Group #16818573 — subgroups

Subgroups — #16818573

Order 3712.

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

normal subgroups only

This group has 240 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, complemented
2	#14271355	C₂	1	2	yes	maximal, complemented
3	#14270912	C₂	1	1	yes	maximal, characteristic, complemented
4	#14270892	C₂	1	2	yes	maximal, complemented
5	C₂₉×#492	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×SD₁₆×C₂₉	—	2	2	no	—
7	C₂₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
8	C₂₉×#127	C₂²	1	1	yes	characteristic
9	#11745309	—	2	2	no	—
10	C₂×#90782	—	2	2	no	—
11	#11745257	—	2	2	no	—
12	#11745254	—	2	2	no	—
13	C₄×D₁₁₆	C₂²	1	2	yes	—
14	C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
15	#11745180	—	2	2	no	—
16	C₄⋊#6597	C₂²	1	2	yes	—
17	C₂×Q₈×C₂₉	D₄	1	2	yes	—
18	C₂×D₄×C₂₉	—	2	2	no	—
19	C₂×D₄×C₂₉	—	2	1	no	—
20	C₂×D₁₁₆	—	2	2	no	—
21	C₂×D₁₁₆	D₄	1	2	yes	—
22	C₂×C₄×D₂₉	—	2	2	no	—
23	SD₁₆×C₂₉	—	4	4	no	—
24	C₂×C₈×C₂₉	—	2	1	no	—
25	C₄⋊C₄×C₂₉	—	2	2	no	—
26	C₄²×C₂₉	C₂³	1	1	yes	characteristic
27	#90782	—	4	4	no	—
28	#90781	—	2	4	no	—
29	#90781	—	2	2	no	—
30	C₄⋊Dic₂₉	D₄	1	2	yes	—
31	C₄×Dic₂₉	—	2	2	no	—
32	C₂×#6597	—	2	2	no	—
33	C₂³×C₂₉	—	4	1	no	—
34	C₂²×D₂₉	—	2	2	no	—
35	Q₈×C₂₉	—	4	2	no	—
36	D₄×C₂₉	—	4	2	no	—
37	D₄×C₂₉	—	4	2	no	—
38	D₄×C₂₉	—	4	2	no	—
39	C₂×C₄×C₂₉	—	2	2	no	—
40	C₂×C₄×C₂₉	C₂×D₄	1	2	yes	—
41	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
42	C₂×Dic₂₉	—	2	2	no	—
43	D₁₁₆	—	2	2	no	—
44	D₁₁₆	—	2	2	no	—
45	D₁₁₆	—	8	2	no	—
46	C₄×D₂₉	—	4	2	no	—
47	C₄×D₂₉	—	4	2	no	—
48	C₈×C₂₉	—	2	2	no	—
49	#6597	—	4	2	no	—
50	#1624	—	29	1	no	maximal, Sylow
51	C₂²×C₂₉	—	8	2	no	—
52	C₂²×C₂₉	—	8	1	no	—
53	C₂²×C₂₉	#120	1	1	yes	characteristic
54	C₂×D₂₉	—	4	2	no	—
55	C₂×D₂₉	—	4	2	no	—
56	C₂×D₂₉	—	4	2	no	—
57	C₄×C₂₉	—	2	1	no	—
58	C₄×C₂₉	—	4	2	no	—
