Group #47983311 — subgroups

Subgroups — #47983311

Order 35456.

196 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 85 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	#31799848	C₂	1	1	yes	maximal, characteristic
2	#31799757	C₂	1	1	yes	maximal, characteristic
3	#31799756	C₂	1	2	yes	maximal
4	#31799756	C₂	1	2	yes	maximal
5	#336×C₂₇₇	C₂	1	1	yes	maximal, characteristic
6	C₂²×#14555660	C₂²	1	2	yes	—
7	C₂×C₄×Dic₂₇₇	C₂²	1	1	yes	characteristic
8	C₂×C₄×Dic₂₇₇	C₂²	1	1	yes	characteristic
9	#22579787	C₄	1	2	yes	—
10	#22579787	C₄	1	2	yes	—
11	C₂²×C₈×C₂₇₇	C₂²	1	2	yes	—
12	C₂×C₄²×C₂₇₇	C₂²	1	1	yes	characteristic
13	C₂²×Dic₂₇₇	C₂×C₄	1	1	yes	characteristic
14	C₂²×Dic₂₇₇	C₂×C₄	1	1	yes	characteristic
15	C₂²×Dic₂₇₇	C₂×C₄	1	2	yes	—
16	C₂×#14555660	—	2	2	no	—
17	C₂×#14555660	—	2	2	no	—
18	C₂×#14555660	—	2	2	no	—
19	C₄×Dic₂₇₇	—	2	1	no	—
20	C₄×Dic₂₇₇	—	2	2	no	—
21	C₄×Dic₂₇₇	—	2	1	no	—
22	C₂²×C₄×C₂₇₇	C₂×C₄	1	2	yes	—
23	C₂²×C₄×C₂₇₇	C₂³	1	1	yes	characteristic
24	C₂×C₈×C₂₇₇	—	2	2	no	—
25	C₂×C₈×C₂₇₇	—	2	2	no	—
26	C₂×C₈×C₂₇₇	—	2	2	no	—
27	C₄²×C₂₇₇	—	2	2	no	—
28	C₂×Dic₂₇₇	—	2	1	no	—
29	C₂×Dic₂₇₇	—	2	1	no	—
30	C₂×Dic₂₇₇	—	2	2	no	—
31	C₂×Dic₂₇₇	—	2	2	no	—
32	C₂×Dic₂₇₇	—	2	2	no	—
33	C₂×Dic₂₇₇	—	2	2	no	—
34	C₂×Dic₂₇₇	—	2	2	no	—
35	#14555660	—	4	2	no	—
36	C₂³×C₂₇₇	C₂²×C₄	1	1	yes	characteristic
37	C₂×C₄×C₂₇₇	—	2	2	no	—
38	C₂×C₄×C₂₇₇	—	2	2	no	—
39	C₂×C₄×C₂₇₇	—	2	2	no	—
40	C₂×C₄×C₂₇₇	#41	1	2	yes	—
41	C₂×C₄×C₂₇₇	#41	1	1	yes	characteristic
42	C₂×C₄×C₂₇₇	#41	1	2	yes	—
43	C₂×C₄×C₂₇₇	#41	1	1	yes	characteristic
44	C₈×C₂₇₇	—	4	2	no	—
45	C₂²×C₂₇₇	#117	1	1	yes	characteristic
46	C₂²×C₂₇₇	#117	1	1	yes	characteristic
47	C₂²×C₂₇₇	#117	1	1	yes	characteristic
48	C₂²×C₂₇₇	#131	1	2	yes	—
49	C₂²×C₂₇₇	#131	1	2	yes	—
50	C₄×C₂₇₇	—	4	2	no	—
51	C₄×C₂₇₇	#126	1	2	yes	—
52	C₄×C₂₇₇	#126	1	2	yes	—
53	Dic₂₇₇	—	4	1	no	—
54	Dic₂₇₇	—	4	1	no	—
55	Dic₂₇₇	—	4	2	no	—
