Finite Group Databasebeta

← #6344094

Subgroups — #6344094

Order 512.

2823 conjugacy classes of subgroups.

The subgroup lattice has 1212 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62805C211yesmaximal, characteristic
2C2×#2989C211yesmaximal, characteristic, complemented
3#60128C211yesmaximal, characteristic, complemented
4#17769C214yesmaximal, complemented
5#17767C214yesmaximal, complemented
6#17765C212yesmaximal, complemented
7#17763C212yesmaximal, complemented
8#17761C212yesmaximal, complemented
9#17759C212yesmaximal, complemented
10#17756C212yesmaximal, complemented
11#17755C212yesmaximal, complemented
12#17753C212yesmaximal, complemented
13#17751C212yesmaximal, complemented
14#17719C211yesmaximal, characteristic, complemented
15#17715C211yesmaximal, characteristic, complemented
16#17713C211yesmaximal, characteristic, complemented
17C2×#1552C211yesmaximal, characteristic, 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#2989—22no—
48#2989—21no—
49#2989—21no—
50#2989C2212yes—
51#2989C2212yes—
52#2989C2214yes—
53C2×#446—21no—
54C2×#436—21no—
55C2×#435—22no—
56#2925C2212yes—
57#2925C2214yes—
58#2924—21no—
59#2924—22no—
60#2923—21no—
61#2923—22no—
62#2920C2211yescharacteristic
63#2920C2212yes—
64C2×#432C2211yescharacteristic
65C2×#432C2212yes—
66C2×#432C2212yes—
67C2×#431C2211yescharacteristic
68#2906C2212yes—
69C2×#423C2212yes—
70C22×C4⋊C8C2211yescharacteristic
71#2880—21no—
72#2875—21no—
73#1561C2214yescomplemented
74#1561C2214yescomplemented
75#1559C2214yescomplemented
76#1559C2214yescomplemented
77#1557C2214yescomplemented
78#1557C2214yescomplemented
79#1556C2214yescomplemented
80#1556C2214yescomplemented
81#1554C2212yescomplemented
82#1554C2214yescomplemented
83#1553C2212yescomplemented
84#1553C2214yescomplemented
85#1552C2212yes—
86#1552C2212yes—
87#1552C2211yescharacteristic
88#1552C2211yescharacteristic
89#1552C2212yes—
90#1552C2212yes—
91#1552C2212yes—
92#1552C2214yescomplemented
93#1552C2214yescomplemented
94#1552C2214yescomplemented
95#1551C2211yescharacteristic
96#1551C2211yescharacteristic
97#1551C2212yes—
98#1550C2212yescomplemented
99#1550C2214yescomplemented
100#1549C2212yescomplemented
101#1549C2214yescomplemented
102#1547C2212yescomplemented
103#1547C2214yescomplemented
104#1546C2212yescomplemented
105#1546C2214yescomplemented
106#1544C2214yescomplemented
107#1542C2212yescomplemented
108#1542C2212yescomplemented
109#1540C2212yescomplemented
110#1540C2212yescomplemented
111C2×#332C2212yescomplemented
112C2×#332C2212yescomplemented
113C2×2−1+4—21no—
114C22×#41D411yescharacteristic
115C2×#131—22no—
116C22×M16—22no—
117C23×C8—21no—
118Q82C2×C412yes—
119#557—21no—
120#557—21no—
121#557—22no—
122#557C2×C412yes—
123#557C2×C414yes—
124#556—21no—
125#556—22no—
126#556—22no—
127#556—21no—
128#556—22no—
129#556—24no—
130#556C2×C412yes—
131#556C2×C414yes—
132#555C2×C412yes—
133#555C2×C414yes—
134#554—22no—
135#554—24no—
136#554C2×C412yes—
137#554C2×C414yes—
