Subgroups — #13092138

Order 1472.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₈×C₂₃	C₂	1	1	yes	maximal, characteristic
2	C₄×C₂₃⋊C₈	C₂	1	2	yes	maximal
3	C₂×C₈×C₂₃	C₄	1	2	yes	—
4	C₄²×C₂₃	C₂²	1	1	yes	characteristic
5	C₂×C₂₃⋊C₈	C₄	1	4	yes	—
6	C₂×C₄×C₂₃	C₂×C₄	1	2	yes	—
7	C₂×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
8	C₈×C₂₃	C₈	1	4	yes	complemented
9	C₂₃⋊C₈	—	2	4	no	—
10	C₂²×C₂₃	C₄²	1	1	yes	characteristic
11	C₄×C₂₃	C₂×C₈	1	2	yes	—
12	C₄×C₂₃	M₁₆	1	4	yes	—
13	#322	—	23	1	no	maximal, Sylow
14	C₂×C₂₃	C₄×C₈	1	1	yes	characteristic
15	C₂×C₂₃	#97	1	2	yes	—
16	C₄×C₈	—	23	2	no	—
17	C₄×C₈	D₂₃	1	1	yes	characteristic
18	C₂₃	#322	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₈	—	23	4	no	—
20	C₂×C₈	Dic₂₃	1	2	yes	—
21	C₄²	C₂×D₂₃	1	1	yes	characteristic
22	C₂×C₄	C₄×D₂₃	1	2	yes	—
23	C₂×C₄	C₂×Dic₂₃	1	1	yes	characteristic
24	C₈	—	46	4	no	—
25	C₈	C₂₃⋊C₈	1	4	yes	complemented
26	C₂²	C₄×Dic₂₃	1	1	yes	characteristic
27	C₄	#67262	1	4	yes	—
28	C₄	C₂×C₂₃⋊C₈	1	2	yes	—
29	C₂	C₄×C₂₃⋊C₈	1	1	yes	characteristic
30	C₂	#10624997	1	2	yes	—

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.