Finite Group Databasebeta

← #6344096

Subgroups — #6344096

Order 512.

2795 conjugacy classes of subgroups.

The subgroup lattice has 1192 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62805C211yesmaximal, characteristic
2#60277C211yesmaximal, characteristic, complemented
3#60128C211yesmaximal, characteristic, complemented
4#17768C214yesmaximal, complemented
5#17767C214yesmaximal, complemented
6#17764C212yesmaximal, complemented
7#17763C212yesmaximal, complemented
8#17760C212yesmaximal, complemented
9#17759C212yesmaximal, complemented
10#17757C212yesmaximal, complemented
11#17756C212yesmaximal, complemented
12#17748C212yesmaximal, complemented
13#17747C212yesmaximal, complemented
14#17718C211yesmaximal, characteristic, complemented
15#17716C211yesmaximal, characteristic, complemented
16#17713C211yesmaximal, characteristic, complemented
17C2×#1554C211yesmaximal, characteristic, complemented
18#3523C412yes—
19#3520C414yes—
20#3520C412yes—
21#3518—21no—
22#3515—22no—
23#3515—21no—
24#3511C2211yescharacteristic
25#3511C2212yes—
26#3509C2211yescharacteristic
27#3509C2212yes—
28#3503C2211yescharacteristic
29#3499C2211yescharacteristic
30#3495—21no—
31#3495—22no—
32#3489—21no—
33#3482C412yes—
34#3482C414yes—
35#3482C412yes—
36Q8×#41—21no—
37#3475—22no—
38#3475—21no—
39#3461—21no—
40#3461—22no—
41#3444C2211yescharacteristic
42#3444C2212yes—
43C2×#533C2211yescharacteristic
44C2×#533C2212yes—
45C4×2−1+4—21no—
46C2×C4×#41C2211yescharacteristic
47#2989C2212yes—
48#2989C2212yes—
49#2989C2214yes—
50#2983—21no—
51#2975—21no—
52#2973—22no—
53#2965—22no—
54#2965—21no—
55#2965—21no—
56#2925C2212yes—
57#2925C2214yes—
58#2924—21no—
59#2924—22no—
60#2923—21no—
61#2923—22no—
62#2920C2211yescharacteristic
63#2920C2212yes—
64#2920C2212yes—
65#2920C2212yes—
66C2×#432C2211yescharacteristic
67C2×#432C2212yes—
68C2×#431C2211yescharacteristic
69C2×#431C2211yescharacteristic
70#2906C2212yes—
71#2880—21no—
72#2875—21no—
73#1561C2214yescomplemented
74#1560C2214yescomplemented
75#1559C2214yescomplemented
76#1559C2214yescomplemented
77#1559C2214yescomplemented
78#1558C2214yescomplemented
79#1557C2214yescomplemented
80#1556C2214yescomplemented
81#1554C2212yes—
82#1554C2212yes—
83#1554C2211yescharacteristic
84#1554C2211yescharacteristic
85#1554C2212yes—
86#1554C2212yes—
87#1554C2212yes—
88#1554C2214yescomplemented
89#1554C2214yescomplemented
90#1553C2211yescharacteristic
91#1553C2211yescharacteristic
92#1553C2212yes—
93#1553C2214yescomplemented
94#1552C2212yescomplemented
95#1552C2214yescomplemented
96#1551C2212yescomplemented
97#1551C2214yescomplemented
98#1550C2212yescomplemented
99#1550C2214yescomplemented
100#1550C2214yescomplemented
101#1549C2214yescomplemented
102#1548C2212yescomplemented
103#1548C2214yescomplemented
104#1547C2212yescomplemented
105#1546C2212yescomplemented
106#1544C2212yescomplemented
107#1543C2212yescomplemented
