Finite Group Databasebeta

← #6343227

Subgroups — #6343227

Order 512.

2648 conjugacy classes of subgroups.

The subgroup lattice has 1069 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62761C211yesmaximal, characteristic
2#60294C211yesmaximal, characteristic, complemented
3#60281C211yesmaximal, characteristic, complemented
4#17524C214yesmaximal, complemented
5#17523C214yesmaximal, complemented
6#17516C214yesmaximal, complemented
7#17514C214yesmaximal, complemented
8#17506C214yesmaximal, complemented
9#17496C211yesmaximal, characteristic, complemented
10#17494C211yesmaximal, characteristic, complemented
11#17469C214yesmaximal, complemented
12#17467C211yesmaximal, characteristic, complemented
13#17464C211yesmaximal, characteristic, complemented
14#3557—22no—
15#3556C411yescharacteristic
16#3555—21no—
17#3555C412yes—
18#3554—21no—
19#3554C412yes—
20#3553—22no—
21#3552C412yes—
22#3552C412yes—
23#3550C411yescharacteristic
24#3550C411yescharacteristic
25#3548C411yescharacteristic
26#3541—22no—
27#3541C414yes—
28#3531—22no—
29#3482C2212yes—
30#3482C2212yes—
31#3480—21no—
32#3480C2212yes—
33Q8×#41—21no—
34Q8×#41C2212yes—
35#3461—22no—
36#3461C2214yes—
37#3455—22no—
38#3444C2211yescharacteristic
39#3444C2211yescharacteristic
40C2×#533C2211yescharacteristic
41#2995—22no—
42#2995—22no—
43#2990C2214yes—
44#2989C2212yes—
45#2988C2212yes—
46#2987—21no—
47#2985—21no—
48#2981—21no—
49#2980—21no—
50#2978—22no—
51#2977—22no—
52#2968—22no—
53#2966—22no—
54#2965C2214yes—
55#2965C2214yes—
56#2925C2214yes—
57#2922C2214yes—
58#2920C2211yescharacteristic
59#2920C2211yescharacteristic
60C2×#432C2211yescharacteristic
61C2×#431C2211yescharacteristic
62#1497C2212yes—
63#1497C2212yes—
64#1497C2212yes—
65#1497C2214yescomplemented
66#1496C2212yes—
67#1495C2214yescomplemented
68#1494C2214yescomplemented
69#1493C2214yescomplemented
70#1491C2214yes—
71#1491C2214yescomplemented
72#1489C2214yescomplemented
73#1488C2214yes—
74#1488C2214yescomplemented
75#1487C2214yescomplemented
76#1485C2212yes—
77#1485C2212yes—
78#1485C2212yes—
79#1485C2214yescomplemented
80#1484C2212yes—
81#1483C2214yes—
82#1483C2214yescomplemented
83#1482C2212yes—
84#1482C2212yes—
85#1482C2214yescomplemented
86#1481C2212yes—
87#1481C2212yes—
88#1481C2214yes—
89#1481C2214yescomplemented
90#1479C2214yes—
91#1479C2214yescomplemented
92#1477C2214yes—
93#1477C2214yescomplemented
94#1476C2214yescomplemented
95C2×Q8⋊C8C2214yescomplemented
96#564—22no—
97#563—24no—
98#563—24no—
99#563—22no—
100#563—22no—
101#563—24no—
102#563—24no—
103#562—22no—
104#562—24no—
105#562—24no—
106#559—21no—
107#559—22no—
108#559—22no—
