Finite Group Databasebeta

← #10574602

Subgroups — #10574602

Order 512.

6305 conjugacy classes of subgroups.

The subgroup lattice has 1197 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62810C211yesmaximal, characteristic
2#60343C211yesmaximal, characteristic, complemented
3#60339C213yesmaximal, complemented
4#60335C212yesmaximal, complemented
5#60331C212yesmaximal, complemented
6#60330C213yesmaximal, complemented
7C8×2−1+4C211yesmaximal, characteristic, complemented
8#60325C211yesmaximal, characteristic, complemented
9#60321C213yesmaximal, complemented
10#60311C216yesmaximal, complemented
11#60306C213yesmaximal, complemented
12#60305C216yesmaximal, complemented
13C8×H(5,𝔽2)C211yesmaximal, characteristic, complemented
14#60301C212yesmaximal, complemented
15#60298C216yesmaximal, complemented
16#60294C213yesmaximal, complemented
17#60290C213yesmaximal, complemented
18#60283C211yesmaximal, characteristic, complemented
19#60218C212yesmaximal, complemented
20#60215C216yesmaximal, complemented
21#60204C213yesmaximal, complemented
22C2×#2966C213yesmaximal, complemented
23C2×C8×#41C211yesmaximal, characteristic, complemented
24#3524C412yes—
25#3521C416yes—
26#3516C412yes—
27#3513C416yes—
28#3512C413yes—
29#3510C413yes—
30#3504C411yescharacteristic
31#3500C411yescharacteristic
32#3495C413yes—
33#3494C413yes—
34#3489C411yescharacteristic
35#3488C411yescharacteristic
36#3482C2212yes—
37#3481C2216yes—
38#3480C2212yes—
39#3475C2216yes—
40#3461C2213yes—
41#3460C2213yes—
42#3444C2213yes—
43C2×#529C2213yes—
44C4×2−1+4C2211yescharacteristic
45C4×H(5,𝔽2)C2211yescharacteristic
46C2×C4×#41C2211yescharacteristic
47#2994C2216yescomplemented
48#2994C2216yescomplemented
49#2994C22112yescomplemented
50#2994C2216yescomplemented
51#2994C2216yescomplemented
52#2993C2216yescomplemented
53#2993C2216yescomplemented
54#2993C2216yescomplemented
55#2993C2216yescomplemented
56#2992C22112yescomplemented
57#2991C2212yescomplemented
58#2990C2216yescomplemented
59#2990C2216yescomplemented
60#2990C2216yescomplemented
61#2989C2213yescomplemented
62#2989C2213yescomplemented
63#2989C2213yescomplemented
64#2989C2213yescomplemented
65#2988C2211yescharacteristic
66#2988C2211yescharacteristic
67#2988C2213yescomplemented
68#2988C2213yescomplemented
69#2988C2216yescomplemented
70#2988C2212yescomplemented
71#2986C2216yescomplemented
72#2985C2216yescomplemented
73#2985C2216yescomplemented
74#2984C2212yescomplemented
75#2984C2212yescomplemented
76#2983C2213yescomplemented
77#2982C2213yescomplemented
78#2982C2212yescomplemented
79#2981C2216yescomplemented
80#2981C2216yescomplemented
81#2979C2216yescomplemented
82#2977C22112yescomplemented
83#2977C22112yescomplemented
84#2976C22112yescomplemented
85#2975C2213yescomplemented
86#2974C2216yescomplemented
87#2974C22112yescomplemented
88#2974C2216yescomplemented
89#2972C2213yescomplemented
90#2972C2216yescomplemented
91#2971C2212yescomplemented
92#2971C2212yescomplemented
93#2970C2216yescomplemented
94#2970C2216yescomplemented
95#2969C2216yescomplemented
96#2969C2216yescomplemented
97#2969C2216yescomplemented
98#2969C2216yescomplemented
99#2968C22112yescomplemented
100#2968C22112yescomplemented
101#2966C2213yescomplemented
102#2966C2216yescomplemented
103#2966C2216yescomplemented
104#2966C2216yescomplemented
105#2966C2216yescomplemented
106#2966C2216yescomplemented
107#2966C2216yescomplemented
108#2966C2216yescomplemented
109#2966C2211yescharacteristic, complemented
110#2966C2216yescomplemented
111#2966C2213yescomplemented
112#2966C2213yescomplemented
113#2966C2216yescomplemented
114#2966C22112yescomplemented
115#2966C2216yescomplemented
116#2966C2216yescomplemented
117#2965C2216yescomplemented
118#2965C2213yescomplemented
