Finite Group Databasebeta

← C2×#51594 #7707482

Subgroups — C2×#51594 #7707482

Order 512.

5110 conjugacy classes of subgroups.

The subgroup lattice has 1314 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2806C211yesmaximal, characteristic, complemented
2C2×#2806C211yesmaximal, characteristic, complemented
3C2×#2792C211yesmaximal, characteristic, complemented
4C2×#2791C211yesmaximal, characteristic, complemented
5C2×#2791C211yesmaximal, characteristic, complemented
6C2×#2768C211yesmaximal, characteristic
7C2×#2755C211yesmaximal, characteristic, complemented
8C2×#2726C211yesmaximal, characteristic, complemented
9C2×#2726C211yesmaximal, characteristic, complemented
10C2×#2720C211yesmaximal, characteristic
11C2×#2704C211yesmaximal, characteristic
12C2×#2704C211yesmaximal, characteristic
13#51594C2132yesmaximal, direct product factor
14C2×#2582C211yesmaximal, characteristic, complemented
15C2×#2552C211yesmaximal, characteristic, complemented
16C2×#2565C211yesmaximal, characteristic, complemented
17C2×#2584C211yesmaximal, characteristic, complemented
18C2×#2586C211yesmaximal, characteristic, complemented
19C2×#2586C211yesmaximal, characteristic, complemented
20C2×#2556C211yesmaximal, characteristic
21C2×#2522C211yesmaximal, characteristic
22C2×#2438C211yesmaximal, characteristic
23C2×#2441C211yesmaximal, characteristic
24C2×#2423C211yesmaximal, characteristic
25C2×#2423C211yesmaximal, characteristic
26C2×#2462C211yesmaximal, characteristic, complemented
27C2×#2462C211yesmaximal, characteristic, complemented
28C2×#2667C211yesmaximal, characteristic
29C2×#2659C211yesmaximal, characteristic
30C2×#2378C211yesmaximal, characteristic
31C2×#2368C211yesmaximal, characteristic
32C2×#2323C211yesmaximal, characteristic
33C22×#125C2211yescharacteristic
34C22×#125C2211yescharacteristic
35C22×#125C2211yescharacteristic
36C22×#125C2211yescharacteristic
37C22×#125C2211yescharacteristic
38C22×C22⋊Q8C2211yescharacteristic
39C22×C22⋊Q8C2211yescharacteristic
40C22×C22⋊Q8C2211yescharacteristic
41C22×C22⋊Q8C2211yescharacteristic
42C22×C4×Q8C2211yescharacteristic
43C22×C4×Q8C2211yescharacteristic
44C22×C4×Q8C2211yescharacteristic
45C22×#117C2211yescharacteristic
46#2806C22116yescomplemented
47#2806C22116yescomplemented
48#2792C22116yescomplemented
49#2791C22116yescomplemented
50#2791C22116yescomplemented
51#2768C22116yes—
52#2755C22116yescomplemented
53#2726C22116yescomplemented
54#2726C22116yescomplemented
55#2720C22116yes—
56#2704C22116yes—
57#2704C22116yes—
58#2667C22116yes—
59#2659C22116yes—
60#2586C22116yescomplemented
61#2586C22116yescomplemented
62#2584C22116yescomplemented
63#2582C22116yescomplemented
64#2565C22116yescomplemented
65#2556C22116yes—
66#2552C22116yescomplemented
67#2522C22116yes—
68#2462C22116yescomplemented
69#2462C22116yescomplemented
70#2441C22116yes—
71#2438C22116yes—
72#2423C22116yes—
73#2423C22116yes—
74C2×#400C2211yescharacteristic
75C2×#400C2211yescharacteristic
76C2×#399C2211yescharacteristic
77C2×#399C2211yescharacteristic
78C2×#399C2211yescharacteristic
79C2×#399C2211yescharacteristic
80C2×#398C2211yescharacteristic
81C2×#398C2211yescharacteristic
82C2×#398C2211yescharacteristic
83C2×#398C2211yescharacteristic
84C2×#398C2211yescharacteristic
85C2×#398C2211yescharacteristic
86C2×#398C2211yescharacteristic
87C2×#398C2211yescharacteristic
88C2×#398C2211yescharacteristic
89C2×#398C2211yescharacteristic
90C2×#398C2211yescharacteristic
91C2×#398C2211yescharacteristic
92C2×#398C2211yescharacteristic
93C2×#398C2211yescharacteristic
94C2×#398C2211yescharacteristic
95C2×#398C2211yescharacteristic
96C2×#398C2211yescharacteristic
97C2×#398C2211yescharacteristic
98C2×#398C2211yescharacteristic
99C2×#398C2211yescharacteristic
100C2×#398C2211yescharacteristic
101C2×#398C2211yescharacteristic
102C2×#398C2211yescharacteristic