109#559C2×C412yes—
110Q82—21no—
111Q82C2×C412yes—
112#557—21no—
113#557—21no—
114#557—22no—
115#557—22no—
116#557C2×C412yes—
117#557C2×C412yes—
118#557C2×C412yes—
119#557C2×C412yes—
120#556—21no—
121#556—22no—
122#556—22no—
123#556—22no—
124#556C2×C412yes—
125#556C2×C412yes—
126#556C2×C414yes—
127#556C2×C412yes—
128#554—21no—
129#554—22no—
130#554—22no—
131#554—24no—
132#554—24no—
133#554—22no—
134#554C2×C414yes—
135#554C2×C412yes—
136#553—22no—
137#553—24no—
138#553—24no—
139#553C2×C414yes—
140#552—22no—
141#552—24no—
142#552—24no—
143#552C2×C414yes—
144#550—21no—
145#550C2×C412yes—
146D4×Q8—21no—
147D4×Q8—22no—
148D4×Q8C2×C414yes—
149D4×Q8C2×C412yes—
150D4×Q8C2×C412yes—
151D4×Q8C2×C412yes—
152#548—22no—
153#548—22no—
154#548C2×C414yes—
155#548C2×C414yes—
156#547—22no—
157#547C2×C414yes—
158#547C2×C412yes—
159#547C2×C412yes—
160#544—22no—
161#544C2×C414yes—
162#542—22no—
163#542—24no—
164#542—22no—
165#542—22no—
166#542—22no—
167#542—22no—
168#542—22no—
169#542—24no—
170#542C2×C414yes—
171#542C2×C414yes—
172#541—24no—
173#541—22no—
174#541—22no—
175#541—22no—
176#541—22no—
177#541—24no—
178#541C2×C414yes—
179#541C2×C414yes—
180#540—22no—
181#540—22no—
182#539—24no—
183#539—24no—
184#539—24no—
185#539—24no—
186#539—24no—
187#539—24no—
188#538—24no—
189#538—24no—
190#537—22no—
191#537C2×C414yes—
192#536—22no—
193#536—22no—
194#536C2×C414yes—
195#536C2×C414yes—
196#533—22no—
197#533—24no—
198#533—22no—
199#533—24no—
200#533—21no—
201#533—21no—
202#533—21no—
203#533—21no—
204#533C2×C411yescharacteristic
205#533C2×C411yescharacteristic
206#533C2×C412yes—
207#533C2×C411yescharacteristic
208#533C2×C411yescharacteristic
209#533C2×C411yescharacteristic
210#533D411yescharacteristic
211#533D411yescharacteristic
212#533C2312yes—
213#533C2311yescharacteristic
214#533C2311yescharacteristic
215#533C2311yescharacteristic
216#533C2314yes—
217#532—22no—
218#532C2×C411yescharacteristic
219#532C2×C411yescharacteristic
220#532C2×C411yescharacteristic
221#532D411yescharacteristic
222#532D411yescharacteristic
223#532C2311yescharacteristic
224C2×C4⋊Q8C2×C411yescharacteristic
225C2×C4⋊Q8C2×C411yescharacteristic
226#529—24no—
227#529—24no—
228#529—24no—
229#529—24no—
230#529—22no—
231#529—24no—
232#529—24no—
233#529—21no—
234#529—21no—
235#529—21no—
236#529—21no—
237#529C2×C412yes—
238#529C2×C412yes—
239#529C2×C412yes—
240#529D412yes—
241#529D412yes—
242#529D412yes—
243#529D412yes—
244#529C2312yes—
245#529C2314yes—
246C2×#125—21no—
247#525—21no—
248#525—21no—
249#525C2×C412yes—
250#525C2×C412yes—
251#525D412yes—
252#525D412yes—
253C2×C22⋊Q8—21no—
254C2×C22⋊Q8C2×C412yes—
255C4×#41—22no—
