Subgroups — #6551

Order 224.

146 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	#1161	C₂	1	4	yes	maximal, complemented
3	Q₈×D₇	C₂	1	4	yes	maximal, complemented
4	#1157	C₂	1	6	yes	maximal, complemented
5	C₇×Q₈	C₂²	1	4	yes	—
6	C₂×C₄×C₇	C₂²	1	3	yes	—
7	C₂²⋊D₇	C₂²	1	4	yes	—
8	D₂₈	C₂²	1	6	yes	—
9	C₄×D₇	C₂²	1	12	yes	—
10	Dic₁₄	C₂²	1	6	yes	—
11	2₋¹⁺⁴	—	7	1	no	maximal, Sylow
12	C₂²×C₇	C₂³	1	1	yes	characteristic
13	C₂×D₇	C₂³	1	4	yes	—
14	C₄×C₇	C₂³	1	6	yes	—
15	Dic₇	C₂³	1	4	yes	—
16	#41	—	7	4	no	—
17	#41	—	7	6	no	—
18	C₂×Q₈	—	7	4	no	—
19	C₂×Q₈	D₇	1	1	yes	characteristic, complemented
20	C₂×C₇	—	2	1	no	—
21	C₂×C₇	C₂⁴	1	1	yes	characteristic
22	D₇	—	2	4	no	—
23	Q₈	—	7	6	no	—
24	Q₈	C₂×D₇	1	4	yes	—
25	D₄	—	7	4	no	—
26	D₄	—	7	6	no	—
27	C₂×C₄	—	7	12	no	—
28	C₂×C₄	C₂×D₇	1	3	yes	—
29	C₇	2₋¹⁺⁴	1	1	yes	characteristic, complemented, Sylow
30	C₂²	—	7	4	no	—
31	C₂²	C₂²×D₇	1	1	yes	characteristic
32	C₄	—	7	4	no	—
33	C₄	C₂²×D₇	1	6	yes	—
34	C₂	—	2	1	no	—
35	C₂	—	14	4	no	—
36	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.