Subgroups — #13092815

Order 1472.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10625040	C₂	1	2	yes	maximal
2	C₄×C₈×C₂₃	C₂	1	1	yes	maximal, characteristic
3	#10624999	C₂	1	4	yes	maximal
4	C₂×Dic₄₆	—	2	2	no	—
5	C₂×C₈×C₂₃	C₂²	1	2	yes	—
6	C₄²×C₂₃	C₂²	1	1	yes	characteristic
7	C₄⋊Dic₂₃	—	2	2	no	—
8	C₄⋊Dic₂₃	C₂²	1	4	yes	—
9	C₂×C₄×C₂₃	D₄	1	2	yes	—
10	C₂×C₄×C₂₃	C₂³	1	1	yes	characteristic
11	C₂×Dic₂₃	—	2	4	no	—
12	Dic₄₆	—	4	4	no	—
13	C₈×C₂₃	Q₈	1	4	yes	complemented
14	C₂²×C₂₃	C₂×D₄	1	1	yes	characteristic
15	C₄×C₂₃	SD₁₆	1	4	yes	—
16	C₄×C₂₃	C₂×Q₈	1	2	yes	—
17	Dic₂₃	—	4	4	no	—
18	#498	—	23	1	no	maximal, Sylow
19	C₂×C₂₃	C₄⋊Q₈	1	1	yes	characteristic
20	C₂×C₂₃	C₂×SD₁₆	1	2	yes	—
21	C₄⋊Q₈	—	23	2	no	—
22	#106	—	23	4	no	—
23	C₄×C₈	D₂₃	1	1	yes	characteristic
24	C₂₃	#498	1	1	yes	characteristic, complemented, Sylow
25	C₂×Q₈	—	46	2	no	—
26	C₂×C₈	C₂×D₂₃	1	2	yes	—
27	C₄⋊C₄	—	23	4	no	—
28	C₄⋊C₄	—	46	2	no	—
29	C₄²	C₂×D₂₃	1	1	yes	characteristic
30	Q₈	—	92	4	no	—
31	C₂×C₄	—	46	4	no	—
32	C₂×C₄	D₉₂	1	2	yes	—
33	C₂×C₄	C₂²×D₂₃	1	1	yes	characteristic
34	C₈	Dic₄₆	1	4	yes	complemented
35	C₂²	C₂×D₉₂	1	1	yes	characteristic
36	C₄	—	92	4	no	—
37	C₄	#67263	1	4	yes	—
38	C₄	C₂×Dic₄₆	1	2	yes	—
39	C₂	#10625040	1	1	yes	characteristic
40	C₂	C₂×#67263	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.