Subgroups — #89314

Order 448.

34 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×D₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	D₁₁₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇⋊C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×D₈	—	2	1	no	—
5	D₅₆	—	2	1	no	—
6	C₇×C₁₆	C₂²	1	1	yes	characteristic
7	D₃₂	—	7	1	no	maximal, Sylow
8	C₇×D₄	—	4	1	no	—
9	D₂₈	—	4	1	no	—
10	C₇×C₈	D₄	1	1	yes	characteristic
11	D₁₆	—	7	1	no	—
12	D₁₆	D₇	1	1	yes	characteristic, complemented
13	C₃₂	—	7	1	no	—
14	C₂²×C₇	—	8	1	no	—
15	C₂×D₇	—	8	1	no	—
16	C₄×C₇	D₈	1	1	yes	characteristic
17	D₈	—	2	1	no	—
18	D₈	—	14	1	no	—
19	C₁₆	C₂×D₇	1	1	yes	characteristic
20	C₂×C₇	—	16	1	no	—
21	C₂×C₇	D₁₆	1	1	yes	characteristic
22	D₇	—	16	1	no	—
23	D₄	—	4	1	no	—
24	D₄	—	28	1	no	—
25	C₈	C₂²⋊D₇	1	1	yes	characteristic
26	C₇	D₃₂	1	1	yes	characteristic, complemented, Sylow
27	C₂²	—	8	1	no	—
28	C₂²	—	56	1	no	—
29	C₄	#1141	1	1	yes	characteristic
30	C₂	—	16	1	no	—
31	C₂	—	112	1	no	—
32	C₂	#6400	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.