Group #16827852 — subgroups

Subgroups — #16827852

Order 3712.

472 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 181 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×#11745232	C₂	1	1	yes	maximal, characteristic
2	#14271058	C₂	1	8	yes	maximal
3	#14271032	C₂	1	2	yes	maximal
4	#14271028	C₂	1	2	yes	maximal
5	C₄²×Dic₂₉	C₂	1	1	yes	maximal, characteristic
6	C₂×C₂₉×#125	C₂	1	1	yes	maximal, characteristic
7	C₂₉×#125	—	2	4	no	—
8	C₂×C₄⋊C₄×C₂₉	C₂²	1	2	yes	—
9	C₂×C₄⋊C₄×C₂₉	C₂²	1	4	yes	—
10	C₂×C₄²×C₂₉	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊Dic₂₉	C₂²	1	2	yes	—
12	C₂×#90779	C₂²	1	8	yes	—
13	C₂×#90779	C₂²	1	4	yes	—
14	C₂×C₄×Dic₂₉	C₂²	1	4	yes	—
15	C₂×C₄×Dic₂₉	C₂²	1	1	yes	characteristic
16	C₂×C₄×Dic₂₉	C₂²	1	1	yes	characteristic
17	#11745232	—	2	4	no	—
18	#11745179	C₂²	1	8	yes	—
19	C₂²×C₄×C₂₉	C₂³	1	4	yes	—
20	C₂²×C₄×C₂₉	C₂³	1	2	yes	—
21	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
22	C₂²×Dic₂₉	C₂³	1	4	yes	—
23	C₂²×Dic₂₉	C₂³	1	2	yes	—
24	C₂²×Dic₂₉	C₂³	1	2	yes	—
25	C₄⋊C₄×C₂₉	—	2	8	no	—
26	C₄⋊C₄×C₂₉	—	2	4	no	—
27	C₄²×C₂₉	D₄	1	4	yes	—
28	C₄⋊Dic₂₉	—	2	4	no	—
29	#90779	—	2	8	no	—
30	#90779	—	2	16	no	—
31	C₄×Dic₂₉	—	2	8	no	—
32	C₄×Dic₂₉	Q₈	1	4	yes	—
33	C₄×Dic₂₉	Q₈	1	4	yes	—
34	C₂³×C₂₉	C₂⁴	1	1	yes	characteristic
35	C₂×C₄×C₂₉	—	2	4	no	—
36	C₂×C₄×C₂₉	—	2	4	no	—
37	C₂×C₄×C₂₉	—	2	8	no	—
38	C₂×C₄×C₂₉	C₂×D₄	1	4	yes	—
39	C₂×C₄×C₂₉	C₂×D₄	1	2	yes	—
40	C₂×C₄×C₂₉	C₂×Q₈	1	2	yes	—
41	C₂×C₄×C₂₉	C₂×Q₈	1	2	yes	—
42	C₂×Dic₂₉	—	2	4	no	—
43	C₂×Dic₂₉	—	2	4	no	—
44	C₂×Dic₂₉	—	2	8	no	—
45	C₂×Dic₂₉	C₂×Q₈	1	4	yes	—
46	C₂×Dic₂₉	C₂×Q₈	1	4	yes	—
47	C₂×Dic₂₉	#41	1	8	yes	—
48	#2859	—	29	1	no	maximal, Sylow
49	C₂²×C₂₉	C₂²×D₄	1	1	yes	characteristic
50	C₂²×C₂₉	C₂²×Q₈	1	1	yes	characteristic
51	C₂²×C₂₉	C₂²×Q₈	1	1	yes	characteristic
52	C₂²×C₂₉	C₂×#41	1	4	yes	—
53	C₄×C₂₉	—	2	4	no	—
54	C₄×C₂₉	—	4	4	no	—
55	C₄×C₂₉	C₄⋊Q₈	1	4	yes	—
56	Dic₂₉	—	2	4	no	—
