Subgroups — #29504611

Order 15296.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₁₉₁₂	C₂	1	1	yes	maximal, characteristic, complemented
2	D₃₈₂₄	C₂	1	1	yes	maximal, characteristic
3	C₃₂×C₂₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	Dic₉₅₆	—	2	1	no	—
5	D₁₉₁₂	—	2	1	no	—
6	C₁₆×C₂₃₉	C₂²	1	1	yes	characteristic
7	Dic₄₇₈	—	4	1	no	—
8	D₉₅₆	—	4	1	no	—
9	C₈×C₂₃₉	D₄	1	1	yes	characteristic
10	C₂×D₂₃₉	—	8	1	no	—
11	C₄×C₂₃₉	D₈	1	1	yes	characteristic
12	Dic₂₃₉	—	8	1	no	—
13	C₂×C₂₃₉	D₁₆	1	1	yes	characteristic
14	D₂₃₉	—	16	1	no	—
15	C₂₃₉	SD₆₄	1	1	yes	characteristic, complemented, Sylow
16	SD₆₄	—	239	1	no	maximal, Sylow
17	Q₃₂	—	239	1	no	—
18	D₁₆	—	239	1	no	—
19	C₃₂	D₂₃₉	1	1	yes	characteristic, complemented
20	Q₁₆	—	478	1	no	—
21	D₈	—	478	1	no	—
22	C₁₆	C₂×D₂₃₉	1	1	yes	characteristic
23	Q₈	—	956	1	no	—
24	D₄	—	956	1	no	—
25	C₈	D₉₅₆	1	1	yes	characteristic
26	C₂²	—	1912	1	no	—
27	C₄	—	1912	1	no	—
28	C₄	D₁₉₁₂	1	1	yes	characteristic
29	C₂	—	3824	1	no	—
30	C₂	D₃₈₂₄	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.