Group #31805930 — subgroups

Subgroups — #31805930

Order 17792.

140 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 140 conjugacy classes of subgroups — too many to draw. Only its 53 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	#22581356	C₂	1	1	yes	maximal, characteristic
2	#22581248	C₂	1	1	yes	maximal, characteristic
3	#22581084	C₂	1	1	yes	maximal, characteristic
4	#22580703	C₂	1	1	yes	maximal, characteristic
5	#22580702	C₂	1	1	yes	maximal, characteristic
6	#22580701	C₂	1	1	yes	maximal, characteristic
7	#477×C₁₃₉	C₂	1	1	yes	maximal, characteristic
8	#17984842	C₂²	1	1	yes	characteristic
9	#17984775	—	2	1	no	—
10	#17984775	—	2	1	no	—
11	#17984775	—	2	1	no	—
12	C₄⋊(C₁₃₉⋊C₈)	—	2	1	no	—
13	C₄⋊(C₁₃₉⋊C₈)	C₂²	1	1	yes	characteristic
14	C₄⋊(C₁₃₉⋊C₈)	C₂²	1	1	yes	characteristic
15	#17984766	—	2	1	no	—
16	#17984753	—	2	1	no	—
17	C₄×C₁₃₉⋊C₈	C₂²	1	1	yes	characteristic
18	C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
19	C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
20	#107×C₁₃₉	—	2	1	no	—
21	C₄⋊C₈×C₁₃₉	C₂²	1	1	yes	characteristic
22	#103×C₁₃₉	—	2	1	no	—
23	C₂×Dic₂₇₈	—	2	1	no	—
24	C₂×C₁₃₉⋊C₈	—	2	1	no	—
25	C₂×C₁₃₉⋊C₈	—	2	1	no	—
26	C₂×C₁₃₉⋊C₈	D₄	1	1	yes	characteristic
27	C₂×C₁₃₉⋊C₈	D₄	1	1	yes	characteristic
28	C₄⋊Dic₁₃₉	—	2	1	no	—
29	C₄⋊Dic₁₃₉	—	2	1	no	—
30	C₂×Q₈×C₁₃₉	—	2	1	no	—
31	C₂×Q₈×C₁₃₉	D₄	1	1	yes	characteristic
32	C₂×C₈×C₁₃₉	—	2	1	no	—
33	C₄⋊C₄×C₁₃₉	—	2	1	no	—
34	C₄⋊C₄×C₁₃₉	—	2	1	no	—
35	C₄⋊C₄×C₁₃₉	—	2	1	no	—
36	C₄⋊C₄×C₁₃₉	D₄	1	1	yes	characteristic
37	C₄²×C₁₃₉	—	2	1	no	—
38	C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
39	Dic₂₇₈	—	8	1	no	—
40	C₂×Dic₁₃₉	—	4	1	no	—
41	C₁₃₉⋊C₈	—	2	1	no	—
42	C₁₃₉⋊C₈	—	4	1	no	—
43	C₁₃₉⋊C₈	—	4	1	no	—
44	C₁₃₉⋊C₈	Q₁₆	1	2	yes	—
45	Q₈×C₁₃₉	—	2	1	no	—
46	Q₈×C₁₃₉	—	2	1	no	—
47	Q₈×C₁₃₉	—	8	1	no	—
48	C₂×C₄×C₁₃₉	—	2	1	no	—
49	C₂×C₄×C₁₃₉	—	2	1	no	—
50	C₂×C₄×C₁₃₉	—	4	1	no	—
51	C₂×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
52	C₂×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
53	C₂×C₄×C₁₃₉	#41	1	1	yes	characteristic
54	C₈×C₁₃₉	—	4	1	no	—
55	C₂²×C₁₃₉	#121	1	1	yes	characteristic
56	C₄×C₁₃₉	—	2	1	no	—
57	C₄×C₁₃₉	—	4	1	no	—
58	C₄×C₁₃₉	—	4	1	no	—
59	C₄×C₁₃₉	—	8	1	no	—
60	C₄×C₁₃₉	C₂×Q₁₆	1	1	yes	characteristic
61	C₄×C₁₃₉	#137	1	1	yes	characteristic
62	C₄×C₁₃₉	#137	1	1	yes	characteristic
63	C₄×C₁₃₉	#137	1	1	yes	characteristic
64	Dic₁₃₉	—	8	1	no	—
65	C₂×C₁₃₉	#462	1	1	yes	characteristic
66	C₂×C₁₃₉	#470	1	1	yes	characteristic
67	C₂×C₁₃₉	#472	1	1	yes	characteristic
68	C₁₃₉	#1696	1	1	yes	characteristic, complemented, Sylow
69	#1696	—	139	1	no	maximal, Sylow
70	#500	—	139	1	no	—
71	#477	—	139	1	no	—
72	#477	D₁₃₉	1	1	yes	characteristic
73	#446	—	139	1	no	—
74	#334	—	139	1	no	—
75	#333	—	139	1	no	—
76	#333	—	139	1	no	—
77	C₄⋊Q₈	—	139	1	no	—
78	C₄⋊Q₈	C₂×D₁₃₉	1	1	yes	characteristic
79	C₄×Q₈	C₂×D₁₃₉	1	1	yes	characteristic
80	#107	—	2	1	no	—
81	#107	—	278	1	no	—
82	#107	—	278	1	no	—
83	#107	—	278	1	no	—
84	C₄⋊C₈	—	278	1	no	—
85	C₄⋊C₈	—	139	1	no	—
86	C₄⋊C₈	—	139	1	no	—
87	C₄⋊C₈	C₂×D₁₃₉	1	1	yes	characteristic
88	#103	—	2	1	no	—
89	#103	—	278	1	no	—
90	#97	—	278	1	no	—
91	C₄×C₈	—	139	1	no	—
92	C₂×Q₈	—	2	1	no	—
93	C₂×Q₈	—	278	1	no	—
94	C₂×Q₈	C₂²⋊D₁₃₉	1	1	yes	characteristic
95	C₂×C₈	—	2	1	no	—
96	C₂×C₈	—	278	1	no	—
97	C₂×C₈	—	278	1	no	—
98	C₂×C₈	—	139	1	no	—
99	C₂×C₈	—	139	1	no	—
100	C₄⋊C₄	—	2	1	no	—
101	C₄⋊C₄	—	2	1	no	—
102	C₄⋊C₄	—	2	1	no	—
103	C₄⋊C₄	—	278	1	no	—
104	C₄⋊C₄	—	278	1	no	—
105	C₄⋊C₄	C₂²⋊D₁₃₉	1	1	yes	characteristic
106	C₄²	—	2	1	no	—
107	C₄²	C₂²×D₁₃₉	1	1	yes	characteristic
108	Q₈	—	2	1	no	—
109	Q₈	—	2	1	no	—
110	Q₈	—	8	1	no	—
111	Q₈	—	1112	1	no	—
112	C₂×C₄	—	2	1	no	—
113	C₂×C₄	—	2	1	no	—
114	C₂×C₄	—	4	1	no	—
115	C₂×C₄	—	556	1	no	—
116	C₂×C₄	D₄×D₁₃₉	1	1	yes	characteristic
117	C₂×C₄	C₂×C₂²⋊D₁₃₉	1	1	yes	characteristic
118	C₂×C₄	#14555784	1	1	yes	characteristic
119	C₈	—	4	1	no	—
120	C₈	—	278	1	no	—
121	C₈	—	556	1	no	—
122	C₈	—	556	1	no	—
123	C₈	—	139	2	no	—
124	C₂²	#17984814	1	1	yes	characteristic
125	C₄	—	2	1	no	—
126	C₄	—	4	1	no	—
127	C₄	—	4	1	no	—
128	C₄	—	8	1	no	—
129	C₄	—	1112	1	no	—
130	C₄	Q₁₆×D₁₃₉	1	1	yes	characteristic
131	C₄	#17984872	1	1	yes	characteristic
132	C₄	#17984873	1	1	yes	characteristic
133	C₄	#17984874	1	1	yes	characteristic
134	C₂	#22581161	1	1	yes	characteristic
135	C₂	#22581209	1	1	yes	characteristic
136	C₂	#22581221	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#22581356

