Subgroups — #41003220

Order 26944.

122 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₆₈₄	C₂	1	4	yes	maximal
2	#27212366	C₂	1	2	yes	maximal
3	C₄×C₈×C₄₂₁	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₈₄₂	C₂²	1	4	yes	—
5	Dic₁₆₈₄	—	2	8	no	—
6	C₄⋊Dic₄₂₁	—	2	4	no	—
7	C₂×C₈×C₄₂₁	C₂²	1	2	yes	—
8	C₄²×C₄₂₁	C₂²	1	1	yes	characteristic
9	Dic₈₄₂	—	2	8	no	—
10	C₂×Dic₄₂₁	—	2	4	no	—
11	C₂×C₄×C₄₂₁	D₄	1	2	yes	—
12	C₂×C₄×C₄₂₁	C₂³	1	1	yes	characteristic
13	C₈×C₄₂₁	D₄	1	4	yes	—
14	C₂²×C₄₂₁	C₂×D₄	1	1	yes	characteristic
15	C₄×C₄₂₁	Q₁₆	1	4	yes	complemented
16	C₄×C₄₂₁	C₂×D₄	1	2	yes	—
17	Dic₄₂₁	—	4	4	no	—
18	C₂×C₄₂₁	#127	1	1	yes	characteristic
19	C₂×C₄₂₁	C₂×Q₁₆	1	2	yes	—
20	C₄₂₁	#494	1	1	yes	characteristic, complemented, Sylow
21	#494	—	421	1	no	maximal, Sylow
22	C₂×Q₁₆	—	421	4	no	—
23	C₄⋊Q₈	—	421	2	no	—
24	C₄×C₈	D₄₂₁	1	1	yes	characteristic
25	C₂×Q₈	—	421	4	no	—
26	Q₁₆	—	842	8	no	—
27	C₂×C₈	C₂×D₄₂₁	1	2	yes	—
28	C₄⋊C₄	—	842	4	no	—
29	C₄²	C₂×D₄₂₁	1	1	yes	characteristic
30	Q₈	—	842	8	no	—
31	C₂×C₄	—	842	4	no	—
32	C₂×C₄	D₁₆₈₄	1	2	yes	—
33	C₂×C₄	C₂²×D₄₂₁	1	1	yes	characteristic
34	C₈	D₁₆₈₄	1	4	yes	—
35	C₂²	C₂×D₁₆₈₄	1	1	yes	characteristic
36	C₄	—	1684	4	no	—
37	C₄	Dic₁₆₈₄	1	4	yes	complemented
38	C₄	C₂×D₁₆₈₄	1	2	yes	—
39	C₂	#27212363	1	1	yes	characteristic
40	C₂	C₂×Dic₁₆₈₄	1	2	yes	—

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.