Finite Group Databasebeta

← #10574372

Subgroups — #10574372

Order 512.

6476 conjugacy classes of subgroups.

The subgroup lattice has 807 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62815C211yesmaximal, characteristic
2#60275C218yesmaximal, complemented
3#60274C218yesmaximal, complemented
4#60273C218yesmaximal, complemented
5#60271C218yesmaximal, complemented
6#60270C218yesmaximal, complemented
7#60268C218yesmaximal, complemented
8#60192C211yesmaximal, characteristic, complemented
9C2×#2960C211yesmaximal, characteristic, complemented
10#60144C211yesmaximal, characteristic, complemented
11#60143C212yesmaximal, complemented
12#60142C212yesmaximal, complemented
13C2×#2931C211yesmaximal, characteristic, complemented
14#60126C212yesmaximal, complemented
15C2×#2922C211yesmaximal, characteristic, complemented
16#60100C212yesmaximal, complemented
17#60099C211yesmaximal, characteristic, complemented
18C2×#568C2212yes—
19C2×#568C2212yes—
20C22×#131C2212yes—
21#3512C414yes—
22#3511C414yes—
23#3510C414yes—
24#3509C412yes—
25#3508C412yes—
26#3507C414yes—
27#3506C414yes—
28#3505C418yes—
29#3480C2218yes—
30#3475C2218yes—
31#3455C2214yes—
32#3449C2212yes—
33#3444C2214yes—
34C2×#533C2211yescharacteristic
35C2×#532C2211yescharacteristic
36#3428C2212yes—
37C2×C4×#41C2211yescharacteristic
38#2995C22132yescomplemented
39#2994C22116yescomplemented
40#2994C22116yescomplemented
41#2994C22132yescomplemented
42#2993C22116yescomplemented
43#2993C22116yescomplemented
44#2993C22132yescomplemented
45#2992C22132yescomplemented
46#2991C22116yescomplemented
47#2990C22116yescomplemented
48#2989C22116yescomplemented
49#2988C22116yescomplemented
50Q8×M16C2218yescomplemented
51#2962C2218yescomplemented
52#2961C2214yescomplemented
53#2960C2214yescomplemented
54#2960C2214yescomplemented
55#2960C2214yescomplemented
56#2960C2214yescomplemented
57#2960C2214yescomplemented
58C2×#446C2214yescomplemented
59C2×C8×Q8C2214yescomplemented
60#2935C22116yescomplemented
61#2935C2218yescomplemented
62D4×M16C2218yescomplemented
63#2933C22116yes—
64#2933C22116yescomplemented
65#2933C22116yescomplemented
66#2932C2214yes—
67#2932C2218yescomplemented
68#2931C2214yes—
69#2931C2214yes—
70#2931C2214yes—
71#2931C2214yescomplemented
72#2931C2218yescomplemented
73#2931C2214yescomplemented
74#2930C2218yes—
75#2929C2218yes—
76C2×#436C2214yescomplemented
77C2×C8×D4C2214yescomplemented
78#2925C22116yescomplemented
79#2924C22116yescomplemented
80#2923C2218yescomplemented
81#2922C2214yes—
82#2922C2214yes—
83#2922C2214yescomplemented
84#2922C2218yescomplemented
85#2922C2214yescomplemented
86C2×#433C2214yescomplemented
87C2×#431C2214yescomplemented
88#2906C2218yes—
89#2906C22116yescomplemented
