Subgroups — #6406

Order 224.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×D₄	C₂	1	1	yes	maximal, characteristic
2	C₄⋊Dic₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂³×C₇	—	2	1	no	—
5	C₇×D₄	—	2	1	no	—
6	C₇×D₄	C₄	1	2	yes	complemented
7	C₂×C₄×C₇	C₂²	1	1	yes	characteristic
8	C₂×Dic₇	—	2	1	no	—
9	C₇⋊C₈	—	2	1	no	—
10	#102	—	7	1	no	maximal, Sylow
11	C₂²×C₇	—	2	2	no	—
12	C₂²×C₇	—	4	1	no	—
13	C₂²×C₇	—	4	1	no	—
14	C₂²×C₇	D₄	1	1	yes	characteristic
15	C₄×C₇	C₂×C₄	1	1	yes	characteristic
16	C₄×C₇	D₄	1	1	yes	characteristic
17	Dic₇	—	4	1	no	—
18	C₂×D₄	D₇	1	1	yes	characteristic
19	C₂×C₈	—	7	1	no	—
20	C₄⋊C₄	—	7	1	no	—
21	C₂×C₇	—	4	2	no	—
22	C₂×C₇	C₂²⋊C₄	1	1	yes	characteristic
23	C₂×C₇	D₈	1	1	yes	characteristic
24	C₂×C₇	SD₁₆	1	1	yes	characteristic
25	C₂³	—	2	1	no	—
26	D₄	—	2	1	no	—
27	D₄	Dic₇	1	2	yes	complemented
28	C₂×C₄	—	14	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	—	2	2	no	—
33	C₂²	—	4	1	no	—
34	C₂²	—	4	1	no	—
35	C₂²	C₂²⋊D₇	1	1	yes	characteristic
36	C₄	—	28	1	no	—
37	C₄	C₂×Dic₇	1	1	yes	characteristic
38	C₄	C₂²⋊D₇	1	1	yes	characteristic
39	C₂	—	4	2	no	—
40	C₂	#1141	1	1	yes	characteristic
41	C₂	#1142	1	1	yes	characteristic
42	C₂	C₂²⋊Dic₇	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.