Finite Group Databasebeta

← C2×#51475 #7707342

Subgroups — C2×#51475 #7707342

Order 512.

4480 conjugacy classes of subgroups.

The subgroup lattice has 1238 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2802C211yesmaximal, characteristic, complemented
2C2×#2777C211yesmaximal, characteristic
3C2×#2776C211yesmaximal, characteristic, complemented
4C2×#2776C211yesmaximal, characteristic, complemented
5C2×#2772C211yesmaximal, characteristic
6C2×#2772C211yesmaximal, characteristic
7C2×#2768C211yesmaximal, characteristic
8C2×#2764C211yesmaximal, characteristic
9C2×#2762C211yesmaximal, characteristic, complemented
10C2×#2762C211yesmaximal, characteristic, complemented
11C2×#2755C211yesmaximal, characteristic, complemented
12C2×#2739C211yesmaximal, characteristic
13#51475C2132yesmaximal, direct product factor
14C2×#2582C211yesmaximal, characteristic, complemented
15C2×#2612C211yesmaximal, characteristic, complemented
16C2×#2604C211yesmaximal, characteristic
17C2×#2606C211yesmaximal, characteristic, complemented
18C2×#2606C211yesmaximal, characteristic, complemented
19C2×#2594C211yesmaximal, characteristic
20C2×#2587C211yesmaximal, characteristic
21C2×#2585C211yesmaximal, characteristic, complemented
22C2×#2527C211yesmaximal, characteristic
23C2×#2533C211yesmaximal, characteristic, complemented
24C2×#2533C211yesmaximal, characteristic, complemented
25C2×#2532C211yesmaximal, characteristic
26C2×#2532C211yesmaximal, characteristic
27C2×#2530C211yesmaximal, characteristic
28C2×#2647C211yesmaximal, characteristic, complemented
29C2×#2637C211yesmaximal, characteristic
30C2×#2383C211yesmaximal, characteristic
31C2×#2356C211yesmaximal, characteristic, complemented
32C2×#2320C211yesmaximal, characteristic, complemented
33C22×#126C2211yescharacteristic
34C22×C4×Q8C2211yescharacteristic
35C22×C4×Q8C2211yescharacteristic
36#2802C22116yescomplemented
37#2777C22116yes—
38#2776C22116yescomplemented
39#2776C22116yescomplemented
40#2772C22116yes—
41#2772C22116yes—
42#2768C22116yes—
43#2764C22116yes—
44#2762C22116yescomplemented
45#2762C22116yescomplemented
46#2755C22116yescomplemented
47#2739C22116yes—
48#2647C22116yescomplemented
49#2637C22116yes—
50#2612C22116yescomplemented
51#2606C22116yescomplemented
52#2606C22116yescomplemented
53#2604C22116yes—
54#2594C22116yes—
55#2587C22116yes—
56#2585C22116yescomplemented
57#2582C22116yescomplemented
58#2533C22116yescomplemented
59#2533C22116yescomplemented
60#2532C22116yes—
61#2532C22116yes—
62#2530C22116yes—
63#2527C22116yes—
64C2×#401C2211yescharacteristic
65C2×#401C2211yescharacteristic
66C2×#400C2211yescharacteristic
67C2×#400C2211yescharacteristic
68C2×#400C2211yescharacteristic
69C2×#400C2211yescharacteristic
70C2×#400C2211yescharacteristic
71C2×#400C2211yescharacteristic
72C2×#400C2211yescharacteristic
73C2×#400C2211yescharacteristic
74C2×#400C2211yescharacteristic
75C2×#400C2211yescharacteristic
76C2×#400C2211yescharacteristic
77C2×#400C2211yescharacteristic
78C2×#400C2211yescharacteristic
79C2×#400C2211yescharacteristic