90#2906C2218yescomplemented
91#2906C22116yescomplemented
92#2905C2212yes—
93#2905C2212yes—
94#2905C2214yescomplemented
95#2905C2218yescomplemented
96C2×#424C2212yes—
97C2×#424C2211yescharacteristic
98C2×#424C2211yescharacteristic
99C2×#424C2218yescomplemented
100C2×#423C2211yescharacteristic
101C2×#423C2211yescharacteristic
102C2×#423C2214yescomplemented
103#2879C2212yes—
104C2×#408C2211yescharacteristic
105C2×#408C2211yescharacteristic
106C2×#408C2212yes—
107#2873C2212yes—
108C2×#405C2212yes—
109C2×C4×M16C2211yescharacteristic
110C22×C4×C8C2211yescharacteristic
111C22×#41C2311yescharacteristic
112C22×#41C2312yes—
113#568—48no—
114#568—48no—
115C2×#131—48no—
116C2×#131C2318yes—
117C2×#131C2318yes—
118C2×#131C2318yes—
119C2×#131C2318yes—
120C2×#131C2318yes—
121C2×#131C2318yes—
122C22×M16C2311yescharacteristic
123C22×M16C2311yescharacteristic
124C22×M16C2312yes—
125C22×M16C2312yes—
126C22×M16C2318yes—
127C22×M16C2318yes—
128C22×M16C2314yes—
129C23×C8C2311yescharacteristic
130C23×C8C2311yescharacteristic
131C23×C8C2314yes—
132#559C2×C4116yes—
133#559C2×C418yes—
134#557C2×C418yes—
135#556C2×C418yes—
136#556C2×C418yes—
137#556C2×C4116yes—
138#555C2×C418yes—
139#554C2×C418yes—
140#553C2×C4116yes—
141#553C2×C4116yes—
142#553C2×C4132yes—
143#552C2×C4116yes—
144#552C2×C4116yes—
145#551C2×C4132yes—
146#550C2×C418yes—
147#548C2×C4116yes—
148#547C2×C418yes—
149#546C2×C4116yes—
150#542C2×C4116yes—
151#541C2×C418yes—
152#540C2×C418yes—
153#539C2×C4116yes—
154#538C2×C4116yes—
155#537C2×C418yes—
156#536C2×C414yes—
157#536C2×C414yes—
158#535C2×C414yes—
159#535C2×C414yes—
160#534C2×C418yes—
161#533C2×C414yes—
162#533C2×C412yes—
163#533C2×C412yes—
164#533C2×C418yes—
165#533C2312yes—
166#533C2312yes—
167#533C2314yes—
168#532C2×C414yes—
169#532C2×C412yes—
170#532C2×C412yes—
171#532C2×C418yes—
172#532C2312yes—
173#532C2312yes—
174#532C2314yes—
175#532C2318yes—
176C2×C4⋊Q8C2×C411yescharacteristic
177C2×C4⋊Q8C2×C412yes—
178C2×#127C2×C411yescharacteristic
179#529C2×C4116yes—
180#529C2×C4116yes—
181#529C23116yes—
182#529C23132yes—
183C2×#125C2×C412yes—
184C2×#124C2×C412yes—
185#525C2×C4116yes—
186#525C2318yes—
187#525C2318yes—
188C2×C22⋊Q8C2×C414yes—
189C2×#121C2×C414yes—
190#520C2×C418yes—
191#520C2×C418yes—
192#519C2×C414yes—
193#518C2×C418yes—
194#518C2×C414yes—
195C4×#41C2×C412yes—
196C4×#41C2×C412yes—
197C4×#41C2×C412yes—
198C4×#41C2×C412yes—
199C4×#41C23116yes—
200C4×#41C2314yes—
201C4×#41C2314yes—
202C4×#41C2318yes—
203C4×#41C2318yes—
204C2×C4×Q8C2×C412yes—
205C2×C4×Q8C2314yes—
206C2×C4×D4C2×C414yes—
207C2×C4×D4C2×C412yes—
208C2×C4×D4C2314yes—
209C2×#117C2312yes—
210C2×#117C2311yescharacteristic
211C2×#117C2318yes—
212C2×#117C2312yes—
