Group #16835409 — subgroups

Subgroups — #16835409

Order 3712.

260 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 114 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×C₄⋊#6599	C₂	1	2	yes	maximal
2	#14272029	C₂	1	4	yes	maximal
3	C₄²×Dic₂₉	C₂	1	1	yes	maximal, characteristic
4	C₂²×#6599	C₂²	1	4	yes	—
5	C₂×C₄²×C₂₉	C₄	1	1	yes	characteristic
6	C₂×C₄×Dic₂₉	C₄	1	2	yes	—
7	C₂×C₄×Dic₂₉	C₄	1	1	yes	characteristic
8	C₂×C₄×Dic₂₉	C₂²	1	2	yes	—
9	C₂×C₄×Dic₂₉	C₂²	1	1	yes	characteristic
10	C₄⋊#6599	—	2	4	no	—
11	C₂²×C₄×C₂₉	C₂×C₄	1	2	yes	—
12	C₂²×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
13	C₂²×Dic₂₉	C₂×C₄	1	1	yes	characteristic
14	C₂²×Dic₂₉	C₂×C₄	1	2	yes	—
15	C₂²×Dic₂₉	C₂³	1	1	yes	characteristic
16	C₂×#6599	—	2	4	no	—
17	C₂×#6599	—	2	8	no	—
18	C₄²×C₂₉	—	2	2	no	—
19	C₄×Dic₂₉	—	2	4	no	—
20	C₄×Dic₂₉	—	2	4	no	—
21	C₄×Dic₂₉	C₈	1	4	yes	complemented
22	C₄×Dic₂₉	D₄	1	2	yes	—
23	C₄×Dic₂₉	Q₈	1	2	yes	—
24	C₂³×C₂₉	C₂²×C₄	1	1	yes	characteristic
25	C₂×C₄×C₂₉	—	2	2	no	—
26	C₂×C₄×C₂₉	—	2	2	no	—
27	C₂×C₄×C₂₉	C₄⋊C₄	1	2	yes	—
28	C₂×C₄×C₂₉	C₂×C₈	1	2	yes	—
29	C₂×C₄×C₂₉	M₁₆	1	4	yes	—
30	C₂×C₄×C₂₉	M₁₆	1	2	yes	—
31	C₂×Dic₂₉	—	2	2	no	—
32	C₂×Dic₂₉	—	2	2	no	—
33	C₂×Dic₂₉	—	2	2	no	—
34	C₂×Dic₂₉	C₄⋊C₄	1	2	yes	—
35	C₂×Dic₂₉	C₂×C₈	1	4	yes	—
36	C₂×Dic₂₉	C₂×D₄	1	1	yes	characteristic
37	C₂×Dic₂₉	C₂×Q₈	1	1	yes	characteristic
38	C₂×Dic₂₉	#41	1	4	yes	—
39	#6599	—	4	4	no	—
40	#1831	—	29	1	no	maximal, Sylow
41	C₂²×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
42	C₂²×C₂₉	#117	1	2	yes	—
43	C₂²×C₂₉	C₂²×C₈	1	1	yes	characteristic
44	C₂²×C₂₉	C₂×M₁₆	1	2	yes	—
45	C₂²×C₂₉	C₂×M₁₆	1	1	yes	characteristic
46	C₄×C₂₉	—	2	4	no	—
47	C₄×C₂₉	C₄⋊C₈	1	4	yes	—
48	Dic₂₉	—	2	2	no	—
49	Dic₂₉	—	2	4	no	—
