Subgroups — #27212967

Order 13504.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20269917	C₂	1	2	yes	maximal
2	C₄×C₈×C₂₁₁	C₂	1	1	yes	maximal, characteristic
3	C₂₁₁⋊C₁₆	—	2	2	no	—
4	C₂×C₈×C₂₁₁	C₄	1	1	yes	characteristic
5	C₂×C₈×C₂₁₁	C₂²	1	1	yes	characteristic
6	C₄²×C₂₁₁	C₄	1	1	yes	characteristic
7	C₂×C₄×C₂₁₁	—	2	1	no	—
8	C₂×C₄×C₂₁₁	C₂×C₄	1	1	yes	characteristic
9	C₈×C₂₁₁	C₈	1	2	yes	—
10	C₈×C₂₁₁	D₄	1	1	yes	characteristic
11	C₈×C₂₁₁	Q₈	1	1	yes	characteristic
12	C₂²×C₂₁₁	M₁₆	1	1	yes	characteristic
13	C₄×C₂₁₁	—	2	2	no	—
14	C₄×C₂₁₁	C₄⋊C₄	1	1	yes	characteristic
15	C₄×C₂₁₁	C₂×C₈	1	1	yes	characteristic
16	C₂×C₂₁₁	—	2	1	no	—
17	C₂×C₂₁₁	C₄⋊C₈	1	1	yes	characteristic
18	C₂₁₁	#364	1	1	yes	characteristic, complemented, Sylow
19	#364	—	211	1	no	maximal, Sylow
20	M₃₂	—	211	2	no	—
21	C₄×C₈	D₂₁₁	1	1	yes	characteristic
22	C₂×C₈	Dic₂₁₁	1	1	yes	characteristic
23	C₂×C₈	C₂×D₂₁₁	1	1	yes	characteristic
24	C₄²	Dic₂₁₁	1	1	yes	characteristic
25	C₁₆	—	422	2	no	—
26	C₂×C₄	—	2	1	no	—
27	C₂×C₄	C₂×Dic₂₁₁	1	1	yes	characteristic
28	C₈	C₂₁₁⋊C₈	1	2	yes	—
29	C₈	D₈₄₄	1	1	yes	characteristic
30	C₈	Dic₄₂₂	1	1	yes	characteristic
31	C₂²	#16809946	1	1	yes	characteristic
32	C₄	—	2	2	no	—
33	C₄	C₄⋊Dic₂₁₁	1	1	yes	characteristic
34	C₄	C₂×C₂₁₁⋊C₈	1	1	yes	characteristic
35	C₂	—	2	1	no	—
36	C₂	C₄⋊(C₂₁₁⋊C₈)	1	1	yes	characteristic

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

N	H ≅ G/N	type
18. C₂₁₁	#364	semidirect

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