Finite Group Databasebeta

← C2×#3566 #62742

Subgroups — C2×#3566 #62742

Order 256.

3347 conjugacy classes of subgroups.

The subgroup lattice has 952 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3566C2132yesmaximal, direct product factor
2C2×#563C211yesmaximal, characteristic, complemented
3C2×#562C211yesmaximal, characteristic, complemented
4C2×#562C211yesmaximal, characteristic, complemented
5C2×#560C211yesmaximal, characteristic, complemented
6C2×#559C211yesmaximal, characteristic, complemented
7C2×#556C211yesmaximal, characteristic, complemented
8C2×#555C211yesmaximal, characteristic, complemented
9C2×#553C211yesmaximal, characteristic, complemented
10C2×#553C211yesmaximal, characteristic, complemented
11C2×#553C211yesmaximal, characteristic, complemented
12C2×#552C211yesmaximal, characteristic, complemented
13C2×#552C211yesmaximal, characteristic, complemented
14C2×#552C211yesmaximal, characteristic, complemented
15C2×#551C211yesmaximal, characteristic, complemented
16C2×#551C211yesmaximal, characteristic, complemented
17C2×#551C211yesmaximal, characteristic, complemented
18C2×#542C211yesmaximal, characteristic, complemented
19C2×#542C211yesmaximal, characteristic, complemented
20C2×#542C211yesmaximal, characteristic, complemented
21C2×#541C211yesmaximal, characteristic, complemented
22C2×#541C211yesmaximal, characteristic, complemented
23C2×#540C211yesmaximal, characteristic, complemented
24C2×#539C211yesmaximal, characteristic, complemented
25C2×#539C211yesmaximal, characteristic, complemented
26C2×#539C211yesmaximal, characteristic, complemented
27C2×#538C211yesmaximal, characteristic, complemented
28C2×#538C211yesmaximal, characteristic, complemented
29C2×#538C211yesmaximal, characteristic, complemented
30C2×#529C211yesmaximal, characteristic, complemented
31C2×#529C211yesmaximal, characteristic, complemented
32C2×#529C211yesmaximal, characteristic, complemented
33#563C22116yescomplemented
34#562C22116yescomplemented
35#562C22116yescomplemented
36#560C22116yescomplemented
37#559C22116yescomplemented
38#556C22116yescomplemented
39#555C22116yescomplemented
40#553C22116yescomplemented
41#553C22116yescomplemented
42#553C22116yescomplemented
43#552C22116yescomplemented
44#552C22116yescomplemented
45#552C22116yescomplemented
46#551C22116yescomplemented
47#551C22116yescomplemented
48#551C22116yescomplemented
49#542C22116yescomplemented
50#542C22116yescomplemented
51#542C22116yescomplemented
52#541C22116yescomplemented
53#541C22116yescomplemented
54#540C22116yescomplemented
55#539C22116yescomplemented
56#539C22116yescomplemented
57#539C22116yescomplemented
58#538C22116yescomplemented
59#538C22116yescomplemented
60#538C22116yescomplemented
61C2×C4⋊Q8C2211yescharacteristic, complemented
62C2×C4⋊Q8C2211yescharacteristic, complemented
63C2×C4⋊Q8C2211yescharacteristic, complemented
64C2×#127C2211yescharacteristic
65#529C22116yescomplemented
66#529C22116yescomplemented
67#529C22116yescomplemented
68C2×#126C2211yescharacteristic
69C2×#126C2211yescharacteristic
70C2×#126C2211yescharacteristic
71C2×#126C2211yescharacteristic
72C2×#126C2211yescharacteristic
73C2×#126C2211yescharacteristic
74C2×#126C2211yescharacteristic
75C2×#126C2211yescharacteristic
76C2×#126C2211yescharacteristic
77C2×#126C2211yescharacteristic
78C2×#126C2211yescharacteristic
79C2×#126C2211yescharacteristic
80C2×#126C2211yescharacteristic
81C2×#126C2211yescharacteristic
82C2×#126C2211yescharacteristic, complemented
83C2×#126C2211yescharacteristic, complemented
84C2×#126C2211yescharacteristic, complemented
85C2×#126C2211yescharacteristic, complemented
86C2×#126C2211yescharacteristic, complemented
