Group #16835434 — subgroups

Subgroups — #16835434

Order 3712.

212 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 86 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	2	yes	maximal
2	C₂×#11745211	C₂	1	2	yes	maximal
3	#14272168	C₂	1	1	yes	maximal, characteristic
4	#14272167	C₂	1	1	yes	maximal, characteristic
5	#97×D₂₉	C₂	1	1	yes	maximal, characteristic
6	C₂×#90796	C₂²	1	2	yes	—
7	C₂×#90796	C₂²	1	1	yes	characteristic
8	C₂×#90796	C₂²	1	1	yes	characteristic
9	C₂×C₈×D₂₉	C₂²	1	2	yes	—
10	C₄²×D₂₉	C₂²	1	1	yes	characteristic
11	#11745220	—	2	2	no	—
12	C₄⋊#6599	—	2	2	no	—
13	#11745212	—	2	4	no	—
14	#11745211	—	2	4	no	—
15	C₂₉×#97	C₄	1	1	yes	characteristic
16	#11745163	C₄	1	2	yes	—
17	#11745151	C₄	1	1	yes	characteristic
18	C₂×C₄×D₂₉	Q₈	1	2	yes	—
19	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
20	C₂×#6599	—	2	2	no	—
21	C₂×#6599	—	2	1	no	—
22	C₂×#6599	—	2	1	no	—
23	#90796	—	2	2	no	—
24	#90796	—	2	2	no	—
25	#90796	—	2	2	no	—
26	#90796	—	2	2	no	—
27	C₂×C₈×C₂₉	C₂×C₄	1	2	yes	—
28	C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
29	C₄×Dic₂₉	C₂×C₄	1	1	yes	characteristic
30	C₄×Dic₂₉	D₄	1	2	yes	—
31	C₂×#6597	C₂×C₄	1	2	yes	—
32	C₈×D₂₉	D₄	1	4	yes	—
33	C₈×D₂₉	Q₈	1	4	yes	—
34	C₂²×D₂₉	C₂×Q₈	1	1	yes	characteristic
35	C₂×C₄×C₂₉	C₄⋊C₄	1	2	yes	—
36	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
37	C₂×Dic₂₉	C₄⋊C₄	1	2	yes	—
38	C₂×Dic₂₉	C₂×D₄	1	1	yes	characteristic
39	C₄×D₂₉	—	4	2	no	—
40	C₄×D₂₉	C₂×D₄	1	2	yes	—
41	C₄×D₂₉	C₂×Q₈	1	2	yes	—
42	#6599	—	4	1	no	—
43	#6599	—	4	2	no	—
44	#6599	—	4	1	no	—
45	C₈×C₂₉	C₄⋊C₄	1	4	yes	—
46	#6597	C₄⋊C₄	1	4	yes	—
47	#1849	—	29	1	no	maximal, Sylow
48	C₂²×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
49	C₂×D₂₉	—	2	2	no	—
50	C₂×D₂₉	C₄⋊Q₈	1	2	yes	—
51	C₄×C₂₉	—	2	2	no	—
52	C₄×C₂₉	C₂×C₄⋊C₄	1	2	yes	—
53	Dic₂₉	—	2	2	no	—
54	Dic₂₉	#127	1	1	yes	characteristic
55	Dic₂₉	C₄⋊Q₈	1	1	yes	characteristic
56	C₂×#108	—	29	2	no	—
57	C₂×#108	—	29	2	no	—
58	#423	—	29	1	no	—
59	#423	—	29	1	no	—
60	C₂×#97	—	29	1	no	—
61	C₂×C₂₉	#384	1	1	yes	characteristic
62	C₂×C₂₉	#430	1	2	yes	—
63	D₂₉	—	2	2	no	—
64	C₂×M₁₆	—	29	2	no	—
65	C₂×M₁₆	—	29	1	no	—
66	C₂×M₁₆	—	29	1	no	—
67	C₂²×C₈	—	29	2	no	—
68	C₂×C₄²	—	29	1	no	—
69	#108	—	58	4	no	—
70	#108	—	58	4	no	—
71	C₄⋊C₈	—	58	2	no	—
72	C₄⋊C₈	—	58	2	no	—
73	#97	—	29	2	no	—
74	#97	—	29	1	no	—
75	#97	#1181	1	1	yes	characteristic
76	C₂₉	#1849	1	1	yes	characteristic, complemented, Sylow
77	C₂²×C₄	—	29	1	no	—
78	C₂²×C₄	—	29	2	no	—
79	M₁₆	—	58	2	no	—
80	M₁₆	—	58	2	no	—
81	M₁₆	—	58	2	no	—
82	M₁₆	—	58	2	no	—
83	C₂×C₈	—	29	2	no	—
84	C₂×C₈	—	29	4	no	—
85	C₂×C₈	—	29	4	no	—
86	C₂×C₈	—	58	2	no	—
87	C₂×C₈	—	58	1	no	—
88	C₂×C₈	—	58	1	no	—
89	C₂×C₈	C₂×#1181	1	2	yes	—
90	C₄²	—	29	2	no	—
91	C₄²	—	29	1	no	—
92	C₄²	C₂×#1181	1	1	yes	characteristic
93	C₂³	—	29	1	no	—
94	C₂×C₄	—	29	1	no	—
95	C₂×C₄	—	29	2	no	—
96	C₂×C₄	—	29	2	no	—
97	C₂×C₄	—	29	2	no	—
98	C₂×C₄	—	116	2	no	—
99	C₂×C₄	C₄⋊#1181	1	2	yes	—
100	C₂×C₄	C₂²×#1181	1	1	yes	characteristic
101	C₈	—	29	4	no	—
102	C₈	—	116	2	no	—
103	C₈	—	116	1	no	—
104	C₈	—	116	1	no	—
105	C₈	C₄⋊#1181	1	4	yes	—
106	C₂²	—	29	2	no	—
107	C₂²	—	58	2	no	—
108	C₂²	C₂×C₄⋊#1181	1	1	yes	characteristic
109	C₄	—	2	2	no	—
110	C₄	—	29	1	no	—
111	C₄	—	29	1	no	—
112	C₄	—	58	2	no	—
113	C₄	C₂×C₄⋊#1181	1	2	yes	—
114	C₂	—	58	2	no	—
115	C₂	#14272109	1	1	yes	characteristic
116	C₂	#14272178	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11745212

