Group #20267688 — subgroups

Subgroups — #20267688

Order 6592.

170 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 170 conjugacy classes of subgroups — too many to draw. Only its 77 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×C₄⋊Dic₁₀₃	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₁₀₃⋊C₄	C₂	1	1	yes	maximal, characteristic
3	C₂×Dic₁₀₃⋊C₄	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₁₀₃⋊C₄	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄×Dic₁₀₃	C₂	1	1	yes	maximal, characteristic
6	C₁₀₃⋊#95	C₂	1	1	yes	maximal, characteristic
7	#95×C₁₀₃	C₂	1	1	yes	maximal, characteristic
8	C₂²×Dic₁₀₃	C₂²	1	1	yes	characteristic
9	C₂²×Dic₁₀₃	C₂²	1	1	yes	characteristic
10	C₂²×Dic₁₀₃	C₂²	1	1	yes	characteristic
11	C₂²×Dic₁₀₃	C₂²	1	1	yes	characteristic
12	C₄⋊Dic₁₀₃	—	2	2	no	—
13	Dic₁₀₃⋊C₄	—	2	2	no	—
14	Dic₁₀₃⋊C₄	—	2	2	no	—
15	Dic₁₀₃⋊C₄	C₄	1	4	yes	complemented
16	C₄×Dic₁₀₃	—	2	2	no	—
17	C₂²×C₄×C₁₀₃	C₂²	1	1	yes	characteristic
18	C₂²×C₄×C₁₀₃	C₂²	1	1	yes	characteristic
19	C₂²×C₄×C₁₀₃	C₂²	1	1	yes	characteristic
20	C₂³×C₁₀₃	C₂³	1	1	yes	characteristic
21	C₂×C₄×C₁₀₃	—	2	1	no	—
22	C₂×C₄×C₁₀₃	—	2	1	no	—
23	C₂×C₄×C₁₀₃	—	2	1	no	—
24	C₂×C₄×C₁₀₃	—	2	1	no	—
25	C₂×C₄×C₁₀₃	—	2	1	no	—
26	C₂×C₄×C₁₀₃	—	2	1	no	—
27	C₂×C₄×C₁₀₃	—	2	1	no	—
28	C₂×C₄×C₁₀₃	C₂×C₄	1	2	yes	—
29	C₂×C₄×C₁₀₃	Q₈	1	2	yes	—
30	C₂×Dic₁₀₃	—	2	1	no	—
31	C₂×Dic₁₀₃	—	2	1	no	—
32	C₂×Dic₁₀₃	—	2	1	no	—
33	C₂×Dic₁₀₃	—	2	1	no	—
34	C₂×Dic₁₀₃	—	2	1	no	—
35	C₂×Dic₁₀₃	—	2	1	no	—
36	C₂×Dic₁₀₃	—	2	1	no	—
37	C₂×Dic₁₀₃	C₂×C₄	1	2	yes	—
38	C₂×Dic₁₀₃	C₂×C₄	1	2	yes	—
39	C₂×Dic₁₀₃	D₄	1	2	yes	—
40	C₂×Dic₁₀₃	D₄	1	2	yes	—
41	C₂×Dic₁₀₃	Q₈	1	2	yes	—
42	C₂²×C₁₀₃	C₂²×C₄	1	1	yes	characteristic
43	C₂²×C₁₀₃	C₂×D₄	1	1	yes	characteristic
44	C₂²×C₁₀₃	C₂×D₄	1	1	yes	characteristic
45	C₂²×C₁₀₃	C₂×Q₈	1	1	yes	characteristic
46	C₂²×C₁₀₃	C₂×Q₈	1	1	yes	characteristic
47	C₂²×C₁₀₃	#41	1	1	yes	characteristic
48	C₂²×C₁₀₃	#41	1	1	yes	characteristic
49	C₄×C₁₀₃	—	2	2	no	—
50	C₄×C₁₀₃	—	2	2	no	—
51	C₄×C₁₀₃	—	4	1	no	—
52	Dic₁₀₃	—	2	2	no	—
53	Dic₁₀₃	—	2	2	no	—
54	Dic₁₀₃	—	4	1	no	—
55	Dic₁₀₃	C₄⋊C₄	1	4	yes	complemented
56	C₂×C₁₀₃	C₂×C₄⋊C₄	1	1	yes	characteristic
