Subgroups — C₇×#349 #89391

Order 448.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×M₁₆	C₂	1	1	yes	maximal, characteristic
2	C₇×M₃₂	C₂	1	2	yes	maximal, complemented
3	C₂²×C₄×C₇	C₄	1	1	yes	characteristic
4	C₇×M₁₆	—	2	2	no	—
5	C₂×C₇×C₈	C₄	1	1	yes	characteristic
6	C₂×C₇×C₈	C₂²	1	1	yes	characteristic
7	C₇×C₁₆	—	2	2	no	—
8	#349	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
9	C₂³×C₇	C₈	1	1	yes	characteristic
10	C₂×C₄×C₇	—	2	1	no	—
11	C₂×C₄×C₇	—	2	1	no	—
12	C₂×C₄×C₇	C₈	1	1	yes	characteristic
13	C₂×C₄×C₇	C₂×C₄	1	1	yes	characteristic
14	C₇×C₈	—	2	1	no	—
15	C₇×C₈	D₄	1	2	yes	—
16	C₂×M₁₆	C₂×C₇	1	1	yes	characteristic
17	M₃₂	C₂×C₇	1	2	yes	complemented
18	C₂²×C₇	—	2	1	no	—
19	C₂²×C₇	—	4	1	no	—
20	C₂²×C₇	C₂×C₈	1	1	yes	characteristic
21	C₄×C₇	—	2	1	no	—
22	C₄×C₇	C₂²⋊C₄	1	1	yes	characteristic
23	C₄×C₇	M₁₆	1	1	yes	characteristic
24	C₂²×C₄	C₄×C₇	1	1	yes	characteristic
25	M₁₆	—	2	2	no	—
26	C₂×C₈	C₄×C₇	1	1	yes	characteristic
27	C₂×C₈	C₂²×C₇	1	1	yes	characteristic
28	C₁₆	—	2	2	no	—
29	C₂×C₇	—	2	1	no	—
30	C₂×C₇	—	4	1	no	—
31	C₂×C₇	C₂²⋊C₈	1	1	yes	characteristic
32	C₂³	C₇×C₈	1	1	yes	characteristic
33	C₂×C₄	—	2	1	no	—
34	C₂×C₄	—	2	1	no	—
35	C₂×C₄	C₇×C₈	1	1	yes	characteristic
36	C₂×C₄	C₂×C₄×C₇	1	1	yes	characteristic
37	C₈	—	2	1	no	—
38	C₈	C₇×D₄	1	2	yes	—
39	C₇	#349	1	1	yes	characteristic, direct product factor, Sylow
40	C₂²	—	2	1	no	—
41	C₂²	—	4	1	no	—
42	C₂²	C₂×C₇×C₈	1	1	yes	characteristic
43	C₄	—	2	1	no	—
44	C₄	C₇×C₂²⋊C₄	1	1	yes	characteristic
45	C₄	C₇×M₁₆	1	1	yes	characteristic
46	C₂	—	2	1	no	—
47	C₂	—	4	1	no	—
48	C₂	C₇×C₂²⋊C₈	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₇	C₂²⋊C₄
commutator	C₂²	C₂×C₇×C₈
Frattini, cosocle	C₂×C₈	C₂²×C₇
socle	C₂×C₇	C₂²⋊C₈
prime radical	C₂³×C₇	C₈
LCS	G ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ 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
8. #349	C₇	direct (N × H)
17. M₃₂	C₂×C₇	semidirect
39. C₇	#349	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×M₁₆	2
C₇×M₃₂	2
#349	7

Subgroups — C7×#349 #89391

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#349 #89391