Finite Group Databasebeta

← #10574493

Subgroups — #10574493

Order 512.

6837 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62800C211yesmaximal, characteristic
2#60328C212yesmaximal, complemented
3#60325C212yesmaximal, complemented
4#60323C216yesmaximal, complemented
5#60321C216yesmaximal, complemented
6#60308C212yesmaximal, complemented
7#60306C216yesmaximal, complemented
8#60305C216yesmaximal, complemented
9C8×H(5,𝔽2)C212yesmaximal, complemented
10#60274C212yesmaximal, complemented
11#60268C213yesmaximal, complemented
12#60263C211yesmaximal, characteristic, complemented
13#60239C216yesmaximal, complemented
14#60236C213yesmaximal, complemented
15#60218C212yesmaximal, complemented
16#60204C213yesmaximal, complemented
17C2×C8×#41C211yesmaximal, characteristic, complemented
18D4×#131C216yesmaximal, complemented
19C2×#2931C213yesmaximal, complemented
20C22×#131C2216yescomplemented
21#3522C412yes—
22#3519C416yes—
23#3517C412yes—
24#3514C416yes—
25#3511C413yes—
26#3508C413yes—
27#3503C411yescharacteristic
28#3498C411yescharacteristic
29#3494C416yes—
30#3488C412yes—
31#3483C2212yes—
32#3481C2216yes—
33#3480C2212yes—
34D4×#41C2216yes—
35#3460C2216yes—
36#3444C2213yes—
37C2×#532C2213yes—
38C4×H(5,𝔽2)C2212yes—
39C2×C4×#41C2211yescharacteristic
40#2994C22112yescomplemented
41#2994C22112yescomplemented
42#2993C22112yescomplemented
43#2993C22112yescomplemented
44#2991C2212yescomplemented
45#2991C2216yescomplemented
46#2991C2214yescomplemented
47#2990C2216yescomplemented
48#2990C2216yescomplemented
49#2989C2216yescomplemented
50#2989C2216yescomplemented
51#2988C2212yes—
52#2988C2216yescomplemented
53#2988C2214yescomplemented
54#2981C22112yescomplemented
55#2981C22112yescomplemented
56#2979C2216yescomplemented
57#2979C2216yescomplemented
58#2979C22112yescomplemented
59#2977C22124yescomplemented
60#2976C22124yescomplemented
61#2975C2216yescomplemented
62#2974C22112yescomplemented
63#2974C22112yescomplemented
64#2972C2216yescomplemented
65#2972C22112yescomplemented
66#2971C2214yescomplemented
67#2969C22112yescomplemented
68#2966C2216yescomplemented
69#2966C2216yescomplemented
70#2966C2216yescomplemented
71#2966C2216yescomplemented
72#2966C22112yescomplemented
73#2965C2216yescomplemented
74#2965C2216yescomplemented
75C8×#41C2211yescharacteristic
76C8×#41C2211yescharacteristic
77C8×#41C2213yescomplemented
78C8×#41C2213yescomplemented
79C8×#41C2211yescharacteristic, complemented
80C8×#41C2213yescomplemented
81C8×#41C2213yescomplemented
82C8×#41C2211yescharacteristic, complemented
83C8×#41C2216yescomplemented
84C8×#41C2216yescomplemented
85C8×#41C2214yescomplemented
86Q8×M16C2212yescomplemented
87#2960C2211yescharacteristic, complemented
88#2960C2213yescomplemented
89C2×C8×Q8C2211yescharacteristic, complemented
90C2×C8×Q8C2211yescharacteristic, complemented
