Subgroups — C₂×C₂²⋊D₇ #1163

Order 112.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×D₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²⋊D₇	C₂	1	4	yes	maximal, direct product factor
4	C₂×Dic₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₇	—	2	2	no	—
6	C₂²×C₇	C₂²	1	1	yes	characteristic
7	C₂²×C₇	C₂²	1	2	yes	complemented
8	C₂×D₇	—	2	2	no	—
9	C₂×D₇	C₂²	1	2	yes	complemented
10	Dic₇	C₂²	1	2	yes	complemented
11	C₂×D₄	—	7	1	no	maximal, Sylow
12	C₂×C₇	—	2	2	no	—
13	C₂×C₇	D₄	1	2	yes	complemented
14	C₂×C₇	C₂³	1	1	yes	characteristic
15	D₇	—	2	2	no	—
16	C₂³	—	7	1	no	—
17	C₂³	D₇	1	1	yes	characteristic, complemented
18	D₄	—	7	4	no	—
19	C₂×C₄	—	7	1	no	—
20	C₇	C₂×D₄	1	1	yes	characteristic, complemented, Sylow
21	C₂²	—	2	2	no	—
22	C₂²	—	7	2	no	—
23	C₂²	—	14	2	no	—
24	C₂²	C₂×D₇	1	1	yes	characteristic
25	C₂²	C₂×D₇	1	2	yes	complemented
26	C₄	—	7	2	no	—
27	C₂	—	2	2	no	—
28	C₂	—	14	2	no	—
29	C₂	C₂²⋊D₇	1	2	yes	direct product factor
30	C₂	C₂²×D₇	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.