Subgroups — #13092819

Order 1472.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10625041	C₂	1	2	yes	maximal
2	C₄×C₈×C₂₃	C₂	1	1	yes	maximal, characteristic
3	#10625000	C₂	1	2	yes	maximal
4	#10624999	C₂	1	2	yes	maximal
5	C₂×C₈×C₂₃	C₂²	1	1	yes	characteristic
6	C₂×C₈×C₂₃	C₂²	1	1	yes	characteristic
7	C₄²×C₂₃	C₂²	1	1	yes	characteristic
8	C₄⋊Dic₂₃	C₂²	1	4	yes	—
9	Dic₂₃⋊C₄	—	2	4	no	—
10	C₂×C₄×C₂₃	D₄	1	2	yes	—
11	C₂×C₄×C₂₃	C₂³	1	1	yes	characteristic
12	C₂×Dic₂₃	—	2	4	no	—
13	C₈×C₂₃	Q₈	1	2	yes	—
14	C₈×C₂₃	Q₈	1	2	yes	—
15	C₂²×C₂₃	C₂×D₄	1	1	yes	characteristic
16	C₄×C₂₃	—	2	2	no	—
17	C₄×C₂₃	C₂×Q₈	1	1	yes	characteristic
18	C₄×C₂₃	C₂×Q₈	1	1	yes	characteristic
19	Dic₂₃	—	4	4	no	—
20	#499	—	23	1	no	maximal, Sylow
21	C₂×C₂₃	C₄⋊Q₈	1	1	yes	characteristic
22	C₂×C₂₃	#135	1	2	yes	—
23	#125	—	23	2	no	—
24	#107	—	23	2	no	—
25	#106	—	23	2	no	—
26	C₄×C₈	D₂₃	1	1	yes	characteristic
27	C₂₃	#499	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₈	C₂×D₂₃	1	1	yes	characteristic
29	C₂×C₈	C₂×D₂₃	1	1	yes	characteristic
30	C₄⋊C₄	—	23	4	no	—
31	C₄⋊C₄	—	46	4	no	—
32	C₄²	C₂×D₂₃	1	1	yes	characteristic
33	C₂×C₄	—	46	4	no	—
34	C₂×C₄	D₉₂	1	2	yes	—
35	C₂×C₄	C₂²×D₂₃	1	1	yes	characteristic
36	C₈	Dic₄₆	1	2	yes	—
37	C₈	Dic₄₆	1	2	yes	—
38	C₂²	C₂×D₉₂	1	1	yes	characteristic
39	C₄	—	2	2	no	—
40	C₄	—	92	4	no	—
41	C₄	C₂×Dic₄₆	1	1	yes	characteristic
42	C₄	C₂×Dic₄₆	1	1	yes	characteristic
43	C₂	#10625040	1	1	yes	characteristic
44	C₂	#10625075	1	2	yes	—

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

N	H ≅ G/N	type
27. C₂₃	#499	semidirect

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