87C2×#126C2211yescharacteristic, complemented
88C2×#125C2211yescharacteristic, complemented
89C2×#125C2211yescharacteristic, complemented
90C2×#125C2211yescharacteristic, complemented
91C2×#125C2211yescharacteristic, complemented
92C2×#125C2211yescharacteristic, complemented
93C2×#125C2211yescharacteristic, complemented
94C2×#125C2211yescharacteristic, complemented
95C2×#125C2211yescharacteristic, complemented
96C2×#125C2211yescharacteristic, complemented
97C2×#125C2211yescharacteristic, complemented
98C2×#125C2211yescharacteristic, complemented
99C2×#125C2211yescharacteristic, complemented
100C2×#124C2211yescharacteristic
101C2×#124C2211yescharacteristic
102C2×#124C2211yescharacteristic
103C2×#124C2211yescharacteristic
104C2×#124C2211yescharacteristic
105C2×#124C2211yescharacteristic
106C2×#124C2211yescharacteristic
107C2×#124C2211yescharacteristic
108C2×#124C2211yescharacteristic
109C2×#124C2211yescharacteristic, complemented
110C2×#124C2211yescharacteristic, complemented
111C2×#124C2211yescharacteristic, complemented
112C2×#123C2211yescharacteristic
113C2×#123C2211yescharacteristic
114C2×#123C2211yescharacteristic
115C2×#123C2211yescharacteristic
116C2×#123C2211yescharacteristic
117C2×#123C2211yescharacteristic
118C2×#123C2211yescharacteristic
119C2×#123C2211yescharacteristic
120C2×#123C2211yescharacteristic
121C2×#123C2211yescharacteristic
122C2×#123C2211yescharacteristic
123C2×#123C2211yescharacteristic
124C2×#123C2211yescharacteristic
125C2×#123C2211yescharacteristic
126C2×#123C2211yescharacteristic
127C2×#123C2211yescharacteristic
128C2×#123C2211yescharacteristic
129C2×#123C2211yescharacteristic
130C2×#123C2211yescharacteristic, complemented
131C2×#123C2211yescharacteristic, complemented
132C2×#123C2211yescharacteristic, complemented
133C2×#123C2211yescharacteristic, complemented
134C2×#123C2211yescharacteristic, complemented
135C2×#123C2211yescharacteristic, complemented
136C2×C22⋊Q8C2211yescharacteristic
137C2×C22⋊Q8C2211yescharacteristic
138C2×C22⋊Q8C2211yescharacteristic
139C2×C22⋊Q8C2211yescharacteristic
140C2×C22⋊Q8C2211yescharacteristic
141C2×C22⋊Q8C2211yescharacteristic
142C2×C22⋊Q8C2211yescharacteristic
143C2×C22⋊Q8C2211yescharacteristic
144C2×C22⋊Q8C2211yescharacteristic
145C2×C22⋊Q8C2211yescharacteristic, complemented
146C2×C22⋊Q8C2211yescharacteristic, complemented
147C2×C22⋊Q8C2211yescharacteristic, complemented
148C2×C22⋊Q8C2211yescharacteristic, complemented
149C2×C22⋊Q8C2211yescharacteristic, complemented
150C2×C22⋊Q8C2211yescharacteristic, complemented
151C2×C22⋊Q8C2211yescharacteristic, complemented
152C2×C22⋊Q8C2211yescharacteristic, complemented
153C2×C22⋊Q8C2211yescharacteristic, complemented
154C2×#121C2211yescharacteristic
155C2×#121C2211yescharacteristic
156C2×#121C2211yescharacteristic
157C2×#121C2211yescharacteristic
158C2×#121C2211yescharacteristic
159C2×#121C2211yescharacteristic
160C2×#121C2211yescharacteristic
161C2×#121C2211yescharacteristic
162C2×#121C2211yescharacteristic
163C2×#121C2211yescharacteristic
164C2×#121C2211yescharacteristic
165C2×#121C2211yescharacteristic
166C2×#121C2211yescharacteristic
167C2×#121C2211yescharacteristic
168C2×#121C2211yescharacteristic
169C2×#121C2211yescharacteristic, complemented
170C2×#121C2211yescharacteristic, complemented
171C2×#121C2211yescharacteristic, complemented
172C2×#120C2211yescharacteristic
173C2×#120C2211yescharacteristic
174C2×#120C2211yescharacteristic
175C2×#120C2211yescharacteristic
176C2×C4×Q8C2211yescharacteristic, complemented
177C2×C4×Q8C2211yescharacteristic, complemented
178C2×C4×Q8C2211yescharacteristic, complemented
179C2×C4×Q8C2211yescharacteristic, complemented
180C2×C4×Q8C2211yescharacteristic, complemented
