Finite Group Databasebeta

← #6394034

Subgroups — #6394034

Order 512.

2808 conjugacy classes of subgroups.

The subgroup lattice has 1127 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62752C211yesmaximal, characteristic
2#60264C211yesmaximal, characteristic, complemented
3#34081C211yesmaximal, characteristic, complemented
4#22529C214yesmaximal, complemented
5#22507C214yesmaximal, complemented
6#22506C214yesmaximal, complemented
7#22506C214yesmaximal, complemented
8#21858C212yesmaximal, complemented
9#21857C211yesmaximal, characteristic, complemented
10#21846C212yesmaximal, complemented
11#21845C211yesmaximal, characteristic, complemented
12#21419C212yesmaximal, complemented
13#21418C211yesmaximal, characteristic, complemented
14#21330C212yesmaximal, complemented
15#21329C211yesmaximal, characteristic, complemented
16#3565C414yescomplemented
17#3564—22no—
18#3563—21no—
19#3563C412yescomplemented
20#3561—21no—
21#3559C412yescomplemented
22#3555C412yescomplemented
23#3552C412yescomplemented
24#3547C412yescomplemented
25#3544C412yescomplemented
26#3538—21no—
27#3536—21no—
28#3535—22no—
29#3531—22no—
30#3482—22no—
31Q8×#41C2212yes—
32#3475C2212yes—
33#3475C2214yes—
34#3461—22no—
35#3461—22no—
36#3458C2212yes—
37#3455C2212yes—
38#3444C2211yescharacteristic
39C2×#533C2211yescharacteristic
40C2×#529C2211yescharacteristic
41#2995—22no—
42#2994—22no—
43#2993—22no—
44#2992—22no—
45Q8×M16C2212yes—
46D4×M16C2212yes—
47D4×M16C2214yes—
48#2921C2212yes—
49#2920C2211yescharacteristic
50#2905C2212yes—
51C2×#423C2211yescharacteristic
52#2337—21no—
53#2336—21no—
54#2335—22no—
55#2334—22no—
56#2333—21no—
57#2332—21no—
58#2298C2212yes—
59#2295C2212yes—
60#2293C2212yes—
61#2290C2212yes—
62#2290C2212yes—
63#2283C2211yescharacteristic
64C4×#117C2211yescharacteristic
65C4×#117C2212yes—
66#1995C2214yes—
67#1995C2214yes—
68#1995C2212yes—
69#1995C2212yes—
70#1995C2212yes—
71#1994C2214yes—
72#1994C2212yes—
73#1994C2212yes—
74#1994C2211yescharacteristic
75#1994C2211yescharacteristic
76#1986C2214yes—
77#1986C2214yes—
78#1986C2214yes—
79#1963C2212yes—
80#1962C2211yescharacteristic
81#1962C2211yescharacteristic
82#1897C2214yes—
83#1897C2214yes—
84#1896C2214yes—
85#1871C2212yes—
86#1871C2212yes—
87#1871C2214yes—
88#1871C2214yes—
89#1826C2212yes—
90#1826C2212yes—
91#1826C2214yes—
92#1826C2214yes—
93#1806C2214yes—
94#1806C2214yes—
95#1806C2214yes—
96#1759C2214yes—
97#1759C2214yes—
98C4×#104C2214yes—
99#1733C2214yes—
100#1733C2214yes—
101C2×#339C2214yes—
102C22×M16C2312yes—
103C22×M16C2314yes—
104#564—22no—
105#563—24no—
106#563—24no—
107#563—22no—
108#563—22no—
109#563—24no—
110#563—24no—
111#562—22no—
112#562—24no—
113#562—24no—
114Q82C2×C412yescomplemented
115#557—22no—
116#557C2×C412yescomplemented
117#557C2×C414yescomplemented
118#556—24no—
119#556—22no—
120#556C2×C412yes—
121#556C2×C414yescomplemented
122#555C2×C412yes—