56	C₂×C₂₇₇	#383	1	1	yes	characteristic
57	C₂×C₂₇₇	#433	1	1	yes	characteristic
58	C₂×C₂₇₇	#433	1	2	yes	—
59	C₂×C₂₇₇	#433	1	1	yes	characteristic
60	C₂×C₂₇₇	#433	1	2	yes	—
61	C₂₇₇	#1840	1	1	yes	characteristic, complemented, Sylow
62	#1840	—	277	1	no	maximal, Sylow
63	#376	—	277	1	no	—
64	#336	—	277	2	no	—
65	#336	—	277	2	no	—
66	#336	—	277	1	no	—
67	#336	D₂₇₇	1	1	yes	characteristic
68	C₂²×C₈	—	277	2	no	—
69	C₂²×C₈	C₂×D₂₇₇	1	2	yes	—
70	C₂×C₄²	—	277	1	no	—
71	C₂×C₄²	—	277	1	no	—
72	C₂×C₄²	C₂×D₂₇₇	1	1	yes	characteristic
73	#95	—	277	2	no	—
74	#95	—	277	2	no	—
75	C₂²×C₄	—	277	1	no	—
76	C₂²×C₄	—	277	1	no	—
77	C₂²×C₄	—	277	2	no	—
78	C₂²×C₄	C₄×D₂₇₇	1	2	yes	—
79	C₂²×C₄	C₂²×D₂₇₇	1	1	yes	characteristic
80	C₂×C₈	—	2	2	no	—
81	C₂×C₈	—	2	2	no	—
82	C₂×C₈	—	2	2	no	—
83	C₂×C₈	—	554	2	no	—
84	C₂×C₈	—	554	2	no	—
85	C₂×C₈	—	554	2	no	—
86	C₄²	—	2	2	no	—
87	C₄²	—	554	1	no	—
88	C₄²	—	554	2	no	—
89	C₄²	—	554	1	no	—
90	C₂³	C₂×C₄×D₂₇₇	1	1	yes	characteristic
91	C₂×C₄	—	2	2	no	—
92	C₂×C₄	—	2	2	no	—
93	C₂×C₄	—	2	2	no	—
94	C₂×C₄	—	554	1	no	—
95	C₂×C₄	—	554	1	no	—
96	C₂×C₄	—	554	2	no	—
97	C₂×C₄	—	554	2	no	—
98	C₂×C₄	—	554	2	no	—
99	C₂×C₄	—	554	2	no	—
100	C₂×C₄	—	554	2	no	—
101	C₂×C₄	#17984562	1	1	yes	characteristic
102	C₂×C₄	#17984562	1	2	yes	—
103	C₂×C₄	#17984563	1	2	yes	—
104	C₂×C₄	#17984564	1	1	yes	characteristic
105	C₈	—	4	2	no	—
106	C₈	—	1108	2	no	—
107	C₂²	#22579836	1	1	yes	characteristic
108	C₂²	#22579837	1	1	yes	characteristic
109	C₂²	#22579838	1	1	yes	characteristic
110	C₂²	#22579886	1	2	yes	—
111	C₂²	#22579888	1	2	yes	—
112	C₄	—	4	2	no	—
113	C₄	—	1108	1	no	—
114	C₄	—	1108	1	no	—
115	C₄	—	1108	2	no	—
116	C₄	#22579873	1	2	yes	—
117	C₄	#22579875	1	2	yes	—
118	C₂	#31799869	1	1	yes	characteristic
119	C₂	#31800060	1	2	yes	—
120	C₂	#31800061	1	1	yes	characteristic
121	C₂	#31800062	1	2	yes	—
122	C₂	#31800064	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#31799848

