Subgroups — #89337

Order 448.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#124	C₂	1	1	yes	maximal, characteristic
2	#6410	C₂	1	2	yes	maximal, complemented
3	C₂×C₇×Q₈	C₂²	1	1	yes	characteristic
4	C₂×C₇×D₄	C₄	1	1	yes	characteristic
5	C₇×C₂²⋊C₄	—	2	2	no	—
6	C₄²×C₇	C₄	1	1	yes	characteristic
7	#1136	—	2	2	no	—
8	#355	—	7	1	no	maximal, Sylow
9	C₂³×C₇	—	2	1	no	—
10	C₇×Q₈	—	4	1	no	—
11	C₇×D₄	—	4	1	no	—
12	C₂×C₄×C₇	—	2	1	no	—
13	C₂×C₄×C₇	C₂×C₄	1	1	yes	characteristic
14	C₂×C₄×C₇	D₄	1	2	yes	—
15	C₇⋊C₈	—	4	2	no	—
16	#124	D₇	1	1	yes	characteristic
17	#101	—	7	2	no	—
18	C₂²×C₇	—	4	2	no	—
19	C₂²×C₇	—	4	1	no	—
20	C₂²×C₇	C₂²⋊C₄	1	1	yes	characteristic
21	C₄×C₇	—	2	2	no	—
22	C₄×C₇	—	2	1	no	—
23	C₄×C₇	—	4	1	no	—
24	C₂×Q₈	C₂×D₇	1	1	yes	characteristic
25	C₂×D₄	Dic₇	1	1	yes	characteristic
26	M₁₆	—	14	2	no	—
27	C₂²⋊C₄	—	2	2	no	—
28	C₄²	Dic₇	1	1	yes	characteristic
29	C₂×C₇	—	2	1	no	—
30	C₂×C₇	—	8	1	no	—
31	C₂×C₇	#99	1	1	yes	characteristic
32	C₂³	—	2	1	no	—
33	Q₈	—	4	1	no	—
34	D₄	—	4	1	no	—
35	C₂×C₄	—	2	1	no	—
36	C₂×C₄	C₂×Dic₇	1	1	yes	characteristic
37	C₂×C₄	C₂²⋊D₇	1	2	yes	—
38	C₈	—	28	2	no	—
39	C₇	#355	1	1	yes	characteristic, complemented, Sylow
40	C₂²	—	4	2	no	—
41	C₂²	—	4	1	no	—
42	C₂²	C₂²⋊Dic₇	1	1	yes	characteristic
43	C₄	—	2	2	no	—
44	C₄	—	2	1	no	—
45	C₄	—	4	1	no	—
46	C₂	—	2	1	no	—
47	C₂	—	8	1	no	—
48	C₂	#6408	1	1	yes	characteristic

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

N	H ≅ G/N	type
2. #6410	C₂	semidirect
39. C₇	#355	semidirect

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