Subgroups — C₂×#1131 #6463

Order 224.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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