Subgroups — #89475

Order 448.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#6433	C₂	1	1	yes	maximal, characteristic
2	#6432	C₂	1	1	yes	maximal, characteristic
3	C₇×#97	C₂	1	1	yes	maximal, characteristic
4	#6390	C₂	1	4	yes	maximal
5	C₂×Dic₁₄	C₂²	1	2	yes	—
6	C₂×C₇×C₈	C₂²	1	2	yes	—
7	C₄²×C₇	C₂²	1	1	yes	characteristic
8	C₄⋊Dic₇	—	2	2	no	—
9	C₄⋊Dic₇	C₂²	1	2	yes	—
10	Dic₇⋊C₄	—	2	2	no	—
11	#491	—	7	1	no	maximal, Sylow
12	C₂×C₄×C₇	D₄	1	2	yes	—
13	C₂×C₄×C₇	C₂³	1	1	yes	characteristic
14	C₂×Dic₇	—	2	2	no	—
15	C₂×Dic₇	—	2	2	no	—
16	Dic₁₄	—	2	4	no	—
17	C₇×C₈	—	2	2	no	—
18	C₄⋊Q₈	—	7	1	no	—
19	#125	—	7	1	no	—
20	#103	—	7	4	no	—
21	#97	D₇	1	1	yes	characteristic
22	C₂²×C₇	C₂×D₄	1	1	yes	characteristic
23	C₄×C₇	—	2	2	no	—
24	C₄×C₇	#41	1	2	yes	—
25	Dic₇	—	4	2	no	—
26	Dic₇	—	4	2	no	—
27	C₂×Q₈	—	7	2	no	—
28	C₂×C₈	C₂×D₇	1	2	yes	—
29	C₄⋊C₄	—	7	2	no	—
30	C₄⋊C₄	—	14	2	no	—
31	C₄⋊C₄	—	14	2	no	—
32	C₄²	C₂×D₇	1	1	yes	characteristic
33	C₂×C₇	#124	1	1	yes	characteristic
34	C₂×C₇	#137	1	2	yes	—
35	Q₈	—	14	4	no	—
36	C₂×C₄	—	14	2	no	—
37	C₂×C₄	—	14	2	no	—
38	C₂×C₄	D₂₈	1	2	yes	—
39	C₂×C₄	C₂²×D₇	1	1	yes	characteristic
40	C₈	—	2	2	no	—
41	C₇	#491	1	1	yes	characteristic, complemented, Sylow
42	C₂²	C₂×D₂₈	1	1	yes	characteristic
43	C₄	—	2	2	no	—
44	C₄	—	28	2	no	—
45	C₄	—	28	2	no	—
46	C₄	#1157	1	2	yes	—
47	C₂	#6438	1	1	yes	characteristic
48	C₂	#6472	1	2	yes	—

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

N	H ≅ G/N	type
41. C₇	#491	semidirect

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