Finite Group Databasebeta

← #6344175

Subgroups — #6344175

Order 512.

2787 conjugacy classes of subgroups.

The subgroup lattice has 1191 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62805C211yesmaximal, characteristic
2#60282C211yesmaximal, characteristic, complemented
3#60278C211yesmaximal, characteristic, complemented
4#17780C214yesmaximal, complemented
5#17779C212yesmaximal, complemented
6#17778C212yesmaximal, complemented
7#17775C214yesmaximal, complemented
8#17774C212yesmaximal, complemented
9#17772C212yesmaximal, complemented
10#17757C211yesmaximal, characteristic, complemented
11#17756C212yesmaximal, complemented
12#17748C212yesmaximal, complemented
13#17747C211yesmaximal, characteristic, complemented
14#17718C211yesmaximal, characteristic, complemented
15#17716C211yesmaximal, characteristic, complemented
16#17713C212yesmaximal, complemented
17C2×#1554C212yesmaximal, complemented
18#3523—21no—
19#3520—21no—
20#3520—22no—
21#3518—21no—
22#3515—21no—
23#3515—22no—
24#3511C2211yescharacteristic
25#3511C2212yes—
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#3444C2212yes—
42#3444C2211yescharacteristic
43C2×#533C2212yes—
44C2×#533C2211yescharacteristic
45C4×2−1+4C412yes—
46C2×C4×#41C2211yescharacteristic
47#2991C2212yes—
48#2990C2212yes—
49#2990C2212yes—
50#2990C2212yes—
51#2990C2214yes—
52#2990C2214yes—
53#2984—21no—
54#2983—21no—
55#2974—21no—
56#2974—22no—
57#2973—22no—
58#2972—21no—
59#2970—21no—
60#2970—22no—
61#2970—21no—
62#2965—22no—
63#2965—21no—
64C8×#41—21no—
65#2920C2211yescharacteristic
66#2920C2211yescharacteristic
67#2920C2211yescharacteristic
68#2920C2212yes—
69C2×#432C2212yes—
70C2×#432C2212yes—
71C2×#431C2212yes—
72C2×#431C2211yescharacteristic
73#1561C2212yescomplemented
74#1560C2212yescomplemented
75#1559C2214yescomplemented
76#1559C2214yescomplemented
77#1558C2214yescomplemented
78#1557C2214yescomplemented
79#1556C2214yescomplemented
80#1554C2211yescharacteristic
81#1554C2212yes—
82#1554C2212yes—
83#1554C2212yes—
84#1554C2212yes—
85#1554C2211yescharacteristic
86#1554C2212yes—
87#1554C2214yescomplemented
88#1554C2214yescomplemented
89#1554C2212yescomplemented
90#1553C2211yescharacteristic
91#1553C2212yes—
92#1553C2211yescharacteristic
93#1553C2212yescomplemented
94#1552C2214yescomplemented
95#1552C2214yescomplemented
96#1551C2214yescomplemented
97#1551C2214yescomplemented
98#1550C2212yescomplemented
99#1550C2214yescomplemented
100#1550C2214yescomplemented
101#1549C2212yescomplemented
102#1548C2212yescomplemented
103#1548C2212yescomplemented
104#1547C2212yescomplemented
105#1546C2212yescomplemented
106#1544C2212yescomplemented
107#1543C2212yescomplemented
108#1542C2214yescomplemented
109#1542C2214yescomplemented
110C2×#333C2214yescomplemented
111#1540C2214yescomplemented
112C2×#332C2214yescomplemented
113C2×2−1+4C2×C412yes—
114C22×#41C2×C411yescharacteristic
115Q82—21no—
116#557—21no—
117#557—22no—
118#557—21no—
119#557—21no—
120#557—22no—
121#556—21no—