213C22×C42C2311yescharacteristic
214C22×C42C2312yes—
215#446C2318yes—
216#446C2318yes—
217#446C2318yes—
218#446C2318yes—
219#446C23116yes—
220#446C23132yes—
221C8×Q8C2318yes—
222C8×Q8C2318yes—
223C8×Q8C2318yes—
224C8×Q8C2318yes—
225C8×Q8C23116yes—
226#436C2318yes—
227#436C2318yes—
228#436C2318yes—
229#436C2318yes—
230#436C23132yes—
231#436C23116yes—
232#436C23132yes—
233#435C23132yes—
234#435C23132yes—
235#435C23132yes—
236#435C23132yes—
237#435C23132yes—
238C8×D4C2318yes—
239C8×D4C2318yes—
240C8×D4C2318yes—
241C8×D4C2318yes—
242C8×D4C23132yes—
243C8×D4C23116yes—
244C8×D4C23132yes—
245#433C2318yes—
246#433C2318yes—
247#433C2318yes—
248#433C2318yes—
249#433C23132yes—
250#433C23132yes—
251#432C23132yes—
252#431C2318yes—
253#431C2318yes—
254#431C2318yes—
255#431C2318yes—
256#431C23132yes—
257#424C2312yes—
258#424C2314yes—
259#424C2312yes—
260#424C2314yes—
261#424C2314yes—
262#424C2318yes—
263#424C2314yes—
264#424C2312yes—
265#424C2312yes—
266#424C2318yes—
267#424C2318yes—
268#424C23132yes—
269#424C2318yes—
270#424C2318yes—
271#424C23132yes—
272#424C23132yes—
273#423C2312yes—
274#423C2312yes—
275#423C2312yes—
276#423C2312yes—
277#423C2314yes—
278#423C2314yes—
279#423C2318yes—
280#423C23116yes—
281#423C2318yes—
282#423C23132yes—
283C2×C4⋊C8C2314yes—
284C2×C4⋊C8C2314yes—
285C2×C4⋊C8C23116yes—
286C2×C4⋊C8C2314yes—
287C2×C4⋊C8C2318yes—
288C2×C4⋊C8C2314yes—
289C2×C4⋊C8C23132yes—
290#408C2312yes—
291#408C2312yes—
292#408C2314yes—
293#408C2312yes—
294#408C2314yes—
295#408C2312yes—
296#408C2314yes—
297#408C2314yes—
298#408C2318yes—
299#408C2318yes—
300#408C2318yes—
301#407C2318yes—
302C2×C22⋊C8C2314yes—
303C2×C22⋊C8C2314yes—
304C2×C22⋊C8C2318yes—
305#405C2318yes—
306#405C2318yes—
307#405C2318yes—
308#405C2318yes—
309C4×M16C2314yes—
310C4×M16C2314yes—
311C4×M16C2318yes—
312C2×#97C2312yes—
313C2×#97C2314yes—
314C2×C4×C8C2312yes—
315C2×C4×C8C2312yes—
316C2×C4×C8C2312yes—
317C2×C4×C8C2312yes—
318C2×C4×C8C2312yes—
319C2×C4×C8C2312yes—
320C2×C4×C8C2312yes—
321C2×C4×C8C2314yes—
322C2×#41—28no—
323C2×#41—24no—
324C2×#41—24no—
325C2×#41—28no—
326C2×#41C22×C412yes—
327C2×#41C22×C412yes—
328C2×#41C22×C414yes—
329C2×#41C22×C414yes—
330C2×#41C22×C4116yes—
331C2×#41C2412yes—
332C2×#41C2414yes—
333C2×#41C2412yes—
334C2×#41C2414yes—
335C22×Q8C22×C411yescharacteristic
336C22×Q8C22×C412yes—
337C22×Q8C22×C414yes—
338C22×D4C22×C412yes—
339C22×D4C22×C411yescharacteristic
340C22×D4C22×C414yes—
341C22×D4C22×C412yes—
342C22×D4C22×C414yes—
343C23×C4C22×C412yes—
344C23×C4C22×C414yes—
345C23×C4C2414yes—
346C23×C4C2412yes—
347C23×C4C2411yescharacteristic
348#131—416no—
349#131—416no—
350#131—416no—
351#131—416no—
352#131—416no—
353#131—416no—
354C2×M16—28no—
