Subgroups — C₂×C₄×Dic₇₆₁ #37566849

Order 24352.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₇₆₁	C₂	1	2	yes	maximal
2	C₄×Dic₇₆₁	C₂	1	4	yes	maximal, direct product factor
3	C₂²×C₄×C₇₆₁	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₇₆₁	C₄	1	8	yes	direct product factor
5	C₂×Dic₇₆₁	C₂²	1	4	yes	—
6	C₂³×C₇₆₁	C₂²	1	1	yes	characteristic
7	C₂×C₄×C₇₆₁	C₄	1	4	yes	complemented
8	C₂×C₄×C₇₆₁	C₂²	1	2	yes	—
9	C₂²×C₇₆₁	C₂×C₄	1	4	yes	—
10	C₂²×C₇₆₁	C₂×C₄	1	2	yes	—
11	C₂²×C₇₆₁	C₂³	1	1	yes	characteristic
12	C₄×C₇₆₁	C₂×C₄	1	4	yes	complemented
13	Dic₇₆₁	C₂×C₄	1	8	yes	direct product factor
14	C₂×C₇₆₁	C₄²	1	4	yes	complemented
15	C₂×C₇₆₁	C₂²×C₄	1	2	yes	—
16	C₂×C₇₆₁	C₂²×C₄	1	1	yes	characteristic
17	C₇₆₁	C₂×C₄²	1	1	yes	characteristic, complemented, Sylow
18	C₂×C₄²	—	761	1	no	maximal, Sylow
19	C₂²×C₄	—	761	2	no	—
20	C₂²×C₄	D₇₆₁	1	1	yes	characteristic
21	C₄²	—	761	4	no	—
22	C₂³	C₂×D₇₆₁	1	1	yes	characteristic
23	C₂×C₄	—	761	8	no	—
24	C₂×C₄	—	761	4	no	—
25	C₂×C₄	Dic₇₆₁	1	4	yes	direct product factor
26	C₂×C₄	C₂×D₇₆₁	1	2	yes	—
27	C₂²	C₄×D₇₆₁	1	4	yes	—
28	C₂²	C₂×Dic₇₆₁	1	2	yes	—
29	C₂²	C₂²×D₇₆₁	1	1	yes	characteristic
30	C₄	—	761	8	no	—
31	C₄	C₂×Dic₇₆₁	1	4	yes	direct product factor
32	C₂	C₄×Dic₇₆₁	1	4	yes	direct product factor
33	C₂	C₂×C₄×D₇₆₁	1	2	yes	—
34	C₂	C₂²×Dic₇₆₁	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.