Finite Group Databasebeta

← C2×#55769 #8102972

Subgroups — C2×#55769 #8102972

Order 512.

4202 conjugacy classes of subgroups.

The subgroup lattice has 1228 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#55769C2132yesmaximal, direct product factor
2C2×#2805C211yesmaximal, characteristic, complemented
3C2×#2794C211yesmaximal, characteristic, complemented
4C2×#2794C211yesmaximal, characteristic, complemented
5C2×#2776C211yesmaximal, characteristic, complemented
6C2×#2776C211yesmaximal, characteristic, complemented
7C2×#2774C211yesmaximal, characteristic, complemented
8C2×#2771C211yesmaximal, characteristic
9C2×#2767C211yesmaximal, characteristic, complemented
10C2×#2764C211yesmaximal, characteristic
11C2×#2758C211yesmaximal, characteristic, complemented
12C2×#2758C211yesmaximal, characteristic, complemented
13C2×#2755C211yesmaximal, characteristic, complemented
14C2×#2744C211yesmaximal, characteristic
15C2×#2742C211yesmaximal, characteristic
16C2×#2742C211yesmaximal, characteristic
17C2×#2739C211yesmaximal, characteristic
18C2×#2833C211yesmaximal, characteristic, complemented
19C2×#2833C211yesmaximal, characteristic, complemented
20C2×#2839C211yesmaximal, characteristic, complemented
21C2×#2575C211yesmaximal, characteristic
22C2×#2569C211yesmaximal, characteristic
23C2×#2588C211yesmaximal, characteristic, complemented
24C2×#2527C211yesmaximal, characteristic
25C2×#2533C211yesmaximal, characteristic, complemented
26C2×#2533C211yesmaximal, characteristic, complemented
27C2×#2497C211yesmaximal, characteristic
28C2×#2493C211yesmaximal, characteristic
29C2×#2493C211yesmaximal, characteristic
30C2×#2667C211yesmaximal, characteristic
31C2×#2665C211yesmaximal, characteristic
32C2×#2652C211yesmaximal, characteristic
33#2839C22116yescomplemented
34#2833C22116yescomplemented
35#2833C22116yescomplemented
36#2805C22116yescomplemented
37#2794C22116yescomplemented
38#2794C22116yescomplemented
39#2776C22116yescomplemented
40#2776C22116yescomplemented
41#2774C22116yescomplemented
42#2771C22116yes—
43#2767C22116yescomplemented
44#2764C22116yes—
45#2758C22116yescomplemented
46#2758C22116yescomplemented
47#2755C22116yescomplemented
48#2744C22116yes—
49#2742C22116yes—
50#2742C22116yes—
51#2739C22116yes—
52#2667C22116yes—
53#2665C22116yes—
54#2652C22116yes—
55#2588C22116yescomplemented
56#2575C22116yes—
57#2569C22116yes—
58#2533C22116yescomplemented
59#2533C22116yescomplemented
60#2527C22116yes—
61#2497C22116yes—
62#2493C22116yes—
63#2493C22116yes—
64C2×#401C2211yescharacteristic
65C2×#401C2211yescharacteristic
66C2×#401C2211yescharacteristic
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×#400C2211yescharacteristic
82C2×#400C2211yescharacteristic
83C2×#400C2211yescharacteristic
84C2×#400C2211yescharacteristic
85C2×#400C2211yescharacteristic
86C2×#400C2211yescharacteristic
87C2×#400C2211yescharacteristic
88C2×#400C2211yescharacteristic
89C2×#400C2211yescharacteristic
90C2×#400C2211yescharacteristic
91C2×#400C2211yescharacteristic
92C2×#400C2211yescharacteristic
93C2×#400C2211yescharacteristic
94C2×#400C2211yescharacteristic
95C2×#400C2211yescharacteristic
96C2×#400C2211yescharacteristic
97C2×#400C2211yescharacteristic
98C2×#400C2211yescharacteristic
99C2×#400C2211yescharacteristic
