Subgroups — #13066832

Order 1408.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₁₇₆	C₂	1	1	yes	maximal, characteristic, complemented
2	D₃₅₂	C₂	1	1	yes	maximal, characteristic
3	C₁₁×C₆₄	C₂	1	1	yes	maximal, characteristic, complemented
4	Dic₈₈	—	2	1	no	—
5	D₁₇₆	—	2	1	no	—
6	C₁₁×C₃₂	C₂²	1	1	yes	characteristic
7	Dic₄₄	—	4	1	no	—
8	D₈₈	—	4	1	no	—
9	C₁₁×C₁₆	D₄	1	1	yes	characteristic
10	SD₁₂₈	—	11	1	no	maximal, Sylow
11	D₄₄	—	8	1	no	—
12	Dic₂₂	—	8	1	no	—
13	C₈×C₁₁	D₈	1	1	yes	characteristic
14	Q₆₄	—	11	1	no	—
15	D₃₂	—	11	1	no	—
16	C₆₄	D₁₁	1	1	yes	characteristic, complemented
17	C₂×D₁₁	—	16	1	no	—
18	C₄×C₁₁	D₁₆	1	1	yes	characteristic
19	Dic₁₁	—	16	1	no	—
20	Q₃₂	—	22	1	no	—
21	D₁₆	—	22	1	no	—
22	C₃₂	C₂×D₁₁	1	1	yes	characteristic
23	C₂×C₁₁	D₃₂	1	1	yes	characteristic
24	D₁₁	—	32	1	no	—
25	Q₁₆	—	44	1	no	—
26	D₈	—	44	1	no	—
27	C₁₆	D₄₄	1	1	yes	characteristic
28	C₁₁	SD₁₂₈	1	1	yes	characteristic, complemented, Sylow
29	Q₈	—	88	1	no	—
30	D₄	—	88	1	no	—
31	C₈	D₈₈	1	1	yes	characteristic
32	C₂²	—	176	1	no	—
33	C₄	—	176	1	no	—
34	C₄	D₁₇₆	1	1	yes	characteristic
35	C₂	—	352	1	no	—
36	C₂	D₃₅₂	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.