Group #16835415 — subgroups

Subgroups — #16835415

Order 3712.

224 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 74 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	#14272109	C₂	1	1	yes	maximal, characteristic
2	#14272107	C₂	1	1	yes	maximal, characteristic
3	#14272037	C₂	1	4	yes	maximal
4	#97×D₂₉	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄⋊#1181	—	2	2	no	—
6	C₂×C₄⋊#1181	C₂²	1	2	yes	—
7	C₂×C₄⋊#1181	C₂²	1	2	yes	—
8	C₂×C₈×D₂₉	C₂²	1	2	yes	—
9	C₄²×D₂₉	C₂²	1	1	yes	characteristic
10	(C₂×#1181)⋊C₄	—	2	2	no	—
11	C₂₉×#97	C₄	1	1	yes	characteristic, complemented
12	#11745163	C₄	1	2	yes	complemented
13	#11745151	C₄	1	1	yes	characteristic, complemented
14	C₂²×#1181	—	2	2	no	—
15	C₂²×#1181	—	2	2	no	—
16	C₂×C₄×D₂₉	D₄	1	2	yes	—
17	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
18	C₄⋊#1181	—	2	4	no	—
19	C₄⋊#1181	—	2	4	no	—
20	C₄⋊#1181	—	4	4	no	—
21	C₂×C₈×C₂₉	C₂×C₄	1	2	yes	—
22	C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
23	C₄×Dic₂₉	C₂×C₄	1	1	yes	characteristic
24	C₄×Dic₂₉	Q₈	1	2	yes	—
25	C₂×#6597	C₂×C₄	1	2	yes	—
26	C₈×D₂₉	—	2	2	no	—
27	C₈×D₂₉	—	2	2	no	—
28	C₂²×D₂₉	C₂×D₄	1	1	yes	characteristic
29	C₂×#1181	—	4	2	no	—
30	C₂×#1181	—	4	2	no	—
31	C₂×#1181	—	4	4	no	—
32	C₂×#1181	—	4	2	no	—
33	C₂×#1181	—	4	2	no	—
34	C₂×C₄×C₂₉	C₄⋊C₄	1	2	yes	—
35	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
36	C₂×Dic₂₉	C₄⋊C₄	1	2	yes	—
37	C₂×Dic₂₉	C₂×Q₈	1	1	yes	characteristic
38	C₄×D₂₉	—	2	2	no	—
39	C₄×D₂₉	—	2	2	no	—
40	C₄×D₂₉	#41	1	2	yes	—
41	C₄×D₂₉	#41	1	2	yes	—
42	C₈×C₂₉	—	2	2	no	—
43	#6597	—	2	2	no	—
44	#1836	—	29	1	no	maximal, Sylow
45	C₂²×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
46	C₂×D₂₉	#124	1	1	yes	characteristic
47	C₂×D₂₉	#124	1	1	yes	characteristic
48	C₂×D₂₉	AGL(1,ℤ/8)	1	2	yes	—
49	C₂×D₂₉	#137	1	2	yes	—