138#554C2×C414yes—
139#554C2×C412yes—
140#553C2×C414yes—
141#553C2×C414yes—
142#553C2×C414yes—
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#552C2×C414yes—
154#552C2×C414yes—
155#552C2×C414yes—
156#551—24no—
157#551—24no—
158#551—24no—
159D4×Q8—22no—
160D4×Q8—21no—
161D4×Q8—22no—
162D4×Q8—21no—
163D4×Q8C2×C412yes—
164#548—22no—
165#548—22no—
166#548—22no—
167#548—22no—
168#547—24no—
169#547—22no—
170#547—22no—
171#547—21no—
172#547—22no—
173#547—21no—
174#547C2×C414yes—
175#547C2×C412yes—
176#546—24no—
177#546—22no—
178#544—21no—
179#544—22no—
180#542—22no—
181#542—24no—
182#542—22no—
183#542—22no—
184#542—22no—
185#541—22no—
186#541—24no—
187#541—22no—
188#541—22no—
189#541—22no—
190#539—24no—
191#539—24no—
192#539—24no—
193#537—21no—
194#537—22no—
195#536—21no—
196#536—22no—
197#536—21no—
198#536—22no—
199#533—22no—
200#533—24no—
201#533—22no—
202#533—21no—
203#533—21no—
204#533—22no—
205#533—21no—
206#533—22no—
207#533—21no—
208#533—22no—
209#533C2×C412yes—
210#533C2×C414yes—
211#533C2×C412yes—
212#533C2×C414yes—
213#533C2311yescharacteristic
214#533C2311yescharacteristic
215#533C2312yes—
216#533C2312yes—
217#533C2312yes—
218#533C2312yes—
219#533C2311yescharacteristic
220#533C2312yes—
221#533C2312yes—
222#532C2311yescharacteristic
223#532C2311yescharacteristic
224#532C2311yescharacteristic
225#532C2312yes—
226#532C2312yes—
227C2×C4⋊Q8C2311yescharacteristic
228C2×C4⋊Q8C2311yescharacteristic
229C2×C4⋊Q8C2312yes—
230C2×C4⋊Q8C2312yes—
231#529—24no—
232#529—24no—
233#529—24no—
234#529—22no—
235#529—24no—
236#529—22no—
237#529—21no—
238#529—21no—
239#529—22no—
240#529—21no—
241#529—22no—
242#529—21no—
243#529—22no—
244#529C2×C412yes—
245#529C2×C414yes—
246#529C2×C412yes—
247#529C2×C414yes—
248C2×#125C2×C412yes—
249C2×#125C2×C414yes—
250#525—21no—
251#525—22no—
252#525—21no—
253#525—22no—
254#525C2×C412yes—
255#525C2×C414yes—
256C2×C22⋊Q8—21no—
257C2×C22⋊Q8—22no—
258C2×C22⋊Q8—21no—
259C2×C22⋊Q8—22no—
260#520—21no—
261#520—24no—
262#520—22no—
263#520—21no—
264#520—22no—
265#519—22no—
266#519—21no—
267#519—22no—
268C4×#41—22no—
269C4×#41—24no—
270C4×#41—21no—
271C4×#41—22no—
272C4×#41—21no—
273C4×#41—22no—
274C4×#41C2×C412yes—
275C4×#41C2×C414yes—
276C4×#41C2×C412yes—
277C4×#41C2×C411yescharacteristic
278C4×#41C2×C411yescharacteristic
279C4×#41D412yes—
280C4×#41D411yescharacteristic
281C4×#41D411yescharacteristic
282C4×#41D411yescharacteristic
283C4×#41D411yescharacteristic
284C4×#41D412yes—
285C4×#41C2311yescharacteristic
286C4×#41C2311yescharacteristic
287C4×#41C2312yes—
288C2×C4×Q8—22no—
289C2×C4×Q8—21no—
290C2×C4×Q8—22no—
291C2×C4×Q8—21no—
292C2×C4×Q8—22no—
293C2×C4×Q8C2×C411yescharacteristic
294C2×C4×Q8D411yescharacteristic
295C2×C4×D4C2×C411yescharacteristic
296C2×C4×D4C2×C412yes—
297C2×C4×D4D412yes—
298C2×C4×D4D411yescharacteristic
299C2×#117C2×C412yes—
300C2×#117C2×C414yes—
301C2×#117D411yescharacteristic
302C2×#117D412yes—
303C22×C42C2311yescharacteristic
304C22×C42C2312yes—
305#446—22no—