181C2×C4×Q8C2211yescharacteristic, complemented
182C2×C4×D4C2211yescharacteristic
183C2×C4×D4C2211yescharacteristic
184C2×C4×D4C2211yescharacteristic
185C2×C4×D4C2211yescharacteristic
186C2×C4×D4C2211yescharacteristic
187C2×C4×D4C2211yescharacteristic
188C2×C4×D4C2211yescharacteristic
189C2×C4×D4C2211yescharacteristic
190C2×C4×D4C2211yescharacteristic
191C2×C4×D4C2211yescharacteristic
192C2×C4×D4C2211yescharacteristic
193C2×C4×D4C2211yescharacteristic
194C2×C4×D4C2211yescharacteristic, complemented
195C2×C4×D4C2211yescharacteristic, complemented
196C2×C4×D4C2211yescharacteristic, complemented
197C2×C4×D4C2211yescharacteristic, complemented
198C2×C4×D4C2211yescharacteristic, complemented
199C2×C4×D4C2211yescharacteristic, complemented
200C2×#117C2211yescharacteristic
201C2×#117C2211yescharacteristic
202C2×#117C2211yescharacteristic
203C2×#117C2211yescharacteristic
204C2×#117C2211yescharacteristic
205C2×#117C2211yescharacteristic
206C2×#117C2211yescharacteristic, complemented
207C2×#117C2211yescharacteristic, complemented
208C2×#117C2211yescharacteristic, complemented
209C2×#117C2211yescharacteristic, complemented
210C2×#117C2211yescharacteristic, complemented
211C2×#117C2211yescharacteristic, complemented
212C22×C4⋊C4C2211yescharacteristic, complemented
213C22×C4⋊C4C2211yescharacteristic, complemented
214C22×C4⋊C4C2211yescharacteristic, complemented
215C22×C22⋊C4C2211yescharacteristic
216C22×C22⋊C4C2211yescharacteristic
217C22×C22⋊C4C2211yescharacteristic
218C22×C42C2211yescharacteristic, complemented
219C25C2311yescharacteristic
220C22×Q8C2311yescharacteristic
221C22×Q8C2311yescharacteristic
222C22×Q8C2311yescharacteristic
223C22×Q8C2311yescharacteristic
224C22×Q8C2311yescharacteristic
225C22×Q8C2311yescharacteristic
226C22×D4C2311yescharacteristic
227C22×D4C2311yescharacteristic
228C22×D4C2311yescharacteristic
229C22×D4C2311yescharacteristic
230C22×D4C2311yescharacteristic
231C22×D4C2311yescharacteristic
232C22×D4C2311yescharacteristic
233C22×D4C2311yescharacteristic
234C22×D4C2311yescharacteristic
235C22×D4C2311yescharacteristic
236C22×D4C2311yescharacteristic
237C22×D4C2311yescharacteristic
238C22×D4C2311yescharacteristic
239C22×D4C2311yescharacteristic
240C22×D4C2311yescharacteristic
241C22×D4C2311yescharacteristic
242C22×D4C2311yescharacteristic
243C22×D4C2311yescharacteristic
244C23×C4C2311yescharacteristic
245C23×C4C2311yescharacteristic
246C23×C4C2311yescharacteristic
247C23×C4C2311yescharacteristic
248C23×C4C2311yescharacteristic
249C23×C4C2311yescharacteristic
250C23×C4C2311yescharacteristic
251C23×C4C2311yescharacteristic
252C23×C4C2311yescharacteristic
253C23×C4C2311yescharacteristic
254C23×C4C2311yescharacteristic
255C23×C4C2311yescharacteristic
256C23×C4C2311yescharacteristic
257C23×C4C2311yescharacteristic
258C23×C4C2311yescharacteristic
259C23×C4C2311yescharacteristic
260C23×C4C2311yescharacteristic
261C23×C4C2311yescharacteristic
262C4⋊Q8C2318yescomplemented
263C4⋊Q8C2318yescomplemented
264C4⋊Q8C2318yescomplemented
265#127C2318yes—
266#126C2318yes—
267#126C2318yes—
268#126C2318yes—
269#126C2318yes—
270#126C2318yes—
271#126C2318yes—
272#126C2318yes—
273#126C2318yes—
274#126C2318yes—
275#126C2318yes—
276#126C2318yes—
277#126C2318yes—
278#126C2318yes—
279#126C2318yes—
280#126C2318yescomplemented
281#126C2318yescomplemented
282#126C2318yescomplemented
283#126C2318yescomplemented
284#126C2318yescomplemented
285#126C2318yescomplemented
286#125C2318yescomplemented
287#125C2318yescomplemented
288#125C2318yescomplemented
289#125C2318yescomplemented
290#125C2318yescomplemented
291#125C2318yescomplemented
292#125C2318yescomplemented
293#125C2318yescomplemented
294#125C2318yescomplemented
