Group #20267931 — subgroups

Subgroups — #20267931

Order 6592.

158 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 45 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×Q₈×D₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#13110094	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#13110092	C₂	1	1	yes	maximal, characteristic, complemented
4	#15692996	C₂	1	1	yes	maximal, characteristic
5	#15692944	C₂	1	1	yes	maximal, characteristic, complemented
6	(C₂×D₁₀₃)⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	#103×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×Dic₂₀₆	—	2	1	no	—
9	C₂×Dic₂₀₆	C₂²	1	1	yes	characteristic
10	Q₈×D₁₀₃	—	2	2	no	—
11	Q₈×D₁₀₃	—	2	2	no	—
12	C₂×D₄₁₂	—	2	1	no	—
13	C₂×D₄₁₂	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₁₀₃	—	2	1	no	—
15	C₂×C₄×D₁₀₃	C₂²	1	1	yes	characteristic
16	#13110094	—	2	2	no	—
17	#13110092	—	2	2	no	—
18	C₂×C₁₀₃⋊C₈	C₂²	1	1	yes	characteristic
19	(C₂×D₁₀₃)⋊C₄	—	2	1	no	—
20	C₂×Q₈×C₁₀₃	C₂²	1	1	yes	characteristic
21	C₂×C₈×C₁₀₃	C₂²	1	1	yes	characteristic
22	C₄⋊C₄×C₁₀₃	C₂²	1	1	yes	characteristic
23	C₂²×D₁₀₃	—	2	1	no	—
24	C₂²×D₁₀₃	D₄	1	1	yes	characteristic
25	Q₈×C₁₀₃	—	2	1	no	—
26	Q₈×C₁₀₃	D₄	1	2	yes	complemented
27	C₂×C₄×C₁₀₃	—	2	1	no	—
28	C₂×C₄×C₁₀₃	—	2	1	no	—
29	C₂×C₄×C₁₀₃	C₂³	1	1	yes	characteristic
30	C₂×Dic₁₀₃	—	2	1	no	—
31	C₂×Dic₁₀₃	D₄	1	1	yes	characteristic
32	D₄₁₂	—	2	1	no	—
33	D₄₁₂	—	2	1	no	—
34	D₄₁₂	—	4	2	no	—
35	C₄×D₁₀₃	—	2	4	no	—
36	C₄×D₁₀₃	—	2	1	no	—
37	C₄×D₁₀₃	—	2	1	no	—
38	Dic₂₀₆	—	2	4	no	—
39	Dic₂₀₆	—	2	1	no	—
40	Dic₂₀₆	D₄	1	2	yes	complemented
41	C₈×C₁₀₃	—	2	1	no	—
42	C₁₀₃⋊C₈	—	2	1	no	—
43	C₂²×C₁₀₃	C₂×D₄	1	1	yes	characteristic
44	C₂×D₁₀₃	—	2	1	no	—
45	C₂×D₁₀₃	—	2	1	no	—
46	C₂×D₁₀₃	—	4	1	no	—
47	C₂×D₁₀₃	—	4	1	no	—
48	C₂×D₁₀₃	—	4	1	no	—
49	C₂×D₁₀₃	SD₁₆	1	2	yes	complemented
50	C₄×C₁₀₃	—	2	2	no	—
51	C₄×C₁₀₃	—	4	1	no	—
52	C₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
53	C₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
54	Dic₁₀₃	—	2	1	no	—
55	Dic₁₀₃	—	2	2	no	—
56	C₂×C₁₀₃	#120	1	1	yes	characteristic
57	C₂×C₁₀₃	C₂×SD₁₆	1	1	yes	characteristic
58	C₂×C₁₀₃	#137	1	1	yes	characteristic
59	D₁₀₃	—	2	2	no	—
60	D₁₀₃	—	8	1	no	—
61	C₁₀₃	#448	1	1	yes	characteristic, complemented, Sylow
62	#448	—	103	1	no	maximal, Sylow
63	C₂²×Q₈	—	103	1	no	—
64	C₂×SD₁₆	—	103	1	no	—
65	C₂×SD₁₆	—	103	1	no	—
66	#121	—	103	1	no	—
67	#103	—	103	1	no	—
68	#103	D₁₀₃	1	1	yes	characteristic, complemented
69	C₂²⋊C₈	—	103	1	no	—
70	C₂×Q₈	—	103	1	no	—
71	C₂×Q₈	—	206	1	no	—
72	C₂×Q₈	—	206	2	no	—
73	C₂×Q₈	—	206	2	no	—
74	C₂×Q₈	C₂×D₁₀₃	1	1	yes	characteristic
75	C₂×D₄	—	103	1	no	—
76	C₂×D₄	—	206	1	no	—
77	C₂²×C₄	—	103	1	no	—
78	C₂²×C₄	—	206	1	no	—
79	SD₁₆	—	206	2	no	—
80	SD₁₆	—	206	2	no	—
81	C₂×C₈	—	103	1	no	—
82	C₂×C₈	C₂×D₁₀₃	1	1	yes	characteristic
83	C₄⋊C₄	C₂×D₁₀₃	1	1	yes	characteristic
84	C₂²⋊C₄	—	206	1	no	—
85	C₂³	—	103	1	no	—
86	C₂³	—	206	1	no	—
87	Q₈	—	2	1	no	—
88	Q₈	—	103	2	no	—
89	Q₈	—	206	4	no	—
90	Q₈	—	206	1	no	—
91	Q₈	D₄₁₂	1	2	yes	complemented
92	D₄	—	412	2	no	—
93	D₄	—	206	1	no	—
94	D₄	—	206	1	no	—
95	C₂×C₄	—	2	1	no	—
96	C₂×C₄	—	2	1	no	—
97	C₂×C₄	—	103	1	no	—
98	C₂×C₄	—	206	4	no	—
99	C₂×C₄	—	206	1	no	—
100	C₂×C₄	—	206	1	no	—
101	C₂×C₄	—	206	1	no	—
102	C₂×C₄	C₂²×D₁₀₃	1	1	yes	characteristic
103	C₈	—	2	1	no	—
104	C₈	—	206	1	no	—
105	C₂²	—	103	2	no	—
106	C₂²	—	412	1	no	—
107	C₂²	—	412	1	no	—
108	C₂²	—	412	1	no	—
109	C₂²	—	206	1	no	—
110	C₂²	—	206	1	no	—
111	C₂²	D₄×D₁₀₃	1	1	yes	characteristic
112	C₄	—	2	2	no	—
113	C₄	—	4	1	no	—
114	C₄	—	206	1	no	—
115	C₄	—	206	2	no	—
116	C₄	D₄×D₁₀₃	1	1	yes	characteristic
117	C₄	C₂×D₄₁₂	1	1	yes	characteristic
118	C₂	—	824	1	no	—
119	C₂	—	206	2	no	—
120	C₂	#15692991	1	1	yes	characteristic
121	C₂	SD₁₆×D₁₀₃	1	1	yes	characteristic
122	C₂	#15693053	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×Q₈×D₁₀₃

