Subgroups — #6503

Order 224.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×D₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂²⋊D₇	C₂	1	4	yes	maximal, complemented
3	C₂×D₂₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×Dic₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂³×C₇	C₂²	1	2	yes	—
6	C₂²×D₇	C₂²	1	2	yes	—
7	C₇×D₄	—	2	2	no	—
8	C₂×C₄×C₇	C₂²	1	1	yes	characteristic
9	C₂²⋊D₇	—	2	8	no	—
10	C₂×Dic₇	C₂²	1	2	yes	—
11	D₂₈	—	2	2	no	—
12	#127	—	7	1	no	maximal, Sylow
13	C₂²×C₇	—	2	4	no	—
14	C₂²×C₇	—	2	2	no	—
15	C₂²×C₇	C₂³	1	1	yes	characteristic
16	C₂×D₇	—	2	2	no	—
17	C₂×D₇	—	2	4	no	—
18	C₄×C₇	D₄	1	2	yes	complemented
19	Dic₇	D₄	1	4	yes	complemented
20	C₂×D₄	—	7	4	no	—
21	C₂×D₄	—	7	1	no	—
22	C₂×D₄	D₇	1	1	yes	characteristic, complemented
23	C₄²	—	7	1	no	—
24	C₂×C₇	—	4	2	no	—
25	C₂×C₇	C₂×D₄	1	2	yes	—
26	C₂×C₇	C₂×D₄	1	1	yes	characteristic
27	D₇	—	4	2	no	—
28	C₂³	—	7	2	no	—
29	C₂³	C₂×D₇	1	2	yes	—
30	D₄	—	2	2	no	—
31	D₄	—	14	8	no	—
32	D₄	—	14	2	no	—
33	C₂×C₄	—	7	2	no	—
34	C₂×C₄	C₂×D₇	1	1	yes	characteristic
35	C₇	#127	1	1	yes	characteristic, complemented, Sylow
36	C₂²	—	2	4	no	—
37	C₂²	—	2	2	no	—
38	C₂²	—	14	4	no	—
39	C₂²	—	14	2	no	—
40	C₂²	C₂²×D₇	1	1	yes	characteristic
41	C₄	—	7	4	no	—
42	C₄	C₂²⋊D₇	1	2	yes	complemented
43	C₂	—	4	2	no	—
44	C₂	—	28	2	no	—
45	C₂	D₄×D₇	1	2	yes	—
46	C₂	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.