122#556—22no—
123#556—22no—
124#556—21no—
125#556—21no—
126#556—22no—
127#556—22no—
128#556—24no—
129#555—22no—
130#555—21no—
131#554—21no—
132#554—22no—
133#554—21no—
134#554—22no—
135#554—22no—
136#554—24no—
137#553—22no—
138#553—22no—
139#553—22no—
140#552—22no—
141#552—22no—
142#552—22no—
143#552—22no—
144#552—22no—
145#552—22no—
146#552—24no—
147#552—24no—
148#552—24no—
149#552—22no—
150#552—24no—
151#552—22no—
152#552—24no—
153#551—24no—
154#551—24no—
155#551—24no—
156D4×Q8—22no—
157D4×Q8—21no—
158D4×Q8—21no—
159D4×Q8—21no—
160D4×Q8—22no—
161#548—22no—
162#548—22no—
163#548—22no—
164#548—22no—
165#547—22no—
166#547—24no—
167#547—21no—
168#547—22no—
169#547—21no—
170#547—22no—
171#547—21no—
172#547—22no—
173#546—22no—
174#546—24no—
175#544C2×C414yes—
176#544C2×C412yes—
177#542—22no—
178#542—24no—
179#542C2×C414yes—
180#542C2×C414yes—
181#542C2×C414yes—
182#541—22no—
183#541—24no—
184#541C2×C414yes—
185#541C2×C414yes—
186#541C2×C414yes—
187#539—24no—
188#539—24no—
189#539—24no—
190#537C2×C412yes—
191#537C2×C414yes—
192#536C2×C414yes—
193#536C2×C412yes—
194#536C2×C412yes—
195#536C2×C414yes—
196#533—22no—
197#533—24no—
198#533—22no—
199#533—21no—
200#533—22no—
201#533—21no—
202#533—21no—
203#533—22no—
204#533—21no—
205#533—22no—
206#533C2×C414yes—
207#533C2×C412yes—
208#533C2×C414yes—
209#533C2×C412yes—
210#533C2312yes—
211#533C2312yes—
212#533C2312yes—
213#533C2312yes—
214#533C2311yescharacteristic
215#533C2311yescharacteristic
216#533C2312yes—
217#533C2311yescharacteristic
218#533C2312yes—
219#532C2311yescharacteristic
220#532C2312yes—
221#532C2312yes—
222#532C2311yescharacteristic
223#532C2311yescharacteristic
224C2×C4⋊Q8C2312yes—
225C2×C4⋊Q8C2311yescharacteristic
226C2×C4⋊Q8C2312yes—
227C2×C4⋊Q8C2311yescharacteristic
228#529—24no—
229#529—24no—
230#529—24no—
231#529—22no—
232#529—24no—
233#529—22no—
234#529—21no—
235#529—22no—
236#529—21no—
237#529—21no—
238#529—22no—
239#529—21no—
240#529—22no—
241#529C2×C414yes—
242#529C2×C412yes—
243#529C2×C414yes—
244#529C2×C412yes—
245C2×#125—22no—
246C2×#125—21no—
247#525—22no—
248#525—21no—
249#525—22no—
250#525—21no—
251#525C2×C414yes—
252#525C2×C412yes—
253C2×C22⋊Q8—22no—
254C2×C22⋊Q8—21no—
255C2×C22⋊Q8C2×C414yes—
256C2×C22⋊Q8C2×C412yes—
257#520—24no—
258#520—22no—
259#520C2×C412yes—
260#520C2×C414yes—
261#520C2×C412yes—
262#519—22no—
263#519C2×C412yes—
264#519C2×C414yes—
265C4×#41—24no—
266C4×#41—22no—
267C4×#41—22no—
268C4×#41—21no—
269C4×#41—22no—
270C4×#41—21no—
271C4×#41C2×C414yes—
272C4×#41C2×C412yes—
273C4×#41C2×C411yescharacteristic
274C4×#41C2×C412yes—
275C4×#41C2×C411yescharacteristic
276C4×#41D411yescharacteristic
277C4×#41D412yes—
278C4×#41D411yescharacteristic
279C4×#41D411yescharacteristic
280C4×#41D412yes—
281C4×#41D411yescharacteristic
282C4×#41C2311yescharacteristic
283C4×#41C2312yes—
284C4×#41C2311yescharacteristic
285C2×C4×Q8—22no—
286C2×C4×Q8—22no—
287C2×C4×Q8—21no—
288C2×C4×Q8C2×C414yes—
289C2×C4×Q8C2×C412yes—