91#2935C2216yescomplemented
92#2935C2216yescomplemented
93#2935C22112yescomplemented
94D4×M16C2216yescomplemented
95D4×M16C22112yescomplemented
96#2933C22112yescomplemented
97#2933C22124yescomplemented
98#2931C2213yescomplemented
99#2931C2213yescomplemented
100#2931C2216yescomplemented
101#2931C2216yescomplemented
102#2931C2216yescomplemented
103#2931C2216yescomplemented
104#2931C2216yescomplemented
105#2931C22112yescomplemented
106#2931C2216yescomplemented
107#2931C2216yescomplemented
108#2929C2216yescomplemented
109#2929C2216yescomplemented
110#2929C22124yescomplemented
111C2×#436C2216yescomplemented
112C2×#436C2216yescomplemented
113C2×C8×D4C2213yescomplemented
114C2×C8×D4C2213yescomplemented
115C2×C8×D4C22112yescomplemented
116C2×C8×D4C2216yescomplemented
117C2×C8×D4C2216yescomplemented
118#2925C2216yescomplemented
119#2922C2216yescomplemented
120#2920C2213yescomplemented
121C2×#431C2213yescomplemented
122#2906C2216yescomplemented
123C2×#423C2213yescomplemented
124#2880C22112yescomplemented
125C2×#408C2216yescomplemented
126C4×#131C2216yescomplemented
127C22×C4×C8C2213yescomplemented
128C2×H(5,𝔽2)C2×C412yes—
129C22×#41C2×C411yescharacteristic
130C22×#41C2316yes—
131C2×#131—424no—
132C2×#131C2316yes—
133C2×#131C2316yes—
134C2×#131C23112yes—
135C2×#131C23112yes—
136C2×#131C23112yes—
137C22×M16C2316yes—
138C22×M16C23112yes—
139C23×C8C2313yes—
140C23×C8C2313yes—
141C23×C8C23112yes—
142#559C2×C416yes—
143#559C2×C416yes—
144Q82C2×C412yes—
145#557C2×C412yes—
146#556C2×C416yes—
147#555C2×C4112yes—
148#555C2×C416yes—
149#554C2×C416yes—
150#554C2×C416yes—
151#553C2×C4112yes—
152#553C2×C4112yes—
153#553C2×C4112yes—
154#551C2×C4124yes—
155#550C2×C416yes—
156#550C2×C412yes—
157#550C2×C414yes—
158#550C2×C412yes—
159#550C2×C416yes—
160D4×Q8C2×C416yes—
161#548C2×C4112yes—
162#548C2×C414yes—
163#547C2×C4112yes—
164#547C2×C416yes—
165#546C2×C4124yes—
166#546C2×C4112yes—
167#546C2×C4112yes—
168#546C2×C4112yes—
169D42C2×C4112yes—
170D42C2×C416yes—
171D42C2×C416yes—
172#544C2×C416yes—
173#542C2×C4112yes—
174#542C2×C4112yes—
175#540C2×C4112yes—
176#540C2×C4112yes—
177#538C2×C4124yes—
178#537C2×C416yes—
179#535C2×C416yes—
180#535C2×C416yes—
181#533C2×C413yes—
182#533C2×C413yes—
183#533C2311yescharacteristic
184#532C2×C416yes—
185#532C2×C416yes—
186#532C2×C416yes—
187#532C2×C416yes—
188#532C2×C413yes—
189#532C2×C413yes—
190#532C2313yes—
191#532C2316yes—
192#532C2316yes—
193#532C2316yes—
194#532C23112yes—
195C2×C4⋊Q8C2×C413yes—
196C2×#127C2×C413yes—
197#529C2×C416yes—
198#529C2×C416yes—
199#529C2×C416yes—
200#529C2×C416yes—
201#529C2316yes—
202#529C2316yes—
203#529C23112yes—
204C2×#124C2×C416yes—
205#525C2×C416yes—
206#525C2×C416yes—
207#525C2316yes—
208#525C23124yes—
209C2×#121C2×C416yes—
210C2×#121C2×C416yes—
211#520C2×C412yes—
212#520C2×C416yes—
213#520C2×C414yes—
