Group #31807957 — subgroups

Subgroups — #31807957

Order 17792.

210 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 65 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	#22581002	C₂	1	1	yes	maximal, characteristic, complemented
2	#22580979	C₂	1	2	yes	maximal, complemented
3	#22580970	C₂	1	2	yes	maximal
4	#22580710	C₂	1	1	yes	maximal, characteristic, complemented
5	#408×C₁₃₉	C₂	1	1	yes	maximal, characteristic
6	C₂×#14555769	C₂²	1	2	yes	—
7	#17984801	C₂²	1	2	yes	—
8	#17984778	—	2	2	no	—
9	Dic₁₃₉⋊C₈	—	2	4	no	—
10	#17984769	—	2	4	no	—
11	C₂×#41×C₁₃₉	C₂²	1	1	yes	characteristic
12	C₂×M₁₆×C₁₃₉	C₂²	1	1	yes	characteristic
13	C₂²×C₈×C₁₃₉	C₂²	1	1	yes	characteristic
14	C₂²⋊C₈×C₁₃₉	—	2	2	no	—
15	#14555769	—	2	2	no	—
16	#14555769	—	2	2	no	—
17	C₂×C₁₃₉⋊C₈	—	2	2	no	—
18	C₄⋊Dic₁₃₉	—	2	2	no	—
19	C₂²⋊Dic₁₃₉	—	2	2	no	—
20	C₄×Dic₁₃₉	D₄	1	4	yes	—
21	#41×C₁₃₉	—	2	2	no	—
22	#41×C₁₃₉	—	2	2	no	—
23	C₂×Q₈×C₁₃₉	Q₈	1	1	yes	characteristic
24	C₂×D₄×C₁₃₉	—	2	1	no	—
25	C₂×D₄×C₁₃₉	Q₈	1	1	yes	characteristic
26	C₂²×C₄×C₁₃₉	—	2	1	no	—
27	C₂²×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
28	M₁₆×C₁₃₉	—	2	2	no	—
29	C₂×C₈×C₁₃₉	—	2	2	no	—
30	C₂×C₈×C₁₃₉	—	2	1	no	—
31	C₂×C₈×C₁₃₉	D₄	1	2	yes	—
32	C₂×Dic₁₃₉	—	2	4	no	—
33	C₁₃₉⋊C₈	—	4	2	no	—
34	C₂³×C₁₃₉	—	2	1	no	—
35	C₂³×C₁₃₉	#41	1	1	yes	characteristic
36	Q₈×C₁₃₉	—	2	2	no	—
37	D₄×C₁₃₉	—	2	2	no	—
38	D₄×C₁₃₉	—	4	2	no	—
39	C₂×C₄×C₁₃₉	—	2	1	no	—
40	C₂×C₄×C₁₃₉	—	4	1	no	—
41	C₂×C₄×C₁₃₉	—	4	1	no	—
42	C₂×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
43	C₂×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
44	C₂×C₄×C₁₃₉	C₂×Q₈	1	1	yes	characteristic
45	C₂×C₄×C₁₃₉	#41	1	2	yes	—
46	C₈×C₁₃₉	—	2	2	no	—
47	C₈×C₁₃₉	—	4	1	no	—
48	C₂²×C₁₃₉	—	4	1	no	—
49	C₂²×C₁₃₉	—	4	2	no	—
50	C₂²×C₁₃₉	—	4	1	no	—
51	C₂²×C₁₃₉	C₂²⋊Q₈	1	1	yes	characteristic
52	C₂²×C₁₃₉	#123	1	2	yes	—
53	C₄×C₁₃₉	—	4	1	no	—
54	C₄×C₁₃₉	C₂²⋊Q₈	1	2	yes	—
55	C₄×C₁₃₉	#123	1	1	yes	characteristic
56	C₄×C₁₃₉	#127	1	1	yes	characteristic
57	Dic₁₃₉	—	4	4	no	—
58	C₂×C₁₃₉	—	2	2	no	—
59	C₂×C₁₃₉	—	2	1	no	—
60	C₂×C₁₃₉	—	8	1	no	—
61	C₂×C₁₃₉	#399	1	1	yes	characteristic
62	C₁₃₉	#2098	1	1	yes	characteristic, complemented, Sylow
63	#2098	—	139	1	no	maximal, Sylow
64	#430	—	139	1	no	—
65	#424	—	139	2	no	—
66	#421	—	139	2	no	—
67	#408	D₁₃₉	1	1	yes	characteristic
68	H(3,ℤ/4)	—	139	1	no	—
69	C₂×#41	C₂×D₁₃₉	1	1	yes	characteristic
70	C₂×M₁₆	—	139	2	no	—
71	C₂×M₁₆	C₂×D₁₃₉	1	1	yes	characteristic
72	C₂²×C₈	C₂×D₁₃₉	1	1	yes	characteristic
73	#117	—	139	2	no	—
74	#108	—	278	2	no	—
75	C₄⋊C₈	—	278	4	no	—
76	#104	—	278	4	no	—
77	C₂²⋊C₈	—	2	2	no	—
78	#41	—	2	2	no	—
79	#41	—	2	2	no	—
80	C₂×Q₈	Dic₂₇₈	1	1	yes	characteristic
81	C₂×D₄	—	2	1	no	—
82	C₂×D₄	Dic₂₇₈	1	1	yes	characteristic
83	C₂²×C₄	—	2	1	no	—
84	C₂²×C₄	C₂²×D₁₃₉	1	1	yes	characteristic
85	M₁₆	—	2	2	no	—
86	M₁₆	—	278	2	no	—
87	M₁₆	—	278	2	no	—
88	C₂×C₈	—	2	2	no	—
89	C₂×C₈	—	2	1	no	—
90	C₂×C₈	—	278	2	no	—
91	C₂×C₈	C₂²⋊D₁₃₉	1	2	yes	—
92	C₄⋊C₄	—	278	2	no	—
93	C₂²⋊C₄	—	278	2	no	—
94	C₄²	—	139	4	no	—
95	C₂³	—	2	1	no	—
96	C₂³	#14555785	1	1	yes	characteristic
97	Q₈	—	2	2	no	—
98	D₄	—	2	2	no	—
99	D₄	—	4	2	no	—
100	C₂×C₄	—	2	1	no	—
101	C₂×C₄	—	4	1	no	—
102	C₂×C₄	—	4	1	no	—
103	C₂×C₄	—	278	4	no	—
104	C₂×C₄	D₄×D₁₃₉	1	2	yes	—
105	C₂×C₄	C₂×C₂²⋊D₁₃₉	1	1	yes	characteristic
106	C₂×C₄	C₂×Dic₂₇₈	1	1	yes	characteristic
107	C₂×C₄	#14555784	1	2	yes	—
108	C₈	—	2	2	no	—
109	C₈	—	4	1	no	—
110	C₈	—	556	2	no	—
111	C₂²	—	4	1	no	—
112	C₂²	—	4	2	no	—
113	C₂²	—	4	1	no	—
114	C₂²	#17984821	1	1	yes	characteristic
115	C₂²	#17984824	1	2	yes	—
116	C₄	—	4	1	no	—
117	C₄	—	556	4	no	—
118	C₄	#17984819	1	2	yes	—
119	C₄	#17984823	1	1	yes	characteristic
120	C₄	#17984838	1	1	yes	characteristic
121	C₂	—	2	2	no	—
122	C₂	—	2	1	no	—
123	C₂	—	8	1	no	—
124	C₂	#22580889	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#22581002