119#2965C2213yescomplemented
120C8×#41C2211yescharacteristic
121C8×#41C2211yescharacteristic
122C8×#41C2213yescomplemented
123C8×#41C2211yescharacteristic, complemented
124C8×#41C2213yescomplemented
125C8×#41C2211yescharacteristic, complemented
126C8×#41C2213yescomplemented
127C8×#41C2213yescomplemented
128C8×#41C2213yescomplemented
129C8×#41C2216yescomplemented
130C8×#41C2213yescomplemented
131C8×#41C2216yescomplemented
132C8×#41C2212yescomplemented
133Q8×M16C2212yescomplemented
134#2962C2216yescomplemented
135#2960C2213yescomplemented
136#2960C2213yescomplemented
137#2960C2216yescomplemented
138C2×#446C2213yescomplemented
139C2×C8×Q8C2211yescharacteristic, complemented
140C2×C8×Q8C2211yescharacteristic, complemented
141C2×C8×Q8C2213yescomplemented
142C2×C8×Q8C2212yescomplemented
143#2935C2216yescomplemented
144D4×M16C2216yescomplemented
145#2933C22112yescomplemented
146#2931C2213yescomplemented
147#2931C2213yescomplemented
148#2931C2216yescomplemented
149#2929C2216yescomplemented
150#2929C2216yescomplemented
151#2929C22112yescomplemented
152C2×#436C2213yescomplemented
153C2×#435C2216yescomplemented
154C2×C8×D4C2213yescomplemented
155C2×C8×D4C2213yescomplemented
156C2×C8×D4C2213yescomplemented
157C2×C8×D4C2216yescomplemented
158C2×C8×D4C2216yescomplemented
159#2925C2216yescomplemented
160#2925C2216yescomplemented
161#2924C22112yescomplemented
162#2922C2216yescomplemented
163#2920C2213yescomplemented
164C2×#433C2216yescomplemented
165C2×#432C2213yescomplemented
166C2×#431C2213yescomplemented
167C4×#131C2216yescomplemented
168C2×#405C2216yescomplemented
169C22×C4×C8C2213yescomplemented
170C2×2−1+4C2×C411yescharacteristic
171C2×H(5,𝔽2)C2×C411yescharacteristic
172C22×#41C2×C411yescharacteristic
173C2×#131C2316yes—
174C2×#131C2316yes—
175C22×M16C2316yes—
176C23×C8C2313yes—
177C23×C8C2313yes—
178C23×C8C2316yes—
179#559C2×C416yes—
180#559C2×C416yes—
181#557C2×C412yes—
182#557C2×C412yes—
183#556C2×C416yes—
184#556C2×C416yes—
185#556C2×C416yes—
186#555C2×C416yes—
187#554C2×C416yes—
188#554C2×C416yes—
189#554C2×C416yes—
190#553C2×C4112yes—
191#553C2×C416yes—
192#553C2×C416yes—
193#553C2×C416yes—
194#553C2×C4112yes—
195#553C2×C416yes—
196#552C2×C4112yes—
197#552C2×C416yes—
198#552C2×C416yes—
199#552C2×C416yes—
200#552C2×C416yes—
201#551C2×C4112yes—
202#551C2×C4112yes—
203#551C2×C4112yes—
204#551C2×C4112yes—
205#550C2×C412yes—
206D4×Q8C2×C412yes—
207#548C2×C412yes—
208#548C2×C412yes—
209#548C2×C412yes—
210#548C2×C412yes—
211#547C2×C416yes—
212#547C2×C416yes—
213#546C2×C416yes—
214#546C2×C416yes—
215#546C2×C416yes—
216#546C2×C4112yes—
217#546C2×C416yes—
218D42C2×C416yes—
219#544C2×C413yes—
220#544C2×C413yes—
221#542C2×C416yes—
222#542C2×C416yes—
223#542C2×C416yes—
224#542C2×C416yes—
225#541C2×C416yes—
226#541C2×C416yes—
227#540C2×C416yes—
228#540C2×C416yes—
229#539C2×C4112yes—
230#538C2×C4112yes—
231#537C2×C413yes—
232#537C2×C413yes—
233#536C2×C413yes—
234#536C2×C413yes—
235#535C2×C413yes—
236#535C2×C413yes—
237#533C2×C413yes—
238#533C2×C413yes—
239#533C2313yes—
240#533C2316yes—
241#532C2×C413yes—
242#532C2×C413yes—
243#532C2313yes—
244#532C2316yes—
245#529C2×C416yes—
246#529C2×C416yes—
247#529C2×C416yes—
248#529C2×C416yes—
249#529C2×C413yes—
250#529C2×C413yes—
251#529C2×C416yes—
252#529C2×C416yes—
253#529C2×C416yes—
254#529C2313yes—
255#529C2316yes—
256#529C2316yes—
257#529C2316yes—
258#529C2311yescharacteristic
259#529C2316yes—
260#529C2316yes—
261#529C23112yes—
262#529C2316yes—
263C2×#126C2×C416yes—
264C2×#125C2×C413yes—
265C2×#124C2×C413yes—
266#525C2×C413yes—
267#525C2×C413yes—
268#525C2×C416yes—
269#525C2316yes—
270#525C23112yes—
271C2×#123C2×C416yes—
272C2×C22⋊Q8C2×C413yes—
273C2×#121C2×C413yes—
274#520C2×C411yescharacteristic