100C2×#399C2211yescharacteristic
101C2×#399C2211yescharacteristic
102C2×#398C2211yescharacteristic
103C2×#398C2211yescharacteristic
104C2×#398C2211yescharacteristic
105C2×#398C2211yescharacteristic
106C2×#398C2211yescharacteristic
107C2×#398C2211yescharacteristic
108C2×#398C2211yescharacteristic
109C2×#398C2211yescharacteristic
110C2×#398C2211yescharacteristic
111C2×#398C2211yescharacteristic
112C2×#398C2211yescharacteristic
113C2×#398C2211yescharacteristic
114C2×#397C2211yescharacteristic
115C2×#397C2211yescharacteristic
116C2×#397C2211yescharacteristic
117C2×#396C2211yescharacteristic
118C2×#396C2211yescharacteristic
119C2×#396C2211yescharacteristic
120C2×#395C2211yescharacteristic
121C2×#395C2211yescharacteristic
122C2×#395C2211yescharacteristic
123C2×#395C2211yescharacteristic
124C2×#395C2211yescharacteristic
125C2×#395C2211yescharacteristic
126C2×#393C2211yescharacteristic
127C2×#393C2211yescharacteristic
128C2×#391C2211yescharacteristic
129C2×#391C2211yescharacteristic
130C2×#391C2211yescharacteristic
131C2×#391C2211yescharacteristic
132C2×#391C2211yescharacteristic
133C2×#391C2211yescharacteristic
134C2×#389C2211yescharacteristic
135C2×#389C2211yescharacteristic
136C2×#389C2211yescharacteristic
137C2×#389C2211yescharacteristic
138C2×#389C2211yescharacteristic
139C2×#389C2211yescharacteristic
140C2×#389C2211yescharacteristic
141C2×#389C2211yescharacteristic
142C2×#389C2211yescharacteristic
143C2×#389C2211yescharacteristic
144C2×#389C2211yescharacteristic
145C2×#389C2211yescharacteristic
146C2×#388C2211yescharacteristic
147C2×#388C2211yescharacteristic
148C2×#388C2211yescharacteristic
149C2×#388C2211yescharacteristic
150C2×#388C2211yescharacteristic
151C2×#388C2211yescharacteristic
152C2×#387C2211yescharacteristic
153C2×#387C2211yescharacteristic
154C2×#387C2211yescharacteristic
155C2×#387C2211yescharacteristic
156C2×#387C2211yescharacteristic
157C2×#387C2211yescharacteristic
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×#385C2211yescharacteristic
191C2×#385C2211yescharacteristic
192C2×#385C2211yescharacteristic
193C2×#385C2211yescharacteristic
194C2×#385C2211yescharacteristic
195C2×#385C2211yescharacteristic
196C2×#384C2211yescharacteristic
197C2×#383C2211yescharacteristic
198C2×#383C2211yescharacteristic
199C2×#383C2211yescharacteristic
200C2×#383C2211yescharacteristic
201C2×#382C2211yescharacteristic
202C2×#382C2211yescharacteristic
203C2×#381C2211yescharacteristic
204C2×#381C2211yescharacteristic
205C2×#381C2211yescharacteristic
206C2×#381C2211yescharacteristic
207C2×#380C2211yescharacteristic
208C2×#380C2211yescharacteristic
209C2×#380C2211yescharacteristic
210C2×#380C2211yescharacteristic
211C2×#380C2211yescharacteristic
212C2×C4×C4⋊C4C2211yescharacteristic
213C2×C4×C4⋊C4C2211yescharacteristic
214C2×C4×C22⋊C4C2211yescharacteristic
215C2×C4×C22⋊C4C2211yescharacteristic
216C2×C4×C22⋊C4C2211yescharacteristic
217C2×#376C2211yescharacteristic
218C22×#95C2211yescharacteristic
219C23×Q8C2311yescharacteristic
220C23×Q8C2311yescharacteristic
221C24×C4C2311yescharacteristic
222C24×C4C2311yescharacteristic
223C24×C4C2311yescharacteristic
224C22×C4⋊C4C2311yescharacteristic
225C22×C4⋊C4C2311yescharacteristic
226C22×C4⋊C4C2311yescharacteristic