C₂

yes

maximal, characteristic, complemented

#22580979

C₂

yes

maximal, complemented

#22580970

C₂

yes

maximal

#22580710

C₂

yes

maximal, characteristic, complemented

#408×C₁₃₉

C₂

yes

maximal, characteristic

C₂×#14555769

C₂²

yes

—

#17984801

C₂²

yes

—

#17984778

—

Dic₁₃₉⋊C₈

—

#17984769

—

C₂×#41×C₁₃₉

C₂²

yes

characteristic

C₂×M₁₆×C₁₃₉

C₂²

yes

characteristic

C₂²×C₈×C₁₃₉

C₂²

yes

characteristic

C₂²⋊C₈×C₁₃₉

—

#14555769

—

#14555769

—

C₂×C₁₃₉⋊C₈

—

C₄⋊Dic₁₃₉

—

C₂²⋊Dic₁₃₉

—

C₄×Dic₁₃₉

D₄

yes

—

#41×C₁₃₉

—

#41×C₁₃₉

—

C₂×Q₈×C₁₃₉

Q₈

yes

characteristic

C₂×D₄×C₁₃₉

—

C₂×D₄×C₁₃₉

Q₈

yes

characteristic

C₂²×C₄×C₁₃₉

—

C₂²×C₄×C₁₃₉

C₂³

yes

characteristic

M₁₆×C₁₃₉

—

C₂×C₈×C₁₃₉

—

C₂×C₈×C₁₃₉

—

C₂×C₈×C₁₃₉

D₄

yes

—

C₂×Dic₁₃₉

—

C₁₃₉⋊C₈

—

C₂³×C₁₃₉

—

C₂³×C₁₃₉

#41

yes

characteristic

Q₈×C₁₃₉

—

D₄×C₁₃₉

—

D₄×C₁₃₉

—

C₂×C₄×C₁₃₉

—

C₂×C₄×C₁₃₉

—

C₂×C₄×C₁₃₉

—

C₂×C₄×C₁₃₉

C₂×D₄

yes

—

C₂×C₄×C₁₃₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₃₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₁₃₉