57	Dic₂₉	—	4	4	no	—
58	Dic₂₉	#125	1	8	yes	complemented
59	C₂×#125	—	29	1	no	—
60	C₂×#125	D₂₉	1	1	yes	characteristic
61	#389	—	29	8	no	—
62	#384	—	29	2	no	—
63	#382	—	29	2	no	—
64	C₄³	—	29	1	no	—
65	C₂×C₂₉	C₂×#125	1	2	yes	—
66	C₂×C₂₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
67	C₂×C₂₉	#532	1	2	yes	—
68	C₂×C₂₉	#533	1	2	yes	—
69	#125	—	2	4	no	—
70	#125	—	58	4	no	—
71	C₂×C₄⋊C₄	—	29	4	no	—
72	C₂×C₄⋊C₄	—	29	8	no	—
73	C₂×C₄⋊C₄	—	29	2	no	—
74	C₂×C₄⋊C₄	C₂×D₂₉	1	2	yes	—
75	C₂×C₄⋊C₄	C₂×D₂₉	1	4	yes	—
76	C₂×C₄²	—	29	1	no	—
77	C₂×C₄²	—	29	1	no	—
78	C₂×C₄²	—	29	4	no	—
79	C₂×C₄²	C₂×D₂₉	1	1	yes	characteristic
80	#95	—	29	8	no	—
81	C₂₉	#2859	1	1	yes	characteristic, complemented, Sylow
82	C₂²×C₄	—	29	2	no	—
83	C₂²×C₄	—	29	2	no	—
84	C₂²×C₄	—	29	4	no	—
85	C₂²×C₄	C₂²×D₂₉	1	4	yes	—
86	C₂²×C₄	C₂²×D₂₉	1	2	yes	—
87	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
88	C₄⋊C₄	—	2	8	no	—
89	C₄⋊C₄	—	2	4	no	—
90	C₄⋊C₄	—	58	16	no	—
91	C₄⋊C₄	—	58	8	no	—
92	C₄⋊C₄	—	58	4	no	—
93	C₄²	—	29	4	no	—
94	C₄²	—	29	4	no	—
95	C₄²	—	58	8	no	—
96	C₄²	C₂²⋊D₂₉	1	4	yes	—
97	C₂³	C₂³×D₂₉	1	1	yes	characteristic
98	C₂×C₄	—	2	4	no	—
99	C₂×C₄	—	2	8	no	—
100	C₂×C₄	—	2	4	no	—
101	C₂×C₄	—	29	4	no	—
102	C₂×C₄	—	29	8	no	—
103	C₂×C₄	—	29	4	no	—
104	C₂×C₄	—	58	4	no	—
105	C₂×C₄	—	58	8	no	—
106	C₂×C₄	—	58	4	no	—
107	C₂×C₄	Q₈×D₂₉	1	2	yes	—
108	C₂×C₄	Q₈×D₂₉	1	2	yes	—
109	C₂×C₄	C₂×C₂²⋊D₂₉	1	4	yes	—
110	C₂×C₄	C₂×C₂²⋊D₂₉	1	2	yes	—
111	C₂²	C₂×Q₈×D₂₉	1	1	yes	characteristic
112	C₂²	C₂×Q₈×D₂₉	1	1	yes	characteristic
113	C₂²	#41×D₂₉	1	4	yes	—
114	C₂²	C₂²×C₂²⋊D₂₉	1	1	yes	characteristic
115	C₄	—	2	4	no	—
116	C₄	—	4	4	no	—
117	C₄	—	29	8	no	—
118	C₄	—	58	4	no	—
119	C₄	—	116	4	no	—
120	C₄	#11745306	1	4	yes	—
121	C₂	#125×D₂₉	1	2	yes	—
122	C₂	C₂×#11745306	1	1	yes	characteristic
123	C₂	#14271709	1	2	yes	—
124	C₂	#14271719	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11745232

