Group #16820486 — subgroups

Subgroups — #16820486

Order 3712.

228 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 97 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	#14271187	C₂	1	1	yes	maximal, characteristic
2	C₄×#90777	C₂	1	1	yes	maximal, characteristic
3	#14270932	C₂	1	4	yes	maximal
4	C₂×C₂₉×#125	C₂	1	1	yes	maximal, characteristic
5	C₂₉×#125	—	2	1	no	—
6	C₂₉×#125	—	2	1	no	—
7	C₂₉×#125	—	2	2	no	—
8	C₂×C₄⋊C₄×C₂₉	C₄	1	4	yes	—
9	C₂×C₄⋊C₄×C₂₉	C₂²	1	2	yes	—
10	C₂×C₄²×C₂₉	C₂²	1	1	yes	characteristic
11	C₂×#90777	C₂²	1	2	yes	—
12	C₂×#90777	C₂²	1	2	yes	—
13	C₄⋊#6597	—	2	2	no	—
14	#11745151	—	2	1	no	—
15	C₄×#6597	—	2	1	no	—
16	C₂²×C₄×C₂₉	C₂×C₄	1	4	yes	—
17	C₂²×C₄×C₂₉	C₂×C₄	1	2	yes	—
18	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
19	C₄⋊C₄×C₂₉	—	2	4	no	—
20	C₄⋊C₄×C₂₉	—	2	4	no	—
21	C₄⋊C₄×C₂₉	—	2	2	no	—
22	C₄⋊C₄×C₂₉	—	2	2	no	—
23	C₄²×C₂₉	D₄	1	1	yes	characteristic
24	C₄²×C₂₉	D₄	1	1	yes	characteristic
25	C₄²×C₂₉	D₄	1	2	yes	—
26	#90777	—	2	2	no	—
27	#90777	—	2	4	no	—
28	#90777	Q₈	1	4	yes	—
29	C₂×#6597	—	2	2	no	—
30	C₂×#6597	—	2	2	no	—
31	C₂³×C₂₉	C₂²×C₄	1	1	yes	characteristic
32	C₂×C₄×C₂₉	—	2	4	no	—
33	C₂×C₄×C₂₉	—	4	2	no	—
34	C₂×C₄×C₂₉	—	4	4	no	—
35	C₂×C₄×C₂₉	C₂²⋊C₄	1	2	yes	—
36	C₂×C₄×C₂₉	C₂²⋊C₄	1	2	yes	—
37	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
38	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
39	C₂×C₄×C₂₉	C₂×Q₈	1	2	yes	—
40	C₂×C₄×C₂₉	#41	1	2	yes	—
41	#6597	—	2	4	no	—
42	#6597	—	4	2	no	—
43	#1998	—	29	1	no	maximal, Sylow
44	C₂²×C₂₉	—	2	2	no	—
45	C₂²×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
46	C₂²×C₂₉	C₄×Q₈	1	2	yes	—
47	C₄×C₂₉	—	2	2	no	—
48	C₄×C₂₉	—	2	2	no	—
49	C₄×C₂₉	—	4	4	no	—
50	C₄×C₂₉	C₂²⋊Q₈	1	2	yes	—
51	C₄×C₂₉	#124	1	1	yes	characteristic
