Subgroups — #1159

Order 112.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×D₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²⋊D₇	C₂	1	2	yes	maximal, complemented
3	C₂×Dic₇	C₂	1	2	yes	maximal, complemented
4	C₄×D₇	C₂	1	1	yes	maximal, characteristic, complemented
5	Dic₁₄	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₇	C₂²	1	2	yes	—
7	C₂×D₇	C₂²	1	1	yes	characteristic
8	C₄×C₇	C₂²	1	1	yes	characteristic
9	Dic₇	C₂²	1	2	yes	—
10	Dic₇	C₂²	1	1	yes	characteristic
11	#41	—	7	1	no	maximal, Sylow
12	C₂×C₇	—	2	2	no	—
13	C₂×C₇	C₂³	1	1	yes	characteristic
14	D₇	—	2	1	no	—
15	Q₈	—	7	1	no	—
16	D₄	—	7	2	no	—
17	D₄	D₇	1	1	yes	characteristic, complemented
18	C₂×C₄	—	7	2	no	—
19	C₂×C₄	—	7	1	no	—
20	C₇	#41	1	1	yes	characteristic, complemented, Sylow
21	C₂²	—	7	1	no	—
22	C₂²	C₂×D₇	1	2	yes	—
23	C₄	—	7	1	no	—
24	C₄	—	7	2	no	—
25	C₄	C₂×D₇	1	1	yes	characteristic
26	C₂	—	2	2	no	—
27	C₂	—	14	1	no	—
28	C₂	C₂²×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.