774C2semidirect
10. #17756C2semidirect
11. #17753C2semidirect
12. #17749C2semidirect
13. #17747C2semidirect
14. #17740C2semidirect
15. #17737C2semidirect
16. #17734C2semidirect
17. C2×#1559C2semidirect
73. #1561C22semidirect
74. #1560C22semidirect
82. #1559C22semidirect
83. #1559C22semidirect
84. #1559C22semidirect
85. #1558C22semidirect
89. #1557C22semidirect
90. #1556C22semidirect
91. #1554C22semidirect
92. #1554C22semidirect
93. #1553C22semidirect
94. #1552C22semidirect
95. #1552C22semidirect
96. #1551C22semidirect
97. #1551C22semidirect
98. #1550C22semidirect
99. #1550C22semidirect
100. #1549C22semidirect
101. #1548C22semidirect
102. #1548C22semidirect
103. #1547C22semidirect
104. #1546C22semidirect
105. #1544C22semidirect
106. #1543C22semidirect
107. #1542C22semidirect
108. #1542C22semidirect
109. #1542C22semidirect
110. C2×#333C22semidirect
111. #1540C22semidirect
112. C2×#332C22semidirect

Maximal subgroups

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

subgroupindex
#628052
#602822
#602632
#177812
#177802
#177792
#177782
#177752
#177742
#177562
#177532
#177492
#177472
#177402
#177372
#177342
C2×#15592