Subgroups — #41011612

Order 27008.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₆₇₅₂	C₂	1	1	yes	maximal, characteristic
2	C₂₁₁⋊C₆₄	C₂	1	1	yes	maximal, characteristic, complemented
3	Q₆₄×C₂₁₁	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃₃₇₆	—	2	1	no	—
5	Q₃₂×C₂₁₁	—	2	1	no	—
6	C₃₂×C₂₁₁	C₂²	1	1	yes	characteristic
7	D₁₆₈₈	—	4	1	no	—
8	Q₁₆×C₂₁₁	—	4	1	no	—
9	C₁₆×C₂₁₁	D₄	1	1	yes	characteristic
10	D₈₄₄	—	8	1	no	—
11	Q₈×C₂₁₁	—	8	1	no	—
12	C₈×C₂₁₁	D₈	1	1	yes	characteristic
13	C₂×D₂₁₁	—	16	1	no	—
14	C₄×C₂₁₁	—	16	1	no	—
15	C₄×C₂₁₁	D₁₆	1	1	yes	characteristic
16	C₂×C₂₁₁	D₃₂	1	1	yes	characteristic
17	D₂₁₁	—	32	1	no	—
18	C₂₁₁	SD₁₂₈	1	1	yes	characteristic, complemented, Sylow
19	SD₁₂₈	—	211	1	no	maximal, Sylow
20	Q₆₄	D₂₁₁	1	1	yes	characteristic, complemented
21	D₃₂	—	211	1	no	—
22	C₆₄	—	211	1	no	—
23	Q₃₂	—	2	1	no	—
24	D₁₆	—	422	1	no	—
25	C₃₂	C₂×D₂₁₁	1	1	yes	characteristic
26	Q₁₆	—	4	1	no	—
27	D₈	—	844	1	no	—
28	C₁₆	C₂²⋊D₂₁₁	1	1	yes	characteristic
29	Q₈	—	8	1	no	—
30	D₄	—	1688	1	no	—
31	C₈	#16809947	1	1	yes	characteristic
32	C₂²	—	3376	1	no	—
33	C₄	—	16	1	no	—
34	C₄	#20269918	1	1	yes	characteristic
35	C₂	—	6752	1	no	—
36	C₂	#27212981	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.