50	Dic₂₉	#124	1	2	yes	—
51	Dic₂₉	#125	1	2	yes	—
52	C₂×C₄⋊C₈	—	29	2	no	—
53	C₄³	—	29	1	no	—
54	#336	—	29	4	no	—
55	C₂×C₂₉	#382	1	1	yes	characteristic
56	C₂×C₂₉	C₂×C₄⋊C₈	1	1	yes	characteristic
57	C₂×C₂₉	#423	1	1	yes	characteristic
58	C₂×C₂₉	#431	1	2	yes	—
59	C₂×C₂₉	#432	1	2	yes	—
60	C₂²×C₈	—	29	4	no	—
61	C₂×C₄²	—	29	1	no	—
62	C₂×C₄²	—	29	1	no	—
63	C₂×C₄²	—	29	2	no	—
64	C₂×C₄²	—	29	2	no	—
65	C₂×C₄²	#1181	1	1	yes	characteristic
66	C₄⋊C₈	—	58	4	no	—
67	C₂₉	#1831	1	1	yes	characteristic, complemented, Sylow
68	C₂²×C₄	—	29	1	no	—
69	C₂²×C₄	—	29	2	no	—
70	C₂²×C₄	—	29	1	no	—
71	C₂²×C₄	C₂×#1181	1	2	yes	—
72	C₂²×C₄	C₂×#1181	1	1	yes	characteristic
73	C₂×C₈	—	58	4	no	—
74	C₂×C₈	—	58	8	no	—
75	C₄²	—	2	2	no	—
76	C₄²	—	29	4	no	—
77	C₄²	—	29	2	no	—
78	C₄²	—	29	2	no	—
79	C₄²	—	58	4	no	—
80	C₄²	—	58	4	no	—
81	C₂³	C₂²×#1181	1	1	yes	characteristic
82	C₂×C₄	—	2	2	no	—
83	C₂×C₄	—	2	2	no	—
84	C₂×C₄	—	29	1	no	—
85	C₂×C₄	—	29	1	no	—
86	C₂×C₄	—	29	4	no	—
87	C₂×C₄	—	29	4	no	—
88	C₂×C₄	—	29	2	no	—
89	C₂×C₄	—	58	2	no	—
90	C₂×C₄	—	58	2	no	—
91	C₂×C₄	—	58	2	no	—
92	C₂×C₄	D₂₉⋊C₈	1	2	yes	—
93	C₂×C₄	#90796	1	4	yes	—
94	C₂×C₄	C₄⋊#1181	1	2	yes	—
95	C₂×C₄	#90800	1	2	yes	—
96	C₈	—	116	4	no	—
97	C₂²	C₂×D₂₉⋊C₈	1	1	yes	characteristic
98	C₂²	C₂×#90796	1	2	yes	—
99	C₂²	C₂×C₄⋊#1181	1	1	yes	characteristic
100	C₂²	#11745345	1	2	yes	—
101	C₂²	C₂×#90800	1	1	yes	characteristic
102	C₄	—	2	4	no	—
103	C₄	—	29	2	no	—
104	C₄	—	29	2	no	—
105	C₄	—	58	2	no	—
106	C₄	—	58	4	no	—
107	C₄	#11745220	1	4	yes	—
108	C₂	#14272107	1	1	yes	characteristic
109	C₂	C₂×#11745220	1	1	yes	characteristic
110	C₂	#14272167	1	1	yes	characteristic
111	C₂	#14272182	1	2	yes	—
112	C₂	#14272184	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄⋊#6599