306#446—22no—
307#446—24no—
308#436—22no—
309#436—22no—
310#436—24no—
311#435—24no—
312#435—24no—
313#435—24no—
314#435—24no—
315#433—24no—
316#433—24no—
317#433—24no—
318#432—22no—
319#432—21no—
320#432—21no—
321#432—22no—
322#432—22no—
323#432—22no—
324#432—22no—
325#432—21no—
326#432C2311yescharacteristic
327#432C2311yescharacteristic
328#432C2312yes—
329#432C2312yes—
330#432C2314yes—
331#432C2314yes—
332#432C2314yes—
333#431—21no—
334#431—21no—
335#431—21no—
336#431—22no—
337#431C2312yes—
338#431C2312yes—
339#431C2312yes—
340#431C2314yes—
341#424—22no—
342#424—24no—
343#423—22no—
344#423—22no—
345#423C2312yes—
346#423C2314yes—
347#423C2314yes—
348#423C2314yes—
349C2×C4⋊C8—21no—
350C2×C4⋊C8—21no—
351C2×C4⋊C8—21no—
352C2×C4⋊C8—22no—
353C2×C4⋊C8C2312yes—
354C2×C4⋊C8C2312yes—
355C2×C4⋊C8C2312yes—
356C2×C4⋊C8C2314yes—
357C2×C4⋊C8C2312yes—
358C2×C4⋊C8C2311yescharacteristic
359C2×C4⋊C8C2311yescharacteristic
360#408—22no—
361#408—24no—
362#407—21no—
363#407—22no—
364C2×C22⋊C8—21no—
365C2×C22⋊C8—22no—
366C2×C22⋊C8—21no—
367C2×C22⋊C8—22no—
368#405—22no—
369#405—24no—
370C4×M16—21no—
371C4×M16—22no—
372C2×#97—21no—
373C2×#97—22no—
374C2×#97—22no—
375C2×C4×C8—21no—
376#333C2314yes—
377#333C2312yes—
378#333C2312yes—
379#332C2314yes—
380#332C2314yes—
381#332C2314yes—
382#332C2314yes—
383#332C2314yes—
384#332C2312yes—
385#332C2312yes—
386#332C2312yes—
387#332C2314yes—
388#332C2312yes—
389#332C2314yes—
390#332C2314yes—
391#332C2314yes—
392#332C2314yes—
393#331C2314yes—
394#331C2312yes—
395#331C2312yes—
3962−1+4—48no—
397C2×#41—22no—
398C2×#41—24no—
399C2×#41—22no—
400C2×#41—21no—
401C2×#41—21no—
402C2×#41—22no—
403C2×#41—44no—
404C2×#41C22⋊C412yes—
405C2×#41C22⋊C411yescharacteristic
406C2×#41C22⋊C411yescharacteristic
407C2×#41C22×C412yes—
408C2×#41C2×D411yescharacteristic
409C2×#41C2×D411yescharacteristic
410C2×#41C2×D412yes—
411C22×Q8—22no—
412C22×Q8—22no—
413C22×Q8—21no—
414C22×Q8—21no—
415C22×Q8—22no—
416C22×Q8C22⋊C411yescharacteristic
417C22×D4C22⋊C411yescharacteristic
418C22×D4C22⋊C412yes—
419C23×C4C22×C411yescharacteristic
420C23×C4C22×C412yes—
421C23×C4C2×D411yescharacteristic
422C23×C4C2×D412yes—
423C23×C4C2×D411yescharacteristic
424C23×C4C2×D412yes—
425#131—48no—
426C2×M16—24no—
427C2×M16—22no—
428C2×M16—24no—
429C2×M16—24no—
430C2×M16—84no—
431C22×C8—22no—
432C22×C8—21no—
433C22×C8—24no—
434C22×C8—22no—
435C22×C8—21no—
436C22×C8—22no—
437C22×C8—22no—
438C22×C8—82no—
439C4⋊Q8—22no—
440C4⋊Q8—24no—
441C4⋊Q8—24no—
442C4⋊Q8—22no—
443C4⋊Q8—22no—
444C4⋊Q8—21no—
445C4⋊Q8—22no—
446C4⋊Q8—21no—
447C4⋊Q8—21no—
448C4⋊Q8—21no—
449C4⋊Q8—22no—
450C4⋊Q8—22no—
451C4⋊Q8C22×C412yes—
452C4⋊Q8C22×C414yes—
453C4⋊Q8C22×C412yes—
454C4⋊Q8C22×C414yes—
455C4⋊Q8C2411yescharacteristic
456C4⋊Q8C2412yes—
457C4⋊Q8C2412yes—
458C4⋊Q8C2411yescharacteristic
459C4⋊Q8C2411yescharacteristic
460#127C2411yescharacteristic
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#126—24no—
474#125—24no—
475#125—24no—
476#125—24no—