355C2×M16—24no—
356C2×M16—28no—
357C2×M16—24no—
358C2×M16—48no—
359C2×M16—416no—
360C2×M16—416no—
361C2×M16C2412yes—
362C2×M16C2414yes—
363C2×M16C2414yes—
364C2×M16C2414yes—
365C2×M16C2412yes—
366C2×M16C2414yes—
367C2×M16C2412yes—
368C2×M16C2412yes—
369C2×M16C24116yes—
370C2×M16C24116yes—
371C2×M16C24116yes—
372C22×C8—24no—
373C22×C8—24no—
374C22×C8—48no—
375C22×C8C2411yescharacteristic
376C22×C8C2411yescharacteristic
377C22×C8C2414yes—
378C22×C8C2412yes—
379C22×C8C2412yes—
380C22×C8C2411yescharacteristic
381C22×C8C2411yescharacteristic
382C22×C8C2412yes—
383C22×C8C2412yes—
384C22×C8C2412yes—
385C22×C8C2414yes—
386C22×C8C2412yes—
387C22×C8C24116yes—
388C22×C8C24116yes—
389C22×C8C24116yes—
390C4⋊Q8C22×C414yes—
391C4⋊Q8C22×C412yes—
392C4⋊Q8C22×C412yes—
393C4⋊Q8C22×C414yes—
394C4⋊Q8C22×C414yes—
395C4⋊Q8C22×C414yes—
396C4⋊Q8C22×C414yes—
397C4⋊Q8C22×C418yes—
398#127C22×C412yes—
399#127C22×C412yes—
400#127C22×C414yes—
401#127C22×C418yes—
402#126C22×C4132yes—
403#126C22×C4132yes—
404#126C22×C4132yes—
405#125C22×C414yes—
406#125C22×C414yes—
407#125C22×C418yes—
408#125C22×C4116yes—
409#125C22×C4132yes—
410#124C22×C414yes—
411#124C22×C414yes—
412#124C22×C418yes—
413#124C22×C4116yes—
414#124C22×C4132yes—
415#124C22×C418yes—
416#124C22×C418yes—
417#123C22×C4132yes—
418#123C22×C4116yes—
419#123C22×C4116yes—
420#123C22×C4132yes—
421#123C22×C4132yes—
422C22⋊Q8C22×C418yes—
423C22⋊Q8C22×C418yes—
424C22⋊Q8C22×C418yes—
425C22⋊Q8C22×C418yes—
426C22⋊Q8C22×C4116yes—
427C22⋊Q8C22×C4116yes—
428C22⋊Q8C22×C4116yes—
429C22⋊Q8C22×C4132yes—
430#121C22×C418yes—
431#121C22×C418yes—
432#121C22×C418yes—
433#121C22×C418yes—
434#121C22×C4116yes—
435#121C22×C4116yes—
436#121C22×C4116yes—
437#121C22×C4132yes—
438#121C22×C4132yes—
439#120C22×C4116yes—
440#120C22×C4116yes—
441C4×Q8C22×C414yes—
442C4×Q8C22×C414yes—
443C4×Q8C22×C414yes—
444C4×Q8C22×C414yes—
445C4×Q8C22×C418yes—
446C4×Q8C22×C418yes—
447C4×Q8C22×C4116yes—
448C4×Q8C22×C4116yes—
449C4×Q8C22×C4116yes—
450C4×Q8C2418yes—
451C4×Q8C2418yes—
452C4×D4C22×C418yes—
453C4×D4C22×C414yes—
454C4×D4C22×C418yes—
455C4×D4C22×C414yes—
456C4×D4C22×C418yes—
457C4×D4C22×C418yes—
458C4×D4C22×C414yes—
459C4×D4C22×C414yes—
460C4×D4C22×C418yes—
461C4×D4C22×C418yes—
462C4×D4C22×C4132yes—
463C4×D4C22×C4116yes—
464C4×D4C22×C4132yes—
465C4×D4C22×C4116yes—
466C4×D4C22×C4132yes—
467C4×D4C22×C4116yes—
468C4×D4C2418yes—
469C4×D4C2418yes—
470C4×D4C24132yes—
471#117C22×C412yes—
472#117C22×C412yes—
473#117C22×C414yes—
474#117C22×C414yes—
475#117C22×C414yes—
476#117C22×C4116yes—
477#117C22×C414yes—
478#117C22×C4116yes—
479#117C22×C4116yes—
480#117C22×C4132yes—
481#117C2412yes—
482#117C2414yes—
483#117C2412yes—
484#117C2414yes—