C₂

yes

maximal, characteristic

#14271058

C₂

yes

maximal

#14271032

C₂

yes

maximal

#14271028

C₂

yes

maximal

C₄²×Dic₂₉

C₂

yes

maximal, characteristic

C₂×C₂₉×#125

C₂

yes

maximal, characteristic

C₂₉×#125

—

C₂×C₄⋊C₄×C₂₉

C₂²

yes

—

C₂×C₄⋊C₄×C₂₉

C₂²

yes

—

C₂×C₄²×C₂₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₂₉

C₂²

yes

—

C₂×#90779

C₂²

yes

—

C₂×#90779

C₂²

yes

—

C₂×C₄×Dic₂₉

C₂²

yes

—

C₂×C₄×Dic₂₉

C₂²

yes

characteristic

C₂×C₄×Dic₂₉

C₂²

yes

characteristic

#11745232

—

#11745179

C₂²

yes

—

C₂²×C₄×C₂₉

C₂³

yes

—

C₂²×C₄×C₂₉

C₂³

yes

—

C₂²×C₄×C₂₉

C₂³

yes

characteristic

C₂²×Dic₂₉

C₂³

yes

—

C₂²×Dic₂₉

C₂³

yes

—

C₂²×Dic₂₉

C₂³

yes

—

C₄⋊C₄×C₂₉

—

C₄⋊C₄×C₂₉

—

C₄²×C₂₉

D₄

yes

—

C₄⋊Dic₂₉

—

#90779

—

#90779

—

C₄×Dic₂₉

—

C₄×Dic₂₉

Q₈

yes

—

C₄×Dic₂₉

Q₈

yes

—

C₂³×C₂₉

C₂⁴

yes

characteristic

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₂×D₄

yes

—

C₂×C₄×C₂₉

C₂×D₄

yes

—

C₂×C₄×C₂₉

C₂×Q₈

yes

—

C₂×C₄×C₂₉

C₂×Q₈

yes

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

C₂×Q₈

yes

—

C₂×Dic₂₉

C₂×Q₈

yes

—

C₂×Dic₂₉

#41

yes

—

#2859

—

maximal, Sylow

C₂²×C₂₉

C₂²×D₄

yes

characteristic

C₂²×C₂₉

C₂²×Q₈

yes

characteristic

C₂²×C₂₉

C₂²×Q₈

yes

characteristic

C₂²×C₂₉

C₂×#41

yes

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

C₄⋊Q₈

yes

—

Dic₂₉

—

Dic₂₉

—

Dic₂₉

yes

—

D₂₉

yes

—

—

—

C₄³

—

C₂×C₂₉

C₂×#125

yes

—

C₂×C₂₉

C₂×C₄⋊Q₈

yes

characteristic

C₂×C₂₉

#532

yes

—

C₂×C₂₉

#533

yes

—

#125

—

#125

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₂₉

yes

—

C₂×C₄⋊C₄

C₂×D₂₉

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×D₂₉

yes

characteristic

#95

—

C₂₉

#2859

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₂₉

yes

—

C₂²×C₄

C₂²×D₂₉

yes

—

C₂²×C₄

C₂²×D₂₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

—

C₄²

—

C₄²

C₂²⋊D₂₉

yes

—

C₂³

C₂³×D₂₉

yes

characteristic

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

Q₈×D₂₉

yes

—

108

C₂×C₄

Q₈×D₂₉

yes

—

109

C₂×C₄

C₂×C₂²⋊D₂₉

yes

—

110

C₂×C₄

C₂×C₂²⋊D₂₉

yes

—

111

C₂²

C₂×Q₈×D₂₉

yes

characteristic

112

C₂²

C₂×Q₈×D₂₉

yes

characteristic

113

C₂²

#41×D₂₉

yes

—

114

C₂²

C₂²×C₂²⋊D₂₉

yes

characteristic

115

C₄

—

116

C₄

—

117

C₄

—

118

C₄

—

119

C₄

—

116

—

120

C₄

#11745306

yes

—

121

C₂

#125×D₂₉

yes

—

122

C₂

C₂×#11745306

yes

characteristic

123

C₂

#14271709

yes

—

124

C₂

#14271719

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₂₉
commutator, socle, prime radical, cosocle	C₂³×C₂₉	C₂⁴
Fitting	C₂×C₂₉×#125	C₂
hypercenter	C₂×#125	D₂₉
hypocenter	C₂₉	#2859
LCS	G ▷ C₂³×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂³ ◁ C₂×#125

subgroup

G/H

center, Frattini

C₂³

C₂³×D₂₉

commutator, socle, prime radical, cosocle

C₂³×C₂₉

C₂⁴

Fitting

C₂×C₂₉×#125

C₂

D₂₉

C₂₉

G ▷ C₂³×C₂₉ ▷ C₂₉

C₁ ◁ C₂³ ◁ C₂×#125

N	H ≅ G/N	type
58. Dic₂₉	#125	semidirect
81. C₂₉	#2859	semidirect

H ≅ G/N

type

58. Dic₂₉

#125

semidirect

81. C₂₉

#2859

semidirect

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

subgroup	index
C₂×#11745232	2
#14271058	2
#14271032	2
#14271028	2
C₄²×Dic₂₉	2
C₂×C₂₉×#125	2
#2859	29

subgroup

index

C₄²×Dic₂₉

C₂×C₂₉×#125

#2859

Subgroups — #16827852

Conjugacy classes of subgroups

Complements

Maximal subgroups