477#125—24no—
478#125—22no—
479#125—24no—
480#125—24no—
481#125—24no—
482#125—22no—
483#125—24no—
484#125—22no—
485#125—24no—
486#125—22no—
487#125—21no—
488#125—21no—
489#125—22no—
490#125C22×C414yes—
491#125C22×C412yes—
492#125C22×C414yes—
493#125C22×C414yes—
494#125C22×C414yes—
495#124—22no—
496#124—24no—
497#124—24no—
498#124—24no—
499#124—24no—
500#124—22no—
501#124—21no—
502#124—21no—
503#124—22no—
504#124C22×C412yes—
505#123—24no—
506#123—24no—
507#123—24no—
508#123—24no—
509#123—22no—
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—
519#123—24no—
520C22⋊Q8—22no—
521C22⋊Q8—24no—
522C22⋊Q8—24no—
523C22⋊Q8—22no—
524C22⋊Q8—22no—
525C22⋊Q8—24no—
526C22⋊Q8—22no—
527C22⋊Q8—24no—
528C22⋊Q8—22no—
529C22⋊Q8—24no—
530C22⋊Q8—22no—
531C22⋊Q8—21no—
532C22⋊Q8—22no—
533C22⋊Q8—21no—
534C22⋊Q8—22no—
535C22⋊Q8—22no—
536C22⋊Q8—22no—
537C22⋊Q8—22no—
538C22⋊Q8—22no—
539C22⋊Q8—22no—
540C22⋊Q8—21no—
541C22⋊Q8—22no—
542C22⋊Q8—21no—
543C22⋊Q8—22no—
544C22⋊Q8—24no—
545C22⋊Q8—22no—
546C22⋊Q8—24no—
547C22⋊Q8—22no—
548C22⋊Q8—24no—
549C22⋊Q8—24no—
550C22⋊Q8—24no—
551C22⋊Q8—24no—
552C22⋊Q8—24no—
553C22⋊Q8—24no—
554C22⋊Q8C22×C412yes—
555C22⋊Q8C22×C414yes—
556C22⋊Q8C22×C412yes—
557C22⋊Q8C22×C414yes—
558#121—24no—
559#121—24no—
560#121—24no—
561#121—22no—
562#121—24no—
563#121—21no—
564#121—21no—
565#121—21no—
566#121—22no—
567#121—21no—
568#121—22no—
569#121C22×C412yes—
570#121C22×C414yes—
571#121C22×C412yes—
572#121C22×C414yes—
573#120—22no—
574#120—24no—
575C4×Q8—22no—
576C4×Q8—24no—
577C4×Q8—22no—
578C4×Q8—24no—
579C4×Q8—22no—
580C4×Q8—24no—
581C4×Q8—22no—
582C4×Q8—24no—
583C4×Q8—22no—
584C4×Q8—22no—
585C4×Q8—24no—
586C4×Q8—22no—
587C4×Q8—24no—
588C4×Q8—22no—
589C4×Q8—21no—
590C4×Q8—22no—
591C4×Q8—21no—
592C4×Q8—22no—
593C4×Q8—22no—
594C4×Q8—22no—
595C4×Q8—22no—
596C4×Q8—22no—
597C4×Q8—22no—
598C4×Q8—21no—
599C4×Q8—22no—
600C4×Q8—21no—
601C4×Q8—22no—
602C4×Q8C22⋊C411yescharacteristic
603C4×Q8C22⋊C411yescharacteristic
604C4×Q8C22⋊C412yes—
605C4×Q8C22⋊C411yescharacteristic
606C4×Q8C22⋊C411yescharacteristic
607C4×Q8C22⋊C412yes—
608C4×Q8C22×C412yes—
609C4×Q8C22×C414yes—
610C4×Q8C22×C412yes—
611C4×Q8C22×C414yes—
612C4×Q8C22×C411yescharacteristic
613C4×Q8C22×C411yescharacteristic
614C4×Q8C22×C412yes—
615C4×Q8C2×D411yescharacteristic
616C4×Q8C2×D411yescharacteristic
617C4×Q8C2×D412yes—
618C4×D4—24no—
619C4×D4—22no—
620C4×D4—24no—
621C4×D4—22no—
622C4×D4—24no—
623C4×D4—22no—
624C4×D4—22no—
625C4×D4—24no—
626C4×D4—22no—
627C4×D4—24no—
628C4×D4—22no—
629C4×D4—24no—
630C4×D4—22no—
631C4×D4—24no—
632C4×D4—24no—
633C4×D4—24no—
634C4×D4—24no—
635C4×D4—21no—
636C4×D4—21no—
637C4×D4—21no—
638C4×D4—22no—
639C4×D4—21no—
640C4×D4—22no—
641C4×D4C22⋊C412yes—
642C4×D4C22⋊C411yescharacteristic
643C4×D4C22⋊C411yescharacteristic
644C4×D4C22⋊C412yes—
645C4×D4C22⋊C412yes—
646C4×D4C22⋊C412yes—
647C4×D4C22⋊C412yes—
648C4×D4C22⋊C412yes—
649C4×D4C22⋊C411yescharacteristic
650C4×D4C22⋊C412yes—
651C4×D4C22⋊C412yes—
652C4×D4C22⋊C412yes—