103C2×#398C2211yescharacteristic
104C2×#398C2211yescharacteristic
105C2×#398C2211yescharacteristic
106C2×#398C2211yescharacteristic
107C2×#398C2211yescharacteristic
108C2×#396C2211yescharacteristic
109C2×#396C2211yescharacteristic
110C2×#396C2211yescharacteristic
111C2×#396C2211yescharacteristic
112C2×#395C2211yescharacteristic
113C2×#395C2211yescharacteristic
114C2×#395C2211yescharacteristic
115C2×#395C2211yescharacteristic
116C2×#395C2211yescharacteristic
117C2×#395C2211yescharacteristic
118C2×#395C2211yescharacteristic
119C2×#395C2211yescharacteristic
120C2×#395C2211yescharacteristic
121C2×#395C2211yescharacteristic
122#2378C22116yes—
123#2368C22116yes—
124#2323C22116yes—
125C2×#391C2211yescharacteristic
126C2×#391C2211yescharacteristic
127C2×#391C2211yescharacteristic
128C2×#391C2211yescharacteristic
129C2×#391C2211yescharacteristic
130C2×#391C2211yescharacteristic
131C2×#391C2211yescharacteristic
132C2×#391C2211yescharacteristic
133C2×#391C2211yescharacteristic
134C2×#391C2211yescharacteristic
135C2×#391C2211yescharacteristic
136C2×#389C2211yescharacteristic
137C2×#389C2211yescharacteristic
138C2×#389C2211yescharacteristic
139C2×#389C2211yescharacteristic
140C2×#389C2211yescharacteristic
141C2×#389C2211yescharacteristic
142C2×#389C2211yescharacteristic
143C2×#389C2211yescharacteristic
144C2×#389C2211yescharacteristic
145C2×#389C2211yescharacteristic
146C2×#389C2211yescharacteristic
147C2×#389C2211yescharacteristic
148C2×#389C2211yescharacteristic
149C2×#389C2211yescharacteristic
150C2×#389C2211yescharacteristic
151C2×#389C2211yescharacteristic
152C2×#389C2211yescharacteristic
153C2×#389C2211yescharacteristic
154C2×#389C2211yescharacteristic
155C2×#389C2211yescharacteristic
156C2×#389C2211yescharacteristic
157C2×#389C2211yescharacteristic
158C2×#389C2211yescharacteristic
159C2×#389C2211yescharacteristic
160C2×#389C2211yescharacteristic
161C2×#388C2211yescharacteristic
162C2×#388C2211yescharacteristic
163C2×#388C2211yescharacteristic
164C2×#388C2211yescharacteristic
165C2×#388C2211yescharacteristic
166C2×#388C2211yescharacteristic
167C2×#388C2211yescharacteristic
168C2×#388C2211yescharacteristic
169C2×#387C2211yescharacteristic
170C2×#387C2211yescharacteristic
171C2×#387C2211yescharacteristic
172C2×#387C2211yescharacteristic
173C2×#387C2211yescharacteristic
174C2×#387C2211yescharacteristic
175C2×#387C2211yescharacteristic
176C2×#387C2211yescharacteristic
177C2×#387C2211yescharacteristic
178C2×#387C2211yescharacteristic
179C2×#387C2211yescharacteristic
180C2×#387C2211yescharacteristic
181C2×#387C2211yescharacteristic
182C2×#387C2211yescharacteristic
183C2×#387C2211yescharacteristic
184C2×#387C2211yescharacteristic
185C2×#387C2211yescharacteristic
186C2×#387C2211yescharacteristic
187C2×#387C2211yescharacteristic
188C2×#387C2211yescharacteristic
189C2×#387C2211yescharacteristic
190C2×#387C2211yescharacteristic
191C2×#387C2211yescharacteristic
192C2×#387C2211yescharacteristic
193C2×#387C2211yescharacteristic
194C2×#387C2211yescharacteristic
195C2×#385C2211yescharacteristic
196C2×#385C2211yescharacteristic
197C2×#385C2211yescharacteristic
198C2×#385C2211yescharacteristic
199C2×#384C2211yescharacteristic
200C2×#384C2211yescharacteristic
201C2×#384C2211yescharacteristic
202C2×#384C2211yescharacteristic
203C2×#382C2211yescharacteristic
204C2×#381C2211yescharacteristic
205C2×#380C2211yescharacteristic
206C2×#380C2211yescharacteristic
207C2×#380C2211yescharacteristic
208C2×#380C2211yescharacteristic
209C2×#380C2211yescharacteristic
210C2×C4×C4⋊C4C2211yescharacteristic
211C2×C4×C4⋊C4C2211yescharacteristic
212C2×C4×C4⋊C4C2211yescharacteristic
213C2×C4×C4⋊C4C2211yescharacteristic
214C2×C4×C4⋊C4C2211yescharacteristic
215C2×C4×C22⋊C4C2211yescharacteristic
216C2×C4×C22⋊C4C2211yescharacteristic
217C2×C4×C22⋊C4C2211yescharacteristic
218C22×#95C2211yescharacteristic