50	#1181	—	8	2	no	—
51	#1181	—	8	2	no	—
52	C₄×C₂₉	—	2	2	no	—
53	C₄×C₂₉	#117	1	2	yes	—
54	Dic₂₉	—	2	2	no	—
55	Dic₂₉	#125	1	2	yes	—
56	C₂×#97	—	29	1	no	—
57	#384	—	29	1	no	—
58	#382	—	29	1	no	—
59	#340	—	29	4	no	—
60	C₂×C₂₉	#382	1	1	yes	characteristic
61	C₂×C₂₉	#428	1	2	yes	—
62	D₂₉	#489	1	2	yes	—
63	D₂₉	#490	1	1	yes	characteristic
64	D₂₉	#491	1	1	yes	characteristic
65	C₂²×C₈	—	29	2	no	—
66	C₂×C₄⋊C₄	—	29	2	no	—
67	C₂×C₄⋊C₄	—	29	2	no	—
68	C₂×C₄⋊C₄	—	58	2	no	—
69	C₂×C₄²	—	29	1	no	—
70	#97	—	29	2	no	—
71	#97	—	29	1	no	—
72	#97	#1181	1	1	yes	characteristic, complemented
73	#95	—	58	2	no	—
74	C₂₉	#1836	1	1	yes	characteristic, complemented, Sylow
75	C₂²×C₄	—	29	1	no	—
76	C₂²×C₄	—	29	2	no	—
77	C₂²×C₄	—	58	2	no	—
78	C₂²×C₄	—	58	2	no	—
79	C₂×C₈	—	29	2	no	—
80	C₂×C₈	—	58	2	no	—
81	C₂×C₈	—	58	2	no	—
82	C₂×C₈	C₂×#1181	1	2	yes	—
83	C₄⋊C₄	—	58	4	no	—
84	C₄⋊C₄	—	58	4	no	—
85	C₄⋊C₄	—	116	4	no	—
86	C₄²	—	29	2	no	—
87	C₄²	—	29	1	no	—
88	C₄²	C₂×#1181	1	1	yes	characteristic
89	C₂³	—	29	1	no	—
90	C₂×C₄	—	29	1	no	—
91	C₂×C₄	—	29	2	no	—
92	C₂×C₄	—	29	2	no	—
93	C₂×C₄	—	29	2	no	—
94	C₂×C₄	—	58	2	no	—
95	C₂×C₄	—	58	2	no	—
96	C₂×C₄	—	116	2	no	—
97	C₂×C₄	—	116	2	no	—
98	C₂×C₄	—	116	4	no	—
99	C₂×C₄	—	116	2	no	—
100	C₂×C₄	—	116	2	no	—
101	C₂×C₄	C₄⋊#1181	1	2	yes	—
102	C₂×C₄	C₂²×#1181	1	1	yes	characteristic
103	C₈	—	2	2	no	—
104	C₈	—	58	2	no	—
105	C₂²	—	29	1	no	—
106	C₂²	—	29	1	no	—
107	C₂²	—	29	2	no	—
108	C₂²	—	29	2	no	—
109	C₂²	C₂×C₄⋊#1181	1	1	yes	characteristic
110	C₄	—	2	2	no	—
111	C₄	—	29	2	no	—
112	C₄	—	58	2	no	—
113	C₄	—	232	2	no	—
114	C₄	—	232	2	no	—
115	C₄	#11745345	1	2	yes	—
116	C₂	—	29	1	no	—
117	C₂	—	29	2	no	—
118	C₂	—	29	1	no	—
119	C₂	#14272107	1	1	yes	characteristic
120	C₂	#14272174	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14272109

