Group #16834358 — subgroups

Subgroups — #16834358

Order 3712.

138 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 138 conjugacy classes of subgroups — too many to draw. Only its 44 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	#14272185	C₂	1	1	yes	maximal, characteristic
2	C₄×#90796	C₂	1	1	yes	maximal, characteristic
3	#14271219	C₂	1	1	yes	maximal, characteristic
4	C₂×#90796	—	2	1	no	—
5	C₄²×D₂₉	C₂²	1	1	yes	characteristic
6	#11745219	C₄	1	2	yes	—
7	#11745218	—	2	1	no	—
8	#11745218	—	2	1	no	—
9	C₄⋊#6599	—	2	1	no	—
10	C₄×#6599	C₄	1	2	yes	—
11	C₂₉×C₄⋊C₈	C₄	1	1	yes	characteristic
12	#11745168	—	2	1	no	—
13	#11745163	—	2	1	no	—
14	C₄⋊#6597	C₄	1	1	yes	characteristic
15	C₂×C₄×D₂₉	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄×D₂₉	D₄	1	1	yes	characteristic
17	C₂×C₄×D₂₉	Q₈	1	1	yes	characteristic
18	C₂×#6599	—	2	2	no	—
19	C₂×#6599	—	2	2	no	—
20	#90796	—	2	2	no	—
21	#90796	—	2	2	no	—
22	C₂×C₈×C₂₉	—	2	1	no	—
23	C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
24	C₄×Dic₂₉	C₂×C₄	1	1	yes	characteristic
25	C₄×Dic₂₉	D₄	1	1	yes	characteristic
26	C₄×Dic₂₉	D₄	1	1	yes	characteristic
27	C₂×#6597	—	2	1	no	—
28	C₂²×D₂₉	C₄⋊C₄	1	1	yes	characteristic
29	C₂×C₄×C₂₉	C₄²	1	1	yes	characteristic
30	C₂×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
31	C₂×C₄×C₂₉	C₄⋊C₄	1	1	yes	characteristic
32	C₂×Dic₂₉	C₂²⋊C₄	1	1	yes	characteristic
33	C₂×Dic₂₉	C₂²⋊C₄	1	1	yes	characteristic
34	C₂×Dic₂₉	C₄⋊C₄	1	1	yes	characteristic
35	C₄×D₂₉	—	2	1	no	—
36	C₄×D₂₉	—	2	1	no	—
37	C₄×D₂₉	—	4	1	no	—
38	C₄×D₂₉	—	4	1	no	—
39	#6599	—	2	4	no	—
40	#6599	—	4	2	no	—
41	C₈×C₂₉	—	4	1	no	—
42	#6597	—	4	1	no	—
43	#1291	—	29	1	no	maximal, Sylow
44	C₂²×C₂₉	#95	1	1	yes	characteristic
45	C₂×D₂₉	—	2	1	no	—
46	C₂×D₂₉	—	2	1	no	—
47	C₂×D₂₉	—	2	1	no	—
48	C₄×C₂₉	—	2	1	no	—
49	C₄×C₂₉	—	2	1	no	—
50	C₄×C₂₉	#104	1	1	yes	characteristic
51	C₄×C₂₉	#104	1	1	yes	characteristic
52	Dic₂₉	—	2	1	no	—
53	Dic₂₉	—	2	1	no	—
54	Dic₂₉	—	2	1	no	—
55	#432	—	29	1	no	—
56	#432	—	29	1	no	—
57	C₄×M₁₆	—	29	1	no	—
58	C₂×C₂₉	#338	1	1	yes	characteristic
59	C₂×C₂₉	#339	1	1	yes	characteristic
60	C₂×C₂₉	#344	1	1	yes	characteristic
61	D₂₉	—	4	1	no	—
62	C₂×M₁₆	—	58	1	no	—
63	C₂×C₄²	—	29	1	no	—
64	C₄⋊C₈	—	29	1	no	—
65	C₄⋊C₈	—	58	1	no	—
66	C₄⋊C₈	#1181	1	1	yes	characteristic
67	C₂²⋊C₈	—	29	2	no	—
68	C₂²⋊C₈	—	58	1	no	—
69	#97	—	58	1	no	—
70	#97	—	58	1	no	—
71	#97	—	58	1	no	—
72	C₄×C₈	—	29	2	no	—
73	C₂₉	#1291	1	1	yes	characteristic, complemented, Sylow
74	C₂²×C₄	—	29	1	no	—
75	C₂²×C₄	—	29	1	no	—
76	C₂²×C₄	—	29	1	no	—
77	M₁₆	—	58	2	no	—
78	M₁₆	—	58	2	no	—
79	C₂×C₈	—	2	1	no	—
80	C₂×C₈	—	58	2	no	—
81	C₂×C₈	—	58	2	no	—
82	C₂×C₈	—	58	1	no	—
83	C₄²	—	29	1	no	—
84	C₄²	—	29	1	no	—
85	C₄²	—	29	1	no	—
86	C₄²	C₂×#1181	1	1	yes	characteristic
87	C₂³	—	29	1	no	—
88	C₂×C₄	—	29	1	no	—
89	C₂×C₄	—	29	1	no	—
90	C₂×C₄	—	29	1	no	—
91	C₂×C₄	—	58	1	no	—
92	C₂×C₄	—	58	1	no	—
93	C₂×C₄	—	116	1	no	—
94	C₂×C₄	—	116	1	no	—
95	C₂×C₄	C₄×#1181	1	1	yes	characteristic
96	C₂×C₄	C₄⋊#1181	1	1	yes	characteristic
97	C₂×C₄	C₂²⋊#1181	1	1	yes	characteristic
98	C₈	—	4	1	no	—
99	C₈	—	58	4	no	—
100	C₈	—	116	2	no	—
101	C₈	—	116	1	no	—
102	C₂²	—	58	1	no	—
103	C₂²	—	58	1	no	—
104	C₂²	—	58	1	no	—
105	C₂²	(C₂×#1181)⋊C₄	1	1	yes	characteristic
106	C₄	—	2	1	no	—
107	C₄	—	2	1	no	—
108	C₄	—	58	1	no	—
109	C₄	—	58	1	no	—
110	C₄	—	58	1	no	—
111	C₄	#11745224	1	1	yes	characteristic
112	C₄	#11745226	1	1	yes	characteristic
113	C₂	—	116	1	no	—
114	C₂	#14272032	1	1	yes	characteristic
115	C₂	#14272033	1	1	yes	characteristic
116	C₂	#14272046	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14272185

