Group #16835300 — subgroups

Subgroups — #16835300

Order 3712.

224 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 90 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×#11745212	C₂	1	1	yes	maximal, characteristic
2	#14272128	C₂	1	2	yes	maximal
3	C₂×#11745208	C₂	1	1	yes	maximal, characteristic
4	#14272033	C₂	1	2	yes	maximal
5	#14271198	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄×#1181	C₂²	1	1	yes	characteristic
7	C₂×#90796	C₂²	1	2	yes	—
8	C₂×D₂₉⋊C₈	C₂²	1	1	yes	characteristic
9	C₂×C₈×D₂₉	C₂²	1	1	yes	characteristic
10	#11745254	C₂²	1	2	yes	—
11	#11745218	—	2	2	no	—
12	C₄×#6599	—	2	2	no	—
13	#11745212	C₄	1	4	yes	complemented
14	#11745208	C₄	1	4	yes	complemented
15	C₂₉×#106	C₄	1	1	yes	characteristic, complemented
16	#11745165	C₄	1	1	yes	characteristic, complemented
17	#11745155	C₄	1	2	yes	complemented
18	C₂²×#1181	—	2	1	no	—
19	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
20	C₂×#6599	—	2	2	no	—
21	C₂×#6599	D₄	1	2	yes	—
22	C₄×#1181	—	2	1	no	—
23	C₄×#1181	C₂×C₄	1	2	yes	—
24	#90796	—	2	2	no	—
25	#90796	C₂×C₄	1	4	yes	—
26	D₂₉⋊C₈	C₂×C₄	1	2	yes	—
27	D₂₉⋊C₈	Q₈	1	2	yes	—
28	C₂×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
29	C₄⋊C₄×C₂₉	C₂×C₄	1	2	yes	—
30	#90781	—	2	2	no	—
31	C₄⋊Dic₂₉	C₂×C₄	1	2	yes	—
32	C₄×Dic₂₉	—	2	2	no	—
33	C₂×#6597	C₂×C₄	1	1	yes	characteristic
34	C₈×D₂₉	C₂×C₄	1	2	yes	—
35	C₈×D₂₉	C₂×C₄	1	2	yes	—
36	C₂²×D₂₉	#41	1	1	yes	characteristic
37	C₂×#1181	—	2	2	no	—
38	C₂×#1181	—	4	2	no	—
39	C₂×C₄×C₂₉	—	2	2	no	—
40	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
41	C₂×Dic₂₉	—	2	2	no	—
42	C₂×Dic₂₉	C₂×D₄	1	1	yes	characteristic
43	C₄×D₂₉	C₂²×C₄	1	1	yes	characteristic
44	C₄×D₂₉	C₂²×C₄	1	1	yes	characteristic
45	C₄×D₂₉	C₂×Q₈	1	1	yes	characteristic
46	C₄×D₂₉	#41	1	1	yes	characteristic
47	#6599	—	2	4	no	—
48	#6599	C₄⋊C₄	1	4	yes	—
49	C₈×C₂₉	C₄²	1	2	yes	—
50	#6597	C₄²	1	2	yes	—
51	#1773	—	29	1	no	maximal, Sylow
52	C₂²×C₂₉	C₄×D₄	1	1	yes	characteristic
53	C₂×D₂₉	—	2	2	no	—
54	C₂×D₂₉	#117	1	1	yes	characteristic