295#125C2318yescomplemented
296#125C2318yescomplemented
297#125C2318yescomplemented
298#124C2318yes—
299#124C2318yes—
300#124C2318yes—
301#124C2318yes—
302#124C2318yes—
303#124C2318yes—
304#124C2318yes—
305#124C2318yes—
306#124C2318yes—
307#124C2318yescomplemented
308#124C2318yescomplemented
309#124C2318yescomplemented
310#123C2318yes—
311#123C2318yes—
312#123C2318yes—
313#123C2318yes—
314#123C2318yes—
315#123C2318yes—
316#123C2318yes—
317#123C2318yes—
318#123C2318yes—
319#123C2318yes—
320#123C2318yes—
321#123C2318yes—
322#123C2318yes—
323#123C2318yes—
324#123C2318yes—
325#123C2318yes—
326#123C2318yes—
327#123C2318yes—
328#123C2318yescomplemented
329#123C2318yescomplemented
330#123C2318yescomplemented
331#123C2318yescomplemented
332#123C2318yescomplemented
333#123C2318yescomplemented
334C22⋊Q8C2318yes—
335C22⋊Q8C2318yes—
336C22⋊Q8C2318yes—
337C22⋊Q8C2318yes—
338C22⋊Q8C2318yes—
339C22⋊Q8C2318yes—
340C22⋊Q8C2318yes—
341C22⋊Q8C2318yes—
342C22⋊Q8C2318yes—
343C22⋊Q8C2318yescomplemented
344C22⋊Q8C2318yescomplemented
345C22⋊Q8C2318yescomplemented
346C22⋊Q8C2318yescomplemented
347C22⋊Q8C2318yescomplemented
348C22⋊Q8C2318yescomplemented
349C22⋊Q8C2318yescomplemented
350C22⋊Q8C2318yescomplemented
351C22⋊Q8C2318yescomplemented
352#121C2318yes—
353#121C2318yes—
354#121C2318yes—
355#121C2318yes—
356#121C2318yes—
357#121C2318yes—
358#121C2318yes—
359#121C2318yes—
360#121C2318yes—
361#121C2318yes—
362#121C2318yes—
363#121C2318yes—
364#121C2318yes—
365#121C2318yes—
366#121C2318yes—
367#121C2318yescomplemented
368#121C2318yescomplemented
369#121C2318yescomplemented
370#120C2318yes—
371#120C2318yes—
372#120C2318yes—
373#120C2318yes—
374C4×Q8C2318yescomplemented
375C4×Q8C2318yescomplemented
376C4×Q8C2318yescomplemented
377C4×Q8C2318yescomplemented
378C4×Q8C2318yescomplemented
379C4×Q8C2318yescomplemented
380C4×D4C2318yes—
381C4×D4C2318yes—
382C4×D4C2318yes—
383C4×D4C2318yes—
384C4×D4C2318yes—
385C4×D4C2318yes—
386C4×D4C2318yes—
387C4×D4C2318yes—
388C4×D4C2318yes—
389C4×D4C2318yes—
390C4×D4C2318yes—
391C4×D4C2318yes—
392C4×D4C2318yescomplemented
393C4×D4C2318yescomplemented
394C4×D4C2318yescomplemented
395C4×D4C2318yescomplemented
396C4×D4C2318yescomplemented
397C4×D4C2318yescomplemented
398#117C2318yes—
399#117C2318yes—
400#117C2318yes—
401#117C2318yes—
402#117C2318yes—
403#117C2318yes—
404#117C2318yescomplemented
405#117C2318yescomplemented
406#117C2318yescomplemented
407#117C2318yescomplemented
408#117C2318yescomplemented
409#117C2318yescomplemented
410C2×C4⋊C4C2311yescharacteristic
411C2×C4⋊C4C2311yescharacteristic
412C2×C4⋊C4C2311yescharacteristic
413C2×C4⋊C4C2311yescharacteristic
414C2×C4⋊C4C2311yescharacteristic
415C2×C4⋊C4C2311yescharacteristic
416C2×C4⋊C4C2311yescharacteristic
417C2×C4⋊C4C2311yescharacteristic
418C2×C4⋊C4C2311yescharacteristic
419C2×C4⋊C4C2311yescharacteristic
420C2×C4⋊C4C2311yescharacteristic
421C2×C4⋊C4C2311yescharacteristic
422C2×C4⋊C4C2311yescharacteristic
423C2×C4⋊C4C2311yescharacteristic
424C2×C4⋊C4C2311yescharacteristic
425C2×C4⋊C4C2311yescharacteristic
426C2×C4⋊C4C2311yescharacteristic
427C2×C4⋊C4C2311yescharacteristic
428C2×C4⋊C4C2311yescharacteristic
429C2×C4⋊C4C2311yescharacteristic
430C2×C4⋊C4C2311yescharacteristic
431C2×C4⋊C4C2311yescharacteristic
432C2×C4⋊C4C2311yescharacteristic
433C2×C4⋊C4C2311yescharacteristic
434C2×C4⋊C4C2311yescharacteristic
435C2×C4⋊C4C2311yescharacteristic
436C2×C4⋊C4C2311yescharacteristic
437C2×C4⋊C4C2311yescharacteristic
438C2×C4⋊C4C2311yescharacteristic
439C2×C4⋊C4C2311yescharacteristic
440C2×C4⋊C4C2311yescharacteristic
441C2×C4⋊C4C2311yescharacteristic
442C2×C4⋊C4C2311yescharacteristic
443C2×C4⋊C4C2311yescharacteristic
444C2×C4⋊C4C2311yescharacteristic
