Group #31807947 — subgroups

Subgroups — #31807947

Order 17792.

254 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 254 conjugacy classes of subgroups — too many to draw. Only its 93 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×#17984773	C₂	1	2	yes	maximal
2	C₂×#17984766	C₂	1	2	yes	maximal
3	#22580823	C₂	1	1	yes	maximal, characteristic
4	#22580708	C₂	1	1	yes	maximal, characteristic
5	#391×C₁₃₉	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₁₃₉⋊C₈	C₂²	1	2	yes	—
7	C₂×C₄⋊Dic₁₃₉	—	2	2	no	—
8	C₂×C₄⋊Dic₁₃₉	C₂²	1	2	yes	—
9	#17984773	—	2	4	no	—
10	#17984766	—	2	4	no	—
11	C₂²×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
13	C₂×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
14	#95×C₁₃₉	—	2	2	no	—
15	C₂²×Dic₁₃₉	—	2	2	no	—
16	C₂×C₁₃₉⋊C₈	—	2	2	no	—
17	C₂×C₁₃₉⋊C₈	—	2	2	no	—
18	C₂×C₁₃₉⋊C₈	D₄	1	4	yes	—
19	C₄⋊Dic₁₃₉	—	2	2	no	—
20	C₄⋊Dic₁₃₉	—	2	2	no	—
21	C₄⋊Dic₁₃₉	—	4	4	no	—
22	C₂×Q₈×C₁₃₉	—	2	1	no	—
23	C₂×Q₈×C₁₃₉	—	2	2	no	—
24	C₂×Q₈×C₁₃₉	—	2	2	no	—
25	C₂×Q₈×C₁₃₉	Q₈	1	2	yes	—
26	C₂²×C₄×C₁₃₉	—	2	1	no	—
27	C₂²×C₄×C₁₃₉	—	2	1	no	—
28	C₂²×C₄×C₁₃₉	D₄	1	2	yes	—
29	C₂²×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
30	C₄⋊C₄×C₁₃₉	—	2	2	no	—
31	C₄²×C₁₃₉	—	2	2	no	—
32	C₂×Dic₁₃₉	—	4	2	no	—
33	C₂×Dic₁₃₉	—	4	4	no	—
34	C₁₃₉⋊C₈	—	2	4	no	—
35	C₂³×C₁₃₉	C₂×D₄	1	1	yes	characteristic
36	Q₈×C₁₃₉	—	2	4	no	—
37	Q₈×C₁₃₉	—	4	2	no	—
38	C₂×C₄×C₁₃₉	—	2	2	no	—
39	C₂×C₄×C₁₃₉	—	2	2	no	—
40	C₂×C₄×C₁₃₉	—	2	2	no	—
41	C₂×C₄×C₁₃₉	—	4	1	no	—
42	C₂×C₄×C₁₃₉	—	4	1	no	—
43	C₂×C₄×C₁₃₉	—	4	1	no	—
44	C₂×C₄×C₁₃₉	—	4	2	no	—
45	C₂×C₄×C₁₃₉	SD₁₆	1	4	yes	—
46	C₂×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
47	C₂×C₄×C₁₃₉	C₂×Q₈	1	1	yes	characteristic
48	C₂×C₄×C₁₃₉	#41	1	2	yes	—
49	C₂×C₄×C₁₃₉	#41	1	1	yes	characteristic
50	C₂²×C₁₃₉	C₂²⋊Q₈	1	1	yes	characteristic
51	C₂²×C₁₃₉	#123	1	1	yes	characteristic
52	C₂²×C₁₃₉	#127	1	1	yes	characteristic
53	C₂²×C₁₃₉	C₂×SD₁₆	1	2	yes	—
54	C₂²×C₁₃₉	#137	1	2	yes	—
55	C₄×C₁₃₉	—	2	4	no	—
56	C₄×C₁₃₉	—	4	2	no	—
57	C₄×C₁₃₉	—	8	1	no	—
58	C₄×C₁₃₉	C₂²⋊Q₈	1	2	yes	—
59	C₄×C₁₃₉	#123	1	2	yes	—