52	C₄×C₂₉	C₄⋊Q₈	1	1	yes	characteristic
53	C₂×#125	D₂₉	1	1	yes	characteristic
54	#423	—	29	1	no	—
55	C₄×M₁₆	—	29	1	no	—
56	#343	—	29	4	no	—
57	C₂×C₂₉	—	2	2	no	—
58	C₂×C₂₉	#391	1	1	yes	characteristic
59	C₂×C₂₉	#413	1	2	yes	—
60	C₂×M₁₆	—	29	2	no	—
61	C₂×M₁₆	—	29	2	no	—
62	#125	—	2	1	no	—
63	#125	—	2	1	no	—
64	#125	—	2	2	no	—
65	C₂×C₄⋊C₄	Dic₂₉	1	4	yes	—
66	C₂×C₄⋊C₄	C₂×D₂₉	1	2	yes	—
67	C₂×C₄²	C₂×D₂₉	1	1	yes	characteristic
68	C₄⋊C₈	—	58	2	no	—
69	#97	—	58	1	no	—
70	C₄×C₈	—	58	1	no	—
71	C₂₉	#1998	1	1	yes	characteristic, complemented, Sylow
72	C₂²×C₄	C₂×Dic₂₉	1	4	yes	—
73	C₂²×C₄	C₂×Dic₂₉	1	2	yes	—
74	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
75	M₁₆	—	29	4	no	—
76	M₁₆	—	58	2	no	—
77	M₁₆	—	58	4	no	—
78	C₂×C₈	—	58	2	no	—
79	C₂×C₈	—	58	2	no	—
80	C₄⋊C₄	—	2	4	no	—
81	C₄⋊C₄	—	2	4	no	—
82	C₄⋊C₄	—	2	2	no	—
83	C₄⋊C₄	—	2	2	no	—
84	C₄²	C₂²⋊D₂₉	1	1	yes	characteristic
85	C₄²	C₂²⋊D₂₉	1	1	yes	characteristic
86	C₄²	C₂²⋊D₂₉	1	2	yes	—
87	C₂³	C₂²×Dic₂₉	1	1	yes	characteristic
88	C₂×C₄	—	2	4	no	—
89	C₂×C₄	—	4	2	no	—
90	C₂×C₄	—	4	4	no	—
91	C₂×C₄	C₂²⋊Dic₂₉	1	2	yes	—
92	C₂×C₄	C₂²⋊Dic₂₉	1	2	yes	—
93	C₂×C₄	Q₈×D₂₉	1	2	yes	—
94	C₂×C₄	#90809	1	2	yes	—
95	C₂×C₄	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
96	C₂×C₄	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
97	C₈	—	58	4	no	—
98	C₈	—	116	2	no	—
99	C₂²	—	2	2	no	—
100	C₂²	Q₈×Dic₂₉	1	2	yes	—
101	C₂²	C₂×C₂²⋊Dic₂₉	1	1	yes	characteristic
102	C₄	—	2	2	no	—
103	C₄	—	2	2	no	—
104	C₄	—	4	4	no	—
105	C₄	#11745306	1	1	yes	characteristic
106	C₄	#11745308	1	2	yes	—
107	C₄	#11745309	1	1	yes	characteristic
108	C₂	—	2	2	no	—
109	C₂	#14271070	1	1	yes	characteristic
110	C₂	#14271147	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14271187

