Subgroups — C₂×C₂²⋊Dic₇ #6515

Order 224.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₇	C₂	1	1	yes	maximal, characteristic
2	C₂²×Dic₇	C₂	1	2	yes	maximal, complemented
3	C₂²⋊Dic₇	C₂	1	4	yes	maximal, direct product factor
4	C₂³×C₇	—	2	4	no	—
5	C₂³×C₇	C₄	1	4	yes	complemented
6	C₂³×C₇	C₂²	1	2	yes	—
7	C₂³×C₇	C₂²	1	1	yes	characteristic
8	C₂×Dic₇	—	2	4	no	—
9	C₂×Dic₇	C₂²	1	4	yes	complemented
10	C₂×C₂²⋊C₄	—	7	1	no	maximal, Sylow
11	C₂²×C₇	—	2	8	no	—
12	C₂²×C₇	—	2	4	no	—
13	C₂²×C₇	C₂×C₄	1	2	yes	—
14	C₂²×C₇	C₂×C₄	1	4	yes	complemented
15	C₂²×C₇	D₄	1	4	yes	—
16	C₂²×C₇	C₂³	1	1	yes	characteristic
17	Dic₇	—	2	4	no	—
18	C₂⁴	D₇	1	1	yes	characteristic
19	C₂²×C₄	—	7	2	no	—
20	C₂²⋊C₄	—	7	4	no	—
21	C₂×C₇	—	2	4	no	—
22	C₂×C₇	C₂²⋊C₄	1	4	yes	complemented
23	C₂×C₇	C₂²×C₄	1	1	yes	characteristic
24	C₂×C₇	C₂×D₄	1	2	yes	—
25	C₂³	—	2	4	no	—
26	C₂³	Dic₇	1	4	yes	complemented
27	C₂³	C₂×D₇	1	2	yes	—
28	C₂³	C₂×D₇	1	1	yes	characteristic
29	C₂×C₄	—	7	4	no	—
30	C₂×C₄	—	14	4	no	—
31	C₇	C₂×C₂²⋊C₄	1	1	yes	characteristic, complemented, Sylow
32	C₂²	—	2	8	no	—
33	C₂²	—	2	4	no	—
34	C₂²	C₂×Dic₇	1	2	yes	—
35	C₂²	C₂×Dic₇	1	4	yes	complemented
36	C₂²	C₂²⋊D₇	1	4	yes	—
37	C₂²	C₂²×D₇	1	1	yes	characteristic
38	C₄	—	14	4	no	—
39	C₂	—	2	4	no	—
40	C₂	C₂²⋊Dic₇	1	4	yes	direct product factor
41	C₂	C₂²×Dic₇	1	1	yes	characteristic
42	C₂	C₂×C₂²⋊D₇	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.