275#520C2×C413yes—
276#520C2×C412yes—
277#520C2×C411yescharacteristic
278#520C2×C413yes—
279#520C2×C416yes—
280#519C2×C413yes—
281#519C2×C412yes—
282#518C2×C413yes—
283#518C2×C416yes—
284C4×#41C2×C411yescharacteristic
285C4×#41C2×C413yes—
286C4×#41C2×C413yes—
287C4×#41C2×C411yescharacteristic
288C4×#41C2311yescharacteristic
289C4×#41C2313yes—
290C4×#41C2313yes—
291C4×#41C2311yescharacteristic
292C4×#41C2313yes—
293C4×#41C2312yes—
294C4×#41C2313yes—
295C4×#41C2316yes—
296C4×#41C2316yes—
297C4×#41C2316yes—
298C2×C4×Q8C2×C411yescharacteristic
299C2×C4×Q8C2311yescharacteristic
300C2×C4×Q8C2313yes—
301C2×C4×Q8C2312yes—
302C2×C4×D4C2×C413yes—
303C2×C4×D4C2313yes—
304C2×C4×D4C2313yes—
305C2×C4×D4C2316yes—
306C2×C4×D4C2316yes—
307C2×#117C2×C413yes—
308C2×#117C2316yes—
309C22×C42C2313yes—
310#446C2313yes—
311#446C2316yes—
312#446C2316yes—
313#446C2316yes—
314#446C2311yescharacteristic
315#446C2316yes—
316#446C2313yes—
317#446C2313yes—
318#446C2316yes—
319#446C23112yes—
320#446C2316yes—
321#446C2316yes—
322#446C23112yes—
323#446C2316yes—
324#446C2316yes—
325C8×Q8C2311yescharacteristic
326C8×Q8C2313yes—
327C8×Q8C2316yes—
328C8×Q8C2313yes—
329C8×Q8C2313yes—
330C8×Q8C2311yescharacteristic
331C8×Q8C2311yescharacteristic
332C8×Q8C2311yescharacteristic
333C8×Q8C2313yes—
334C8×Q8C2313yes—
335C8×Q8C2316yes—
336C8×Q8C2316yes—
337C8×Q8C2316yes—
338C8×Q8C2312yes—
339C8×Q8C2311yescharacteristic
340C8×Q8C2316yes—
341C8×Q8C2313yes—
342C8×Q8C2313yes—
343C8×Q8C2316yes—
344C8×Q8C2316yes—
345C8×Q8C2312yes—
346#436C2313yes—
347#436C2316yes—
348#436C2316yes—
349#436C2316yes—
350#436C2311yescharacteristic
351#436C2316yes—
352#436C2313yes—
353#436C2316yes—
354#436C2313yes—
355#436C23112yes—
356#436C2316yes—
357#436C2316yes—
358#436C23112yes—
359#436C2316yes—
360#436C2316yes—
361#435C2316yes—
362#435C23112yes—
363#435C23112yes—
364#435C23112yes—
365#435C2312yes—
366#435C2316yes—
367#435C2316yes—
368#435C2316yes—
369#435C2316yes—
370#435C2316yes—
371#435C2316yes—
372#435C23112yes—
373#435C23112yes—
374#435C23112yes—
375#435C23112yes—
376#435C23112yes—
377#435C23112yes—
378#435C23112yes—
379#435C23112yes—
380C8×D4C2313yes—
381C8×D4C2316yes—
382C8×D4C2316yes—
383C8×D4C2313yes—
384C8×D4C2316yes—
385C8×D4C2316yes—
386C8×D4C23112yes—
387C8×D4C2313yes—
388C8×D4C2316yes—
389C8×D4C2313yes—
390C8×D4C2313yes—
391C8×D4C2313yes—
392C8×D4C2313yes—
393C8×D4C2316yes—
394C8×D4C2316yes—
395C8×D4C2313yes—
396C8×D4C2313yes—
397C8×D4C2316yes—
398C8×D4C2316yes—
399C8×D4C23112yes—
400C8×D4C23112yes—
401C8×D4C23112yes—
402C8×D4C2316yes—
403C8×D4C2316yes—
404C8×D4C2312yes—
405C8×D4C2316yes—
406C8×D4C2316yes—
407C8×D4C2316yes—
408C8×D4C2316yes—
409C8×D4C2316yes—
410C8×D4C2316yes—
411C8×D4C2311yescharacteristic
412C8×D4C2313yes—
413C8×D4C2316yes—
414C8×D4C2313yes—
415C8×D4C23112yes—
416C8×D4C2316yes—
417C8×D4C2316yes—
418#433C2316yes—
419#433C23112yes—
420#433C23112yes—
421#433C23112yes—
422#433C2312yes—
423#433C2316yes—
424#433C2316yes—
425#433C23112yes—
426#433C23112yes—
427#433C23112yes—
428#433C23112yes—
429#432C2313yes—
430#432C2316yes—
431#432C2316yes—
432#432C2316yes—
433#432C2311yescharacteristic
434#432C2316yes—
435#432C23112yes—
436#432C2316yes—
437#432C2316yes—
438#431C2316yes—
439#431C2313yes—
440#431C2313yes—
441#431C2313yes—
442#431C2313yes—
443#431C2316yes—
444#431C2313yes—
445#431C2316yes—
446#431C2313yes—
447#431C2316yes—
448#431C2316yes—
449#431C2316yes—
450#431C2316yes—
451#431C23112yes—
452#431C2316yes—
453#431C2316yes—
454#424C2316yes—
455#424C2316yes—
456#424C23112yes—
457#424C23112yes—
458#423C2313yes—
459#423C2313yes—
460#423C2316yes—
461#423C2316yes—
462C2×C4⋊C8C2313yes—
463C2×C4⋊C8C2313yes—
464C2×C4⋊C8C2313yes—
465C2×C4⋊C8C2313yes—
