Subgroups — #41011615

Order 27008.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₃₃₇₆	C₂	1	1	yes	maximal, characteristic
2	C₂₁₁⋊C₆₄	C₂	1	1	yes	maximal, characteristic
3	Q₆₄×C₂₁₁	C₂	1	1	yes	maximal, characteristic
4	Dic₁₆₈₈	—	2	1	no	—
5	Q₃₂×C₂₁₁	—	2	1	no	—
6	C₃₂×C₂₁₁	C₂²	1	1	yes	characteristic
7	Dic₈₄₄	—	4	1	no	—
8	Q₁₆×C₂₁₁	—	4	1	no	—
9	C₁₆×C₂₁₁	D₄	1	1	yes	characteristic
10	Dic₄₂₂	—	8	1	no	—
11	Q₈×C₂₁₁	—	8	1	no	—
12	C₈×C₂₁₁	D₈	1	1	yes	characteristic
13	C₄×C₂₁₁	—	16	1	no	—
14	C₄×C₂₁₁	D₁₆	1	1	yes	characteristic
15	Dic₂₁₁	—	16	1	no	—
16	C₂×C₂₁₁	D₃₂	1	1	yes	characteristic
17	C₂₁₁	Q₁₂₈	1	1	yes	characteristic, complemented, Sylow
18	Q₁₂₈	—	211	1	no	maximal, Sylow
19	Q₆₄	—	211	1	no	—
20	Q₆₄	D₂₁₁	1	1	yes	characteristic
21	C₆₄	—	211	1	no	—
22	Q₃₂	—	2	1	no	—
23	Q₃₂	—	422	1	no	—
24	C₃₂	C₂×D₂₁₁	1	1	yes	characteristic
25	Q₁₆	—	4	1	no	—
26	Q₁₆	—	844	1	no	—
27	C₁₆	C₂²⋊D₂₁₁	1	1	yes	characteristic
28	Q₈	—	8	1	no	—
29	Q₈	—	1688	1	no	—
30	C₈	#16809947	1	1	yes	characteristic
31	C₄	—	16	1	no	—
32	C₄	—	3376	1	no	—
33	C₄	#20269918	1	1	yes	characteristic
34	C₂	#27212981	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
17. C₂₁₁	Q₁₂₈	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.