Subgroups — #6383

Order 224.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₂₈	C₂	1	1	yes	maximal, characteristic
2	C₇×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×D₇	—	2	1	no	—
5	C₂×C₄×C₇	—	2	1	no	—
6	C₂×C₄×C₇	C₂²	1	1	yes	characteristic
7	D₂₈	—	2	1	no	—
8	D₂₈	C₄	1	2	yes	complemented
9	C₇⋊C₈	—	2	1	no	—
10	#102	—	7	1	no	maximal, Sylow
11	C₂²×C₇	D₄	1	1	yes	characteristic
12	C₂×D₇	—	2	2	no	—
13	C₂×D₇	—	4	1	no	—
14	C₂×D₇	—	4	1	no	—
15	C₄×C₇	—	4	1	no	—
16	C₄×C₇	C₂×C₄	1	1	yes	characteristic
17	C₄×C₇	D₄	1	1	yes	characteristic
18	C₂×D₄	—	7	1	no	—
19	C₂×C₈	—	7	1	no	—
20	C₄⋊C₄	D₇	1	1	yes	characteristic, complemented
21	C₂×C₇	C₂²⋊C₄	1	1	yes	characteristic
22	C₂×C₇	D₈	1	1	yes	characteristic
23	C₂×C₇	SD₁₆	1	1	yes	characteristic
24	D₇	—	4	2	no	—
25	C₂³	—	14	1	no	—
26	D₄	—	7	2	no	—
27	D₄	—	14	1	no	—
28	C₂×C₄	—	2	1	no	—
29	C₂×C₄	C₂×D₇	1	1	yes	characteristic
30	C₈	—	14	1	no	—
31	C₇	#102	1	1	yes	characteristic, complemented, Sylow
32	C₂²	—	14	2	no	—
33	C₂²	—	28	1	no	—
34	C₂²	—	28	1	no	—
35	C₂²	C₂²⋊D₇	1	1	yes	characteristic
36	C₄	—	4	1	no	—
37	C₄	C₄×D₇	1	1	yes	characteristic
38	C₄	D₂₈	1	1	yes	characteristic
39	C₂	—	28	2	no	—
40	C₂	(C₂×D₇)⋊C₄	1	1	yes	characteristic
41	C₂	#1141	1	1	yes	characteristic
42	C₂	#1143	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.