Subgroups — C₂×C₇×#106 #90071

Order 448.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₇×C₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₇×C₄⋊C₄	C₂	1	2	yes	maximal
3	C₇×#106	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₄×C₇	—	2	2	no	—
5	C₂²×C₄×C₇	C₂²	1	1	yes	characteristic
6	C₂×C₇×C₈	C₄	1	4	yes	complemented
7	C₂×C₇×C₈	C₂²	1	2	yes	—
8	C₇×C₄⋊C₄	—	2	2	no	—
9	C₇×C₄⋊C₄	C₂²	1	4	yes	—
10	C₂×#106	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
11	C₂³×C₇	D₄	1	1	yes	characteristic
12	C₂×C₄×C₇	—	2	4	no	—
13	C₂×C₄×C₇	—	4	4	no	—
14	C₂×C₄×C₇	C₂×C₄	1	2	yes	—
15	C₂×C₄×C₇	D₄	1	1	yes	characteristic
16	C₂×C₄×C₇	Q₈	1	2	yes	—
17	C₂×C₄×C₇	C₂³	1	1	yes	characteristic
18	C₇×C₈	C₂×C₄	1	4	yes	complemented
19	C₂²×C₈	C₂×C₇	1	1	yes	characteristic
20	C₂×C₄⋊C₄	C₂×C₇	1	2	yes	—
21	#106	C₂×C₇	1	4	yes	direct product factor
22	C₂²×C₇	C₄⋊C₄	1	2	yes	—
23	C₂²×C₇	SD₁₆	1	4	yes	—
24	C₂²×C₇	C₂×D₄	1	1	yes	characteristic
25	C₄×C₇	—	4	4	no	—
26	C₄×C₇	C₄⋊C₄	1	2	yes	—
27	C₄×C₇	C₂²×C₄	1	1	yes	characteristic
28	C₄×C₇	C₂×Q₈	1	1	yes	characteristic
29	C₂²×C₄	—	2	2	no	—
30	C₂²×C₄	C₂²×C₇	1	1	yes	characteristic
31	C₂×C₈	C₄×C₇	1	4	yes	complemented
32	C₂×C₈	C₂²×C₇	1	2	yes	—
33	C₄⋊C₄	—	2	2	no	—
34	C₄⋊C₄	C₂²×C₇	1	4	yes	—
35	C₂×C₇	#106	1	4	yes	direct product factor
36	C₂×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
37	C₂×C₇	C₂×SD₁₆	1	2	yes	—
38	C₂³	C₇×D₄	1	1	yes	characteristic
39	C₂×C₄	—	2	4	no	—
40	C₂×C₄	—	4	4	no	—
41	C₂×C₄	C₂×C₄×C₇	1	2	yes	—
42	C₂×C₄	C₇×D₄	1	1	yes	characteristic
43	C₂×C₄	C₇×Q₈	1	2	yes	—
44	C₂×C₄	C₂³×C₇	1	1	yes	characteristic
45	C₈	C₂×C₄×C₇	1	4	yes	complemented
46	C₇	C₂×#106	1	1	yes	characteristic, direct product factor, Sylow
47	C₂²	C₇×C₄⋊C₄	1	2	yes	—
48	C₂²	C₇×SD₁₆	1	4	yes	—
49	C₂²	C₂×C₇×D₄	1	1	yes	characteristic
50	C₄	—	4	4	no	—
51	C₄	C₇×C₄⋊C₄	1	2	yes	—
52	C₄	C₂²×C₄×C₇	1	1	yes	characteristic
53	C₄	C₂×C₇×Q₈	1	1	yes	characteristic
54	C₂	C₇×#106	1	4	yes	direct product factor
55	C₂	C₂×C₇×C₄⋊C₄	1	1	yes	characteristic
56	C₂	C₂×C₇×SD₁₆	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂³×C₇	D₄
commutator	C₄	C₂²×C₄×C₇
Frattini, cosocle	C₂×C₄	C₂³×C₇
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ C₂²×C₄×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₇×#106	C₂	direct (N × H)
6. C₂×C₇×C₈	C₄	semidirect
10. C₂×#106	C₇	direct (N × H)
18. C₇×C₈	C₂×C₄	semidirect
21. #106	C₂×C₇	direct (N × H)
31. C₂×C₈	C₄×C₇	semidirect
35. C₂×C₇	#106	direct (N × H)
45. C₈	C₂×C₄×C₇	semidirect
46. C₇	C₂×#106	direct (N × H)
54. C₂	C₇×#106	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₇×C₈	2
C₂×C₇×C₄⋊C₄	2
C₇×#106	2
C₂×#106	7

Subgroups — C2×C7×#106 #90071

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#106 #90071