Subgroups — #67290

Order 368.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²⋊D₂₃	C₂	1	2	yes	maximal, complemented
3	C₂×Dic₂₃	C₂	1	2	yes	maximal, complemented
4	C₄×D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
5	Dic₄₆	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₂₃	C₂²	1	2	yes	—
7	C₂×D₂₃	C₂²	1	1	yes	characteristic
8	C₄×C₂₃	C₂²	1	1	yes	characteristic
9	Dic₂₃	C₂²	1	2	yes	—
10	Dic₂₃	C₂²	1	1	yes	characteristic
11	C₂×C₂₃	—	2	2	no	—
12	C₂×C₂₃	C₂³	1	1	yes	characteristic
13	D₂₃	—	2	1	no	—
14	C₂₃	#41	1	1	yes	characteristic, complemented, Sylow
15	#41	—	23	1	no	maximal, Sylow
16	Q₈	—	23	1	no	—
17	D₄	—	23	2	no	—
18	D₄	D₂₃	1	1	yes	characteristic, complemented
19	C₂×C₄	—	23	2	no	—
20	C₂×C₄	—	23	1	no	—
21	C₂²	—	23	1	no	—
22	C₂²	C₂×D₂₃	1	2	yes	—
23	C₄	—	23	1	no	—
24	C₄	—	23	2	no	—
25	C₄	C₂×D₂₃	1	1	yes	characteristic
26	C₂	—	2	2	no	—
27	C₂	—	46	1	no	—
28	C₂	C₂²×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.