Group #20239243 — subgroups

Subgroups — C₄₇×#1633 #20239243

Order 6016.

206 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 76 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈²×C₄₇	C₂	1	1	yes	maximal, characteristic
2	C₄₇×#494	C₂	1	1	yes	maximal, characteristic
3	C₄₇×#477	C₂	1	2	yes	maximal
4	C₄₇×#333	C₂	1	1	yes	maximal, characteristic
5	C₄₇×Q₈⋊C₈	C₂	1	2	yes	maximal
6	C₂×Q₁₆×C₄₇	—	2	2	no	—
7	C₄⋊Q₈×C₄₇	—	2	2	no	—
8	C₄⋊Q₈×C₄₇	—	2	2	no	—
9	C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
10	C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
11	C₄×Q₈×C₄₇	—	2	2	no	—
12	C₄×Q₈×C₄₇	C₂²	1	2	yes	—
13	#107×C₄₇	—	2	2	no	—
14	C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
15	#103×C₄₇	—	2	2	no	—
16	C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
17	C₂×Q₈×C₄₇	—	2	2	no	—
18	C₂×Q₈×C₄₇	—	2	1	no	—
19	C₂×Q₈×C₄₇	D₄	1	2	yes	—
20	C₂×Q₈×C₄₇	D₄	1	2	yes	—
21	Q₁₆×C₄₇	—	4	4	no	—
22	C₂×C₈×C₄₇	—	2	1	no	—
23	C₂×C₈×C₄₇	—	2	2	no	—
24	C₄⋊C₄×C₄₇	—	2	4	no	—
25	C₄⋊C₄×C₄₇	—	2	2	no	—
26	C₄⋊C₄×C₄₇	—	2	2	no	—
27	C₄⋊C₄×C₄₇	—	2	2	no	—
28	C₄⋊C₄×C₄₇	D₄	1	2	yes	—
29	C₄²×C₄₇	—	2	2	no	—
30	C₄²×C₄₇	—	2	2	no	—
31	C₄²×C₄₇	C₂³	1	1	yes	characteristic
32	Q₈×C₄₇	—	2	2	no	—
33	Q₈×C₄₇	—	4	2	no	—
34	Q₈×C₄₇	—	4	2	no	—
35	Q₈×C₄₇	—	8	2	no	—
36	Q₈×C₄₇	Q₁₆	1	4	yes	complemented
37	C₂×C₄×C₄₇	—	2	2	no	—
38	C₂×C₄×C₄₇	—	2	2	no	—
39	C₂×C₄×C₄₇	—	2	2	no	—
40	C₂×C₄×C₄₇	—	4	1	no	—
41	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
42	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
43	C₈×C₄₇	—	2	2	no	—
44	C₈×C₄₇	—	4	2	no	—
45	C₂²×C₄₇	#120	1	1	yes	characteristic
46	C₄×C₄₇	—	2	4	no	—
47	C₄×C₄₇	—	2	1	no	—
48	C₄×C₄₇	—	4	2	no	—
49	C₄×C₄₇	—	4	2	no	—
50	C₄×C₄₇	—	8	1	no	—
51	C₄×C₄₇	C₂×Q₁₆	1	2	yes	—
52	C₄×C₄₇	#137	1	2	yes	—
53	#1633	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
54	C₂×C₄₇	#451	1	2	yes	—
55	C₂×C₄₇	#453	1	1	yes	characteristic
56	Q₈²	C₂×C₄₇	1	1	yes	characteristic
57	#494	C₂×C₄₇	1	1	yes	characteristic
58	#477	C₂×C₄₇	1	2	yes	—
59	#333	C₂×C₄₇	1	1	yes	characteristic
60	Q₈⋊C₈	C₂×C₄₇	1	2	yes	—
61	C₄₇	#1633	1	1	yes	characteristic, direct product factor, Sylow
62	C₂×Q₁₆	—	2	2	no	—
63	C₄⋊Q₈	—	2	2	no	—
64	C₄⋊Q₈	—	2	2	no	—
65	C₄⋊Q₈	C₂²×C₄₇	1	1	yes	characteristic
66	C₄⋊Q₈	C₂²×C₄₇	1	1	yes	characteristic
67	C₄×Q₈	—	2	2	no	—
68	C₄×Q₈	C₂²×C₄₇	1	2	yes	—
69	#107	—	2	2	no	—
70	C₄⋊C₈	C₂²×C₄₇	1	2	yes	—
71	#103	—	2	2	no	—
72	C₄×C₈	C₂²×C₄₇	1	1	yes	characteristic
73	C₂×Q₈	—	2	2	no	—
74	C₂×Q₈	—	2	1	no	—
75	C₂×Q₈	D₄×C₄₇	1	2	yes	—
76	C₂×Q₈	D₄×C₄₇	1	2	yes	—
77	Q₁₆	—	4	4	no	—
78	C₂×C₈	—	2	1	no	—
79	C₂×C₈	—	2	2	no	—
80	C₄⋊C₄	—	2	4	no	—
81	C₄⋊C₄	—	2	2	no	—
82	C₄⋊C₄	—	2	2	no	—
83	C₄⋊C₄	—	2	2	no	—
84	C₄⋊C₄	D₄×C₄₇	1	2	yes	—
85	C₄²	—	2	2	no	—
86	C₄²	—	2	2	no	—
87	C₄²	C₂³×C₄₇	1	1	yes	characteristic
88	Q₈	—	2	2	no	—
89	Q₈	—	4	2	no	—
90	Q₈	—	4	2	no	—
91	Q₈	—	8	2	no	—
92	Q₈	Q₁₆×C₄₇	1	4	yes	complemented
93	C₂×C₄	—	2	2	no	—
94	C₂×C₄	—	2	2	no	—
95	C₂×C₄	—	2	2	no	—
96	C₂×C₄	—	4	1	no	—
97	C₂×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
98	C₂×C₄	C₂×D₄×C₄₇	1	2	yes	—
99	C₈	—	2	2	no	—
100	C₈	—	4	2	no	—
101	C₂²	#120×C₄₇	1	1	yes	characteristic
102	C₄	—	2	4	no	—
103	C₄	—	2	1	no	—
104	C₄	—	4	2	no	—
105	C₄	—	4	2	no	—
106	C₄	—	8	1	no	—
107	C₄	C₂×Q₁₆×C₄₇	1	2	yes	—
108	C₄	#137×C₄₇	1	2	yes	—
109	C₂	C₄₇×#451	1	2	yes	—
110	C₂	C₄₇×#453	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