C₂

yes

maximal, characteristic

#31799757

C₂

yes

maximal, characteristic

#31799756

C₂

yes

maximal

#31799756

C₂

yes

maximal

#336×C₂₇₇

C₂

yes

maximal, characteristic

C₂²×#14555660

C₂²

yes

—

C₂×C₄×Dic₂₇₇

C₂²

yes

characteristic

C₂×C₄×Dic₂₇₇

C₂²

yes

characteristic

#22579787

C₄

yes

—

#22579787

C₄

yes

—

C₂²×C₈×C₂₇₇

C₂²

yes

—

C₂×C₄²×C₂₇₇

C₂²

yes

characteristic

C₂²×Dic₂₇₇

C₂×C₄

yes

characteristic

C₂²×Dic₂₇₇

C₂×C₄

yes

characteristic

C₂²×Dic₂₇₇

C₂×C₄

yes

—

C₂×#14555660

—

C₂×#14555660

—

C₂×#14555660

—

C₄×Dic₂₇₇

—

C₄×Dic₂₇₇

—

C₄×Dic₂₇₇

—

C₂²×C₄×C₂₇₇

C₂×C₄

yes

—

C₂²×C₄×C₂₇₇

C₂³

yes

characteristic

C₂×C₈×C₂₇₇

—

C₂×C₈×C₂₇₇

—

C₂×C₈×C₂₇₇

—

C₄²×C₂₇₇

—

C₂×Dic₂₇₇

—

C₂×Dic₂₇₇

—

C₂×Dic₂₇₇

—

C₂×Dic₂₇₇

—

C₂×Dic₂₇₇

—

C₂×Dic₂₇₇

—

C₂×Dic₂₇₇

—

#14555660

—

C₂³×C₂₇₇

C₂²×C₄

yes

characteristic

C₂×C₄×C₂₇₇

—

C₂×C₄×C₂₇₇

—

C₂×C₄×C₂₇₇

—

C₂×C₄×C₂₇₇

#41

yes

—

C₂×C₄×C₂₇₇

#41

yes

characteristic

C₂×C₄×C₂₇₇

#41

yes

—

C₂×C₄×C₂₇₇

#41

yes

characteristic

C₈×C₂₇₇

—

C₂²×C₂₇₇

yes

C₂²×C₂₇₇

yes

C₂²×C₂₇₇

yes

C₂²×C₂₇₇

yes

—

C₂²×C₂₇₇

#131

yes

—

C₄×C₂₇₇

—

C₄×C₂₇₇

#126

yes

—

C₄×C₂₇₇

#126

yes

—

Dic₂₇₇

—

Dic₂₇₇

—

Dic₂₇₇

—

C₂×C₂₇₇

yes

C₂×C₂₇₇

yes

C₂×C₂₇₇

yes

—

C₂×C₂₇₇

#433

yes

characteristic

C₂×C₂₇₇

#433

yes

—

C₂₇₇

#1840

yes

characteristic, complemented, Sylow

#1840

—

277

maximal, Sylow

#376

—

277

—

#336

—

277

—

#336

—

277

—

#336

—

277

—

#336

D₂₇₇

yes

characteristic

C₂²×C₈

—

277

—

C₂²×C₈

C₂×D₂₇₇

yes

—

C₂×C₄²

—

277

—

C₂×C₄²

—

277

—

C₂×C₄²

C₂×D₂₇₇

yes

characteristic

#95

—

277

—

#95

—

277

—

C₂²×C₄

—

277

—

C₂²×C₄

—

277

—

C₂²×C₄

—

277

—

C₂²×C₄

C₄×D₂₇₇

yes

—

C₂²×C₄

C₂²×D₂₇₇

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

554

—

C₂×C₈

—

554

—

C₂×C₈

—

554

—

C₄²

—

C₄²

—

554

—

C₄²

—

554

—

C₄²

—

554

—

C₂³

C₂×C₄×D₂₇₇

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

554

—

C₂×C₄

—

554

—

C₂×C₄

—

554

—

C₂×C₄

—

554

—

C₂×C₄

—

554

—

C₂×C₄

—

554

—

100

C₂×C₄

—

554

—

101

C₂×C₄

#17984562

yes

characteristic

102

C₂×C₄

#17984562

yes

—

103

C₂×C₄

#17984563

yes

—

104

C₂×C₄

#17984564

yes

characteristic

105

C₈

—

106

C₈

—

1108

—

107

C₂²

#22579836

yes

characteristic

108

C₂²

#22579837

yes

characteristic

109

C₂²

#22579838

yes

characteristic

110

C₂²

#22579886

yes

—

111

C₂²

#22579888

yes

—

112

C₄

—

113

C₄

—

1108

—

114

C₄

—

1108

—

115

C₄

—

1108

—

116

C₄

#22579873

yes

—

117

C₄

#22579875

yes

—

118

C₂

#31799869

yes

characteristic

119

C₂

#31800060

yes

—

120

C₂

#31800061

yes

characteristic

121

C₂

#31800062

yes

—

122

C₂

#31800064

yes

characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₂₇₇
commutator, socle, prime radical	C₂³×C₂₇₇	C₂²×C₄
Fitting	#336×C₂₇₇	C₂
cosocle	C₂²×C₄×C₂₇₇	C₂³
hypercenter	#336	D₂₇₇
hypocenter	C₂₇₇	#1840
LCS	G ▷ C₂³×C₂₇₇ ▷ C₂₇₇
UCS	C₁ ◁ C₂²×C₄ ◁ #336

subgroup

G/H

center, Frattini

C₂²×C₄

C₂²×D₂₇₇

commutator, socle, prime radical

C₂³×C₂₇₇

C₂²×C₄

Fitting

#336×C₂₇₇

C₂

cosocle

C₂²×C₄×C₂₇₇

C₂³

D₂₇₇

C₂₇₇

G ▷ C₂³×C₂₇₇ ▷ C₂₇₇

C₁ ◁ C₂²×C₄ ◁ #336

N	H ≅ G/N	type
61. C₂₇₇	#1840	semidirect

H ≅ G/N

type

61. C₂₇₇

#1840

semidirect

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

subgroup	index
#31799848	2
#31799757	2
#31799756	2
#336×C₂₇₇	2
#1840	277

subgroup

index

#336×C₂₇₇

277

Subgroups — #47983311

Conjugacy classes of subgroups

Complements

Maximal subgroups