Group #16818862 — subgroups

Subgroups — #16818862

Order 3712.

156 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 156 conjugacy classes of subgroups — too many to draw. Only its 61 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	#14271543	C₂	1	1	yes	maximal, characteristic
2	#14271448	C₂	1	2	yes	maximal
3	#14270916	C₂	1	1	yes	maximal, characteristic
4	#14270910	C₂	1	2	yes	maximal
5	C₈×Q₈×C₂₉	C₂	1	1	yes	maximal, characteristic
6	C₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic
7	C₂×Dic₁₁₆	—	2	1	no	—
8	C₂×Dic₁₁₆	—	2	1	no	—
9	#11745231	C₂²	1	2	yes	—
10	C₂₉×C₄⋊C₈	—	2	1	no	—
11	C₂₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
12	C₄×C₈×C₂₉	—	2	1	no	—
13	C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
14	#11745183	—	2	2	no	—
15	#11745156	—	2	2	no	—
16	C₄⋊#6597	C₂²	1	2	yes	—
17	C₂×Q₈×C₂₉	D₄	1	1	yes	characteristic
18	C₂×Dic₅₈	—	2	2	no	—
19	C₂×C₈×C₂₉	—	2	1	no	—
20	C₂×C₈×C₂₉	D₄	1	1	yes	characteristic
21	C₂×C₈×C₂₉	D₄	1	1	yes	characteristic
22	C₄⋊C₄×C₂₉	—	2	1	no	—
23	C₄⋊C₄×C₂₉	D₄	1	1	yes	characteristic
24	C₄²×C₂₉	—	2	1	no	—
25	C₄²×C₂₉	C₂³	1	1	yes	characteristic
26	C₄⋊Dic₂₉	—	2	2	no	—
27	C₄⋊Dic₂₉	—	2	2	no	—
28	C₂×#6597	—	2	2	no	—
29	Dic₁₁₆	—	4	2	no	—
30	Dic₁₁₆	—	4	2	no	—
31	Q₈×C₂₉	—	2	1	no	—
32	Q₈×C₂₉	Q₁₆	1	2	yes	complemented
33	C₂×C₄×C₂₉	—	2	1	no	—
34	C₂×C₄×C₂₉	—	2	1	no	—
35	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
36	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
37	C₂×C₄×C₂₉	#41	1	1	yes	characteristic
38	C₂×Dic₂₉	—	4	2	no	—
39	Dic₅₈	—	4	2	no	—
40	Dic₅₈	—	4	2	no	—
41	C₈×C₂₉	—	2	1	no	—
42	C₈×C₂₉	—	4	1	no	—
43	C₈×C₂₉	SD₁₆	1	2	yes	—
44	#6597	—	4	2	no	—
45	#1670	—	29	1	no	maximal, Sylow
46	C₂²×C₂₉	#121	1	1	yes	characteristic
47	C₄×C₂₉	—	2	2	no	—
48	C₄×C₂₉	—	2	1	no	—
49	C₄×C₂₉	—	4	1	no	—
50	C₄×C₂₉	C₂×SD₁₆	1	1	yes	characteristic
51	C₄×C₂₉	C₂×Q₁₆	1	1	yes	characteristic