466C2×C4⋊C8C2316yes—
467C2×C4⋊C8C2316yes—
468C2×C4⋊C8C2316yes—
469C2×C4⋊C8C2316yes—
470#408C2316yes—
471#408C2316yes—
472#408C23112yes—
473#408C23112yes—
474#407C2316yes—
475#407C23112yes—
476C2×C22⋊C8C2316yes—
477C2×C22⋊C8C2316yes—
478C2×C22⋊C8C2316yes—
479C2×C22⋊C8C2316yes—
480C2×C22⋊C8C23112yes—
481#405C2316yes—
482#405C23112yes—
483#405C23112yes—
484#405C23112yes—
485#405C2312yes—
486#405C2316yes—
487#405C2316yes—
488#405C2316yes—
489#405C2316yes—
490C4×M16C2316yes—
491C4×M16C2316yes—
492C4×M16C2316yes—
493C2×#97C2316yes—
494C2×#97C2316yes—
495C2×C4×C8C2311yescharacteristic
496C2×C4×C8C2313yes—
497C2×C4×C8C2313yes—
498C2×C4×C8C2313yes—
499C2×C4×C8C2313yes—
500C2×C4×C8C2313yes—
501C2×C4×C8C2313yes—
502C2×C4×C8C2313yes—
503C2×C4×C8C2313yes—
504C2×C4×C8C2313yes—
505C2×C4×C8C2313yes—
506C2×C4×C8C2313yes—
507C2×C4×C8C2316yes—
508C2×C4×C8C2316yes—
509C2×C4×C8C2316yes—
5102−1+4—28no—
511H(5,𝔽2)—28no—
512C2×#41—28no—
513C2×#41C22×C413yes—
514C2×#41C22×C413yes—
515C2×#41C22×C411yescharacteristic
516C2×#41C22×C413yes—
517C2×#41C22×C413yes—
518C2×#41C22×C416yes—
519C2×#41C22×C412yes—
520C2×#41C22×C416yes—
521C2×#41C22×C411yescharacteristic
522C2×#41C2416yes—
523C22×Q8C22×C411yescharacteristic
524C22×Q8C22×C413yes—
525C22×Q8C22×C412yes—
526C22×D4C22×C413yes—
527C22×D4C22×C413yes—
528C22×D4C22×C416yes—
529C22×D4C22×C416yes—
530C23×C4C22×C413yes—
531C23×C4C22×C413yes—
532C23×C4C2416yes—
533C23×C4C2413yes—
534#131—412no—
535#131—412no—
536C2×M16—412no—
537C2×M16C2416yes—
538C2×M16C2412yes—
539C2×M16C24112yes—
540C2×M16C2416yes—
541C2×M16C2416yes—
542C2×M16C2416yes—
543C2×M16C2416yes—
544C22×C8—46no—
545C22×C8—412no—
546C22×C8—46no—
547C22×C8C2411yescharacteristic
548C22×C8C2413yes—
549C22×C8C2413yes—
550C22×C8C2411yescharacteristic
551C22×C8C2413yes—
552C22×C8C2416yes—
553C22×C8C2413yes—
554C22×C8C2412yes—
555C22×C8C2413yes—
556C22×C8C2413yes—
557C22×C8C2413yes—
558C22×C8C2413yes—
559C22×C8C2413yes—
560C22×C8C2413yes—
561C22×C8C2416yes—
562C22×C8C24112yes—
563C22×C8C2416yes—
564C22×C8C2416yes—
565C22×C8C2416yes—
566C4⋊Q8C22×C413yes—
567C4⋊Q8C22×C413yes—
568C4⋊Q8C22×C413yes—
569C4⋊Q8C22×C416yes—
570C4⋊Q8C22×C416yes—
571C4⋊Q8C22×C416yes—
572#127C22×C413yes—
573#127C22×C416yes—
574#126C22×C416yes—
575#126C22×C4112yes—
576#126C22×C4112yes—
577#126C22×C4112yes—
578#126C22×C412yes—
579#126C22×C416yes—
580#126C22×C416yes—
581#126C22×C4112yes—
582#126C22×C4112yes—
583#126C22×C4112yes—
584#126C22×C4112yes—
585#125C22×C413yes—
586#125C22×C416yes—
587#125C22×C416yes—
588#125C22×C416yes—
589#125C22×C411yescharacteristic
590#125C22×C416yes—
591#125C22×C416yes—
592#125C22×C416yes—
593#125C22×C4112yes—
594#125C22×C416yes—
595#125C22×C4112yes—
596#124C22×C413yes—
597#124C22×C416yes—
598#124C22×C416yes—
599#124C22×C416yes—
600#124C22×C411yescharacteristic
601#124C22×C416yes—
602#124C22×C416yes—
603#124C22×C416yes—
604#124C22×C416yes—
605#124C22×C4112yes—
606#124C22×C4112yes—
607#123C22×C416yes—
608#123C22×C4112yes—
609#123C22×C4112yes—
610#123C22×C4112yes—
611#123C22×C412yes—
612#123C22×C416yes—
613#123C22×C416yes—
614#123C22×C416yes—
615#123C22×C416yes—
616#123C22×C4112yes—
617#123C22×C4112yes—
618#123C22×C4112yes—
619#123C22×C4112yes—
620#123C22×C4112yes—
621#123C22×C4112yes—
622C22⋊Q8C22×C413yes—
623C22⋊Q8C22×C416yes—
624C22⋊Q8C22×C416yes—
625C22⋊Q8C22×C416yes—
626C22⋊Q8C22×C411yescharacteristic
627C22⋊Q8C22×C413yes—
628C22⋊Q8C22×C413yes—
629C22⋊Q8C22×C416yes—
630C22⋊Q8C22×C416yes—
631C22⋊Q8C22×C416yes—
632C22⋊Q8C22×C416yes—
633C22⋊Q8C22×C4112yes—
634C22⋊Q8C22×C4112yes—
635C22⋊Q8C22×C416yes—
636C22⋊Q8C22×C416yes—
637C22⋊Q8C22×C4112yes—
638C22⋊Q8C22×C416yes—
639C22⋊Q8C22×C416yes—
640C22⋊Q8C22×C4112yes—
641#121C22×C413yes—
642#121C22×C416yes—
643#121C22×C416yes—