C₂

yes

maximal, characteristic

C₄×#90777

C₂

yes

maximal, characteristic

#14270932

C₂

yes

maximal

C₂×C₂₉×#125

C₂

yes

maximal, characteristic

C₂₉×#125

—

C₂₉×#125

—

C₂₉×#125

—

C₂×C₄⋊C₄×C₂₉

C₄

yes

—

C₂×C₄⋊C₄×C₂₉

C₂²

yes

—

C₂×C₄²×C₂₉

C₂²

yes

characteristic

C₂×#90777

C₂²

yes

—

C₂×#90777

C₂²

yes

—

C₄⋊#6597

—

#11745151

—

C₄×#6597

—

C₂²×C₄×C₂₉

C₂×C₄

yes

—

C₂²×C₄×C₂₉

C₂×C₄

yes

—

C₂²×C₄×C₂₉

C₂³

yes

characteristic

C₄⋊C₄×C₂₉

—

C₄⋊C₄×C₂₉

—

C₄⋊C₄×C₂₉

—

C₄⋊C₄×C₂₉

—

C₄²×C₂₉

D₄

yes

characteristic

C₄²×C₂₉

D₄

yes

characteristic

C₄²×C₂₉

D₄

yes

—

#90777

—

#90777

—

#90777

Q₈

yes

—

C₂×#6597

—

C₂×#6597

—

C₂³×C₂₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₂²⋊C₄

yes

—

C₂×C₄×C₂₉

C₂²⋊C₄

yes

—

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

C₂×Q₈

yes

—

C₂×C₄×C₂₉

#41

yes

—

—

—

—

C₂²×C₂₉

—

C₂²×C₂₉

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₂₉

C₄×Q₈

yes

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

C₂²⋊Q₈

yes

—

C₄×C₂₉

#124

yes

characteristic

C₄×C₂₉

C₄⋊Q₈

yes

characteristic

C₂×#125

D₂₉

yes

characteristic

#423

—

C₄×M₁₆

—

#343

—

C₂×C₂₉

—

C₂×C₂₉

#391

yes

characteristic

C₂×C₂₉

#413

yes

—

C₂×M₁₆

—

C₂×M₁₆

—

#125

—

#125

—

#125

—

C₂×C₄⋊C₄

Dic₂₉

yes

—

C₂×C₄⋊C₄

C₂×D₂₉

yes

—

C₂×C₄²

C₂×D₂₉

yes

characteristic

C₄⋊C₈

—

#97

—

C₄×C₈

—

C₂₉

#1998

yes

characteristic, complemented, Sylow

C₂²×C₄

C₂×Dic₂₉

yes

—

C₂²×C₄

C₂×Dic₂₉

yes

—

C₂²×C₄

C₂²×D₂₉

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

C₂²⋊D₂₉

yes

characteristic

C₄²

C₂²⋊D₂₉

yes

characteristic

C₄²

C₂²⋊D₂₉

yes

—

C₂³

C₂²×Dic₂₉

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂²⋊Dic₂₉

yes

—

C₂×C₄

C₂²⋊Dic₂₉

yes

—

C₂×C₄

Q₈×D₂₉

yes

—

C₂×C₄

#90809

yes

—

C₂×C₄

C₂×C₂²⋊D₂₉

yes

characteristic

C₂×C₄

C₂×C₂²⋊D₂₉

yes

characteristic

C₈

—

C₈

—

116

—

C₂²

—

100

C₂²

Q₈×Dic₂₉

yes

—

101

C₂²

C₂×C₂²⋊Dic₂₉

yes

characteristic

102

C₄

—

103

C₄

—

104

C₄

—

105

C₄

#11745306

yes

characteristic

106

C₄

#11745308

yes

—

107

C₄

#11745309

yes

characteristic

108

C₂

—

109

C₂

#14271070

yes

characteristic

110

C₂

#14271147

yes

—

	subgroup	G/H
center	C₂²	C₂×C₂²⋊Dic₂₉
commutator, prime radical	C₂³×C₂₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₂₉
Fitting	C₂×C₂₉×#125	C₂
socle	C₂²×C₂₉	C₂×C₂²⋊C₄
cosocle	C₂²×C₄×C₂₉	C₂³
hypercenter	C₂×#125	D₂₉
hypocenter	C₂₉	#1998
LCS	G ▷ C₂³×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×#125

subgroup

G/H

center

C₂²

C₂×C₂²⋊Dic₂₉

commutator, prime radical

C₂³×C₂₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₂₉

Fitting

C₂×C₂₉×#125

C₂

socle

C₂²×C₂₉

C₂×C₂²⋊C₄

cosocle

C₂²×C₄×C₂₉

C₂³

D₂₉

C₂₉

G ▷ C₂³×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×#125

N	H ≅ G/N	type
71. C₂₉	#1998	semidirect

H ≅ G/N

type

71. C₂₉

#1998

semidirect

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

subgroup	index
#14271187	2
C₄×#90777	2
#14270932	2
C₂×C₂₉×#125	2
#1998	29

subgroup

index

C₂×C₂₉×#125

Subgroups — #16820486

Conjugacy classes of subgroups

Complements

Maximal subgroups