445C2×C4⋊C4C2311yescharacteristic
446C2×C4⋊C4C2311yescharacteristic
447C2×C4⋊C4C2311yescharacteristic
448C2×C4⋊C4C2311yescharacteristic
449C2×C4⋊C4C2311yescharacteristic
450C2×C4⋊C4C2311yescharacteristic
451C2×C4⋊C4C2311yescharacteristic
452C2×C4⋊C4C2311yescharacteristic
453C2×C4⋊C4C2311yescharacteristic
454C2×C4⋊C4C2311yescharacteristic
455C2×C4⋊C4C2311yescharacteristic
456C2×C4⋊C4C2311yescharacteristic
457C2×C4⋊C4C2311yescharacteristic
458C2×C4⋊C4C2318yescomplemented
459C2×C4⋊C4C2318yescomplemented
460C2×C4⋊C4C2318yescomplemented
461C2×C22⋊C4C2311yescharacteristic
462C2×C22⋊C4C2311yescharacteristic
463C2×C22⋊C4C2311yescharacteristic
464C2×C22⋊C4C2311yescharacteristic
465C2×C22⋊C4C2311yescharacteristic
466C2×C22⋊C4C2311yescharacteristic
467C2×C22⋊C4C2311yescharacteristic
468C2×C22⋊C4C2311yescharacteristic
469C2×C22⋊C4C2311yescharacteristic
470C2×C22⋊C4C2311yescharacteristic
471C2×C22⋊C4C2311yescharacteristic
472C2×C22⋊C4C2311yescharacteristic
473C2×C22⋊C4C2318yes—
474C2×C22⋊C4C2318yes—
475C2×C22⋊C4C2318yes—
476C2×C22⋊C4C2311yescharacteristic
477C2×C22⋊C4C2311yescharacteristic
478C2×C22⋊C4C2311yescharacteristic
479C2×C22⋊C4C2311yescharacteristic
480C2×C22⋊C4C2311yescharacteristic
481C2×C22⋊C4C2311yescharacteristic
482C2×C22⋊C4C2311yescharacteristic
483C2×C22⋊C4C2311yescharacteristic
484C2×C22⋊C4C2311yescharacteristic
485C2×C22⋊C4C2311yescharacteristic
486C2×C22⋊C4C2311yescharacteristic
487C2×C22⋊C4C2311yescharacteristic
488C2×C22⋊C4C2311yescharacteristic
489C2×C22⋊C4C2311yescharacteristic
490C2×C22⋊C4C2311yescharacteristic
491C2×C22⋊C4C2311yescharacteristic
492C2×C22⋊C4C2311yescharacteristic
493C2×C22⋊C4C2311yescharacteristic
494C2×C22⋊C4C2311yescharacteristic
495C2×C22⋊C4C2311yescharacteristic
496C2×C22⋊C4C2311yescharacteristic
497C2×C22⋊C4C2311yescharacteristic
498C2×C22⋊C4C2311yescharacteristic
499C2×C22⋊C4C2311yescharacteristic
500C2×C22⋊C4C2311yescharacteristic
501C2×C22⋊C4C2311yescharacteristic
502C2×C22⋊C4C2311yescharacteristic
503C2×C22⋊C4C2311yescharacteristic
504C2×C22⋊C4C2311yescharacteristic
505C2×C22⋊C4C2311yescharacteristic
506C2×C22⋊C4C2311yescharacteristic
507C2×C22⋊C4C2311yescharacteristic
508C2×C22⋊C4C2311yescharacteristic
509C2×C22⋊C4C2311yescharacteristic
510C2×C22⋊C4C2311yescharacteristic
511C2×C22⋊C4C2311yescharacteristic
512C2×C42C2311yescharacteristic
513C2×C42C2311yescharacteristic
514C2×C42C2311yescharacteristic
515C2×C42C2311yescharacteristic
516C2×C42C2311yescharacteristic
517C2×C42C2311yescharacteristic
518C2×C42C2311yescharacteristic
519C2×C42C2311yescharacteristic
520C2×C42C2311yescharacteristic
521C2×C42C2311yescharacteristic
522C2×C42C2311yescharacteristic
523C2×C42C2311yescharacteristic
524C2×C42C2311yescharacteristic
525C2×C42C2311yescharacteristic
526C2×C42C2311yescharacteristic
527C2×C42C2311yescharacteristic
528C2×C42C2318yescomplemented
529C24—42no—
530C24—42no—
531C24—42no—
532C24C2411yescharacteristic
533C24C2411yescharacteristic
534C24C2411yescharacteristic
535C24C2411yescharacteristic
536C24C2411yescharacteristic
537C24C2411yescharacteristic
538C24C2411yescharacteristic
539C24C2414yes—
540C2×Q8—42no—
541C2×Q8—42no—
542C2×Q8—42no—
543C2×Q8—42no—
544C2×Q8—42no—
545C2×Q8—42no—
546C2×Q8C2414yes—
547C2×Q8C2414yes—
548C2×Q8C2414yes—
549C2×Q8C2414yes—
550C2×Q8C2414yes—
551C2×Q8C2414yes—
552C2×D4—42no—
553C2×D4—42no—
554C2×D4—42no—
555C2×D4—42no—
556C2×D4—42no—
557C2×D4—42no—
558C2×D4—42no—
559C2×D4—42no—
560C2×D4—42no—
561C2×D4—42no—
562C2×D4—42no—
563C2×D4—42no—
564C2×D4—42no—
565C2×D4—42no—
566C2×D4—42no—
567C2×D4—42no—
568C2×D4—42no—
569C2×D4—42no—
570C2×D4C2414yes—
571C2×D4C2414yes—
572C2×D4C2414yes—
573C2×D4C2414yes—
574C2×D4C2414yes—