214#518C2×C416yes—
215#518C2×C4112yes—
216C4×#41C2×C411yescharacteristic
217C4×#41C2×C413yes—
218C4×#41C2×C413yes—
219C4×#41C2×C411yescharacteristic
220C4×#41C2311yescharacteristic
221C4×#41C2313yes—
222C4×#41C2313yes—
223C4×#41C2311yescharacteristic
224C4×#41C2316yes—
225C4×#41C2314yes—
226C4×#41C2316yes—
227C4×#41C2316yes—
228C2×C4×Q8C2×C411yescharacteristic
229C2×C4×Q8C2311yescharacteristic
230C2×C4×D4C2×C413yes—
231C2×C4×D4C2313yes—
232C2×C4×D4C2316yes—
233C2×C4×D4C23112yes—
234C2×C4×D4C2316yes—
235C2×#117C2×C413yes—
236C22×C42C2313yes—
237#446C2312yes—
238#446C2312yes—
239#446C2316yes—
240#446C2316yes—
241#446C23112yes—
242C8×Q8C2311yescharacteristic
243C8×Q8C2311yescharacteristic
244C8×Q8C2311yescharacteristic
245C8×Q8C2311yescharacteristic
246C8×Q8C2313yes—
247C8×Q8C2313yes—
248C8×Q8C2313yes—
249C8×Q8C2313yes—
250C8×Q8C2312yes—
251C8×Q8C2312yes—
252C8×Q8C2316yes—
253C8×Q8C2316yes—
254C8×Q8C2314yes—
255#436C2316yes—
256#436C2316yes—
257#436C23112yes—
258#436C23112yes—
259#436C23112yes—
260#436C23112yes—
261#436C23112yes—
262#436C23112yes—
263#436C23124yes—
264#436C23112yes—
265#436C23112yes—
266#436C2316yes—
267#436C2316yes—
268#436C23112yes—
269#435C23112yes—
270#435C23112yes—
271#435C23124yes—
272#435C23124yes—
273#435C23124yes—
274#435C23124yes—
275#435C23112yes—
276#435C23112yes—
277#435C23124yes—
278C8×D4C2313yes—
279C8×D4C23112yes—
280C8×D4C23112yes—
281C8×D4C2316yes—
282C8×D4C2316yes—
283C8×D4C2316yes—
284C8×D4C23112yes—
285C8×D4C2313yes—
286C8×D4C23112yes—
287C8×D4C23112yes—
288C8×D4C23112yes—
289C8×D4C23112yes—
290C8×D4C2316yes—
291C8×D4C23124yes—
292C8×D4C2313yes—
293C8×D4C23112yes—
294C8×D4C2313yes—
295C8×D4C23112yes—
296C8×D4C2313yes—
297C8×D4C2313yes—
298C8×D4C2316yes—
299C8×D4C2316yes—
300C8×D4C2313yes—
301C8×D4C2313yes—
302C8×D4C23112yes—
303C8×D4C23112yes—
304C8×D4C23112yes—
305C8×D4C2316yes—
306C8×D4C2316yes—
307C8×D4C23112yes—
308#433C23112yes—
309#433C23112yes—
310#433C23124yes—
311#432C2316yes—
312#432C2316yes—
313#432C23112yes—
314#431C2313yes—
315#431C2313yes—
316#431C2316yes—
317#431C2313yes—
318#431C2313yes—
319#431C2316yes—
320#431C2316yes—
321#431C2316yes—
322#431C23112yes—
323#431C23112yes—
324#431C23112yes—
325#424C2316yes—
326#424C23124yes—
327#424C2312yes—
328#423C2313yes—
329#423C2316yes—
330#423C2316yes—
331#423C2316yes—
332#423C23112yes—
333#423C2311yescharacteristic
334C2×C4⋊C8C2316yes—
335C2×C4⋊C8C2316yes—
336C2×C4⋊C8C2313yes—
337C2×C4⋊C8C23112yes—
338C2×C4⋊C8C2313yes—
339#408C2316yes—
340#408C23112yes—
341#408C23112yes—
342#408C23112yes—
343#408C2316yes—
344#408C23124yes—
345#408C23124yes—
346#407C2316yes—
347#407C23124yes—
348C2×C22⋊C8C23112yes—
349C2×C22⋊C8C23112yes—
350C2×C22⋊C8C2316yes—
351C2×C22⋊C8C23124yes—
352#405C2312yes—
353#405C2316yes—
354#405C23112yes—
355#405C23112yes—
356C4×M16C2316yes—