123#555C2×C414yescomplemented
124#554—24no—
125#554—22no—
126#554C2×C412yes—
127#554C2×C412yescomplemented
128#554C2×C414yescomplemented
129#554C2×C414yescomplemented
130#553C2×C414yes—
131#553C2×C414yescomplemented
132#553C2×C414yescomplemented
133#552—24no—
134#552—22no—
135#552—24no—
136#552—22no—
137#552—22no—
138#552—24no—
139#552C2×C414yes—
140#552C2×C414yescomplemented
141#552C2×C414yescomplemented
142#551—24no—
143#551—24no—
144#551—24no—
145D4×Q8—22no—
146D4×Q8—22no—
147D4×Q8C2×C412yescomplemented
148#548—22no—
149#548—22no—
150#547—24no—
151#547—22no—
152#547C2×C412yes—
153#547C2×C414yescomplemented
154#546—24no—
155#546—22no—
156#544—22no—
157#544—22no—
158#544—22no—
159#544—22no—
160#544C2×C414yescomplemented
161#544C2×C414yescomplemented
162#544C2×C414yescomplemented
163#544C2×C414yescomplemented
164#543—22no—
165#543—22no—
166#542—24no—
167#542—22no—
168#542—24no—
169#542—24no—
170#542—22no—
171#542C2×C414yescomplemented
172#542C2×C414yescomplemented
173#541—24no—
174#541—24no—
175#541—22no—
176#541—24no—
177#541—22no—
178#541C2×C414yescomplemented
179#540C2×C414yescomplemented
180#539—24no—
181#539—24no—
182#539—24no—
183#539—22no—
184#539—22no—
185#539—22no—
186#539—22no—
187#538—22no—
188#538—22no—
189#537—22no—
190#537—22no—
191#536—22no—
192#536—24no—
193#536—22no—
194#533—22no—
195#533—24no—
196#533—24no—
197#533—24no—
198#533—21no—
199#533—21no—
200#533—21no—
201#533—21no—
202#533C2×C411yescharacteristic, complemented
203#533C2×C411yescharacteristic, complemented
204#533C2×C412yescomplemented
205#533C2×C412yescomplemented
206#533C2312yes—
207#533C2312yes—
208#533C2311yescharacteristic
209#533C2314yes—
210#532C2×C411yescharacteristic, complemented
211#532C2×C411yescharacteristic, complemented
212#532C2311yescharacteristic
213C2×C4⋊Q8C2×C411yescharacteristic, complemented
214C2×C4⋊Q8C2×C411yescharacteristic, complemented
215#529—24no—
216#529—22no—
217#529—24no—
218#529—24no—
219#529—24no—
220#529—24no—
221#529—24no—
222#529—21no—
223#529—21no—
224#529—21no—
225#529—21no—
226#529C2×C412yes—
227#529C2×C412yes—
228#529C2×C412yes—
229#529C2×C412yes—
230#529C2×C412yescomplemented
231#529C2×C412yescomplemented
232#529D412yes—
233#529D412yes—
234#529D412yes—
235#529D412yes—
236C2×#126D412yes—
237C2×#125C2×C412yescomplemented
238C2×#125D411yescharacteristic
239C2×#124D411yescharacteristic
240#525—21no—
241#525—21no—
242#525C2314yes—
243#525C2312yes—
244C2×#123D412yes—
245C2×C22⋊Q8—21no—
246C2×C22⋊Q8—21no—
247C2×C22⋊Q8D411yescharacteristic
248C2×#121D411yescharacteristic
249C4×#41—24no—
250C4×#41—22no—
251C4×#41—21no—
252C4×#41—21no—
253C4×#41C2312yes—
254C4×#41C2314yes—
255C2×C4×Q8—22no—
256C2×C4×Q8—21no—
257C2×C4×Q8—21no—
258C2×C4×Q8C2311yescharacteristic
259C2×C4×D4C2311yescharacteristic
260C2×C4×D4C2312yes—
261C2×#117C2312yes—
262C2×#117C2314yes—
263C2×#117C2312yes—
264C2×#117C2312yes—
