Group #16818128 — subgroups

Subgroups — #16818128

Order 3712.

194 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 194 conjugacy classes of subgroups — too many to draw. Only its 59 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	#14271719	C₂	1	1	yes	maximal, characteristic
2	#14271218	C₂	1	2	yes	maximal
3	#14270905	C₂	1	1	yes	maximal, characteristic, complemented
4	#14270904	C₂	1	2	yes	maximal, complemented
5	C₂₉×#330	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#125	C₂²	1	1	yes	characteristic
7	#11745258	—	2	2	no	—
8	#11745254	C₄	1	2	yes	—
9	#11745250	C₄	1	2	yes	—
10	#11745249	—	2	2	no	—
11	C₄²×D₂₉	C₂²	1	1	yes	characteristic
12	#11745232	C₂²	1	1	yes	characteristic
13	C₂₉×#97	C₂²	1	2	yes	—
14	#11745168	—	2	2	no	—
15	#11745162	—	2	2	no	—
16	#11745151	C₂²	1	2	yes	—
17	C₂×C₄×D₂₉	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄×D₂₉	D₄	1	2	yes	—
19	C₂×Dic₅₈	—	2	2	no	—
20	C₂×C₈×C₂₉	—	2	2	no	—
21	C₄⋊C₄×C₂₉	—	2	2	no	—
22	C₄⋊C₄×C₂₉	C₂×C₄	1	2	yes	—
23	C₄²×C₂₉	C₂³	1	1	yes	characteristic
24	#90781	—	2	2	no	—
25	C₄⋊Dic₂₉	C₂×C₄	1	2	yes	—
26	#90779	—	2	2	no	—
27	#90779	—	2	2	no	—
28	C₄×Dic₂₉	—	2	2	no	—
29	C₄×Dic₂₉	C₂×C₄	1	1	yes	characteristic
30	C₄×Dic₂₉	D₄	1	2	yes	—
31	C₂×#6597	—	2	2	no	—
32	C₂²×D₂₉	C₂²⋊C₄	1	1	yes	characteristic
33	C₂×C₄×C₂₉	—	2	2	no	—
34	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
35	C₂×C₄×C₂₉	C₂×D₄	1	2	yes	—
36	C₂×Dic₂₉	—	2	2	no	—
37	C₂×Dic₂₉	C₂²⋊C₄	1	2	yes	—
38	C₂×Dic₂₉	C₂²⋊C₄	1	1	yes	characteristic
39	C₄×D₂₉	—	2	2	no	—
40	C₄×D₂₉	—	4	2	no	—
41	Dic₅₈	—	4	4	no	—
42	C₈×C₂₉	—	4	2	no	—
43	#6597	—	4	2	no	—
44	#1537	—	29	1	no	maximal, Sylow
45	C₂²×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
46	C₂×D₂₉	—	2	1	no	—
47	C₂×D₂₉	—	2	2	no	—
48	C₄×C₂₉	—	2	1	no	—
49	C₄×C₂₉	—	2	2	no	—
50	C₄×C₂₉	—	4	2	no	—
51	Dic₂₉	—	2	2	no	—
52	Dic₂₉	—	4	2	no	—
53	Dic₂₉	#101	1	2	yes	—
54	#533	—	29	1	no	—
55	#432	—	29	2	no	—
56	#330	—	29	1	no	—
57	#330	—	29	2	no	—
58	#330	D₂₉	1	1	yes	characteristic, complemented
59	C₂×C₂₉	C₂×#101	1	1	yes	characteristic
60	C₂×C₂₉	#421	1	2	yes	—
61	D₂₉	—	4	1	no	—
62	C₄⋊Q₈	—	29	2	no	—
63	#125	—	29	1	no	—
64	#125	C₂×D₂₉	1	1	yes	characteristic
65	C₂²⋊Q₈	—	58	2	no	—
66	C₄×Q₈	—	58	2	no	—
67	#117	—	29	2	no	—
68	C₂×C₄²	—	29	1	no	—
69	C₄⋊C₈	—	58	2	no	—
70	C₂²⋊C₈	—	58	2	no	—
71	#97	—	29	2	no	—
72	#97	C₂×D₂₉	1	2	yes	—
73	C₂₉	#1537	1	1	yes	characteristic, complemented, Sylow
74	C₂×Q₈	—	58	2	no	—
75	C₂²×C₄	—	29	1	no	—
76	C₂²×C₄	—	29	2	no	—
77	C₂×C₈	—	2	2	no	—
78	C₂×C₈	—	58	2	no	—
79	C₄⋊C₄	—	2	2	no	—
80	C₄⋊C₄	—	29	2	no	—
81	C₄⋊C₄	—	58	2	no	—
82	C₄⋊C₄	—	58	2	no	—
83	C₄⋊C₄	C₄×D₂₉	1	2	yes	—
84	C₂²⋊C₄	—	58	2	no	—
85	C₄²	—	29	1	no	—
86	C₄²	—	29	2	no	—
87	C₄²	—	58	2	no	—
88	C₄²	C₂²×D₂₉	1	1	yes	characteristic
89	C₂³	—	29	1	no	—
90	Q₈	—	116	4	no	—
91	C₂×C₄	—	2	2	no	—
92	C₂×C₄	—	29	1	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	C₂×C₄×D₂₉	1	1	yes	characteristic
98	C₂×C₄	D₄×D₂₉	1	2	yes	—
99	C₈	—	4	2	no	—
100	C₈	—	116	2	no	—
101	C₂²	—	58	1	no	—
102	C₂²	—	58	2	no	—
103	C₂²	C₂²⋊C₄×D₂₉	1	1	yes	characteristic
104	C₄	—	2	1	no	—
105	C₄	—	2	2	no	—
106	C₄	—	4	2	no	—
107	C₄	—	29	2	no	—
108	C₄	—	58	2	no	—
109	C₄	—	116	2	no	—
110	C₂	—	116	1	no	—
111	C₂	#101×D₂₉	1	1	yes	characteristic
112	C₂	#14271178	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14271719

