Group #16818638 — subgroups

Subgroups — #16818638

Order 3712.

218 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 53 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	#14271879	C₂	1	1	yes	maximal, characteristic
2	#14271542	C₂	1	1	yes	maximal, characteristic, complemented
3	#14271454	C₂	1	2	yes	maximal, complemented
4	#14270890	C₂	1	2	yes	maximal, complemented
5	C₂₉×#333	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
7	#11745309	—	2	2	no	—
8	C₂×#90785	—	2	2	no	—
9	#11745257	—	2	2	no	—
10	#11745254	—	2	2	no	—
11	C₄×D₁₁₆	C₂²	1	2	yes	—
12	#11745231	C₂²	1	1	yes	characteristic
13	C₂₉×C₄⋊C₈	C₂²	1	2	yes	—
14	#11745169	—	2	2	no	—
15	#11745165	—	2	2	no	—
16	C₄×#6597	C₂²	1	1	yes	characteristic
17	C₂×Q₈×C₂₉	D₄	1	2	yes	—
18	C₂×D₁₁₆	—	2	2	no	—
19	C₂×D₁₁₆	D₄	1	2	yes	—
20	C₂×C₄×D₂₉	—	2	2	no	—
21	C₂×Dic₅₈	—	2	1	no	—
22	C₂×C₈×C₂₉	—	2	2	no	—
23	C₄⋊C₄×C₂₉	—	2	2	no	—
24	C₄²×C₂₉	C₂³	1	1	yes	characteristic
25	#90785	—	4	4	no	—
26	#90781	—	2	4	no	—
27	#90781	—	2	2	no	—
28	C₄⋊Dic₂₉	—	2	2	no	—
29	C₄⋊Dic₂₉	D₄	1	2	yes	—
30	C₄×Dic₂₉	—	2	2	no	—
31	C₂×#6597	—	2	1	no	—
32	C₂²×D₂₉	—	2	2	no	—
33	Q₈×C₂₉	—	4	2	no	—
34	C₂×C₄×C₂₉	—	2	2	no	—
35	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
36	C₂×C₄×C₂₉	C₂×D₄	1	2	yes	—
37	C₂×Dic₂₉	—	2	2	no	—
38	C₂×Dic₂₉	—	4	1	no	—
39	D₁₁₆	—	2	2	no	—
40	D₁₁₆	—	2	2	no	—
41	D₁₁₆	—	8	2	no	—
42	C₄×D₂₉	—	4	2	no	—
43	C₄×D₂₉	—	4	2	no	—
44	Dic₅₈	—	4	2	no	—
45	C₈×C₂₉	—	4	2	no	—
46	#6597	—	2	2	no	—
47	#1634	—	29	1	no	maximal, Sylow
48	C₂²×C₂₉	#120	1	1	yes	characteristic
49	C₂×D₂₉	—	4	2	no	—
50	C₂×D₂₉	—	4	2	no	—
51	C₂×D₂₉	—	4	2	no	—
52	C₄×C₂₉	—	2	1	no	—
53	C₄×C₂₉	—	4	2	no	—
54	C₄×C₂₉	#135	1	2	yes	—
55	C₄×C₂₉	#137	1	2	yes	—
56	Dic₂₉	—	4	2	no	—
57	Dic₂₉	—	8	1	no	—
58	#555	—	29	1	no	—
59	#494	—	29	1	no	—
60	#476	—	29	2	no	—
61	#333	D₂₉	1	1	yes	characteristic, complemented
62	D₄⋊C₈	—	29	2	no	—
63	C₂×C₂₉	#452	1	2	yes	—
64	C₂×C₂₉	#453	1	1	yes	characteristic
65	D₂₉	—	8	2	no	—
66	C₂×Q₁₆	—	58	2	no	—
67	C₄⋊Q₈	—	29	1	no	—
68	C₄⋊Q₈	C₂×D₂₉	1	1	yes	characteristic
69	#124	—	58	2	no	—
70	#121	—	58	2	no	—
71	C₄×D₄	—	29	2	no	—
72	#117	—	58	2	no	—
73	#106	—	58	2	no	—
74	C₄⋊C₈	C₂×D₂₉	1	2	yes	—
75	#102	—	58	2	no	—
76	C₄×C₈	—	29	1	no	—
77	C₂₉	#1634	1	1	yes	characteristic, complemented, Sylow
78	C₂×Q₈	—	58	1	no	—
79	C₂×Q₈	D₁₁₆	1	2	yes	—
80	C₂×D₄	—	29	2	no	—
81	C₂×D₄	—	58	2	no	—
82	C₂²×C₄	—	58	2	no	—
83	Q₁₆	—	116	4	no	—
84	C₂×C₈	—	2	2	no	—
85	C₂×C₈	—	58	1	no	—
86	C₄⋊C₄	—	2	2	no	—
87	C₄⋊C₄	—	29	2	no	—
88	C₄⋊C₄	—	58	2	no	—
89	C₂²⋊C₄	—	58	4	no	—
90	C₂²⋊C₄	—	58	2	no	—
91	C₄²	—	58	2	no	—
92	C₄²	C₂²×D₂₉	1	1	yes	characteristic
93	C₂³	—	58	2	no	—
94	Q₈	—	4	2	no	—
95	Q₈	—	116	2	no	—
96	D₄	—	58	2	no	—
97	D₄	—	58	2	no	—
98	D₄	—	232	2	no	—
99	C₂×C₄	—	2	2	no	—
100	C₂×C₄	—	58	2	no	—
101	C₂×C₄	—	116	2	no	—
102	C₂×C₄	—	116	2	no	—
103	C₂×C₄	—	116	1	no	—
104	C₂×C₄	C₂×D₁₁₆	1	1	yes	characteristic
105	C₂×C₄	D₄×D₂₉	1	2	yes	—
106	C₈	—	4	2	no	—
107	C₈	—	58	2	no	—
108	C₂²	—	116	2	no	—
109	C₂²	—	116	2	no	—
110	C₂²	—	116	2	no	—
111	C₂²	#11745244	1	1	yes	characteristic
112	C₄	—	2	1	no	—
113	C₄	—	4	2	no	—
114	C₄	—	116	2	no	—
115	C₄	—	232	1	no	—
116	C₄	#11745278	1	2	yes	—
117	C₄	#11745280	1	2	yes	—
118	C₂	—	232	2	no	—
119	C₂	#14271328	1	2	yes	—
120	C₂	#14271333	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14271879