59	C₄×C₂₉	#135	1	2	yes	—
60	C₄×C₂₉	AGL(1,ℤ/8)	1	2	yes	—
61	Dic₂₉	—	4	2	no	—
62	#555	—	29	1	no	—
63	#492	D₂₉	1	1	yes	characteristic, complemented
64	#459	—	29	2	no	—
65	#333	—	29	1	no	—
66	D₄⋊C₈	—	29	2	no	—
67	C₂×C₂₉	—	16	1	no	—
68	C₂×C₂₉	#449	1	2	yes	—
69	C₂×C₂₉	#453	1	1	yes	characteristic
70	D₂₉	—	8	2	no	—
71	C₂×SD₁₆	—	2	2	no	—
72	C₂×D₈	—	58	2	no	—
73	C₄⋊Q₈	C₂×D₂₉	1	1	yes	characteristic
74	#127	C₂×D₂₉	1	1	yes	characteristic
75	#124	—	58	2	no	—
76	#121	—	58	2	no	—
77	C₄×D₄	—	29	2	no	—
78	#117	—	58	2	no	—
79	C₄⋊C₈	—	29	2	no	—
80	#102	—	58	2	no	—
81	C₄×C₈	C₂×D₂₉	1	1	yes	characteristic
82	C₂₉	#1624	1	1	yes	characteristic, complemented, Sylow
83	C₂×Q₈	C₂²⋊D₂₉	1	2	yes	—
84	C₂×D₄	—	2	2	no	—
85	C₂×D₄	—	2	1	no	—
86	C₂×D₄	—	29	2	no	—
87	C₂×D₄	—	58	2	no	—
88	C₂²×C₄	—	58	2	no	—
89	SD₁₆	—	4	4	no	—
90	D₈	—	116	4	no	—
91	C₂×C₈	—	2	1	no	—
92	C₂×C₈	—	58	2	no	—
93	C₄⋊C₄	—	2	2	no	—
94	C₄⋊C₄	—	29	2	no	—
95	C₂²⋊C₄	—	58	4	no	—
96	C₂²⋊C₄	—	58	2	no	—
97	C₄²	—	58	2	no	—
98	C₄²	C₂²×D₂₉	1	1	yes	characteristic
99	C₂³	—	4	1	no	—
100	C₂³	—	58	2	no	—
101	Q₈	—	4	2	no	—
102	D₄	—	4	2	no	—
103	D₄	—	4	2	no	—
104	D₄	—	4	2	no	—
105	D₄	—	58	2	no	—
106	D₄	—	58	2	no	—
107	D₄	—	232	2	no	—
108	C₂×C₄	—	2	2	no	—
109	C₂×C₄	—	58	2	no	—
110	C₂×C₄	—	116	2	no	—
111	C₂×C₄	—	116	2	no	—
112	C₂×C₄	D₄×D₂₉	1	2	yes	—
113	C₂×C₄	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
114	C₈	—	2	2	no	—
115	C₈	—	116	2	no	—
116	C₂²	—	8	2	no	—
117	C₂²	—	8	1	no	—
118	C₂²	—	116	2	no	—
119	C₂²	—	116	2	no	—
120	C₂²	—	116	2	no	—
121	C₂²	#11745299	1	1	yes	characteristic
122	C₄	—	2	1	no	—
123	C₄	—	4	2	no	—
124	C₄	—	116	2	no	—
125	C₄	#11745276	1	2	yes	—
126	C₄	#11745278	1	2	yes	—
127	C₂	—	16	1	no	—
128	C₂	—	232	2	no	—
129	C₂	#14271307	1	2	yes	—
130	C₂	#14271330	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14271879