108#1542C2212yescomplemented
109#1542C2214yescomplemented
110C2×#333C2212yescomplemented
111#1540C2212yescomplemented
112C2×#332C2212yescomplemented
113C2×2−1+4—21no—
114C22×#41D411yescharacteristic
115C2×#131—22no—
116Q82—21no—
117#557—21no—
118#557—22no—
119#557C2×C412yes—
120#557C2×C412yes—
121#557C2×C414yes—
122#556—22no—
123#556—21no—
124#556—22no—
125#556—24no—
126#556C2×C412yes—
127#556C2×C414yes—
128#556C2×C412yes—
129#556C2×C414yes—
130#555—22no—
131#555—21no—
132#554—21no—
133#554—22no—
134#554—22no—
135#554—21no—
136#554—22no—
137#554—24no—
138#553—22no—
139#553—22no—
140#553—22no—
141#552—22no—
142#552—22no—
143#552—22no—
144#552—24no—
145#552—24no—
146#552—24no—
147#552—22no—
148#552—24no—
149#552—22no—
150#552—24no—
151#552C2×C414yes—
152#552C2×C414yes—
153#552C2×C414yes—
154#551—24no—
155#551—24no—
156#551—24no—
157D4×Q8—22no—
158D4×Q8—21no—
159D4×Q8C2×C412yes—
160D4×Q8C2×C414yes—
161D4×Q8C2×C412yes—
162#548—22no—
163#548C2×C414yes—
164#548C2×C414yes—
165#548C2×C414yes—
166#547—24no—
167#547—22no—
168#547—22no—
169#547—21no—
170#547C2×C412yes—
171#547C2×C414yes—
172#547C2×C414yes—
173#547C2×C412yes—
174#546—24no—
175#546—22no—
176#544—21no—
177#544—22no—
178#542—22no—
179#542—24no—
180#542—22no—
181#542—22no—
182#542—22no—
183#541—22no—
184#541—24no—
185#541—22no—
186#541—22no—
187#541—22no—
188#539—24no—
189#539—24no—
190#539—24no—
191#537—21no—
192#537—22no—
193#536—21no—
194#536—22no—
195#536—21no—
196#536—22no—
197#533—22no—
198#533—24no—
199#533—22no—
200#533—21no—
201#533—21no—
202#533—22no—
203#533—21no—
204#533—22no—
205#533—21no—
206#533—22no—
207#533C2×C412yes—
208#533C2×C414yes—
209#533C2×C412yes—
210#533C2×C414yes—
211#533C2311yescharacteristic
212#533C2312yes—
213#533C2312yes—
214#533C2312yes—
215#533C2312yes—
216#533C2311yescharacteristic
217#533C2312yes—
218#533C2311yescharacteristic
219#533C2312yes—
220#532C2311yescharacteristic
221#532C2312yes—
222#532C2311yescharacteristic
223#532C2311yescharacteristic
224#532C2312yes—
225C2×C4⋊Q8C2311yescharacteristic
226C2×C4⋊Q8C2312yes—
227C2×C4⋊Q8C2311yescharacteristic
228C2×C4⋊Q8C2312yes—
229#529—24no—
230#529—24no—
231#529—24no—
232#529—22no—
233#529—24no—
234#529—22no—
235#529—21no—
236#529—21no—
237#529—22no—
238#529—21no—
239#529—22no—
240#529—21no—
241#529—22no—
242#529C2×C412yes—
243#529C2×C414yes—
244#529C2×C412yes—
245#529C2×C414yes—
246C2×#125—21no—
247C2×#125—22no—
248#525—21no—
249#525—22no—
250#525—21no—
251#525—22no—
252#525C2×C412yes—
253#525C2×C414yes—
254C2×C22⋊Q8—21no—
255C2×C22⋊Q8—22no—
256C2×C22⋊Q8C2×C412yes—
257C2×C22⋊Q8C2×C414yes—
258#520—21no—
259#520—22no—
260#520—24no—
261#520—21no—
262#520—22no—
263#519—22no—
264#519—21no—
265#519—22no—
266C4×#41—24no—
267C4×#41—22no—
268C4×#41—21no—
269C4×#41—22no—
270C4×#41—21no—
271C4×#41—22no—
272C4×#41C2×C412yes—
273C4×#41C2×C414yes—
274C4×#41C2×C412yes—
275C4×#41C2×C411yescharacteristic