60	Dic₁₃₉	—	8	2	no	—
61	C₂×C₁₃₉	#399	1	1	yes	characteristic
62	C₂×C₁₃₉	#475	1	2	yes	—
63	C₂×C₁₃₉	#483	1	2	yes	—
64	C₂×C₁₃₉	#492	1	1	yes	characteristic
65	C₂×C₁₃₉	#497	1	1	yes	characteristic
66	C₁₃₉	#2096	1	1	yes	characteristic, complemented, Sylow
67	#2096	—	139	1	no	maximal, Sylow
68	C₂×#106	—	139	2	no	—
69	C₂×#103	—	139	2	no	—
70	#391	D₁₃₉	1	1	yes	characteristic
71	#384	—	139	1	no	—
72	#336	—	139	1	no	—
73	C₂²×Q₈	C₂×D₁₃₉	1	1	yes	characteristic
74	C₂²×C₈	—	139	2	no	—
75	C₂×C₄⋊C₄	—	278	2	no	—
76	C₂×C₄⋊C₄	—	139	2	no	—
77	C₂×C₄⋊C₄	C₂×D₁₃₉	1	1	yes	characteristic
78	C₂×C₄²	C₂×D₁₃₉	1	1	yes	characteristic
79	#106	—	278	4	no	—
80	#103	—	278	4	no	—
81	#95	—	2	2	no	—
82	C₂×Q₈	—	2	1	no	—
83	C₂×Q₈	—	2	2	no	—
84	C₂×Q₈	—	2	2	no	—
85	C₂×Q₈	Dic₂₇₈	1	2	yes	—
86	C₂²×C₄	—	2	1	no	—
87	C₂²×C₄	—	2	1	no	—
88	C₂²×C₄	—	278	2	no	—
89	C₂²×C₄	C₂²⋊D₁₃₉	1	2	yes	—
90	C₂²×C₄	C₂²×D₁₃₉	1	1	yes	characteristic
91	C₂×C₈	—	278	2	no	—
92	C₂×C₈	—	278	2	no	—
93	C₂×C₈	—	139	4	no	—
94	C₄⋊C₄	—	2	2	no	—
95	C₄⋊C₄	—	278	2	no	—
96	C₄⋊C₄	—	278	2	no	—
97	C₄⋊C₄	—	556	4	no	—
98	C₄²	—	2	2	no	—
99	C₂³	C₂×C₂²⋊D₁₃₉	1	1	yes	characteristic
100	Q₈	—	2	4	no	—
101	Q₈	—	4	2	no	—
102	C₂×C₄	—	2	2	no	—
103	C₂×C₄	—	2	2	no	—
104	C₂×C₄	—	2	2	no	—
105	C₂×C₄	—	4	1	no	—
106	C₂×C₄	—	4	1	no	—
107	C₂×C₄	—	4	1	no	—
108	C₂×C₄	—	4	2	no	—
109	C₂×C₄	—	556	2	no	—
110	C₂×C₄	—	556	4	no	—
111	C₂×C₄	#14555772	1	4	yes	—
112	C₂×C₄	D₄×D₁₃₉	1	2	yes	—
113	C₂×C₄	C₂×Dic₂₇₈	1	1	yes	characteristic
114	C₂×C₄	#14555784	1	2	yes	—
115	C₂×C₄	#14555785	1	1	yes	characteristic
116	C₈	—	278	4	no	—
117	C₂²	#17984821	1	1	yes	characteristic
118	C₂²	#17984823	1	1	yes	characteristic
119	C₂²	#17984838	1	1	yes	characteristic
120	C₂²	C₂×#14555772	1	2	yes	—
121	C₂²	#17984872	1	2	yes	—
122	C₄	—	2	4	no	—
123	C₄	—	4	2	no	—
124	C₄	—	8	1	no	—
125	C₄	—	1112	2	no	—
126	C₄	#17984819	1	2	yes	—
127	C₄	#17984824	1	2	yes	—
128	C₂	#22580889	1	1	yes	characteristic
129	C₂	#22581238	1	2	yes	—
130	C₂	#22581281	1	2	yes	—
131	C₂	#22581327	1	1	yes	characteristic
132	C₂	#22581348	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#17984773

