Subgroups — #6475

Order 224.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#1159	C₂	1	2	yes	maximal, complemented
2	C₇×D₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#1142	C₂	1	2	yes	maximal, complemented
4	Dic₂₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈×D₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×D₄	C₂²	1	2	yes	—
7	C₂²⋊D₇	—	2	2	no	—
8	C₂×Dic₇	—	2	2	no	—
9	C₄×D₇	C₂²	1	1	yes	characteristic
10	Dic₁₄	C₂²	1	2	yes	—
11	C₇×C₈	C₂²	1	1	yes	characteristic
12	C₇⋊C₈	C₂²	1	1	yes	characteristic
13	#135	—	7	1	no	maximal, Sylow
14	C₂²×C₇	—	2	2	no	—
15	C₂×D₇	D₄	1	1	yes	characteristic
16	C₄×C₇	C₂³	1	1	yes	characteristic
17	Dic₇	—	2	2	no	—
18	Dic₇	D₄	1	1	yes	characteristic
19	#41	—	7	2	no	—
20	Q₁₆	—	7	1	no	—
21	SD₁₆	—	7	2	no	—
22	D₈	D₇	1	1	yes	characteristic, complemented
23	C₂×C₈	—	7	1	no	—
24	C₂×C₇	—	4	2	no	—
25	C₂×C₇	C₂×D₄	1	1	yes	characteristic
26	D₇	—	2	1	no	—
27	Q₈	—	7	2	no	—
28	D₄	—	14	2	no	—
29	D₄	C₂×D₇	1	2	yes	—
30	C₂×C₄	—	7	1	no	—
31	C₂×C₄	—	14	2	no	—
32	C₈	—	7	1	no	—
33	C₈	C₂×D₇	1	1	yes	characteristic
34	C₇	#135	1	1	yes	characteristic, complemented, Sylow
35	C₂²	—	2	2	no	—
36	C₂²	—	7	1	no	—
37	C₄	—	7	1	no	—
38	C₄	—	14	2	no	—
39	C₄	C₂²×D₇	1	1	yes	characteristic
40	C₂	—	4	2	no	—
41	C₂	—	14	1	no	—
42	C₂	D₄×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.