219C23×Q8C2311yescharacteristic
220C23×Q8C2311yescharacteristic
221C23×Q8C2311yescharacteristic
222C23×Q8C2311yescharacteristic
223C24×C4C2311yescharacteristic
224C24×C4C2311yescharacteristic
225C24×C4C2311yescharacteristic
226C2×#125—44no—
227C2×#125—44no—
228C2×#125—44no—
229C2×#125—44no—
230C2×#125—44no—
231C2×#125C2318yes—
232C2×#125C2318yes—
233C2×#125C2318yes—
234C2×#125C2318yes—
235C2×#125C2318yes—
236C2×C22⋊Q8—44no—
237C2×C22⋊Q8—44no—
238C2×C22⋊Q8—44no—
239C2×C22⋊Q8Q8116yescomplemented
240C2×C22⋊Q8C2318yes—
241C2×C22⋊Q8C2318yes—
242C2×C22⋊Q8C2318yes—
243C2×C22⋊Q8C2318yes—
244C2×C4×Q8—44no—
245C2×C4×Q8—44no—
246C2×C4×Q8—44no—
247C2×C4×Q8C2318yes—
248C2×C4×Q8C2318yes—
249C2×C4×Q8C2318yes—
250C2×#117—44no—
251C2×#117C2318yes—
252C22×C4⋊C4C2311yescharacteristic
253C22×C4⋊C4C2311yescharacteristic
254C22×C4⋊C4C2311yescharacteristic
255C22×C4⋊C4C2311yescharacteristic
256C22×C4⋊C4C2311yescharacteristic
257C22×C4⋊C4C2311yescharacteristic
258C22×C4⋊C4C2311yescharacteristic
259C22×C4⋊C4C2311yescharacteristic
260C22×C4⋊C4C2311yescharacteristic
261C22×C4⋊C4C2311yescharacteristic
262C22×C4⋊C4C2311yescharacteristic
263C22×C4⋊C4C2311yescharacteristic
264C22×C4⋊C4C2311yescharacteristic
265C22×C4⋊C4C2311yescharacteristic
266C22×C4⋊C4C2311yescharacteristic
267C22×C4⋊C4C2311yescharacteristic
268C22×C4⋊C4C2311yescharacteristic
269C22×C4⋊C4C2311yescharacteristic
270C22×C4⋊C4C2311yescharacteristic
271C22×C4⋊C4C2311yescharacteristic
272C22×C4⋊C4C2311yescharacteristic
273C22×C4⋊C4C2311yescharacteristic
274C22×C4⋊C4C2311yescharacteristic
275C22×C4⋊C4C2311yescharacteristic
276C22×C4⋊C4C2311yescharacteristic
277C22×C4⋊C4C2311yescharacteristic
278C22×C4⋊C4C2311yescharacteristic
279C22×C4⋊C4C2311yescharacteristic
280C22×C4⋊C4C2311yescharacteristic
281C22×C4⋊C4C2311yescharacteristic
282C22×C4⋊C4C2311yescharacteristic
283C22×C4⋊C4C2311yescharacteristic
284C22×C4⋊C4C2311yescharacteristic
285C22×C4⋊C4C2311yescharacteristic
286C22×C4⋊C4C2311yescharacteristic
287C22×C4⋊C4C2311yescharacteristic
288C22×C4⋊C4C2311yescharacteristic
289C22×C4⋊C4C2311yescharacteristic
290C22×C4⋊C4C2311yescharacteristic
291C22×C4⋊C4C2311yescharacteristic
292C22×C4⋊C4C2311yescharacteristic
293C22×C4⋊C4C2311yescharacteristic
294C22×C4⋊C4C2311yescharacteristic
295C22×C4⋊C4C2311yescharacteristic
296C22×C4⋊C4C2311yescharacteristic
297C22×C4⋊C4C2311yescharacteristic
298C22×C4⋊C4C2311yescharacteristic
299C22×C4⋊C4C2311yescharacteristic
300C22×C4⋊C4C2311yescharacteristic
301C22×C4⋊C4C2311yescharacteristic
302C22×C4⋊C4C2311yescharacteristic
303C22×C4⋊C4C2311yescharacteristic
304C22×C4⋊C4C2311yescharacteristic
305C22×C4⋊C4C2311yescharacteristic
306C22×C4⋊C4C2311yescharacteristic
307C22×C4⋊C4C2311yescharacteristic
308C22×C4⋊C4C2311yescharacteristic
309C22×C4⋊C4C2311yescharacteristic
310C22×C4⋊C4C2311yescharacteristic
311C22×C4⋊C4C2311yescharacteristic
312C22×C4⋊C4C2311yescharacteristic
313C22×C4⋊C4C2311yescharacteristic
314C22×C4⋊C4C2311yescharacteristic
315C22×C4⋊C4C2311yescharacteristic
316C22×C22⋊C4C2311yescharacteristic
317C22×C22⋊C4C2311yescharacteristic
318C22×C22⋊C4C2311yescharacteristic
319C22×C22⋊C4C2311yescharacteristic
320C22×C22⋊C4C2311yescharacteristic
321C22×C22⋊C4C2311yescharacteristic
322C22×C22⋊C4C2311yescharacteristic
323C22×C22⋊C4C2311yescharacteristic
324C22×C22⋊C4C2311yescharacteristic
325C22×C22⋊C4C2311yescharacteristic
326C22×C22⋊C4C2311yescharacteristic
327C22×C22⋊C4C2311yescharacteristic
328C22×C42C2311yescharacteristic
329C22×C42C2311yescharacteristic
330C22×C42C2311yescharacteristic
331C22×C42C2311yescharacteristic
332C22×C42C2311yescharacteristic
333C22×C42C2311yescharacteristic
334C22×C42C2311yescharacteristic
335C22×C42C2311yescharacteristic
336C22×C42C2311yescharacteristic
337C22×C42C2311yescharacteristic
338C22×C42C2311yescharacteristic