227C22×C4⋊C4C2311yescharacteristic
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×C22⋊C4C2311yescharacteristic
271C22×C22⋊C4C2311yescharacteristic
272C22×C22⋊C4C2311yescharacteristic
273C22×C22⋊C4C2311yescharacteristic
274C22×C22⋊C4C2311yescharacteristic
275C22×C22⋊C4C2311yescharacteristic
276C22×C22⋊C4C2311yescharacteristic
277C22×C22⋊C4C2311yescharacteristic
278C22×C22⋊C4C2311yescharacteristic
279C22×C22⋊C4C2311yescharacteristic
280C22×C22⋊C4C2311yescharacteristic
281C22×C22⋊C4C2311yescharacteristic
282C22×C42C2311yescharacteristic
283C22×C42C2311yescharacteristic
284C22×C42C2311yescharacteristic
285C22×C42C2311yescharacteristic
286C22×C42C2311yescharacteristic
287C22×C42C2311yescharacteristic
288C22×C42C2311yescharacteristic
289C22×C42C2311yescharacteristic
290C22×C42C2311yescharacteristic
291C22×C42C2311yescharacteristic
292C22×C42C2311yescharacteristic
293C22×C42C2311yescharacteristic
294#401C2318yes—
295#401C2318yes—
296#401C2318yes—
297#400C2318yes—
298#400C2318yes—
299#400C2318yes—
300#400C2318yes—
301#400C2318yes—
302#400C2318yes—
303#400C2318yes—
304#400C2318yes—
305#400C2318yes—
306#400C2318yes—
307#400C2318yes—
308#400C2318yes—
309#400C2318yes—
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#400C2318yes—
326#400C2318yes—
327#400C2318yes—
328#400C2318yes—
329#400C2318yes—
330#399C2318yes—
331#399C2318yes—
332#398C2318yes—
333#398C2318yes—
334#398C2318yes—
335#398C2318yes—
336#398C2318yes—
337#398C2318yes—
338#398C2318yes—
339#398C2318yes—
340#398C2318yes—
341#398C2318yes—
342#398C2318yes—
343#398C2318yes—
344#397C2318yes—
345#397C2318yes—
346#397C2318yes—
347#396C2318yes—
348#396C2318yes—
349#396C2318yes—
350#395C2318yes—
351#395C2318yes—
352#395C2318yes—
353#395C2318yes—
354#395C2318yes—
355#395C2318yes—
356#393C2318yes—
357#393C2318yes—
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#388C2318yes—
377#388C2318yes—
378#388C2318yes—
379#388C2318yes—
380#388C2318yes—
381#388C2318yes—
382#387C2318yes—
383#387C2318yes—
384#387C2318yes—
385#387C2318yes—
386#387C2318yes—
387#387C2318yes—
388#387C2318yes—
389#387C2318yes—
390#387C2318yes—
391#387C2318yes—
392#387C2318yes—
393#387C2318yes—
394#387C2318yes—
395#387C2318yes—
396#387C2318yes—
397#387C2318yes—
398#387C2318yes—
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#385C2318yes—
421#385C2318yes—
422#385C2318yes—
423#385C2318yes—
424#385C2318yes—
425#385C2318yes—
426#384C2318yes—
427#383C2318yes—
428#383C2318yes—
429#383C2318yes—
430#383C2318yes—
431#382C2318yes—
432#382C2318yes—
433#381C2318yes—
434#381C2318yes—
435#381C2318yes—
436#381C2318yes—
437#380C2318yes—
438#380C2318yes—
439#380C2318yes—
440#380C2318yes—
441#380C2318yes—
442C4×C4⋊C4C2318yes—
443C4×C4⋊C4C2318yes—
444C4×C22⋊C4C2318yes—
445C4×C22⋊C4C2318yes—
446C4×C22⋊C4C2318yes—
447#376C2318yes—
448C2×#95C2318yes—
449C2×#95C2311yescharacteristic
450C2×#95C2311yescharacteristic
451C2×#95C2311yescharacteristic
452C2×#95C2311yescharacteristic
453C2×#95C2311yescharacteristic
454C2×#95C2311yescharacteristic
455C2×#95C2311yescharacteristic
456C2×#95C2311yescharacteristic
457C2×#95C2311yescharacteristic
458C2×#95C2311yescharacteristic
459C2×#95C2311yescharacteristic
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
529C25C2411yescharacteristic