C₂

yes

maximal

C₂×#17984766

C₂

yes

maximal

#22580823

C₂

yes

maximal, characteristic

#22580708

C₂

yes

maximal, characteristic

#391×C₁₃₉

C₂

yes

maximal, characteristic

C₂²×C₁₃₉⋊C₈

C₂²

yes

—

C₂×C₄⋊Dic₁₃₉

—

C₂×C₄⋊Dic₁₃₉

C₂²

yes

—

#17984773

—

#17984766

—

C₂²×Q₈×C₁₃₉

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₁₃₉

C₂²

yes

characteristic

C₂×C₄²×C₁₃₉

C₂²

yes

characteristic

#95×C₁₃₉

—

C₂²×Dic₁₃₉

—

C₂×C₁₃₉⋊C₈

—

C₂×C₁₃₉⋊C₈

—

C₂×C₁₃₉⋊C₈

D₄

yes

—

C₄⋊Dic₁₃₉

—

C₄⋊Dic₁₃₉

—

C₄⋊Dic₁₃₉

—

C₂×Q₈×C₁₃₉

—

C₂×Q₈×C₁₃₉

—

C₂×Q₈×C₁₃₉

—

C₂×Q₈×C₁₃₉

Q₈

yes

—

C₂²×C₄×C₁₃₉

—

C₂²×C₄×C₁₃₉

—

C₂²×C₄×C₁₃₉

D₄

yes

—

C₂²×C₄×C₁₃₉

C₂³

yes

characteristic

C₄⋊C₄×C₁₃₉

—

C₄²×C₁₃₉

—

C₂×Dic₁₃₉

—

C₂×Dic₁₃₉

—

C₁₃₉⋊C₈

—

C₂³×C₁₃₉

C₂×D₄

yes

characteristic

Q₈×C₁₃₉

—

Q₈×C₁₃₉

—

C₂×C₄×C₁₃₉

—

C₂×C₄×C₁₃₉

—

C₂×C₄×C₁₃₉

—

C₂×C₄×C₁₃₉

—

C₂×C₄×C₁₃₉

—

C₂×C₄×C₁₃₉

—

C₂×C₄×C₁₃₉

—

C₂×C₄×C₁₃₉

SD₁₆

yes

—

C₂×C₄×C₁₃₉

C₂×D₄

yes

—

C₂×C₄×C₁₃₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₁₃₉

#41

yes

—

C₂×C₄×C₁₃₉

#41

yes

characteristic

C₂²×C₁₃₉

C₂²⋊Q₈

yes

C₂²×C₁₃₉

yes

C₂²×C₁₃₉

yes

C₂²×C₁₃₉

C₂×SD₁₆

yes

—

C₂²×C₁₃₉

#137

yes

—

C₄×C₁₃₉

—

C₄×C₁₃₉

—

C₄×C₁₃₉

—

C₄×C₁₃₉

C₂²⋊Q₈

yes

—

C₄×C₁₃₉

#123

yes

—

Dic₁₃₉

—

C₂×C₁₃₉

#399

yes

characteristic

C₂×C₁₃₉

#475

yes

—

C₂×C₁₃₉

#483

yes

—

C₂×C₁₃₉

yes

C₂×C₁₃₉

yes

C₁₃₉

yes

characteristic, complemented, Sylow

#2096

—

139

maximal, Sylow

C₂×#106

—

139

—

C₂×#103

—

139

—

#391

D₁₃₉

yes

characteristic

#384

—

139

—

#336

—

139

—

C₂²×Q₈

C₂×D₁₃₉

yes

characteristic

C₂²×C₈

—

139

—

C₂×C₄⋊C₄

—

278

—

C₂×C₄⋊C₄

—

139

—

C₂×C₄⋊C₄

C₂×D₁₃₉

yes

characteristic

C₂×C₄²

C₂×D₁₃₉

yes

characteristic

#106

—

278

—

#103

—

278

—

#95

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

Dic₂₇₈

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

278

—

C₂²×C₄

C₂²⋊D₁₃₉

yes

—

C₂²×C₄

C₂²×D₁₃₉

yes

characteristic

C₂×C₈

—

278

—

C₂×C₈

—

278

—

C₂×C₈

—

139

—

C₄⋊C₄

—

C₄⋊C₄

—

278

—

C₄⋊C₄

—

278

—

C₄⋊C₄

—

556

—

C₄²

—

C₂³

C₂×C₂²⋊D₁₃₉

yes

characteristic

100

Q₈

—

101

Q₈

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

556

—

110

C₂×C₄

—

556

—

111

C₂×C₄

#14555772

yes

—

112

C₂×C₄

D₄×D₁₃₉

yes

—

113

C₂×C₄

C₂×Dic₂₇₈

yes

characteristic

114

C₂×C₄

#14555784

yes

—

115

C₂×C₄

#14555785

yes

characteristic

116

C₈

—

278

—

117

C₂²

#17984821

yes

characteristic

118

C₂²

#17984823

yes

characteristic

119

C₂²

#17984838

yes

characteristic

120

C₂²

C₂×#14555772

yes

—

121

C₂²

#17984872

yes

—

122

C₄

—

123

C₄

—

124

C₄

—

125

C₄

—

1112

—

126

C₄

#17984819

yes

—

127

C₄

#17984824

yes

—

128

C₂

#22580889

yes

characteristic

129

C₂

#22581238

yes

—

130

C₂

#22581281

yes

—

131

C₂

#22581327

yes

characteristic

132

C₂

#22581348

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₁₃₉
commutator, cosocle	C₂²×C₄×C₁₃₉	C₂³
Frattini	C₂²×C₄	C₂²×D₁₃₉
Fitting	#391×C₁₃₉	C₂
socle, prime radical	C₂³×C₁₃₉	C₂×D₄
hypercenter	#391	D₁₃₉
hypocenter	C₁₃₉	#2096
LCS	G ▷ C₂²×C₄×C₁₃₉ ▷ C₂×C₁₃₉ ▷ C₁₃₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #391

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₁₃₉

commutator, cosocle

C₂²×C₄×C₁₃₉

C₂³

Frattini

C₂²×C₄

C₂²×D₁₃₉

Fitting

#391×C₁₃₉

C₂

socle, prime radical

C₂³×C₁₃₉

C₂×D₄

D₁₃₉

C₁₃₉

G ▷ C₂²×C₄×C₁₃₉ ▷ C₂×C₁₃₉ ▷ C₁₃₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #391

N	H ≅ G/N	type
66. C₁₃₉	#2096	semidirect

H ≅ G/N

type

66. C₁₃₉

#2096

semidirect

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

subgroup	index
C₂×#17984773	2
C₂×#17984766	2
#22580823	2
#22580708	2
#391×C₁₃₉	2
#2096	139

subgroup

index

#391×C₁₃₉

139

Subgroups — #31807947

Conjugacy classes of subgroups

Complements

Maximal subgroups