Q₈²×C₄₇

C₂

yes

maximal, characteristic

C₄₇×#494

C₂

yes

maximal, characteristic

C₄₇×#477

C₂

yes

maximal

C₄₇×#333

C₂

yes

maximal, characteristic

C₄₇×Q₈⋊C₈

C₂

yes

maximal

C₂×Q₁₆×C₄₇

—

C₄⋊Q₈×C₄₇

—

C₄⋊Q₈×C₄₇

—

C₄⋊Q₈×C₄₇

C₂²

yes

characteristic

C₄⋊Q₈×C₄₇

C₂²

yes

characteristic

C₄×Q₈×C₄₇

—

C₄×Q₈×C₄₇

C₂²

yes

—

#107×C₄₇

—

C₄⋊C₈×C₄₇

C₂²

yes

—

#103×C₄₇

—

C₄×C₈×C₄₇

C₂²

yes

characteristic

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

D₄

yes

—

C₂×Q₈×C₄₇

D₄

yes

—

Q₁₆×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

D₄

yes

—

C₄²×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

C₂³

yes

characteristic

Q₈×C₄₇

—

Q₈×C₄₇

—

Q₈×C₄₇

—

Q₈×C₄₇

—

Q₈×C₄₇

Q₁₆

yes

complemented

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₈×C₄₇

—

C₈×C₄₇

—

C₂²×C₄₇

#120

yes

characteristic

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

C₂×Q₁₆

yes

—

C₄×C₄₇

#137

yes

—

#1633

C₄₇

yes

maximal, characteristic, direct product factor, Sylow

C₂×C₄₇

#451

yes

—

C₂×C₄₇

#453

yes

characteristic

Q₈²

C₂×C₄₇

yes

characteristic

#494

C₂×C₄₇

yes

characteristic

#477

C₂×C₄₇

yes

—

#333

C₂×C₄₇

yes

characteristic

Q₈⋊C₈

C₂×C₄₇

yes

—

C₄₇

#1633

yes

characteristic, direct product factor, Sylow

C₂×Q₁₆

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

C₂²×C₄₇

yes

characteristic

C₄⋊Q₈

C₂²×C₄₇

yes

characteristic

C₄×Q₈

—

C₄×Q₈

C₂²×C₄₇

yes

—

#107

—

C₄⋊C₈

C₂²×C₄₇

yes

—

#103

—

C₄×C₈

C₂²×C₄₇

yes

characteristic

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

D₄×C₄₇

yes

—

C₂×Q₈

D₄×C₄₇

yes

—

Q₁₆

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

D₄×C₄₇

yes

—

C₄²

—

C₄²

—

C₄²

C₂³×C₄₇

yes

characteristic

Q₈

—

Q₈

—

Q₈

—

Q₈

—

Q₈

Q₁₆×C₄₇

yes

complemented

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×D₄×C₄₇

yes

characteristic

C₂×C₄

C₂×D₄×C₄₇

yes

—

C₈

—

100

C₈

—

101

C₂²

#120×C₄₇

yes

characteristic

102

C₄

—

103

C₄

—

104

C₄

—

105

C₄

—

106

C₄

—

107

C₄

C₂×Q₁₆×C₄₇

yes

—

108

C₄

#137×C₄₇

yes

—

109

C₂

C₄₇×#451

yes

—

110

C₂

C₄₇×#453

yes

characteristic

	subgroup	G/H
center, socle, prime radical	C₂²×C₄₇	#120
commutator, Frattini, cosocle	C₄²	C₂³×C₄₇
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄₇ ◁ C₄²×C₄₇ ◁ G

subgroup

G/H

center, socle, prime radical

C₂²×C₄₇

#120

commutator, Frattini, cosocle

C₄²

C₂³×C₄₇

LCS

G ▷ C₄² ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂²×C₄₇ ◁ C₄²×C₄₇ ◁ G

N	H ≅ G/N	type
36. Q₈×C₄₇	Q₁₆	semidirect
53. #1633	C₄₇	direct (N × H)
61. C₄₇	#1633	direct (N × H)
92. Q₈	Q₁₆×C₄₇	semidirect

H ≅ G/N

type

36. Q₈×C₄₇

Q₁₆

semidirect

53. #1633

C₄₇

direct (N × H)

61. C₄₇

#1633

direct (N × H)

92. Q₈

Q₁₆×C₄₇

semidirect

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

subgroup	index
Q₈²×C₄₇	2
C₄₇×#494	2
C₄₇×#477	2
C₄₇×#333	2
C₄₇×Q₈⋊C₈	2
#1633	47

subgroup

index

Q₈²×C₄₇

C₄₇×#494

C₄₇×#477

C₄₇×#333

C₄₇×Q₈⋊C₈

#1633

Subgroups — C₄₇×#1633 #20239243

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C47×#1633 #20239243

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#1633 #20239243