Subgroups — #89249

Order 448.

66 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	C₄×C₇⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₄×C₇⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₂×C₇×C₈	C₄	1	2	yes	—
5	C₄²×C₇	C₂²	1	1	yes	characteristic
6	C₂×C₇⋊C₈	C₄	1	2	yes	—
7	C₂×C₇⋊C₈	C₄	1	2	yes	—
8	#322	—	7	1	no	maximal, Sylow
9	C₂×C₄×C₇	C₂×C₄	1	1	yes	characteristic
10	C₂×C₄×C₇	C₂×C₄	1	1	yes	characteristic
11	C₂×C₄×C₇	C₂×C₄	1	1	yes	characteristic
12	C₇×C₈	—	2	2	no	—
13	C₇⋊C₈	—	2	2	no	—
14	C₇⋊C₈	C₈	1	4	yes	complemented
15	C₄×C₈	—	7	1	no	—
16	C₄×C₈	—	7	1	no	—
17	C₄×C₈	D₇	1	1	yes	characteristic
18	C₂²×C₇	C₄²	1	1	yes	characteristic
19	C₄×C₇	C₂×C₈	1	2	yes	—
20	C₄×C₇	M₁₆	1	2	yes	—
21	C₄×C₇	M₁₆	1	2	yes	—
22	C₂×C₈	—	7	2	no	—
23	C₂×C₈	—	7	2	no	—
24	C₂×C₈	Dic₇	1	2	yes	—
25	C₄²	C₂×D₇	1	1	yes	characteristic
26	C₂×C₇	C₄×C₈	1	1	yes	characteristic
27	C₂×C₇	#97	1	1	yes	characteristic
28	C₂×C₇	#97	1	1	yes	characteristic
29	C₂×C₄	C₄×D₇	1	1	yes	characteristic
30	C₂×C₄	C₄×D₇	1	1	yes	characteristic
31	C₂×C₄	C₂×Dic₇	1	1	yes	characteristic
32	C₈	—	2	2	no	—
33	C₈	—	7	4	no	—
34	C₈	—	14	2	no	—
35	C₇	#322	1	1	yes	characteristic, complemented, Sylow
36	C₂²	C₄×Dic₇	1	1	yes	characteristic
37	C₄	C₈×D₇	1	2	yes	—
38	C₄	#1131	1	2	yes	—
39	C₄	#1136	1	2	yes	—
40	C₂	#6377	1	1	yes	characteristic
41	C₂	C₈×Dic₇	1	1	yes	characteristic
42	C₂	#6389	1	1	yes	characteristic

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

N	H ≅ G/N	type
14. C₇⋊C₈	C₈	semidirect
35. C₇	#322	semidirect

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