653C4×D4C22⋊C411yescharacteristic
654C4×D4C22⋊C412yes—
655C4×D4C22×C412yes—
656C4×D4C22×C414yes—
657C4×D4C22×C412yes—
658C4×D4C22×C414yes—
659C4×D4C22×C412yes—
660C4×D4C22×C411yescharacteristic
661C4×D4C22×C412yes—
662C4×D4C22×C412yes—
663C4×D4C22×C412yes—
664C4×D4C22×C411yescharacteristic
665C4×D4C22×C412yes—
666C4×D4C2×D412yes—
667C4×D4C2×D411yescharacteristic
668C4×D4C2×D412yes—
669C4×D4C2×D411yescharacteristic
670C4×D4C2×D412yes—
671C4×D4C2×D412yes—
672C4×D4C2×D412yes—
673#117—22no—
674#117—24no—
675#117—22no—
676#117—24no—
677#117—22no—
678#117—21no—
679#117—21no—
680#117—22no—
681#117—24no—
682#117—22no—
683#117—24no—
684#117—24no—
685#117—24no—
686#117—24no—
687#117—22no—
688#117—22no—
689#117—24no—
690#117—22no—
691#117—24no—
692#117C22⋊C411yescharacteristic
693#117C22⋊C412yes—
694#117C22⋊C412yes—
695#117C22⋊C412yes—
696#117C22⋊C412yes—
697#117C22⋊C411yescharacteristic
698#117C22⋊C412yes—
699#117C22×C414yes—
700#117C22×C412yes—
701#117C22×C414yes—
702#117C22×C414yes—
703#117C22×C414yes—
704#117C2×D411yescharacteristic
705#117C2×D412yes—
706#117C2×D411yescharacteristic
707#117C2×D412yes—
708#117C2×D412yes—
709#117C2×D412yes—
710#117C2×D412yes—
711C2×C4⋊C4—24no—
712C2×C4⋊C4—22no—
713C2×C4⋊C4—22no—
714C2×C4⋊C4—24no—
715C2×C4⋊C4—22no—
716C2×C4⋊C4—21no—
717C2×C4⋊C4—21no—
718C2×C4⋊C4—22no—
719C2×C4⋊C4—24no—
720C2×C4⋊C4—22no—
721C2×C4⋊C4C22⋊C411yescharacteristic
722C2×C4⋊C4C22⋊C412yes—
723C2×C4⋊C4C22⋊C411yescharacteristic
724C2×C4⋊C4C22⋊C412yes—
725C2×C4⋊C4C22×C412yes—
726C2×C4⋊C4C22×C414yes—
727C2×C4⋊C4C22×C412yes—
728C2×C4⋊C4C22×C414yes—
729C2×C22⋊C4—22no—
730C2×C22⋊C4—24no—
731C2×C22⋊C4C22⋊C412yes—
732C2×C22⋊C4C22⋊C412yes—
733C2×C22⋊C4C22⋊C412yes—
734C2×C42—24no—
735C2×C42—22no—
736C2×C42—24no—
737C2×C42—22no—
738C2×C42C22×C411yescharacteristic
739C2×C42C22×C412yes—
740C2×C42C22×C411yescharacteristic
741C2×C42C22×C412yes—
742C2×C42C22×C411yescharacteristic
743C2×C42C22×C412yes—
744C2×C42C2×D411yescharacteristic
745C2×C42C2×D412yes—
746C2×C42C2×D411yescharacteristic
747C2×C42C2×D412yes—
748C2×C42C2×D411yescharacteristic
749C2×C42C2×D412yes—
750C2×C42C2×D411yescharacteristic
751C2×C42C2×D412yes—
752C2×C42C2×D411yescharacteristic
753C2×C42C2×D412yes—
754C2×C42C2×D412yes—
755C2×C42C2×D411yescharacteristic
756C2×C42C2411yescharacteristic
757C2×C42C2412yes—
758C2×C42C2412yes—
759C2×C42C2411yescharacteristic
760C2×C42C2411yescharacteristic
761C4⋊C8—22no—
762C4⋊C8—22no—
763C4⋊C8—22no—
764C4⋊C8—24no—
765C4⋊C8—24no—
766C4⋊C8—21no—
767C4⋊C8—24no—
768C4⋊C8—22no—
769C4⋊C8—21no—
770C4⋊C8—24no—
771C4⋊C8—22no—
772C4⋊C8C2414yes—
773C4⋊C8C2412yes—
774C4⋊C8C2412yes—
775C4⋊C8C2414yes—
776C4⋊C8C2412yes—
777C4⋊C8C2412yes—
778C22⋊C8—21no—
779C22⋊C8—21no—
780C22⋊C8—22no—
781C22⋊C8—24no—
782C22⋊C8—22no—
783C22⋊C8—22no—
784C22⋊C8—22no—
785C22⋊C8—24no—
786C22⋊C8—24no—
787C22⋊C8—24no—
788C22⋊C8—22no—
789#97—21no—
790#97—21no—
791#97—22no—
792#97—22no—
793#97—24no—
794#97—24no—
795#97—24no—
796C4×C8—22no—
797C4×C8—22no—
