Subgroups — C₇×#361 #89403

Order 448.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×D₈	C₂	1	1	yes	maximal, characteristic
2	C₇×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#108	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₇×D₄	—	2	1	no	—
5	C₇×D₈	—	2	1	no	—
6	C₇×D₈	C₄	1	2	yes	—
7	C₇×M₁₆	—	2	1	no	—
8	C₂×C₇×C₈	C₂²	1	1	yes	characteristic
9	C₇×C₁₆	—	2	1	no	—
10	#361	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
11	C₂³×C₇	—	4	1	no	—
12	C₇×D₄	—	2	2	no	—
13	C₇×D₄	—	4	1	no	—
14	C₂×C₄×C₇	D₄	1	1	yes	characteristic
15	C₇×C₈	—	4	1	no	—
16	C₇×C₈	C₂×C₄	1	1	yes	characteristic
17	C₇×C₈	D₄	1	1	yes	characteristic
18	C₂×D₈	C₂×C₇	1	1	yes	characteristic
19	M₃₂	C₂×C₇	1	1	yes	characteristic, complemented
20	#108	C₂×C₇	1	1	yes	characteristic, complemented
21	C₂²×C₇	—	4	2	no	—
22	C₂²×C₇	—	8	2	no	—
23	C₂²×C₇	SD₁₆	1	1	yes	characteristic
24	C₄×C₇	C₂²⋊C₄	1	1	yes	characteristic
25	C₄×C₇	D₈	1	1	yes	characteristic
26	C₂×D₄	—	2	1	no	—
27	D₈	—	2	1	no	—
28	D₈	C₄×C₇	1	2	yes	—
29	M₁₆	—	2	1	no	—
30	C₂×C₈	C₂²×C₇	1	1	yes	characteristic
31	C₁₆	—	2	1	no	—
32	C₂×C₇	—	2	1	no	—
33	C₂×C₇	—	8	2	no	—
34	C₂×C₇	#102	1	1	yes	characteristic
35	C₂³	—	4	1	no	—
36	D₄	—	2	2	no	—
37	D₄	—	4	1	no	—
38	C₂×C₄	C₇×D₄	1	1	yes	characteristic
39	C₈	—	4	1	no	—
40	C₈	C₂×C₄×C₇	1	1	yes	characteristic
41	C₈	C₇×D₄	1	1	yes	characteristic
42	C₇	#361	1	1	yes	characteristic, direct product factor, Sylow
43	C₂²	—	4	2	no	—
44	C₂²	—	8	2	no	—
45	C₂²	C₇×SD₁₆	1	1	yes	characteristic
46	C₄	C₇×C₂²⋊C₄	1	1	yes	characteristic
47	C₄	C₇×D₈	1	1	yes	characteristic
48	C₂	—	2	1	no	—
49	C₂	—	8	2	no	—
50	C₂	C₇×#102	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₇	#102
commutator	C₈	C₂×C₄×C₇
Frattini, cosocle	C₂×C₈	C₂²×C₇
prime radical	C₂×C₇×D₈	C₂
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₇ ◁ C₂×C₄×C₇ ◁ C₂×C₇×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇×M₃₂	C₂	semidirect
3. C₇×#108	C₂	semidirect
10. #361	C₇	direct (N × H)
19. M₃₂	C₂×C₇	semidirect
20. #108	C₂×C₇	semidirect
42. C₇	#361	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₇×D₈	2
C₇×M₃₂	2
C₇×#108	2
#361	7

Subgroups — C7×#361 #89403

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#361 #89403