357C4×M16C23112yes—
358C2×C4×C8C2311yescharacteristic
359C2×C4×C8C2313yes—
360C2×C4×C8C2313yes—
361C2×C4×C8C2313yes—
362C2×C4×C8C2313yes—
363C2×C4×C8C2313yes—
364C2×C4×C8C2313yes—
365C2×C4×C8C2313yes—
366C2×C4×C8C2313yes—
367C2×C4×C8C2313yes—
368C2×C4×C8C2313yes—
369C2×C4×C8C2313yes—
370C2×C4×C8C23112yes—
371H(5,𝔽2)—216no—
372C2×#41—28no—
373C2×#41—412no—
374C2×#41—412no—
375C2×#41C22×C413yes—
376C2×#41C22×C413yes—
377C2×#41C22×C411yescharacteristic
378C2×#41C22×C416yes—
379C2×#41C22×C414yes—
380C2×#41C22×C416yes—
381C2×#41C22×C4112yes—
382C2×#41C22×C4112yes—
383C2×#41C22×C411yescharacteristic
384C2×#41C2416yes—
385C2×#41C24112yes—
386C22×Q8C22×C411yescharacteristic
387C22×Q8C22×C416yes—
388C22×D4C22×C413yes—
389C22×D4C22×C416yes—
390C22×D4C22×C4112yes—
391C22×D4C22×C416yes—
392C22×D4C22×C4112yes—
393C22×D4C22×C416yes—
394C23×C4C22×C413yes—
395C23×C4C22×C413yes—
396C23×C4C2413yes—
397C23×C4C24112yes—
398#131—224no—
399#131—424no—
400#131—424no—
401#131—424no—
402#131—412no—
403C2×M16—424no—
404C2×M16—412no—
405C2×M16C2416yes—
406C2×M16C24112yes—
407C2×M16C2412yes—
408C2×M16C24124yes—
409C2×M16C24112yes—
410C2×M16C24112yes—
411C22×C8—212no—
412C22×C8—424no—
413C22×C8—46no—
414C22×C8C2411yescharacteristic
415C22×C8C2413yes—
416C22×C8C2413yes—
417C22×C8C2413yes—
418C22×C8C2413yes—
419C22×C8C2413yes—
420C22×C8C24112yes—
421C22×C8C2413yes—
422C22×C8C24112yes—
423C22×C8C24124yes—
424C22×C8C2413yes—
425C22×C8C2413yes—
426C22×C8C2413yes—
427C22×C8C2413yes—
428C22×C8C24112yes—
429C22×C8C2411yescharacteristic
430C4⋊Q8C22×C413yes—
431C4⋊Q8C22×C416yes—
432C4⋊Q8C22×C416yes—
433C4⋊Q8C22×C416yes—
434C4⋊Q8C22×C411yescharacteristic
435C4⋊Q8C22×C411yescharacteristic
436C4⋊Q8C22×C4112yes—
437#127C22×C413yes—
438#127C22×C416yes—
439#127C22×C416yes—
440#127C22×C416yes—
441#127C22×C4112yes—
442#126C22×C4112yes—
443#126C22×C4112yes—
444#126C22×C4124yes—
445#125C22×C412yes—
446#125C22×C416yes—
447#125C22×C416yes—
448#125C22×C4112yes—
449#124C22×C416yes—
450#124C22×C4112yes—
451#124C22×C4112yes—
452#124C22×C4112yes—
453#124C22×C416yes—
454#124C22×C416yes—
455#124C22×C4112yes—
456#124C22×C4124yes—
457#123C22×C4112yes—
458#123C22×C4112yes—
459#123C22×C4112yes—
460#123C22×C4124yes—
461#123C22×C4124yes—
462#123C22×C4124yes—
463C22⋊Q8C22×C412yes—
464C22⋊Q8C22×C412yes—
465C22⋊Q8C22×C416yes—
466C22⋊Q8C22×C416yes—
467C22⋊Q8C22×C416yes—
468C22⋊Q8C22×C416yes—
469C22⋊Q8C22×C4124yes—
470C22⋊Q8C22×C4124yes—
471C22⋊Q8C22×C4112yes—
472#121C22×C416yes—
473#121C22×C416yes—
474#121C22×C4112yes—
475#121C22×C4112yes—
476#121C22×C4112yes—
477#121C22×C4112yes—
478#121C22×C4112yes—
479#121C22×C4112yes—
480#121C22×C416yes—
481#121C22×C416yes—
482#121C22×C416yes—
483#121C22×C416yes—
484#121C22×C4124yes—
485#121C22×C4124yes—
486#121C22×C4112yes—
487#121C22×C4112yes—
488#121C22×C4112yes—