276C4×#41C2×C411yescharacteristic
277C4×#41D412yes—
278C4×#41D411yescharacteristic
279C4×#41D411yescharacteristic
280C4×#41D411yescharacteristic
281C4×#41D411yescharacteristic
282C4×#41D412yes—
283C4×#41C2311yescharacteristic
284C4×#41C2311yescharacteristic
285C4×#41C2312yes—
286C2×C4×Q8—22no—
287C2×C4×Q8—21no—
288C2×C4×Q8—22no—
289C2×C4×Q8C2×C412yes—
290C2×C4×Q8C2×C414yes—
291C2×C4×Q8C2×C411yescharacteristic
292C2×C4×Q8D411yescharacteristic
293C2×C4×D4C2×C411yescharacteristic
294C2×C4×D4C2×C412yes—
295C2×C4×D4D412yes—
296C2×C4×D4D411yescharacteristic
297C2×#117—21no—
298C2×#117—22no—
299C2×#117D411yescharacteristic
300C2×#117D412yes—
301C22×C42C2311yescharacteristic
302C22×C42C2312yes—
303#446—22no—
304#446—22no—
305#446—24no—
306#436—22no—
307#436—24no—
308#436—22no—
309#435—24no—
310#435—24no—
311#435—24no—
312#435—24no—
313#433—24no—
314#433—24no—
315#433—24no—
316#432—22no—
317#432—21no—
318#432—21no—
319#432—22no—
320#432—22no—
321#432—21no—
322#432—22no—
323#432—22no—
324#432C2312yes—
325#432C2314yes—
326#432C2311yescharacteristic
327#432C2311yescharacteristic
328#432C2312yes—
329#432C2314yes—
330#432C2314yes—
331#431—21no—
332#431—21no—
333#431—21no—
334#431—21no—
335#431—21no—
336#431—22no—
337#431—22no—
338#431—22no—
339#431C2312yes—
340#431C2312yes—
341#431C2312yes—
342#431C2314yes—
343#431C2311yescharacteristic
344#431C2311yescharacteristic
345#431C2312yes—
346#424—22no—
347#424—24no—
348#423C2312yes—
349#423C2314yes—
350#423C2314yes—
351#423C2314yes—
352C2×C4⋊C8C2312yes—
353C2×C4⋊C8C2312yes—
354C2×C4⋊C8C2312yes—
355C2×C4⋊C8C2314yes—
356#408—22no—
357#408—24no—
358#407—21no—
359#407—22no—
360#407—22no—
361#407—22no—
362C2×C22⋊C8—21no—
363C2×C22⋊C8—22no—
364C2×C22⋊C8—21no—
365C2×C22⋊C8—21no—
366#405—22no—
367#405—24no—
368C4×M16—21no—
369C4×M16—22no—
370C4×M16—22no—
371C4×M16—22no—
372C2×#97—21no—
373C2×#97—22no—
374C2×C4×C8—21no—
375C2×C4×C8—21no—
376#333C2314yes—
377#333C2314yes—
378#333C2312yes—
379#333C2314yes—
380#333C2314yes—
381#333C2312yes—
382#333C2314yes—
383#332C2314yes—
384#332C2314yes—
385#332C2312yes—
386#332C2312yes—
387#332C2314yes—
388#332C2314yes—
389#332C2312yes—
390#332C2312yes—
391#332C2314yes—
392#332C2314yes—
393#331C2312yes—
394#331C2312yes—
395#331C2314yes—
3962−1+4—48no—
397C2×#41—22no—
398C2×#41—24no—
399C2×#41—21no—
400C2×#41—22no—
401C2×#41—21no—
402C2×#41—44no—
403C2×#41C22⋊C412yes—
404C2×#41C22⋊C411yescharacteristic
405C2×#41C22⋊C411yescharacteristic
406C2×#41C22×C412yes—
407C2×#41C22×C414yes—
408C2×#41C2×D411yescharacteristic
409C2×#41C2×D411yescharacteristic
410C2×#41C2×D412yes—
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×D411yescharacteristic
422C23×C4C2×D411yescharacteristic
423C23×C4C2×D412yes—
424C23×C4C2×D412yes—
425#131—48no—
426C2×M16—24no—
427C2×M16—22no—
428C2×M16—24no—
429C2×M16—24no—
430C22×C8—24no—
431C22×C8—22no—
432C22×C8—22no—
433C22×C8—22no—
434C4⋊Q8—22no—
