Subgroups — #27212968

Order 13504.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20269917	C₂	1	1	yes	maximal, characteristic
2	#20269913	C₂	1	1	yes	maximal, characteristic
3	#106×C₂₁₁	C₂	1	1	yes	maximal, characteristic
4	#16809946	—	2	1	no	—
5	C₂₁₁⋊C₁₆	C₄	1	2	yes	complemented
6	C₂×C₈×C₂₁₁	C₂²	1	1	yes	characteristic
7	C₄⋊C₄×C₂₁₁	—	2	1	no	—
8	C₂₁₁⋊C₈	—	4	1	no	—
9	C₂×C₄×C₂₁₁	—	4	1	no	—
10	C₂×C₄×C₂₁₁	D₄	1	1	yes	characteristic
11	C₈×C₂₁₁	C₂×C₄	1	1	yes	characteristic
12	C₈×C₂₁₁	Q₈	1	1	yes	characteristic
13	C₂²×C₂₁₁	SD₁₆	1	1	yes	characteristic
14	C₄×C₂₁₁	—	8	1	no	—
15	C₄×C₂₁₁	C₄⋊C₄	1	1	yes	characteristic
16	C₄×C₂₁₁	SD₁₆	1	1	yes	characteristic
17	C₂×C₂₁₁	—	2	1	no	—
18	C₂×C₂₁₁	#106	1	1	yes	characteristic
19	C₂₁₁	#365	1	1	yes	characteristic, complemented, Sylow
20	#365	—	211	1	no	maximal, Sylow
21	M₃₂	—	211	1	no	—
22	#108	—	211	1	no	—
23	#106	D₂₁₁	1	1	yes	characteristic
24	M₁₆	—	422	1	no	—
25	C₂×C₈	C₂×D₂₁₁	1	1	yes	characteristic
26	C₄⋊C₄	—	2	1	no	—
27	C₁₆	—	211	2	no	—
28	C₂×C₄	—	4	1	no	—
29	C₂×C₄	C₂²⋊D₂₁₁	1	1	yes	characteristic
30	C₈	—	844	1	no	—
31	C₈	C₄×D₂₁₁	1	1	yes	characteristic
32	C₈	Dic₄₂₂	1	1	yes	characteristic
33	C₂²	#16809950	1	1	yes	characteristic
34	C₄	—	8	1	no	—
35	C₄	Dic₂₁₁⋊C₄	1	1	yes	characteristic
36	C₄	#16809949	1	1	yes	characteristic
37	C₂	—	2	1	no	—
38	C₂	#20269908	1	1	yes	characteristic

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

N	H ≅ G/N	type
5. C₂₁₁⋊C₁₆	C₄	semidirect
19. C₂₁₁	#365	semidirect

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