Subgroups — (C₂×D₇)⋊C₈ #6394

Order 224.

50 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	C₂²×D₇	C₄	1	1	yes	characteristic
5	C₂×C₄×C₇	C₂²	1	1	yes	characteristic
6	C₂×Dic₇	C₄	1	1	yes	characteristic
7	C₄×D₇	—	2	1	no	—
8	C₄×D₇	—	2	1	no	—
9	C₇×C₈	—	2	1	no	—
10	C₇⋊C₈	—	2	1	no	—
11	C₂²⋊C₈	—	7	1	no	maximal, Sylow
12	C₂²×C₇	C₂×C₄	1	1	yes	characteristic
13	C₂×D₇	—	2	1	no	—
14	C₂×D₇	—	2	1	no	—
15	C₂×D₇	C₈	1	2	yes	complemented
16	C₄×C₇	D₄	1	1	yes	characteristic
17	C₄×C₇	D₄	1	1	yes	characteristic
18	Dic₇	—	2	1	no	—
19	C₂²×C₄	—	7	1	no	—
20	C₂×C₈	—	7	1	no	—
21	C₂×C₈	D₇	1	1	yes	characteristic, complemented
22	C₂×C₇	C₂²⋊C₄	1	1	yes	characteristic
23	C₂×C₇	C₂×C₈	1	1	yes	characteristic
24	C₂×C₇	M₁₆	1	1	yes	characteristic
25	D₇	—	2	2	no	—
26	C₂³	—	7	1	no	—
27	C₂×C₄	—	7	1	no	—
28	C₂×C₄	—	14	1	no	—
29	C₂×C₄	—	14	1	no	—
30	C₂×C₄	C₂×D₇	1	1	yes	characteristic
31	C₈	—	2	1	no	—
32	C₈	—	14	1	no	—
33	C₇	C₂²⋊C₈	1	1	yes	characteristic, complemented, Sylow
34	C₂²	—	7	2	no	—
35	C₂²	—	14	1	no	—
36	C₂²	—	14	1	no	—
37	C₂²	C₄×D₇	1	1	yes	characteristic
38	C₄	—	14	1	no	—
39	C₄	D₂₈	1	1	yes	characteristic
40	C₄	C₂²⋊D₇	1	1	yes	characteristic
41	C₂	—	14	2	no	—
42	C₂	C₈×D₇	1	1	yes	characteristic
43	C₂	#1131	1	1	yes	characteristic
44	C₂	(C₂×D₇)⋊C₄	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.