435C4⋊Q8—24no—
436C4⋊Q8—24no—
437C4⋊Q8—22no—
438C4⋊Q8—22no—
439C4⋊Q8—21no—
440C4⋊Q8—22no—
441C4⋊Q8—21no—
442C4⋊Q8—21no—
443C4⋊Q8—22no—
444C4⋊Q8—21no—
445C4⋊Q8—22no—
446C4⋊Q8C22×C412yes—
447C4⋊Q8C22×C414yes—
448C4⋊Q8C22×C412yes—
449C4⋊Q8C22×C414yes—
450C4⋊Q8C2412yes—
451C4⋊Q8C2411yescharacteristic
452C4⋊Q8C2412yes—
453C4⋊Q8C2411yescharacteristic
454C4⋊Q8C2411yescharacteristic
455#127C2411yescharacteristic
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—24no—
465#126—22no—
466#126—24no—
467#126—22no—
468#126—24no—
469#125—24no—
470#125—24no—
471#125—24no—
472#125—24no—
473#125—22no—
474#125—24no—
475#125—24no—
476#125—24no—
477#125—22no—
478#125—24no—
479#125—22no—
480#125—24no—
481#125—22no—
482#125—21no—
483#125—22no—
484#125—22no—
485#125—22no—
486#125—22no—
487#125—21no—
488#125C22×C412yes—
489#125C22×C414yes—
490#124—22no—
491#124—24no—
492#124—24no—
493#124—24no—
494#124—24no—
495#124—21no—
496#124—22no—
497#124—21no—
498#124C22×C412yes—
499#124C22×C414yes—
500#123—24no—
501#123—24no—
502#123—24no—
503#123—22no—
504#123—24no—
505#123—22no—
506#123—24no—
507#123—22no—
508#123—24no—
509#123—24no—
510#123—24no—
511#123—24no—
512#123—24no—
513#123—24no—
514#123—24no—
515C22⋊Q8—22no—
516C22⋊Q8—24no—
517C22⋊Q8—22no—
518C22⋊Q8—24no—
519C22⋊Q8—22no—
520C22⋊Q8—24no—
521C22⋊Q8—22no—
522C22⋊Q8—24no—
523C22⋊Q8—22no—
524C22⋊Q8—24no—
525C22⋊Q8—22no—
526C22⋊Q8—21no—
527C22⋊Q8—22no—
528C22⋊Q8—22no—
529C22⋊Q8—22no—
530C22⋊Q8—21no—
531C22⋊Q8—22no—
532C22⋊Q8—21no—
533C22⋊Q8—22no—
534C22⋊Q8—21no—
535C22⋊Q8—22no—
536C22⋊Q8—24no—
537C22⋊Q8—22no—
538C22⋊Q8—24no—
539C22⋊Q8—22no—
540C22⋊Q8—24no—
541C22⋊Q8—24no—
542C22⋊Q8—24no—
543C22⋊Q8—24no—
544C22⋊Q8—24no—
545C22⋊Q8—24no—
546C22⋊Q8C22×C414yes—
547C22⋊Q8C22×C412yes—
548C22⋊Q8C22×C414yes—
549C22⋊Q8C22×C414yes—
550C22⋊Q8C22×C414yes—
551C22⋊Q8C22×C412yes—
552C22⋊Q8C22×C414yes—
553#121—24no—
554#121—24no—
555#121—24no—
556#121—22no—
557#121—24no—
558#121—21no—
559#121—21no—
560#121—22no—
561#121—21no—
562#121—22no—
563#121—21no—
564#121—22no—
565#121C22×C412yes—
566#121C22×C412yes—
567#121C22×C414yes—
568#120—22no—
569#120—24no—
570C4×Q8—22no—
571C4×Q8—24no—
572C4×Q8—22no—
573C4×Q8—24no—
574C4×Q8—22no—
575C4×Q8—24no—
576C4×Q8—22no—
577C4×Q8—24no—
578C4×Q8—22no—
579C4×Q8—22no—
580C4×Q8—24no—
581C4×Q8—22no—
582C4×Q8—24no—
583C4×Q8—22no—
584C4×Q8—21no—
585C4×Q8—22no—
586C4×Q8—22no—
587C4×Q8—22no—
588C4×Q8—21no—
589C4×Q8—22no—
590C4×Q8—21no—
591C4×Q8—22no—
592C4×Q8—21no—
593C4×Q8—22no—
594C4×Q8C22⋊C411yescharacteristic
595C4×Q8C22⋊C411yescharacteristic
596C4×Q8C22⋊C411yescharacteristic
597C4×Q8C22⋊C412yes—
598C4×Q8C22⋊C411yescharacteristic
599C4×Q8C22⋊C412yes—
600C4×Q8C22×C414yes—
601C4×Q8C22×C412yes—
602C4×Q8C22×C414yes—
603C4×Q8C22×C414yes—
604C4×Q8C22×C414yes—
605C4×Q8C22×C412yes—
606C4×Q8C22×C414yes—
607C4×Q8C22×C411yescharacteristic
608C4×Q8C22×C411yescharacteristic
609C4×Q8C22×C412yes—
