Subgroups — #89306

Order 448.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×M₃₂	C₂	1	1	yes	maximal, characteristic
2	C₈×Dic₇	C₂	1	1	yes	maximal, characteristic
3	#6386	C₂	1	1	yes	maximal, characteristic
4	C₂×C₇×C₈	C₂²	1	1	yes	characteristic
5	C₄×Dic₇	C₄	1	1	yes	characteristic
6	C₂×C₇⋊C₈	C₄	1	1	yes	characteristic
7	C₇×C₁₆	—	2	1	no	—
8	C₇⋊C₁₆	—	2	1	no	—
9	#364	—	7	1	no	maximal, Sylow
10	C₂×C₄×C₇	C₂×C₄	1	1	yes	characteristic
11	C₂×Dic₇	—	2	1	no	—
12	C₇×C₈	D₄	1	1	yes	characteristic
13	C₇×C₈	Q₈	1	1	yes	characteristic
14	C₇⋊C₈	C₈	1	2	yes	—
15	M₃₂	—	7	1	no	—
16	M₃₂	D₇	1	1	yes	characteristic
17	C₄×C₈	—	7	1	no	—
18	C₂²×C₇	M₁₆	1	1	yes	characteristic
19	C₄×C₇	C₄⋊C₄	1	1	yes	characteristic
20	C₄×C₇	C₂×C₈	1	1	yes	characteristic
21	Dic₇	—	2	2	no	—
22	C₂×C₈	—	7	1	no	—
23	C₂×C₈	C₂×D₇	1	1	yes	characteristic
24	C₄²	—	7	1	no	—
25	C₁₆	—	2	1	no	—
26	C₁₆	—	14	1	no	—
27	C₂×C₇	—	2	1	no	—
28	C₂×C₇	C₄⋊C₈	1	1	yes	characteristic
29	C₂×C₄	—	14	1	no	—
30	C₂×C₄	C₄×D₇	1	1	yes	characteristic
31	C₈	—	7	2	no	—
32	C₈	Dic₁₄	1	1	yes	characteristic
33	C₈	C₂²⋊D₇	1	1	yes	characteristic
34	C₇	#364	1	1	yes	characteristic, complemented, Sylow
35	C₂²	#1131	1	1	yes	characteristic
36	C₄	—	14	2	no	—
37	C₄	C₈×D₇	1	1	yes	characteristic
38	C₄	Dic₇⋊C₄	1	1	yes	characteristic
39	C₂	—	2	1	no	—
40	C₂	Dic₇⋊C₈	1	1	yes	characteristic

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

N	H ≅ G/N	type
34. C₇	#364	semidirect

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