Subgroups — #31779005

Order 17536.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₂₁₉₂	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄₃₈₄	C₂	1	1	yes	maximal, characteristic
3	C₆₄×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
4	Dic₁₀₉₆	—	2	1	no	—
5	D₂₁₉₂	—	2	1	no	—
6	C₃₂×C₁₃₇	C₂²	1	1	yes	characteristic
7	Dic₅₄₈	—	4	1	no	—
8	D₁₀₉₆	—	4	1	no	—
9	C₁₆×C₁₃₇	D₄	1	1	yes	characteristic
10	Dic₂₇₄	—	8	1	no	—
11	D₅₄₈	—	8	1	no	—
12	C₈×C₁₃₇	D₈	1	1	yes	characteristic
13	C₂×D₁₃₇	—	16	1	no	—
14	C₄×C₁₃₇	D₁₆	1	1	yes	characteristic
15	Dic₁₃₇	—	16	1	no	—
16	C₂×C₁₃₇	D₃₂	1	1	yes	characteristic
17	D₁₃₇	—	32	1	no	—
18	C₁₃₇	SD₁₂₈	1	1	yes	characteristic, complemented, Sylow
19	SD₁₂₈	—	137	1	no	maximal, Sylow
20	Q₆₄	—	137	1	no	—
21	D₃₂	—	137	1	no	—
22	C₆₄	D₁₃₇	1	1	yes	characteristic, complemented
23	Q₃₂	—	274	1	no	—
24	D₁₆	—	274	1	no	—
25	C₃₂	C₂×D₁₃₇	1	1	yes	characteristic
26	Q₁₆	—	548	1	no	—
27	D₈	—	548	1	no	—
28	C₁₆	D₅₄₈	1	1	yes	characteristic
29	Q₈	—	1096	1	no	—
30	D₄	—	1096	1	no	—
31	C₈	D₁₀₉₆	1	1	yes	characteristic
32	C₂²	—	2192	1	no	—
33	C₄	—	2192	1	no	—
34	C₄	D₂₁₉₂	1	1	yes	characteristic
35	C₂	—	4384	1	no	—
36	C₂	D₄₃₈₄	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.