610C4×Q8C2×D411yescharacteristic
611C4×Q8C2×D412yes—
612C4×Q8C2×D411yescharacteristic
613C4×D4—24no—
614C4×D4—22no—
615C4×D4—24no—
616C4×D4—22no—
617C4×D4—24no—
618C4×D4—22no—
619C4×D4—22no—
620C4×D4—24no—
621C4×D4—22no—
622C4×D4—24no—
623C4×D4—24no—
624C4×D4—22no—
625C4×D4—22no—
626C4×D4—24no—
627C4×D4—24no—
628C4×D4—24no—
629C4×D4—24no—
630C4×D4—21no—
631C4×D4—21no—
632C4×D4—22no—
633C4×D4—21no—
634C4×D4—22no—
635C4×D4—21no—
636C4×D4—22no—
637C4×D4C22⋊C412yes—
638C4×D4C22⋊C411yescharacteristic
639C4×D4C22⋊C412yes—
640C4×D4C22⋊C412yes—
641C4×D4C22⋊C412yes—
642C4×D4C22⋊C411yescharacteristic
643C4×D4C22⋊C412yes—
644C4×D4C22⋊C412yes—
645C4×D4C22⋊C411yescharacteristic
646C4×D4C22⋊C411yescharacteristic
647C4×D4C22⋊C412yes—
648C4×D4C22⋊C412yes—
649C4×D4C22⋊C412yes—
650C4×D4C22⋊C412yes—
651C4×D4C22×C412yes—
652C4×D4C22×C412yes—
653C4×D4C22×C414yes—
654C4×D4C22×C412yes—
655C4×D4C22×C411yescharacteristic
656C4×D4C22×C411yescharacteristic
657C4×D4C22×C412yes—
658C4×D4C22×C412yes—
659C4×D4C22×C412yes—
660C4×D4C22×C412yes—
661C4×D4C2×D412yes—
662C4×D4C2×D411yescharacteristic
663C4×D4C2×D412yes—
664C4×D4C2×D412yes—
665C4×D4C2×D412yes—
666C4×D4C2×D412yes—
667C4×D4C2×D411yescharacteristic
668#117—24no—
669#117—22no—
670#117—22no—
671#117—24no—
672#117—22no—
673#117—21no—
674#117—22no—
675#117—22no—
676#117—22no—
677#117—22no—
678#117—21no—
679#117—24no—
680#117—22no—
681#117—24no—
682#117—24no—
683#117—24no—
684#117—24no—
685#117—22no—
686#117—22no—
687#117—24no—
688#117—22no—
689#117—24no—
690#117C22⋊C411yescharacteristic
691#117C22⋊C412yes—
692#117C22⋊C412yes—
693#117C22⋊C412yes—
694#117C22⋊C412yes—
695#117C22⋊C411yescharacteristic
696#117C22⋊C412yes—
697#117C22×C412yes—
698#117C22×C414yes—
699#117C2×D411yescharacteristic
700#117C2×D412yes—
701#117C2×D411yescharacteristic
702#117C2×D412yes—
703#117C2×D412yes—
704#117C2×D412yes—
705#117C2×D412yes—
706C2×C4⋊C4—24no—
707C2×C4⋊C4—22no—
708C2×C4⋊C4—22no—
709C2×C4⋊C4—24no—
710C2×C4⋊C4—21no—
711C2×C4⋊C4—22no—
712C2×C4⋊C4—21no—
713C2×C4⋊C4—22no—
714C2×C4⋊C4—22no—
715C2×C4⋊C4—21no—
716C2×C4⋊C4—24no—
717C2×C4⋊C4—22no—
718C2×C4⋊C4C22⋊C411yescharacteristic
719C2×C4⋊C4C22⋊C412yes—
720C2×C4⋊C4C22⋊C411yescharacteristic
721C2×C4⋊C4C22⋊C412yes—
722C2×C4⋊C4C22×C412yes—
723C2×C4⋊C4C22×C414yes—
724C2×C22⋊C4—22no—
725C2×C22⋊C4—24no—
726C2×C22⋊C4C22⋊C412yes—
727C2×C22⋊C4C22⋊C412yes—
728C2×C22⋊C4C22⋊C412yes—
729C2×C42—24no—
730C2×C42—22no—
731C2×C42—24no—
732C2×C42—22no—
733C2×C42C22×C411yescharacteristic
734C2×C42C22×C412yes—
735C2×C42C22×C411yescharacteristic
736C2×C42C22×C412yes—
737C2×C42C22×C411yescharacteristic
738C2×C42C22×C412yes—
739C2×C42C2×D411yescharacteristic
740C2×C42C2×D412yes—
741C2×C42C2×D411yescharacteristic
742C2×C42C2×D412yes—
743C2×C42C2×D411yescharacteristic
744C2×C42C2×D412yes—
745C2×C42C2×D411yescharacteristic
746C2×C42C2×D412yes—
747C2×C42C2×D411yescharacteristic
748C2×C42C2×D412yes—
