Subgroups — #6411

Order 224.

44 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	C₄×Dic₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#1136	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×Q₈	C₄	1	1	yes	characteristic, complemented
5	C₇×D₄	—	2	1	no	—
6	C₇×D₄	C₄	1	1	yes	characteristic, complemented
7	C₂×C₄×C₇	—	2	1	no	—
8	C₂×C₄×C₇	C₂²	1	1	yes	characteristic
9	C₂×Dic₇	—	2	1	no	—
10	C₇⋊C₈	—	2	1	no	—
11	#104	—	7	1	no	maximal, Sylow
12	C₂²×C₇	—	2	1	no	—
13	C₂²×C₇	D₄	1	1	yes	characteristic
14	C₄×C₇	—	2	1	no	—
15	C₄×C₇	C₂×C₄	1	1	yes	characteristic
16	C₄×C₇	D₄	1	1	yes	characteristic
17	Dic₇	—	2	2	no	—
18	#41	D₇	1	1	yes	characteristic
19	M₁₆	—	7	1	no	—
20	C₄²	—	7	1	no	—
21	C₂×C₇	—	2	1	no	—
22	C₂×C₇	—	4	1	no	—
23	C₂×C₇	C₂²⋊C₄	1	1	yes	characteristic
24	Q₈	Dic₇	1	1	yes	characteristic, complemented
25	D₄	—	2	1	no	—
26	D₄	Dic₇	1	1	yes	characteristic, complemented
27	C₂×C₄	—	2	1	no	—
28	C₂×C₄	—	14	1	no	—
29	C₂×C₄	C₂×D₇	1	1	yes	characteristic
30	C₈	—	14	1	no	—
31	C₇	#104	1	1	yes	characteristic, complemented, Sylow
32	C₂²	—	2	1	no	—
33	C₂²	C₂²⋊D₇	1	1	yes	characteristic
34	C₄	—	2	1	no	—
35	C₄	—	14	2	no	—
36	C₄	C₂×Dic₇	1	1	yes	characteristic
37	C₄	C₂²⋊D₇	1	1	yes	characteristic
38	C₂	—	2	1	no	—
39	C₂	—	4	1	no	—
40	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.