256C4×#41—22no—
257C4×#41—22no—
258C4×#41—21no—
259C4×#41—21no—
260C4×#41C2312yes—
261C4×#41C2314yes—
262C4×#41C2312yes—
263C4×#41C2312yes—
264C4×#41C2312yes—
265C2×C4×Q8—22no—
266C2×C4×Q8—21no—
267C2×C4×Q8C2312yes—
268C2×C4×Q8C2314yes—
269C2×#117—21no—
270C22×C42C2311yescharacteristic
271#446—24no—
272#446—24no—
273#446—22no—
274#446—24no—
275C8×Q8—22no—
276#436—24no—
277#436—24no—
278#436—22no—
279#435—24no—
280#435—24no—
281#435—24no—
282#435—24no—
283#435—24no—
284#435—24no—
285#435—24no—
286C8×D4—24no—
287C8×D4—22no—
288C8×D4—24no—
289#433—24no—
290#433—24no—
291#433—24no—
292#433—24no—
293#432—21no—
294#432—21no—
295#432—21no—
296#432—21no—
297#432—21no—
298#432—21no—
299#432C2312yes—
300#432C2312yes—
301#432C2314yes—
302#431—21no—
303#431—21no—
304#431C2312yes—
305#431C2311yescharacteristic
306#431C2311yescharacteristic
307#431C2314yes—
308#431C2312yes—
309#431C2312yes—
310#431C2312yes—
311#431C2312yes—
312#431C2314yes—
313#431C2314yes—
314#424—24no—
315#423—21no—
316#423—21no—
317#423C2314yes—
318C2×C4⋊C8C2312yes—
319C2×C4⋊C8C2312yes—
320C2×C4⋊C8C2314yes—
321#408—24no—
322#408—24no—
323#407—21no—
324#407—21no—
325C2×C22⋊C8—21no—
326C2×C22⋊C8—21no—
327#405—24no—
328C4×M16C2312yes—
329C4×M16C2312yes—
330C4×M16C2314yes—
331C2×#97—21no—
332C2×C4×C8—21no—
333C2×C4×C8C2314yes—
334Q8⋊C8C2314yes—
335Q8⋊C8C2314yes—
336Q8⋊C8C2314yes—
337Q8⋊C8C2314yes—
338Q8⋊C8C2314yes—
339Q8⋊C8C2314yes—
340Q8⋊C8C2314yes—
341Q8⋊C8C2314yes—
342Q8⋊C8C2314yes—
343Q8⋊C8C2314yes—
344Q8⋊C8C2314yes—
345Q8⋊C8C2314yes—
346D4⋊C8C2314yes—
347D4⋊C8C2314yes—
348D4⋊C8C2314yes—
349D4⋊C8C2314yes—
350C2×#41—22no—
351C2×#41—21no—
352C2×#41—21no—
353C2×#41C22×C412yes—
354C2×#41C22×C414yes—
355C2×#41C22×C412yes—
356C2×#41C2×D412yes—
357C2×#41C2×D412yes—
358C22×Q8—22no—
359C22×Q8—21no—
360C22×Q8C22×C412yes—
361C22×Q8C22×C414yes—
362C23×C4C22×C411yescharacteristic
363C23×C4C2×D411yescharacteristic
364C23×C4C2×D411yescharacteristic
365C2×M16—22no—
366C2×M16—22no—
367C2×M16—24no—
368C2×M16—24no—
369C22×C8—22no—
370C22×C8—24no—
371C22×C8—22no—
372C22×C8—24no—
373C4⋊Q8—22no—
374C4⋊Q8—22no—
375C4⋊Q8—24no—
376C4⋊Q8—24no—
377C4⋊Q8—22no—
378C4⋊Q8—22no—
379C4⋊Q8—22no—
380C4⋊Q8—24no—
381C4⋊Q8—24no—
382C4⋊Q8—21no—
383C4⋊Q8—21no—
384C4⋊Q8—21no—
385C4⋊Q8—21no—
386C4⋊Q8C22⋊C411yescharacteristic
387C4⋊Q8C22⋊C411yescharacteristic
388C4⋊Q8C22⋊C411yescharacteristic
389C4⋊Q8C22×C412yes—
390C4⋊Q8C22×C411yescharacteristic
391C4⋊Q8C22×C411yescharacteristic
392C4⋊Q8C22×C411yescharacteristic
393C4⋊Q8C22×C414yes—
394C4⋊Q8C22×C412yes—
395C4⋊Q8C22×C411yescharacteristic
396C4⋊Q8C22×C411yescharacteristic
397C4⋊Q8C22×C411yescharacteristic