C₂

yes

maximal

#14272029

C₂

yes

maximal

C₄²×Dic₂₉

C₂

yes

maximal, characteristic

C₂²×#6599

C₂²

yes

—

C₂×C₄²×C₂₉

C₄

yes

characteristic

C₂×C₄×Dic₂₉

C₄

yes

—

C₂×C₄×Dic₂₉

C₄

yes

characteristic

C₂×C₄×Dic₂₉

C₂²

yes

—

C₂×C₄×Dic₂₉

C₂²

yes

characteristic

C₄⋊#6599

—

C₂²×C₄×C₂₉

C₂×C₄

yes

—

C₂²×C₄×C₂₉

C₂×C₄

yes

characteristic

C₂²×Dic₂₉

C₂×C₄

yes

characteristic

C₂²×Dic₂₉

C₂×C₄

yes

—

C₂²×Dic₂₉

C₂³

yes

characteristic

C₂×#6599

—

C₂×#6599

—

C₄²×C₂₉

—

C₄×Dic₂₉

—

C₄×Dic₂₉

—

C₄×Dic₂₉

C₈

yes

complemented

C₄×Dic₂₉

D₄

yes

—

C₄×Dic₂₉

Q₈

yes

—

C₂³×C₂₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₄⋊C₄

yes

—

C₂×C₄×C₂₉

C₂×C₈

yes

—

C₂×C₄×C₂₉

M₁₆

yes

—

C₂×C₄×C₂₉

M₁₆

yes

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

C₄⋊C₄

yes

—

C₂×Dic₂₉

C₂×C₈

yes

—

C₂×Dic₂₉

C₂×D₄

yes

characteristic

C₂×Dic₂₉

C₂×Q₈

yes

characteristic

C₂×Dic₂₉

#41

yes

—

#6599

—

#1831

—

maximal, Sylow

C₂²×C₂₉

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₂₉

#117

yes

—

C₂²×C₂₉

C₂²×C₈

yes

characteristic

C₂²×C₂₉

C₂×M₁₆

yes

—

C₂²×C₂₉

C₂×M₁₆

yes

characteristic

C₄×C₂₉

—

C₄×C₂₉

C₄⋊C₈

yes

—

Dic₂₉

—

Dic₂₉

—

Dic₂₉

#124

yes

—

Dic₂₉

#125

yes

—

C₂×C₄⋊C₈

—

C₄³

—

#336

—

C₂×C₂₉

#382

yes

characteristic

C₂×C₂₉

C₂×C₄⋊C₈

yes

C₂×C₂₉

yes

C₂×C₂₉

yes

—

C₂×C₂₉

#432

yes

—

C₂²×C₈

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

#1181

yes

characteristic

C₄⋊C₈

—

C₂₉

#1831

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×#1181

yes

—

C₂²×C₄

C₂×#1181

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₂³

C₂²×#1181

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

D₂₉⋊C₈

yes

—

C₂×C₄

#90796

yes

—

C₂×C₄

C₄⋊#1181

yes

—

C₂×C₄

#90800

yes

—

C₈

—

116

—

C₂²

C₂×D₂₉⋊C₈

yes

characteristic

C₂²

C₂×#90796

yes

—

C₂²

C₂×C₄⋊#1181

yes

characteristic

100

C₂²

#11745345

yes

—

101

C₂²

C₂×#90800

yes

characteristic

102

C₄

—

103

C₄

—

104

C₄

—

105

C₄

—

106

C₄

—

107

C₄

#11745220

yes

—

108

C₂

#14272107

yes

characteristic

109

C₂

C₂×#11745220

yes

characteristic

110

C₂

#14272167

yes

characteristic

111

C₂

#14272182

yes

—

112

C₂

#14272184

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂²×#1181
commutator	C₂²×C₂₉	C₂²×C₈
Fitting	C₂×C₄²×C₂₉	C₄
socle, prime radical	C₂³×C₂₉	C₂²×C₄
cosocle	C₂²×Dic₂₉	C₂³
hypercenter	C₂×C₄²	#1181
hypocenter	C₂₉	#1831
LCS	G ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄²

subgroup

G/H

center, Frattini

C₂³

C₂²×#1181

commutator

C₂²×C₂₉

C₂²×C₈

Fitting

C₂×C₄²×C₂₉

C₄

socle, prime radical

C₂³×C₂₉

C₂²×C₄

cosocle

C₂²×Dic₂₉

C₂³

C₂×C₄²

C₂₉

G ▷ C₂²×C₂₉ ▷ C₂₉

C₁ ◁ C₂³ ◁ C₂×C₄²

N	H ≅ G/N	type
21. C₄×Dic₂₉	C₈	semidirect
67. C₂₉	#1831	semidirect

H ≅ G/N

type

21. C₄×Dic₂₉

C₈

semidirect

67. C₂₉

#1831

semidirect

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

subgroup	index
C₂×C₄⋊#6599	2
#14272029	2
C₄²×Dic₂₉	2
#1831	29

subgroup

index

C₂×C₄⋊#6599

#14272029

C₄²×Dic₂₉

#1831

Subgroups — #16835409

Conjugacy classes of subgroups

Complements

Maximal subgroups