339C22×C42C2311yescharacteristic
340C22×C42C2311yescharacteristic
341C22×C42C2311yescharacteristic
342C22×C42C2311yescharacteristic
343C22×C42C2311yescharacteristic
344#400C2318yes—
345#400C2318yes—
346#399C2318yes—
347#399C2318yes—
348#399C2318yes—
349#399C2318yes—
350#398C2318yes—
351#398C2318yes—
352#398C2318yes—
353#398C2318yes—
354#398C2318yes—
355#398C2318yes—
356#398C2318yes—
357#398C2318yes—
358#398C2318yes—
359#398C2318yes—
360#398C2318yes—
361#398C2318yes—
362#398C2318yes—
363#398C2318yes—
364#398C2318yes—
365#398C2318yes—
366#398C2318yes—
367#398C2318yes—
368#398C2318yes—
369#398C2318yes—
370#398C2318yes—
371#398C2318yes—
372#398C2318yes—
373#398C2318yes—
374#398C2318yes—
375#398C2318yes—
376#398C2318yes—
377#398C2318yes—
378#396C2318yes—
379#396C2318yes—
380#396C2318yes—
381#396C2318yes—
382#395C2318yes—
383#395C2318yes—
384#395C2318yes—
385#395C2318yes—
386#395C2318yes—
387#395C2318yes—
388#395C2318yes—
389#395C2318yes—
390#395C2318yes—
391#395C2318yes—
392#391C2318yes—
393#391C2318yes—
394#391C2318yes—
395#391C2318yes—
396#391C2318yes—
397#391C2318yes—
398#391C2318yes—
399#391C2318yes—
400#391C2318yes—
401#391C2318yes—
402#391C2318yes—
403#389C2318yes—
404#389C2318yes—
405#389C2318yes—
406#389C2318yes—
407#389C2318yes—
408#389C2318yes—
409#389C2318yes—
410#389C2318yes—
411#389C2318yes—
412#389C2318yes—
413#389C2318yes—
414#389C2318yes—
415#389C2318yes—
416#389C2318yes—
417#389C2318yes—
418#389C2318yes—
419#389C2318yes—
420#389C2318yes—
421#389C2318yes—
422#389C2318yes—
423#389C2318yes—
424#389C2318yes—
425#389C2318yes—
426#389C2318yes—
427#389C2318yes—
428#388C2318yes—
429#388C2318yes—
430#388C2318yes—
431#388C2318yes—
432#388C2318yes—
433#388C2318yes—
434#388C2318yes—
435#388C2318yes—
436#387C2318yes—
437#387C2318yes—
438#387C2318yes—
439#387C2318yes—
440#387C2318yes—
441#387C2318yes—
442#387C2318yes—
443#387C2318yes—
444#387C2318yes—
445#387C2318yes—
446#387C2318yes—
447#387C2318yes—
448#387C2318yes—
449#387C2318yes—
450#387C2318yes—
451#387C2318yes—
452#387C2318yes—
453#387C2318yes—
454#387C2318yes—
455#387C2318yes—
456#387C2318yes—
457#387C2318yes—
458#387C2318yes—
459#387C2318yes—
460#387C2318yes—
461#387C2318yes—
462#385C2318yes—
463#385C2318yes—
464#385C2318yes—
465#385C2318yes—
466#384C2318yes—
467#384C2318yes—
468#384C2318yes—
469#384C2318yes—
470#382C2318yes—
471#381C2318yes—
472#380C2318yes—
473#380C2318yes—
474#380C2318yes—
475#380C2318yes—
476#380C2318yes—
477C4×C4⋊C4C2318yes—
478C4×C4⋊C4C2318yes—
479C4×C4⋊C4C2318yes—
480C4×C4⋊C4C2318yes—
481C4×C4⋊C4C2318yes—
482C4×C22⋊C4C2318yes—
483C4×C22⋊C4C2318yes—
484C4×C22⋊C4C2318yes—
485C2×#95C2318yes—
486C2×#95C2311yescharacteristic
487C2×#95C2311yescharacteristic
488C2×#95C2311yescharacteristic
489C2×#95C2311yescharacteristic
490C2×#95C2311yescharacteristic
491C2×#95C2311yescharacteristic
492C2×#95C2311yescharacteristic
493C2×#95C2311yescharacteristic
494C2×#95C2311yescharacteristic
495C2×#95C2311yescharacteristic
496C2×#95C2311yescharacteristic
497C2×#95C2311yescharacteristic
498C2×#95C2311yescharacteristic
499C2×#95C2311yescharacteristic
500C2×#95C2311yescharacteristic
501C2×#95C2311yescharacteristic
502C2×#95C2311yescharacteristic
503C2×#95C2311yescharacteristic
504C2×#95C2311yescharacteristic
505C2×#95C2311yescharacteristic
506C2×#95C2311yescharacteristic
507C2×#95C2311yescharacteristic
508C2×#95C2311yescharacteristic
509C2×#95C2311yescharacteristic
510C2×#95C2311yescharacteristic
511C2×#95C2311yescharacteristic
512C2×#95C2311yescharacteristic
513C2×#95C2311yescharacteristic
514C2×#95C2311yescharacteristic
515C2×#95C2311yescharacteristic
516C2×#95C2311yescharacteristic
517C2×#95C2311yescharacteristic
518C2×#95C2311yescharacteristic
519C2×#95C2311yescharacteristic
520C2×#95C2311yescharacteristic
521C2×#95C2311yescharacteristic
522C2×#95C2311yescharacteristic