749C2×C42C2×D412yes—
750C2×C42C2×D411yescharacteristic
751C2×C42C2411yescharacteristic
752C2×C42C2412yes—
753C2×C42C2412yes—
754C2×C42C2411yescharacteristic
755C2×C42C2411yescharacteristic
756C4⋊C8—24no—
757C4⋊C8—22no—
758C4⋊C8—22no—
759C4⋊C8—22no—
760C4⋊C8—24no—
761C4⋊C8—22no—
762C4⋊C8—24no—
763C4⋊C8—24no—
764C4⋊C8C2412yes—
765C4⋊C8C2412yes—
766C4⋊C8C2412yes—
767C4⋊C8C2412yes—
768C4⋊C8C2414yes—
769C4⋊C8C2414yes—
770C22⋊C8—21no—
771C22⋊C8—21no—
772C22⋊C8—22no—
773C22⋊C8—22no—
774C22⋊C8—21no—
775C22⋊C8—21no—
776C22⋊C8—24no—
777C22⋊C8—22no—
778C22⋊C8—22no—
779C22⋊C8—22no—
780C22⋊C8—24no—
781C22⋊C8—22no—
782C22⋊C8—24no—
783C22⋊C8—24no—
784#97—21no—
785#97—21no—
786#97—22no—
787#97—22no—
788#97—24no—
789#97—24no—
790#97—24no—
791C4×C8—22no—
792C4×C8—21no—
793C4×C8—21no—
794C4×C8—22no—
795C4×C8—22no—
796C4×C8—22no—
797C4×C8—24no—
798C24C2×C22⋊C411yescharacteristic
799C24C2×C22⋊C412yes—
800#41—24no—
801#41—24no—
802#41—44no—
803#41—44no—
804#41—42no—
805#41—42no—
806#41—44no—
807#41—48no—
808#41—416no—
809#41—48no—
810#41—44no—
811#41—82no—
812#41—84no—
813C2×Q8—24no—
814C2×Q8—22no—
815C2×Q8—24no—
816C2×Q8—22no—
817C2×Q8—21no—
818C2×Q8—21no—
819C2×Q8—22no—
820C2×Q8—42no—
821C2×Q8—48no—
822C2×Q8—48no—
823C2×Q8—44no—
824C2×Q8—82no—
825C2×Q8—84no—
826C2×Q8C2×C22⋊C411yescharacteristic
827C2×Q8C2×C22⋊C411yescharacteristic
828C2×Q8C2×C22⋊C412yes—
829C2×Q8C23×C414yes—
830C2×Q8C23×C412yes—
831C2×D4—22no—
832C2×D4—24no—
833C2×D4—22no—
834C2×D4—22no—
835C2×D4—24no—
836C2×D4—21no—
837C2×D4—21no—
838C2×D4—42no—
839C2×D4—44no—
840C2×D4C2×C22⋊C412yes—
841C2×D4C2×C22⋊C411yescharacteristic
842C2×D4C2×C22⋊C412yes—
843C2×D4C2×C22⋊C411yescharacteristic
844C2×D4C2×C22⋊C412yes—
845C2×D4C2×C22⋊C412yes—
846C2×D4C2×C22⋊C412yes—
847C2×D4C23×C412yes—
848C22×C4—24no—
849C22×C4—24no—
850C22×C4—22no—
851C22×C4—24no—
852C22×C4—22no—
853C22×C4—22no—
854C22×C4—24no—
855C22×C4—22no—
856C22×C4—22no—
857C22×C4—24no—
858C22×C4—42no—
859C22×C4—44no—
860C22×C4—44no—
861C22×C4—81no—
862C22×C4—82no—
863C22×C4C2×C22⋊C411yescharacteristic
864C22×C4C2×C22⋊C411yescharacteristic
865C22×C4C2×C22⋊C411yescharacteristic
866C22×C4C2×C22⋊C412yes—
867C22×C4C2×C22⋊C411yescharacteristic
868C22×C4C2×C22⋊C411yescharacteristic
869C22×C4C2×C22⋊C412yes—
870C22×C4C2×C22⋊C412yes—
871C22×C4C2×C22⋊C412yes—
872C22×C4C2×C22⋊C412yes—
873C22×C4C2×C22⋊C411yescharacteristic
874C22×C4C2×C22⋊C412yes—
875C22×C4C2×C22⋊C411yescharacteristic
876C22×C4C2×C22⋊C412yes—
877C22×C4C2×C22⋊C412yes—
878C22×C4C2×C22⋊C411yescharacteristic
879C22×C4C2×C22⋊C411yescharacteristic
880C22×C4C2×C22⋊C412yes—
881C22×C4C23×C411yescharacteristic
882C22×C4C23×C412yes—
883C22×C4C23×C411yescharacteristic
884C22×C4C23×C412yes—
885C22×C4C23×C411yescharacteristic
886C22×C4C22×D411yescharacteristic
887C22×C4C22×D411yescharacteristic
888C22×C4C22×D412yes—
889C22×C4C22×D411yescharacteristic
890C22×C4C22×D411yescharacteristic
