Subgroups — #10625078

Order 736.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#67288	C₂	1	1	yes	maximal, characteristic
2	M₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₂₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#67262	C₂	1	2	yes	maximal, complemented
5	C₈×D₂₃	C₂	1	2	yes	maximal, complemented
6	C₂×C₄×C₂₃	C₂²	1	1	yes	characteristic
7	C₂²⋊D₂₃	C₄	1	2	yes	—
8	D₉₂	C₄	1	1	yes	characteristic
9	C₄×D₂₃	C₂²	1	2	yes	—
10	Dic₄₆	C₄	1	1	yes	characteristic
11	C₈×C₂₃	C₂²	1	2	yes	—
12	C₂₃⋊C₈	C₂²	1	1	yes	characteristic
13	C₂₃⋊C₈	C₂²	1	1	yes	characteristic
14	C₂²×C₂₃	C₂×C₄	1	1	yes	characteristic
15	C₂×D₂₃	C₂×C₄	1	2	yes	—
16	C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
17	C₄×C₂₃	C₂³	1	1	yes	characteristic
18	Dic₂₃	C₂×C₄	1	2	yes	—
19	C₂×C₂₃	—	2	1	no	—
20	C₂×C₂₃	C₂²×C₄	1	1	yes	characteristic
21	D₂₃	—	2	2	no	—
22	#131	—	23	1	no	maximal, Sylow
23	C₂₃	#131	1	1	yes	characteristic, complemented, Sylow
24	#41	—	23	1	no	—
25	M₁₆	—	23	2	no	—
26	M₁₆	D₂₃	1	1	yes	characteristic, complemented
27	C₂×C₈	—	23	1	no	—
28	C₂×C₈	—	23	2	no	—
29	Q₈	—	23	1	no	—
30	D₄	—	23	2	no	—
31	D₄	—	23	1	no	—
32	C₂×C₄	—	23	2	no	—
33	C₂×C₄	C₂×D₂₃	1	1	yes	characteristic
34	C₈	—	23	1	no	—
35	C₈	—	23	1	no	—
36	C₈	C₂×D₂₃	1	2	yes	—
37	C₂²	—	23	2	no	—
38	C₂²	C₄×D₂₃	1	1	yes	characteristic
39	C₄	—	23	2	no	—
40	C₄	C₄×D₂₃	1	1	yes	characteristic
41	C₄	C₂²×D₂₃	1	1	yes	characteristic
42	C₂	—	2	1	no	—
43	C₂	—	46	2	no	—
44	C₂	C₂×C₄×D₂₃	1	1	yes	characteristic

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

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