57	C₂×C₁₀₃	C₄×D₄	1	1	yes	characteristic
58	C₂×C₁₀₃	C₄×Q₈	1	1	yes	characteristic
59	C₂×C₁₀₃	#121	1	1	yes	characteristic
60	C₂×C₁₀₃	C₂²⋊Q₈	1	1	yes	characteristic
61	C₂×C₁₀₃	#125	1	1	yes	characteristic
62	C₂×C₁₀₃	C₄⋊Q₈	1	1	yes	characteristic
63	C₁₀₃	#389	1	1	yes	characteristic, complemented, Sylow
64	#389	—	103	1	no	maximal, Sylow
65	C₂×C₄⋊C₄	—	103	1	no	—
66	C₂×C₄⋊C₄	—	103	1	no	—
67	C₂×C₄⋊C₄	—	103	1	no	—
68	C₂×C₄⋊C₄	—	103	1	no	—
69	C₂×C₄²	—	103	1	no	—
70	#95	—	103	1	no	—
71	#95	D₁₀₃	1	1	yes	characteristic
72	C₂²×C₄	—	103	1	no	—
73	C₂²×C₄	—	103	1	no	—
74	C₂²×C₄	—	103	1	no	—
75	C₂²×C₄	—	103	1	no	—
76	C₂²×C₄	C₂×D₁₀₃	1	1	yes	characteristic
77	C₂²×C₄	C₂×D₁₀₃	1	1	yes	characteristic
78	C₂²×C₄	C₂×D₁₀₃	1	1	yes	characteristic
79	C₄⋊C₄	—	103	4	no	—
80	C₄⋊C₄	—	206	2	no	—
81	C₄⋊C₄	—	206	2	no	—
82	C₄⋊C₄	—	206	2	no	—
83	C₄²	—	206	2	no	—
84	C₂³	C₂²×D₁₀₃	1	1	yes	characteristic
85	C₂×C₄	—	2	1	no	—
86	C₂×C₄	—	2	1	no	—
87	C₂×C₄	—	2	1	no	—
88	C₂×C₄	—	2	1	no	—
89	C₂×C₄	—	2	1	no	—
90	C₂×C₄	—	2	1	no	—
91	C₂×C₄	—	2	1	no	—
92	C₂×C₄	—	103	2	no	—
93	C₂×C₄	—	103	2	no	—
94	C₂×C₄	—	103	2	no	—
95	C₂×C₄	—	103	2	no	—
96	C₂×C₄	—	103	2	no	—
97	C₂×C₄	—	206	1	no	—
98	C₂×C₄	—	206	1	no	—
99	C₂×C₄	—	206	1	no	—
100	C₂×C₄	—	206	1	no	—
101	C₂×C₄	—	206	1	no	—
102	C₂×C₄	—	206	1	no	—
103	C₂×C₄	—	206	1	no	—
104	C₂×C₄	Dic₂₀₆	1	2	yes	—
105	C₂×C₄	C₄×D₁₀₃	1	2	yes	—
106	C₂²	C₂×C₄×D₁₀₃	1	1	yes	characteristic
107	C₂²	D₄×D₁₀₃	1	1	yes	characteristic
108	C₂²	D₄×D₁₀₃	1	1	yes	characteristic
109	C₂²	Q₈×D₁₀₃	1	1	yes	characteristic
110	C₂²	C₂×Dic₂₀₆	1	1	yes	characteristic
111	C₂²	#13110104	1	1	yes	characteristic
112	C₂²	#13110105	1	1	yes	characteristic
113	C₄	—	2	2	no	—
114	C₄	—	2	2	no	—
115	C₄	—	4	1	no	—
116	C₄	—	103	4	no	—
117	C₄	—	412	1	no	—
118	C₄	—	206	2	no	—
119	C₄	—	206	2	no	—
120	C₂	C₄⋊C₄×D₁₀₃	1	1	yes	characteristic
121	C₂	(C₂²⋊D₁₀₃)⋊C₄	1	1	yes	characteristic
122	C₂	C₄×Dic₂₀₆	1	1	yes	characteristic
123	C₂	#15692994	1	1	yes	characteristic
124	C₂	#15692998	1	1	yes	characteristic
125	C₂	#15693011	1	1	yes	characteristic
126	C₂	#15693020	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄⋊Dic₁₀₃

