Subgroups — #41011602

Order 27008.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27212976	C₂	1	2	yes	maximal
2	C₂×C₃₂×C₂₁₁	C₂	1	1	yes	maximal, characteristic
3	#20269913	—	2	2	no	—
4	C₂×C₁₆×C₂₁₁	C₂²	1	1	yes	characteristic
5	C₃₂×C₂₁₁	C₄	1	2	yes	—
6	#16809946	—	4	2	no	—
7	C₂×C₈×C₂₁₁	D₄	1	1	yes	characteristic
8	C₁₆×C₂₁₁	C₂×C₄	1	1	yes	characteristic
9	C₁₆×C₂₁₁	Q₈	1	1	yes	characteristic
10	C₂₁₁⋊C₈	—	8	2	no	—
11	C₂×C₄×C₂₁₁	D₈	1	1	yes	characteristic
12	C₈×C₂₁₁	C₄⋊C₄	1	1	yes	characteristic
13	C₈×C₂₁₁	Q₁₆	1	1	yes	characteristic
14	C₂²×C₂₁₁	Q₃₂	1	1	yes	characteristic
15	C₄×C₂₁₁	#107	1	1	yes	characteristic
16	C₄×C₂₁₁	D₁₆	1	1	yes	characteristic
17	C₂×C₂₁₁	—	2	1	no	—
18	C₂×C₂₁₁	#366	1	1	yes	characteristic
19	C₂₁₁	#1425	1	1	yes	characteristic, complemented, Sylow
20	#1425	—	211	1	no	maximal, Sylow
21	C₂×C₃₂	D₂₁₁	1	1	yes	characteristic
22	#368	—	211	2	no	—
23	C₂×C₁₆	C₂×D₂₁₁	1	1	yes	characteristic
24	#108	—	422	2	no	—
25	C₃₂	Dic₂₁₁	1	2	yes	—
26	M₁₆	—	844	2	no	—
27	C₂×C₈	D₈₄₄	1	1	yes	characteristic
28	C₁₆	C₂×Dic₂₁₁	1	1	yes	characteristic
29	C₁₆	Dic₄₂₂	1	1	yes	characteristic
30	C₂×C₄	D₁₆₈₈	1	1	yes	characteristic
31	C₈	—	1688	2	no	—
32	C₈	C₄⋊Dic₂₁₁	1	1	yes	characteristic
33	C₈	Dic₈₄₄	1	1	yes	characteristic
34	C₂²	Dic₁₆₈₈	1	1	yes	characteristic
35	C₄	#20269911	1	1	yes	characteristic
36	C₄	D₃₃₇₆	1	1	yes	characteristic
37	C₂	—	2	1	no	—
38	C₂	#27212972	1	1	yes	characteristic

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

N	H ≅ G/N	type
19. C₂₁₁	#1425	semidirect

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