Group #23765451 — subgroups

Subgroups — #23765451

Order 10112.

154 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 154 conjugacy classes of subgroups — too many to draw. Only its 55 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	C₂×Dic₆₃₂	C₂	1	2	yes	maximal
2	#19098943	C₂	1	1	yes	maximal, characteristic
3	C₄×Dic₃₁₆	C₂	1	1	yes	maximal, characteristic
4	#19098368	C₂	1	2	yes	maximal
5	C₄⋊C₁₆×C₇₉	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₃₁₆	—	2	1	no	—
7	C₂×Dic₃₁₆	C₂²	1	2	yes	—
8	C₂×Dic₃₁₆	C₂²	1	1	yes	characteristic
9	#14579161	—	2	1	no	—
10	C₄×Dic₁₅₈	—	2	1	no	—
11	Dic₆₃₂	—	2	4	no	—
12	#14579095	C₂²	1	1	yes	characteristic
13	#14579086	—	2	1	no	—
14	C₂×C₁₆×C₇₉	C₂²	1	2	yes	—
15	C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
16	C₂×Dic₁₅₈	—	2	1	no	—
17	C₂×Dic₁₅₈	—	2	2	no	—
18	Dic₃₁₆	—	2	2	no	—
19	Dic₃₁₆	—	2	1	no	—
20	Dic₃₁₆	—	2	2	no	—
21	Dic₃₁₆	—	4	2	no	—
22	Dic₃₁₆	D₄	1	2	yes	—
23	C₄⋊Dic₇₉	—	2	1	no	—
24	C₄⋊Dic₇₉	—	4	1	no	—
25	C₄⋊Dic₇₉	—	4	1	no	—
26	Dic₇₉⋊C₄	—	4	1	no	—
27	C₄×Dic₇₉	—	4	1	no	—
28	C₂×C₈×C₇₉	D₄	1	1	yes	characteristic
29	C₂×C₈×C₇₉	C₂³	1	1	yes	characteristic
30	C₄²×C₇₉	D₄	1	1	yes	characteristic
31	C₁₆×C₇₉	—	2	2	no	—
32	C₂×C₄×C₇₉	D₈	1	1	yes	characteristic
33	C₂×C₄×C₇₉	D₈	1	1	yes	characteristic
34	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
35	C₂×Dic₇₉	—	4	1	no	—
36	C₂×Dic₇₉	—	4	1	no	—
37	C₂×Dic₇₉	—	4	2	no	—
38	Dic₁₅₈	—	2	2	no	—
39	Dic₁₅₈	—	4	1	no	—
40	Dic₁₅₈	—	4	2	no	—
41	Dic₁₅₈	—	4	2	no	—
42	C₈×C₇₉	—	2	1	no	—
43	C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
44	C₈×C₇₉	#41	1	1	yes	characteristic
45	C₂²×C₇₉	C₂×D₈	1	1	yes	characteristic
46	C₄×C₇₉	—	2	1	no	—
47	C₄×C₇₉	Q₃₂	1	2	yes	complemented
48	C₄×C₇₉	#121	1	1	yes	characteristic
49	C₄×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
