Subgroups — #89256

Order 448.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₇×C₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₇⋊C₁₆	C₂	1	2	yes	maximal
3	C₂×C₇×C₈	C₄	1	1	yes	characteristic
4	C₂×C₇×C₈	C₂²	1	1	yes	characteristic
5	C₄²×C₇	C₄	1	1	yes	characteristic
6	C₇⋊C₁₆	C₄	1	4	yes	complemented
7	#346	—	7	1	no	maximal, Sylow
8	C₂×C₄×C₇	C₈	1	2	yes	—
9	C₂×C₄×C₇	C₂×C₄	1	1	yes	characteristic
10	C₇×C₈	C₈	1	2	yes	—
11	C₇×C₈	C₂×C₄	1	2	yes	—
12	C₂×C₁₆	—	7	2	no	—
13	C₄×C₈	D₇	1	1	yes	characteristic
14	C₂²×C₇	C₂×C₈	1	1	yes	characteristic
15	C₄×C₇	—	2	2	no	—
16	C₄×C₇	C₄²	1	1	yes	characteristic
17	C₄×C₇	C₂×C₈	1	1	yes	characteristic
18	C₂×C₈	Dic₇	1	1	yes	characteristic
19	C₂×C₈	C₂×D₇	1	1	yes	characteristic
20	C₄²	Dic₇	1	1	yes	characteristic
21	C₁₆	—	7	4	no	—
22	C₂×C₇	C₄×C₈	1	1	yes	characteristic
23	C₂×C₇	M₃₂	1	2	yes	—
24	C₂×C₄	C₇⋊C₈	1	2	yes	—
25	C₂×C₄	C₂×Dic₇	1	1	yes	characteristic
26	C₈	C₇⋊C₈	1	2	yes	—
27	C₈	C₄×D₇	1	2	yes	—
28	C₇	#346	1	1	yes	characteristic, complemented, Sylow
29	C₂²	C₂×C₇⋊C₈	1	1	yes	characteristic
30	C₄	—	2	2	no	—
31	C₄	C₂×C₇⋊C₈	1	1	yes	characteristic
32	C₄	C₄×Dic₇	1	1	yes	characteristic
33	C₂	C₄×C₇⋊C₈	1	1	yes	characteristic
34	C₂	#6386	1	2	yes	—

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
6. C₇⋊C₁₆	C₄	semidirect
28. C₇	#346	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.