798C4×C8—22no—
799C4×C8—24no—
800C24C2×C22⋊C411yescharacteristic
801C24C2×C22⋊C412yes—
802#41—24no—
803#41—24no—
804#41—44no—
805#41—44no—
806#41—42no—
807#41—42no—
808#41—48no—
809#41—44no—
810#41—416no—
811#41—48no—
812#41—44no—
813#41—81no—
814#41—82no—
815#41—81no—
816#41—82no—
817C2×Q8—24no—
818C2×Q8—22no—
819C2×Q8—24no—
820C2×Q8—22no—
821C2×Q8—22no—
822C2×Q8—21no—
823C2×Q8—21no—
824C2×Q8—22no—
825C2×Q8—42no—
826C2×Q8—48no—
827C2×Q8—48no—
828C2×Q8—44no—
829C2×Q8—81no—
830C2×Q8—82no—
831C2×Q8—81no—
832C2×Q8—82no—
833C2×Q8C2×C22⋊C411yescharacteristic
834C2×Q8C2×C22⋊C411yescharacteristic
835C2×Q8C2×C22⋊C412yes—
836C2×Q8C23×C412yes—
837C2×D4—22no—
838C2×D4—24no—
839C2×D4—22no—
840C2×D4—22no—
841C2×D4—24no—
842C2×D4—21no—
843C2×D4—21no—
844C2×D4—42no—
845C2×D4—44no—
846C2×D4C2×C22⋊C412yes—
847C2×D4C2×C22⋊C411yescharacteristic
848C2×D4C2×C22⋊C412yes—
849C2×D4C2×C22⋊C411yescharacteristic
850C2×D4C2×C22⋊C412yes—
851C2×D4C2×C22⋊C412yes—
852C2×D4C2×C22⋊C412yes—
853C2×D4C23×C412yes—
854C22×C4—24no—
855C22×C4—24no—
856C22×C4—22no—
857C22×C4—24no—
858C22×C4—22no—
859C22×C4—22no—
860C22×C4—24no—
861C22×C4—22no—
862C22×C4—22no—
863C22×C4—24no—
864C22×C4—41no—
865C22×C4—42no—
866C22×C4—41no—
867C22×C4—42no—
868C22×C4—44no—
869C22×C4—42no—
870C22×C4—44no—
871C22×C4C2×C22⋊C411yescharacteristic
872C22×C4C2×C22⋊C411yescharacteristic
873C22×C4C2×C22⋊C411yescharacteristic
874C22×C4C2×C22⋊C411yescharacteristic
875C22×C4C2×C22⋊C412yes—
876C22×C4C2×C22⋊C412yes—
877C22×C4C2×C22⋊C411yescharacteristic
878C22×C4C2×C22⋊C411yescharacteristic
879C22×C4C2×C22⋊C412yes—
880C22×C4C2×C22⋊C412yes—
881C22×C4C2×C22⋊C412yes—
882C22×C4C2×C22⋊C411yescharacteristic
883C22×C4C2×C22⋊C412yes—
884C22×C4C2×C22⋊C412yes—
885C22×C4C2×C22⋊C412yes—
886C22×C4C2×C22⋊C411yescharacteristic
887C22×C4C2×C22⋊C411yescharacteristic
888C22×C4C2×C22⋊C412yes—
889C22×C4C23×C411yescharacteristic
890C22×C4C23×C412yes—
891C22×C4C23×C411yescharacteristic
892C22×C4C23×C412yes—
893C22×C4C23×C411yescharacteristic
894C22×C4C22×D411yescharacteristic
895C22×C4C22×D412yes—
896C22×C4C22×D411yescharacteristic
897C22×C4C22×D411yescharacteristic
898C22×C4C22×D412yes—
899C22×C4C22×D411yescharacteristic
900C22×C4C22×D412yes—
901C22×C4C22×D411yescharacteristic
902C22×C4C22×D412yes—
903C22×C4C22×D411yescharacteristic
904M16—48no—
905M16—44no—
906M16—84no—
907M16—84no—
908C2×C8—22no—
909C2×C8—24no—
910C2×C8—22no—
911C2×C8—22no—
912C2×C8—22no—
913C2×C8—24no—
914C2×C8—42no—
915C2×C8—44no—
916C2×C8—42no—
917C2×C8—48no—
918C2×C8—44no—
919C2×C8—82no—
920C2×C8—82no—
921C4⋊C4—24no—
922C4⋊C4—22no—
923C4⋊C4—24no—
924C4⋊C4—24no—
925C4⋊C4—24no—
926C4⋊C4—24no—
927C4⋊C4—22no—
928C4⋊C4—24no—
929C4⋊C4—22no—
930C4⋊C4—24no—
931C4⋊C4—24no—
932C4⋊C4—24no—
933C4⋊C4—24no—
934C4⋊C4—22no—
935C4⋊C4—24no—
936C4⋊C4—22no—
937C4⋊C4—24no—
938C4⋊C4—22no—
939C4⋊C4—22no—
940C4⋊C4—24no—
941C4⋊C4—24no—
942C4⋊C4—22no—
943C4⋊C4—24no—
944C4⋊C4—22no—
945C4⋊C4—22no—
946C4⋊C4—24no—
947C4⋊C4—22no—