489#121C22×C4124yes—
490#120C22×C4112yes—
491#120C22×C4124yes—
492#120C22×C4124yes—
493C4×Q8C22×C411yescharacteristic
494C4×Q8C22×C413yes—
495C4×Q8C22×C411yescharacteristic
496C4×Q8C22×C413yes—
497C4×Q8C22×C411yescharacteristic
498C4×Q8C22×C413yes—
499C4×Q8C22×C416yes—
500C4×Q8C22×C414yes—
501C4×Q8C22×C416yes—
502C4×Q8C22×C416yes—
503C4×Q8C22×C416yes—
504C4×Q8C2411yescharacteristic
505C4×Q8C2413yes—
506C4×Q8C2412yes—
507C4×Q8C2412yes—
508C4×D4C22×C413yes—
509C4×D4C22×C416yes—
510C4×D4C22×C413yes—
511C4×D4C22×C413yes—
512C4×D4C22×C416yes—
513C4×D4C22×C413yes—
514C4×D4C22×C413yes—
515C4×D4C22×C416yes—
516C4×D4C22×C413yes—
517C4×D4C22×C4112yes—
518C4×D4C22×C4112yes—
519C4×D4C22×C4112yes—
520C4×D4C22×C4124yes—
521C4×D4C22×C4112yes—
522C4×D4C22×C4112yes—
523C4×D4C22×C4112yes—
524C4×D4C22×C4112yes—
525C4×D4C22×C416yes—
526C4×D4C22×C4112yes—
527C4×D4C22×C4112yes—
528C4×D4C22×C4112yes—
529C4×D4C22×C4112yes—
530C4×D4C22×C416yes—
531C4×D4C22×C416yes—
532C4×D4C22×C416yes—
533C4×D4C2413yes—
534C4×D4C24112yes—
535C4×D4C2416yes—
536C4×D4C24112yes—
537C4×D4C2416yes—
538C4×D4C2416yes—
539C4×D4C2413yes—
540C4×D4C24112yes—
541C4×D4C24112yes—
542#117C22×C413yes—
543#117C22×C413yes—
544#117C22×C416yes—
545#117C22×C416yes—
546#117C22×C413yes—
547#117C22×C413yes—
548#117C22×C416yes—
549#117C22×C4112yes—
550#117C22×C4112yes—
551#117C22×C416yes—
552#117C22×C4112yes—
553#117C2412yes—
554#117C24112yes—
555C2×C4⋊C4C22×C413yes—
556C2×C4⋊C4C22×C413yes—
557C2×C4⋊C4C22×C416yes—
558C2×C4⋊C4C22×C4112yes—
559C2×C4⋊C4C22×C416yes—
560C2×C22⋊C4C22×C416yes—
561C2×C22⋊C4C22×C4112yes—
562C2×C22⋊C4C22×C4124yes—
563C2×C22⋊C4C22×C4112yes—
564C2×C42C22×C413yes—
565C2×C42C22×C413yes—
566C2×C42C22×C413yes—
567C2×C42C22×C413yes—
568C2×C42C22×C413yes—
569C2×C42C22×C413yes—
570C2×C42C2413yes—
571C2×C42C2413yes—
572C2×C42C2413yes—
573C2×C42C24112yes—
574C2×C42C2413yes—
575C2×C42C2413yes—
576C2×C42C2411yescharacteristic
577C4⋊C8C2413yes—
578C4⋊C8C2416yes—
579C4⋊C8C24112yes—
580C4⋊C8C2416yes—
581C4⋊C8C24112yes—
582C4⋊C8C2413yes—
583C4⋊C8C24112yes—
584C4⋊C8C2416yes—
585C4⋊C8C2413yes—
586C4⋊C8C2413yes—
587C4⋊C8C2416yes—
588C4⋊C8C24112yes—
589C4⋊C8C2412yes—
590C4⋊C8C2412yes—
591C4⋊C8C2414yes—
592C4⋊C8C2414yes—
593C22⋊C8C2416yes—
594C22⋊C8C24112yes—
595C22⋊C8C24112yes—
596C22⋊C8C24112yes—
597C22⋊C8C24124yes—
598C22⋊C8C24112yes—
599C22⋊C8C2416yes—
600C22⋊C8C24124yes—
601C22⋊C8C2416yes—
602C22⋊C8C2416yes—
603C22⋊C8C24112yes—
604C22⋊C8C24112yes—
605#97C2414yes—
606#97C24112yes—
607#97C24112yes—
608C4×C8C2411yescharacteristic
609C4×C8C2411yescharacteristic
610C4×C8C2413yes—
611C4×C8C2413yes—
612C4×C8C2413yes—
613C4×C8C2413yes—
614C4×C8C2413yes—
615C4×C8C2413yes—
616C4×C8C2413yes—
617C4×C8C2413yes—
618C4×C8C2413yes—
619C4×C8C2413yes—
620C4×C8C24112yes—
621C4×C8C24112yes—
622C4×C8C2411yescharacteristic