C₂

yes

maximal, characteristic

C₂×Dic₁₀₃⋊C₄

C₂

yes

maximal, characteristic

C₂×Dic₁₀₃⋊C₄

C₂

yes

maximal, characteristic

C₂×Dic₁₀₃⋊C₄

C₂

yes

maximal, characteristic

C₂×C₄×Dic₁₀₃

C₂

yes

maximal, characteristic

C₁₀₃⋊#95

C₂

yes

maximal, characteristic

#95×C₁₀₃

C₂

yes

maximal, characteristic

C₂²×Dic₁₀₃

C₂²

yes

characteristic

C₂²×Dic₁₀₃

C₂²

yes

characteristic

C₂²×Dic₁₀₃

C₂²

yes

characteristic

C₂²×Dic₁₀₃

C₂²

yes

characteristic

C₄⋊Dic₁₀₃

—

Dic₁₀₃⋊C₄

—

Dic₁₀₃⋊C₄

—

Dic₁₀₃⋊C₄

C₄

yes

complemented

C₄×Dic₁₀₃

—

C₂²×C₄×C₁₀₃

C₂²

yes

characteristic

C₂²×C₄×C₁₀₃

C₂²

yes

characteristic

C₂²×C₄×C₁₀₃

C₂²

yes

characteristic

C₂³×C₁₀₃

C₂³

yes

characteristic

C₂×C₄×C₁₀₃

—

C₂×C₄×C₁₀₃

—

C₂×C₄×C₁₀₃

—

C₂×C₄×C₁₀₃

—

C₂×C₄×C₁₀₃

—

C₂×C₄×C₁₀₃

—

C₂×C₄×C₁₀₃

—

C₂×C₄×C₁₀₃

C₂×C₄

yes

—

C₂×C₄×C₁₀₃

Q₈

yes

—

C₂×Dic₁₀₃

—

C₂×Dic₁₀₃

—

C₂×Dic₁₀₃

—

C₂×Dic₁₀₃

—

C₂×Dic₁₀₃

—

C₂×Dic₁₀₃

—

C₂×Dic₁₀₃

—

C₂×Dic₁₀₃

C₂×C₄

yes

—

C₂×Dic₁₀₃

C₂×C₄

yes

—

C₂×Dic₁₀₃

D₄

yes

—

C₂×Dic₁₀₃

D₄

yes

—

C₂×Dic₁₀₃

Q₈

yes

—

C₂²×C₁₀₃

C₂²×C₄

yes

characteristic

C₂²×C₁₀₃

C₂×D₄

yes

characteristic

C₂²×C₁₀₃

C₂×D₄

yes

characteristic

C₂²×C₁₀₃

C₂×Q₈

yes

characteristic

C₂²×C₁₀₃

C₂×Q₈

yes

C₂²×C₁₀₃

yes

C₂²×C₁₀₃

yes

C₄×C₁₀₃

—

C₄×C₁₀₃

—

C₄×C₁₀₃

—

Dic₁₀₃

—

Dic₁₀₃

—

Dic₁₀₃

—

Dic₁₀₃

C₄⋊C₄

yes

complemented

C₂×C₁₀₃

C₂×C₄⋊C₄

yes

characteristic

C₂×C₁₀₃

C₄×D₄

yes

characteristic

C₂×C₁₀₃

C₄×Q₈

yes

characteristic

C₂×C₁₀₃

#121

yes

characteristic

C₂×C₁₀₃

C₂²⋊Q₈

yes

characteristic

C₂×C₁₀₃

#125

yes

characteristic

C₂×C₁₀₃

C₄⋊Q₈

yes

characteristic

C₁₀₃

#389

yes

characteristic, complemented, Sylow

#389

—

103

maximal, Sylow

C₂×C₄⋊C₄

—

103

—

C₂×C₄⋊C₄

—

103

—

C₂×C₄⋊C₄

—

103

—

C₂×C₄⋊C₄

—

103

—

C₂×C₄²

—

103

—

#95

—

103

—

#95

D₁₀₃

yes

characteristic

C₂²×C₄

—

103

—

C₂²×C₄

—

103

—