948C4⋊C4—21no—
949C4⋊C4—21no—
950C4⋊C4—22no—
951C4⋊C4—21no—
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⋊C411yescharacteristic
959C4⋊C4C2×C22⋊C412yes—
960C4⋊C4C2×C22⋊C412yes—
961C4⋊C4C2×C22⋊C412yes—
962C4⋊C4C2×C22⋊C412yes—
963C4⋊C4C2×C22⋊C412yes—
964C4⋊C4C2×C22⋊C412yes—
965C4⋊C4C2×C22⋊C412yes—
966C4⋊C4C2×C22⋊C411yescharacteristic
967C4⋊C4C23×C414yes—
968C4⋊C4C23×C412yes—
969C4⋊C4C23×C414yes—
970C4⋊C4C23×C412yes—
971C22⋊C4—24no—
972C22⋊C4—22no—
973C22⋊C4—24no—
974C22⋊C4—24no—
975C22⋊C4—24no—
976C22⋊C4—24no—
977C22⋊C4—22no—
978C22⋊C4—22no—
979C22⋊C4—24no—
980C22⋊C4—22no—
981C22⋊C4—22no—
982C22⋊C4—22no—
983C22⋊C4—24no—
984C22⋊C4—24no—
985C22⋊C4—22no—
986C22⋊C4—22no—
987C22⋊C4—24no—
988C22⋊C4—24no—
989C22⋊C4—22no—
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—
1001C22⋊C4C2×C22⋊C412yes—
1002C42—24no—
1003C42—22no—
1004C42—22no—
1005C42—24no—
1006C42—24no—
1007C42—24no—
1008C42—24no—
1009C42—24no—
1010C42—22no—
1011C42C2×C22⋊C412yes—
1012C42C2×C22⋊C411yescharacteristic
1013C42C2×C22⋊C411yescharacteristic
1014C42C2×C22⋊C412yes—
1015C42C2×C22⋊C411yescharacteristic
1016C42C2×C22⋊C412yes—
1017C42C2×C22⋊C412yes—
1018C42C2×C22⋊C411yescharacteristic
1019C42C2×C22⋊C411yescharacteristic
1020C42C2×C22⋊C412yes—
1021C42C2×C22⋊C411yescharacteristic
1022C42C2×C22⋊C412yes—
1023C42C23×C411yescharacteristic
1024C42C23×C412yes—
1025C42C23×C411yescharacteristic
1026C42C23×C412yes—
1027C42C23×C411yescharacteristic
1028C42C22×D411yescharacteristic
1029C42C22×D412yes—
1030C42C22×D411yescharacteristic
1031C42C22×D411yescharacteristic
1032C42C22×D411yescharacteristic
1033C42C22×D412yes—
1034C42C22×D412yes—
1035C42C22×D411yescharacteristic
1036C42C22×D412yes—
1037C42C22×D411yescharacteristic
1038C42C2511yescharacteristic
1039C23—22no—
1040C23—22no—
1041C23—24no—
1042C23—22no—
1043C23—41no—
1044C23—42no—
1045C23—42no—
1046C23C22×C22⋊C411yescharacteristic
1047C23C22×C22⋊C412yes—
1048C23C22×C22⋊C412yes—
1049C23C22×C22⋊C411yescharacteristic
1050C23C22×C22⋊C411yescharacteristic
1051Q8—22no—
1052Q8—22no—
1053Q8—42no—
1054Q8—42no—
1055Q8—48no—
1056Q8—42no—
1057Q8—41no—
1058Q8—42no—
1059Q8—41no—
1060Q8—44no—
1061Q8—42no—
1062Q8—44no—
1063Q8—82no—
1064Q8—84no—
1065D4—24no—
1066D4—24no—
1067D4—22no—
1068D4—22no—
1069D4—42no—
1070D4—42no—
1071D4—42no—
1072D4—42no—
1073D4—48no—
1074D4—44no—
1075D4—44no—
1076D4—41no—
1077D4—41no—
1078D4—42no—
1079D4—82no—
1080D4—84no—
1081C2×C4—22no—
1082C2×C4—22no—
1083C2×C4—24no—
1084C2×C4—22no—
1085C2×C4—21no—
1086C2×C4—21no—
1087C2×C4—21no—
1088C2×C4—22no—
1089C2×C4—22no—
1090C2×C4—21no—
1091C2×C4—21no—
1092C2×C4—22no—
1093C2×C4—21no—
1094C2×C4—22no—
1095C2×C4—22no—
1096C2×C4—22no—
1097C2×C4—24no—
1098C2×C4—22no—
1099C2×C4—22no—
1100C2×C4—24no—
1101C2×C4—22no—
1102C2×C4—24no—
1103C2×C4—22no—
1104C2×C4—24no—
1105C2×C4—22no—
1106C2×C4—41no—
1107C2×C4—42no—
1108C2×C4—41no—
1109C2×C4—42no—
1110C2×C4—41no—
1111C2×C4—42no—
1112C2×C4—41no—
1113C2×C4—42no—
1114C2×C4—41no—
1115C2×C4—42no—
