Subgroups — #6553

Order 224.

166 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	#1161	C₂	1	2	yes	maximal, complemented
3	D₄×D₇	C₂	1	6	yes	maximal, complemented
4	#1157	C₂	1	3	yes	maximal, complemented
5	C₂×D₂₈	C₂	1	3	yes	maximal, complemented
6	C₂²×D₇	C₂²	1	6	yes	complemented
7	C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
8	C₇×D₄	C₂²	1	3	yes	complemented
9	C₂×C₄×C₇	C₂²	1	3	yes	complemented
10	C₂²⋊D₇	C₂²	1	6	yes	complemented
11	D₂₈	C₂²	1	3	yes	complemented
12	D₂₈	C₂²	1	6	yes	complemented
13	C₄×D₇	C₂²	1	6	yes	complemented
14	Dic₁₄	C₂²	1	1	yes	characteristic, complemented
15	H(5,𝔽₂)	—	7	1	no	maximal, Sylow
16	C₂²×C₇	C₂³	1	3	yes	—
17	C₂×D₇	—	4	6	no	—
18	C₂×D₇	C₂³	1	6	yes	—
19	C₄×C₇	C₂³	1	1	yes	characteristic
20	C₄×C₇	C₂³	1	3	yes	—
21	Dic₇	C₂³	1	2	yes	—
22	#41	—	7	2	no	—
23	#41	—	7	3	no	—
24	#41	D₇	1	1	yes	characteristic, complemented
25	C₂×D₄	—	7	6	no	—
26	C₂×D₄	—	7	3	no	—
27	C₂×C₇	—	2	3	no	—
28	C₂×C₇	C₂⁴	1	1	yes	characteristic
29	D₇	—	2	6	no	—
30	C₂³	—	7	6	no	—
31	Q₈	—	7	1	no	—
32	Q₈	C₂×D₇	1	1	yes	characteristic, complemented
33	D₄	—	7	6	no	—
34	D₄	—	7	6	no	—
35	D₄	—	7	3	no	—
36	D₄	C₂×D₇	1	3	yes	complemented
37	C₂×C₄	—	7	6	no	—
38	C₂×C₄	C₂×D₇	1	3	yes	complemented
39	C₇	H(5,𝔽₂)	1	1	yes	characteristic, complemented, Sylow
40	C₂²	—	7	6	no	—
41	C₂²	—	28	6	no	—
42	C₂²	C₂²×D₇	1	3	yes	—
43	C₄	—	7	2	no	—
44	C₄	C₂²×D₇	1	3	yes	—
45	C₄	C₂²×D₇	1	1	yes	characteristic
46	C₂	—	2	3	no	—
47	C₂	—	14	6	no	—
48	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.