Group #16827868 — subgroups

Subgroups — #16827868

Order 3712.

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

normal subgroups only

This group has 504 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×#11745250	C₂	1	2	yes	maximal
2	#14271067	C₂	1	8	yes	maximal
3	#14271029	C₂	1	1	yes	maximal, characteristic
4	#14271028	C₂	1	2	yes	maximal
5	C₄²×Dic₂₉	C₂	1	1	yes	maximal, characteristic
6	C₂₉×#382	C₂	1	1	yes	maximal, characteristic
7	C₂²×Dic₅₈	C₂²	1	4	yes	—
8	C₂×C₄⋊C₄×C₂₉	C₂²	1	2	yes	—
9	C₂×C₄²×C₂₉	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊Dic₂₉	C₂²	1	2	yes	—
11	C₂×#90779	C₂²	1	4	yes	—
12	C₂×C₄×Dic₂₉	C₂²	1	4	yes	—
13	C₂×C₄×Dic₂₉	C₂²	1	1	yes	characteristic
14	C₂×C₄×Dic₂₉	C₂²	1	1	yes	characteristic
15	#11745250	—	2	8	no	—
16	C₂₉×#95	C₂²	1	4	yes	—
17	#11745179	C₂²	1	8	yes	—
18	#11745179	C₂²	1	4	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	C₂×Dic₅₈	—	2	8	no	—
26	C₂×Dic₅₈	—	2	16	no	—
27	C₄⋊C₄×C₂₉	—	2	4	no	—
28	C₄²×C₂₉	Q₈	1	4	yes	complemented
29	C₄⋊Dic₂₉	—	2	4	no	—
30	#90779	—	2	8	no	—
31	C₄×Dic₂₉	—	2	8	no	—
32	C₄×Dic₂₉	D₄	1	4	yes	—
33	C₄×Dic₂₉	Q₈	1	4	yes	complemented
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	2	yes	—
39	C₂×C₄×C₂₉	C₂×Q₈	1	4	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×D₄	1	4	yes	—
46	C₂×Dic₂₉	C₂×Q₈	1	4	yes	—
47	C₂×Dic₂₉	#41	1	8	yes	—
48	Dic₅₈	—	4	16	no	—
49	#2862	—	29	1	no	maximal, Sylow
50	C₂²×C₂₉	C₂²×D₄	1	1	yes	characteristic
51	C₂²×C₂₉	C₂²×Q₈	1	1	yes	characteristic
52	C₂²×C₂₉	C₂²×Q₈	1	1	yes	characteristic
53	C₂²×C₂₉	C₂×#41	1	4	yes	—
54	C₄×C₂₉	—	2	4	no	—
55	C₄×C₂₉	—	4	4	no	—
56	C₄×C₂₉	C₄⋊Q₈	1	4	yes	—
57	Dic₂₉	—	2	4	no	—
58	Dic₂₉	—	4	4	no	—
59	Dic₂₉	#124	1	8	yes	—
60	C₂×C₄⋊Q₈	—	29	2	no	—
61	#391	—	29	8	no	—
62	#382	—	29	2	no	—
63	#382	—	29	1	no	—
64	#382	D₂₉	1	1	yes	characteristic
65	C₄³	—	29	1	no	—
66	C₂×C₂₉	C₂×#124	1	2	yes	—
67	C₂×C₂₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
68	C₂×C₂₉	#533	1	2	yes	—
69	C₂×C₂₉	#533	1	2	yes	—
70	C₂²×Q₈	—	29	4	no	—
71	C₄⋊Q₈	—	58	8	no	—
72	C₂×C₄⋊C₄	—	29	4	no	—
73	C₂×C₄⋊C₄	—	29	2	no	—
74	C₂×C₄⋊C₄	C₂×D₂₉	1	2	yes	—
75	C₂×C₄²	—	29	1	no	—
76	C₂×C₄²	—	29	1	no	—
77	C₂×C₄²	—	29	4	no	—
78	C₂×C₄²	C₂×D₂₉	1	1	yes	characteristic
79	#95	—	29	8	no	—
80	#95	—	29	4	no	—
81	#95	C₂×D₂₉	1	4	yes	—
82	C₂₉	#2862	1	1	yes	characteristic, complemented, Sylow
83	C₂×Q₈	—	58	8	no	—
84	C₂×Q₈	—	58	16	no	—
85	C₂²×C₄	—	29	2	no	—
86	C₂²×C₄	—	29	2	no	—
87	C₂²×C₄	—	29	4	no	—
88	C₂²×C₄	C₂²×D₂₉	1	4	yes	—
89	C₂²×C₄	C₂²×D₂₉	1	2	yes	—
90	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
91	C₄⋊C₄	—	2	4	no	—
92	C₄⋊C₄	—	58	8	no	—
93	C₄⋊C₄	—	58	4	no	—
94	C₄²	—	29	4	no	—
95	C₄²	—	29	4	no	—
96	C₄²	—	58	8	no	—
97	C₄²	Dic₅₈	1	4	yes	complemented
98	C₂³	C₂³×D₂₉	1	1	yes	characteristic
99	Q₈	—	116	16	no	—
100	C₂×C₄	—	2	4	no	—
101	C₂×C₄	—	2	4	no	—
102	C₂×C₄	—	2	8	no	—
103	C₂×C₄	—	29	4	no	—
104	C₂×C₄	—	29	8	no	—
105	C₂×C₄	—	29	4	no	—
106	C₂×C₄	—	58	4	no	—
107	C₂×C₄	—	58	4	no	—
108	C₂×C₄	—	58	8	no	—
109	C₂×C₄	C₂×Dic₅₈	1	4	yes	—
110	C₂×C₄	C₂×Dic₅₈	1	2	yes	—
111	C₂×C₄	D₄×D₂₉	1	2	yes	—
112	C₂×C₄	Q₈×D₂₉	1	2	yes	—
113	C₂²	C₂²×Dic₅₈	1	1	yes	characteristic
114	C₂²	C₂×D₄×D₂₉	1	1	yes	characteristic
115	C₂²	C₂×Q₈×D₂₉	1	1	yes	characteristic
116	C₂²	#41×D₂₉	1	4	yes	—
117	C₄	—	2	4	no	—
118	C₄	—	4	4	no	—
119	C₄	—	29	8	no	—
120	C₄	—	58	4	no	—
121	C₄	—	116	4	no	—
122	C₄	#11745250	1	4	yes	—
123	C₂	#124×D₂₉	1	2	yes	—
124	C₂	C₂×#11745250	1	1	yes	characteristic
125	C₂	#14271716	1	2	yes	—
126	C₂	#14271719	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11745250