485#117C2418yes—
486#117C24116yes—
487C2×C4⋊C4C22×C412yes—
488C2×C4⋊C4C22×C414yes—
489C2×C4⋊C4C22×C414yes—
490C2×C4⋊C4C22×C4116yes—
491C2×C4⋊C4C22×C414yes—
492C2×C4⋊C4C22×C418yes—
493C2×C4⋊C4C22×C414yes—
494C2×C22⋊C4C22×C412yes—
495C2×C22⋊C4C22×C414yes—
496C2×C22⋊C4C22×C414yes—
497C2×C22⋊C4C22×C4116yes—
498C2×C22⋊C4C22×C418yes—
499C2×C42C22×C414yes—
500C2×C42C22×C412yes—
501C2×C42C22×C411yescharacteristic
502C2×C42C22×C411yescharacteristic
503C2×C42C22×C414yes—
504C2×C42C22×C411yescharacteristic
505C2×C42C22×C411yescharacteristic
506C2×C42C22×C414yes—
507C2×C42C2412yes—
508C2×C42C2411yescharacteristic
509C2×C42C2414yes—
510C2×C42C24116yes—
511C2×C42C2412yes—
512C2×C42C2412yes—
513C2×C42C2418yes—
514C2×C42C2411yescharacteristic
515C4⋊C8C2418yes—
516C4⋊C8C2418yes—
517C4⋊C8C2418yes—
518C4⋊C8C24116yes—
519C4⋊C8C24132yes—
520C4⋊C8C2418yes—
521C4⋊C8C2418yes—
522C4⋊C8C24132yes—
523C4⋊C8C2418yes—
524C4⋊C8C24116yes—
525C4⋊C8C2418yes—
526C4⋊C8C2418yes—
527C22⋊C8C2418yes—
528C22⋊C8C2418yes—
529C22⋊C8C24116yes—
530C22⋊C8C2418yes—
531C22⋊C8C2418yes—
532C22⋊C8C24116yes—
533C22⋊C8C24132yes—
534#97C2418yes—
535#97C24116yes—
536#97C24116yes—
537C4×C8C2412yes—
538C4×C8C2412yes—
539C4×C8C2412yes—
540C4×C8C2412yes—
541C4×C8C2412yes—
542C4×C8C2412yes—
543C4×C8C2412yes—
544C4×C8C2412yes—
545C4×C8C2418yes—
546C4×C8C24116yes—
547C4×C8C24116yes—
548C24C23×C414yes—
549C24C23×C412yes—
550C24C23×C411yescharacteristic
551#41—28no—
552#41—216no—
553#41—216no—
554#41—28no—
555#41—24no—
556#41—28no—
557#41—24no—
558#41—28no—
559#41—28no—
560#41—24no—
561#41—24no—
562#41—28no—
563#41—432no—
564C2×Q8—28no—
565C2×Q8—24no—
566C2×Q8—48no—
567C2×Q8C23×C412yes—
568C2×Q8C23×C414yes—
569C2×Q8C23×C412yes—
570C2×Q8C23×C414yes—
571C2×Q8C23×C418yes—
572C2×Q8C23×C418yes—
573C2×D4—28no—
574C2×D4—216no—
575C2×D4—28no—
576C2×D4—24no—
577C2×D4—48no—
578C2×D4C23×C414yes—
579C2×D4C23×C418yes—
580C2×D4C23×C414yes—
581C2×D4C23×C418yes—
582C2×D4C23×C412yes—
583C2×D4C23×C414yes—
584C2×D4C23×C412yes—
585C2×D4C23×C414yes—
586C2×D4C23×C418yes—
587C2×D4C23×C4132yes—
588C2×D4C23×C418yes—
589C22×C4—28no—
590C22×C4—24no—
591C22×C4—24no—
592C22×C4—28no—
593C22×C4—44no—
594C22×C4—48no—
595C22×C4C23×C412yes—
596C22×C4C23×C412yes—
597C22×C4C23×C414yes—
598C22×C4C23×C412yes—
599C22×C4C23×C412yes—
600C22×C4C23×C418yes—
601C22×C4C23×C414yes—
602C22×C4C23×C418yes—
603C22×C4C23×C412yes—
604C22×C4C23×C414yes—
605C22×C4C23×C412yes—
606C22×C4C23×C412yes—
607C22×C4C23×C418yes—
608C22×C4C23×C418yes—
609C22×C4C23×C4132yes—
610C22×C4C23×C411yescharacteristic
611C22×C4C23×C411yescharacteristic
612C22×C4C23×C411yescharacteristic
613C22×C4H(5,𝔽2)14yes—
614C22×C42−1+414yes—
615C22×C4C2514yes—
616C22×C4C2518yes—