C₂

yes

maximal, characteristic, complemented

C₂×#13110094

C₂

yes

maximal, characteristic, complemented

C₂×#13110092

C₂

yes

maximal, characteristic, complemented

#15692996

C₂

yes

maximal, characteristic

#15692944

C₂

yes

maximal, characteristic, complemented

(C₂×D₁₀₃)⋊C₈

C₂

yes

maximal, characteristic, complemented

#103×C₁₀₃

C₂

yes

maximal, characteristic, complemented

C₂×Dic₂₀₆

—

C₂×Dic₂₀₆

C₂²

yes

characteristic

Q₈×D₁₀₃

—

Q₈×D₁₀₃

—

C₂×D₄₁₂

—

C₂×D₄₁₂

C₂²

yes

characteristic

C₂×C₄×D₁₀₃

—

C₂×C₄×D₁₀₃

C₂²

yes

characteristic

#13110094

—

#13110092

—

C₂×C₁₀₃⋊C₈

C₂²

yes

characteristic

(C₂×D₁₀₃)⋊C₄

—

C₂×Q₈×C₁₀₃

C₂²

yes

characteristic

C₂×C₈×C₁₀₃

C₂²

yes

characteristic

C₄⋊C₄×C₁₀₃

C₂²

yes

characteristic

C₂²×D₁₀₃

—

C₂²×D₁₀₃

D₄

yes

characteristic

Q₈×C₁₀₃

—

Q₈×C₁₀₃

D₄

yes

complemented

C₂×C₄×C₁₀₃

—

C₂×C₄×C₁₀₃

—

C₂×C₄×C₁₀₃

C₂³

yes

characteristic

C₂×Dic₁₀₃

—

C₂×Dic₁₀₃

D₄

yes

characteristic

D₄₁₂

—

D₄₁₂

—

D₄₁₂

—

C₄×D₁₀₃

—

C₄×D₁₀₃

—

C₄×D₁₀₃

—

Dic₂₀₆

—

Dic₂₀₆

—

Dic₂₀₆

D₄

yes

complemented

C₈×C₁₀₃

—

C₁₀₃⋊C₈

—

C₂²×C₁₀₃

C₂×D₄

yes

characteristic

C₂×D₁₀₃

—

C₂×D₁₀₃

—

C₂×D₁₀₃

—

C₂×D₁₀₃

—

C₂×D₁₀₃

—

C₂×D₁₀₃

SD₁₆

yes

complemented

C₄×C₁₀₃

—

C₄×C₁₀₃

—

C₄×C₁₀₃

C₂×D₄

yes

characteristic

C₄×C₁₀₃

C₂×D₄

yes

characteristic

Dic₁₀₃

—

Dic₁₀₃

—

C₂×C₁₀₃

#120

yes

characteristic

C₂×C₁₀₃

C₂×SD₁₆

yes

characteristic

C₂×C₁₀₃

#137

yes

characteristic

D₁₀₃

—

D₁₀₃

—

C₁₀₃

#448

yes

characteristic, complemented, Sylow

#448

—

103

maximal, Sylow

C₂²×Q₈

—

103

—

C₂×SD₁₆

—

103

—

C₂×SD₁₆

—

103

—

#121

—

103

—

#103

—

103

—

#103

D₁₀₃

yes

characteristic, complemented

C₂²⋊C₈

—

103

—

C₂×Q₈

—

103

—

C₂×Q₈

—

206

—

C₂×Q₈

—

206

—

C₂×Q₈

—

206

—

C₂×Q₈

C₂×D₁₀₃

yes

characteristic

C₂×D₄

—

103

—

C₂×D₄

—

206

—

C₂²×C₄

—

103

—

C₂²×C₄

—

206

—

SD₁₆

—

206

—

SD₁₆

—

206

—

C₂×C₈

—

103

—

C₂×C₈

C₂×D₁₀₃

yes

characteristic

C₄⋊C₄

C₂×D₁₀₃

yes

characteristic

C₂²⋊C₄

—

206

—

C₂³

—

103

—

C₂³

—

206

—