C₂

yes

maximal, characteristic

#22581248

C₂

yes

maximal, characteristic

#22581084

C₂

yes

maximal, characteristic

#22580703

C₂

yes

maximal, characteristic

#22580702

C₂

yes

maximal, characteristic

#22580701

C₂

yes

maximal, characteristic

#477×C₁₃₉

C₂

yes

maximal, characteristic

#17984842

C₂²

yes

—

—

—

C₄⋊(C₁₃₉⋊C₈)

—

C₄⋊(C₁₃₉⋊C₈)

C₂²

yes

characteristic

C₄⋊(C₁₃₉⋊C₈)

C₂²

yes

characteristic

#17984766

—

#17984753

—

C₄×C₁₃₉⋊C₈

C₂²

yes

characteristic

C₄⋊Q₈×C₁₃₉

C₂²

yes

characteristic

C₄×Q₈×C₁₃₉

C₂²

yes

characteristic

#107×C₁₃₉

—

C₄⋊C₈×C₁₃₉

C₂²

yes

characteristic

#103×C₁₃₉

—

C₂×Dic₂₇₈

—

C₂×C₁₃₉⋊C₈

—

C₂×C₁₃₉⋊C₈

—

C₂×C₁₃₉⋊C₈

D₄

yes

characteristic

C₂×C₁₃₉⋊C₈

D₄

yes

characteristic

C₄⋊Dic₁₃₉

—

C₄⋊Dic₁₃₉

—

C₂×Q₈×C₁₃₉

—

C₂×Q₈×C₁₃₉

D₄

yes

characteristic

C₂×C₈×C₁₃₉

—

C₄⋊C₄×C₁₃₉

—

C₄⋊C₄×C₁₃₉

—

C₄⋊C₄×C₁₃₉

—

C₄⋊C₄×C₁₃₉

D₄

yes

characteristic

C₄²×C₁₃₉

—

C₄²×C₁₃₉

C₂³

yes

characteristic

Dic₂₇₈

—

C₂×Dic₁₃₉

—

C₁₃₉⋊C₈

—

C₁₃₉⋊C₈

—

C₁₃₉⋊C₈

—

C₁₃₉⋊C₈

Q₁₆

yes

—

Q₈×C₁₃₉

—

Q₈×C₁₃₉

—

Q₈×C₁₃₉

—

C₂×C₄×C₁₃₉

—

C₂×C₄×C₁₃₉

—

C₂×C₄×C₁₃₉

—

C₂×C₄×C₁₃₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₃₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₃₉