C₂²×C₄

—

103

—

C₂²×C₄

—

103

—

C₂²×C₄

C₂×D₁₀₃

yes

characteristic

C₂²×C₄

C₂×D₁₀₃

yes

characteristic

C₂²×C₄

C₂×D₁₀₃

yes

characteristic

C₄⋊C₄

—

103

—

C₄⋊C₄

—

206

—

C₄⋊C₄

—

206

—

C₄⋊C₄

—

206

—

C₄²

—

206

—

C₂³

C₂²×D₁₀₃

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

103

—

C₂×C₄

—

103

—

C₂×C₄

—

103

—

C₂×C₄

—

103

—

C₂×C₄

—

103

—

C₂×C₄

—

206

—

C₂×C₄

—

206

—

C₂×C₄

—

206

—

100

C₂×C₄

—

206

—

101

C₂×C₄

—

206

—

102

C₂×C₄

—

206

—

103

C₂×C₄

—

206

—

104

C₂×C₄

Dic₂₀₆

yes

—

105

C₂×C₄

C₄×D₁₀₃

yes

—

106

C₂²

C₂×C₄×D₁₀₃

yes

characteristic

107

C₂²

D₄×D₁₀₃

yes

characteristic

108

C₂²

D₄×D₁₀₃

yes

characteristic

109

C₂²

Q₈×D₁₀₃

yes

characteristic

110

C₂²

C₂×Dic₂₀₆

yes

characteristic

111

C₂²

#13110104

yes

characteristic

112

C₂²

#13110105

yes

characteristic

113

C₄

—

114

C₄

—

115

C₄

—

116

C₄

—

103

—

117

C₄

—

412

—

118

C₄

—

206

—

119

C₄

—

206

—

120

C₂

C₄⋊C₄×D₁₀₃

yes

characteristic

121

C₂

(C₂²⋊D₁₀₃)⋊C₄

yes

characteristic

122

C₂

C₄×Dic₂₀₆

yes

characteristic

123

C₂

#15692994

yes

characteristic

124

C₂

#15692998

yes

characteristic

125

C₂

#15693011

yes

characteristic

126

C₂

#15693020

yes

characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂²×D₁₀₃
commutator	C₂²×C₁₀₃	C₂²×C₄
Fitting	#95×C₁₀₃	C₂
socle	C₂³×C₁₀₃	C₂³
hypercenter	#95	D₁₀₃
hypocenter	C₁₀₃	#389
LCS	G ▷ C₂²×C₁₀₃ ▷ C₁₀₃
UCS	C₁ ◁ C₂³ ◁ #95

subgroup

G/H

center, Frattini

C₂³

C₂²×D₁₀₃

commutator

C₂²×C₁₀₃

C₂²×C₄

Fitting

#95×C₁₀₃

C₂

socle

C₂³×C₁₀₃

C₂³

D₁₀₃

C₁₀₃

G ▷ C₂²×C₁₀₃ ▷ C₁₀₃

C₁ ◁ C₂³ ◁ #95

N	H ≅ G/N	type
15. Dic₁₀₃⋊C₄	C₄	semidirect
55. Dic₁₀₃	C₄⋊C₄	semidirect
63. C₁₀₃	#389	semidirect

H ≅ G/N

type

15. Dic₁₀₃⋊C₄

C₄

semidirect

55. Dic₁₀₃

C₄⋊C₄

semidirect

63. C₁₀₃

#389

semidirect

Subgroups — #20267688

Conjugacy classes of subgroups

Complements