265C2×#117C2312yes—
266C22×C42C2312yes—
267C22×C42C2311yescharacteristic
268#446—24no—
269#446—22no—
270C8×Q8—22no—
271#436—22no—
272#436—24no—
273#435—24no—
274#435—24no—
275#435—24no—
276C8×D4—24no—
277C8×D4—22no—
278#433—24no—
279#433—24no—
280#432—21no—
281#432—21no—
282#431—21no—
283#431—21no—
284#424—24no—
285#424—24no—
286#423—21no—
287#423—21no—
288#423C2312yes—
289#423C2314yes—
290#423C2312yes—
291#423C2311yescharacteristic
292#423C2311yescharacteristic
293C2×C4⋊C8—21no—
294C2×C4⋊C8—21no—
295C2×#104C2314yes—
296C2×#104C2314yes—
297C2×#104C2314yes—
298C2×#104C2314yes—
299#407C2314yes—
300#407C2312yes—
301C4×M16C2312yes—
302C4×M16C2314yes—
303#391—22no—
304#390—22no—
305#389—22no—
306#389—22no—
307#388—22no—
308#388—22no—
309#388—22no—
310#388—22no—
311#388—22no—
312#388—22no—
313#387—22no—
314#387—22no—
315#387—22no—
316#387—22no—
317#387—22no—
318#387—22no—
319#386—22no—
320#386—22no—
321#385—22no—
322#385—22no—
323#383—21no—
324#382—21no—
325#381—21no—
326#380—21no—
327C4×C4⋊C4—22no—
328C4×C4⋊C4—22no—
329C4×C4⋊C4—21no—
330C4×C4⋊C4—21no—
331C4×C4⋊C4C2312yes—
332C4×C4⋊C4C2312yes—
333C4×C4⋊C4C2312yes—
334C4×C22⋊C4—21no—
335C4×C22⋊C4—21no—
336C4×C22⋊C4—22no—
337C4×C22⋊C4—22no—
338C4×C22⋊C4C2311yescharacteristic
339C4×C22⋊C4C2311yescharacteristic
340C4×C22⋊C4C2312yes—
341C4×C22⋊C4C2312yes—
342#376C2312yes—
343#376C2312yes—
344#376C2312yes—
345C43C2311yescharacteristic
346C43C2311yescharacteristic
347C43C2312yes—
348#339C2314yes—
349#339C2314yes—
350#339C2314yes—
351#339C2314yes—
352#339C2314yes—
353#339C2314yes—
354#339C2314yes—
355#339C2314yes—
356#339C2314yes—
357#339C2314yes—
358#339C2314yes—
359#339C2314yes—
360C2×#41—24no—
361C2×#41—22no—
362C2×#41—21no—
363C2×#41—21no—
364C2×#41C2412yes—
365C22×Q8—22no—
366C22×Q8—21no—
367C22×Q8—21no—
368C22×Q8C2×D411yescharacteristic
369C22×D4C2×D412yes—
370C22×D4C2×D411yescharacteristic
371C23×C4—22no—
372C23×C4C2×D411yescharacteristic
373C23×C4C2×D411yescharacteristic
374C23×C4C2412yes—
375C23×C4C2411yescharacteristic
376C2×M16—22no—
377C2×M16—24no—
378C2×M16—44no—
379C2×M16—44no—
380C2×M16—44no—
381C2×M16C2414yes—
382C2×M16C2412yes—
383C2×M16C2412yes—
384C22×C8—22no—
385C22×C8—24no—
386C4⋊Q8—22no—
387C4⋊Q8—24no—
388C4⋊Q8—24no—
389C4⋊Q8—24no—
390C4⋊Q8—24no—
391C4⋊Q8—22no—
392C4⋊Q8—24no—
393C4⋊Q8—24no—
394C4⋊Q8—21no—
395C4⋊Q8—21no—
396C4⋊Q8—21no—
397C4⋊Q8—21no—
398C4⋊Q8C22×C411yescharacteristic
399C4⋊Q8C22×C412yes—
400C4⋊Q8C22×C412yes—
401C4⋊Q8C22×C412yes—
402C4⋊Q8C22×C412yes—
403C4⋊Q8C22×C411yescharacteristic
404C4⋊Q8C22×C411yescharacteristic
405C4⋊Q8C22×C414yes—
406C4⋊Q8C22×C414yes—
407#127C22×C411yescharacteristic
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—24no—
417#126—24no—
418#126—24no—
419#126—24no—
420#126—24no—
421#126—22no—
422#126—22no—
423#126C22⋊C414yes—
424#126C22⋊C414yes—
425#126C22⋊C414yes—
426#126C22⋊C414yes—
427#125—24no—