644#121C22×C416yes—
645#121C22×C411yescharacteristic
646#121C22×C413yes—
647#121C22×C413yes—
648#121C22×C416yes—
649#121C22×C416yes—
650#121C22×C416yes—
651#121C22×C416yes—
652#121C22×C4112yes—
653#121C22×C4112yes—
654#121C22×C416yes—
655#121C22×C4112yes—
656#121C22×C416yes—
657#121C22×C416yes—
658#121C22×C416yes—
659#121C22×C4112yes—
660#120C22×C416yes—
661#120C22×C416yes—
662#120C22×C4112yes—
663#120C22×C4112yes—
664C4×Q8C22×C411yescharacteristic
665C4×Q8C22×C413yes—
666C4×Q8C22×C411yescharacteristic
667C4×Q8C22×C413yes—
668C4×Q8C22×C411yescharacteristic
669C4×Q8C22×C413yes—
670C4×Q8C22×C416yes—
671C4×Q8C22×C416yes—
672C4×Q8C22×C412yes—
673C4×Q8C22×C416yes—
674C4×Q8C22×C413yes—
675C4×Q8C22×C416yes—
676C4×Q8C22×C413yes—
677C4×Q8C22×C412yes—
678C4×Q8C22×C416yes—
679C4×Q8C22×C416yes—
680C4×Q8C22×C416yes—
681C4×Q8C2411yescharacteristic
682C4×Q8C2413yes—
683C4×Q8C2416yes—
684C4×Q8C2413yes—
685C4×Q8C2411yescharacteristic
686C4×Q8C2416yes—
687C4×D4C22×C413yes—
688C4×D4C22×C416yes—
689C4×D4C22×C413yes—
690C4×D4C22×C413yes—
691C4×D4C22×C416yes—
692C4×D4C22×C413yes—
693C4×D4C22×C413yes—
694C4×D4C22×C416yes—
695C4×D4C22×C413yes—
696C4×D4C22×C416yes—
697C4×D4C22×C416yes—
698C4×D4C22×C416yes—
699C4×D4C22×C4112yes—
700C4×D4C22×C416yes—
701C4×D4C22×C4112yes—
702C4×D4C22×C4112yes—
703C4×D4C22×C416yes—
704C4×D4C22×C413yes—
705C4×D4C22×C416yes—
706C4×D4C22×C416yes—
707C4×D4C22×C413yes—
708C4×D4C22×C416yes—
709C4×D4C22×C4112yes—
710C4×D4C22×C416yes—
711C4×D4C22×C416yes—
712C4×D4C22×C416yes—
713C4×D4C22×C416yes—
714C4×D4C22×C416yes—
715C4×D4C22×C416yes—
716C4×D4C22×C416yes—
717C4×D4C22×C416yes—
718C4×D4C22×C416yes—
719C4×D4C2413yes—
720C4×D4C2416yes—
721C4×D4C2416yes—
722C4×D4C2413yes—
723C4×D4C2416yes—
724C4×D4C2416yes—
725C4×D4C2413yes—
726C4×D4C24112yes—
727C4×D4C2416yes—
728C4×D4C2412yes—
729C4×D4C2411yescharacteristic
730C4×D4C2416yes—
731#117C22×C413yes—
732#117C22×C413yes—
733#117C22×C416yes—
734#117C22×C416yes—
735#117C22×C413yes—
736#117C22×C413yes—
737#117C22×C4112yes—
738#117C22×C4112yes—
739#117C22×C413yes—
740#117C22×C416yes—
741#117C22×C416yes—
742#117C22×C413yes—
743#117C22×C416yes—
744#117C22×C4112yes—
745#117C22×C416yes—
746#117C22×C416yes—
747#117C22×C416yes—
748#117C22×C416yes—
749#117C2416yes—
750#117C24112yes—
751#117C2412yes—
752#117C2416yes—
753C2×C4⋊C4C22×C413yes—
754C2×C4⋊C4C22×C413yes—
755C2×C4⋊C4C22×C416yes—
756C2×C4⋊C4C22×C416yes—
757C2×C4⋊C4C22×C413yes—
758C2×C4⋊C4C22×C416yes—
759C2×C4⋊C4C22×C416yes—
760C2×C4⋊C4C22×C413yes—
761C2×C4⋊C4C22×C416yes—
762C2×C4⋊C4C22×C416yes—
763C2×C22⋊C4C22×C416yes—
764C2×C22⋊C4C22×C416yes—
765C2×C22⋊C4C22×C416yes—
766C2×C22⋊C4C22×C416yes—
767C2×C22⋊C4C22×C4112yes—
768C2×C22⋊C4C22×C416yes—
769C2×C22⋊C4C22×C416yes—
770C2×C42C22×C413yes—
771C2×C42C22×C413yes—
772C2×C42C22×C413yes—
773C2×C42C22×C413yes—
774C2×C42C22×C413yes—
775C2×C42C22×C413yes—
776C2×C42C2413yes—
777C2×C42C2416yes—
778C2×C42C2413yes—
779C2×C42C2413yes—
780C2×C42C2416yes—
781C2×C42C2416yes—
782C2×C42C2413yes—
783C2×C42C2413yes—
784C2×C42C2411yescharacteristic
785C4⋊C8C2413yes—
786C4⋊C8C2413yes—
787C4⋊C8C2413yes—
788C4⋊C8C2416yes—
789C4⋊C8C2413yes—
790C4⋊C8C2416yes—
791C4⋊C8C2416yes—
792C4⋊C8C2416yes—
793C4⋊C8C2416yes—
794C4⋊C8C24112yes—
795C4⋊C8C2413yes—
796C4⋊C8C2413yes—
797C4⋊C8C24112yes—
798C4⋊C8C2416yes—
799C4⋊C8C2416yes—
800C4⋊C8C2411yescharacteristic
801C4⋊C8C2411yescharacteristic
802C4⋊C8C2416yes—
803C4⋊C8C2416yes—
804C4⋊C8C2416yes—
805C4⋊C8C2412yes—
806C4⋊C8C2412yes—
807C4⋊C8C2416yes—
808C4⋊C8C2416yes—
809C22⋊C8C2416yes—
810C22⋊C8C2416yes—
811C22⋊C8C2416yes—
812C22⋊C8C2416yes—
813C22⋊C8C24112yes—
814C22⋊C8C2416yes—
815C22⋊C8C2416yes—
816C22⋊C8C2416yes—
817C22⋊C8C24112yes—
818C22⋊C8C2416yes—