50	Dic₇₉	—	4	2	no	—
51	Dic₇₉	—	8	2	no	—
52	Dic₇₉	—	8	1	no	—
53	C₂×C₇₉	#459	1	1	yes	characteristic
54	C₂×C₇₉	C₂×Q₃₂	1	1	yes	characteristic
55	C₂×C₇₉	#510	1	1	yes	characteristic
56	#2209	—	79	1	no	maximal, Sylow
57	C₇₉	#2209	1	1	yes	characteristic, complemented, Sylow
58	C₂×Q₃₂	—	79	2	no	—
59	#494	—	79	1	no	—
60	C₄×Q₁₆	—	79	1	no	—
61	C₄⋊C₁₆	D₇₉	1	1	yes	characteristic
62	#358	—	79	2	no	—
63	C₂×Q₁₆	—	79	1	no	—
64	C₂×Q₁₆	—	79	2	no	—
65	C₂×Q₁₆	—	158	1	no	—
66	C₄⋊Q₈	—	158	1	no	—
67	C₄×Q₈	—	158	1	no	—
68	Q₃₂	—	158	4	no	—
69	C₂×C₁₆	C₂×D₇₉	1	2	yes	—
70	#107	—	79	1	no	—
71	#103	—	158	1	no	—
72	C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
73	C₂×Q₈	—	158	2	no	—
74	C₂×Q₈	—	158	1	no	—
75	Q₁₆	—	316	2	no	—
76	Q₁₆	—	79	2	no	—
77	Q₁₆	—	158	2	no	—
78	Q₁₆	—	158	2	no	—
79	Q₁₆	—	158	1	no	—
80	C₂×C₈	D₃₁₆	1	1	yes	characteristic
81	C₂×C₈	C₂²×D₇₉	1	1	yes	characteristic
82	C₄⋊C₄	—	316	1	no	—
83	C₄⋊C₄	—	316	1	no	—
84	C₄⋊C₄	—	316	1	no	—
85	C₄⋊C₄	—	158	1	no	—
86	C₄²	—	316	1	no	—
87	C₄²	D₃₁₆	1	1	yes	characteristic
88	C₁₆	—	2	2	no	—
89	Q₈	—	316	1	no	—
90	Q₈	—	316	2	no	—
91	Q₈	—	316	2	no	—
92	Q₈	—	158	2	no	—
93	C₂×C₄	—	316	1	no	—
94	C₂×C₄	—	316	1	no	—
95	C₂×C₄	—	316	2	no	—
96	C₂×C₄	D₆₃₂	1	1	yes	characteristic
97	C₂×C₄	D₆₃₂	1	1	yes	characteristic
98	C₂×C₄	C₂×D₃₁₆	1	1	yes	characteristic
99	C₈	—	2	1	no	—
100	C₈	D₄×D₇₉	1	1	yes	characteristic
101	C₈	#11929625	1	1	yes	characteristic
102	C₂²	C₂×D₆₃₂	1	1	yes	characteristic
103	C₄	—	2	1	no	—
104	C₄	—	316	2	no	—
105	C₄	—	632	1	no	—
106	C₄	—	632	2	no	—
107	C₄	Dic₆₃₂	1	2	yes	complemented
108	C₄	#14579136	1	1	yes	characteristic
109	C₄	#14579189	1	1	yes	characteristic
110	C₂	#19098759	1	1	yes	characteristic
111	C₂	C₂×Dic₆₃₂	1	1	yes	characteristic
112	C₂	#19099006	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×Dic₆₃₂