428#125—24no—
429#125—24no—
430#125—24no—
431#125—22no—
432#125—24no—
433#125—24no—
434#125—24no—
435#125—24no—
436#125—24no—
437#125—24no—
438#125—24no—
439#125—24no—
440#125—24no—
441#125—22no—
442#125—22no—
443#125—21no—
444#125—21no—
445#125C22⋊C412yes—
446#125C22⋊C412yes—
447#125C22⋊C412yes—
448#125C22⋊C412yes—
449#125C22×C414yes—
450#125C22×C414yes—
451#125C22×C412yes—
452#125C22×C414yes—
453#125C22×C414yes—
454#124—22no—
455#124—24no—
456#124—24no—
457#124—24no—
458#124—24no—
459#124—24no—
460#124—24no—
461#124—21no—
462#124—21no—
463#124C22⋊C412yes—
464#124C22⋊C412yes—
465#124C22⋊C412yes—
466#124C22⋊C412yes—
467#124C22×C412yes—
468#123—24no—
469#123—24no—
470#123—24no—
471#123—22no—
472#123—22no—
473#123—22no—
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#123—24no—
483#123—24no—
484#123—24no—
485#123C22⋊C414yes—
486#123C22⋊C414yes—
487#123C22⋊C414yes—
488#123C22⋊C414yes—
489C22⋊Q8—22no—
490C22⋊Q8—24no—
491C22⋊Q8—22no—
492C22⋊Q8—22no—
493C22⋊Q8—22no—
494C22⋊Q8—22no—
495C22⋊Q8—21no—
496C22⋊Q8—21no—
497C22⋊Q8—22no—
498C22⋊Q8—22no—
499C22⋊Q8—22no—
500C22⋊Q8—22no—
501C22⋊Q8—21no—
502C22⋊Q8—21no—
503C22⋊Q8—24no—
504C22⋊Q8—24no—
505C22⋊Q8—24no—
506C22⋊Q8—22no—
507C22⋊Q8—24no—
508C22⋊Q8—24no—
509C22⋊Q8—24no—
510C22⋊Q8—22no—
511C22⋊Q8—24no—
512C22⋊Q8—24no—
513C22⋊Q8—24no—
514C22⋊Q8—24no—
515C22⋊Q8—24no—
516C22⋊Q8—24no—
517C22⋊Q8—24no—
518C22⋊Q8—24no—
519C22⋊Q8—24no—
520C22⋊Q8—24no—
521C22⋊Q8—24no—
522C22⋊Q8—24no—
523C22⋊Q8—24no—
524C22⋊Q8—24no—
525C22⋊Q8C22⋊C412yes—
526C22⋊Q8C22⋊C412yes—
527C22⋊Q8C22⋊C412yes—
528C22⋊Q8C22⋊C412yes—
529C22⋊Q8C22×C412yes—
530C22⋊Q8C22×C412yes—
531C22⋊Q8C22×C414yes—
532C22⋊Q8C22×C414yes—
533#121—24no—
534#121—24no—
535#121—22no—
536#121—24no—
537#121—24no—
538#121—21no—
539#121—21no—
540#121—21no—
541#121—21no—
542#121—24no—
543#121—24no—
544#121C22⋊C412yes—
545#121C22⋊C412yes—
546#121C22⋊C412yes—
547#121C22⋊C412yes—
548#121C22×C412yes—
549#121C22×C412yes—
550#121C22×C414yes—
551#121C22×C414yes—
552#120—22no—
553#120—24no—
554C4×Q8—22no—
555C4×Q8—22no—
556C4×Q8—24no—
557C4×Q8—22no—
558C4×Q8—24no—
559C4×Q8—22no—
560C4×Q8—22no—
561C4×Q8—22no—
562C4×Q8—22no—
563C4×Q8—21no—
564C4×Q8—21no—
565C4×Q8—22no—
566C4×Q8—22no—
567C4×Q8—24no—
568C4×Q8—22no—
569C4×Q8—22no—
570C4×Q8—24no—
571C4×Q8—21no—
572C4×Q8—21no—
573C4×Q8C22×C412yes—
574C4×Q8C22×C412yes—
575C4×Q8C22×C414yes—
576C4×Q8C22×C414yes—
577C4×Q8C22×C412yes—
578C4×Q8C22×C412yes—
579C4×Q8C2×D412yes—
580C4×Q8C2×D412yes—
581C4×D4—24no—
582C4×D4—22no—
583C4×D4—22no—
584C4×D4—22no—
585C4×D4—22no—
586C4×D4—24no—
587C4×D4—24no—
588C4×D4—22no—
589C4×D4—22no—
590C4×D4—22no—
591C4×D4—24no—
592C4×D4—24no—
593C4×D4—24no—
594C4×D4—24no—
595C4×D4—24no—
596C4×D4—21no—
597C4×D4—21no—
598C4×D4—21no—
599C4×D4—21no—
600C4×D4C22×C412yes—
601C4×D4C22×C412yes—
602C4×D4C22×C414yes—
603C4×D4C22×C414yes—
604C4×D4C22×C412yes—
605C4×D4C22×C414yes—