80C2×#400C2211yescharacteristic
81C2×#399C2211yescharacteristic
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×#397C2211yescharacteristic
100C2×#397C2211yescharacteristic
101C2×#397C2211yescharacteristic
102C2×#397C2211yescharacteristic
103C2×#397C2211yescharacteristic
104C2×#396C2211yescharacteristic
105C2×#396C2211yescharacteristic
106C2×#396C2211yescharacteristic
107C2×#396C2211yescharacteristic
108C2×#395C2211yescharacteristic
109C2×#395C2211yescharacteristic
110C2×#393C2211yescharacteristic
111C2×#393C2211yescharacteristic
112#2383C22116yes—
113#2356C22116yescomplemented
114#2320C22116yescomplemented
115C2×#391C2211yescharacteristic
116C2×#391C2211yescharacteristic
117C2×#391C2211yescharacteristic
118C2×#391C2211yescharacteristic
119C2×#391C2211yescharacteristic
120C2×#391C2211yescharacteristic
121C2×#391C2211yescharacteristic
122C2×#391C2211yescharacteristic
123C2×#389C2211yescharacteristic
124C2×#389C2211yescharacteristic
125C2×#389C2211yescharacteristic
126C2×#389C2211yescharacteristic
127C2×#389C2211yescharacteristic
128C2×#389C2211yescharacteristic
129C2×#389C2211yescharacteristic
130C2×#389C2211yescharacteristic
131C2×#389C2211yescharacteristic
132C2×#389C2211yescharacteristic
133C2×#389C2211yescharacteristic
134C2×#389C2211yescharacteristic
135C2×#389C2211yescharacteristic
136C2×#389C2211yescharacteristic
137C2×#389C2211yescharacteristic
138C2×#389C2211yescharacteristic
139C2×#389C2211yescharacteristic
140C2×#389C2211yescharacteristic
141C2×#389C2211yescharacteristic
142C2×#389C2211yescharacteristic
143C2×#388C2211yescharacteristic
144C2×#388C2211yescharacteristic
145C2×#388C2211yescharacteristic
146C2×#388C2211yescharacteristic
147C2×#388C2211yescharacteristic
148C2×#388C2211yescharacteristic
149C2×#388C2211yescharacteristic
150C2×#388C2211yescharacteristic
151C2×#388C2211yescharacteristic
152C2×#388C2211yescharacteristic
153C2×#388C2211yescharacteristic
154C2×#388C2211yescharacteristic
155C2×#388C2211yescharacteristic
156C2×#388C2211yescharacteristic
157C2×#388C2211yescharacteristic
158C2×#387C2211yescharacteristic
159C2×#387C2211yescharacteristic
160C2×#387C2211yescharacteristic
161C2×#387C2211yescharacteristic
162C2×#387C2211yescharacteristic
163C2×#387C2211yescharacteristic
164C2×#387C2211yescharacteristic
165C2×#387C2211yescharacteristic
166C2×#387C2211yescharacteristic
167C2×#387C2211yescharacteristic
168C2×#387C2211yescharacteristic
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×#385C2211yescharacteristic
192C2×#385C2211yescharacteristic
193C2×#385C2211yescharacteristic
194C2×#385C2211yescharacteristic
195C2×#384C2211yescharacteristic
196C2×#383C2211yescharacteristic
197C2×#383C2211yescharacteristic
198C2×#383C2211yescharacteristic
199C2×#383C2211yescharacteristic
200C2×#383C2211yescharacteristic
201C2×#383C2211yescharacteristic
202C2×#382C2211yescharacteristic
203C2×#382C2211yescharacteristic
204C2×#382C2211yescharacteristic
205C2×#382C2211yescharacteristic
206C2×#381C2211yescharacteristic
207C2×#380C2211yescharacteristic