290C2×C4×Q8D411yescharacteristic
291C2×C4×Q8D411yescharacteristic
292C2×C4×D4D411yescharacteristic
293C2×C4×D4D412yes—
294C2×C4×D4D411yescharacteristic
295C2×C4×D4D412yes—
296C2×#117—22no—
297C2×#117—21no—
298C2×#117C2×C411yescharacteristic
299C2×#117C2×C412yes—
300C22×C42C2312yes—
301C22×C42C2311yescharacteristic
302#446—22no—
303#446—24no—
304#446—22no—
305#446—22no—
306#446—24no—
307C8×Q8—22no—
308#436—24no—
309#436—22no—
310#435—24no—
311#435—24no—
312#435—24no—
313#435—24no—
314#435—24no—
315#435—24no—
316#435—24no—
317C8×D4—22no—
318C8×D4—24no—
319C8×D4—22no—
320C8×D4—22no—
321C8×D4—24no—
322#432—22no—
323#432—22no—
324#432—22no—
325#432—22no—
326#432—21no—
327#432—21no—
328#432—21no—
329#432—22no—
330#432C2314yes—
331#432C2314yes—
332#432C2311yescharacteristic
333#432C2312yes—
334#432C2311yescharacteristic
335#432C2312yes—
336#432C2314yes—
337#431—21no—
338#431—22no—
339#431—22no—
340#431—21no—
341#431—22no—
342#431—21no—
343#431—21no—
344#431—21no—
345#431C2314yes—
346#431C2312yes—
347#431C2312yes—
348#431C2312yes—
349#431C2311yescharacteristic
350#431C2312yes—
351#431C2311yescharacteristic
352#423C2312yes—
353#423C2312yes—
354#423C2312yes—
355#423C2314yes—
356C2×C4⋊C8C2314yes—
357C2×C4⋊C8C2314yes—
358C2×C4⋊C8C2314yes—
359C2×C4⋊C8C2312yes—
360#407—21no—
361#407—21no—
362#407—21no—
363#407—22no—
364C2×C22⋊C8—22no—
365C2×C22⋊C8—21no—
366C2×C22⋊C8—22no—
367C2×C22⋊C8—22no—
368C4×M16—21no—
369C4×M16—22no—
370C4×M16—21no—
371C4×M16—21no—
372C2×#97—22no—
373C2×#97—22no—
374C2×C4×C8—22no—
375C2×C4×C8—21no—
376#333C2312yes—
377#333C2314yes—
378#333C2314yes—
379#333C2314yes—
380#333C2314yes—
381#333C2314yes—
382#333C2312yes—
383#332C2312yes—
384#332C2314yes—
385#332C2314yes—
386#332C2314yes—
387#332C2314yes—
388#332C2312yes—
389#332C2314yes—
390#332C2314yes—
391#332C2312yes—
392#332C2312yes—
393#331C2312yes—
394#331C2314yes—
395#331C2312yes—
3962−1+4—48no—
397C2×#41—24no—
398C2×#41—22no—
399C2×#41—21no—
400C2×#41—22no—
401C2×#41—21no—
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—22no—
426C2×M16—22no—
427C2×M16—22no—
428C2×M16—24no—
429C22×C8—24no—
430C22×C8—22no—
431C22×C8—24no—
432C22×C8—24no—
433C4⋊Q8—22no—
434C4⋊Q8—24no—
435C4⋊Q8—24no—
436C4⋊Q8—22no—
437C4⋊Q8—21no—
438C4⋊Q8—21no—
439C4⋊Q8—21no—
440C4⋊Q8—22no—
441C4⋊Q8—22no—
442C4⋊Q8—22no—
443C4⋊Q8—21no—
444C4⋊Q8—22no—
445C4⋊Q8C22×C414yes—
446C4⋊Q8C22×C412yes—
447C4⋊Q8C22×C414yes—
448C4⋊Q8C22×C412yes—
449C4⋊Q8C2411yescharacteristic
450C4⋊Q8C2412yes—
451C4⋊Q8C2411yescharacteristic
452C4⋊Q8C2412yes—
453C4⋊Q8C2411yescharacteristic
454#127C2411yescharacteristic
455#126—24no—
456#126—24no—
457#126—24no—
458#126—24no—
459#126—24no—
460#126—24no—
461#126—24no—
462#126—24no—
463#126—24no—
464#126—22no—
465#126—24no—
466#126—24no—
467#126—22no—
468#125—24no—
469#125—24no—
470#125—24no—
471#125—24no—
472#125—22no—
473#125—24no—
474#125—24no—
475#125—24no—
476#125—22no—
477#125—24no—
478#125—24no—
479#125—22no—
480#125—21no—
481#125—22no—
482#125—22no—
