Subgroups — #6464

Order 224.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#1157	C₂	1	1	yes	maximal, characteristic
2	C₂×C₇×C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#1136	C₂	1	1	yes	maximal, characteristic, complemented
4	#1131	C₂	1	2	yes	maximal, complemented
5	C₈×D₇	C₂	1	2	yes	maximal, complemented
6	C₂×C₄×C₇	C₂²	1	1	yes	characteristic
7	C₂²⋊D₇	C₄	1	2	yes	—
8	D₂₈	C₄	1	1	yes	characteristic
9	C₄×D₇	C₂²	1	2	yes	—
10	Dic₁₄	C₄	1	1	yes	characteristic
11	C₇×C₈	C₂²	1	1	yes	characteristic
12	C₇×C₈	C₂²	1	1	yes	characteristic
13	C₇⋊C₈	C₂²	1	2	yes	—
14	#131	—	7	1	no	maximal, Sylow
15	C₂²×C₇	C₂×C₄	1	1	yes	characteristic
16	C₂×D₇	C₂×C₄	1	2	yes	—
17	C₄×C₇	C₂×C₄	1	1	yes	characteristic
18	C₄×C₇	C₂³	1	1	yes	characteristic
19	Dic₇	C₂×C₄	1	2	yes	—
20	#41	—	7	1	no	—
21	M₁₆	—	7	1	no	—
22	M₁₆	—	7	2	no	—
23	C₂×C₈	—	7	2	no	—
24	C₂×C₈	D₇	1	1	yes	characteristic, complemented
25	C₂×C₇	—	2	1	no	—
26	C₂×C₇	C₂²×C₄	1	1	yes	characteristic
27	D₇	—	2	2	no	—
28	Q₈	—	7	1	no	—
29	D₄	—	7	2	no	—
30	D₄	—	7	1	no	—
31	C₂×C₄	—	7	2	no	—
32	C₂×C₄	C₂×D₇	1	1	yes	characteristic
33	C₈	—	7	2	no	—
34	C₈	C₂×D₇	1	1	yes	characteristic
35	C₈	C₂×D₇	1	1	yes	characteristic
36	C₇	#131	1	1	yes	characteristic, complemented, Sylow
37	C₂²	—	7	2	no	—
38	C₂²	C₄×D₇	1	1	yes	characteristic
39	C₄	—	7	2	no	—
40	C₄	C₄×D₇	1	1	yes	characteristic
41	C₄	C₂²×D₇	1	1	yes	characteristic
42	C₂	—	2	1	no	—
43	C₂	—	14	2	no	—
44	C₂	C₂×C₄×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.