623C4×C8C2411yescharacteristic
624C4×C8C2413yes—
625C4×C8C2413yes—
626C4×C8C2414yes—
627C24C23×C413yes—
628C24C23×C4112yes—
629#41—24no—
630#41—216no—
631#41—212no—
632#41—212no—
633#41—224no—
634#41—212no—
635#41—212no—
636#41—412no—
637#41—412no—
638#41—424no—
639#41—424no—
640#41—412no—
641#41#13118yescomplemented
642C2×Q8—24no—
643C2×Q8—412no—
644C2×Q8C23×C413yes—
645C2×Q8C23×C412yes—
646C2×Q8C23×C412yes—
647C2×Q8C23×C416yes—
648C2×Q8C23×C4112yes—
649C2×Q8C23×C411yescharacteristic
650C2×D4—212no—
651C2×D4—248no—
652C2×D4—224no—
653C2×D4—412no—
654C2×D4—412no—
655C2×D4—424no—
656C2×D4C23×C416yes—
657C2×D4C23×C4112yes—
658C2×D4C23×C416yes—
659C2×D4C23×C4112yes—
660C2×D4C23×C416yes—
661C2×D4C23×C413yes—
662C2×D4C23×C4112yes—
663C2×D4C23×C416yes—
664C2×D4C23×C4112yes—
665C2×D4C23×C4112yes—
666C2×D4C23×C4112yes—
667C2×D4C23×C4124yes—
668C2×D4C23×C413yes—
669C22×C4—212no—
670C22×C4—26no—
671C22×C4—26no—
672C22×C4—412no—
673C22×C4—46no—
674C22×C4—412no—
675C22×C4C23×C411yescharacteristic
676C22×C4C23×C411yescharacteristic
677C22×C4C23×C413yes—
678C22×C4C23×C413yes—
679C22×C4C23×C413yes—
680C22×C4C23×C413yes—
681C22×C4C23×C413yes—
682C22×C4C23×C413yes—
683C22×C4C23×C413yes—
684C22×C4C23×C413yes—
685C22×C4C23×C413yes—
686C22×C4C23×C4112yes—
687C22×C4C23×C413yes—
688C22×C4C23×C413yes—
689C22×C4C23×C413yes—
690C22×C4C23×C4112yes—
691C22×C4C23×C4112yes—
692C22×C4C23×C4124yes—
693C22×C4C23×C413yes—
694C22×C4C2513yes—
695C22×C4C2513yes—
696C22×C4C25112yes—
697C22×C4C2511yescharacteristic
698M16—212no—
699M16—24no—
700M16—224no—
701M16—424no—
702M16—412no—
703M16—412no—
704C2×C8—26no—
705C2×C8—22no—
706C2×C8—26no—
707C2×C8—26no—
708C2×C8—26no—
709C2×C8—26no—
710C2×C8—26no—
711C2×C8—224no—
712C2×C8—43no—
713C2×C8—43no—
714C2×C8—43no—
715C2×C8—43no—
716C2×C8—412no—
717C2×C8—424no—
718C2×C8—412no—
719C2×C8H(5,𝔽2)14yescomplemented
720C2×C8C2511yescharacteristic
721C2×C8C2511yescharacteristic
722C2×C8C2513yes—
723C2×C8C2513yes—
724C2×C8C2514yes—
725C2×C8C2513yes—
726C2×C8C2513yes—
727C2×C8C25112yes—
728C2×C8C2511yescharacteristic
729C2×C8C2511yescharacteristic
730C4⋊C4C23×C413yes—
731C4⋊C4C23×C416yes—
732C4⋊C4C23×C4112yes—
733C4⋊C4C23×C416yes—
734C4⋊C4C23×C4112yes—
735C4⋊C4C23×C413yes—
736C4⋊C4C23×C413yes—
737C4⋊C4C23×C416yes—
738C4⋊C4C23×C413yes—
739C4⋊C4C23×C416yes—
740C4⋊C4C23×C4112yes—
741C4⋊C4C23×C412yes—
742C4⋊C4C23×C412yes—
743C4⋊C4C23×C414yes—
744C4⋊C4C23×C414yes—
745C4⋊C4C23×C4112yes—
746C4⋊C4C23×C412yes—
747C4⋊C4C23×C412yes—
748C4⋊C4C23×C4112yes—
749C4⋊C4C23×C4112yes—
750C22⋊C4C23×C416yes—
751C22⋊C4C23×C4112yes—
752C22⋊C4C23×C4112yes—
753C22⋊C4C23×C4112yes—
754C22⋊C4C23×C4124yes—
755C22⋊C4C23×C4112yes—
756C22⋊C4C23×C416yes—
757C22⋊C4C23×C416yes—
758C22⋊C4C23×C416yes—
759C22⋊C4C23×C4124yes—
760C22⋊C4C23×C4112yes—
761C22⋊C4C23×C4112yes—
762C22⋊C4C23×C414yes—