483#125—22no—
484#125—22no—
485#125—21no—
486#125—22no—
487#125C22×C412yes—
488#125C22×C414yes—
489#124—22no—
490#124—24no—
491#124—24no—
492#124—24no—
493#124—24no—
494#124—21no—
495#124—21no—
496#124—22no—
497#124C22×C412yes—
498#124C22×C414yes—
499#123—24no—
500#123—24no—
501#123—24no—
502#123—22no—
503#123—24no—
504#123—22no—
505#123—24no—
506#123—24no—
507#123—22no—
508#123—24no—
509#123—24no—
510#123—24no—
511#123—24no—
512#123—24no—
513#123—24no—
514C22⋊Q8—22no—
515C22⋊Q8—24no—
516C22⋊Q8—22no—
517C22⋊Q8—24no—
518C22⋊Q8—24no—
519C22⋊Q8—22no—
520C22⋊Q8—22no—
521C22⋊Q8—24no—
522C22⋊Q8—22no—
523C22⋊Q8—24no—
524C22⋊Q8—21no—
525C22⋊Q8—22no—
526C22⋊Q8—22no—
527C22⋊Q8—22no—
528C22⋊Q8—22no—
529C22⋊Q8—22no—
530C22⋊Q8—21no—
531C22⋊Q8—22no—
532C22⋊Q8—21no—
533C22⋊Q8—21no—
534C22⋊Q8—22no—
535C22⋊Q8—24no—
536C22⋊Q8—22no—
537C22⋊Q8—24no—
538C22⋊Q8—22no—
539C22⋊Q8—24no—
540C22⋊Q8—24no—
541C22⋊Q8—24no—
542C22⋊Q8—24no—
543C22⋊Q8—24no—
544C22⋊Q8—24no—
545C22⋊Q8C22×C412yes—
546C22⋊Q8C22×C414yes—
547C22⋊Q8C22×C414yes—
548C22⋊Q8C22×C414yes—
549C22⋊Q8C22×C414yes—
550C22⋊Q8C22×C414yes—
551C22⋊Q8C22×C412yes—
552#121—24no—
553#121—24no—
554#121—24no—
555#121—22no—
556#121—24no—
557#121—21no—
558#121—22no—
559#121—21no—
560#121—22no—
561#121—21no—
562#121—21no—
563#121—22no—
564#121C22×C412yes—
565#121C22×C414yes—
566#121C22×C412yes—
567#120—24no—
568#120—22no—
569C4×Q8—22no—
570C4×Q8—24no—
571C4×Q8—22no—
572C4×Q8—24no—
573C4×Q8—22no—
574C4×Q8—24no—
575C4×Q8—22no—
576C4×Q8—24no—
577C4×Q8—22no—
578C4×Q8—24no—
579C4×Q8—22no—
580C4×Q8—24no—
581C4×Q8—22no—
582C4×Q8—21no—
583C4×Q8—22no—
584C4×Q8—22no—
585C4×Q8—22no—
586C4×Q8—22no—
587C4×Q8—21no—
588C4×Q8—22no—
589C4×Q8—22no—
590C4×Q8—21no—
591C4×Q8—21no—
592C4×Q8—22no—
593C4×Q8C22⋊C411yescharacteristic
594C4×Q8C22⋊C411yescharacteristic
595C4×Q8C22⋊C411yescharacteristic
596C4×Q8C22⋊C412yes—
597C4×Q8C22⋊C411yescharacteristic
598C4×Q8C22⋊C412yes—
599C4×Q8C22×C412yes—
600C4×Q8C22×C414yes—
601C4×Q8C22×C414yes—
602C4×Q8C22×C414yes—
603C4×Q8C22×C414yes—
604C4×Q8C22×C414yes—
605C4×Q8C22×C412yes—
606C4×Q8C2×D411yescharacteristic
607C4×Q8C2×D411yescharacteristic
608C4×Q8C2×D411yescharacteristic
609C4×Q8C2×D412yes—
610C4×Q8C2×D411yescharacteristic
611C4×Q8C2×D412yes—
612C4×D4—24no—
613C4×D4—22no—
614C4×D4—22no—
615C4×D4—24no—
616C4×D4—24no—
617C4×D4—22no—
618C4×D4—24no—
619C4×D4—22no—
620C4×D4—22no—
621C4×D4—24no—
622C4×D4—22no—
623C4×D4—24no—
624C4×D4—22no—
625C4×D4—24no—
626C4×D4—24no—
627C4×D4—24no—
628C4×D4—24no—
629C4×D4—21no—
630C4×D4—21no—
631C4×D4—22no—
632C4×D4—21no—
633C4×D4—22no—
634C4×D4—22no—
635C4×D4—21no—
636C4×D4C22⋊C412yes—
637C4×D4C22⋊C411yescharacteristic
638C4×D4C22⋊C412yes—
639C4×D4C22⋊C411yescharacteristic
640C4×D4C22⋊C411yescharacteristic
641C4×D4C22⋊C412yes—
642C4×D4C22⋊C412yes—
643C4×D4C22⋊C412yes—
644C4×D4C22⋊C412yes—
645C4×D4C22⋊C412yes—
646C4×D4C22⋊C412yes—
647C4×D4C22⋊C412yes—
648C4×D4C22⋊C411yescharacteristic
649C4×D4C22⋊C412yes—
650C4×D4C22×C412yes—
