Subgroups — #89258

Order 448.

46 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	#6386	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	—	2	2	no	—
7	#364	—	7	1	no	maximal, Sylow
8	C₂×C₄×C₇	—	2	1	no	—
9	C₂×C₄×C₇	C₂×C₄	1	1	yes	characteristic
10	C₇×C₈	C₈	1	2	yes	—
11	C₇×C₈	D₄	1	1	yes	characteristic
12	C₇×C₈	Q₈	1	1	yes	characteristic
13	M₃₂	—	7	2	no	—
14	C₄×C₈	D₇	1	1	yes	characteristic
15	C₂²×C₇	M₁₆	1	1	yes	characteristic
16	C₄×C₇	—	2	2	no	—
17	C₄×C₇	C₄⋊C₄	1	1	yes	characteristic
18	C₄×C₇	C₂×C₈	1	1	yes	characteristic
19	C₂×C₈	Dic₇	1	1	yes	characteristic
20	C₂×C₈	C₂×D₇	1	1	yes	characteristic
21	C₄²	Dic₇	1	1	yes	characteristic
22	C₁₆	—	14	2	no	—
23	C₂×C₇	—	2	1	no	—
24	C₂×C₇	C₄⋊C₈	1	1	yes	characteristic
25	C₂×C₄	—	2	1	no	—
26	C₂×C₄	C₂×Dic₇	1	1	yes	characteristic
27	C₈	C₇⋊C₈	1	2	yes	—
28	C₈	Dic₁₄	1	1	yes	characteristic
29	C₈	D₂₈	1	1	yes	characteristic
30	C₇	#364	1	1	yes	characteristic, complemented, Sylow
31	C₂²	#1136	1	1	yes	characteristic
32	C₄	—	2	2	no	—
33	C₄	C₂×C₇⋊C₈	1	1	yes	characteristic
34	C₄	C₄⋊Dic₇	1	1	yes	characteristic
35	C₂	—	2	1	no	—
36	C₂	C₄⋊(C₇⋊C₈)	1	1	yes	characteristic

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

N	H ≅ G/N	type
30. C₇	#364	semidirect

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