Subgroups — #6514

Order 224.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#41	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₁₄	C₂	1	1	yes	maximal, characteristic, complemented
3	#1144	C₂	1	2	yes	maximal, complemented
4	#1142	C₂	1	2	yes	maximal, complemented
5	#1136	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×Q₈	C₂²	1	1	yes	characteristic
7	C₇×D₄	—	2	1	no	—
8	C₇×D₄	C₂²	1	1	yes	characteristic
9	C₂×C₄×C₇	—	2	1	no	—
10	C₂×C₄×C₇	C₂²	1	1	yes	characteristic
11	C₂×Dic₇	—	2	1	no	—
12	Dic₁₄	—	2	1	no	—
13	Dic₁₄	C₂²	1	2	yes	—
14	C₇⋊C₈	C₂²	1	2	yes	—
15	#137	—	7	1	no	maximal, Sylow
16	C₂²×C₇	—	2	1	no	—
17	C₂²×C₇	D₄	1	1	yes	characteristic
18	C₄×C₇	—	2	1	no	—
19	C₄×C₇	D₄	1	1	yes	characteristic
20	C₄×C₇	C₂³	1	1	yes	characteristic
21	Dic₇	—	2	2	no	—
22	#41	D₇	1	1	yes	characteristic
23	C₂×Q₈	—	7	1	no	—
24	Q₁₆	—	7	2	no	—
25	SD₁₆	—	7	2	no	—
26	M₁₆	—	7	1	no	—
27	C₂×C₇	—	2	1	no	—
28	C₂×C₇	—	4	1	no	—
29	C₂×C₇	C₂×D₄	1	1	yes	characteristic
30	Q₈	—	7	2	no	—
31	Q₈	—	14	1	no	—
32	Q₈	C₂×D₇	1	1	yes	characteristic
33	D₄	—	2	1	no	—
34	D₄	C₂×D₇	1	1	yes	characteristic
35	C₂×C₄	—	2	1	no	—
36	C₂×C₄	—	14	1	no	—
37	C₂×C₄	C₂×D₇	1	1	yes	characteristic
38	C₈	—	7	2	no	—
39	C₇	#137	1	1	yes	characteristic, complemented, Sylow
40	C₂²	—	2	1	no	—
41	C₂²	C₂²⋊D₇	1	1	yes	characteristic
42	C₄	—	2	1	no	—
43	C₄	—	14	2	no	—
44	C₄	C₂²⋊D₇	1	1	yes	characteristic
45	C₄	C₂²×D₇	1	1	yes	characteristic
46	C₂	—	2	1	no	—
47	C₂	—	4	1	no	—
48	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.