52	C₄×C₂₉	#135	1	1	yes	characteristic
53	C₄×C₂₉	AGL(1,ℤ/8)	1	1	yes	characteristic
54	Dic₂₉	—	8	2	no	—
55	#494	—	29	1	no	—
56	#475	—	29	2	no	—
57	C₈×Q₈	D₂₉	1	1	yes	characteristic
58	#335	—	29	1	no	—
59	#332	—	29	2	no	—
60	C₂×C₂₉	#460	1	1	yes	characteristic
61	C₂×C₂₉	#467	1	1	yes	characteristic
62	C₂×C₂₉	#473	1	1	yes	characteristic
63	C₂×Q₁₆	—	58	1	no	—
64	C₂×Q₁₆	—	58	1	no	—
65	C₄⋊Q₈	—	29	2	no	—
66	C₄×Q₈	C₂×D₂₉	1	1	yes	characteristic
67	#106	—	58	2	no	—
68	C₄⋊C₈	—	2	1	no	—
69	C₄⋊C₈	—	29	2	no	—
70	C₄⋊C₈	C₂×D₂₉	1	1	yes	characteristic
71	#103	—	58	2	no	—
72	C₄×C₈	—	2	1	no	—
73	C₄×C₈	C₂×D₂₉	1	1	yes	characteristic
74	C₂₉	#1670	1	1	yes	characteristic, complemented, Sylow
75	C₂×Q₈	—	58	2	no	—
76	C₂×Q₈	D₁₁₆	1	1	yes	characteristic
77	Q₁₆	—	116	2	no	—
78	Q₁₆	—	116	2	no	—
79	C₂×C₈	—	2	1	no	—
80	C₂×C₈	—	58	2	no	—
81	C₂×C₈	C₂²⋊D₂₉	1	1	yes	characteristic
82	C₂×C₈	C₂²⋊D₂₉	1	1	yes	characteristic
83	C₄⋊C₄	—	2	1	no	—
84	C₄⋊C₄	—	58	2	no	—
85	C₄⋊C₄	—	58	2	no	—
86	C₄⋊C₄	D₁₁₆	1	1	yes	characteristic
87	C₄²	—	2	1	no	—
88	C₄²	C₂²×D₂₉	1	1	yes	characteristic
89	Q₈	—	2	1	no	—
90	Q₈	—	116	2	no	—
91	Q₈	—	116	2	no	—
92	Q₈	Dic₁₁₆	1	2	yes	complemented
93	C₂×C₄	—	2	1	no	—
94	C₂×C₄	—	2	1	no	—
95	C₂×C₄	—	116	2	no	—
96	C₂×C₄	C₂×D₁₁₆	1	1	yes	characteristic
97	C₂×C₄	#90805	1	1	yes	characteristic
98	C₂×C₄	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
99	C₈	—	2	1	no	—
100	C₈	—	4	1	no	—
101	C₈	—	116	2	no	—
102	C₈	#90784	1	2	yes	—
103	C₂²	#11745292	1	1	yes	characteristic
104	C₄	—	2	2	no	—
105	C₄	—	2	1	no	—
106	C₄	—	4	1	no	—
107	C₄	—	232	2	no	—
108	C₄	#11745266	1	1	yes	characteristic
109	C₄	C₂×Dic₁₁₆	1	1	yes	characteristic
110	C₄	C₂×#90784	1	1	yes	characteristic
111	C₄	#11745311	1	1	yes	characteristic
112	C₂	#14271363	1	1	yes	characteristic
113	C₂	#14271404	1	1	yes	characteristic
114	C₂	#14271438	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14271543