#41

yes

—

C₈×C₁₃₉

—

C₈×C₁₃₉

—

C₂²×C₁₃₉

—

C₂²×C₁₃₉

—

C₂²×C₁₃₉

—

C₂²×C₁₃₉

C₂²⋊Q₈

yes

characteristic

C₂²×C₁₃₉

#123

yes

—

C₄×C₁₃₉

—

C₄×C₁₃₉

C₂²⋊Q₈

yes

—

C₄×C₁₃₉

yes

C₄×C₁₃₉

yes

Dic₁₃₉

—

C₂×C₁₃₉

—

C₂×C₁₃₉

—

C₂×C₁₃₉

—

C₂×C₁₃₉

#399

yes

characteristic

C₁₃₉

#2098

yes

characteristic, complemented, Sylow

#2098

—

139

maximal, Sylow

#430

—

139

—

#424

—

139

—

#421

—

139

—

#408

D₁₃₉

yes

characteristic

H(3,ℤ/4)

—

139

—

C₂×#41

C₂×D₁₃₉

yes

characteristic

C₂×M₁₆

—

139

—

C₂×M₁₆

C₂×D₁₃₉

yes

characteristic

C₂²×C₈

C₂×D₁₃₉

yes

characteristic

#117

—

139

—

#108

—

278

—

C₄⋊C₈

—

278

—

#104

—

278

—

C₂²⋊C₈

—

#41

—

#41

—

C₂×Q₈

Dic₂₇₈

yes

characteristic

C₂×D₄

—

C₂×D₄

Dic₂₇₈

yes

characteristic

C₂²×C₄

—

C₂²×C₄

C₂²×D₁₃₉

yes

characteristic

M₁₆

—

M₁₆

—

278

—

M₁₆

—

278

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

278

—

C₂×C₈

C₂²⋊D₁₃₉

yes

—

C₄⋊C₄

—

278

—

C₂²⋊C₄

—

278

—

C₄²

—

139

—

C₂³

—

C₂³

#14555785

yes

characteristic

Q₈

—

D₄

—

D₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

278

—

104

C₂×C₄

D₄×D₁₃₉

yes

—

105

C₂×C₄

C₂×C₂²⋊D₁₃₉

yes

characteristic

106

C₂×C₄

C₂×Dic₂₇₈

yes

characteristic

107

C₂×C₄

#14555784

yes

—

108

C₈

—

109

C₈

—

110

C₈

—

556

—

111

C₂²

—

112

C₂²

—

113

C₂²

—

114

C₂²

#17984821

yes

characteristic

115

C₂²

#17984824

yes

—

116

C₄

—

117

C₄

—

556

—

118

C₄

#17984819

yes

—

119

C₄

#17984823

yes

characteristic

120

C₄

#17984838

yes

characteristic

121

C₂

—

122

C₂

—

123

C₂

—

124

C₂

#22580889

yes

characteristic

	subgroup	G/H
center	C₄	#17984838
commutator, cosocle	C₂²×C₄×C₁₃₉	C₂³
Frattini	C₂²×C₄	C₂²×D₁₃₉
Fitting	#408×C₁₃₉	C₂
socle	C₂×C₁₃₉	#399
prime radical	C₂×#41×C₁₃₉	C₂²
hypercenter	#408	D₁₃₉
hypocenter	C₁₃₉	#2098
LCS	G ▷ C₂²×C₄×C₁₃₉ ▷ C₂×C₁₃₉ ▷ C₁₃₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #408

subgroup

G/H

center

C₄

#17984838

commutator, cosocle

C₂²×C₄×C₁₃₉

C₂³

Frattini

C₂²×C₄

C₂²×D₁₃₉

Fitting

#408×C₁₃₉

C₂

socle

C₂×C₁₃₉

#399

prime radical

C₂×#41×C₁₃₉

C₂²

D₁₃₉

C₁₃₉

G ▷ C₂²×C₄×C₁₃₉ ▷ C₂×C₁₃₉ ▷ C₁₃₉

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #408

N	H ≅ G/N	type
1. #22581002	C₂	semidirect
2. #22580979	C₂	semidirect
4. #22580710	C₂	semidirect
62. C₁₃₉	#2098	semidirect

H ≅ G/N

type

1. #22581002

C₂

semidirect

2. #22580979

C₂

semidirect

4. #22580710

C₂

semidirect

62. C₁₃₉

#2098

semidirect

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

subgroup	index
#22581002	2
#22580979	2
#22580970	2
#22580710	2
#408×C₁₃₉	2
#2098	139

subgroup

index

#408×C₁₃₉

139

Subgroups — #31807957

Conjugacy classes of subgroups

Complements

Maximal subgroups