C₂

yes

maximal, characteristic

#14271218

C₂

yes

maximal

#14270905

C₂

yes

maximal, characteristic, complemented

#14270904

C₂

yes

maximal, complemented

C₂₉×#330

C₂

yes

maximal, characteristic, complemented

C₂₉×#125

C₂²

yes

characteristic

#11745258

—

#11745254

C₄

yes

—

#11745250

C₄

yes

—

#11745249

—

C₄²×D₂₉

C₂²

yes

characteristic

#11745232

C₂²

yes

characteristic

C₂₉×#97

C₂²

yes

—

#11745168

—

#11745162

—

#11745151

C₂²

yes

—

C₂×C₄×D₂₉

C₂×C₄

yes

characteristic

C₂×C₄×D₂₉

D₄

yes

—

C₂×Dic₅₈

—

C₂×C₈×C₂₉

—

C₄⋊C₄×C₂₉

—

C₄⋊C₄×C₂₉

C₂×C₄

yes

—

C₄²×C₂₉

C₂³

yes

characteristic

#90781

—

C₄⋊Dic₂₉

C₂×C₄

yes

—

#90779

—

#90779

—

C₄×Dic₂₉

—

C₄×Dic₂₉

C₂×C₄

yes

characteristic

C₄×Dic₂₉

D₄

yes

—

C₂×#6597

—

C₂²×D₂₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₂₉

C₂×D₄

yes

—

C₂×Dic₂₉

—

C₂×Dic₂₉

C₂²⋊C₄

yes

—

C₂×Dic₂₉

C₂²⋊C₄

yes

characteristic

C₄×D₂₉

—

C₄×D₂₉

—

Dic₅₈

—

C₈×C₂₉

—

#6597

—

#1537

—

maximal, Sylow

C₂²×C₂₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×D₂₉

—

C₂×D₂₉

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

—

Dic₂₉

—

Dic₂₉

—

Dic₂₉

#101

yes

—

—

—

—

—

D₂₉

yes

characteristic, complemented

C₂×C₂₉

C₂×#101

yes

characteristic

C₂×C₂₉

#421

yes

—

D₂₉

—

C₄⋊Q₈

—

#125

—

#125

C₂×D₂₉

yes

characteristic

C₂²⋊Q₈

—

C₄×Q₈

—

#117

—

C₂×C₄²

—

C₄⋊C₈

—

C₂²⋊C₈

—

#97

—

#97

C₂×D₂₉

yes

—

C₂₉

#1537

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

C₄×D₂₉

yes

—

C₂²⋊C₄

—

C₄²

—

C₄²

—

C₄²

—

C₄²

C₂²×D₂₉

yes

characteristic

C₂³

—

Q₈

—

116

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

116

—

C₂×C₄

C₂×C₄×D₂₉

yes

characteristic

C₂×C₄

D₄×D₂₉

yes

—

C₈

—

100

C₈

—

116

—

101

C₂²

—

102

C₂²

—

103

C₂²

C₂²⋊C₄×D₂₉

yes

characteristic

104

C₄

—

105

C₄

—

106

C₄

—

107

C₄

—

108

C₄

—

109

C₄

—

116

—

110

C₂

—

116

—

111

C₂

#101×D₂₉

yes

characteristic

112

C₂

#14271178

yes

—

	subgroup	G/H
center	C₂²	C₂²⋊C₄×D₂₉
commutator	C₂×C₄×C₂₉	C₂²×C₄
Frattini	C₄²	C₂²×D₂₉
Fitting	C₂₉×#330	C₂
socle	C₂²×C₂₉	C₂×C₂²⋊C₄
prime radical	C₂²×D₂₉	C₂²⋊C₄
cosocle	C₄²×C₂₉	C₂³
hypercenter	#330	D₂₉
hypocenter	C₂₉	#1537
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #330

subgroup

G/H

center

C₂²

C₂²⋊C₄×D₂₉

commutator

C₂×C₄×C₂₉

C₂²×C₄

Frattini

C₄²

C₂²×D₂₉

Fitting

C₂₉×#330

C₂

socle

C₂²×C₂₉

C₂×C₂²⋊C₄

prime radical

C₂²×D₂₉

C₂²⋊C₄

cosocle

C₄²×C₂₉

C₂³

D₂₉

C₂₉

G ▷ C₂×C₄×C₂₉ ▷ C₂²×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #330

N	H ≅ G/N	type
3. #14270905	C₂	semidirect
4. #14270904	C₂	semidirect
5. C₂₉×#330	C₂	semidirect
58. #330	D₂₉	semidirect
73. C₂₉	#1537	semidirect

H ≅ G/N

type

3. #14270905

C₂

semidirect

4. #14270904

C₂

semidirect

5. C₂₉×#330

C₂

semidirect

58. #330

D₂₉

semidirect

73. C₂₉

#1537

semidirect

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

subgroup	index
#14271719	2
#14271218	2
#14270905	2
#14270904	2
C₂₉×#330	2
#1537	29

subgroup

index

C₂₉×#330

Subgroups — #16818128

Conjugacy classes of subgroups

Complements

Maximal subgroups