#41

yes

characteristic

C₈×C₁₃₉

—

C₂²×C₁₃₉

#121

yes

characteristic

C₄×C₁₃₉

—

C₄×C₁₃₉

—

C₄×C₁₃₉

—

C₄×C₁₃₉

—

C₄×C₁₃₉

C₂×Q₁₆

yes

C₄×C₁₃₉

yes

C₄×C₁₃₉

yes

C₄×C₁₃₉

yes

Dic₁₃₉

—

C₂×C₁₃₉

yes

C₂×C₁₃₉

yes

C₂×C₁₃₉

yes

C₁₃₉

yes

characteristic, complemented, Sylow

#1696

—

139

maximal, Sylow

#500

—

139

—

#477

—

139

—

#477

D₁₃₉

yes

characteristic

#446

—

139

—

#334

—

139

—

#333

—

139

—

#333

—

139

—

C₄⋊Q₈

—

139

—

C₄⋊Q₈

C₂×D₁₃₉

yes

characteristic

C₄×Q₈

C₂×D₁₃₉

yes

characteristic

#107

—

#107

—

278

—

#107

—

278

—

#107

—

278

—

C₄⋊C₈

—

278

—

C₄⋊C₈

—

139

—

C₄⋊C₈

—

139

—

C₄⋊C₈

C₂×D₁₃₉

yes

characteristic

#103

—

#103

—

278

—

#97

—

278

—

C₄×C₈

—

139

—

C₂×Q₈

—

C₂×Q₈

—

278

—

C₂×Q₈

C₂²⋊D₁₃₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

278

—

C₂×C₈

—

278

—

C₂×C₈

—

139

—

C₂×C₈

—

139

—

100

C₄⋊C₄

—

101

C₄⋊C₄

—

102

C₄⋊C₄

—

103

C₄⋊C₄

—

278

—

104

C₄⋊C₄

—

278

—

105

C₄⋊C₄

C₂²⋊D₁₃₉

yes

characteristic

106

C₄²

—

107

C₄²

C₂²×D₁₃₉

yes

characteristic

108

Q₈

—

109

Q₈

—

110

Q₈

—

111

Q₈

—

1112

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

556

—

116

C₂×C₄

D₄×D₁₃₉

yes

characteristic

117

C₂×C₄

C₂×C₂²⋊D₁₃₉

yes

characteristic

118

C₂×C₄

#14555784

yes

characteristic

119

C₈

—

120

C₈

—

278

—

121

C₈

—

556

—

122

C₈

—

556

—

123

C₈

—

139

—

124

C₂²

#17984814

yes

characteristic

125

C₄

—

126

C₄

—

127

C₄

—

128

C₄

—

129

C₄

—

1112

—

130

C₄

Q₁₆×D₁₃₉

yes

characteristic

131

C₄

#17984872

yes

characteristic

132

C₄

#17984873

yes

characteristic

133

C₄

#17984874

yes

characteristic

134

C₂

#22581161

yes

characteristic

135

C₂

#22581209

yes

characteristic

136

C₂

#22581221

yes

characteristic

	subgroup	G/H
center	C₂²	#17984814
commutator, cosocle	C₄²×C₁₃₉	C₂³
Frattini	C₄²	C₂²×D₁₃₉
Fitting	#477×C₁₃₉	C₂
socle, prime radical	C₂²×C₁₃₉	#121
hypercenter	#477	D₁₃₉
hypocenter	C₁₃₉	#1696
LCS	G ▷ C₄²×C₁₃₉ ▷ C₂²×C₁₃₉ ▷ C₁₃₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #477

subgroup

G/H

center

C₂²

#17984814

commutator, cosocle

C₄²×C₁₃₉

C₂³

Frattini

C₄²

C₂²×D₁₃₉

Fitting

#477×C₁₃₉

C₂

C₂²×C₁₃₉

D₁₃₉

C₁₃₉

G ▷ C₄²×C₁₃₉ ▷ C₂²×C₁₃₉ ▷ C₁₃₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #477

N	H ≅ G/N	type
68. C₁₃₉	#1696	semidirect

H ≅ G/N

type

68. C₁₃₉

#1696

semidirect

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

subgroup	index
#22581356	2
#22581248	2
#22581084	2
#22580703	2
#22580702	2
#22580701	2
#477×C₁₃₉	2
#1696	139

subgroup

index

#477×C₁₃₉

139

Subgroups — #31805930

Conjugacy classes of subgroups

Complements

Maximal subgroups