208C2×C4×C4⋊C4C2211yescharacteristic
209C2×C4×C4⋊C4C2211yescharacteristic
210C2×C4×C4⋊C4C2211yescharacteristic
211C2×C4×C4⋊C4C2211yescharacteristic
212C2×C4×C4⋊C4C2211yescharacteristic
213C2×C4×C22⋊C4C2211yescharacteristic
214C2×#376C2211yescharacteristic
215C2×#376C2211yescharacteristic
216C2×#376C2211yescharacteristic
217C2×#376C2211yescharacteristic
218C2×#376C2211yescharacteristic
219C23×Q8C2311yescharacteristic
220C23×Q8C2311yescharacteristic
221C24×C4C2311yescharacteristic
222C2×#126—28no—
223C2×#126C2318yes—
224C2×C4×Q8—28no—
225C2×C4×Q8—28no—
226C2×C4×Q8C2318yes—
227C2×C4×Q8C2318yes—
228C22×C4⋊C4C2311yescharacteristic
229C22×C4⋊C4C2311yescharacteristic
230C22×C4⋊C4C2311yescharacteristic
231C22×C4⋊C4C2311yescharacteristic
232C22×C4⋊C4C2311yescharacteristic
233C22×C4⋊C4C2311yescharacteristic
234C22×C4⋊C4C2311yescharacteristic
235C22×C4⋊C4C2311yescharacteristic
236C22×C4⋊C4C2311yescharacteristic
237C22×C4⋊C4C2311yescharacteristic
238C22×C4⋊C4C2311yescharacteristic
239C22×C4⋊C4C2311yescharacteristic
240C22×C4⋊C4C2311yescharacteristic
241C22×C4⋊C4C2311yescharacteristic
242C22×C4⋊C4C2311yescharacteristic
243C22×C4⋊C4C2311yescharacteristic
244C22×C4⋊C4C2311yescharacteristic
245C22×C4⋊C4C2311yescharacteristic
246C22×C4⋊C4C2311yescharacteristic
247C22×C4⋊C4C2311yescharacteristic
248C22×C4⋊C4C2311yescharacteristic
249C22×C4⋊C4C2311yescharacteristic
250C22×C4⋊C4C2311yescharacteristic
251C22×C4⋊C4C2311yescharacteristic
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×C22⋊C4C2311yescharacteristic
277C22×C22⋊C4C2311yescharacteristic
278C22×C22⋊C4C2311yescharacteristic
279C22×C22⋊C4C2311yescharacteristic
280C22×C22⋊C4C2311yescharacteristic
281C22×C22⋊C4C2311yescharacteristic
282C22×C22⋊C4C2311yescharacteristic
283C22×C22⋊C4C2311yescharacteristic
284C22×C22⋊C4C2311yescharacteristic
285C22×C22⋊C4C2311yescharacteristic
286C22×C22⋊C4C2311yescharacteristic
287C22×C22⋊C4C2311yescharacteristic
288C22×C22⋊C4C2311yescharacteristic
289C22×C22⋊C4C2311yescharacteristic
290C22×C42C2311yescharacteristic
291C22×C42C2311yescharacteristic
292C22×C42C2311yescharacteristic
293C22×C42C2311yescharacteristic
294C22×C42C2311yescharacteristic
295C22×C42C2311yescharacteristic
296C22×C42C2311yescharacteristic
297C22×C42C2311yescharacteristic
298C22×C42C2311yescharacteristic
299C22×C42C2311yescharacteristic
300C22×C42C2311yescharacteristic
301C22×C42C2311yescharacteristic
302C22×C42C2311yescharacteristic
303C22×C42C2311yescharacteristic
304C22×C42C2311yescharacteristic
305C22×C42C2311yescharacteristic
306C22×C42C2311yescharacteristic
307C22×C42C2311yescharacteristic
308#401C2318yes—
309#401C2318yes—
310#400C2318yes—
311#400C2318yes—
312#400C2318yes—
313#400C2318yes—
314#400C2318yes—
315#400C2318yes—
316#400C2318yes—
317#400C2318yes—
318#400C2318yes—
319#400C2318yes—
320#400C2318yes—
321#400C2318yes—
322#400C2318yes—
323#400C2318yes—
324#400C2318yes—
325#399C2318yes—
326#398C2318yes—
327#398C2318yes—
328#398C2318yes—
329#398C2318yes—
330#398C2318yes—
331#398C2318yes—
332#398C2318yes—