651C4×D4C22×C414yes—
652C4×D4C22×C412yes—
653C4×D4C2×D411yescharacteristic
654C4×D4C2×D412yes—
655C4×D4C2×D411yescharacteristic
656C4×D4C2×D412yes—
657C4×D4C2×D411yescharacteristic
658C4×D4C2×D412yes—
659C4×D4C2×D412yes—
660C4×D4C2×D412yes—
661C4×D4C2×D412yes—
662C4×D4C2×D412yes—
663C4×D4C2×D412yes—
664C4×D4C2×D412yes—
665C4×D4C2×D412yes—
666C4×D4C2×D411yescharacteristic
667#117—24no—
668#117—22no—
669#117—22no—
670#117—24no—
671#117—21no—
672#117—22no—
673#117—22no—
674#117—22no—
675#117—22no—
676#117—22no—
677#117—21no—
678#117—24no—
679#117—22no—
680#117—24no—
681#117—24no—
682#117—24no—
683#117—24no—
684#117—22no—
685#117—24no—
686#117—22no—
687#117—24no—
688#117—22no—
689#117C22⋊C411yescharacteristic
690#117C22⋊C412yes—
691#117C22⋊C412yes—
692#117C22⋊C412yes—
693#117C22⋊C412yes—
694#117C22⋊C411yescharacteristic
695#117C22⋊C412yes—
696#117C22×C412yes—
697#117C22×C414yes—
698#117C22×C412yes—
699#117C22×C411yescharacteristic
700#117C22×C411yescharacteristic
701#117C22×C412yes—
702#117C22×C412yes—
703#117C22×C412yes—
704#117C22×C412yes—
705C2×C4⋊C4—24no—
706C2×C4⋊C4—22no—
707C2×C4⋊C4—22no—
708C2×C4⋊C4—24no—
709C2×C4⋊C4—22no—
710C2×C4⋊C4—21no—
711C2×C4⋊C4—22no—
712C2×C4⋊C4—21no—
713C2×C4⋊C4—22no—
714C2×C4⋊C4—21no—
715C2×C4⋊C4—24no—
716C2×C4⋊C4—22no—
717C2×C4⋊C4C22⋊C411yescharacteristic
718C2×C4⋊C4C22⋊C412yes—
719C2×C4⋊C4C22⋊C411yescharacteristic
720C2×C4⋊C4C22⋊C412yes—
721C2×C4⋊C4C22×C414yes—
722C2×C4⋊C4C22×C412yes—
723C2×C22⋊C4—24no—
724C2×C22⋊C4—22no—
725C2×C22⋊C4C22⋊C412yes—
726C2×C22⋊C4C22⋊C412yes—
727C2×C22⋊C4C22⋊C412yes—
728C2×C42—22no—
729C2×C42—24no—
730C2×C42—24no—
731C2×C42—22no—
732C2×C42C22×C412yes—
733C2×C42C22×C411yescharacteristic
734C2×C42C22×C412yes—
735C2×C42C22×C411yescharacteristic
736C2×C42C22×C412yes—
737C2×C42C22×C411yescharacteristic
738C2×C42C2×D412yes—
739C2×C42C2×D411yescharacteristic
740C2×C42C2×D411yescharacteristic
741C2×C42C2×D412yes—
742C2×C42C2×D412yes—
743C2×C42C2×D411yescharacteristic
744C2×C42C2×D412yes—
745C2×C42C2×D411yescharacteristic
746C2×C42C2×D412yes—
747C2×C42C2×D411yescharacteristic
748C2×C42C2×D411yescharacteristic
749C2×C42C2×D412yes—
750C2×C42C2412yes—
751C2×C42C2411yescharacteristic
752C2×C42C2412yes—
753C2×C42C2411yescharacteristic
754C2×C42C2411yescharacteristic
755C4⋊C8—22no—
756C4⋊C8—24no—
757C4⋊C8—24no—
758C4⋊C8—24no—
759C4⋊C8—22no—
760C4⋊C8—22no—
761C4⋊C8—24no—
762C4⋊C8—22no—
763C4⋊C8C2412yes—
764C4⋊C8C2412yes—
765C4⋊C8C2414yes—
766C4⋊C8C2412yes—
767C4⋊C8C2414yes—
768C4⋊C8C2412yes—
769C22⋊C8—21no—
770C22⋊C8—21no—
771C22⋊C8—22no—
772C22⋊C8—21no—
773C22⋊C8—22no—
774C22⋊C8—21no—
775C22⋊C8—22no—
776C22⋊C8—24no—
777C22⋊C8—24no—
778C22⋊C8—24no—
779C22⋊C8—24no—
780C22⋊C8—22no—
781C22⋊C8—22no—
782C22⋊C8—22no—
783#97—21no—
784#97—22no—
785#97—21no—
786#97—24no—
787#97—24no—
788#97—22no—
789#97—24no—
790C4×C8—21no—
791C4×C8—22no—
792C4×C8—21no—
793C4×C8—24no—
794C4×C8—22no—
795C4×C8—22no—
796C4×C8—22no—
797C24C2×C22⋊C412yes—