C₂

yes

maximal, characteristic

#14272107

C₂

yes

maximal, characteristic

#14272037

C₂

yes

maximal

#97×D₂₉

C₂

yes

maximal, characteristic

C₂×C₄⋊#1181

—

C₂×C₄⋊#1181

C₂²

yes

—

C₂×C₄⋊#1181

C₂²

yes

—

C₂×C₈×D₂₉

C₂²

yes

—

C₄²×D₂₉

C₂²

yes

characteristic

(C₂×#1181)⋊C₄

—

C₂₉×#97

C₄

yes

characteristic, complemented

#11745163

C₄

yes

complemented

#11745151

C₄

yes

characteristic, complemented

C₂²×#1181

—

C₂²×#1181

—

C₂×C₄×D₂₉

D₄

yes

—

C₂×C₄×D₂₉

C₂³

yes

—

—

—

C₂×C₈×C₂₉

C₂×C₄

yes

—

C₄²×C₂₉

C₂×C₄

yes

characteristic

C₄×Dic₂₉

C₂×C₄

yes

characteristic

C₄×Dic₂₉

Q₈

yes

—

C₂×#6597

C₂×C₄

yes

—

C₈×D₂₉

—

C₈×D₂₉

—

C₂²×D₂₉

C₂×D₄

yes

—

—

—

—

—

C₂×C₄×C₂₉

C₄⋊C₄

yes

—

C₂×C₄×C₂₉

C₂²×C₄

yes

characteristic

C₂×Dic₂₉

C₄⋊C₄

yes

—

C₂×Dic₂₉

C₂×Q₈

yes

characteristic

C₄×D₂₉

—

C₄×D₂₉

—

C₄×D₂₉

#41

yes

—

C₄×D₂₉

#41

yes

—

C₈×C₂₉

—

#6597

—

#1836

—

maximal, Sylow

C₂²×C₂₉

C₂×C₄⋊C₄

yes

C₂×D₂₉

yes

C₂×D₂₉

yes

C₂×D₂₉

yes

—

C₂×D₂₉

#137

yes

—

#1181

—

#1181

—

C₄×C₂₉

—

C₄×C₂₉

#117

yes

—

Dic₂₉

—

Dic₂₉

#125

yes

—

C₂×#97

—

#384

—

#382

—

#340

—

C₂×C₂₉

#382

yes

characteristic

C₂×C₂₉

#428

yes

—

D₂₉

#489

yes

—

D₂₉

yes

D₂₉

yes

C₂²×C₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

—

—

—

yes

characteristic, complemented

#95

—

C₂₉

#1836

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×#1181

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

116

—

C₄²

—

C₄²

—

C₄²

C₂×#1181

yes

characteristic

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

116

—

C₂×C₄

—

116

—

C₂×C₄

—

116

—

C₂×C₄

—

116

—

100

C₂×C₄

—

116

—

101

C₂×C₄

C₄⋊#1181

yes

—

102

C₂×C₄

C₂²×#1181

yes

characteristic

103

C₈

—

104

C₈

—

105

C₂²

—

106

C₂²

—

107

C₂²

—

108

C₂²

—

109

C₂²

C₂×C₄⋊#1181

yes

characteristic

110

C₄

—

111

C₄

—

112

C₄

—

113

C₄

—

232

—

114

C₄

—

232

—

115

C₄

#11745345

yes

—

116

C₂

—

117

C₂

—

118

C₂

—

119

C₂

#14272107

yes

characteristic

120

C₂

#14272174

yes

—

	subgroup	G/H
center	C₂²	C₂×C₄⋊#1181
commutator	C₂×C₄×C₂₉	C₂²×C₄
Frattini	C₂×C₄	C₂²×#1181
Fitting	C₂₉×#97	C₄
socle	C₂²×C₂₉	C₂×C₄⋊C₄
prime radical	C₂²×D₂₉	C₂×D₄
cosocle	C₂×C₄×D₂₉	C₂³
hypercenter	#97	#1181
hypocenter	C₂₉	#1836
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #97

subgroup

G/H

center

C₂²

C₂×C₄⋊#1181

commutator

C₂×C₄×C₂₉

C₂²×C₄

Frattini

C₂×C₄

C₂²×#1181

Fitting

C₂₉×#97

C₄

socle

C₂²×C₂₉

C₂×C₄⋊C₄

prime radical

C₂²×D₂₉

C₂×D₄

cosocle

C₂×C₄×D₂₉

C₂³

C₂₉

G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #97

N	H ≅ G/N	type
11. C₂₉×#97	C₄	semidirect
12. #11745163	C₄	semidirect
13. #11745151	C₄	semidirect
72. #97	#1181	semidirect
74. C₂₉	#1836	semidirect

H ≅ G/N

type

11. C₂₉×#97

C₄

semidirect

12. #11745163

C₄

semidirect

13. #11745151

C₄

semidirect

72. #97

#1181

semidirect

74. C₂₉

#1836

semidirect

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

subgroup	index
#14272109	2
#14272107	2
#14272037	2
#97×D₂₉	2
#1836	29

subgroup

index

#97×D₂₉

Subgroups — #16835415

Conjugacy classes of subgroups

Complements

Maximal subgroups