Subgroups — #26104194

Order 12032.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₁₅₀₄	C₂	1	1	yes	maximal, characteristic, complemented
2	D₃₀₀₈	C₂	1	1	yes	maximal, characteristic
3	C₄₇×C₁₂₈	C₂	1	1	yes	maximal, characteristic, complemented
4	Dic₇₅₂	—	2	1	no	—
5	D₁₅₀₄	—	2	1	no	—
6	C₄₇×C₆₄	C₂²	1	1	yes	characteristic
7	Dic₃₇₆	—	4	1	no	—
8	D₇₅₂	—	4	1	no	—
9	C₃₂×C₄₇	D₄	1	1	yes	characteristic
10	Dic₁₈₈	—	8	1	no	—
11	D₃₇₆	—	8	1	no	—
12	C₁₆×C₄₇	D₈	1	1	yes	characteristic
13	D₁₈₈	—	16	1	no	—
14	Dic₉₄	—	16	1	no	—
15	C₈×C₄₇	D₁₆	1	1	yes	characteristic
16	SD₂₅₆	—	47	1	no	maximal, Sylow
17	C₂×D₄₇	—	32	1	no	—
18	C₄×C₄₇	D₃₂	1	1	yes	characteristic
19	Dic₄₇	—	32	1	no	—
20	Q₁₂₈	—	47	1	no	—
21	D₆₄	—	47	1	no	—
22	C₁₂₈	D₄₇	1	1	yes	characteristic, complemented
23	C₂×C₄₇	D₆₄	1	1	yes	characteristic
24	D₄₇	—	64	1	no	—
25	Q₆₄	—	94	1	no	—
26	D₃₂	—	94	1	no	—
27	C₆₄	C₂×D₄₇	1	1	yes	characteristic
28	C₄₇	SD₂₅₆	1	1	yes	characteristic, complemented, Sylow
29	Q₃₂	—	188	1	no	—
30	D₁₆	—	188	1	no	—
31	C₃₂	D₁₈₈	1	1	yes	characteristic
32	Q₁₆	—	376	1	no	—
33	D₈	—	376	1	no	—
34	C₁₆	D₃₇₆	1	1	yes	characteristic
35	Q₈	—	752	1	no	—
36	D₄	—	752	1	no	—
37	C₈	D₇₅₂	1	1	yes	characteristic
38	C₂²	—	1504	1	no	—
39	C₄	—	1504	1	no	—
40	C₄	D₁₅₀₄	1	1	yes	characteristic
41	C₂	—	3008	1	no	—
42	C₂	D₃₀₀₈	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.