798C24C2×C22⋊C411yescharacteristic
799#41—24no—
800#41—24no—
801#41—44no—
802#41—44no—
803#41—42no—
804#41—42no—
805#41—44no—
806#41—48no—
807#41—44no—
808#41—416no—
809#41—48no—
810#41—84no—
811#41—82no—
812C2×Q8—24no—
813C2×Q8—22no—
814C2×Q8—22no—
815C2×Q8—24no—
816C2×Q8—21no—
817C2×Q8—22no—
818C2×Q8—21no—
819C2×Q8—42no—
820C2×Q8—44no—
821C2×Q8—48no—
822C2×Q8—48no—
823C2×Q8—84no—
824C2×Q8—82no—
825C2×Q8C2×C22⋊C411yescharacteristic
826C2×Q8C2×C22⋊C411yescharacteristic
827C2×Q8C2×C22⋊C412yes—
828C2×Q8C23×C414yes—
829C2×Q8C23×C412yes—
830C2×D4—24no—
831C2×D4—22no—
832C2×D4—22no—
833C2×D4—24no—
834C2×D4—22no—
835C2×D4—24no—
836C2×D4—21no—
837C2×D4—21no—
838C2×D4—44no—
839C2×D4C2×C22⋊C412yes—
840C2×D4C2×C22⋊C412yes—
841C2×D4C2×C22⋊C412yes—
842C2×D4C2×C22⋊C411yescharacteristic
843C2×D4C2×C22⋊C412yes—
844C2×D4C2×C22⋊C412yes—
845C2×D4C2×C22⋊C411yescharacteristic
846C2×D4C23×C412yes—
847C22×C4—22no—
848C22×C4—24no—
849C22×C4—22no—
850C22×C4—24no—
851C22×C4—22no—
852C22×C4—24no—
853C22×C4—22no—
854C22×C4—24no—
855C22×C4—22no—
856C22×C4—42no—
857C22×C4—44no—
858C22×C4—42no—
859C22×C4—44no—
860C22×C4—42no—
861C22×C4—44no—
862C22×C4C2×C22⋊C412yes—
863C22×C4C2×C22⋊C411yescharacteristic
864C22×C4C2×C22⋊C411yescharacteristic
865C22×C4C2×C22⋊C411yescharacteristic
866C22×C4C2×C22⋊C412yes—
867C22×C4C2×C22⋊C411yescharacteristic
868C22×C4C2×C22⋊C412yes—
869C22×C4C2×C22⋊C412yes—
870C22×C4C2×C22⋊C411yescharacteristic
871C22×C4C2×C22⋊C411yescharacteristic
872C22×C4C2×C22⋊C412yes—
873C22×C4C2×C22⋊C412yes—
874C22×C4C2×C22⋊C411yescharacteristic
875C22×C4C2×C22⋊C411yescharacteristic
876C22×C4C2×C22⋊C412yes—
877C22×C4C2×C22⋊C411yescharacteristic
878C22×C4C2×C22⋊C412yes—
879C22×C4C2×C22⋊C412yes—
880C22×C4C23×C412yes—
881C22×C4C23×C411yescharacteristic
882C22×C4C23×C411yescharacteristic
883C22×C4C23×C411yescharacteristic
884C22×C4C23×C412yes—
885C22×C4C22×D411yescharacteristic
886C22×C4C22×D411yescharacteristic
887C22×C4C22×D412yes—
888C22×C4C22×D411yescharacteristic
889C22×C4C22×D412yes—
890C22×C4C22×D411yescharacteristic
891C22×C4C22×D411yescharacteristic
892C22×C4C22×D412yes—
893C22×C4C22×D412yes—
894C22×C4C22×D411yescharacteristic
895M16—82no—
896M16—82no—
897M16—82no—
898M16—84no—
899C2×C8—22no—
900C2×C8—24no—
901C2×C8—22no—
902C2×C8—22no—
903C2×C8—22no—
904C2×C8—24no—
905C2×C8—84no—
906C2×C8—84no—
907C2×C8—84no—
908C2×C8—82no—
909C4⋊C4—22no—
910C4⋊C4—24no—
911C4⋊C4—24no—
912C4⋊C4—24no—
913C4⋊C4—24no—
914C4⋊C4—24no—
915C4⋊C4—22no—
916C4⋊C4—24no—
917C4⋊C4—22no—
918C4⋊C4—22no—
919C4⋊C4—24no—
920C4⋊C4—22no—
921C4⋊C4—24no—
922C4⋊C4—24no—
923C4⋊C4—24no—
924C4⋊C4—24no—
925C4⋊C4—22no—
926C4⋊C4—24no—
927C4⋊C4—22no—
928C4⋊C4—24no—
929C4⋊C4—22no—
930C4⋊C4—24no—
931C4⋊C4—22no—
932C4⋊C4—24no—
933C4⋊C4—22no—
934C4⋊C4—24no—
935C4⋊C4—21no—
936C4⋊C4—22no—
937C4⋊C4—21no—
938C4⋊C4—22no—
939C4⋊C4—21no—
940C4⋊C4—22no—
941C4⋊C4—21no—
942C4⋊C4C2×C22⋊C412yes—
943C4⋊C4C2×C22⋊C411yescharacteristic
944C4⋊C4C2×C22⋊C412yes—
945C4⋊C4C2×C22⋊C411yescharacteristic