617C22×C4C2511yescharacteristic
618C22×C4C2511yescharacteristic
619C22×C4C2511yescharacteristic
620M16—24no—
621M16—28no—
622M16—28no—
623M16—28no—
624M16—28no—
625M16—24no—
626M16—24no—
627M16—24no—
628M16—416no—
629M16—416no—
630M16—416no—
631C2×C8—22no—
632C2×C8—22no—
633C2×C8—24no—
634C2×C8—24no—
635C2×C8—28no—
636C2×C8—28no—
637C2×C8—24no—
638C2×C8—24no—
639C2×C8—24no—
640C2×C8—22no—
641C2×C8—22no—
642C2×C8—24no—
643C2×C8—416no—
644C2×C8—416no—
645C2×C8—416no—
646C2×C8C2512yes—
647C2×C8C2514yes—
648C2×C8C2512yes—
649C2×C8C2512yes—
650C2×C8C2512yes—
651C2×C8C2514yes—
652C2×C8C2518yes—
653C2×C8C2518yes—
654C4⋊C4C23×C414yes—
655C4⋊C4C23×C418yes—
656C4⋊C4C23×C418yes—
657C4⋊C4C23×C4116yes—
658C4⋊C4C23×C418yes—
659C4⋊C4C23×C414yes—
660C4⋊C4C23×C418yes—
661C4⋊C4C23×C418yes—
662C4⋊C4C23×C4132yes—
663C4⋊C4C23×C418yes—
664C4⋊C4C23×C418yes—
665C4⋊C4C23×C4116yes—
666C4⋊C4C23×C418yes—
667C4⋊C4C23×C4132yes—
668C22⋊C4C23×C414yes—
669C22⋊C4C23×C418yes—
670C22⋊C4C23×C4116yes—
671C22⋊C4C23×C414yes—
672C22⋊C4C23×C418yes—
673C22⋊C4C23×C418yes—
674C22⋊C4C23×C4132yes—
675C22⋊C4C23×C418yes—
676C22⋊C4C23×C4116yes—
677C22⋊C4C23×C4132yes—
678C22⋊C4C23×C4132yes—
679C42C23×C411yescharacteristic
680C42C23×C411yescharacteristic
681C42C23×C414yes—
682C42C23×C418yes—
683C42C23×C411yescharacteristic
684C42C23×C411yescharacteristic
685C42C23×C412yes—
686C42C23×C412yes—
687C42C23×C418yes—
688C42C23×C412yes—
689C42C23×C412yes—
690C42C23×C4132yes—
691C42C23×C418yes—
692C42C2512yes—
693C42C2512yes—
694C42C2518yes—
695C42C2514yes—
696C23—28no—
697C23—24no—
698C23—42no—
699C23—44no—
700C23—48no—
701C23#52014yes—
702C23C24×C414yes—
703C23C24×C418yes—
704C23C24×C411yescharacteristic
705C23C24×C411yescharacteristic
706C23C24×C411yescharacteristic
707Q8—24no—
708Q8—28no—
709Q8—28no—
710Q8—24no—
711Q8—216no—
712Q8—48no—
713D4—28no—
714D4—216no—
715D4—28no—
716D4—216no—
717D4—24no—
718D4—28no—
719D4—28no—
720D4—24no—
721D4—216no—
722D4—48no—
723D4—432no—
724C2×C4—28no—
725C2×C4—24no—
726C2×C4—28no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—28no—
730C2×C4—216no—
731C2×C4—28no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—216no—
736C2×C4—44no—
737C2×C4—48no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—48no—
742C2×C4—432no—
743C2×C4#52014yes—
744C2×C4#52014yes—
745C2×C4#52014yes—
746C2×C4C24×C412yes—
747C2×C4C24×C418yes—
748C2×C4C24×C414yes—
749C2×C4C24×C418yes—
750C2×C4C24×C412yes—
751C2×C4C24×C4116yes—
752C2×C4C24×C412yes—
753C2×C4C24×C411yescharacteristic
754C2×C4C24×C411yescharacteristic
755C2×C4C24×C411yescharacteristic
756C2×C4C24×C412yes—
757C2×C4C2×H(5,𝔽2)12yes—
758C2×C4C2×H(5,𝔽2)12yes—
759C2×C4C2×H(5,𝔽2)12yes—
760C2×C4C2×2−1+412yes—
