Subgroups — #6554

Order 224.

146 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, complemented
2	Q₈×D₇	C₂	1	2	yes	maximal, complemented
3	#1159	C₂	1	6	yes	maximal, complemented
4	#1157	C₂	1	3	yes	maximal, complemented
5	C₂×Dic₁₄	C₂	1	3	yes	maximal, complemented
6	C₇×Q₈	C₂²	1	1	yes	characteristic
7	C₇×D₄	C₂²	1	3	yes	—
8	C₂×C₄×C₇	C₂²	1	3	yes	—
9	C₂²⋊D₇	C₂²	1	6	yes	—
10	C₂×Dic₇	C₂²	1	6	yes	—
11	D₂₈	C₂²	1	1	yes	characteristic
12	C₄×D₇	C₂²	1	6	yes	—
13	Dic₁₄	C₂²	1	3	yes	—
14	Dic₁₄	C₂²	1	6	yes	—
15	2₋¹⁺⁴	—	7	1	no	maximal, Sylow
16	C₂²×C₇	C₂³	1	3	yes	—
17	C₂×D₇	C₂³	1	2	yes	—
18	C₄×C₇	C₂³	1	1	yes	characteristic
19	C₄×C₇	C₂³	1	3	yes	—
20	Dic₇	C₂³	1	6	yes	—
21	#41	—	7	6	no	—
22	#41	—	7	3	no	—
23	#41	D₇	1	1	yes	characteristic, complemented
24	C₂×Q₈	—	7	2	no	—
25	C₂×Q₈	—	7	3	no	—
26	C₂×C₇	—	2	3	no	—
27	C₂×C₇	C₂⁴	1	1	yes	characteristic
28	D₇	—	2	2	no	—
29	Q₈	—	7	6	no	—
30	Q₈	—	7	3	no	—
31	Q₈	C₂×D₇	1	1	yes	characteristic
32	D₄	—	7	6	no	—
33	D₄	—	7	1	no	—
34	D₄	C₂×D₇	1	3	yes	—
35	C₂×C₄	—	7	6	no	—
36	C₂×C₄	—	7	6	no	—
37	C₂×C₄	C₂×D₇	1	3	yes	—
38	C₇	2₋¹⁺⁴	1	1	yes	characteristic, complemented, Sylow
39	C₂²	—	7	2	no	—
40	C₂²	C₂²×D₇	1	3	yes	—
41	C₄	—	7	6	no	—
42	C₄	C₂²×D₇	1	3	yes	—
43	C₄	C₂²×D₇	1	1	yes	characteristic
44	C₂	—	2	3	no	—
45	C₂	—	14	2	no	—
46	C₂	C₂³×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.