530C22×Q8—42no—
531C22×Q8—42no—
532C22×Q8—42no—
533C22×Q8—42no—
534C22×Q8—42no—
535C22×Q8—42no—
536C22×Q8C2414yes—
537C22×Q8C2414yes—
538C23×C4—24no—
539C23×C4—24no—
540C23×C4—24no—
541C23×C4—42no—
542C23×C4—42no—
543C23×C4—42no—
544C23×C4—42no—
545C23×C4—42no—
546C23×C4—42no—
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×C4C2411yescharacteristic
575C23×C4C2411yescharacteristic
576C23×C4C2411yescharacteristic
577C23×C4C2414yes—
578C23×C4C2414yes—
579C23×C4C2414yes—
580C2×C4⋊C4—24no—
581C2×C4⋊C4—24no—
582C2×C4⋊C4—24no—
583C2×C4⋊C4—24no—
584C2×C4⋊C4—42no—
585C2×C4⋊C4—42no—
586C2×C4⋊C4—42no—
587C2×C4⋊C4—42no—
588C2×C4⋊C4—42no—
589C2×C4⋊C4—42no—
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×C22⋊C4—24no—
673C2×C22⋊C4—24no—
674C2×C22⋊C4—24no—
675C2×C22⋊C4—42no—
676C2×C22⋊C4—42no—
677C2×C22⋊C4—42no—
678C2×C22⋊C4—42no—
679C2×C22⋊C4—42no—
680C2×C22⋊C4—42no—
681C2×C22⋊C4—42no—
682C2×C22⋊C4—42no—
683C2×C22⋊C4—42no—
684C2×C22⋊C4C2414yes—
685C2×C22⋊C4C2414yes—
686C2×C22⋊C4C2414yes—
687C2×C22⋊C4C2414yes—
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×C42—42no—
697C2×C42—42no—
698C2×C42—42no—
699C2×C42—42no—
700C2×C42—42no—
701C2×C42—42no—
702C2×C42—42no—
703C2×C42—42no—
704C2×C42—42no—
705C2×C42—42no—
706C2×C42—42no—
707C2×C42—42no—
708C2×C42C2414yes—
709C2×C42C2414yes—
710C2×C42C2414yes—
711C2×C42C2414yes—
712C2×C42C2414yes—
713C2×C42C2414yes—
714C2×C42C2414yes—
715C2×C42C2414yes—
716C2×C42C2414yes—
717C2×C42C2414yes—
718C2×C42C2414yes—
719C2×C42C2414yes—
720#95C2414yes—
721#95C2414yes—
722#95C2414yes—
723#95C2414yes—
724#95C2414yes—
725#95C2414yes—
726#95C2414yes—
727#95C2414yes—
728#95C2414yes—
729#95C2414yes—
730#95C2414yes—
731#95C2414yes—
732#95C2414yes—
733#95C2414yes—
734#95C2414yes—
735#95C2414yes—
736#95C2414yes—
737#95C2414yes—
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—
800C24—22no—
801C24—22no—
802C24—22no—
803C24—22no—
804C24—22no—
805C24—22no—
806C242−1+414yes—
807C24C2512yes—
808C24C2511yescharacteristic
809C2×Q8—44no—
810C2×Q8—44no—
811C2×Q8—44no—
812C2×Q8—44no—
813C2×Q8—44no—
814C2×Q8—44no—
815C2×Q8—88no—
816C2×Q8—88no—
817C22×C4—22no—
818C22×C4—22no—
819C22×C4—22no—
820C22×C4—22no—
821C22×C4—22no—
822C22×C4—22no—
823C22×C4—22no—
824C22×C4—22no—
825C22×C4—22no—
826C22×C4—22no—
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—28no—
907C22×C4—28no—
908C22×C4—28no—
909C22×C4—44no—
910C22×C4—44no—
911C22×C4—44no—
912C22×C4—44no—
913C22×C4—44no—
914C22×C4—44no—
915C22×C4—88no—
916C22×C4—88no—
917C22×C4—88no—
918C22×C42−1+414yes—
919C22×C4C2512yes—
920C22×C4C2512yes—
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—
949C4⋊C4—28no—
950C4⋊C4—28no—
951C4⋊C4—28no—
952C4⋊C4—28no—
953C4⋊C4—44no—
954C4⋊C4—44no—
955C4⋊C4—44no—
956C4⋊C4—44no—
957C4⋊C4—44no—
958C4⋊C4—44no—
959C4⋊C4—44no—
960C4⋊C4—44no—
961C4⋊C4—44no—
962C4⋊C4—44no—
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—
995C22⋊C4—28no—
996C22⋊C4—28no—
997C22⋊C4—28no—
998C22⋊C4—44no—
999C22⋊C4—44no—
1000C22⋊C4—44no—
1001C22⋊C4—44no—
1002C22⋊C4—44no—
1003C22⋊C4—44no—
1004C22⋊C4—44no—
1005C22⋊C4—44no—
1006C22⋊C4—44no—
1007C42—44no—
1008C42—44no—
1009C42—44no—
1010C42—44no—
1011C42—44no—
1012C42—44no—
1013C42—44no—
1014C42—44no—
1015C42—44no—
1016C42—44no—
1017C42—44no—