55	C₂×D₂₉	C₄×Q₈	1	1	yes	characteristic
56	#1181	—	4	2	no	—
57	C₄×C₂₉	—	4	2	no	—
58	C₄×C₂₉	C₂×C₄²	1	1	yes	characteristic
59	C₄×C₂₉	C₄×Q₈	1	1	yes	characteristic
60	Dic₂₉	—	4	2	no	—
61	Dic₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
62	Dic₂₉	C₄×D₄	1	1	yes	characteristic
63	C₂×#108	—	29	1	no	—
64	#427	—	29	1	no	—
65	#405	—	29	2	no	—
66	C₂×#97	—	29	1	no	—
67	#339	—	29	2	no	—
68	C₂×C₂₉	C₄×C₄⋊C₄	1	1	yes	characteristic
69	C₂×C₂₉	#444	1	2	yes	—
70	D₂₉	—	2	1	no	—
71	D₂₉	—	2	1	no	—
72	C₂×M₁₆	—	29	2	no	—
73	C₂²×C₈	—	29	1	no	—
74	C₂²×C₈	—	29	1	no	—
75	#117	—	29	2	no	—
76	C₂×C₄²	—	29	1	no	—
77	#108	—	29	4	no	—
78	#107	—	29	2	no	—
79	#106	—	29	1	no	—
80	#106	#1181	1	1	yes	characteristic, complemented
81	#97	—	29	4	no	—
82	#97	—	58	2	no	—
83	C₄×C₈	—	58	2	no	—
84	C₂₉	#1773	1	1	yes	characteristic, complemented, Sylow
85	C₂²×C₄	—	29	1	no	—
86	C₂²×C₄	—	58	1	no	—
87	M₁₆	—	29	4	no	—
88	M₁₆	—	58	2	no	—
89	C₂×C₈	—	29	2	no	—
90	C₂×C₈	—	29	2	no	—
91	C₂×C₈	—	29	2	no	—
92	C₂×C₈	—	29	1	no	—
93	C₂×C₈	—	29	2	no	—
94	C₂×C₈	—	29	2	no	—
95	C₂×C₈	—	58	2	no	—
96	C₂×C₈	C₂×#1181	1	1	yes	characteristic
97	C₄⋊C₄	—	29	2	no	—
98	C₄⋊C₄	C₂×#1181	1	2	yes	—
99	C₂²⋊C₄	—	58	2	no	—
100	C₄²	—	29	2	no	—
101	C₄²	—	58	2	no	—
102	C₄²	—	58	1	no	—
103	C₂³	—	29	1	no	—
104	C₂×C₄	—	2	2	no	—
105	C₂×C₄	—	29	1	no	—
106	C₂×C₄	—	29	1	no	—
107	C₂×C₄	—	29	1	no	—
108	C₂×C₄	—	29	1	no	—
109	C₂×C₄	—	29	1	no	—
110	C₂×C₄	—	58	2	no	—
111	C₂×C₄	—	58	2	no	—
112	C₂×C₄	—	116	2	no	—
113	C₂×C₄	C₂²×#1181	1	1	yes	characteristic
114	C₈	—	29	4	no	—
115	C₈	—	29	2	no	—
116	C₈	—	58	4	no	—
117	C₈	C₄×#1181	1	2	yes	—
118	C₂²	—	29	1	no	—
119	C₂²	—	29	1	no	—
120	C₂²	—	58	2	no	—
121	C₂²	D₄×#1181	1	1	yes	characteristic
122	C₄	—	4	2	no	—
123	C₄	—	29	1	no	—
124	C₄	—	29	1	no	—
125	C₄	—	116	2	no	—
126	C₄	—	116	2	no	—
127	C₄	C₂×C₄×#1181	1	1	yes	characteristic
128	C₄	Q₈×#1181	1	1	yes	characteristic
129	C₂	—	58	1	no	—
130	C₂	—	58	1	no	—
131	C₂	C₄⋊C₄×#1181	1	1	yes	characteristic
132	C₂	#14272208	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11745212