398C4⋊Q8C22×C411yescharacteristic
399C4⋊Q8C22×C414yes—
400#127—22no—
401#127C22⋊C411yescharacteristic
402#127C22×C411yescharacteristic
403#126—24no—
404#126—24no—
405#126—24no—
406#126—24no—
407#126—24no—
408#126—24no—
409#126—24no—
410#126—24no—
411#126—24no—
412#126—24no—
413#126—24no—
414#126—24no—
415#126—24no—
416#126—22no—
417#126—22no—
418#126—24no—
419#126C22⋊C414yes—
420#126C22⋊C414yes—
421#125—24no—
422#125—24no—
423#125—24no—
424#125—24no—
425#125—24no—
426#125—24no—
427#125—22no—
428#125—24no—
429#125—24no—
430#125—24no—
431#125—24no—
432#125—24no—
433#125—22no—
434#125—22no—
435#125—22no—
436#125—21no—
437#125—21no—
438#125—21no—
439#125—22no—
440#125—21no—
441#125—21no—
442#125—21no—
443#125—24no—
444#125C22⋊C412yes—
445#125C22⋊C412yes—
446#125C22⋊C412yes—
447#125C22×C412yes—
448#125C22×C414yes—
449#124—22no—
450#124—22no—
451#124—24no—
452#124—24no—
453#124—22no—
454#124—24no—
455#124—24no—
456#124—24no—
457#124—24no—
458#124—21no—
459#124—21no—
460#124C22⋊C412yes—
461#124C22⋊C412yes—
462#124C22⋊C412yes—
463#124C22×C412yes—
464#124C22×C414yes—
465#123—24no—
466#123—24no—
467#123—24no—
468#123—22no—
469#123—22no—
470#123—22no—
471#123—24no—
472#123—24no—
473#123—24no—
474#123—24no—
475#123—24no—
476#123—24no—
477#123—24no—
478#123—24no—
479#123—24no—
480#123—24no—
481#123—24no—
482#123C22⋊C414yes—
483#123C22⋊C414yes—
484#123C22⋊C414yes—
485C22⋊Q8—22no—
486C22⋊Q8—24no—
487C22⋊Q8—21no—
488C22⋊Q8—21no—
489C22⋊Q8—22no—
490C22⋊Q8—22no—
491C22⋊Q8—22no—
492C22⋊Q8—21no—
493C22⋊Q8—21no—
494C22⋊Q8—21no—
495C22⋊Q8—22no—
496C22⋊Q8—21no—
497C22⋊Q8—21no—
498C22⋊Q8—21no—
499C22⋊Q8—24no—
500C22⋊Q8—22no—
501C22⋊Q8—24no—
502C22⋊Q8—24no—
503C22⋊Q8—24no—
504C22⋊Q8—24no—
505C22⋊Q8—22no—
506C22⋊Q8—24no—
507C22⋊Q8—24no—
508C22⋊Q8—24no—
509C22⋊Q8—24no—
510C22⋊Q8—24no—
511C22⋊Q8—24no—
512C22⋊Q8—24no—
513C22⋊Q8—24no—
514C22⋊Q8—24no—
515C22⋊Q8—24no—
516C22⋊Q8—24no—
517C22⋊Q8—24no—
518C22⋊Q8C22⋊C412yes—
519C22⋊Q8C22⋊C412yes—
520C22⋊Q8C22⋊C412yes—
521C22⋊Q8C22⋊C412yes—
522C22⋊Q8C22⋊C412yes—
523C22⋊Q8C22⋊C412yes—
524C22⋊Q8C22×C412yes—
525C22⋊Q8C22×C412yes—
526C22⋊Q8C22×C412yes—
527C22⋊Q8C22×C412yes—
528C22⋊Q8C22×C412yes—
529C22⋊Q8C22×C412yes—
530C22⋊Q8C22×C414yes—
531C22⋊Q8C22×C414yes—
532C22⋊Q8C22×C414yes—
533#121—24no—
534#121—24no—
535#121—22no—
536#121—24no—
537#121—24no—
538#121—24no—
539#121—24no—
540#121—24no—
541#121—21no—
542#121—21no—
543#121—21no—
544#121—21no—
545#121—24no—
546#121C22⋊C412yes—
547#121C22⋊C412yes—
548#121C22⋊C412yes—
549#121C22⋊C412yes—
550#121C22⋊C412yes—
551#121C22⋊C412yes—
552#121C22×C412yes—
553#121C22×C412yes—
554#121C22×C414yes—
