Subgroups — #6510

Order 224.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₂₈	C₂	1	1	yes	maximal, characteristic
3	(C₂×D₇)⋊C₄	C₂	1	4	yes	maximal, complemented
4	C₄×Dic₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×D₇	C₂²	1	2	yes	—
6	C₇×Q₈	—	2	2	no	—
7	C₂×C₄×C₇	C₂²	1	2	yes	—
8	C₂×C₄×C₇	C₂²	1	1	yes	characteristic
9	C₂×Dic₇	C₂²	1	2	yes	—
10	D₂₈	—	2	2	no	—
11	#124	—	7	1	no	maximal, Sylow
12	C₂²×C₇	C₂³	1	1	yes	characteristic
13	C₂×D₇	—	2	2	no	—
14	C₂×D₇	—	2	4	no	—
15	C₄×C₇	—	2	2	no	—
16	C₄×C₇	D₄	1	2	yes	—
17	Dic₇	—	2	2	no	—
18	C₂×Q₈	D₇	1	1	yes	characteristic, complemented
19	C₂×D₄	—	7	1	no	—
20	C₂²⋊C₄	—	7	4	no	—
21	C₄²	—	7	1	no	—
22	C₂×C₇	C₂×D₄	1	1	yes	characteristic
23	C₂×C₇	#41	1	2	yes	—
24	D₇	—	4	2	no	—
25	C₂³	—	7	2	no	—
26	Q₈	—	2	2	no	—
27	D₄	—	14	2	no	—
28	C₂×C₄	—	7	2	no	—
29	C₂×C₄	C₂×D₇	1	2	yes	—
30	C₂×C₄	C₂×D₇	1	1	yes	characteristic
31	C₇	#124	1	1	yes	characteristic, complemented, Sylow
32	C₂²	—	14	4	no	—
33	C₂²	—	14	2	no	—
34	C₂²	C₂²×D₇	1	1	yes	characteristic
35	C₄	—	2	2	no	—
36	C₄	—	14	2	no	—
37	C₄	C₂²⋊D₇	1	2	yes	—
38	C₂	—	28	2	no	—
39	C₂	#1161	1	2	yes	—
40	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.