C₂

yes

maximal

C₂×#11745211

C₂

yes

maximal

#14272168

C₂

yes

maximal, characteristic

#14272167

C₂

yes

maximal, characteristic

#97×D₂₉

C₂

yes

maximal, characteristic

C₂×#90796

C₂²

yes

—

C₂×#90796

C₂²

yes

characteristic

C₂×#90796

C₂²

yes

characteristic

C₂×C₈×D₂₉

C₂²

yes

—

C₄²×D₂₉

C₂²

yes

—

—

—

—

C₂₉×#97

C₄

yes

characteristic

#11745163

C₄

yes

—

#11745151

C₄

yes

characteristic

C₂×C₄×D₂₉

Q₈

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

D₄

yes

—

C₂×#6597

C₂×C₄

yes

—

C₈×D₂₉

D₄

yes

—

C₈×D₂₉

Q₈

yes

—

C₂²×D₂₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₂₉

C₄⋊C₄

yes

—

C₂×C₄×C₂₉

C₂²×C₄

yes

characteristic

C₂×Dic₂₉

C₄⋊C₄

yes

—

C₂×Dic₂₉

C₂×D₄

yes

characteristic

C₄×D₂₉

—

C₄×D₂₉

C₂×D₄

yes

—

C₄×D₂₉

C₂×Q₈

yes

—

#6599

—

#6599

—

#6599

—

C₈×C₂₉

C₄⋊C₄

yes

—

#6597

C₄⋊C₄

yes

—

#1849

—

maximal, Sylow

C₂²×C₂₉

C₂×C₄⋊C₄

yes

characteristic

C₂×D₂₉

—

C₂×D₂₉

C₄⋊Q₈

yes

—

C₄×C₂₉

—

C₄×C₂₉

C₂×C₄⋊C₄

yes

—

Dic₂₉

—

Dic₂₉

#127

yes

characteristic

Dic₂₉

C₄⋊Q₈

yes

—

—

—

—

C₂×#97

—

C₂×C₂₉

#384

yes

characteristic

C₂×C₂₉

#430

yes

—

D₂₉

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂²×C₈

—

C₂×C₄²

—

#108

—

#108

—

C₄⋊C₈

—

C₄⋊C₈

—

—

—

yes

C₂₉

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×#1181

yes

—

C₄²

—

C₄²

—

C₄²

C₂×#1181

yes

characteristic

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

116

—

C₂×C₄

C₄⋊#1181

yes

—

100

C₂×C₄

C₂²×#1181

yes

characteristic

101

C₈

—

102

C₈

—

116

—

103

C₈

—

116

—

104

C₈

—

116

—

105

C₈

C₄⋊#1181

yes

—

106

C₂²

—

107

C₂²

—

108

C₂²

C₂×C₄⋊#1181

yes

characteristic

109

C₄

—

110

C₄

—

111

C₄

—

112

C₄

—

113

C₄

C₂×C₄⋊#1181

yes

—

114

C₂

—

115

C₂

#14272109

yes

characteristic

116

C₂

#14272178

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×Q₈
cosocle	C₂×C₄×D₂₉	C₂³
hypercenter	#97	#1181
hypocenter	C₂₉	#1849
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×Q₈

cosocle

C₂×C₄×D₂₉

C₂³

C₂₉

G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #97

N	H ≅ G/N	type
76. C₂₉	#1849	semidirect

H ≅ G/N

type

76. C₂₉

#1849

semidirect

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

subgroup	index
C₂×#11745212	2
C₂×#11745211	2
#14272168	2
#14272167	2
#97×D₂₉	2
#1849	29

subgroup

index

#97×D₂₉

Subgroups — #16835434

Conjugacy classes of subgroups

Complements

Maximal subgroups