C₂

yes

maximal, characteristic

C₄×#90796

C₂

yes

maximal, characteristic

#14271219

C₂

yes

maximal, characteristic

C₂×#90796

—

C₄²×D₂₉

C₂²

yes

characteristic

#11745219

C₄

yes

—

—

—

—

C₄

yes

—

C₂₉×C₄⋊C₈

C₄

yes

—

—

C₄

yes

characteristic

C₂×C₄×D₂₉

C₂×C₄

yes

characteristic

C₂×C₄×D₂₉

D₄

yes

characteristic

C₂×C₄×D₂₉

Q₈

yes

—

—

—

—

C₂×C₈×C₂₉

—

C₄²×C₂₉

C₂×C₄

yes

characteristic

C₄×Dic₂₉

C₂×C₄

yes

characteristic

C₄×Dic₂₉

D₄

yes

characteristic

C₄×Dic₂₉

D₄

yes

characteristic

C₂×#6597

—

C₂²×D₂₉

C₄⋊C₄

yes

characteristic

C₂×C₄×C₂₉

C₄²

yes

characteristic

C₂×C₄×C₂₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₂₉

C₄⋊C₄

yes

characteristic

C₂×Dic₂₉

C₂²⋊C₄

yes

characteristic

C₂×Dic₂₉

C₂²⋊C₄

yes

characteristic

C₂×Dic₂₉

C₄⋊C₄

yes

characteristic

C₄×D₂₉

—

C₄×D₂₉

—

C₄×D₂₉

—

C₄×D₂₉

—

#6599

—

#6599

—

C₈×C₂₉

—

—

—

C₂²×C₂₉

yes

C₂×D₂₉

—

C₂×D₂₉

—

C₂×D₂₉

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

yes

C₄×C₂₉

yes

Dic₂₉

—

Dic₂₉

—

Dic₂₉

—

#432

—

#432

—

C₄×M₁₆

—

C₂×C₂₉

yes

C₂×C₂₉

yes

C₂×C₂₉

yes

D₂₉

—

C₂×M₁₆

—

C₂×C₄²

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

#1181

yes

characteristic

C₂²⋊C₈

—

C₂²⋊C₈

—

#97

—

#97

—

#97

—

C₄×C₈

—

C₂₉

#1291

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄²

—

C₄²

—

C₄²

—

C₄²

C₂×#1181

yes

characteristic

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

116

—

C₂×C₄

—

116

—

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

C₂²⋊#1181

yes

characteristic

C₈

—

C₈

—

100

C₈

—

116

—

101

C₈

—

116

—

102

C₂²

—

103

C₂²

—

104

C₂²

—

105

C₂²

(C₂×#1181)⋊C₄

yes

characteristic

106

C₄

—

107

C₄

—

108

C₄

—

109

C₄

—

110

C₄

—

111

C₄

#11745224

yes

characteristic

112

C₄

#11745226

yes

characteristic

113

C₂

—

116

—

114

C₂

#14272032

yes

characteristic

115

C₂

#14272033

yes

characteristic

116

C₂

#14272046

yes

characteristic

	subgroup	G/H
center	C₂²	(C₂×#1181)⋊C₄
commutator	C₂×C₄×C₂₉	C₄²
Frattini	C₄²	C₂×#1181
Fitting	C₂₉×C₄⋊C₈	C₄
socle	C₂²×C₂₉	#95
prime radical	C₂²×D₂₉	C₄⋊C₄
cosocle	C₄²×D₂₉	C₂²
hypercenter	C₄⋊C₈	#1181
hypocenter	C₂₉	#1291
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄⋊C₈

subgroup

G/H

center

C₂²

(C₂×#1181)⋊C₄

commutator

C₂×C₄×C₂₉

C₄²

Frattini

C₄²

C₂×#1181

Fitting

C₂₉×C₄⋊C₈

C₄

socle

C₂²×C₂₉

#95

prime radical

C₂²×D₂₉

C₄⋊C₄

cosocle

C₄²×D₂₉

C₂²

C₄⋊C₈

C₂₉

G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄⋊C₈

N	H ≅ G/N	type
73. C₂₉	#1291	semidirect

H ≅ G/N

type

73. C₂₉

#1291

semidirect

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

subgroup	index
#14272185	2
C₄×#90796	2
#14271219	2
#1291	29

subgroup

index

Subgroups — #16834358

Conjugacy classes of subgroups

Complements

Maximal subgroups