333#398C2318yes—
334#398C2318yes—
335#398C2318yes—
336#398C2318yes—
337#398C2318yes—
338#398C2318yes—
339#398C2318yes—
340#398C2318yes—
341#398C2318yes—
342#398C2318yes—
343#397C2318yes—
344#397C2318yes—
345#397C2318yes—
346#397C2318yes—
347#397C2318yes—
348#396C2318yes—
349#396C2318yes—
350#396C2318yes—
351#396C2318yes—
352#395C2318yes—
353#395C2318yes—
354#393C2318yes—
355#393C2318yes—
356#391C2318yes—
357#391C2318yes—
358#391C2318yes—
359#391C2318yes—
360#391C2318yes—
361#391C2318yes—
362#391C2318yes—
363#391C2318yes—
364#389C2318yes—
365#389C2318yes—
366#389C2318yes—
367#389C2318yes—
368#389C2318yes—
369#389C2318yes—
370#389C2318yes—
371#389C2318yes—
372#389C2318yes—
373#389C2318yes—
374#389C2318yes—
375#389C2318yes—
376#389C2318yes—
377#389C2318yes—
378#389C2318yes—
379#389C2318yes—
380#389C2318yes—
381#389C2318yes—
382#389C2318yes—
383#389C2318yes—
384#388C2318yes—
385#388C2318yes—
386#388C2318yes—
387#388C2318yes—
388#388C2318yes—
389#388C2318yes—
390#388C2318yes—
391#388C2318yes—
392#388C2318yes—
393#388C2318yes—
394#388C2318yes—
395#388C2318yes—
396#388C2318yes—
397#388C2318yes—
398#388C2318yes—
399#387C2318yes—
400#387C2318yes—
401#387C2318yes—
402#387C2318yes—
403#387C2318yes—
404#387C2318yes—
405#387C2318yes—
406#387C2318yes—
407#387C2318yes—
408#387C2318yes—
409#387C2318yes—
410#387C2318yes—
411#387C2318yes—
412#387C2318yes—
413#387C2318yes—
414#387C2318yes—
415#387C2318yes—
416#387C2318yes—
417#387C2318yes—
418#387C2318yes—
419#387C2318yes—
420#387C2318yes—
421#387C2318yes—
422#387C2318yes—
423#387C2318yes—
424#387C2318yes—
425#387C2318yes—
426#387C2318yes—
427#387C2318yes—
428#387C2318yes—
429#387C2318yes—
430#387C2318yes—
431#387C2318yes—
432#385C2318yes—
433#385C2318yes—
434#385C2318yes—
435#385C2318yes—
436#384C2318yes—
437#383C2318yes—
438#383C2318yes—
439#383C2318yes—
440#383C2318yes—
441#383C2318yes—
442#383C2318yes—
443#382C2318yes—
444#382C2318yes—
445#382C2318yes—
446#382C2318yes—
447#381C2318yes—
448#380C2318yes—
449C4×C4⋊C4C2318yes—
450C4×C4⋊C4C2318yes—
451C4×C4⋊C4C2318yes—
452C4×C4⋊C4C2318yes—
453C4×C4⋊C4C2318yes—
454C4×C22⋊C4C2318yes—
455#376C2318yes—
456#376C2318yes—
457#376C2318yes—
458#376C2318yes—
459#376C2318yes—
460C2×#95C2311yescharacteristic
461C2×#95C2311yescharacteristic
462C2×#95C2311yescharacteristic
463C2×#95C2311yescharacteristic
464C2×#95C2311yescharacteristic
465C2×#95C2311yescharacteristic
466C2×#95C2311yescharacteristic
467C2×#95C2311yescharacteristic
468C2×#95C2311yescharacteristic
469C2×#95C2311yescharacteristic
470C2×#95C2311yescharacteristic
471C2×#95C2311yescharacteristic
472C2×#95C2311yescharacteristic
473C2×#95C2311yescharacteristic
474C2×#95C2311yescharacteristic
475C2×#95C2311yescharacteristic
476C2×#95C2311yescharacteristic
477C2×#95C2311yescharacteristic
478C2×#95C2311yescharacteristic
479C2×#95C2311yescharacteristic
480C2×#95C2311yescharacteristic
481C2×#95C2311yescharacteristic
482C2×#95C2311yescharacteristic
483C2×#95C2311yescharacteristic
484C2×#95C2311yescharacteristic
485C2×#95C2311yescharacteristic