819C22⋊C8C2416yes—
820C22⋊C8C24112yes—
821C22⋊C8C2412yes—
822C22⋊C8C2416yes—
823C22⋊C8C2416yes—
824C22⋊C8C2412yes—
825C22⋊C8C2416yes—
826C22⋊C8C2412yes—
827C22⋊C8C2416yes—
828#97C2416yes—
829#97C2416yes—
830#97C24112yes—
831#97C24112yes—
832#97C2412yes—
833#97C2412yes—
834#97C2416yes—
835#97C2416yes—
836C4×C8C2411yescharacteristic
837C4×C8C2411yescharacteristic
838C4×C8C2413yes—
839C4×C8C2413yes—
840C4×C8C2413yes—
841C4×C8C2413yes—
842C4×C8C2413yes—
843C4×C8C2413yes—
844C4×C8C2413yes—
845C4×C8C2413yes—
846C4×C8C2413yes—
847C4×C8C2413yes—
848C4×C8C2416yes—
849C4×C8C2416yes—
850C4×C8C2416yes—
851C4×C8C24112yes—
852C4×C8C2416yes—
853C4×C8C2411yescharacteristic
854C4×C8C2411yescharacteristic
855C4×C8C2413yes—
856C4×C8C2413yes—
857C4×C8C2416yes—
858C4×C8C2412yes—
859C24C23×C413yes—
860C24C23×C416yes—
861#41—24no—
862#41—28no—
863#41—212no—
864#41—224no—
865#41—212no—
866#41—212no—
867#41—212no—
868#41—46no—
869#41—46no—
870#41—412no—
871#41#13118yescomplemented
872C2×Q8—24no—
873C2×Q8—28no—
874C2×Q8—212no—
875C2×Q8C23×C413yes—
876C2×Q8C23×C416yes—
877C2×Q8C23×C413yes—
878C2×Q8C23×C411yescharacteristic
879C2×Q8C23×C416yes—
880C2×Q8C23×C416yes—
881C2×Q8C23×C411yescharacteristic
882C2×D4—212no—
883C2×D4—224no—
884C2×D4—212no—
885C2×D4—412no—
886C2×D4C23×C416yes—
887C2×D4C23×C412yes—
888C2×D4C23×C416yes—
889C2×D4C23×C416yes—
890C2×D4C23×C416yes—
891C2×D4C23×C413yes—
892C2×D4C23×C416yes—
893C2×D4C23×C413yes—
894C2×D4C23×C411yescharacteristic
895C2×D4C23×C416yes—
896C2×D4C23×C416yes—
897C2×D4C23×C416yes—
898C2×D4C23×C416yes—
899C2×D4C23×C4112yes—
900C2×D4C23×C413yes—
901C22×C4—212no—
902C22×C4—43no—
903C22×C4—43no—
904C22×C4—46no—
905C22×C4—46no—
906C22×C4—46no—
907C22×C4C23×C411yescharacteristic
908C22×C4C23×C411yescharacteristic
909C22×C4C23×C413yes—
910C22×C4C23×C413yes—
911C22×C4C23×C413yes—
912C22×C4C23×C413yes—
913C22×C4C23×C413yes—
914C22×C4C23×C416yes—
915C22×C4C23×C416yes—
916C22×C4C23×C416yes—
917C22×C4C23×C413yes—
918C22×C4C23×C413yes—
919C22×C4C23×C413yes—
920C22×C4C23×C413yes—
921C22×C4C23×C413yes—
922C22×C4C23×C413yes—
923C22×C4C23×C413yes—
924C22×C4C23×C416yes—
925C22×C4C23×C416yes—
926C22×C4C23×C416yes—
927C22×C4C23×C416yes—
928C22×C4C23×C4112yes—
929C22×C4C23×C413yes—
930C22×C4C2513yes—
931C22×C4C2511yescharacteristic
932C22×C4C2512yes—
933C22×C4C2513yes—
934C22×C4C2516yes—
935M16—212no—
936M16—24no—
937M16—412no—
938M16—46no—
939M16—46no—
940M16—46no—
941M16—46no—
942C2×C8—22no—
943C2×C8—26no—
944C2×C8—22no—
945C2×C8—212no—
946C2×C8—26no—
947C2×C8—26no—
948C2×C8—26no—
949C2×C8—24no—
950C2×C8—43no—
951C2×C8—43no—
952C2×C8—412no—
953C2×C8—43no—
954C2×C8—43no—
955C2×C8—43no—
956C2×C8—43no—
957C2×C8—46no—
958C2×C8—46no—
959C2×C8—46no—
960C2×C8—46no—
961C2×C8C2511yescharacteristic
962C2×C8C2511yescharacteristic
963C2×C8C2513yes—
964C2×C8C2513yes—
965C2×C8C2512yes—
966C2×C8C2513yes—
967C2×C8C2513yes—
968C2×C8C2512yes—
969C2×C8C2516yes—
970C2×C8C2516yes—
971C2×C8C2511yescharacteristic
972C2×C8C2511yescharacteristic
973C4⋊C4C23×C413yes—
974C4⋊C4C23×C413yes—
975C4⋊C4C23×C416yes—
976C4⋊C4C23×C416yes—
977C4⋊C4C23×C413yes—
978C4⋊C4C23×C416yes—
979C4⋊C4C23×C416yes—
980C4⋊C4C23×C416yes—
981C4⋊C4C23×C413yes—
982C4⋊C4C23×C416yes—
983C4⋊C4C23×C416yes—
984C4⋊C4C23×C4112yes—
985C4⋊C4C23×C413yes—
986C4⋊C4C23×C416yes—
987C4⋊C4C23×C413yes—
988C4⋊C4C23×C416yes—
989C4⋊C4C23×C4112yes—
990C4⋊C4C23×C4112yes—
991C4⋊C4C23×C4112yes—
992C4⋊C4C23×C411yescharacteristic
993C4⋊C4C23×C412yes—
994C4⋊C4C23×C411yescharacteristic
995C4⋊C4C23×C416yes—
996C4⋊C4C23×C412yes—
997C4⋊C4C23×C416yes—
998C4⋊C4C23×C416yes—
999C4⋊C4C23×C416yes—
1000C4⋊C4C23×C416yes—
1001C4⋊C4C23×C412yes—
1002C4⋊C4C23×C412yes—
1003C4⋊C4C23×C416yes—
1004C4⋊C4C23×C416yes—
1005C22⋊C4C23×C416yes—