763C22⋊C4C23×C4112yes—
764C22⋊C4C23×C4112yes—
765C42C23×C411yescharacteristic
766C42C23×C411yescharacteristic
767C42C23×C413yes—
768C42C23×C413yes—
769C42C23×C413yes—
770C42C23×C413yes—
771C42C23×C413yes—
772C42C23×C413yes—
773C42C23×C413yes—
774C42C23×C413yes—
775C42C23×C413yes—
776C42C23×C413yes—
777C42C23×C4112yes—
778C42C23×C4112yes—
779C42C2511yescharacteristic
780C42C2513yes—
781C42C2511yescharacteristic
782C42C2513yes—
783C42C2514yes—
784C23—26no—
785C23—26no—
786C23—224no—
787C23—43no—
788C23—412no—
789C23—412no—
790C23C24×C4112yes—
791C23C24×C413yes—
792C23C24×C411yescharacteristic
793C23C24×C413yes—
794Q8—212no—
795Q8—26no—
796Q8—24no—
797Q8—24no—
798Q8—412no—
799Q8C2×#13114yescomplemented
800D4—224no—
801D4—224no—
802D4—212no—
803D4—212no—
804D4—224no—
805D4—212no—
806D4—26no—
807D4—212no—
808D4—412no—
809D4—412no—
810D4—424no—
811D4—412no—
812D4C2×#131112yescomplemented
813C2×C4—26no—
814C2×C4—26no—
815C2×C4—23no—
816C2×C4—23no—
817C2×C4—212no—
818C2×C4—23no—
819C2×C4—23no—
820C2×C4—212no—
821C2×C4—26no—
822C2×C4—26no—
823C2×C4—22no—
824C2×C4—26no—
825C2×C4—26no—
826C2×C4—26no—
827C2×C4—224no—
828C2×C4—22no—
829C2×C4—26no—
830C2×C4—26no—
831C2×C4—43no—
832C2×C4—43no—
833C2×C4—43no—
834C2×C4—412no—
835C2×C4—424no—
836C2×C4—412no—
837C2×C4C2×#131112yescomplemented
838C2×C4C24×C411yescharacteristic
839C2×C4C24×C411yescharacteristic
840C2×C4C24×C413yes—
841C2×C4C24×C413yes—
842C2×C4C24×C413yes—
843C2×C4C24×C413yes—
844C2×C4C24×C414yes—
845C2×C4C24×C414yes—
846C2×C4C24×C413yes—
847C2×C4C24×C4112yes—
848C2×C4C24×C411yescharacteristic
849C2×C4C24×C413yes—
850C2×C4C24×C411yescharacteristic
851C2×C4C24×C411yescharacteristic
852C2×C4C2×H(5,𝔽2)12yes—
853C2×C4#58512yes—
854C2×C4C2611yescharacteristic
855C8—23no—
856C8—23no—
857C8—212no—
858C8—21no—
859C8—21no—
860C8—23no—
861C8—23no—
862C8—24no—
863C8C2×H(5,𝔽2)12yes—
864C8C2×H(5,𝔽2)12yes—
865C22—21no—
866C22—21no—
867C22—23no—
868C22—23no—
869C22—23no—
870C22—212no—
871C22—23no—
872C22—212no—
873C22—23no—
874C22—212no—
875C22—412no—
876C22—824no—
877C22C4×H(5,𝔽2)12yes—
878C22C22×#13116yes—
879C22C25×C411yescharacteristic
880C4—21no—
881C4—24no—
882C4—23no—
883C4—21no—
884C4—23no—
885C4—23no—
886C4—24no—
887C4—23no—
888C4—23no—
889C4—212no—
890C4C4×H(5,𝔽2)12yes—
891C4C22×#13116yes—
892C4C22×#13112yes—
893C4#357312yes—
894C4C22×H(5,𝔽2)11yescharacteristic
895C4C2×#58511yescharacteristic
896C2—22no—
897C2—26no—
898C2—43no—
899C2—412no—
900C2C2×C4×H(5,𝔽2)11yescharacteristic
901C2C23×#13111yescharacteristic
902C2C2×#357311yescharacteristic
subgroupG/H
centerC2×C8C25
commutator, socleC22C25×C4
Frattini, cosocleC2×C4C26
prime radical#62800C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C2×C8 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #60328C2semidirect
3. #60325C2semidirect
4. #60323C2semidirect
