Subgroups — #6397

Order 224.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₂₈	C₂	1	1	yes	maximal, characteristic
2	C₇×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	#1136	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×D₇	C₄	1	2	yes	—
5	C₂×C₄×C₇	C₂²	1	1	yes	characteristic
6	D₂₈	—	2	1	no	—
7	D₂₈	—	2	1	no	—
8	C₇×C₈	—	2	1	no	—
9	C₇⋊C₈	—	2	1	no	—
10	#100	—	7	1	no	maximal, Sylow
11	C₂²×C₇	C₂×C₄	1	1	yes	characteristic
12	C₂×D₇	—	2	2	no	—
13	C₂×D₇	—	4	2	no	—
14	C₄×C₇	D₄	1	1	yes	characteristic
15	C₄×C₇	D₄	1	1	yes	characteristic
16	C₂×D₄	—	7	1	no	—
17	M₁₆	—	7	1	no	—
18	M₁₆	D₇	1	1	yes	characteristic, complemented
19	C₂×C₇	—	2	1	no	—
20	C₂×C₇	C₂²⋊C₄	1	1	yes	characteristic
21	D₇	—	4	2	no	—
22	C₂³	—	7	2	no	—
23	D₄	—	14	1	no	—
24	D₄	—	14	1	no	—
25	C₂×C₄	C₂×D₇	1	1	yes	characteristic
26	C₈	—	2	1	no	—
27	C₈	—	14	1	no	—
28	C₇	#100	1	1	yes	characteristic, complemented, Sylow
29	C₂²	—	14	2	no	—
30	C₂²	—	28	2	no	—
31	C₂²	C₄×D₇	1	1	yes	characteristic
32	C₄	D₂₈	1	1	yes	characteristic
33	C₄	C₂²⋊D₇	1	1	yes	characteristic
34	C₂	—	2	1	no	—
35	C₂	—	28	2	no	—
36	C₂	(C₂×D₇)⋊C₄	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.