Subgroups — #41003696

Order 26944.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27212421	C₂	1	2	yes	maximal, complemented
2	#27212355	C₂	1	1	yes	maximal, characteristic
3	C₂×#16809897	—	2	2	no	—
4	C₂×D₁₆₈₄	C₄	1	1	yes	characteristic
5	#20269748	—	2	2	no	—
6	C₄×Dic₄₂₁	C₂²	1	1	yes	characteristic
7	C₂×Q₈×C₄₂₁	C₄	1	1	yes	characteristic
8	#16809897	—	2	4	no	—
9	C₂²×D₄₂₁	—	2	1	no	—
10	D₁₆₈₄	—	4	1	no	—
11	C₂×Dic₄₂₁	D₄	1	2	yes	—
12	Q₈×C₄₂₁	—	4	1	no	—
13	C₂×C₄×C₄₂₁	—	2	1	no	—
14	C₂×C₄×C₄₂₁	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₄₂₁	C₂²⋊C₄	1	1	yes	characteristic
16	C₂×D₄₂₁	—	4	1	no	—
17	C₂×D₄₂₁	—	4	2	no	—
18	C₄×C₄₂₁	—	2	1	no	—
19	C₄×C₄₂₁	—	4	1	no	—
20	Dic₄₂₁	—	2	2	no	—
21	C₂×C₄₂₁	#100	1	1	yes	characteristic
22	C₂×C₄₂₁	#104	1	2	yes	—
23	D₄₂₁	—	8	1	no	—
24	C₄₂₁	#329	1	1	yes	characteristic, complemented, Sylow
25	#329	—	421	1	no	maximal, Sylow
26	#124	—	421	1	no	—
27	#97	—	421	2	no	—
28	C₂×Q₈	#13132997	1	1	yes	characteristic
29	C₂×D₄	—	421	1	no	—
30	C₂×C₈	—	842	2	no	—
31	C₂²⋊C₄	—	842	2	no	—
32	C₄²	—	421	1	no	—
33	C₂³	—	842	1	no	—
34	Q₈	—	4	1	no	—
35	D₄	—	1684	1	no	—
36	C₂×C₄	—	2	1	no	—
37	C₂×C₄	—	421	2	no	—
38	C₂×C₄	C₂×#13132997	1	1	yes	characteristic
39	C₈	—	842	4	no	—
40	C₂²	—	1684	1	no	—
41	C₂²	—	1684	2	no	—
42	C₂²	C₂²⋊#13132997	1	1	yes	characteristic
43	C₄	—	2	1	no	—
44	C₄	—	4	1	no	—
45	C₄	—	842	2	no	—
46	C₂	—	3368	1	no	—
47	C₂	#27212426	1	1	yes	characteristic
48	C₂	#27212431	1	2	yes	—

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

N	H ≅ G/N	type
1. #27212421	C₂	semidirect
24. C₄₂₁	#329	semidirect

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