Subgroups — #89339

Order 448.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#127	C₂	1	1	yes	maximal, characteristic
2	C₄⋊(C₇⋊C₈)	C₂	1	2	yes	maximal, complemented
3	C₂×C₇×D₄	—	2	2	no	—
4	C₂×C₇×D₄	C₄	1	2	yes	—
5	C₄²×C₇	C₂²	1	1	yes	characteristic
6	C₂×C₇⋊C₈	—	2	2	no	—
7	#331	—	7	1	no	maximal, Sylow
8	C₂³×C₇	—	2	2	no	—
9	C₇×D₄	—	4	2	no	—
10	C₇×D₄	—	4	2	no	—
11	C₇×D₄	—	4	2	no	—
12	C₂×C₄×C₇	C₂×C₄	1	1	yes	characteristic
13	C₂×C₄×C₇	D₄	1	2	yes	—
14	C₇⋊C₈	—	4	2	no	—
15	#127	D₇	1	1	yes	characteristic
16	C₄⋊C₈	—	7	2	no	—
17	C₂²×C₇	—	4	2	no	—
18	C₂²×C₇	—	4	4	no	—
19	C₂²×C₇	C₂²⋊C₄	1	1	yes	characteristic
20	C₄×C₇	—	2	1	no	—
21	C₄×C₇	D₈	1	2	yes	—
22	C₄×C₇	SD₁₆	1	2	yes	—
23	C₂×D₄	—	2	2	no	—
24	C₂×D₄	Dic₇	1	2	yes	—
25	C₂×C₈	—	14	2	no	—
26	C₄²	C₂×D₇	1	1	yes	characteristic
27	C₂×C₇	—	8	2	no	—
28	C₂×C₇	#100	1	1	yes	characteristic
29	C₂×C₇	#102	1	2	yes	—
30	C₂³	—	2	2	no	—
31	D₄	—	4	2	no	—
32	D₄	—	4	2	no	—
33	D₄	—	4	2	no	—
34	C₂×C₄	C₂×Dic₇	1	1	yes	characteristic
35	C₂×C₄	C₂²⋊D₇	1	2	yes	—
36	C₈	—	28	2	no	—
37	C₇	#331	1	1	yes	characteristic, complemented, Sylow
38	C₂²	—	4	4	no	—
39	C₂²	—	4	2	no	—
40	C₂²	C₂²⋊Dic₇	1	1	yes	characteristic
41	C₄	—	2	1	no	—
42	C₄	#1141	1	2	yes	—
43	C₄	#1142	1	2	yes	—
44	C₂	—	8	2	no	—
45	C₂	#6406	1	2	yes	—
46	C₂	#6407	1	1	yes	characteristic

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

N	H ≅ G/N	type
2. C₄⋊(C₇⋊C₈)	C₂	semidirect
37. C₇	#331	semidirect

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