523C2×#95C2311yescharacteristic
524C2×#95C2311yescharacteristic
525C2×#95C2311yescharacteristic
526C2×#95C2311yescharacteristic
527C2×#95C2311yescharacteristic
528C2×#95C2311yescharacteristic
529C2×#95C2311yescharacteristic
530C2×#95C2311yescharacteristic
531C2×#95C2311yescharacteristic
532C2×#95C2311yescharacteristic
533C2×#95C2311yescharacteristic
534C2×#95C2311yescharacteristic
535C2×#95C2311yescharacteristic
536C2×#95C2311yescharacteristic
537C2×#95C2311yescharacteristic
538C2×#95C2311yescharacteristic
539C2×#95C2311yescharacteristic
540C2×#95C2311yescharacteristic
541C2×#95C2311yescharacteristic
542C25C2411yescharacteristic
543C22×Q8—24no—
544C22×Q8—24no—
545C22×Q8—24no—
546C22×Q8—42no—
547C22×Q8—42no—
548C22×Q8—42no—
549C22×Q8—42no—
550C22×Q8—42no—
551C22×Q8—42no—
552C22×Q8—42no—
553C22×Q8—42no—
554C22×Q8C2×Q818yes—
555C22×Q8C2414yes—
556C22×Q8C2414yes—
557C22×Q8C2414yes—
558C22×Q8C2414yes—
559C23×C4—24no—
560C23×C4—24no—
561C23×C4—42no—
562C23×C4—42no—
563C23×C4—42no—
564C23×C4—42no—
565C23×C4—42no—
566C23×C4—42no—
567C23×C4C2×Q818yes—
568C23×C4C2411yescharacteristic
569C23×C4C2411yescharacteristic
570C23×C4C2411yescharacteristic
571C23×C4C2411yescharacteristic
572C23×C4C2411yescharacteristic
573C23×C4C2411yescharacteristic
574C23×C4C2411yescharacteristic
575C23×C4C2411yescharacteristic
576C23×C4C2411yescharacteristic
577C23×C4C2411yescharacteristic
578C23×C4C2411yescharacteristic
579C23×C4C2411yescharacteristic
580C23×C4C2411yescharacteristic
581C23×C4C2411yescharacteristic
582C23×C4C2411yescharacteristic
583C23×C4C2411yescharacteristic
584C23×C4C2411yescharacteristic
585C23×C4C2411yescharacteristic
586C23×C4C2411yescharacteristic
587C23×C4C2411yescharacteristic
588C23×C4C2411yescharacteristic
589C23×C4C2411yescharacteristic
590C23×C4C2411yescharacteristic
591C23×C4C2411yescharacteristic
592C23×C4C2411yescharacteristic
593C23×C4C2411yescharacteristic
594C23×C4C2411yescharacteristic
595C23×C4C2411yescharacteristic
596C23×C4C2411yescharacteristic
597C23×C4C2411yescharacteristic
598C23×C4C2414yes—
599C23×C4C2414yes—
600C23×C4C2414yes—
601#125—416no—
602#125—416no—
603#125—416no—
604#125—416no—
605#125—416no—
606C22⋊Q8—416no—
607C22⋊Q8—416no—
608C22⋊Q8—416no—
609C22⋊Q8C2×Q8164yescomplemented
610C4×Q8—416no—
611C4×Q8—416no—
612C4×Q8—416no—
613#117—416no—
614C2×C4⋊C4—24no—
615C2×C4⋊C4—24no—
616C2×C4⋊C4—24no—
617C2×C4⋊C4—24no—
618C2×C4⋊C4—24no—
619C2×C4⋊C4—24no—
620C2×C4⋊C4—24no—
621C2×C4⋊C4—24no—
622C2×C4⋊C4—24no—
623C2×C4⋊C4—24no—
624C2×C4⋊C4—24no—
625C2×C4⋊C4—24no—
626C2×C4⋊C4—24no—
627C2×C4⋊C4—24no—
628C2×C4⋊C4—24no—
629C2×C4⋊C4—24no—
630C2×C4⋊C4—42no—
631C2×C4⋊C4—42no—
632C2×C4⋊C4—42no—
633C2×C4⋊C4—42no—
634C2×C4⋊C4—42no—
635C2×C4⋊C4—42no—
636C2×C4⋊C4—42no—
637C2×C4⋊C4—42no—
638C2×C4⋊C4—42no—
639C2×C4⋊C4—42no—
640C2×C4⋊C4—42no—
641C2×C4⋊C4—42no—
642C2×C4⋊C4—42no—
643C2×C4⋊C4—42no—
644C2×C4⋊C4—42no—
645C2×C4⋊C4—42no—
646C2×C4⋊C4—42no—
647C2×C4⋊C4—42no—
648C2×C4⋊C4—42no—
649C2×C4⋊C4—42no—
650C2×C4⋊C4—42no—
651C2×C4⋊C4—42no—
652C2×C4⋊C4—42no—
653C2×C4⋊C4—42no—
654C2×C4⋊C4—42no—
655C2×C4⋊C4—42no—
656C2×C4⋊C4—42no—
657C2×C4⋊C4—42no—
658C2×C4⋊C4—42no—
659C2×C4⋊C4—42no—
660C2×C4⋊C4—42no—
661C2×C4⋊C4—42no—
662C2×C4⋊C4—42no—
663C2×C4⋊C4—42no—
664C2×C4⋊C4—42no—
665C2×C4⋊C4—42no—
666C2×C4⋊C4—42no—
667C2×C4⋊C4—42no—
668C2×C4⋊C4—42no—
669C2×C4⋊C4—42no—
670C2×C4⋊C4—42no—
671C2×C4⋊C4—42no—
672C2×C4⋊C4—42no—
673C2×C4⋊C4—42no—
674C2×C4⋊C4—42no—
675C2×C4⋊C4C2×Q818yes—
676C2×C4⋊C4C2×Q818yes—
677C2×C4⋊C4C2×Q818yes—
678C2×C4⋊C4C2414yes—
679C2×C4⋊C4C2414yes—
680C2×C4⋊C4C2414yes—
681C2×C4⋊C4C2414yes—
682C2×C4⋊C4C2414yes—
683C2×C4⋊C4C2414yes—
684C2×C4⋊C4C2414yes—
685C2×C4⋊C4C2414yes—
686C2×C4⋊C4C2414yes—
687C2×C4⋊C4C2414yes—
688C2×C4⋊C4C2414yes—
689C2×C4⋊C4C2414yes—
690C2×C4⋊C4C2414yes—
691C2×C4⋊C4C2414yes—
692C2×C4⋊C4C2414yes—
693C2×C4⋊C4C2414yes—
694C2×C4⋊C4C2414yes—