606C4×D4C22×C412yes—
607C4×D4C22×C414yes—
608C4×D4C2×D412yes—
609C4×D4C2×D414yes—
610C4×D4C2×D414yes—
611C4×D4C2×D412yes—
612#117—21no—
613#117—21no—
614#117—24no—
615#117—22no—
616#117—22no—
617#117—24no—
618#117—22no—
619#117—24no—
620#117—24no—
621#117—24no—
622#117—24no—
623#117—22no—
624#117—22no—
625#117—22no—
626#117—24no—
627#117—24no—
628#117—24no—
629#117—42no—
630#117—42no—
631#117C22×C414yes—
632#117C22×C414yes—
633#117C22×C414yes—
634#117C22×C414yes—
635#117C22×C414yes—
636#117C2×D414yes—
637#117C2×D414yes—
638#117C2414yes—
639#117C2412yes—
640C2×C4⋊C4—22no—
641C2×C4⋊C4—22no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4—22no—
645C2×C4⋊C4—24no—
646C2×C4⋊C4—22no—
647C2×C4⋊C4—22no—
648C2×C4⋊C4—22no—
649C2×C4⋊C4—22no—
650C2×C4⋊C4—22no—
651C2×C4⋊C4C22×C412yes—
652C2×C4⋊C4C22×C412yes—
653C2×C4⋊C4C22×C414yes—
654C2×C4⋊C4C22×C414yes—
655C2×C4⋊C4C2×D412yes—
656C2×C4⋊C4C2×D412yes—
657C2×C4⋊C4C2×D411yescharacteristic
658C2×C4⋊C4C2×D412yes—
659C2×C4⋊C4C2×D411yescharacteristic
660C2×C4⋊C4C2×D412yes—
661C2×C22⋊C4—22no—
662C2×C22⋊C4—24no—
663C2×C22⋊C4—22no—
664C2×C22⋊C4—22no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—22no—
668C2×C22⋊C4—22no—
669C2×C22⋊C4C2×D412yes—
670C2×C22⋊C4C2×D412yes—
671C2×C22⋊C4C2×D412yes—
672C2×C22⋊C4C2×D412yes—
673C2×C22⋊C4C2×D412yes—
674C2×C42—22no—
675C2×C42—24no—
676C2×C42—22no—
677C2×C42—24no—
678C2×C42—24no—
679C2×C42—22no—
680C2×C42—21no—
681C2×C42—21no—
682C2×C42—21no—
683C2×C42—21no—
684C2×C42—22no—
685C2×C42—22no—
686C2×C42—42no—
687C2×C42C22×C411yescharacteristic
688C2×C42C22×C411yescharacteristic
689C2×C42C22×C411yescharacteristic
690C2×C42C22×C411yescharacteristic
691C2×C42C2×D411yescharacteristic
692C2×C42C2×D411yescharacteristic
693C2×C42C2×D411yescharacteristic
694C2×C42C2×D411yescharacteristic
695C2×C42C2×D411yescharacteristic
696C2×C42C2×D411yescharacteristic
697C2×C42C2412yes—
698C2×C42C2412yes—
699C2×C42C2412yes—
700C2×C42C2412yes—
701C2×C42C2411yescharacteristic
702C2×C42C2412yes—
703C2×C42C2411yescharacteristic
704C4⋊C8—22no—
705C4⋊C8—22no—
706C4⋊C8—22no—
707C4⋊C8—22no—
708C4⋊C8—21no—
709C4⋊C8—21no—
710C4⋊C8—24no—
711C4⋊C8—24no—
712C4⋊C8—21no—
713C4⋊C8—21no—
714#104—28no—
715#104—44no—
716#104—44no—
717#104—44no—
718C22⋊C8—22no—
719C22⋊C8—22no—
720C22⋊C8—24no—
721C22⋊C8—24no—
722#97—22no—
723#97—24no—
724C4×C8—22no—
725C4×C8—24no—
726#95—22no—
727#95—22no—
728#95—22no—
729#95—22no—
730#95—22no—
731#95—22no—
732#95—21no—
733#95—21no—
734#95—22no—
735#95—22no—
736#95—22no—
737#95—22no—
738#95—22no—
739C24C22×D411yescharacteristic
740C24C22×D412yes—
741#41—24no—
742#41—24no—
743#41—82no—
744#41—82no—
745#41—88no—
746#41—84no—
747C2×Q8—22no—
748C2×Q8—24no—
749C2×Q8—22no—
750C2×Q8—22no—
751C2×Q8—22no—
752C2×Q8—24no—
753C2×Q8—21no—
754C2×Q8—21no—
755C2×Q8—81no—
756C2×Q8—82no—
757C2×Q8—82no—
758C2×Q8—84no—
759C2×Q8C2×C22⋊C412yes—