555#120—22no—
556#120C22⋊C414yes—
557C4×Q8—22no—
558C4×Q8—22no—
559C4×Q8—22no—
560C4×Q8—22no—
561C4×Q8—24no—
562C4×Q8—22no—
563C4×Q8—22no—
564C4×Q8—22no—
565C4×Q8—21no—
566C4×Q8—21no—
567C4×Q8—22no—
568C4×Q8—21no—
569C4×Q8—21no—
570C4×Q8—21no—
571C4×Q8—21no—
572C4×Q8—21no—
573C4×Q8—22no—
574C4×Q8—24no—
575C4×Q8—22no—
576C4×Q8—24no—
577C4×Q8—22no—
578C4×Q8—24no—
579C4×Q8—21no—
580C4×Q8C22×C412yes—
581C4×Q8C22×C412yes—
582C4×Q8C22×C414yes—
583C4×Q8C22×C414yes—
584C4×Q8C22×C412yes—
585C4×Q8C22×C414yes—
586C4×Q8C22×C412yes—
587C4×Q8C22×C412yes—
588C4×Q8C2×D412yes—
589C4×Q8C2×D412yes—
590C4×Q8C2×D412yes—
591C4×Q8C2×D412yes—
592C4×Q8C2412yes—
593C4×Q8C2412yes—
594C4×Q8C2412yes—
595C4×D4—24no—
596C4×D4—24no—
597C4×D4—22no—
598C4×D4—22no—
599C4×D4—22no—
600C4×D4—22no—
601C4×D4—22no—
602C4×D4—22no—
603C4×D4—22no—
604C4×D4—24no—
605C4×D4—22no—
606C4×D4—22no—
607C4×D4—24no—
608C4×D4—24no—
609C4×D4—22no—
610C4×D4—22no—
611C4×D4—24no—
612C4×D4—24no—
613C4×D4—24no—
614C4×D4—21no—
615C4×D4—21no—
616C4×D4—21no—
617C4×D4—21no—
618C4×D4C22×C412yes—
619C4×D4C22×C414yes—
620C4×D4C22×C414yes—
621C4×D4C22×C414yes—
622C4×D4C22×C412yes—
623C4×D4C22×C412yes—
624C4×D4C2×D412yes—
625C4×D4C2×D414yes—
626C4×D4C2×D414yes—
627C4×D4C2×D414yes—
628C4×D4C2×D414yes—
629C4×D4C2×D412yes—
630C4×D4C2×D412yes—
631C4×D4C2×D412yes—
632C4×D4C2412yes—
633#117—21no—
634#117—22no—
635#117—21no—
636#117—21no—
637#117—22no—
638#117—21no—
639#117—21no—
640#117—21no—
641#117—24no—
642#117—22no—
643#117—24no—
644#117—22no—
645#117—22no—
646#117—24no—
647#117—22no—
648#117—24no—
649#117C22×C412yes—
650#117C22×C414yes—
651#117C22×C412yes—
652#117C22×C414yes—
653#117C2×D412yes—
654#117C2×D412yes—
655#117C2×D414yes—
656#117C2×D414yes—
657C2×C4⋊C4—21no—
658C2×C4⋊C4—21no—
659C2×C4⋊C4—21no—
660C2×C4⋊C4—22no—
661C2×C4⋊C4—22no—
662C2×C4⋊C4—24no—
663C2×C4⋊C4—22no—
664C2×C4⋊C4—24no—
665C2×C4⋊C4C22×C412yes—
666C2×C4⋊C4C22×C414yes—
667C2×C22⋊C4—22no—
668C2×C42—22no—
669C2×C42—24no—
670C2×C42—22no—
671C2×C42—24no—
672C2×C42C22×C411yescharacteristic
673C2×C42C22×C411yescharacteristic
674C2×C42C22×C411yescharacteristic
675C2×C42C2×D411yescharacteristic
676C2×C42C2×D411yescharacteristic
677C2×C42C2×D411yescharacteristic
678C2×C42C2×D411yescharacteristic
679C2×C42C2×D411yescharacteristic
680C2×C42C2×D411yescharacteristic
681C2×C42C2411yescharacteristic
682C2×C42C2414yes—
683C2×C42C2411yescharacteristic
684C2×C42C2411yescharacteristic
685C4⋊C8—22no—
686C4⋊C8—22no—
687C4⋊C8—24no—
688C4⋊C8—22no—
689C4⋊C8—22no—
690C4⋊C8—22no—
691C4⋊C8—22no—
692C4⋊C8—24no—
693C4⋊C8—24no—
694C4⋊C8—24no—
695C4⋊C8C2412yes—
696C4⋊C8C2414yes—