695C2×C4⋊C4C2414yes—
696C2×C4⋊C4C2414yes—
697C2×C4⋊C4C2414yes—
698C2×C4⋊C4C2414yes—
699C2×C4⋊C4C2414yes—
700C2×C4⋊C4C2414yes—
701C2×C4⋊C4C2414yes—
702C2×C4⋊C4C2414yes—
703C2×C4⋊C4C2414yes—
704C2×C4⋊C4C2414yes—
705C2×C4⋊C4C2414yes—
706C2×C4⋊C4C2414yes—
707C2×C4⋊C4C2414yes—
708C2×C4⋊C4C2414yes—
709C2×C4⋊C4C2414yes—
710C2×C4⋊C4C2414yes—
711C2×C4⋊C4C2414yes—
712C2×C4⋊C4C2414yes—
713C2×C4⋊C4C2414yes—
714C2×C4⋊C4C2414yes—
715C2×C4⋊C4C2414yes—
716C2×C4⋊C4C2414yes—
717C2×C4⋊C4C2414yes—
718C2×C4⋊C4C2414yes—
719C2×C4⋊C4C2414yes—
720C2×C4⋊C4C2414yes—
721C2×C4⋊C4C2414yes—
722C2×C4⋊C4C2414yes—
723C2×C4⋊C4C2414yes—
724C2×C4⋊C4C2414yes—
725C2×C4⋊C4C2414yes—
726C2×C4⋊C4C2414yes—
727C2×C4⋊C4C2414yes—
728C2×C4⋊C4C2414yes—
729C2×C4⋊C4C2414yes—
730C2×C4⋊C4C2414yes—
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2414yes—
733C2×C4⋊C4C2414yes—
734C2×C4⋊C4C2414yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2414yes—
737C2×C4⋊C4C2414yes—
738C2×C4⋊C4C2414yes—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2414yes—
741C2×C4⋊C4C2414yes—
742C2×C22⋊C4—24no—
743C2×C22⋊C4—24no—
744C2×C22⋊C4—42no—
745C2×C22⋊C4—42no—
746C2×C22⋊C4—42no—
747C2×C22⋊C4—42no—
748C2×C22⋊C4—42no—
749C2×C22⋊C4—42no—
750C2×C22⋊C4—42no—
751C2×C22⋊C4—42no—
752C2×C22⋊C4C2×Q818yes—
753C2×C22⋊C4C2×Q818yes—
754C2×C22⋊C4C2414yes—
755C2×C22⋊C4C2414yes—
756C2×C22⋊C4C2414yes—
757C2×C22⋊C4C2414yes—
758C2×C22⋊C4C2414yes—
759C2×C22⋊C4C2414yes—
760C2×C22⋊C4C2414yes—
761C2×C22⋊C4C2414yes—
762C2×C22⋊C4C2414yes—
763C2×C22⋊C4C2414yes—
764C2×C22⋊C4C2414yes—
765C2×C22⋊C4C2414yes—
766C2×C42—24no—
767C2×C42—24no—
768C2×C42—24no—
769C2×C42—24no—
770C2×C42—24no—
771C2×C42—42no—
772C2×C42—42no—
773C2×C42—42no—
774C2×C42—42no—
775C2×C42—42no—
776C2×C42—42no—
777C2×C42—42no—
778C2×C42—42no—
779C2×C42—42no—
780C2×C42—42no—
781C2×C42—42no—
782C2×C42C2414yes—
783C2×C42C2414yes—
784C2×C42C2414yes—
785C2×C42C2414yes—
786C2×C42C2414yes—
787C2×C42C2414yes—
788C2×C42C2414yes—
789C2×C42C2414yes—
790C2×C42C2414yes—
791C2×C42C2414yes—
792C2×C42C2414yes—
793C2×C42C2414yes—
794C2×C42C2414yes—
795C2×C42C2414yes—
796C2×C42C2414yes—
797C2×C42C2414yes—
798#95C2414yes—
799#95C2414yes—
800#95C2414yes—
801#95C2414yes—
802#95C2414yes—
803#95C2414yes—
804#95C2414yes—
805#95C2414yes—
806#95C2414yes—
807#95C2414yes—
808#95C2414yes—
809#95C2414yes—
810#95C2414yes—
811#95C2414yes—
812#95C2414yes—
813#95C2414yes—
814#95C2414yes—
815#95C2414yes—
816#95C2414yes—
817#95C2414yes—
818#95C2414yes—
819#95C2414yes—
820#95C2414yes—
821#95C2414yes—
822#95C2414yes—
823#95C2414yes—
824#95C2414yes—
825#95C2414yes—
826#95C2414yes—
827#95C2414yes—
828#95C2414yes—
829#95C2414yes—
830#95C2414yes—
831#95C2414yes—
832#95C2414yes—
833#95C2414yes—
834#95C2414yes—
835#95C2414yes—
836#95C2414yes—
837#95C2414yes—
838#95C2414yes—
839#95C2414yes—
840#95C2414yes—
841#95C2414yes—
842#95C2414yes—
843#95C2414yes—
844#95C2414yes—
845#95C2414yes—
846#95C2414yes—
847#95C2414yes—
848#95C2414yes—
849#95C2414yes—
850#95C2414yes—
851#95C2414yes—
852#95C2414yes—
853#95C2414yes—
854C24—22no—
855C24—22no—
856C24—22no—
857C24—22no—
858C24—22no—
859C24—22no—
860C24C22×Q814yes—
861C24C2512yes—
862C24C2511yescharacteristic
863C2×Q8—28no—
864C2×Q8—28no—
865C2×Q8—28no—
866C2×Q8—44no—
867C2×Q8—416no—
868C2×Q8—44no—
869C2×Q8—44no—
870C2×Q8—44no—
871C2×Q8—44no—
872C2×Q8—44no—
873C2×Q8—44no—
874C2×Q8—44no—
875C2×Q8—416no—
876C2×Q8—416no—
877C2×Q8—88no—
878C2×Q8C22×Q8116yes—
879C22×C4—22no—
880C22×C4—22no—
881C22×C4—22no—
882C22×C4—22no—
883C22×C4—22no—
884C22×C4—22no—
885C22×C4—22no—
886C22×C4—22no—
887C22×C4—22no—
888C22×C4—22no—
889C22×C4—22no—
890C22×C4—22no—
891C22×C4—22no—
892C22×C4—22no—
893C22×C4—22no—
894C22×C4—22no—
895C22×C4—22no—
896C22×C4—22no—
897C22×C4—22no—
898C22×C4—22no—
899C22×C4—22no—
900C22×C4—22no—
901C22×C4—22no—
902C22×C4—22no—
903C22×C4—22no—