760C2×Q8C2×C22⋊C412yes—
761C2×Q8C23×C412yes—
762C2×D4—22no—
763C2×D4—22no—
764C2×D4—22no—
765C2×D4—24no—
766C2×D4—24no—
767C2×D4—21no—
768C2×D4—21no—
769C2×D4—82no—
770C2×D4—81no—
771C2×D4C2×C22⋊C414yes—
772C2×D4C2×C22⋊C412yes—
773C2×D4C2×C22⋊C412yes—
774C2×D4C2×C22⋊C414yes—
775C2×D4C23×C412yes—
776C22×C4—22no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—22no—
780C22×C4—22no—
781C22×C4—22no—
782C22×C4—22no—
783C22×C4—22no—
784C22×C4—22no—
785C22×C4—24no—
786C22×C4—24no—
787C22×C4—22no—
788C22×C4—22no—
789C22×C4—22no—
790C22×C4—24no—
791C22×C4—24no—
792C22×C4—22no—
793C22×C4—22no—
794C22×C4—22no—
795C22×C4—44no—
796C22×C4—81no—
797C22×C4—81no—
798C22×C4—82no—
799C22×C4—82no—
800C22×C4C2×C22⋊C411yescharacteristic
801C22×C4C2×C22⋊C411yescharacteristic
802C22×C4C2×C22⋊C411yescharacteristic
803C22×C4C2×C22⋊C411yescharacteristic
804C22×C4C2×C22⋊C411yescharacteristic
805C22×C4C2×C22⋊C411yescharacteristic
806C22×C4C2×C22⋊C411yescharacteristic
807C22×C4C2×C22⋊C411yescharacteristic
808C22×C4C23×C411yescharacteristic
809C22×C4C23×C411yescharacteristic
810C22×C4C23×C414yes—
811C22×C4C22×D412yes—
812C22×C4C22×D411yescharacteristic
813C22×C4C22×D411yescharacteristic
814C22×C4C22×D414yes—
815C22×C4C22×D411yescharacteristic
816C22×C4C22×D411yescharacteristic
817C22×C4C22×D411yescharacteristic
818C22×C4C22×D411yescharacteristic
819C22×C4C22×D412yes—
820C22×C4C22×D412yes—
821C22×C4C22×D411yescharacteristic
822C22×C4C2511yescharacteristic
823M16—24no—
824M16—24no—
825M16—24no—
826M16—24no—
827M16—84no—
828M16—82no—
829C2×C8—22no—
830C2×C8—22no—
831C2×C8—24no—
832C2×C8—82no—
833C2×C8—84no—
834C4⋊C4—22no—
835C4⋊C4—24no—
836C4⋊C4—24no—
837C4⋊C4—24no—
838C4⋊C4—24no—
839C4⋊C4—24no—
840C4⋊C4—24no—
841C4⋊C4—24no—
842C4⋊C4—22no—
843C4⋊C4—22no—
844C4⋊C4—22no—
845C4⋊C4—24no—
846C4⋊C4—24no—
847C4⋊C4—22no—
848C4⋊C4—22no—
849C4⋊C4—22no—
850C4⋊C4—24no—
851C4⋊C4—21no—
852C4⋊C4—21no—
853C4⋊C4—21no—
854C4⋊C4—21no—
855C4⋊C4—24no—
856C4⋊C4—24no—
857C4⋊C4—22no—
858C4⋊C4—22no—
859C4⋊C4—24no—
860C4⋊C4—24no—
861C4⋊C4—22no—
862C4⋊C4—24no—
863C4⋊C4—22no—
864C4⋊C4—24no—
865C4⋊C4—22no—
866C4⋊C4—44no—
867C4⋊C4—44no—
868C4⋊C4—82no—
869C4⋊C4—82no—
870C4⋊C4—82no—
871C4⋊C4C2×C22⋊C412yes—
872C4⋊C4C2×C22⋊C414yes—
873C4⋊C4C2×C22⋊C412yes—
874C4⋊C4C2×C22⋊C414yes—
875C4⋊C4C2×C22⋊C414yes—
876C4⋊C4C2×C22⋊C414yes—
877C4⋊C4C2×C22⋊C414yes—
878C4⋊C4C2×C22⋊C414yes—
879C4⋊C4C2×C22⋊C414yes—
880C4⋊C4C2×C22⋊C412yes—
881C4⋊C4C2×C22⋊C412yes—
882C4⋊C4C2×C22⋊C414yes—
883C4⋊C4C23×C414yes—
884C4⋊C4C23×C414yes—
885C4⋊C4C23×C412yes—
886C4⋊C4C23×C412yes—
887C22⋊C4—24no—
888C22⋊C4—24no—
889C22⋊C4—24no—
890C22⋊C4—22no—
891C22⋊C4—22no—
892C22⋊C4—24no—
893C22⋊C4—24no—
894C22⋊C4—24no—
895C22⋊C4—22no—
896C22⋊C4—22no—
897C22⋊C4—22no—
898C22⋊C4—22no—
899C22⋊C4—24no—
900C22⋊C4—24no—
901C22⋊C4—22no—
902C22⋊C4—24no—
903C22⋊C4—22no—
904C22⋊C4—24no—
905C22⋊C4—22no—
906C22⋊C4—44no—