C₂

yes

maximal

#14271067

C₂

yes

maximal

#14271029

C₂

yes

maximal, characteristic

#14271028

C₂

yes

maximal

C₄²×Dic₂₉

C₂

yes

maximal, characteristic

C₂₉×#382

C₂

yes

maximal, characteristic

C₂²×Dic₅₈

C₂²

yes

—

C₂×C₄⋊C₄×C₂₉

C₂²

yes

—

C₂×C₄²×C₂₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₂₉

C₂²

yes

—

C₂×#90779

C₂²

yes

—

C₂×C₄×Dic₂₉

C₂²

yes

—

C₂×C₄×Dic₂₉

C₂²

yes

characteristic

C₂×C₄×Dic₂₉

C₂²

yes

characteristic

#11745250

—

C₂₉×#95

C₂²

yes

—

#11745179

C₂²

yes

—

#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

—

C₂×Dic₅₈

—

C₂×Dic₅₈

—

C₄⋊C₄×C₂₉

—

C₄²×C₂₉

Q₈

yes

complemented

C₄⋊Dic₂₉

—

#90779

—

C₄×Dic₂₉

—

C₄×Dic₂₉

D₄

yes

—

C₄×Dic₂₉

Q₈

yes

complemented

C₂³×C₂₉

C₂⁴

yes

characteristic

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₂×D₄

yes

—

C₂×C₄×C₂₉

C₂×Q₈

yes

—

C₂×C₄×C₂₉

C₂×Q₈

yes

—

C₂×C₄×C₂₉

C₂×Q₈

yes

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

C₂×D₄

yes

—

C₂×Dic₂₉

C₂×Q₈

yes

—

C₂×Dic₂₉

#41

yes

—

Dic₅₈

—

#2862

—

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

#124

yes

—

C₂×C₄⋊Q₈

—

—

—

—

D₂₉

yes

characteristic

C₄³

—

C₂×C₂₉

C₂×#124

yes

—

C₂×C₂₉

C₂×C₄⋊Q₈

yes

characteristic

C₂×C₂₉

#533

yes

—

C₂×C₂₉

#533

yes

—

C₂²×Q₈

—

C₄⋊Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₂₉

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×D₂₉

yes

—

—

C₂×D₂₉

yes

—

C₂₉

#2862

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

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

—

C₄²

—

C₄²

—

C₄²

—

C₄²

Dic₅₈

yes

complemented

C₂³

C₂³×D₂₉

yes

characteristic

Q₈

—

116

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

C₂×Dic₅₈

yes

—

110

C₂×C₄

C₂×Dic₅₈

yes

—

111

C₂×C₄

D₄×D₂₉

yes

—

112

C₂×C₄

Q₈×D₂₉

yes

—

113

C₂²

C₂²×Dic₅₈

yes

characteristic

114

C₂²

C₂×D₄×D₂₉

yes

characteristic

115

C₂²

C₂×Q₈×D₂₉

yes

characteristic

116

C₂²

#41×D₂₉

yes

—

117

C₄

—

118

C₄

—

119

C₄

—

120

C₄

—

121

C₄

—

116

—

122

C₄

#11745250

yes

—

123

C₂

#124×D₂₉

yes

—

124

C₂

C₂×#11745250

yes

characteristic

125

C₂

#14271716

yes

—

126

C₂

#14271719

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₂₉
commutator, socle, prime radical, cosocle	C₂³×C₂₉	C₂⁴
Fitting	C₂₉×#382	C₂
hypercenter	#382	D₂₉
hypocenter	C₂₉	#2862
LCS	G ▷ C₂³×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂³ ◁ #382

subgroup

G/H

center, Frattini

C₂³

C₂³×D₂₉

commutator, socle, prime radical, cosocle

C₂³×C₂₉

C₂⁴

Fitting

C₂₉×#382

C₂

D₂₉

C₂₉

G ▷ C₂³×C₂₉ ▷ C₂₉

C₁ ◁ C₂³ ◁ #382

N	H ≅ G/N	type
28. C₄²×C₂₉	Q₈	semidirect
33. C₄×Dic₂₉	Q₈	semidirect
82. C₂₉	#2862	semidirect
97. C₄²	Dic₅₈	semidirect

H ≅ G/N

type

28. C₄²×C₂₉

Q₈

semidirect

33. C₄×Dic₂₉

Q₈

semidirect

82. C₂₉

#2862

semidirect

97. C₄²

Dic₅₈

semidirect

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

subgroup	index
C₂×#11745250	2
#14271067	2
#14271029	2
#14271028	2
C₄²×Dic₂₉	2
C₂₉×#382	2
#2862	29

subgroup

index

C₄²×Dic₂₉

C₂₉×#382

#2862

Subgroups — #16827868

Conjugacy classes of subgroups

Complements

Maximal subgroups