946C4⋊C4C2×C22⋊C412yes—
947C4⋊C4C2×C22⋊C412yes—
948C4⋊C4C2×C22⋊C412yes—
949C4⋊C4C2×C22⋊C412yes—
950C4⋊C4C2×C22⋊C411yescharacteristic
951C4⋊C4C2×C22⋊C412yes—
952C4⋊C4C2×C22⋊C411yescharacteristic
953C4⋊C4C2×C22⋊C412yes—
954C4⋊C4C2×C22⋊C412yes—
955C4⋊C4C2×C22⋊C412yes—
956C4⋊C4C23×C412yes—
957C4⋊C4C23×C414yes—
958C4⋊C4C23×C412yes—
959C22⋊C4—22no—
960C22⋊C4—24no—
961C22⋊C4—24no—
962C22⋊C4—24no—
963C22⋊C4—24no—
964C22⋊C4—22no—
965C22⋊C4—24no—
966C22⋊C4—22no—
967C22⋊C4—24no—
968C22⋊C4—22no—
969C22⋊C4—22no—
970C22⋊C4—22no—
971C22⋊C4—24no—
972C22⋊C4—22no—
973C22⋊C4—24no—
974C22⋊C4—22no—
975C22⋊C4—24no—
976C22⋊C4—22no—
977C22⋊C4—24no—
978C22⋊C4C2×C22⋊C412yes—
979C22⋊C4C2×C22⋊C412yes—
980C22⋊C4C2×C22⋊C412yes—
981C22⋊C4C2×C22⋊C412yes—
982C22⋊C4C2×C22⋊C412yes—
983C22⋊C4C2×C22⋊C412yes—
984C22⋊C4C2×C22⋊C412yes—
985C22⋊C4C2×C22⋊C412yes—
986C22⋊C4C2×C22⋊C412yes—
987C22⋊C4C2×C22⋊C412yes—
988C22⋊C4C2×C22⋊C412yes—
989C22⋊C4C2×C22⋊C412yes—
990C42—24no—
991C42—22no—
992C42—24no—
993C42—22no—
994C42—24no—
995C42—24no—
996C42—24no—
997C42—24no—
998C42—22no—
999C42C2×C22⋊C412yes—
1000C42C2×C22⋊C411yescharacteristic
1001C42C2×C22⋊C412yes—
1002C42C2×C22⋊C411yescharacteristic
1003C42C2×C22⋊C412yes—
1004C42C2×C22⋊C411yescharacteristic
1005C42C2×C22⋊C412yes—
1006C42C2×C22⋊C411yescharacteristic
1007C42C2×C22⋊C412yes—
1008C42C2×C22⋊C411yescharacteristic
1009C42C2×C22⋊C411yescharacteristic
1010C42C2×C22⋊C412yes—
1011C42C23×C411yescharacteristic
1012C42C23×C411yescharacteristic
1013C42C23×C412yes—
1014C42C23×C412yes—
1015C42C23×C411yescharacteristic
1016C42C22×D411yescharacteristic
1017C42C22×D412yes—
1018C42C22×D411yescharacteristic
1019C42C22×D411yescharacteristic
1020C42C22×D411yescharacteristic
1021C42C22×D411yescharacteristic
1022C42C22×D411yescharacteristic
1023C42C22×D412yes—
1024C42C22×D412yes—
1025C42C22×D412yes—
1026C42C2511yescharacteristic
1027C23—24no—
1028C23—22no—
1029C23—41no—
1030C23—42no—
1031C23—42no—
1032C23—41no—
1033C23—41no—
1034C23C22×C22⋊C411yescharacteristic
1035C23C22×C22⋊C412yes—
1036C23C22×C22⋊C411yescharacteristic
1037C23C22×C22⋊C411yescharacteristic
1038C23C22×C22⋊C412yes—
1039Q8—22no—
1040Q8—22no—
1041Q8—42no—
1042Q8—44no—
1043Q8—42no—
1044Q8—48no—
1045Q8—42no—
1046Q8—44no—
1047Q8—42no—
1048Q8—44no—
1049Q8—84no—
1050Q8—82no—
1051D4—24no—
1052D4—24no—
1053D4—24no—
1054D4—22no—
1055D4—42no—
1056D4—42no—
1057D4—42no—
1058D4—44no—
1059D4—44no—
1060D4—48no—
1061D4—42no—
1062D4—42no—
1063D4—84no—
1064D4—82no—
1065D4#41314yes—
1066C2×C4—24no—
1067C2×C4—24no—
1068C2×C4—24no—
1069C2×C4—24no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—24no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—24no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—22no—
1080C2×C4—22no—
1081C2×C4—22no—
1082C2×C4—24no—
1083C2×C4—22no—
1084C2×C4—24no—
1085C2×C4—22no—
1086C2×C4—41no—
1087C2×C4—42no—
1088C2×C4—41no—
1089C2×C4—42no—
1090C2×C4—41no—
1091C2×C4—42no—
1092C2×C4—41no—
1093C2×C4—42no—
1094C2×C4—41no—