907C22⋊C4—44no—
908C22⋊C4—81no—
909C22⋊C4—82no—
910C22⋊C4—82no—
911C22⋊C4—81no—
912C22⋊C4C2×C22⋊C414yes—
913C22⋊C4C2×C22⋊C414yes—
914C22⋊C4C2×C22⋊C414yes—
915C22⋊C4C2×C22⋊C414yes—
916C22⋊C4C2×C22⋊C414yes—
917C22⋊C4C2×C22⋊C414yes—
918C22⋊C4C2×C22⋊C414yes—
919C22⋊C4C2×C22⋊C414yes—
920C22⋊C4C2×C22⋊C414yes—
921C22⋊C4C2×C22⋊C414yes—
922C42—24no—
923C42—22no—
924C42—24no—
925C42—22no—
926C42—24no—
927C42—24no—
928C42—24no—
929C42—24no—
930C42—22no—
931C42—22no—
932C42—22no—
933C42—22no—
934C42—22no—
935C42—22no—
936C42—22no—
937C42—22no—
938C42—44no—
939C42—81no—
940C42—81no—
941C42—81no—
942C42—81no—
943C42—82no—
944C42—82no—
945C42C2×C22⋊C411yescharacteristic
946C42C2×C22⋊C411yescharacteristic
947C42C2×C22⋊C411yescharacteristic
948C42C2×C22⋊C411yescharacteristic
949C42C2×C22⋊C411yescharacteristic
950C42C2×C22⋊C411yescharacteristic
951C42C2×C22⋊C411yescharacteristic
952C42C2×C22⋊C411yescharacteristic
953C42C23×C411yescharacteristic
954C42C23×C411yescharacteristic
955C42C23×C411yescharacteristic
956C42C23×C411yescharacteristic
957C42C23×C414yes—
958C42C22×D411yescharacteristic
959C42C22×D414yes—
960C42C22×D411yescharacteristic
961C42C22×D411yescharacteristic
962C42C22×D411yescharacteristic
963C422−1+414yes—
964C23—22no—
965C23—22no—
966C23—22no—
967C23—22no—
968C23—41no—
969C23—42no—
970C23—42no—
971C23—41no—
972C23C22×C22⋊C411yescharacteristic
973C23C22×C22⋊C414yes—
974C23C22×C22⋊C411yescharacteristic
975C23C23×D411yescharacteristic
976Q8—24no—
977Q8—42no—
978Q8—42no—
979Q8—44no—
980Q8—82no—
981Q8—82no—
982Q8—82no—
983Q8—84no—
984Q8—81no—
985Q8—81no—
986Q8—84no—
987D4—24no—
988D4—42no—
989D4—44no—
990D4—42no—
991D4—44no—
992D4—44no—
993D4—44no—
994D4—81no—
995D4—81no—
996D4—82no—
997D4—84no—
998D4—84no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—24no—
1003C2×C4—24no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—24no—
1007C2×C4—21no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—24no—
1011C2×C4—21no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—24no—
1015C2×C4—22no—
1016C2×C4—24no—
1017C2×C4—24no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—42no—
1021C2×C4—42no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—44no—
1033C2×C4—42no—
1034C2×C4—42no—
1035C2×C4—44no—
1036C2×C4—42no—
1037C2×C4—42no—
1038C2×C4—42no—
1039C2×C4—42no—
1040C2×C4—42no—
1041C2×C4—42no—
1042C2×C4—42no—
1043C2×C4—42no—
1044C2×C4—42no—
1045C2×C4—42no—
1046C2×C4—42no—
1047C2×C4—84no—
1048C2×C4—82no—
1049C2×C4—84no—
1050C2×C4—82no—
1051C2×C4—84no—
1052C2×C4—84no—
1053C2×C4—88no—
1054C2×C4C22×C22⋊C411yescharacteristic
1055C2×C4C22×C22⋊C411yescharacteristic
1056C2×C4C22×C22⋊C411yescharacteristic
1057C2×C4C22×C22⋊C414yes—
1058C2×C4C22×C22⋊C414yes—
1059C2×C4C22×C22⋊C414yes—
1060C2×C4C22×C22⋊C411yescharacteristic
1061C2×C4C22×C22⋊C411yescharacteristic
1062C2×C4C22×C22⋊C411yescharacteristic