904C22×C4—22no—
905C22×C4—22no—
906C22×C4—22no—
907C22×C4—22no—
908C22×C4—22no—
909C22×C4—22no—
910C22×C4—22no—
911C22×C4—22no—
912C22×C4—22no—
913C22×C4—22no—
914C22×C4—22no—
915C22×C4—22no—
916C22×C4—22no—
917C22×C4—22no—
918C22×C4—22no—
919C22×C4—22no—
920C22×C4—22no—
921C22×C4—22no—
922C22×C4—22no—
923C22×C4—22no—
924C22×C4—22no—
925C22×C4—22no—
926C22×C4—22no—
927C22×C4—22no—
928C22×C4—22no—
929C22×C4—22no—
930C22×C4—22no—
931C22×C4—22no—
932C22×C4—22no—
933C22×C4—22no—
934C22×C4—22no—
935C22×C4—22no—
936C22×C4—22no—
937C22×C4—22no—
938C22×C4—22no—
939C22×C4—22no—
940C22×C4—22no—
941C22×C4—22no—
942C22×C4—22no—
943C22×C4—22no—
944C22×C4—22no—
945C22×C4—22no—
946C22×C4—22no—
947C22×C4—22no—
948C22×C4—22no—
949C22×C4—22no—
950C22×C4—22no—
951C22×C4—22no—
952C22×C4—22no—
953C22×C4—22no—
954C22×C4—22no—
955C22×C4—22no—
956C22×C4—22no—
957C22×C4—22no—
958C22×C4—22no—
959C22×C4—28no—
960C22×C4—28no—
961C22×C4—44no—
962C22×C4—416no—
963C22×C4—44no—
964C22×C4—44no—
965C22×C4—44no—
966C22×C4—44no—
967C22×C4—44no—
968C22×C4—88no—
969C22×C4—88no—
970C22×C4C22×Q814yes—
971C22×C4C22×Q814yes—
972C22×C4C22×Q814yes—
973C22×C4C22×Q814yes—
974C22×C4C22×Q814yes—
975C22×C4C22×Q814yes—
976C22×C4C22×Q8116yes—
977C22×C4H(5,𝔽2)14yes—
978C22×C4H(5,𝔽2)14yes—
979C22×C42−1+414yes—
980C22×C42−1+414yes—
981C22×C4C2512yes—
982C22×C4C2512yes—
983C22×C4C2512yes—
984C22×C4C2512yes—
985C22×C4C2512yes—
986C22×C4C2512yes—
987C22×C4C2512yes—
988C22×C4C2512yes—
989C22×C4C2512yes—
990C22×C4C2512yes—
991C22×C4C2512yes—
992C22×C4C2512yes—
993C22×C4C2512yes—
994C22×C4C2512yes—
995C22×C4C2512yes—
996C22×C4C2512yes—
997C22×C4C2512yes—
998C22×C4C2512yes—
999C22×C4C2512yes—
1000C22×C4C2512yes—
1001C22×C4C2512yes—
1002C22×C4C2512yes—
1003C22×C4C2512yes—
1004C22×C4C2512yes—
1005C22×C4C2512yes—
1006C22×C4C2512yes—
1007C22×C4C2512yes—
1008C22×C4C2512yes—
1009C22×C4C2512yes—
1010C22×C4C2512yes—
1011C4⋊C4—28no—
1012C4⋊C4—28no—
1013C4⋊C4—28no—
1014C4⋊C4—28no—
1015C4⋊C4—28no—
1016C4⋊C4—28no—
1017C4⋊C4—28no—
1018C4⋊C4—28no—
1019C4⋊C4—28no—
1020C4⋊C4—28no—
1021C4⋊C4—28no—
1022C4⋊C4—28no—
1023C4⋊C4—28no—
1024C4⋊C4—28no—
1025C4⋊C4—28no—
1026C4⋊C4—28no—
1027C4⋊C4—44no—
1028C4⋊C4—44no—
1029C4⋊C4—44no—
1030C4⋊C4—44no—
1031C4⋊C4—44no—
1032C4⋊C4—44no—
1033C4⋊C4—44no—
1034C4⋊C4—44no—
1035C4⋊C4—44no—
1036C4⋊C4—44no—
1037C4⋊C4—44no—
1038C4⋊C4—44no—
1039C4⋊C4—44no—
1040C4⋊C4—44no—
1041C4⋊C4—44no—
1042C4⋊C4—44no—
1043C4⋊C4—44no—
1044C4⋊C4—44no—
1045C4⋊C4—44no—
1046C4⋊C4—44no—
1047C4⋊C4—44no—
1048C4⋊C4—44no—
1049C4⋊C4—44no—
1050C4⋊C4—44no—
1051C4⋊C4—44no—
1052C4⋊C4—44no—
1053C4⋊C4—44no—
1054C4⋊C4—44no—
1055C4⋊C4—44no—
1056C4⋊C4—44no—
1057C4⋊C4—44no—
1058C4⋊C4—44no—
1059C4⋊C4—44no—
1060C4⋊C4—44no—
1061C4⋊C4—44no—
1062C4⋊C4—44no—
1063C4⋊C4—44no—
1064C4⋊C4—44no—
1065C4⋊C4—44no—
1066C4⋊C4—44no—
1067C4⋊C4—44no—
1068C4⋊C4—44no—
1069C4⋊C4—44no—
1070C4⋊C4—44no—
1071C4⋊C4—44no—
1072C4⋊C4C22×Q8116yes—
1073C4⋊C4C22×Q8116yes—
1074C4⋊C4C22×Q8116yes—
1075C22⋊C4—28no—
1076C22⋊C4—28no—
1077C22⋊C4—44no—
1078C22⋊C4—44no—
1079C22⋊C4—44no—
1080C22⋊C4—44no—
1081C22⋊C4—44no—
1082C22⋊C4—44no—
1083C22⋊C4—44no—
1084C22⋊C4—44no—
1085C22⋊C4C22×Q8116yes—
1086C22⋊C4C22×Q8116yes—
1087C42—28no—
1088C42—28no—
1089C42—28no—
1090C42—28no—
1091C42—28no—
1092C42—44no—
1093C42—44no—
1094C42—44no—
1095C42—44no—
1096C42—44no—
1097C42—44no—
1098C42—44no—
1099C42—44no—
1100C42—44no—
1101C42—44no—
1102C42—44no—
1103C23—22no—
1104C23—22no—
1105C23—22no—
1106C23—22no—
1107C23—22no—
1108C23—22no—
1109C23—28no—
1110C23—28no—
1111C23—28no—
1112C23—44no—
1113C23—44no—
1114C23—44no—
1115C23—44no—
1116C23C23×Q814yes—
1117C23C23×Q812yes—
1118C23C2×H(5,𝔽2)12yes—
1119C23C2×H(5,𝔽2)12yes—
1120C23C2×2−1+412yes—
1121C23C2×2−1+412yes—
1122C23#58512yes—
1123C23#58512yes—
1124C23C2611yescharacteristic
1125Q8—416no—
1126Q8—416no—
1127Q8—416no—
