Subgroups — #27212972

Order 13504.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20269911	C₂	1	2	yes	maximal
2	C₂×C₁₆×C₂₁₁	C₂	1	1	yes	maximal, characteristic
3	C₄⋊Dic₂₁₁	—	2	2	no	—
4	C₂×C₈×C₂₁₁	C₂²	1	1	yes	characteristic
5	C₁₆×C₂₁₁	C₄	1	2	yes	complemented
6	C₂×Dic₂₁₁	—	4	2	no	—
7	C₂×C₄×C₂₁₁	D₄	1	1	yes	characteristic
8	C₈×C₂₁₁	C₂×C₄	1	1	yes	characteristic
9	C₈×C₂₁₁	Q₈	1	1	yes	characteristic
10	C₂²×C₂₁₁	D₈	1	1	yes	characteristic
11	C₄×C₂₁₁	C₄⋊C₄	1	1	yes	characteristic
12	C₄×C₂₁₁	Q₁₆	1	1	yes	characteristic
13	Dic₂₁₁	—	8	2	no	—
14	C₂×C₂₁₁	#107	1	1	yes	characteristic
15	C₂×C₂₁₁	D₁₆	1	1	yes	characteristic
16	C₂×C₂₁₁	Q₃₂	1	1	yes	characteristic
17	C₂₁₁	#366	1	1	yes	characteristic, complemented, Sylow
18	#366	—	211	1	no	maximal, Sylow
19	C₂×C₁₆	D₂₁₁	1	1	yes	characteristic
20	#107	—	211	2	no	—
21	C₂×C₈	C₂×D₂₁₁	1	1	yes	characteristic
22	C₄⋊C₄	—	422	2	no	—
23	C₁₆	Dic₂₁₁	1	2	yes	complemented
24	C₂×C₄	—	844	2	no	—
25	C₂×C₄	D₈₄₄	1	1	yes	characteristic
26	C₈	C₂×Dic₂₁₁	1	1	yes	characteristic
27	C₈	Dic₄₂₂	1	1	yes	characteristic
28	C₂²	D₁₆₈₈	1	1	yes	characteristic
29	C₄	—	1688	2	no	—
30	C₄	C₄⋊Dic₂₁₁	1	1	yes	characteristic
31	C₄	Dic₈₄₄	1	1	yes	characteristic
32	C₂	#20269911	1	1	yes	characteristic
33	C₂	D₃₃₇₆	1	1	yes	characteristic
34	C₂	Dic₁₆₈₈	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.