Subgroups — #13092785

Order 1472.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	#10625041	C₂	1	1	yes	maximal, characteristic
3	#10625017	C₂	1	4	yes	maximal
4	#10624985	C₂	1	1	yes	maximal, characteristic
5	C₂×Q₈×C₂₃	C₂²	1	2	yes	—
6	C₄⋊C₄×C₂₃	—	2	2	no	—
7	C₄²×C₂₃	C₂²	1	1	yes	characteristic
8	C₄⋊Dic₂₃	C₂²	1	2	yes	—
9	Dic₂₃⋊C₄	—	2	2	no	—
10	C₂×C₂₃⋊C₈	C₂²	1	2	yes	—
11	Q₈×C₂₃	—	2	4	no	—
12	C₂×C₄×C₂₃	—	2	2	no	—
13	C₂×C₄×C₂₃	D₄	1	2	yes	—
14	C₂×C₄×C₂₃	C₂³	1	1	yes	characteristic
15	C₂×Dic₂₃	—	2	2	no	—
16	C₂₃⋊C₈	—	2	2	no	—
17	C₂²×C₂₃	C₂×D₄	1	1	yes	characteristic
18	C₄×C₂₃	—	2	2	no	—
19	C₄×C₂₃	—	4	2	no	—
20	C₄×C₂₃	#41	1	2	yes	—
21	Dic₂₃	—	4	2	no	—
22	#491	—	23	1	no	maximal, Sylow
23	C₂×C₂₃	#124	1	1	yes	characteristic
24	C₂×C₂₃	#137	1	2	yes	—
25	C₄⋊Q₈	D₂₃	1	1	yes	characteristic
26	#125	—	23	1	no	—
27	#103	—	23	4	no	—
28	#97	—	23	1	no	—
29	C₂₃	#491	1	1	yes	characteristic, complemented, Sylow
30	C₂×Q₈	C₂×D₂₃	1	2	yes	—
31	C₂×C₈	—	23	2	no	—
32	C₄⋊C₄	—	2	2	no	—
33	C₄⋊C₄	—	23	2	no	—
34	C₄⋊C₄	—	46	2	no	—
35	C₄²	C₂×D₂₃	1	1	yes	characteristic
36	Q₈	—	2	4	no	—
37	C₂×C₄	—	2	2	no	—
38	C₂×C₄	—	46	2	no	—
39	C₂×C₄	C₂²⋊D₂₃	1	2	yes	—
40	C₂×C₄	C₂²×D₂₃	1	1	yes	characteristic
41	C₈	—	46	2	no	—
42	C₂²	C₂×C₂²⋊D₂₃	1	1	yes	characteristic
43	C₄	—	2	2	no	—
44	C₄	—	4	2	no	—
45	C₄	—	92	2	no	—
46	C₄	#67290	1	2	yes	—
47	C₂	#10625107	1	1	yes	characteristic
48	C₂	#10625113	1	2	yes	—

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

N	H ≅ G/N	type
29. C₂₃	#491	semidirect

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