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
532C25C2411yescharacteristic
533C22×Q8—24no—
534C22×Q8—24no—
535C22×Q8—24no—
536C22×Q8—24no—
537C22×Q8—42no—
538C22×Q8—42no—
539C22×Q8C2414yes—
540C22×Q8C2414yes—
541C23×C4—42no—
542C23×C4—42no—
543C23×C4—42no—
544C23×C4C2411yescharacteristic
545C23×C4C2411yescharacteristic
546C23×C4C2411yescharacteristic
547C23×C4C2411yescharacteristic
548C23×C4C2411yescharacteristic
549C23×C4C2411yescharacteristic
550C23×C4C2411yescharacteristic
551C23×C4C2411yescharacteristic
552C23×C4C2411yescharacteristic
553C23×C4C2411yescharacteristic
554C23×C4C2411yescharacteristic
555C23×C4C2411yescharacteristic
556C23×C4C2411yescharacteristic
557C23×C4C2411yescharacteristic
558C23×C4C2411yescharacteristic
559C23×C4C2411yescharacteristic
560C23×C4C2411yescharacteristic
561C23×C4C2411yescharacteristic
562C23×C4C2411yescharacteristic
563C23×C4C2411yescharacteristic
564C23×C4C2411yescharacteristic
565C23×C4C2411yescharacteristic
566C23×C4C2411yescharacteristic
567C23×C4C2411yescharacteristic
568C23×C4C2411yescharacteristic
569C23×C4C2411yescharacteristic
570C23×C4C2411yescharacteristic
571C23×C4C2411yescharacteristic
572C23×C4C2411yescharacteristic
573C23×C4C2411yescharacteristic
574C23×C4C2414yes—
575#126—232no—
576C4×Q8—232no—
577C4×Q8—232no—
578C2×C4⋊C4—24no—
579C2×C4⋊C4—24no—
580C2×C4⋊C4—24no—
581C2×C4⋊C4—24no—
582C2×C4⋊C4—24no—
583C2×C4⋊C4—24no—
584C2×C4⋊C4—24no—
585C2×C4⋊C4—24no—
586C2×C4⋊C4—24no—
587C2×C4⋊C4—24no—
588C2×C4⋊C4—24no—
589C2×C4⋊C4—24no—
590C2×C4⋊C4—42no—
591C2×C4⋊C4—42no—
592C2×C4⋊C4—42no—
593C2×C4⋊C4—42no—
594C2×C4⋊C4—42no—
595C2×C4⋊C4—42no—
596C2×C4⋊C4—42no—
597C2×C4⋊C4—42no—
598C2×C4⋊C4—42no—
599C2×C4⋊C4—42no—
600C2×C4⋊C4—42no—
601C2×C4⋊C4—42no—
602C2×C4⋊C4—42no—
603C2×C4⋊C4—42no—
604C2×C4⋊C4—42no—
605C2×C4⋊C4—42no—
606C2×C4⋊C4—42no—
607C2×C4⋊C4—42no—
608C2×C4⋊C4—42no—
609C2×C4⋊C4—42no—
610C2×C4⋊C4—42no—
611C2×C4⋊C4—42no—
612C2×C4⋊C4—42no—
613C2×C4⋊C4—42no—
614C2×C4⋊C4—42no—
615C2×C4⋊C4—42no—
616C2×C4⋊C4—42no—
617C2×C4⋊C4—42no—
618C2×C4⋊C4—42no—
619C2×C4⋊C4—42no—
620C2×C4⋊C4—42no—
621C2×C4⋊C4—42no—
622C2×C4⋊C4—42no—
623C2×C4⋊C4—42no—
624C2×C4⋊C4—42no—
625C2×C4⋊C4—42no—
626C2×C4⋊C4C2414yes—
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2414yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2414yes—
665C2×C4⋊C4C2414yes—
666C2×C4⋊C4C2414yes—
667C2×C4⋊C4C2414yes—
668C2×C4⋊C4C2414yes—
669C2×C4⋊C4C2414yes—
670C2×C4⋊C4C2414yes—
671C2×C4⋊C4C2414yes—
672C2×C4⋊C4C2414yes—
673C2×C4⋊C4C2414yes—
674C2×C22⋊C4—24no—
675C2×C22⋊C4—24no—
676C2×C22⋊C4—24no—
677C2×C22⋊C4—24no—
678C2×C22⋊C4—24no—
679C2×C22⋊C4—42no—
680C2×C22⋊C4—42no—
681C2×C22⋊C4—42no—
682C2×C22⋊C4—42no—
683C2×C22⋊C4—42no—
684C2×C22⋊C4—42no—
685C2×C22⋊C4—42no—
686C2×C22⋊C4—42no—
687C2×C22⋊C4—42no—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2414yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2414yes—
692C2×C22⋊C4C2414yes—
693C2×C22⋊C4C2414yes—
694C2×C22⋊C4C2414yes—
695C2×C22⋊C4C2414yes—
696C2×C22⋊C4C2414yes—
697C2×C22⋊C4C2414yes—