5. #60321C2semidirect
6. #60308C2semidirect
7. #60306C2semidirect
8. #60305C2semidirect
9. C8×H(5,𝔽2)C2semidirect
10. #60274C2semidirect
11. #60268C2semidirect
12. #60263C2semidirect
13. #60239C2semidirect
14. #60236C2semidirect
15. #60218C2semidirect
16. #60204C2semidirect
17. C2×C8×#41C2semidirect
18. D4×#131C2semidirect
19. C2×#2931C2semidirect
20. C22×#131C22semidirect
40. #2994C22semidirect
41. #2994C22semidirect
42. #2993C22semidirect
43. #2993C22semidirect
44. #2991C22semidirect
45. #2991C22semidirect
46. #2991C22semidirect
47. #2990C22semidirect
48. #2990C22semidirect
49. #2989C22semidirect
50. #2989C22semidirect
52. #2988C22semidirect
53. #2988C22semidirect
54. #2981C22semidirect
55. #2981C22semidirect
56. #2979C22semidirect
57. #2979C22semidirect
58. #2979C22semidirect
59. #2977C22semidirect
60. #2976C22semidirect
61. #2975C22semidirect
62. #2974C22semidirect
63. #2974C22semidirect
64. #2972C22semidirect
65. #2972C22semidirect
66. #2971C22semidirect
67. #2969C22semidirect
68. #2966C22semidirect
69. #2966C22semidirect
70. #2966C22semidirect
71. #2966C22semidirect
72. #2966C22semidirect
73. #2965C22semidirect
74. #2965C22semidirect
77. C8×#41C22semidirect
78. C8×#41C22semidirect
79. C8×#41C22semidirect
80. C8×#41C22semidirect
81. C8×#41C22semidirect
82. C8×#41C22semidirect
83. C8×#41C22semidirect
84. C8×#41C22semidirect
85. C8×#41C22semidirect
86. Q8×M16C22semidirect
87. #2960C22semidirect
88. #2960C22semidirect
89. C2×C8×Q8C22semidirect
90. C2×C8×Q8C22semidirect
91. #2935C22semidirect
92. #2935C22semidirect
93. #2935C22semidirect
94. D4×M16C22semidirect
95. D4×M16C22semidirect
96. #2933C22semidirect
97. #2933C22semidirect
98. #2931C22semidirect
99. #2931C22semidirect
100. #2931C22semidirect
101. #2931C22semidirect
102. #2931C22semidirect
103. #2931C22semidirect
104. #2931C22semidirect
105. #2931C22semidirect
106. #2931C22semidirect
107. #2931C22semidirect
108. #2929C22semidirect
109. #2929C22semidirect
110. #2929C22semidirect
111. C2×#436C22semidirect
112. C2×#436C22semidirect
113. C2×C8×D4C22semidirect
114. C2×C8×D4C22semidirect
115. C2×C8×D4C22semidirect
116. C2×C8×D4C22semidirect
117. C2×C8×D4C22semidirect
118. #2925C22semidirect
119. #2922C22semidirect
120. #2920C22semidirect
121. C2×#431C22semidirect
122. #2906C22semidirect
123. C2×#423C22semidirect
124. #2880C22semidirect
125. C2×#408C22semidirect
126. C4×#131C22semidirect
127. C22×C4×C8C22semidirect
641. #41#131semidirect
719. C2×C8H(5,𝔽2)semidirect
799. Q8C2×#131semidirect
812. D4C2×#131semidirect
837. C2×C4C2×#131semidirect

Maximal subgroups

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

subgroupindex
#628002
#603282
#603252
#603232
#603212
#603082
#603062
#603052
C8×H(5,𝔽2)2
#602742
#602682
#602632
#602392
#602362
#602182
#602042
C2×C8×#412
D4×#1312
C2×#29312