Subgroups — D₇×#107 #89651

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×#107	C₂	1	1	yes	maximal, characteristic, complemented
4	#6392	C₂	1	1	yes	maximal, characteristic, complemented
5	#6381	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×#107	—	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	#107	—	7	1	no	—
28	#107	—	7	2	no	—
29	#107	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	D₈	1	2	yes	—
33	C₂×D₇	Q₁₆	1	2	yes	—
34	C₄×C₇	—	4	2	no	—
35	C₄×C₇	C₂²×C₄	1	1	yes	characteristic
36	C₄×C₇	C₂×Q₈	1	1	yes	characteristic
37	Dic₇	—	4	2	no	—
38	Dic₇	C₄⋊C₄	1	2	yes	—
39	C₂²×C₄	—	7	1	no	—
40	C₂²×C₄	—	14	2	no	—
41	C₂×C₈	—	7	1	no	—
42	C₂×C₈	—	7	4	no	—
43	C₂×C₈	C₂×D₇	1	1	yes	characteristic
44	C₄⋊C₄	—	7	2	no	—
45	C₄⋊C₄	—	14	2	no	—
46	C₄⋊C₄	C₂×D₇	1	2	yes	—
47	C₂×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
48	C₂×C₇	C₂×D₈	1	1	yes	characteristic
49	C₂×C₇	C₂×Q₁₆	1	1	yes	characteristic
50	D₇	#107	1	4	yes	direct product factor
51	C₂³	—	7	1	no	—
52	C₂×C₄	—	2	2	no	—
53	C₂×C₄	—	7	1	no	—
54	C₂×C₄	—	7	2	no	—
55	C₂×C₄	—	7	2	no	—
56	C₂×C₄	—	14	2	no	—
57	C₂×C₄	—	28	4	no	—
58	C₂×C₄	C₂²×D₇	1	1	yes	characteristic
59	C₈	—	7	2	no	—
60	C₈	C₄×D₇	1	2	yes	complemented
61	C₇	C₂×#107	1	1	yes	characteristic, complemented, Sylow
62	C₂²	—	7	2	no	—
63	C₂²	—	7	2	no	—
64	C₂²	—	7	2	no	—
65	C₂²	D₄×D₇	1	1	yes	characteristic
66	C₄	—	4	2	no	—
67	C₄	—	7	2	no	—
68	C₄	—	28	2	no	—
69	C₄	C₂×C₄×D₇	1	1	yes	characteristic
70	C₄	Q₈×D₇	1	1	yes	characteristic
71	C₂	—	7	4	no	—
72	C₂	D₇×C₄⋊C₄	1	1	yes	characteristic
73	C₂	D₇×D₈	1	1	yes	characteristic
74	C₂	D₇×Q₁₆	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₇
commutator	C₄×C₇	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₇
Fitting	C₇×#107	C₂
socle	C₂²×C₇	C₂×D₄
prime radical	C₂²×D₇	D₄
cosocle	C₂×C₄×C₇	C₂³
hypercenter	#107	D₇
hypocenter	C₇	C₂×#107
LCS	G ▷ C₄×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #107

Complements

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

N	H ≅ G/N	type
3. C₇×#107	C₂	semidirect
4. #6392	C₂	semidirect
5. #6381	C₂	semidirect
13. C₈×D₇	C₄	semidirect
23. C₇×C₈	C₂×C₄	semidirect
24. C₇⋊C₈	C₂×C₄	semidirect
29. #107	D₇	direct (N × H)
50. D₇	#107	direct (N × H)
60. C₈	C₄×D₇	semidirect
61. C₇	C₂×#107	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×#107	2
#6392	2
#6381	2
C₂×#107	7

Subgroups — D7×#107 #89651

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₇×#107 #89651