761C2×C4C2×2−1+412yes—
762C2×C4C2×2−1+412yes—
763C2×C4C2611yescharacteristic
764C8—22no—
765C8—22no—
766C8—28no—
767C8—24no—
768C8—28no—
769C8—22no—
770C8—22no—
771C8—24no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—28no—
776C22—216no—
777C22—24no—
778C22—28no—
779C22—44no—
780C22—88no—
781C22—84no—
782C22C2×#52012yes—
783C22C2×#52012yes—
784C22C2×#52012yes—
785C22C25×C411yescharacteristic
786C4—22no—
787C4—28no—
788C4—22no—
789C4—22no—
790C4—216no—
791C4—28no—
792C4—24no—
793C4C2×#52012yes—
794C4C2×#52012yes—
795C4C2×#52012yes—
796C4#357314yes—
797C4C22×H(5,𝔽2)11yescharacteristic
798C4C22×2−1+411yescharacteristic
799C2—22no—
800C2—22no—
801C2—22no—
802C2—44no—
803C2—48no—
804C2C22×#52011yescharacteristic
805C2C2×#357312yes—
subgroupG/H
center, Frattini, cosocleC2×C4C26
commutator, socleC22C25×C4
prime radical#62815C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C2×C4 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #60275C2semidirect
3. #60274C2semidirect
4. #60273C2semidirect
5. #60271C2semidirect
6. #60270C2semidirect
7. #60268C2semidirect
8. #60192C2semidirect
9. C2×#2960C2semidirect
10. #60144C2semidirect
11. #60143C2semidirect
12. #60142C2semidirect
13. C2×#2931C2semidirect
14. #60126C2semidirect
15. C2×#2922C2semidirect
16. #60100C2semidirect
17. #60099C2semidirect
38. #2995C22semidirect
39. #2994C22semidirect
40. #2994C22semidirect
41. #2994C22semidirect
42. #2993C22semidirect
43. #2993C22semidirect
44. #2993C22semidirect
45. #2992C22semidirect
46. #2991C22semidirect
47. #2990C22semidirect
48. #2989C22semidirect
49. #2988C22semidirect
50. Q8×M16C22semidirect
51. #2962C22semidirect
52. #2961C22semidirect
53. #2960C22semidirect
54. #2960C22semidirect
55. #2960C22semidirect
56. #2960C22semidirect
57. #2960C22semidirect
58. C2×#446C22semidirect
59. C2×C8×Q8C22semidirect
60. #2935C22semidirect
61. #2935C22semidirect
62. D4×M16C22semidirect
64. #2933C22semidirect
65. #2933C22semidirect
67. #2932C22semidirect
71. #2931C22semidirect
72. #2931C22semidirect
73. #2931C22semidirect
76. C2×#436C22semidirect
77. C2×C8×D4C22semidirect
78. #2925C22semidirect
79. #2924C22semidirect
80. #2923C22semidirect
83. #2922C22semidirect
84. #2922C22semidirect
85. #2922C22semidirect
86. C2×#433C22semidirect
87. C2×#431C22semidirect
89. #2906C22semidirect
90. #2906C22semidirect
91. #2906C22semidirect
94. #2905C22semidirect
95. #2905C22semidirect
99. C2×#424C22semidirect
102. C2×#423C22semidirect

Maximal subgroups

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

subgroupindex
#628152
#602752
#602742
#602732
#602712
#602702
#602682
#601922
C2×#29602
#601442
#601432
#601422
C2×#29312
#601262
C2×#29222
#601002
#600992