575C2×D4C2414yes—
576C2×D4C2414yes—
577C2×D4C2414yes—
578C2×D4C2414yes—
579C2×D4C2414yes—
580C2×D4C2414yes—
581C2×D4C2414yes—
582C2×D4C2414yes—
583C2×D4C2414yes—
584C2×D4C2414yes—
585C2×D4C2414yes—
586C2×D4C2414yes—
587C2×D4C2414yes—
588C22×C4—42no—
589C22×C4—42no—
590C22×C4—42no—
591C22×C4—42no—
592C22×C4—42no—
593C22×C4—42no—
594C22×C4—42no—
595C22×C4—42no—
596C22×C4—42no—
597C22×C4—42no—
598C22×C4—42no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—42no—
603C22×C4—42no—
604C22×C4—42no—
605C22×C4—42no—
606C22×C4C2411yescharacteristic
607C22×C4C2411yescharacteristic
608C22×C4C2411yescharacteristic
609C22×C4C2411yescharacteristic
610C22×C4C2411yescharacteristic
611C22×C4C2411yescharacteristic
612C22×C4C2411yescharacteristic
613C22×C4C2411yescharacteristic
614C22×C4C2411yescharacteristic
615C22×C4C2411yescharacteristic
616C22×C4C2411yescharacteristic
617C22×C4C2411yescharacteristic
618C22×C4C2411yescharacteristic
619C22×C4C2411yescharacteristic
620C22×C4C2411yescharacteristic
621C22×C4C2411yescharacteristic
622C22×C4C2411yescharacteristic
623C22×C4C2411yescharacteristic
624C22×C4C2411yescharacteristic
625C22×C4C2411yescharacteristic
626C22×C4C2411yescharacteristic
627C22×C4C2411yescharacteristic
628C22×C4C2411yescharacteristic
629C22×C4C2411yescharacteristic
630C22×C4C2414yes—
631C22×C4C2414yes—
632C22×C4C2414yes—
633C22×C4C2414yes—
634C22×C4C2414yes—
635C22×C4C2414yes—
636C22×C4C2414yes—
637C22×C4C2414yes—
638C22×C4C2414yes—
639C22×C4C2414yes—
640C22×C4C2414yes—
641C22×C4C2414yes—
642C22×C4C2414yes—
643C22×C4C2414yes—
644C22×C4C2414yes—
645C22×C4C2414yes—
646C22×C4C2414yes—
647C22×C4C2414yes—
648C4⋊C4C2414yes—
649C4⋊C4C2414yes—
650C4⋊C4C2414yes—
651C4⋊C4C2414yes—
652C4⋊C4C2414yes—
653C4⋊C4C2414yes—
654C4⋊C4C2414yes—
655C4⋊C4C2414yes—
656C4⋊C4C2414yes—
657C4⋊C4C2414yes—
658C4⋊C4C2414yes—
659C4⋊C4C2414yes—
660C4⋊C4C2414yes—
661C4⋊C4C2414yes—
662C4⋊C4C2414yes—
663C4⋊C4C2414yes—
664C4⋊C4C2414yes—
665C4⋊C4C2414yes—
666C4⋊C4C2414yes—
667C4⋊C4C2414yes—
668C4⋊C4C2414yes—
669C4⋊C4C2414yes—
670C4⋊C4C2414yes—
671C4⋊C4C2414yes—
672C4⋊C4C2414yes—
673C4⋊C4C2414yes—
674C4⋊C4C2414yes—
675C4⋊C4C2414yes—
676C4⋊C4C2414yes—
677C4⋊C4C2414yes—
678C4⋊C4C2414yes—
679C4⋊C4C2414yes—
680C4⋊C4C2414yes—
681C4⋊C4C2414yes—
682C4⋊C4C2414yes—
683C4⋊C4C2414yes—
684C4⋊C4C2414yes—
685C4⋊C4C2414yes—
686C4⋊C4C2414yes—
687C4⋊C4C2414yes—
688C4⋊C4C2414yes—
689C4⋊C4C2414yes—
690C4⋊C4C2414yes—
691C4⋊C4C2414yes—
692C4⋊C4C2414yes—
693C4⋊C4C2414yes—
694C4⋊C4C2414yes—
695C4⋊C4C2414yes—
696C22⋊C4C2414yes—
697C22⋊C4C2414yes—
698C22⋊C4C2414yes—
699C22⋊C4C2414yes—
700C22⋊C4C2414yes—
701C22⋊C4C2414yes—
702C22⋊C4C2414yes—
703C22⋊C4C2414yes—
704C22⋊C4C2414yes—
705C22⋊C4C2414yes—
706C22⋊C4C2414yes—
707C22⋊C4C2414yes—
708C22⋊C4C2414yes—
709C22⋊C4C2414yes—
710C22⋊C4C2414yes—
711C22⋊C4C2414yes—
712C22⋊C4C2414yes—
713C22⋊C4C2414yes—
714C22⋊C4C2414yes—
715C22⋊C4C2414yes—
716C22⋊C4C2414yes—
717C22⋊C4C2414yes—
718C22⋊C4C2414yes—
719C22⋊C4C2414yes—
720C22⋊C4C2414yes—
721C22⋊C4C2414yes—
722C22⋊C4C2414yes—
723C22⋊C4C2414yes—
724C22⋊C4C2414yes—
725C22⋊C4C2414yes—
726C22⋊C4C2414yes—
727C22⋊C4C2414yes—
728C22⋊C4C2414yes—
729C22⋊C4C2414yes—
730C22⋊C4C2414yes—
731C22⋊C4C2414yes—
732C22⋊C4C2414yes—
733C22⋊C4C2414yes—
734C22⋊C4C2414yes—
735C22⋊C4C2414yes—
736C22⋊C4C2414yes—
737C22⋊C4C2414yes—
738C22⋊C4C2414yes—
739C22⋊C4C2414yes—
740C22⋊C4C2414yes—
741C22⋊C4C2414yes—
742C22⋊C4C2414yes—
743C22⋊C4C2414yes—
744C42C2414yes—
745C42C2414yes—
746C42C2414yes—
747C42C2414yes—
748C42C2414yes—
749C42C2414yes—
750C42C2414yes—
751C42C2414yes—
752C42C2414yes—
753C42C2414yes—
754C42C2414yes—
755C42C2414yes—
756C42C2414yes—
757C42C2414yes—
758C42C2414yes—