C₂

yes

maximal, characteristic

#14272128

C₂

yes

maximal

C₂×#11745208

C₂

yes

maximal, characteristic

#14272033

C₂

yes

maximal

#14271198

C₂

yes

maximal, characteristic

C₂×C₄×#1181

C₂²

yes

characteristic

C₂×#90796

C₂²

yes

—

C₂×D₂₉⋊C₈

C₂²

yes

characteristic

C₂×C₈×D₂₉

C₂²

yes

characteristic

#11745254

C₂²

yes

—

#11745218

—

C₄×#6599

—

#11745212

C₄

yes

complemented

#11745208

C₄

yes

complemented

C₂₉×#106

C₄

yes

characteristic, complemented

#11745165

C₄

yes

characteristic, complemented

#11745155

C₄

yes

complemented

C₂²×#1181

—

C₂×C₄×D₂₉

C₂³

yes

characteristic

C₂×#6599

—

C₂×#6599

D₄

yes

—

C₄×#1181

—

C₄×#1181

C₂×C₄

yes

—

#90796

—

#90796

C₂×C₄

yes

—

D₂₉⋊C₈

C₂×C₄

yes

—

D₂₉⋊C₈

Q₈

yes

—

C₂×C₈×C₂₉

C₂×C₄

yes

characteristic

C₄⋊C₄×C₂₉

C₂×C₄

yes

—

#90781

—

C₄⋊Dic₂₉

C₂×C₄

yes

—

C₄×Dic₂₉

—

C₂×#6597

C₂×C₄

yes

characteristic

C₈×D₂₉

C₂×C₄

yes

—

C₈×D₂₉

C₂×C₄

yes

—

C₂²×D₂₉

yes

—

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₂²×C₄

yes

characteristic

C₂×Dic₂₉

—

C₂×Dic₂₉

C₂×D₄

yes

characteristic

C₄×D₂₉

C₂²×C₄

yes

characteristic

C₄×D₂₉

C₂²×C₄

yes

characteristic

C₄×D₂₉

C₂×Q₈

yes

C₄×D₂₉

yes

—

C₄⋊C₄

yes

—

C₈×C₂₉

C₄²

yes

—

#6597

C₄²

yes

—

#1773

—

maximal, Sylow

C₂²×C₂₉

C₄×D₄

yes

characteristic

C₂×D₂₉

—

C₂×D₂₉

#117

yes

characteristic

C₂×D₂₉

C₄×Q₈

yes

characteristic

#1181

—

C₄×C₂₉

—

C₄×C₂₉

C₂×C₄²

yes

characteristic

C₄×C₂₉

C₄×Q₈

yes

characteristic

Dic₂₉

—

Dic₂₉

C₂×C₄⋊C₄

yes

characteristic

Dic₂₉

C₄×D₄

yes

—

—

—

C₂×#97

—

#339

—

C₂×C₂₉

C₄×C₄⋊C₄

yes

characteristic

C₂×C₂₉

#444

yes

—

D₂₉

—

D₂₉

—

C₂×M₁₆

—

C₂²×C₈

—

C₂²×C₈

—

#117

—

C₂×C₄²

—

—

—

—

yes

characteristic, complemented

#97

—

#97

—

C₄×C₈

—

C₂₉

#1773

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×#1181

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

C₂×#1181

yes

—

C₂²⋊C₄

—

100

C₄²

—

101

C₄²

—

102

C₄²

—

103

C₂³

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

116

—

113

C₂×C₄

C₂²×#1181

yes

characteristic

114

C₈

—

115

C₈

—

116

C₈

—

117

C₈

C₄×#1181

yes

—

118

C₂²

—

119

C₂²

—

120

C₂²

—

121

C₂²

D₄×#1181

yes

characteristic

122

C₄

—

123

C₄

—

124

C₄

—

125

C₄

—

116

—

126

C₄

—

116

—

127

C₄

C₂×C₄×#1181

yes

characteristic

128

C₄

Q₈×#1181

yes

characteristic

129

C₂

—

130

C₂

—

131

C₂

C₄⋊C₄×#1181

yes

characteristic

132

C₂

#14272208

yes

—

	subgroup	G/H
center	C₂²	D₄×#1181
commutator	C₄×C₂₉	C₂×C₄²
Frattini	C₂×C₄	C₂²×#1181
Fitting	C₂₉×#106	C₄
socle	C₂²×C₂₉	C₄×D₄
prime radical	C₂²×D₂₉	#41
cosocle	C₂×C₄×D₂₉	C₂³
hypercenter	#106	#1181
hypocenter	C₂₉	#1773
LCS	G ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #106

subgroup

G/H

center

C₂²

D₄×#1181

commutator

C₄×C₂₉

C₂×C₄²

Frattini

C₂×C₄

C₂²×#1181

Fitting

C₂₉×#106

C₄

socle

C₂²×C₂₉

C₄×D₄

prime radical

C₂²×D₂₉

#41

cosocle

C₂×C₄×D₂₉

C₂³

C₂₉

G ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ #106

N	H ≅ G/N	type
13. #11745212	C₄	semidirect
14. #11745208	C₄	semidirect
15. C₂₉×#106	C₄	semidirect
16. #11745165	C₄	semidirect
17. #11745155	C₄	semidirect
80. #106	#1181	semidirect
84. C₂₉	#1773	semidirect

H ≅ G/N

type

13. #11745212

C₄

semidirect

14. #11745208

C₄

semidirect

15. C₂₉×#106

C₄

semidirect

16. #11745165

C₄

semidirect

17. #11745155

C₄

semidirect

80. #106

#1181

semidirect

84. C₂₉

#1773

semidirect

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

subgroup	index
C₂×#11745212	2
#14272128	2
C₂×#11745208	2
#14272033	2
#14271198	2
#1773	29

subgroup

index

Subgroups — #16835300

Conjugacy classes of subgroups

Complements

Maximal subgroups