C₂

yes

maximal, characteristic

#14271542

C₂

yes

maximal, characteristic, complemented

#14271454

C₂

yes

maximal, complemented

#14270890

C₂

yes

maximal, complemented

C₂₉×#333

C₂

yes

maximal, characteristic, complemented

C₂₉×C₄⋊Q₈

C₂²

yes

—

—

—

—

C₄×D₁₁₆

C₂²

yes

—

#11745231

C₂²

yes

characteristic

C₂₉×C₄⋊C₈

C₂²

yes

—

#11745169

—

#11745165

—

C₄×#6597

C₂²

yes

characteristic

C₂×Q₈×C₂₉

D₄

yes

—

C₂×D₁₁₆

—

C₂×D₁₁₆

D₄

yes

—

C₂×C₄×D₂₉

—

C₂×Dic₅₈

—

C₂×C₈×C₂₉

—

C₄⋊C₄×C₂₉

—

C₄²×C₂₉

C₂³

yes

—

—

—

C₄⋊Dic₂₉

—

C₄⋊Dic₂₉

D₄

yes

—

C₄×Dic₂₉

—

C₂×#6597

—

C₂²×D₂₉

—

Q₈×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

C₂×D₄

yes

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

D₁₁₆

—

D₁₁₆

—

D₁₁₆

—

C₄×D₂₉

—

C₄×D₂₉

—

Dic₅₈

—

C₈×C₂₉

—

—

—

C₂²×C₂₉

yes

C₂×D₂₉

—

C₂×D₂₉

—

C₂×D₂₉

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

#135

yes

—

C₄×C₂₉

#137

yes

—

Dic₂₉

—

Dic₂₉

—

—

—

—

D₂₉

yes

characteristic, complemented

D₄⋊C₈

—

C₂×C₂₉

#452

yes

—

C₂×C₂₉

#453

yes

characteristic

D₂₉

—

C₂×Q₁₆

—

C₄⋊Q₈

—

C₄⋊Q₈

C₂×D₂₉

yes

characteristic

#124

—

#121

—

C₄×D₄

—

#117

—

#106

—

C₄⋊C₈

C₂×D₂₉

yes

—

#102

—

C₄×C₈

—

C₂₉

#1634

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

D₁₁₆

yes

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

Q₁₆

—

116

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

C₂²×D₂₉

yes

characteristic

C₂³

—

Q₈

—

Q₈

—

116

—

D₄

—

D₄

—

D₄

—

232

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

116

—

102

C₂×C₄

—

116

—

103

C₂×C₄

—

116

—

104

C₂×C₄

C₂×D₁₁₆

yes

characteristic

105

C₂×C₄

D₄×D₂₉

yes

—

106

C₈

—

107

C₈

—

108

C₂²

—

116

—

109

C₂²

—

116

—

110

C₂²

—

116

—

111

C₂²

#11745244

yes

characteristic

112

C₄

—

113

C₄

—

114

C₄

—

116

—

115

C₄

—

232

—

116

C₄

#11745278

yes

—

117

C₄

#11745280

yes

—

118

C₂

—

232

—

119

C₂

#14271328

yes

—

120

C₂

#14271333

yes

characteristic

	subgroup	G/H
center	C₂²	#11745244
commutator, cosocle	C₄²×C₂₉	C₂³
Frattini	C₄²	C₂²×D₂₉
Fitting	C₂₉×#333	C₂
socle	C₂²×C₂₉	#120
prime radical	#14271879	C₂
hypercenter	#333	D₂₉
hypocenter	C₂₉	#1634
LCS	G ▷ C₄²×C₂₉ ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #333

subgroup

G/H

center

C₂²

#11745244

commutator, cosocle

C₄²×C₂₉

C₂³

Frattini

C₄²

C₂²×D₂₉

Fitting

C₂₉×#333

C₂

C₂²×C₂₉

C₂

D₂₉

C₂₉

G ▷ C₄²×C₂₉ ▷ C₂²×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #333

N	H ≅ G/N	type
2. #14271542	C₂	semidirect
3. #14271454	C₂	semidirect
4. #14270890	C₂	semidirect
5. C₂₉×#333	C₂	semidirect
61. #333	D₂₉	semidirect
77. C₂₉	#1634	semidirect

H ≅ G/N

type

2. #14271542

C₂

semidirect

3. #14271454

C₂

semidirect

4. #14270890

C₂

semidirect

5. C₂₉×#333

C₂

semidirect

61. #333

D₂₉

semidirect

77. C₂₉

#1634

semidirect

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

subgroup	index
#14271879	2
#14271542	2
#14271454	2
#14270890	2
C₂₉×#333	2
#1634	29

subgroup

index

C₂₉×#333

Subgroups — #16818638

Conjugacy classes of subgroups

Complements

Maximal subgroups