1006C22⋊C4C23×C416yes—
1007C22⋊C4C23×C416yes—
1008C22⋊C4C23×C416yes—
1009C22⋊C4C23×C416yes—
1010C22⋊C4C23×C416yes—
1011C22⋊C4C23×C4112yes—
1012C22⋊C4C23×C416yes—
1013C22⋊C4C23×C416yes—
1014C22⋊C4C23×C416yes—
1015C22⋊C4C23×C416yes—
1016C22⋊C4C23×C416yes—
1017C22⋊C4C23×C4112yes—
1018C22⋊C4C23×C4112yes—
1019C22⋊C4C23×C4112yes—
1020C22⋊C4C23×C4112yes—
1021C22⋊C4C23×C416yes—
1022C22⋊C4C23×C412yes—
1023C22⋊C4C23×C416yes—
1024C22⋊C4C23×C412yes—
1025C22⋊C4C23×C412yes—
1026C22⋊C4C23×C416yes—
1027C22⋊C4C23×C416yes—
1028C22⋊C4C23×C412yes—
1029C22⋊C4C23×C412yes—
1030C22⋊C4C23×C416yes—
1031C22⋊C4C23×C416yes—
1032C42C23×C411yescharacteristic
1033C42C23×C411yescharacteristic
1034C42C23×C413yes—
1035C42C23×C413yes—
1036C42C23×C413yes—
1037C42C23×C413yes—
1038C42C23×C413yes—
1039C42C23×C413yes—
1040C42C23×C413yes—
1041C42C23×C413yes—
1042C42C23×C413yes—
1043C42C23×C413yes—
1044C42C23×C416yes—
1045C42C23×C4112yes—
1046C42C23×C416yes—
1047C42C23×C416yes—
1048C42C23×C416yes—
1049C42C2511yescharacteristic
1050C42C2511yescharacteristic
1051C42C2513yes—
1052C42C2512yes—
1053C42C2516yes—
1054C42C2513yes—
1055C23—26no—
1056C23—26no—
1057C23—212no—
1058C23—43no—
1059C23—46no—
1060C23—46no—
1061C23C24×C416yes—
1062C23C24×C413yes—
1063C23C24×C412yes—
1064C23C24×C413yes—
1065C23C24×C411yescharacteristic
1066Q8—212no—
1067Q8—26no—
1068Q8—26no—
1069Q8—22no—
1070Q8—46no—
1071Q8—46no—
1072Q8C2×#13114yes—
1073D4—212no—
1074D4—212no—
1075D4—212no—
1076D4—212no—
1077D4—24no—
1078D4—212no—
1079D4—26no—
1080D4—26no—
1081D4—22no—
1082D4—412no—
1083D4—46no—
1084D4—46no—
1085D4—46no—
1086D4—46no—
1087D4C2×#131112yes—
1088C2×C4—26no—
1089C2×C4—212no—
1090C2×C4—22no—
1091C2×C4—26no—
1092C2×C4—21no—
1093C2×C4—23no—
1094C2×C4—21no—
1095C2×C4—23no—
1096C2×C4—26no—
1097C2×C4—23no—
1098C2×C4—23no—
1099C2×C4—22no—
1100C2×C4—22no—
1101C2×C4—26no—
1102C2×C4—22no—
1103C2×C4—26no—
1104C2×C4—26no—
1105C2×C4—26no—
1106C2×C4—212no—
1107C2×C4—212no—
1108C2×C4—43no—
1109C2×C4—43no—
1110C2×C4—43no—
1111C2×C4—43no—
1112C2×C4—43no—
1113C2×C4—412no—
1114C2×C4—43no—
1115C2×C4—43no—
1116C2×C4—46no—
1117C2×C4—46no—
1118C2×C4—46no—
1119C2×C4—46no—
1120C2×C4C2×#131112yes—
1121C2×C4C24×C411yescharacteristic
1122C2×C4C24×C413yes—
1123C2×C4C24×C411yescharacteristic
1124C2×C4C24×C411yescharacteristic
1125C2×C4C24×C411yescharacteristic
1126C2×C4C24×C413yes—
1127C2×C4C24×C412yes—
1128C2×C4C24×C413yes—
1129C2×C4C24×C416yes—
1130C2×C4C24×C412yes—
1131C2×C4C24×C413yes—
1132C2×C4C24×C413yes—
1133C2×C4C24×C412yes—
1134C2×C4C24×C416yes—
1135C2×C4C24×C416yes—
1136C2×C4C24×C413yes—
1137C2×C4C24×C411yescharacteristic
1138C2×C4C2611yescharacteristic
1139C8—21no—
1140C8—23no—
1141C8—21no—
1142C8—23no—
1143C8—26no—
1144C8—23no—
1145C8—23no—
1146C8—22no—
1147C8—26no—
1148C8—22no—
1149C8#58512yes—
1150C8#58512yes—
1151C22—21no—
1152C22—23no—
1153C22—21no—
1154C22—23no—
1155C22—22no—
1156C22—23no—
1157C22—26no—
1158C22—22no—
1159C22—23no—
1160C22—26no—
1161C22—26no—
1162C22—23no—
1163C22—22no—
1164C22—412no—
1165C22—812no—
1166C22C22×#13116yes—
1167C22#357312yes—
1168C22C25×C411yescharacteristic
1169C4—21no—
1170C4—22no—
1171C4—23no—
1172C4—26no—
1173C4—21no—
1174C4—21no—
1175C4—23no—
1176C4—23no—
1177C4—26no—
1178C4—22no—
1179C4—21no—
1180C4—23no—
1181C4—26no—
1182C4—23no—
1183C4—22no—
1184C4C22×#13116yes—
1185C4C22×#13112yes—
1186C4C2×#58511yescharacteristic
1187C4C2×#58511yescharacteristic
1188C2—22no—
1189C2—26no—
1190C2—42no—
1191C2—43no—
1192C2—46no—
1193C2C4×#58511yescharacteristic
1194C2C23×#13111yescharacteristic
1195C2C2×#357311yescharacteristic
subgroupG/H
centerC2×C8C25
commutator, socleC22C25×C4
Frattini, cosocleC2×C4C26
prime radical#62810C2
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. #60343C2semidirect