759C42C2414yes—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—22no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—44no—
782C23—44no—
783C23—44no—
784C23—88no—
785C23C2512yes—
786C23C2512yes—
787C23C2512yes—
788C23C2512yes—
789C23C2512yes—
790C23C2512yes—
791C23C2512yes—
792C23C2511yescharacteristic
793Q8—44no—
794Q8—44no—
795Q8—44no—
796Q8—44no—
797Q8—44no—
798Q8—44no—
799D4—44no—
800D4—44no—
801D4—44no—
802D4—44no—
803D4—44no—
804D4—44no—
805D4—44no—
806D4—44no—
807D4—44no—
808D4—44no—
809D4—44no—
810D4—44no—
811D4—44no—
812D4—44no—
813D4—44no—
814D4—44no—
815D4—44no—
816D4—44no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—44no—
842C2×C4—44no—
843C2×C4—44no—
844C2×C4—44no—
845C2×C4—44no—
846C2×C4—44no—
847C2×C4—44no—
848C2×C4—44no—
849C2×C4—44no—
850C2×C4—44no—
851C2×C4—44no—
852C2×C4—44no—
853C2×C4—44no—
854C2×C4—44no—
855C2×C4—44no—
856C2×C4—44no—
857C2×C4—44no—
858C2×C4—44no—
859C2×C4C2512yes—
860C2×C4C2512yes—
861C2×C4C2512yes—
862C2×C4C2512yes—
863C2×C4C2512yes—
864C2×C4C2512yes—
865C2×C4C2512yes—
866C2×C4C2512yes—
867C2×C4C2512yes—
868C2×C4C2512yes—
869C2×C4C2512yes—
870C2×C4C2512yes—
871C2×C4C2512yes—
872C2×C4C2512yes—
873C2×C4C2512yes—
874C2×C4C2512yes—
875C2×C4C2512yes—
876C2×C4C2512yes—
877C2×C4C2512yes—
878C2×C4C2512yes—
879C2×C4C2512yes—
880C2×C4C2512yes—
881C2×C4C2512yes—
882C2×C4C2512yes—
883C22—22no—
884C22—22no—
885C22—22no—
886C22—22no—
887C22—22no—
888C22—22no—
889C22—22no—
890C22—22no—
891C22—22no—
892C22—22no—
893C22—22no—
894C22—22no—
895C22—22no—
896C22—22no—
897C22—22no—
898C22—22no—
899C22—22no—
900C22—22no—
901C22—22no—
902C22—22no—
903C22—22no—
904C22—44no—
905C22—44no—
906C22—44no—
907C22—44no—
908C22—44no—
909C22—44no—
910C22—44no—
911C22—88no—
912C22#58512yes—
913C22#58512yes—
914C22#58512yes—
915C22C2611yescharacteristic
916C4—22no—
917C4—22no—
918C4—22no—
919C4—22no—
920C4—22no—
921C4—22no—
922C4—22no—
923C4—22no—
924C4—22no—
925C4—22no—
926C4—22no—
927C4—22no—
928C4—22no—
929C4—22no—
930C4—22no—
931C4—22no—
932C4—22no—
933C4—22no—
934C4—22no—
935C4—22no—
936C4—22no—
937C4—22no—
938C4—22no—
939C4—22no—
940C2—42no—
941C2—42no—
942C2—42no—
943C2—42no—
944C2—42no—
945C2—42no—
946C2—42no—
947C2#356614yesdirect product factor
948C2C2×#58511yescharacteristic
949C2C2×#58511yescharacteristic
950C2C2×#58511yescharacteristic
subgroupG/H
center, socleC23C25
commutator, Frattini, cosocleC22C26
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #3566C2direct (N × H)
2. C2×#563C2semidirect
3. C2×#562C2semidirect
4. C2×#562C2semidirect
5. C2×#560C2semidirect
6. C2×#559C2semidirect
7. C2×#556C2semidirect
8. C2×#555C2semidirect
9. C2×#553C2semidirect
10. C2×#553C2semidirect
11. C2×#553C2semidirect
12. C2×#552C2semidirect
13. C2×#552C2semidirect
14. C2×#552C2semidirect
15. C2×#551C2semidirect
16. C2×#551C2semidirect
17. C2×#551C2semidirect
18. C2×#542C2semidirect
19. C2×#542C2semidirect
20. C2×#542C2semidirect
21. C2×#541C2semidirect
22. C2×#541C2semidirect
23. C2×#540C2semidirect
24. C2×#539C2semidirect
25. C2×#539C2semidirect
26. C2×#539C2semidirect
27. C2×#538C2semidirect
28. C2×#538C2semidirect
29. C2×#538C2semidirect
30. C2×#529C2semidirect
31. C2×#529C2semidirect
32. C2×#529C2semidirect
33. #563C22semidirect
34. #562C22semidirect
35. #562C22semidirect
36. #560C22semidirect
37. #559C22semidirect
38. #556C22semidirect
39. #555C22semidirect
40. #553C22semidirect
41. #553C22semidirect
42. #553C22semidirect
43. #552C22semidirect
44. #552C22semidirect
45. #552C22semidirect
46. #551C22semidirect
47. #551C22semidirect
48. #551C22semidirect
49. #542C22semidirect
50. #542C22semidirect
51. #542C22semidirect
52. #541C22semidirect
53. #541C22semidirect
54. #540C22semidirect