C₂

yes

maximal

#19098943

C₂

yes

maximal, characteristic

C₄×Dic₃₁₆

C₂

yes

maximal, characteristic

#19098368

C₂

yes

maximal

C₄⋊C₁₆×C₇₉

C₂

yes

maximal, characteristic

C₂×Dic₃₁₆

—

C₂×Dic₃₁₆

C₂²

yes

—

C₂×Dic₃₁₆

C₂²

yes

characteristic

#14579161

—

C₄×Dic₁₅₈

—

Dic₆₃₂

—

#14579095

C₂²

yes

characteristic

#14579086

—

C₂×C₁₆×C₇₉

C₂²

yes

—

C₄×C₈×C₇₉

C₂²

yes

characteristic

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

Dic₃₁₆

—

Dic₃₁₆

—

Dic₃₁₆

—

Dic₃₁₆

—

Dic₃₁₆

D₄

yes

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

Dic₇₉⋊C₄

—

C₄×Dic₇₉

—

C₂×C₈×C₇₉

D₄

yes

characteristic

C₂×C₈×C₇₉

C₂³

yes

characteristic

C₄²×C₇₉

D₄

yes

characteristic

C₁₆×C₇₉

—

C₂×C₄×C₇₉

D₈

yes

characteristic

C₂×C₄×C₇₉

D₈

yes

characteristic

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

Dic₁₅₈

—

Dic₁₅₈

—

Dic₁₅₈

—

Dic₁₅₈

—

C₈×C₇₉

—

C₈×C₇₉

C₂×D₄

yes

characteristic

C₈×C₇₉

#41

yes

characteristic

C₂²×C₇₉

C₂×D₈

yes

characteristic

C₄×C₇₉

—

C₄×C₇₉

Q₃₂

yes

C₄×C₇₉

yes

C₄×C₇₉

yes

Dic₇₉

—

Dic₇₉

—

Dic₇₉

—

C₂×C₇₉

#459

yes

characteristic

C₂×C₇₉

C₂×Q₃₂

yes

C₂×C₇₉

yes

—

C₇₉

yes

characteristic, complemented, Sylow

C₂×Q₃₂

—

#494

—

C₄×Q₁₆

—

C₄⋊C₁₆

D₇₉

yes

characteristic

#358

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×Q₁₆

—

158

—

C₄⋊Q₈

—

158

—

C₄×Q₈

—

158

—

Q₃₂

—

158

—

C₂×C₁₆

C₂×D₇₉

yes

—

#107

—

#103

—

158

—

C₄×C₈

C₂×D₇₉

yes

characteristic

C₂×Q₈

—

158

—

C₂×Q₈

—

158

—

Q₁₆

—

316

—

Q₁₆

—

Q₁₆

—

158

—

Q₁₆

—

158

—

Q₁₆

—

158

—

C₂×C₈

D₃₁₆

yes

characteristic

C₂×C₈

C₂²×D₇₉

yes

characteristic

C₄⋊C₄

—

316

—

C₄⋊C₄

—

316

—

C₄⋊C₄

—

316

—

C₄⋊C₄

—

158

—

C₄²

—

316

—

C₄²

D₃₁₆

yes

characteristic

C₁₆

—

Q₈

—

316

—

Q₈

—

316

—

Q₈

—

316

—

Q₈

—

158

—

C₂×C₄

—

316

—

C₂×C₄

—

316

—

C₂×C₄

—

316

—

C₂×C₄

D₆₃₂

yes

characteristic

C₂×C₄

D₆₃₂

yes

characteristic

C₂×C₄

C₂×D₃₁₆

yes

characteristic

C₈

—

100

C₈

D₄×D₇₉

yes

characteristic

101

C₈

#11929625

yes

characteristic

102

C₂²

C₂×D₆₃₂

yes

characteristic

103

C₄

—

104

C₄

—

316

—

105

C₄

—

632

—

106

C₄

—

632

—

107

C₄

Dic₆₃₂

yes

complemented

108

C₄

#14579136

yes

characteristic

109

C₄

#14579189

yes

characteristic

110

C₂

#19098759

yes

characteristic

111

C₂

C₂×Dic₆₃₂

yes

characteristic

112

C₂

#19099006

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×D₆₃₂
commutator, cosocle	C₂×C₈×C₇₉	C₂³
Frattini	C₂×C₈	C₂²×D₇₉
Fitting	C₄⋊C₁₆×C₇₉	C₂
socle, prime radical	C₂²×C₇₉	C₂×D₈
hypercenter	C₄⋊C₁₆	D₇₉
hypocenter	C₇₉	#2209
LCS	G ▷ C₂×C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄⋊C₁₆

subgroup

G/H

center

C₂²

C₂×D₆₃₂

commutator, cosocle

C₂×C₈×C₇₉

C₂³

Frattini

C₂×C₈

C₂²×D₇₉

Fitting

C₄⋊C₁₆×C₇₉

C₂

socle, prime radical

C₂²×C₇₉

C₂×D₈

hypercenter

C₄⋊C₁₆

D₇₉

hypocenter

C₇₉

#2209

LCS

G ▷ C₂×C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄⋊C₁₆

N	H ≅ G/N	type
47. C₄×C₇₉	Q₃₂	semidirect
57. C₇₉	#2209	semidirect
107. C₄	Dic₆₃₂	semidirect

H ≅ G/N

type

47. C₄×C₇₉

Q₃₂

semidirect

57. C₇₉

#2209

semidirect

107. C₄

Dic₆₃₂

semidirect

Subgroups — #23765451

Conjugacy classes of subgroups

Complements