698C2×C22⋊C4C2414yes—
699C2×C22⋊C4C2414yes—
700C2×C22⋊C4C2414yes—
701C2×C22⋊C4C2414yes—
702C2×C42—24no—
703C2×C42—24no—
704C2×C42—24no—
705C2×C42—24no—
706C2×C42—24no—
707C2×C42—24no—
708C2×C42—24no—
709C2×C42—42no—
710C2×C42—42no—
711C2×C42—42no—
712C2×C42—42no—
713C2×C42—42no—
714C2×C42—42no—
715C2×C42—42no—
716C2×C42—42no—
717C2×C42—42no—
718C2×C42—42no—
719C2×C42#4118yes—
720C2×C42C2414yes—
721C2×C42C2414yes—
722C2×C42C2414yes—
723C2×C42C2414yes—
724C2×C42C2414yes—
725C2×C42C2414yes—
726C2×C42C2414yes—
727C2×C42C2414yes—
728C2×C42C2414yes—
729C2×C42C2414yes—
730C2×C42C2414yes—
731C2×C42C2414yes—
732C2×C42C2414yes—
733C2×C42C2414yes—
734C2×C42C2414yes—
735C2×C42C2414yes—
736C2×C42C2414yes—
737C2×C42C2414yes—
738#95C2414yes—
739#95C2414yes—
740#95C2414yes—
741#95C2414yes—
742#95C2414yes—
743#95C2414yes—
744#95C2414yes—
745#95C2414yes—
746#95C2414yes—
747#95C2414yes—
748#95C2414yes—
749#95C2414yes—
750#95C2414yes—
751#95C2414yes—
752#95C2414yes—
753#95C2414yes—
754#95C2414yes—
755#95C2414yes—
756#95C2414yes—
757#95C2414yes—
758#95C2414yes—
759#95C2414yes—
760#95C2414yes—
761#95C2414yes—
762#95C2414yes—
763#95C2414yes—
764#95C2414yes—
765#95C2414yes—
766#95C2414yes—
767#95C2414yes—
768#95C2414yes—
769#95C2414yes—
770#95C2414yes—
771#95C2414yes—
772#95C2414yes—
773#95C2414yes—
774#95C2414yes—
775#95C2414yes—
776#95C2414yes—
777#95C2414yes—
778#95C2414yes—
779#95C2414yes—
780#95C2414yes—
781#95C2414yes—
782#95C2414yes—
783#95C2414yes—
784#95C2414yes—
785#95C2414yes—
786#95C2414yes—
787#95C2414yes—
788#95C2414yes—
789#95C2414yes—
790#95C2414yes—
791#95C2414yes—
792#95C2414yes—
793#95C2414yes—
794#95C2414yes—
795#95C2414yes—
796#95C2414yes—
797#95C2414yes—
798#95C2414yes—
799#95C2414yes—
800#95C2414yes—
801#95C2414yes—
802#95C2414yes—
803#95C2414yes—
804#95C2414yes—
805#95C2414yes—
806#95C2414yes—
807#95C2414yes—
808#95C2414yes—
809#95C2414yes—
810C24—22no—
811C24—22no—
812C24—22no—
813C24—22no—
814C24—22no—
815C24—22no—
816C24—22no—
817C24C2512yes—
818C24C2511yescharacteristic
819C2×Q8—28no—
820C2×Q8—28no—
821C2×Q8—28no—
822C2×Q8—28no—
823C2×Q8—44no—
824C2×Q8—44no—
825C2×Q8—416no—
826C2×Q8—416no—
827C22×C4—22no—
828C22×C4—22no—
829C22×C4—22no—
830C22×C4—22no—
831C22×C4—22no—
832C22×C4—22no—
833C22×C4—22no—
834C22×C4—22no—
835C22×C4—22no—
836C22×C4—22no—
837C22×C4—22no—
838C22×C4—22no—
839C22×C4—22no—
840C22×C4—22no—
841C22×C4—22no—
842C22×C4—22no—
843C22×C4—22no—
844C22×C4—22no—
845C22×C4—22no—
846C22×C4—22no—
847C22×C4—22no—
848C22×C4—22no—
849C22×C4—22no—
850C22×C4—22no—
851C22×C4—22no—
852C22×C4—22no—
853C22×C4—22no—
854C22×C4—22no—
855C22×C4—22no—
856C22×C4—22no—
857C22×C4—22no—
858C22×C4—22no—
859C22×C4—22no—
860C22×C4—22no—
861C22×C4—22no—
862C22×C4—22no—
863C22×C4—22no—
864C22×C4—22no—
865C22×C4—22no—
866C22×C4—22no—
867C22×C4—22no—
868C22×C4—22no—
869C22×C4—22no—
870C22×C4—22no—
871C22×C4—22no—
872C22×C4—22no—
873C22×C4—22no—
874C22×C4—22no—
875C22×C4—22no—
876C22×C4—22no—
877C22×C4—22no—
878C22×C4—22no—
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—44no—