C₂

yes

maximal, characteristic

#14271448

C₂

yes

maximal

#14270916

C₂

yes

maximal, characteristic

#14270910

C₂

yes

maximal

C₈×Q₈×C₂₉

C₂

yes

maximal, characteristic

C₄×Q₈×C₂₉

C₂²

yes

characteristic

C₂×Dic₁₁₆

—

C₂×Dic₁₁₆

—

#11745231

C₂²

yes

—

C₂₉×C₄⋊C₈

—

C₂₉×C₄⋊C₈

C₂²

yes

characteristic

C₄×C₈×C₂₉

—

C₄×C₈×C₂₉

C₂²

yes

—

—

C₂²

yes

—

C₂×Q₈×C₂₉

D₄

yes

characteristic

C₂×Dic₅₈

—

C₂×C₈×C₂₉

—

C₂×C₈×C₂₉

D₄

yes

characteristic

C₂×C₈×C₂₉

D₄

yes

characteristic

C₄⋊C₄×C₂₉

—

C₄⋊C₄×C₂₉

D₄

yes

characteristic

C₄²×C₂₉

—

C₄²×C₂₉

C₂³

yes

characteristic

C₄⋊Dic₂₉

—

C₄⋊Dic₂₉

—

C₂×#6597

—

Dic₁₁₆

—

Dic₁₁₆

—

Q₈×C₂₉

—

Q₈×C₂₉

Q₁₆

yes

complemented

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

#41

yes

characteristic

C₂×Dic₂₉

—

Dic₅₈

—

Dic₅₈

—

C₈×C₂₉

—

C₈×C₂₉

—

C₈×C₂₉

SD₁₆

yes

—

—

—

C₂²×C₂₉

yes

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

C₂×SD₁₆

yes

characteristic

C₄×C₂₉

C₂×Q₁₆

yes

C₄×C₂₉

yes

C₄×C₂₉

yes

Dic₂₉

—

#494

—

#475

—

C₈×Q₈

D₂₉

yes

characteristic

#335

—

#332

—

C₂×C₂₉

yes

C₂×C₂₉

yes

C₂×C₂₉

yes

C₂×Q₁₆

—

C₂×Q₁₆

—

C₄⋊Q₈

—

C₄×Q₈

C₂×D₂₉

yes

characteristic

#106

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

C₂×D₂₉

yes

characteristic

#103

—

C₄×C₈

—

C₄×C₈

C₂×D₂₉

yes

characteristic

C₂₉

#1670

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

D₁₁₆

yes

characteristic

Q₁₆

—

116

—

Q₁₆

—

116

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂²⋊D₂₉

yes

characteristic

C₂×C₈

C₂²⋊D₂₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

D₁₁₆

yes

characteristic

C₄²

—

C₄²

C₂²×D₂₉

yes

characteristic

Q₈

—

Q₈

—

116

—

Q₈

—

116

—

Q₈

Dic₁₁₆

yes

complemented

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

116

—

C₂×C₄

C₂×D₁₁₆

yes

characteristic

C₂×C₄

#90805

yes

characteristic

C₂×C₄

C₂×C₂²⋊D₂₉

yes

characteristic

C₈

—

100

C₈

—

101

C₈

—

116

—

102

C₈

#90784

yes

—

103

C₂²

#11745292

yes

characteristic

104

C₄

—

105

C₄

—

106

C₄

—

107

C₄

—

232

—

108

C₄

#11745266

yes

characteristic

109

C₄

C₂×Dic₁₁₆

yes

characteristic

110

C₄

C₂×#90784

yes

characteristic

111

C₄

#11745311

yes

characteristic

112

C₂

#14271363

yes

characteristic

113

C₂

#14271404

yes

characteristic

114

C₂

#14271438

yes

characteristic

	subgroup	G/H
center	C₂²	#11745292
commutator, cosocle	C₄²×C₂₉	C₂³
Frattini	C₄²	C₂²×D₂₉
Fitting	C₈×Q₈×C₂₉	C₂
socle, prime radical	C₂²×C₂₉	#121
hypercenter	C₈×Q₈	D₂₉
hypocenter	C₂₉	#1670
LCS	G ▷ C₄²×C₂₉ ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈×Q₈

subgroup

G/H

center

C₂²

#11745292

commutator, cosocle

C₄²×C₂₉

C₂³

Frattini

C₄²

C₂²×D₂₉

Fitting

C₈×Q₈×C₂₉

C₂

socle, prime radical

C₂²×C₂₉

#121

hypercenter

C₈×Q₈

D₂₉

hypocenter

C₂₉

#1670

LCS

G ▷ C₄²×C₂₉ ▷ C₂²×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₈×Q₈

N	H ≅ G/N	type
32. Q₈×C₂₉	Q₁₆	semidirect
74. C₂₉	#1670	semidirect
92. Q₈	Dic₁₁₆	semidirect

H ≅ G/N

type

32. Q₈×C₂₉

Q₁₆

semidirect

74. C₂₉

#1670

semidirect

92. Q₈

Dic₁₁₆

semidirect

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

subgroup	index
#14271543	2
#14271448	2
#14270916	2
#14270910	2
C₈×Q₈×C₂₉	2
#1670	29

subgroup

index

C₈×Q₈×C₂₉

Subgroups — #16818862

Conjugacy classes of subgroups

Complements

Maximal subgroups