55. #539C22semidirect
56. #539C22semidirect
57. #539C22semidirect
58. #538C22semidirect
59. #538C22semidirect
60. #538C22semidirect
61. C2×C4⋊Q8C22semidirect
62. C2×C4⋊Q8C22semidirect
63. C2×C4⋊Q8C22semidirect
65. #529C22semidirect
66. #529C22semidirect
67. #529C22semidirect
82. C2×#126C22semidirect
83. C2×#126C22semidirect
84. C2×#126C22semidirect
85. C2×#126C22semidirect
86. C2×#126C22semidirect
87. C2×#126C22semidirect
88. C2×#125C22semidirect
89. C2×#125C22semidirect
90. C2×#125C22semidirect
91. C2×#125C22semidirect
92. C2×#125C22semidirect
93. C2×#125C22semidirect
94. C2×#125C22semidirect
95. C2×#125C22semidirect
96. C2×#125C22semidirect
97. C2×#125C22semidirect
98. C2×#125C22semidirect
99. C2×#125C22semidirect
109. C2×#124C22semidirect
110. C2×#124C22semidirect
111. C2×#124C22semidirect
130. C2×#123C22semidirect
131. C2×#123C22semidirect
132. C2×#123C22semidirect
133. C2×#123C22semidirect
134. C2×#123C22semidirect
135. C2×#123C22semidirect
145. C2×C22⋊Q8C22semidirect
146. C2×C22⋊Q8C22semidirect
147. C2×C22⋊Q8C22semidirect
148. C2×C22⋊Q8C22semidirect
149. C2×C22⋊Q8C22semidirect
150. C2×C22⋊Q8C22semidirect
151. C2×C22⋊Q8C22semidirect
152. C2×C22⋊Q8C22semidirect
153. C2×C22⋊Q8C22semidirect
169. C2×#121C22semidirect
170. C2×#121C22semidirect
171. C2×#121C22semidirect
176. C2×C4×Q8C22semidirect
177. C2×C4×Q8C22semidirect
178. C2×C4×Q8C22semidirect
179. C2×C4×Q8C22semidirect
180. C2×C4×Q8C22semidirect
181. C2×C4×Q8C22semidirect
194. C2×C4×D4C22semidirect
195. C2×C4×D4C22semidirect
196. C2×C4×D4C22semidirect
197. C2×C4×D4C22semidirect
198. C2×C4×D4C22semidirect
199. C2×C4×D4C22semidirect
206. C2×#117C22semidirect
207. C2×#117C22semidirect
208. C2×#117C22semidirect
209. C2×#117C22semidirect
210. C2×#117C22semidirect
211. C2×#117C22semidirect
212. C22×C4⋊C4C22semidirect
213. C22×C4⋊C4C22semidirect
214. C22×C4⋊C4C22semidirect
218. C22×C42C22semidirect
262. C4⋊Q8C23semidirect
263. C4⋊Q8C23semidirect
264. C4⋊Q8C23semidirect
280. #126C23semidirect
281. #126C23semidirect
282. #126C23semidirect
283. #126C23semidirect
284. #126C23semidirect
285. #126C23semidirect
286. #125C23semidirect
287. #125C23semidirect
288. #125C23semidirect
289. #125C23semidirect
290. #125C23semidirect
291. #125C23semidirect
292. #125C23semidirect
293. #125C23semidirect
294. #125C23semidirect
295. #125C23semidirect
296. #125C23semidirect
297. #125C23semidirect
307. #124C23semidirect
308. #124C23semidirect
309. #124C23semidirect
328. #123C23semidirect
329. #123C23semidirect
330. #123C23semidirect
331. #123C23semidirect
332. #123C23semidirect
333. #123C23semidirect
343. C22⋊Q8C23semidirect
344. C22⋊Q8C23semidirect
345. C22⋊Q8C23semidirect
346. C22⋊Q8C23semidirect
347. C22⋊Q8C23semidirect
348. C22⋊Q8C23semidirect
349. C22⋊Q8C23semidirect
350. C22⋊Q8C23semidirect
351. C22⋊Q8C23semidirect
367. #121C23semidirect
368. #121C23semidirect
369. #121C23semidirect
374. C4×Q8C23semidirect
375. C4×Q8C23semidirect
376. C4×Q8C23semidirect
377. C4×Q8C23semidirect
378. C4×Q8C23semidirect
379. C4×Q8C23semidirect
392. C4×D4C23semidirect
393. C4×D4C23semidirect
394. C4×D4C23semidirect
395. C4×D4C23semidirect
396. C4×D4C23semidirect
397. C4×D4C23semidirect
404. #117C23semidirect
405. #117C23semidirect
406. #117C23semidirect
407. #117C23semidirect
408. #117C23semidirect
409. #117C23semidirect
458. C2×C4⋊C4C23semidirect
459. C2×C4⋊C4C23semidirect
460. C2×C4⋊C4C23semidirect
528. C2×C42C23semidirect
947. C2#3566direct (N × H)

Maximal subgroups

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

subgroupindex
#35662
C2×#5632
C2×#5622
C2×#5602
C2×#5592
C2×#5562
C2×#5552
C2×#5532
C2×#5522
C2×#5512
C2×#5422
C2×#5412
C2×#5402
C2×#5392
C2×#5382
C2×#5292