913C22×C4—44no—
914C22×C4—44no—
915C22×C4—88no—
916C22×C4C2×#4114yes—
917C22×C4C2×#4114yes—
918C22×C4C2×#4114yes—
919C22×C42−1+414yes—
920C22×C42−1+414yes—
921C22×C4C2512yes—
922C22×C4C2512yes—
923C22×C4C2512yes—
924C22×C4C2512yes—
925C22×C4C2512yes—
926C22×C4C2512yes—
927C22×C4C2512yes—
928C22×C4C2512yes—
929C22×C4C2512yes—
930C22×C4C2512yes—
931C22×C4C2512yes—
932C22×C4C2512yes—
933C22×C4C2512yes—
934C22×C4C2512yes—
935C22×C4C2512yes—
936C22×C4C2512yes—
937C22×C4C2512yes—
938C22×C4C2512yes—
939C22×C4C2512yes—
940C22×C4C2512yes—
941C22×C4C2512yes—
942C22×C4C2512yes—
943C22×C4C2512yes—
944C22×C4C2512yes—
945C22×C4C2512yes—
946C22×C4C2512yes—
947C22×C4C2512yes—
948C22×C4C2512yes—
949C22×C4C2512yes—
950C22×C4C2512yes—
951C4⋊C4—28no—
952C4⋊C4—28no—
953C4⋊C4—28no—
954C4⋊C4—28no—
955C4⋊C4—28no—
956C4⋊C4—28no—
957C4⋊C4—28no—
958C4⋊C4—28no—
959C4⋊C4—28no—
960C4⋊C4—28no—
961C4⋊C4—28no—
962C4⋊C4—28no—
963C4⋊C4—44no—
964C4⋊C4—44no—
965C4⋊C4—44no—
966C4⋊C4—44no—
967C4⋊C4—44no—
968C4⋊C4—44no—
969C4⋊C4—44no—
970C4⋊C4—44no—
971C4⋊C4—44no—
972C4⋊C4—44no—
973C4⋊C4—44no—
974C4⋊C4—44no—
975C4⋊C4—44no—
976C4⋊C4—44no—
977C4⋊C4—44no—
978C4⋊C4—44no—
979C4⋊C4—44no—
980C4⋊C4—44no—
981C4⋊C4—44no—
982C4⋊C4—44no—
983C4⋊C4—44no—
984C4⋊C4—44no—
985C4⋊C4—44no—
986C4⋊C4—44no—
987C4⋊C4—44no—
988C4⋊C4—44no—
989C4⋊C4—44no—
990C4⋊C4—44no—
991C4⋊C4—44no—
992C4⋊C4—44no—
993C4⋊C4—44no—
994C4⋊C4—44no—
995C4⋊C4—44no—
996C4⋊C4—44no—
997C4⋊C4—44no—
998C4⋊C4—44no—
999C22⋊C4—28no—
1000C22⋊C4—28no—
1001C22⋊C4—28no—
1002C22⋊C4—28no—
1003C22⋊C4—28no—
1004C22⋊C4—44no—
1005C22⋊C4—44no—
1006C22⋊C4—44no—
1007C22⋊C4—44no—
1008C22⋊C4—44no—
1009C22⋊C4—44no—
1010C22⋊C4—44no—
1011C22⋊C4—44no—
1012C22⋊C4—44no—
1013C42—28no—
1014C42—28no—
1015C42—28no—
1016C42—28no—
1017C42—28no—
1018C42—28no—
1019C42—28no—
1020C42—44no—
1021C42—44no—
1022C42—44no—
1023C42—44no—
1024C42—44no—
1025C42—44no—
1026C42—44no—
1027C42—44no—
1028C42—44no—
1029C42—44no—
1030C42C2×#41116yes—
1031C23—22no—
1032C23—22no—
1033C23—22no—
1034C23—22no—
1035C23—22no—
1036C23—22no—
1037C23—22no—
1038C23—44no—
1039C23—44no—
1040C23—44no—
1041C23—44no—
1042C23—44no—
1043C23—44no—
1044C23—44no—
1045C23C22×#4112yes—
1046C23C2×2−1+412yes—
1047C23C2×2−1+412yes—
1048C23#58512yes—
1049C23#58512yes—
1050C23#58512yes—
1051C23#58512yes—
1052C23C2611yescharacteristic
1053Q8—416no—
1054Q8—416no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—28no—
1066C2×C4—28no—
1067C2×C4—28no—
1068C2×C4—28no—
1069C2×C4—28no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—22no—
1080C2×C4—22no—
1081C2×C4—22no—
1082C2×C4—22no—
1083C2×C4—22no—
1084C2×C4—22no—
1085C2×C4—22no—
1086C2×C4—22no—
1087C2×C4—22no—
1088C2×C4—22no—
1089C2×C4—22no—
1090C2×C4—22no—
1091C2×C4—22no—
1092C2×C4—22no—
1093C2×C4—22no—
1094C2×C4—22no—
1095C2×C4—22no—
1096C2×C4—22no—
1097C2×C4—22no—
1098C2×C4—22no—
1099C2×C4—22no—
1100C2×C4—22no—
1101C2×C4—22no—
1102C2×C4—22no—
1103C2×C4—22no—
1104C2×C4—22no—
1105C2×C4—22no—
1106C2×C4—22no—
1107C2×C4—22no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—22no—