1063C2×C4C22×C22⋊C411yescharacteristic
1064C2×C4C22×C22⋊C411yescharacteristic
1065C2×C4C22×C22⋊C411yescharacteristic
1066C2×C4C22×C22⋊C411yescharacteristic
1067C2×C4C24×C411yescharacteristic
1068C2×C4C23×D411yescharacteristic
1069C2×C4C2×2−1+412yes—
1070C2×C4#58512yes—
1071C8—42no—
1072C8—42no—
1073C8—44no—
1074C22—21no—
1075C22—21no—
1076C22—21no—
1077C22—21no—
1078C22—21no—
1079C22—21no—
1080C22—24no—
1081C22—24no—
1082C22—21no—
1083C22—24no—
1084C22—21no—
1085C22—42no—
1086C22—42no—
1087C22—42no—
1088C22—82no—
1089C22—82no—
1090C22—82no—
1091C22C23×C22⋊C411yescharacteristic
1092C22#348912yes—
1093C4—21no—
1094C4—21no—
1095C4—21no—
1096C4—21no—
1097C4—21no—
1098C4—21no—
1099C4—21no—
1100C4—21no—
1101C4—24no—
1102C4—24no—
1103C4—24no—
1104C4—21no—
1105C4—21no—
1106C4—44no—
1107C4—42no—
1108C4—44no—
1109C4—42no—
1110C4—44no—
1111C4—42no—
1112C4—82no—
1113C4—82no—
1114C4—82no—
1115C4C4×2−1+412yes—
1116C4#349911yescharacteristic
1117C4#350011yescharacteristic
1118C2—22no—
1119C2—41no—
1120C2—41no—
1121C2—44no—
1122C2—82no—
1123C2#3425911yescharacteristic
1124C2#6009311yescharacteristic
1125C2#6009311yescharacteristic
subgroupG/H
centerC2×C4C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
socleC22C23×C22⋊C4
prime radical#62752C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4 ◁ C2×#529 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #60264C2semidirect
3. #34081C2semidirect
4. #22529C2semidirect
5. #22507C2semidirect
6. #22506C2semidirect
7. #22506C2semidirect
8. #21858C2semidirect
9. #21857C2semidirect
10. #21846C2semidirect
11. #21845C2semidirect
12. #21419C2semidirect
13. #21418C2semidirect
14. #21330C2semidirect
15. #21329C2semidirect
16. #3565C4semidirect
19. #3563C4semidirect
21. #3559C4semidirect
22. #3555C4semidirect
23. #3552C4semidirect
24. #3547C4semidirect
25. #3544C4semidirect
114. Q82C2×C4semidirect
116. #557C2×C4semidirect
117. #557C2×C4semidirect
121. #556C2×C4semidirect
123. #555C2×C4semidirect
127. #554C2×C4semidirect
128. #554C2×C4semidirect
129. #554C2×C4semidirect
131. #553C2×C4semidirect
132. #553C2×C4semidirect
140. #552C2×C4semidirect
141. #552C2×C4semidirect
147. D4×Q8C2×C4semidirect
153. #547C2×C4semidirect
160. #544C2×C4semidirect
161. #544C2×C4semidirect
162. #544C2×C4semidirect
163. #544C2×C4semidirect
171. #542C2×C4semidirect
172. #542C2×C4semidirect
178. #541C2×C4semidirect
179. #540C2×C4semidirect
202. #533C2×C4semidirect
203. #533C2×C4semidirect
204. #533C2×C4semidirect
205. #533C2×C4semidirect
210. #532C2×C4semidirect
211. #532C2×C4semidirect
213. C2×C4⋊Q8C2×C4semidirect
214. C2×C4⋊Q8C2×C4semidirect
230. #529C2×C4semidirect
231. #529C2×C4semidirect
237. C2×#125C2×C4semidirect

Maximal subgroups

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

subgroupindex
#627522
#602642
#340812
#225292
#225072
#225062
#218582
#218572
#218462
#218452
#214192
#214182
#213302
#213292