Q₈

—

Q₈

—

103

—

Q₈

—

206

—

Q₈

—

206

—

Q₈

D₄₁₂

yes

complemented

D₄

—

412

—

D₄

—

206

—

D₄

—

206

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

103

—

C₂×C₄

—

206

—

C₂×C₄

—

206

—

100

C₂×C₄

—

206

—

101

C₂×C₄

—

206

—

102

C₂×C₄

C₂²×D₁₀₃

yes

characteristic

103

C₈

—

104

C₈

—

206

—

105

C₂²

—

103

—

106

C₂²

—

412

—

107

C₂²

—

412

—

108

C₂²

—

412

—

109

C₂²

—

206

—

110

C₂²

—

206

—

111

C₂²

D₄×D₁₀₃

yes

characteristic

112

C₄

—

113

C₄

—

114

C₄

—

206

—

115

C₄

—

206

—

116

C₄

D₄×D₁₀₃

yes

characteristic

117

C₄

C₂×D₄₁₂

yes

characteristic

118

C₂

—

824

—

119

C₂

—

206

—

120

C₂

#15692991

yes

characteristic

121

C₂

SD₁₆×D₁₀₃

yes

characteristic

122

C₂

#15693053

yes

characteristic

	subgroup	G/H
center	C₂²	D₄×D₁₀₃
commutator	C₂×C₄×C₁₀₃	C₂³
Frattini	C₂×C₄	C₂²×D₁₀₃
Fitting	#103×C₁₀₃	C₂
socle	C₂²×C₁₀₃	C₂×D₄
hypercenter	#103	D₁₀₃
hypocenter	C₁₀₃	#448
LCS	G ▷ C₂×C₄×C₁₀₃ ▷ C₂×C₁₀₃ ▷ C₁₀₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #103

subgroup

G/H

center

C₂²

D₄×D₁₀₃

commutator

C₂×C₄×C₁₀₃

C₂³

Frattini

C₂×C₄

C₂²×D₁₀₃

Fitting

#103×C₁₀₃

C₂

socle

C₂²×C₁₀₃

C₂×D₄

D₁₀₃

C₁₀₃

G ▷ C₂×C₄×C₁₀₃ ▷ C₂×C₁₀₃ ▷ C₁₀₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ #103

N	H ≅ G/N	type
1. C₂×Q₈×D₁₀₃	C₂	semidirect
2. C₂×#13110094	C₂	semidirect
3. C₂×#13110092	C₂	semidirect
5. #15692944	C₂	semidirect
6. (C₂×D₁₀₃)⋊C₈	C₂	semidirect
7. #103×C₁₀₃	C₂	semidirect
26. Q₈×C₁₀₃	D₄	semidirect
40. Dic₂₀₆	D₄	semidirect
49. C₂×D₁₀₃	SD₁₆	semidirect
61. C₁₀₃	#448	semidirect
68. #103	D₁₀₃	semidirect
91. Q₈	D₄₁₂	semidirect

H ≅ G/N

type

1. C₂×Q₈×D₁₀₃

C₂

semidirect

2. C₂×#13110094

C₂

semidirect

3. C₂×#13110092

C₂

semidirect

5. #15692944

C₂

semidirect

6. (C₂×D₁₀₃)⋊C₈

C₂

semidirect

7. #103×C₁₀₃

C₂

semidirect

26. Q₈×C₁₀₃

D₄

semidirect

40. Dic₂₀₆

D₄

semidirect

49. C₂×D₁₀₃

SD₁₆

semidirect

61. C₁₀₃

#448

semidirect

68. #103

D₁₀₃

semidirect

91. Q₈

D₄₁₂

semidirect

Subgroups — #20267931

Conjugacy classes of subgroups

Complements