1111C2×C4—22no—
1112C2×C4—22no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—22no—
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—44no—
1146C2×C4—44no—
1147C2×C4—44no—
1148C2×C4—44no—
1149C2×C4—44no—
1150C2×C4—44no—
1151C2×C4—44no—
1152C2×C4—44no—
1153C2×C4—44no—
1154C2×C4—44no—
1155C2×C4—44no—
1156C2×C4—44no—
1157C2×C4—44no—
1158C2×C4—44no—
1159C2×C4—44no—
1160C2×C4—44no—
1161C2×C4—44no—
1162C2×C4—44no—
1163C2×C4—44no—
1164C2×C4—44no—
1165C2×C4—44no—
1166C2×C4—44no—
1167C2×C4—44no—
1168C2×C4—44no—
1169C2×C4—44no—
1170C2×C4—88no—
1171C2×C4C22×#4114yes—
1172C2×C4C22×#4114yes—
1173C2×C4C22×#4114yes—
1174C2×C4C2×2−1+414yes—
1175C2×C4C2×2−1+414yes—
1176C22—42no—
1177C22—42no—
1178C22—42no—
1179C22—42no—
1180C22—42no—
1181C22—42no—
1182C22—42no—
1183C22—88no—
1184C22#349514yes—
1185C22#349514yes—
1186C22#351214yes—
1187C22#355514yes—
1188C22#356514yes—
1189C22#356514yes—
1190C22#356614yes—
1191C22C23×#4111yescharacteristic
1192C22C22×2−1+411yescharacteristic
1193C22C22×2−1+411yescharacteristic
1194C22C2×#58511yescharacteristic
1195C22C2×#58511yescharacteristic
1196C22C2×#58511yescharacteristic
1197C22C2×#58511yescharacteristic
1198C4—24no—
1199C4—24no—
1200C4—24no—
1201C4—24no—
1202C4—24no—
1203C4—42no—
1204C4—42no—
1205C4—42no—
1206C4—42no—
1207C4—42no—
1208C4—42no—
1209C4—42no—
1210C4—42no—
1211C4—42no—
1212C4—42no—
1213C4—42no—
1214C4—42no—
1215C4—42no—
1216C4—42no—
1217C4—42no—
1218C4—42no—
1219C4—42no—
1220C4—42no—
1221C4—42no—
1222C4—42no—
1223C4—42no—
1224C4—42no—
1225C4—42no—
1226C4—42no—
1227C4—42no—
1228C2—82no—
1229C2#5147518yesdirect product factor
1230C2C2×#356511yescharacteristic
1231C2C2×#356511yescharacteristic
1232C2C2×#356611yescharacteristic
1233C2C2×#355511yescharacteristic
1234C2C2×#349511yescharacteristic
1235C2C2×#349511yescharacteristic
1236C2C2×#351211yescharacteristic
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×#2802C2semidirect
3. C2×#2776C2semidirect
4. C2×#2776C2semidirect
9. C2×#2762C2semidirect
10. C2×#2762C2semidirect
11. C2×#2755C2semidirect
13. #51475C2direct (N × H)
14. C2×#2582C2semidirect
15. C2×#2612C2semidirect
17. C2×#2606C2semidirect
18. C2×#2606C2semidirect
21. C2×#2585C2semidirect
23. C2×#2533C2semidirect
24. C2×#2533C2semidirect
28. C2×#2647C2semidirect
31. C2×#2356C2semidirect
32. C2×#2320C2semidirect
36. #2802C22semidirect
38. #2776C22semidirect
39. #2776C22semidirect
44. #2762C22semidirect
45. #2762C22semidirect
46. #2755C22semidirect
48. #2647C22semidirect
50. #2612C22semidirect
51. #2606C22semidirect
52. #2606C22semidirect
56. #2585C22semidirect
57. #2582C22semidirect
58. #2533C22semidirect
59. #2533C22semidirect
113. #2356C22semidirect
114. #2320C22semidirect
1229. C2#51475direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#28022
C2×#27772
C2×#27762
C2×#27722
C2×#27682
C2×#27642
C2×#27622
C2×#27552
C2×#27392
#514752
C2×#25822
C2×#26122
C2×#26042
C2×#26062
C2×#25942
C2×#25872
C2×#25852
C2×#25272
C2×#25332
C2×#25322
C2×#25302
C2×#26472
C2×#26372
C2×#23832
C2×#23562
C2×#23202