697C4⋊C8C2412yes—
698C22⋊C8—22no—
699C22⋊C8—22no—
700C22⋊C8—21no—
701C22⋊C8—21no—
702C22⋊C8—22no—
703C22⋊C8—22no—
704C22⋊C8—22no—
705C22⋊C8—22no—
706C22⋊C8—22no—
707C22⋊C8—24no—
708C22⋊C8—24no—
709C22⋊C8—24no—
710C22⋊C8—24no—
711#97—22no—
712#97—22no—
713#97—22no—
714#97—22no—
715#97—24no—
716#97—24no—
717C4×C8—22no—
718C4×C8—21no—
719C4×C8—21no—
720C4×C8—24no—
721C4×C8—24no—
722C4×C8C2414yes—
723C4×C8C2414yes—
724C24C2×C22⋊C411yescharacteristic
725#41—44no—
726#41—44no—
727#41—44no—
728#41—44no—
729#41—48no—
730#41—82no—
731#41—82no—
732#41—84no—
733C2×Q8—21no—
734C2×Q8—21no—
735C2×Q8—21no—
736C2×Q8—24no—
737C2×Q8—22no—
738C2×Q8—24no—
739C2×Q8—22no—
740C2×Q8—21no—
741C2×Q8—44no—
742C2×Q8—48no—
743C2×Q8—82no—
744C2×Q8—84no—
745C2×Q8C2×C22⋊C412yes—
746C2×Q8C2×C22⋊C412yes—
747C2×Q8C2×C22⋊C412yes—
748C2×Q8C23×C412yes—
749C2×Q8C23×C412yes—
750C2×Q8C23×C412yes—
751C2×D4—22no—
752C2×D4—22no—
753C2×D4—22no—
754C2×D4—24no—
755C2×D4—24no—
756C2×D4—21no—
757C2×D4—21no—
758C2×D4C2×C22⋊C414yes—
759C2×D4C2×C22⋊C412yes—
760C2×D4C2×C22⋊C412yes—
761C2×D4C2×C22⋊C414yes—
762C2×D4C2×C22⋊C414yes—
763C2×D4C2×C22⋊C412yes—
764C2×D4C23×C412yes—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—24no—
768C22×C4—24no—
769C22×C4—22no—
770C22×C4—22no—
771C22×C4—22no—
772C22×C4—24no—
773C22×C4—24no—
774C22×C4—42no—
775C22×C4—42no—
776C22×C4—81no—
777C22×C4C2×C22⋊C411yescharacteristic
778C22×C4C2×C22⋊C411yescharacteristic
779C22×C4C2×C22⋊C411yescharacteristic
780C22×C4C2×C22⋊C411yescharacteristic
781C22×C4C2×C22⋊C411yescharacteristic
782C22×C4C2×C22⋊C411yescharacteristic
783C22×C4C2×C22⋊C411yescharacteristic
784C22×C4C2×C22⋊C411yescharacteristic
785C22×C4C2×C22⋊C411yescharacteristic
786C22×C4C23×C411yescharacteristic
787C22×C4C23×C411yescharacteristic
788C22×C4C23×C411yescharacteristic
789C22×C4C23×C414yes—
790C22×C4C22×D411yescharacteristic
791C22×C4C22×D414yes—
792C22×C4C22×D411yescharacteristic
793C22×C4C22×D411yescharacteristic
794C22×C4C22×D411yescharacteristic
795C22×C4C22×D411yescharacteristic
796C22×C4C22×D411yescharacteristic
797C22×C4C22×D414yes—
798M16—84no—
799M16—84no—
800M16—82no—
801M16—82no—
802C2×C8—24no—
803C2×C8—24no—
804C2×C8—22no—
805C2×C8—22no—
806C2×C8—24no—
807C2×C8—84no—
808C2×C8—82no—
809C2×C8—82no—
810C2×C8—84no—
811C4⋊C4—21no—
812C4⋊C4—22no—
813C4⋊C4—21no—
814C4⋊C4—22no—
815C4⋊C4—21no—
816C4⋊C4—21no—
817C4⋊C4—22no—
818C4⋊C4—22no—
819C4⋊C4—21no—
820C4⋊C4—21no—
821C4⋊C4—22no—
822C4⋊C4—24no—
823C4⋊C4—24no—
824C4⋊C4—22no—
825C4⋊C4—22no—
826C4⋊C4—24no—
827C4⋊C4—22no—
828C4⋊C4—24no—
829C4⋊C4—22no—
830C4⋊C4—24no—
831C4⋊C4—24no—
832C4⋊C4—22no—
833C4⋊C4—21no—