1095C2×C4—42no—
1096C2×C4—41no—
1097C2×C4—41no—
1098C2×C4—42no—
1099C2×C4—42no—
1100C2×C4—42no—
1101C2×C4—41no—
1102C2×C4—41no—
1103C2×C4—42no—
1104C2×C4—48no—
1105C2×C4—44no—
1106C2×C4—44no—
1107C2×C4—48no—
1108C2×C4—44no—
1109C2×C4—84no—
1110C2×C4—82no—
1111C2×C4—84no—
1112C2×C4—82no—
1113C2×C4C22×C22⋊C411yescharacteristic
1114C2×C4C22×C22⋊C411yescharacteristic
1115C2×C4C22×C22⋊C412yes—
1116C2×C4C22×C22⋊C412yes—
1117C2×C4C22×C22⋊C411yescharacteristic
1118C2×C4C22×C22⋊C412yes—
1119C2×C4C22×C22⋊C411yescharacteristic
1120C2×C4C22×C22⋊C411yescharacteristic
1121C2×C4C22×C22⋊C411yescharacteristic
1122C2×C4C22×C22⋊C412yes—
1123C2×C4C22×C22⋊C411yescharacteristic
1124C2×C4C22×C22⋊C412yes—
1125C2×C4C22×C22⋊C411yescharacteristic
1126C2×C4C22×C22⋊C412yes—
1127C2×C4C22×C22⋊C411yescharacteristic
1128C2×C4C24×C411yescharacteristic
1129C2×C4C23×D411yescharacteristic
1130C2×C4C23×D411yescharacteristic
1131C8—42no—
1132C8—44no—
1133C8—42no—
1134C8—42no—
1135C8—44no—
1136C8—42no—
1137C22—22no—
1138C22—22no—
1139C22—21no—
1140C22—21no—
1141C22—21no—
1142C22—22no—
1143C22—21no—
1144C22—21no—
1145C22—22no—
1146C22—21no—
1147C22—21no—
1148C22—21no—
1149C22—22no—
1150C22—21no—
1151C22—42no—
1152C22—42no—
1153C22—42no—
1154C22—84no—
1155C22—82no—
1156C22C2×#41314yes—
1157C22C23×C22⋊C411yescharacteristic
1158C4—21no—
1159C4—21no—
1160C4—22no—
1161C4—21no—
1162C4—22no—
1163C4—21no—
1164C4—22no—
1165C4—21no—
1166C4—22no—
1167C4—21no—
1168C4—21no—
1169C4—21no—
1170C4—22no—
1171C4—22no—
1172C4—21no—
1173C4—44no—
1174C4—42no—
1175C4—42no—
1176C4—44no—
1177C4—42no—
1178C4C2×#41312yes—
1179C4#358412yes—
1180C4#358612yes—
1181C2—24no—
1182C2—41no—
1183C2—41no—
1184C2—42no—
1185C2—41no—
1186C2—82no—
1187C2C22×#41311yescharacteristic
1188C2#6008611yescharacteristic
1189C2#6008811yescharacteristic
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. #60278C2semidirect
4. #17780C2semidirect
5. #17779C2semidirect
6. #17778C2semidirect
7. #17775C2semidirect
8. #17774C2semidirect
9. #17772C2semidirect
10. #17757C2semidirect
11. #17756C2semidirect
12. #17748C2semidirect
13. #17747C2semidirect
14. #17718C2semidirect
15. #17716C2semidirect
16. #17713C2semidirect
17. C2×#1554C2semidirect
73. #1561C22semidirect
74. #1560C22semidirect
75. #1559C22semidirect
76. #1559C22semidirect
77. #1558C22semidirect
78. #1557C22semidirect
79. #1556C22semidirect
87. #1554C22semidirect
88. #1554C22semidirect
89. #1554C22semidirect
93. #1553C22semidirect
94. #1552C22semidirect
95. #1552C22semidirect
96. #1551C22semidirect
97. #1551C22semidirect
98. #1550C22semidirect
99. #1550C22semidirect
100. #1550C22semidirect
101. #1549C22semidirect
102. #1548C22semidirect
103. #1548C22semidirect
104. #1547C22semidirect
105. #1546C22semidirect
106. #1544C22semidirect
107. #1543C22semidirect
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
#602782
#177802
#177792
#177782
#177752
#177742
#177722
#177572
#177562
#177482
#177472
#177182
#177162
#177132
C2×#15542