1128Q8—88no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—28no—
1150C2×C4—28no—
1151C2×C4—28no—
1152C2×C4—28no—
1153C2×C4—28no—
1154C2×C4—28no—
1155C2×C4—28no—
1156C2×C4—28no—
1157C2×C4—28no—
1158C2×C4—28no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—22no—
1189C2×C4—22no—
1190C2×C4—22no—
1191C2×C4—22no—
1192C2×C4—22no—
1193C2×C4—22no—
1194C2×C4—22no—
1195C2×C4—22no—
1196C2×C4—22no—
1197C2×C4—22no—
1198C2×C4—22no—
1199C2×C4—22no—
1200C2×C4—22no—
1201C2×C4—22no—
1202C2×C4—22no—
1203C2×C4—22no—
1204C2×C4—22no—
1205C2×C4—22no—
1206C2×C4—22no—
1207C2×C4—22no—
1208C2×C4—22no—
1209C2×C4—22no—
1210C2×C4—22no—
1211C2×C4—22no—
1212C2×C4—22no—
1213C2×C4—22no—
1214C2×C4—22no—
1215C2×C4—22no—
1216C2×C4—22no—
1217C2×C4—22no—
1218C2×C4—22no—
1219C2×C4—416no—
1220C2×C4—44no—
1221C2×C4—44no—
1222C2×C4—44no—
1223C2×C4—44no—
1224C2×C4—44no—
1225C2×C4—44no—
1226C2×C4—44no—
1227C2×C4—44no—
1228C2×C4—44no—
1229C2×C4—44no—
1230C2×C4—44no—
1231C2×C4—44no—
1232C2×C4—44no—
1233C2×C4—44no—
1234C2×C4—44no—
1235C2×C4—44no—
1236C2×C4—44no—
1237C2×C4—44no—
1238C2×C4—44no—
1239C2×C4—44no—
1240C2×C4—88no—
1241C2×C4—88no—
1242C2×C4C23×Q814yes—
1243C2×C4C23×Q814yes—
1244C2×C4C23×Q814yes—
1245C2×C4C23×Q814yes—
1246C2×C4C23×Q814yes—
1247C2×C4C23×Q814yes—
1248C2×C4C2×H(5,𝔽2)14yes—
1249C2×C4C2×H(5,𝔽2)14yes—
1250C2×C4C2×2−1+414yes—
1251C2×C4C2×2−1+414yes—
1252C22—24no—
1253C22—24no—
1254C22—24no—
1255C22—42no—
1256C22—42no—
1257C22—42no—
1258C22—42no—
1259C22—416no—
1260C22#350114yes—
1261C22#350214yes—
1262C22#350314yes—
1263C22#353314yes—
1264C22#353514yes—
1265C22#354814yes—
1266C22#356314yes—
1267C22C24×Q811yescharacteristic
1268C22C22×H(5,𝔽2)11yescharacteristic
1269C22C22×H(5,𝔽2)11yescharacteristic
1270C22C22×2−1+411yescharacteristic
1271C22C22×2−1+411yescharacteristic
1272C22C2×#58511yescharacteristic
1273C22C2×#58511yescharacteristic
1274C4—24no—
1275C4—24no—
1276C4—24no—
1277C4—24no—
1278C4—24no—
1279C4—24no—
1280C4—24no—
1281C4—24no—
1282C4—24no—
1283C4—24no—
1284C4—42no—
1285C4—42no—
1286C4—42no—
1287C4—42no—
1288C4—42no—
1289C4—42no—
1290C4—42no—
1291C4—42no—
1292C4—42no—
1293C4—42no—
1294C4—42no—
1295C4—42no—
1296C4—42no—
1297C4—42no—
1298C4—42no—
1299C4—42no—
1300C4—42no—
1301C4—42no—
1302C4—42no—
1303C4—42no—
1304C2—44no—
1305C2#5159418yesdirect product factor
1306C2C2×#353511yescharacteristic
1307C2C2×#353311yescharacteristic
1308C2C2×#356311yescharacteristic
1309C2C2×#354811yescharacteristic
1310C2C2×#350111yescharacteristic
1311C2C2×#350211yescharacteristic
1312C2C2×#350311yescharacteristic
subgroupG/H
center, socleC24C25
commutator, Frattini, cosocleC23C26
prime radicalC25C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#2806C2semidirect
2. C2×#2806C2semidirect
3. C2×#2792C2semidirect
4. C2×#2791C2semidirect
5. C2×#2791C2semidirect
7. C2×#2755C2semidirect
8. C2×#2726C2semidirect
9. C2×#2726C2semidirect
13. #51594C2direct (N × H)
14. C2×#2582C2semidirect
15. C2×#2552C2semidirect
16. C2×#2565C2semidirect
17. C2×#2584C2semidirect
18. C2×#2586C2semidirect
19. C2×#2586C2semidirect
26. C2×#2462C2semidirect
27. C2×#2462C2semidirect
46. #2806C22semidirect
47. #2806C22semidirect
48. #2792C22semidirect
49. #2791C22semidirect
50. #2791C22semidirect
52. #2755C22semidirect
53. #2726C22semidirect
54. #2726C22semidirect
60. #2586C22semidirect
61. #2586C22semidirect
62. #2584C22semidirect
63. #2582C22semidirect
64. #2565C22semidirect
66. #2552C22semidirect
68. #2462C22semidirect
69. #2462C22semidirect
239. C2×C22⋊Q8Q8semidirect
609. C22⋊Q8C2×Q8semidirect
1305. C2#51594direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#28062
C2×#27922
C2×#27912
C2×#27682
C2×#27552
C2×#27262
C2×#27202
C2×#27042
#515942
C2×#25822
C2×#25522
C2×#25652
C2×#25842
C2×#25862
C2×#25562
C2×#25222
C2×#24382
C2×#24412
C2×#24232
C2×#24622
C2×#26672
C2×#26592
C2×#23782
C2×#23682
C2×#23232