834C4⋊C4—21no—
835C4⋊C4—21no—
836C4⋊C4—21no—
837C4⋊C4—24no—
838C4⋊C4—22no—
839C4⋊C4—22no—
840C4⋊C4—24no—
841C4⋊C4—22no—
842C4⋊C4—24no—
843C4⋊C4—24no—
844C4⋊C4—24no—
845C4⋊C4—22no—
846C4⋊C4—24no—
847C4⋊C4—22no—
848C4⋊C4—22no—
849C4⋊C4—22no—
850C4⋊C4—22no—
851C4⋊C4C2×C22⋊C412yes—
852C4⋊C4C2×C22⋊C414yes—
853C4⋊C4C2×C22⋊C412yes—
854C4⋊C4C2×C22⋊C412yes—
855C4⋊C4C2×C22⋊C412yes—
856C4⋊C4C2×C22⋊C414yes—
857C4⋊C4C2×C22⋊C414yes—
858C4⋊C4C2×C22⋊C412yes—
859C4⋊C4C2×C22⋊C412yes—
860C4⋊C4C2×C22⋊C414yes—
861C4⋊C4C2×C22⋊C414yes—
862C4⋊C4C2×C22⋊C414yes—
863C4⋊C4C23×C412yes—
864C4⋊C4C23×C412yes—
865C4⋊C4C23×C412yes—
866C4⋊C4C23×C412yes—
867C22⋊C4—22no—
868C22⋊C4—22no—
869C22⋊C4—22no—
870C22⋊C4—22no—
871C22⋊C4—22no—
872C22⋊C4—22no—
873C22⋊C4—24no—
874C22⋊C4—24no—
875C22⋊C4—24no—
876C22⋊C4—22no—
877C22⋊C4—24no—
878C22⋊C4—22no—
879C22⋊C4—24no—
880C22⋊C4—24no—
881C22⋊C4—22no—
882C22⋊C4—22no—
883C22⋊C4—24no—
884C22⋊C4—22no—
885C22⋊C4—22no—
886C22⋊C4—24no—
887C22⋊C4—22no—
888C22⋊C4C2×C22⋊C414yes—
889C22⋊C4C2×C22⋊C414yes—
890C22⋊C4C2×C22⋊C414yes—
891C22⋊C4C2×C22⋊C414yes—
892C22⋊C4C2×C22⋊C414yes—
893C22⋊C4C2×C22⋊C414yes—
894C22⋊C4C2×C22⋊C414yes—
895C22⋊C4C2×C22⋊C414yes—
896C22⋊C4C2×C22⋊C414yes—
897C42—22no—
898C42—22no—
899C42—22no—
900C42—22no—
901C42—24no—
902C42—24no—
903C42—24no—
904C42—24no—
905C42—22no—
906C42—22no—
907C42—22no—
908C42C2×C22⋊C411yescharacteristic
909C42C2×C22⋊C411yescharacteristic
910C42C2×C22⋊C411yescharacteristic
911C42C2×C22⋊C411yescharacteristic
912C42C2×C22⋊C411yescharacteristic
913C42C2×C22⋊C411yescharacteristic
914C42C23×C411yescharacteristic
915C42C23×C411yescharacteristic
916C42C23×C411yescharacteristic
917C42C23×C414yes—
918C42C22×D414yes—
919C42C22×D411yescharacteristic
920C42C22×D411yescharacteristic
921C42C22×D411yescharacteristic
922C42C22×D411yescharacteristic
923C42C22×D411yescharacteristic
924C42C22×D414yes—
925C42C22×D411yescharacteristic
926C42C2511yescharacteristic
927C23—22no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23C22×C22⋊C411yescharacteristic
932C23C22×C22⋊C411yescharacteristic
933C23C22×C22⋊C414yes—
934C23C22×C22⋊C411yescharacteristic
935Q8—24no—
936Q8—24no—
937Q8—24no—
938Q8—42no—
939Q8—42no—
940Q8—42no—
941Q8—42no—
942Q8—42no—
943Q8—42no—
944Q8—82no—
945Q8—84no—
946Q8—82no—
947Q8—84no—
948Q8—81no—
949D4—24no—
950D4—42no—
951D4—44no—
952D4—42no—
953D4—44no—
954D4—44no—
955D4—42no—
956D4—42no—
957D4—44no—
958D4—81no—
959D4—84no—
960D4—82no—
961D4—82no—
962D4—84no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—24no—
966C2×C4—24no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—28no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—44no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—44no—