1018C42—44no—
1019C23—22no—
1020C23—22no—
1021C23—22no—
1022C23—22no—
1023C23—22no—
1024C23—22no—
1025C23—28no—
1026C23—28no—
1027C23—28no—
1028C23—44no—
1029C23—44no—
1030C23—44no—
1031C23—44no—
1032C23C2×2−1+414yes—
1033C23C2×2−1+412yes—
1034C23C2×2−1+412yes—
1035C23#58512yes—
1036C23#58512yes—
1037C23#58512yes—
1038C23#58512yes—
1039C23#58512yes—
1040C23C2611yescharacteristic
1041Q8—88no—
1042Q8—88no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—28no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—22no—
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—22no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
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—44no—
1134C2×C4—44no—
1135C2×C4—44no—
1136C2×C4—44no—
1137C2×C4—44no—
1138C2×C4—44no—
1139C2×C4—44no—
1140C2×C4—44no—
1141C2×C4—44no—
1142C2×C4—44no—
1143C2×C4—44no—
1144C2×C4—44no—
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—88no—
1163C2×C4—88no—
1164C2×C4—88no—
1165C2×C4C2×2−1+414yes—
1166C22—24no—
1167C22—24no—
1168C22—24no—
1169C22—42no—
1170C22—42no—
1171C22—42no—
1172C22—42no—
1173C22—416no—
1174C22#355714yes—
1175C22#356314yes—
1176C22#356414yes—
1177C22#356414yes—
1178C22#356414yes—
1179C22#356614yes—
1180C22#356614yes—
1181C22C22×2−1+411yescharacteristic
1182C22C22×2−1+411yescharacteristic
1183C22C2×#58511yescharacteristic
1184C22C2×#58511yescharacteristic
1185C22C2×#58511yescharacteristic
1186C22C2×#58511yescharacteristic
1187C22C2×#58511yescharacteristic
1188C4—24no—
1189C4—42no—
1190C4—42no—
1191C4—42no—
1192C4—42no—
1193C4—42no—
1194C4—42no—
1195C4—42no—
1196C4—42no—
1197C4—42no—
1198C4—42no—
1199C4—42no—
1200C4—42no—
1201C4—42no—
1202C4—42no—
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—
1218C2—44no—
1219C2#5576918yesdirect product factor
1220C2C2×#356311yescharacteristic
1221C2C2×#356411yescharacteristic
1222C2C2×#356411yescharacteristic
1223C2C2×#356411yescharacteristic
1224C2C2×#355711yescharacteristic
1225C2C2×#356611yescharacteristic
1226C2C2×#356611yescharacteristic
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. #55769C2direct (N × H)
2. C2×#2805C2semidirect
3. C2×#2794C2semidirect
4. C2×#2794C2semidirect
5. C2×#2776C2semidirect
6. C2×#2776C2semidirect
7. C2×#2774C2semidirect
9. C2×#2767C2semidirect
11. C2×#2758C2semidirect
12. C2×#2758C2semidirect
13. C2×#2755C2semidirect
18. C2×#2833C2semidirect
19. C2×#2833C2semidirect
20. C2×#2839C2semidirect
23. C2×#2588C2semidirect
25. C2×#2533C2semidirect
26. C2×#2533C2semidirect
33. #2839C22semidirect
34. #2833C22semidirect
35. #2833C22semidirect
36. #2805C22semidirect
37. #2794C22semidirect
38. #2794C22semidirect
39. #2776C22semidirect
40. #2776C22semidirect
41. #2774C22semidirect
43. #2767C22semidirect
45. #2758C22semidirect
46. #2758C22semidirect
47. #2755C22semidirect
55. #2588C22semidirect
58. #2533C22semidirect
59. #2533C22semidirect
1219. C2#55769direct (N × H)

Maximal subgroups

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

subgroupindex
#557692
C2×#28052
C2×#27942
C2×#27762
C2×#27742
C2×#27712
C2×#27672
C2×#27642
C2×#27582
C2×#27552
C2×#27442
C2×#27422
C2×#27392
C2×#28332
C2×#28392
C2×#25752
C2×#25692
C2×#25882
C2×#25272
C2×#25332
C2×#24972
C2×#24932
C2×#26672
C2×#26652
C2×#26522