891C22×C4C22×D412yes—
892C22×C4C22×D411yescharacteristic
893C22×C4C22×D412yes—
894C22×C4C22×D412yes—
895C22×C4C22×D411yescharacteristic
896M16—48no—
897M16—44no—
898M16—84no—
899M16—84no—
900C2×C8—24no—
901C2×C8—22no—
902C2×C8—22no—
903C2×C8—24no—
904C2×C8—22no—
905C2×C8—22no—
906C2×C8—48no—
907C2×C8—44no—
908C2×C8—82no—
909C2×C8—82no—
910C4⋊C4—24no—
911C4⋊C4—22no—
912C4⋊C4—24no—
913C4⋊C4—24no—
914C4⋊C4—24no—
915C4⋊C4—24no—
916C4⋊C4—22no—
917C4⋊C4—24no—
918C4⋊C4—22no—
919C4⋊C4—24no—
920C4⋊C4—22no—
921C4⋊C4—24no—
922C4⋊C4—22no—
923C4⋊C4—24no—
924C4⋊C4—24no—
925C4⋊C4—24no—
926C4⋊C4—24no—
927C4⋊C4—22no—
928C4⋊C4—22no—
929C4⋊C4—24no—
930C4⋊C4—24no—
931C4⋊C4—22no—
932C4⋊C4—22no—
933C4⋊C4—24no—
934C4⋊C4—24no—
935C4⋊C4—22no—
936C4⋊C4—22no—
937C4⋊C4—21no—
938C4⋊C4—22no—
939C4⋊C4—21no—
940C4⋊C4—21no—
941C4⋊C4—22no—
942C4⋊C4—21no—
943C4⋊C4C2×C22⋊C412yes—
944C4⋊C4C2×C22⋊C411yescharacteristic
945C4⋊C4C2×C22⋊C412yes—
946C4⋊C4C2×C22⋊C411yescharacteristic
947C4⋊C4C2×C22⋊C412yes—
948C4⋊C4C2×C22⋊C412yes—
949C4⋊C4C2×C22⋊C412yes—
950C4⋊C4C2×C22⋊C412yes—
951C4⋊C4C2×C22⋊C411yescharacteristic
952C4⋊C4C2×C22⋊C412yes—
953C4⋊C4C2×C22⋊C411yescharacteristic
954C4⋊C4C2×C22⋊C412yes—
955C4⋊C4C2×C22⋊C412yes—
956C4⋊C4C2×C22⋊C412yes—
957C4⋊C4C23×C414yes—
958C4⋊C4C23×C412yes—
959C4⋊C4C23×C412yes—
960C22⋊C4—24no—
961C22⋊C4—22no—
962C22⋊C4—24no—
963C22⋊C4—24no—
964C22⋊C4—24no—
965C22⋊C4—24no—
966C22⋊C4—22no—
967C22⋊C4—22no—
968C22⋊C4—24no—
969C22⋊C4—22no—
970C22⋊C4—24no—
971C22⋊C4—22no—
972C22⋊C4—22no—
973C22⋊C4—22no—
974C22⋊C4—24no—
975C22⋊C4—24no—
976C22⋊C4—22no—
977C22⋊C4—24no—
978C22⋊C4—22no—
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—
990C22⋊C4C2×C22⋊C412yes—
991C42—24no—
992C42—22no—
993C42—24no—
994C42—24no—
995C42—24no—
996C42—22no—
997C42—24no—
998C42—24no—
999C42—22no—
1000C42C2×C22⋊C412yes—
1001C42C2×C22⋊C411yescharacteristic
1002C42C2×C22⋊C411yescharacteristic
1003C42C2×C22⋊C412yes—
1004C42C2×C22⋊C411yescharacteristic
1005C42C2×C22⋊C412yes—
1006C42C2×C22⋊C412yes—
1007C42C2×C22⋊C411yescharacteristic
1008C42C2×C22⋊C411yescharacteristic
1009C42C2×C22⋊C412yes—
1010C42C2×C22⋊C411yescharacteristic
1011C42C2×C22⋊C412yes—
1012C42C23×C411yescharacteristic
1013C42C23×C412yes—
1014C42C23×C411yescharacteristic
1015C42C23×C412yes—
1016C42C23×C411yescharacteristic
1017C42C22×D411yescharacteristic
1018C42C22×D411yescharacteristic
1019C42C22×D412yes—
1020C42C22×D411yescharacteristic
1021C42C22×D411yescharacteristic
1022C42C22×D411yescharacteristic
1023C42C22×D412yes—
1024C42C22×D412yes—
1025C42C22×D412yes—
1026C42C22×D411yescharacteristic
1027C42C2511yescharacteristic
1028C23—22no—
1029C23—22no—
1030C23—42no—
1031C23—41no—
1032C23—42no—
1033C23—41no—
1034C23—42no—
1035C23C22×C22⋊C411yescharacteristic
1036C23C22×C22⋊C412yes—
1037C23C22×C22⋊C411yescharacteristic
1038C23C22×C22⋊C412yes—
1039C23C22×C22⋊C411yescharacteristic
1040Q8—22no—
1041Q8—22no—
