Subgroups — #13092233

Order 1472.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic
2	#10625001	C₂	1	1	yes	maximal, characteristic
3	#10624994	C₂	1	1	yes	maximal, characteristic
4	C₂×Q₈×C₂₃	—	2	1	no	—
5	Q₁₆×C₂₃	—	2	1	no	—
6	Q₁₆×C₂₃	C₄	1	2	yes	—
7	C₂×C₈×C₂₃	C₂²	1	1	yes	characteristic
8	#67267	—	2	1	no	—
9	C₂₃⋊C₁₆	—	2	1	no	—
10	Q₈×C₂₃	—	2	2	no	—
11	Q₈×C₂₃	—	4	1	no	—
12	C₂×C₄×C₂₃	—	4	1	no	—
13	C₂×C₄×C₂₃	D₄	1	1	yes	characteristic
14	C₈×C₂₃	C₂×C₄	1	1	yes	characteristic
15	C₈×C₂₃	D₄	1	1	yes	characteristic
16	C₂₃⋊C₈	—	4	1	no	—
17	C₂²×C₂₃	SD₁₆	1	1	yes	characteristic
18	C₄×C₂₃	—	4	2	no	—
19	C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
20	C₄×C₂₃	D₈	1	1	yes	characteristic
21	#362	—	23	1	no	maximal, Sylow
22	C₂×C₂₃	—	2	1	no	—
23	C₂×C₂₃	#102	1	1	yes	characteristic
24	C₂×Q₁₆	D₂₃	1	1	yes	characteristic
25	M₃₂	—	23	1	no	—
26	#108	—	23	1	no	—
27	C₂₃	#362	1	1	yes	characteristic, complemented, Sylow
28	C₂×Q₈	—	2	1	no	—
29	Q₁₆	—	2	1	no	—
30	Q₁₆	Dic₂₃	1	2	yes	—
31	M₁₆	—	46	1	no	—
32	C₂×C₈	C₂×D₂₃	1	1	yes	characteristic
33	C₁₆	—	46	1	no	—
34	Q₈	—	2	2	no	—
35	Q₈	—	4	1	no	—
36	C₂×C₄	—	4	1	no	—
37	C₂×C₄	C₂²⋊D₂₃	1	1	yes	characteristic
38	C₈	—	92	1	no	—
39	C₈	C₂×Dic₂₃	1	1	yes	characteristic
40	C₈	C₂²⋊D₂₃	1	1	yes	characteristic
41	C₂²	#67273	1	1	yes	characteristic
42	C₄	—	4	2	no	—
43	C₄	#67272	1	1	yes	characteristic
44	C₄	C₂²⋊Dic₂₃	1	1	yes	characteristic
45	C₂	—	2	1	no	—
46	C₂	#10625014	1	1	yes	characteristic

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

N	H ≅ G/N	type
27. C₂₃	#362	semidirect

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