C₂

yes

maximal, characteristic, complemented

#14271355

C₂

yes

maximal, complemented

#14270912

C₂

yes

maximal, characteristic, complemented

#14270892

C₂

yes

maximal, complemented

C₂₉×#492

C₂

yes

maximal, characteristic, complemented

C₂×SD₁₆×C₂₉

—

C₂₉×C₄⋊Q₈

C₂²

yes

characteristic

C₂₉×#127

C₂²

yes

—

—

—

—

C₄×D₁₁₆

C₂²

yes

—

C₄×C₈×C₂₉

C₂²

yes

characteristic

#11745180

—

C₄⋊#6597

C₂²

yes

—

C₂×Q₈×C₂₉

D₄

yes

—

C₂×D₄×C₂₉

—

C₂×D₄×C₂₉

—

C₂×D₁₁₆

—

C₂×D₁₁₆

D₄

yes

—

C₂×C₄×D₂₉

—

SD₁₆×C₂₉

—

C₂×C₈×C₂₉

—

C₄⋊C₄×C₂₉

—

C₄²×C₂₉

C₂³

yes

—

—

—

C₄⋊Dic₂₉

D₄

yes

—

C₄×Dic₂₉

—

C₂×#6597

—

C₂³×C₂₉

—

C₂²×D₂₉

—

Q₈×C₂₉

—

D₄×C₂₉

—

D₄×C₂₉

—

D₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₂×D₄

yes

—

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×Dic₂₉

—

D₁₁₆

—

D₁₁₆

—

D₁₁₆

—

C₄×D₂₉

—

C₄×D₂₉

—

C₈×C₂₉

—

#6597

—

#1624

—

maximal, Sylow

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

#120

yes

characteristic

C₂×D₂₉

—

C₂×D₂₉

—

C₂×D₂₉

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

#135

yes

—

C₄×C₂₉

AGL(1,ℤ/8)

yes

—

Dic₂₉

—

#555

—

#492

D₂₉

yes

characteristic, complemented

#459

—

#333

—

D₄⋊C₈

—

C₂×C₂₉

—

C₂×C₂₉

#449

yes

—

C₂×C₂₉

#453

yes

characteristic

D₂₉

—

C₂×SD₁₆

—

C₂×D₈

—

C₄⋊Q₈

C₂×D₂₉

yes

characteristic

#127

C₂×D₂₉

yes

characteristic

#124

—

#121

—

C₄×D₄

—

#117

—

C₄⋊C₈

—

#102

—

C₄×C₈

C₂×D₂₉

yes

characteristic

C₂₉

#1624

yes

characteristic, complemented, Sylow

C₂×Q₈

C₂²⋊D₂₉

yes

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

SD₁₆

—

D₈

—

116

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

C₂²×D₂₉

yes

characteristic

C₂³

—

100

C₂³

—

101

Q₈

—

102

D₄

—

103

D₄

—

104

D₄

—

105

D₄

—

106

D₄

—

107

D₄

—

232

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

116

—

111

C₂×C₄

—

116

—

112

C₂×C₄

D₄×D₂₉

yes

—

113

C₂×C₄

C₂×C₂²⋊D₂₉

yes

characteristic

114

C₈

—

115

C₈

—

116

—

116

C₂²

—

117

C₂²

—

118

C₂²

—

116

—

119

C₂²

—

116

—

120

C₂²

—

116

—

121

C₂²

#11745299

yes

characteristic

122

C₄

—

123

C₄

—

124

C₄

—

116

—

125

C₄

#11745276

yes

—

126

C₄

#11745278

yes

—

127

C₂

—

128

C₂

—

232

—

129

C₂

#14271307

yes

—

130

C₂

#14271330

yes

characteristic

	subgroup	G/H
center	C₂²	#11745299
commutator, cosocle	C₄²×C₂₉	C₂³
Frattini	C₄²	C₂²×D₂₉
Fitting	C₂₉×#492	C₂
socle	C₂²×C₂₉	#120
hypercenter	#492	D₂₉
hypocenter	C₂₉	#1624
LCS	G ▷ C₄²×C₂₉ ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #492

subgroup

G/H

center

C₂²

#11745299

commutator, cosocle

C₄²×C₂₉

C₂³

Frattini

C₄²

C₂²×D₂₉

Fitting

C₂₉×#492

C₂

C₂²×C₂₉

D₂₉

C₂₉

G ▷ C₄²×C₂₉ ▷ C₂²×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #492

N	H ≅ G/N	type
1. #14271879	C₂	semidirect
2. #14271355	C₂	semidirect
3. #14270912	C₂	semidirect
4. #14270892	C₂	semidirect
5. C₂₉×#492	C₂	semidirect
63. #492	D₂₉	semidirect
82. C₂₉	#1624	semidirect

H ≅ G/N

type

1. #14271879

C₂

semidirect

2. #14271355

C₂

semidirect

3. #14270912

C₂

semidirect

4. #14270892

C₂

semidirect

5. C₂₉×#492

C₂

semidirect

63. #492

D₂₉

semidirect

82. C₂₉

#1624

semidirect

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

subgroup	index
#14271879	2
#14271355	2
#14270912	2
#14270892	2
C₂₉×#492	2
#1624	29

subgroup

index

C₂₉×#492

Subgroups — #16818573

Conjugacy classes of subgroups

Complements

Maximal subgroups