1042Q8—42no—
1043Q8—44no—
1044Q8—42no—
1045Q8—48no—
1046Q8—42no—
1047Q8—44no—
1048Q8—42no—
1049Q8—44no—
1050Q8—82no—
1051Q8—84no—
1052D4—24no—
1053D4—24no—
1054D4—22no—
1055D4—22no—
1056D4—42no—
1057D4—42no—
1058D4—42no—
1059D4—42no—
1060D4—44no—
1061D4—48no—
1062D4—44no—
1063D4—42no—
1064D4—42no—
1065D4—84no—
1066D4—82no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—24no—
1071C2×C4—24no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—24no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—24no—
1079C2×C4—22no—
1080C2×C4—24no—
1081C2×C4—22no—
1082C2×C4—24no—
1083C2×C4—22no—
1084C2×C4—41no—
1085C2×C4—42no—
1086C2×C4—41no—
1087C2×C4—42no—
1088C2×C4—41no—
1089C2×C4—42no—
1090C2×C4—42no—
1091C2×C4—42no—
1092C2×C4—42no—
1093C2×C4—41no—
1094C2×C4—41no—
1095C2×C4—42no—
1096C2×C4—41no—
1097C2×C4—42no—
1098C2×C4—41no—
1099C2×C4—42no—
1100C2×C4—41no—
1101C2×C4—42no—
1102C2×C4—42no—
1103C2×C4—41no—
1104C2×C4—48no—
1105C2×C4—44no—
1106C2×C4—48no—
1107C2×C4—44no—
1108C2×C4—44no—
1109C2×C4—82no—
1110C2×C4—84no—
1111C2×C4—82no—
1112C2×C4—84no—
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⋊C412yes—
1122C2×C4C22×C22⋊C411yescharacteristic
1123C2×C4C22×C22⋊C411yescharacteristic
1124C2×C4C22×C22⋊C412yes—
1125C2×C4C22×C22⋊C412yes—
1126C2×C4C22×C22⋊C411yescharacteristic
1127C2×C4C22×C22⋊C411yescharacteristic
1128C2×C4#57514yes—
1129C2×C4C24×C411yescharacteristic
1130C2×C4C23×D411yescharacteristic
1131C2×C4C23×D411yescharacteristic
1132C8—44no—
1133C8—42no—
1134C8—42no—
1135C8—42no—
1136C8—44no—
1137C8—42no—
1138C22—21no—
1139C22—21no—
1140C22—21no—
1141C22—22no—
1142C22—21no—
1143C22—22no—
1144C22—21no—
1145C22—21no—
1146C22—22no—
1147C22—22no—
1148C22—21no—
1149C22—21no—
1150C22—22no—
1151C22—22no—
1152C22—42no—
1153C22—42no—
1154C22—42no—
1155C22—82no—
1156C22—84no—
1157C22#289612yes—
1158C22C23×C22⋊C411yescharacteristic
1159C4—21no—
1160C4—21no—
1161C4—21no—
1162C4—22no—
1163C4—21no—
1164C4—22no—
1165C4—21no—
1166C4—21no—
1167C4—22no—
1168C4—22no—
1169C4—21no—
1170C4—21no—
1171C4—21no—
1172C4—22no—
1173C4—22no—
1174C4—44no—
1175C4—42no—
1176C4—44no—
1177C4—42no—
1178C4—42no—
1179C4#289612yes—
1180C4C2×#57512yes—
1181C4#358612yes—
1182C2—22no—
1183C2—42no—
1184C2—41no—
1185C2—42no—
1186C2—41no—
1187C2—82no—
1188C2#6007611yescharacteristic
1189C2C2×#289611yescharacteristic
1190C2#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. #60277C2semidirect
3. #60128C2semidirect
4. #17768C2semidirect
5. #17767C2semidirect
6. #17764C2semidirect
7. #17763C2semidirect
8. #17760C2semidirect
9. #17759C2semidirect
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. #1559C22semidirect
78. #1558C22semidirect
79. #1557C22semidirect
80. #1556C22semidirect
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
#602772
#601282
#177682
#177672
#177642
#177632
#177602
#177592
#177572
#177562
#177482
#177472
#177182
#177162
#177132
C2×#15542