993C2×C4—44no—
994C2×C4—84no—
995C2×C4—82no—
996C2×C4—84no—
997C2×C4—82no—
998C2×C4—84no—
999C2×C4—82no—
1000C2×C4—84no—
1001C2×C4C22×C22⋊C411yescharacteristic
1002C2×C4C22×C22⋊C411yescharacteristic
1003C2×C4C22×C22⋊C411yescharacteristic
1004C2×C4C22×C22⋊C414yes—
1005C2×C4C22×C22⋊C414yes—
1006C2×C4C22×C22⋊C414yes—
1007C2×C4C22×C22⋊C411yescharacteristic
1008C2×C4C22×C22⋊C411yescharacteristic
1009C2×C4C22×C22⋊C411yescharacteristic
1010C2×C4C22×C22⋊C411yescharacteristic
1011C2×C4C22×C22⋊C411yescharacteristic
1012C2×C4C22×C22⋊C411yescharacteristic
1013C2×C4C24×C411yescharacteristic
1014C2×C4C23×D411yescharacteristic
1015C2×C4C23×D411yescharacteristic
1016C8—44no—
1017C8—44no—
1018C8—42no—
1019C8—44no—
1020C8—42no—
1021C22—21no—
1022C22—21no—
1023C22—21no—
1024C22—24no—
1025C22—21no—
1026C22—21no—
1027C22—21no—
1028C22—24no—
1029C22—21no—
1030C22—21no—
1031C22—21no—
1032C22—24no—
1033C22—42no—
1034C22—42no—
1035C22—42no—
1036C22—82no—
1037C22C23×C22⋊C411yescharacteristic
1038C4—21no—
1039C4—21no—
1040C4—21no—
1041C4—24no—
1042C4—21no—
1043C4—21no—
1044C4—21no—
1045C4—24no—
1046C4—21no—
1047C4—21no—
1048C4—21no—
1049C4—21no—
1050C4—24no—
1051C4—42no—
1052C4—42no—
1053C4—42no—
1054C4—42no—
1055C4—42no—
1056C4—42no—
1057C4—42no—
1058C4#357312yes—
1059C4#358612yes—
1060C2—44no—
1061C2—41no—
1062C2—41no—
1063C2—41no—
1064C2—82no—
1065C2#6006511yescharacteristic
1066C2#6008811yescharacteristic
1067C2#6009311yescharacteristic
subgroupG/H
centerC2×C4C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC42C25
socleC22C23×C22⋊C4
prime radical#62761C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4 ◁ #3444 ◁ G
LECSG ▷ C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #60294C2semidirect
3. #60281C2semidirect
4. #17524C2semidirect
5. #17523C2semidirect
6. #17516C2semidirect
7. #17514C2semidirect
8. #17506C2semidirect
9. #17496C2semidirect
10. #17494C2semidirect
11. #17469C2semidirect
12. #17467C2semidirect
13. #17464C2semidirect
65. #1497C22semidirect
67. #1495C22semidirect
68. #1494C22semidirect
69. #1493C22semidirect
71. #1491C22semidirect
72. #1489C22semidirect
74. #1488C22semidirect
75. #1487C22semidirect
79. #1485C22semidirect
82. #1483C22semidirect
85. #1482C22semidirect
89. #1481C22semidirect
91. #1479C22semidirect
93. #1477C22semidirect
94. #1476C22semidirect
95. C2×Q8⋊C8C22semidirect

Maximal subgroups

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

subgroupindex
#627612
#602942
#602812
#175242
#175232
#175162
#175142
#175062
#174962
#174942
#174692
#174672
#174642