Subgroups — D₇×#106 #89631

Order 448.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×D₇	C₂	1	1	yes	maximal, characteristic
2	D₇×C₄⋊C₄	C₂	1	2	yes	maximal
3	C₇×#106	C₂	1	1	yes	maximal, characteristic, complemented
4	#6391	C₂	1	1	yes	maximal, characteristic, complemented
5	#6382	C₂	1	2	yes	maximal, complemented
6	C₂×C₄×D₇	—	2	2	no	—
7	C₂×C₄×D₇	C₂²	1	1	yes	characteristic
8	C₂×C₇×C₈	C₂²	1	1	yes	characteristic
9	C₇×C₄⋊C₄	C₂²	1	2	yes	—
10	C₄⋊Dic₇	C₂²	1	2	yes	—
11	Dic₇⋊C₄	—	2	2	no	—
12	C₂×C₇⋊C₈	C₂²	1	1	yes	characteristic
13	C₈×D₇	C₄	1	4	yes	complemented
14	C₂×#106	—	7	1	no	maximal, Sylow
15	C₂²×D₇	D₄	1	1	yes	characteristic
16	C₂×C₄×C₇	—	2	2	no	—
17	C₂×C₄×C₇	C₂³	1	1	yes	characteristic
18	C₂×Dic₇	—	2	2	no	—
19	C₂×Dic₇	D₄	1	1	yes	characteristic
20	C₄×D₇	—	4	4	no	—
21	C₄×D₇	C₂×C₄	1	2	yes	—
22	C₄×D₇	Q₈	1	2	yes	—
23	C₇×C₈	C₂×C₄	1	2	yes	complemented
24	C₇⋊C₈	C₂×C₄	1	2	yes	complemented
25	C₂²×C₈	—	7	1	no	—
26	C₂×C₄⋊C₄	—	7	2	no	—
27	#106	—	7	1	no	—
28	#106	—	7	2	no	—
29	#106	D₇	1	1	yes	characteristic, direct product factor
30	C₂²×C₇	C₂×D₄	1	1	yes	characteristic
31	C₂×D₇	C₄⋊C₄	1	2	yes	—
32	C₂×D₇	SD₁₆	1	4	yes	—
33	C₄×C₇	—	4	2	no	—
34	C₄×C₇	C₂²×C₄	1	1	yes	characteristic
35	C₄×C₇	C₂×Q₈	1	1	yes	characteristic
36	Dic₇	—	4	2	no	—
37	Dic₇	C₄⋊C₄	1	2	yes	—
38	C₂²×C₄	—	7	1	no	—
39	C₂²×C₄	—	14	2	no	—
40	C₂×C₈	—	7	1	no	—
41	C₂×C₈	—	7	4	no	—
42	C₂×C₈	C₂×D₇	1	1	yes	characteristic
43	C₄⋊C₄	—	7	2	no	—
44	C₄⋊C₄	—	14	2	no	—
45	C₄⋊C₄	C₂×D₇	1	2	yes	—
46	C₂×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
47	C₂×C₇	C₂×SD₁₆	1	2	yes	—
48	D₇	#106	1	4	yes	direct product factor
49	C₂³	—	7	1	no	—
50	C₂×C₄	—	2	2	no	—
51	C₂×C₄	—	7	1	no	—
52	C₂×C₄	—	7	2	no	—
53	C₂×C₄	—	7	2	no	—
54	C₂×C₄	—	14	2	no	—
55	C₂×C₄	—	28	4	no	—
56	C₂×C₄	C₂²×D₇	1	1	yes	characteristic
57	C₈	—	7	2	no	—
58	C₈	C₄×D₇	1	2	yes	complemented
59	C₇	C₂×#106	1	1	yes	characteristic, complemented, Sylow
60	C₂²	—	7	2	no	—
61	C₂²	—	7	4	no	—
62	C₂²	D₄×D₇	1	1	yes	characteristic
63	C₄	—	4	2	no	—
64	C₄	—	7	2	no	—
65	C₄	—	28	2	no	—
66	C₄	C₂×C₄×D₇	1	1	yes	characteristic
67	C₄	Q₈×D₇	1	1	yes	characteristic
68	C₂	—	7	4	no	—
69	C₂	D₇×C₄⋊C₄	1	1	yes	characteristic
70	C₂	D₇×SD₁₆	1	2	yes	—

	subgroup	G/H
center	C₂²	D₄×D₇
commutator	C₄×C₇	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₇
Fitting	C₇×#106	C₂
socle	C₂²×C₇	C₂×D₄
prime radical	C₂²×D₇	D₄
cosocle	C₂×C₄×C₇	C₂³
hypercenter	#106	D₇
hypocenter	C₇	C₂×#106
LCS	G ▷ C₄×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #106

Complements

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

N	H ≅ G/N	type
3. C₇×#106	C₂	semidirect
4. #6391	C₂	semidirect
5. #6382	C₂	semidirect
13. C₈×D₇	C₄	semidirect
23. C₇×C₈	C₂×C₄	semidirect
24. C₇⋊C₈	C₂×C₄	semidirect
29. #106	D₇	direct (N × H)
48. D₇	#106	direct (N × H)
58. C₈	C₄×D₇	semidirect
59. C₇	C₂×#106	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₈×D₇	2
D₇×C₄⋊C₄	2
C₇×#106	2
#6391	2
#6382	2
C₂×#106	7

Subgroups — D7×#106 #89631

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₇×#106 #89631