1116C2×C4—42no—
1117C2×C4—42no—
1118C2×C4—42no—
1119C2×C4—41no—
1120C2×C4—42no—
1121C2×C4—41no—
1122C2×C4—42no—
1123C2×C4—48no—
1124C2×C4—44no—
1125C2×C4—48no—
1126C2×C4—44no—
1127C2×C4—44no—
1128C2×C4—82no—
1129C2×C4—84no—
1130C2×C4—82no—
1131C2×C4—84no—
1132C2×C4C22×C22⋊C411yescharacteristic
1133C2×C4C22×C22⋊C411yescharacteristic
1134C2×C4C22×C22⋊C412yes—
1135C2×C4C22×C22⋊C411yescharacteristic
1136C2×C4C22×C22⋊C412yes—
1137C2×C4C22×C22⋊C412yes—
1138C2×C4C22×C22⋊C411yescharacteristic
1139C2×C4C22×C22⋊C411yescharacteristic
1140C2×C4C22×C22⋊C412yes—
1141C2×C4C22×C22⋊C411yescharacteristic
1142C2×C4C22×C22⋊C411yescharacteristic
1143C2×C4C22×C22⋊C412yes—
1144C2×C4C22×C22⋊C412yes—
1145C2×C4C22×C22⋊C411yescharacteristic
1146C2×C4C22×C22⋊C411yescharacteristic
1147C2×C4#57514yes—
1148C2×C4C24×C411yescharacteristic
1149C2×C4C23×D411yescharacteristic
1150C2×C4C23×D411yescharacteristic
1151C8—44no—
1152C8—42no—
1153C8—42no—
1154C8—42no—
1155C8—44no—
1156C8—42no—
1157C22—21no—
1158C22—21no—
1159C22—21no—
1160C22—21no—
1161C22—21no—
1162C22—22no—
1163C22—22no—
1164C22—21no—
1165C22—22no—
1166C22—22no—
1167C22—22no—
1168C22—21no—
1169C22—22no—
1170C22—44no—
1171C22—42no—
1172C22—42no—
1173C22—42no—
1174C22—84no—
1175C22#288912yes—
1176C22#289612yes—
1177C22C23×C22⋊C411yescharacteristic
1178C4—21no—
1179C4—21no—
1180C4—21no—
1181C4—22no—
1182C4—21no—
1183C4—22no—
1184C4—21no—
1185C4—21no—
1186C4—22no—
1187C4—22no—
1188C4—21no—
1189C4—21no—
1190C4—22no—
1191C4—21no—
1192C4—22no—
1193C4—42no—
1194C4—44no—
1195C4—42no—
1196C4—44no—
1197C4—42no—
1198C4#289612yes—
1199C4C2×#57512yes—
1200C4#358511yescharacteristic
1201C4#358611yescharacteristic
1202C2—22no—
1203C2—22no—
1204C2—41no—
1205C2—42no—
1206C2—42no—
1207C2—82no—
1208C2C2×#288911yescharacteristic
1209C2C2×#289611yescharacteristic
1210C2#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. C2×#2989C2semidirect
3. #60128C2semidirect
4. #17769C2semidirect
5. #17767C2semidirect
6. #17765C2semidirect
7. #17763C2semidirect
8. #17761C2semidirect
9. #17759C2semidirect
10. #17756C2semidirect
11. #17755C2semidirect
12. #17753C2semidirect
13. #17751C2semidirect
14. #17719C2semidirect
15. #17715C2semidirect
16. #17713C2semidirect
17. C2×#1552C2semidirect
73. #1561C22semidirect
74. #1561C22semidirect
75. #1559C22semidirect
76. #1559C22semidirect
77. #1557C22semidirect
78. #1557C22semidirect
79. #1556C22semidirect
80. #1556C22semidirect
81. #1554C22semidirect
82. #1554C22semidirect
83. #1553C22semidirect
84. #1553C22semidirect
92. #1552C22semidirect
93. #1552C22semidirect
94. #1552C22semidirect
98. #1550C22semidirect
99. #1550C22semidirect
100. #1549C22semidirect
101. #1549C22semidirect
102. #1547C22semidirect
103. #1547C22semidirect
104. #1546C22semidirect
105. #1546C22semidirect
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
C2×#29892
#601282
#177692
#177672
#177652
#177632
#177612
#177592
#177562
#177552
#177532
#177512
#177192
#177152
#177132
C2×#15522