3. #60339C2semidirect
4. #60335C2semidirect
5. #60331C2semidirect
6. #60330C2semidirect
7. C8×2−1+4C2semidirect
8. #60325C2semidirect
9. #60321C2semidirect
10. #60311C2semidirect
11. #60306C2semidirect
12. #60305C2semidirect
13. C8×H(5,𝔽2)C2semidirect
14. #60301C2semidirect
15. #60298C2semidirect
16. #60294C2semidirect
17. #60290C2semidirect
18. #60283C2semidirect
19. #60218C2semidirect
20. #60215C2semidirect
21. #60204C2semidirect
22. C2×#2966C2semidirect
23. C2×C8×#41C2semidirect
47. #2994C22semidirect
48. #2994C22semidirect
49. #2994C22semidirect
50. #2994C22semidirect
51. #2994C22semidirect
52. #2993C22semidirect
53. #2993C22semidirect
54. #2993C22semidirect
55. #2993C22semidirect
56. #2992C22semidirect
57. #2991C22semidirect
58. #2990C22semidirect
59. #2990C22semidirect
60. #2990C22semidirect
61. #2989C22semidirect
62. #2989C22semidirect
63. #2989C22semidirect
64. #2989C22semidirect
67. #2988C22semidirect
68. #2988C22semidirect
69. #2988C22semidirect
70. #2988C22semidirect
71. #2986C22semidirect
72. #2985C22semidirect
73. #2985C22semidirect
74. #2984C22semidirect
75. #2984C22semidirect
76. #2983C22semidirect
77. #2982C22semidirect
78. #2982C22semidirect
79. #2981C22semidirect
80. #2981C22semidirect
81. #2979C22semidirect
82. #2977C22semidirect
83. #2977C22semidirect
84. #2976C22semidirect
85. #2975C22semidirect
86. #2974C22semidirect
87. #2974C22semidirect
88. #2974C22semidirect
89. #2972C22semidirect
90. #2972C22semidirect
91. #2971C22semidirect
92. #2971C22semidirect
93. #2970C22semidirect
94. #2970C22semidirect
95. #2969C22semidirect
96. #2969C22semidirect
97. #2969C22semidirect
98. #2969C22semidirect
99. #2968C22semidirect
100. #2968C22semidirect
101. #2966C22semidirect
102. #2966C22semidirect
103. #2966C22semidirect
104. #2966C22semidirect
105. #2966C22semidirect
106. #2966C22semidirect
107. #2966C22semidirect
108. #2966C22semidirect
109. #2966C22semidirect
110. #2966C22semidirect
111. #2966C22semidirect
112. #2966C22semidirect
113. #2966C22semidirect
114. #2966C22semidirect
115. #2966C22semidirect
116. #2966C22semidirect
117. #2965C22semidirect
118. #2965C22semidirect
119. #2965C22semidirect
122. C8×#41C22semidirect
123. C8×#41C22semidirect
124. C8×#41C22semidirect
125. C8×#41C22semidirect
126. C8×#41C22semidirect
127. C8×#41C22semidirect
128. C8×#41C22semidirect
129. C8×#41C22semidirect
130. C8×#41C22semidirect
131. C8×#41C22semidirect
132. C8×#41C22semidirect
133. Q8×M16C22semidirect
134. #2962C22semidirect
135. #2960C22semidirect
136. #2960C22semidirect
137. #2960C22semidirect
138. C2×#446C22semidirect
139. C2×C8×Q8C22semidirect
140. C2×C8×Q8C22semidirect
141. C2×C8×Q8C22semidirect
142. C2×C8×Q8C22semidirect
143. #2935C22semidirect
144. D4×M16C22semidirect
145. #2933C22semidirect
146. #2931C22semidirect
147. #2931C22semidirect
148. #2931C22semidirect
149. #2929C22semidirect
150. #2929C22semidirect
151. #2929C22semidirect
152. C2×#436C22semidirect
153. C2×#435C22semidirect
154. C2×C8×D4C22semidirect
155. C2×C8×D4C22semidirect
156. C2×C8×D4C22semidirect
157. C2×C8×D4C22semidirect
158. C2×C8×D4C22semidirect
159. #2925C22semidirect
160. #2925C22semidirect
161. #2924C22semidirect
162. #2922C22semidirect
163. #2920C22semidirect
164. C2×#433C22semidirect
165. C2×#432C22semidirect
166. C2×#431C22semidirect
167. C4×#131C22semidirect
168. C2×#405C22semidirect
169. C22×C4×C8C22semidirect
871. #41#131semidirect

Maximal subgroups

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

subgroupindex
#628102
#603432
#603392
#603352
#603312
#603302
C8×2−1+42
#603252
#603212
#603112
#603062
#603052
C8×H(5,𝔽2)2
#603012
#602982
#602942
#602902
#602832
#602182
#602152
#602042
C2×#29662
C2×C8×#412