Subgroups — #6380

Order 224.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂²⋊D₇	C₂	1	1	yes	maximal, characteristic
2	C₇×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²⋊Dic₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂³×C₇	C₂²	1	1	yes	characteristic
5	C₂²×D₇	C₄	1	1	yes	characteristic, complemented
6	C₂×C₄×C₇	—	2	1	no	—
7	C₂²⋊D₇	—	2	1	no	—
8	C₂²⋊D₇	—	2	1	no	—
9	C₂×Dic₇	—	2	1	no	—
10	C₂×Dic₇	C₄	1	1	yes	characteristic, complemented
11	#99	—	7	1	no	maximal, Sylow
12	C₂²×C₇	—	4	1	no	—
13	C₂²×C₇	C₂×C₄	1	1	yes	characteristic
14	C₂²×C₇	D₄	1	1	yes	characteristic
15	C₂²×C₇	D₄	1	1	yes	characteristic
16	C₂×D₇	—	2	1	no	—
17	C₂×D₇	—	4	1	no	—
18	C₄×C₇	—	4	1	no	—
19	Dic₇	—	2	1	no	—
20	Dic₇	—	4	1	no	—
21	C₂×D₄	—	7	1	no	—
22	C₂²⋊C₄	—	7	1	no	—
23	C₂²⋊C₄	D₇	1	1	yes	characteristic, complemented
24	C₂×C₇	—	2	1	no	—
25	C₂×C₇	—	2	1	no	—
26	C₂×C₇	—	2	1	no	—
27	C₂×C₇	C₂²⋊C₄	1	1	yes	characteristic
28	D₇	—	4	1	no	—
29	C₂³	—	7	1	no	—
30	C₂³	C₂×D₇	1	1	yes	characteristic
31	D₄	—	14	1	no	—
32	D₄	—	14	1	no	—
33	C₂×C₄	—	2	1	no	—
34	C₂×C₄	—	7	1	no	—
35	C₂×C₄	—	14	1	no	—
36	C₇	#99	1	1	yes	characteristic, complemented, Sylow
37	C₂²	—	4	1	no	—
38	C₂²	—	14	1	no	—
39	C₂²	—	28	1	no	—
40	C₂²	C₄×D₇	1	1	yes	characteristic
41	C₂²	D₂₈	1	1	yes	characteristic
42	C₂²	C₂²⋊D₇	1	1	yes	characteristic
43	C₄	—	4	1	no	—
44	C₄	—	14	1	no	—
45	C₄	—	28	1	no	—
46	C₂	—	2	1	no	—
47	C₂	—	2	1	no	—
48	C₂	—	2	1	no	—
49	C₂	—	28	1	no	—
50	C₂	(C₂×D₇)⋊C₄	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.