Group #22611848 — subgroups

Subgroups — #22611848

Order 9344.

226 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 61 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×#14556534	C₂	1	2	yes	maximal, complemented
2	#17988823	C₂	1	1	yes	maximal, characteristic
3	#17988391	C₂	1	2	yes	maximal, complemented
4	C₂²⋊#11924003	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×Q₁₆×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₅₈₄	C₂²	1	1	yes	characteristic
7	#14556565	—	2	1	no	—
8	#14556534	—	2	4	no	—
9	C₂×#11924003	C₂²	1	2	yes	—
10	#14556525	C₂²	1	1	yes	characteristic
11	#14556513	—	2	1	no	—
12	C₂²×Q₈×C₇₃	—	2	1	no	—
13	C₂×Q₁₆×C₇₃	—	2	4	no	—
14	C₂×Q₁₆×C₇₃	—	2	1	no	—
15	C₂×Q₁₆×C₇₃	C₂²	1	2	yes	—
16	C₂²×C₈×C₇₃	C₂²	1	1	yes	characteristic
17	C₂×D₂₉₂	—	2	1	no	—
18	C₂×C₂²⋊D₇₃	—	4	1	no	—
19	D₅₈₄	—	2	2	no	—
20	C₄⋊Dic₇₃	—	2	1	no	—
21	#11924005	—	4	1	no	—
22	#11924003	—	2	2	no	—
23	C₂×Q₈×C₇₃	—	2	4	no	—
24	C₂×Q₈×C₇₃	—	2	2	no	—
25	C₂×Q₈×C₇₃	—	4	2	no	—
26	C₂×Q₈×C₇₃	—	4	1	no	—
27	C₂²×C₄×C₇₃	—	4	1	no	—
28	C₂²×C₄×C₇₃	D₄	1	1	yes	characteristic
29	Q₁₆×C₇₃	—	2	4	no	—
30	Q₁₆×C₇₃	—	2	2	no	—
31	Q₁₆×C₇₃	D₄	1	4	yes	complemented
32	C₂×C₈×C₇₃	—	2	2	no	—
33	C₂×C₈×C₇₃	D₄	1	1	yes	characteristic
34	C₂×C₈×C₇₃	C₂³	1	1	yes	characteristic
35	C₂³×C₇₃	D₈	1	1	yes	characteristic
36	C₂²×D₇₃	—	4	1	no	—
37	Q₈×C₇₃	—	2	4	no	—
38	Q₈×C₇₃	—	4	4	no	—
39	Q₈×C₇₃	—	4	2	no	—
40	C₂×C₄×C₇₃	—	2	1	no	—
41	C₂×C₄×C₇₃	—	2	1	no	—
42	C₂×C₄×C₇₃	—	4	4	no	—
43	C₂×C₄×C₇₃	—	4	2	no	—
44	C₂×C₄×C₇₃	D₈	1	1	yes	characteristic
45	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
46	C₂²⋊D₇₃	—	8	2	no	—
47	C₂×Dic₇₃	—	4	1	no	—
48	D₂₉₂	—	4	1	no	—
49	D₂₉₂	—	4	1	no	—
50	C₈×C₇₃	—	2	1	no	—
51	C₈×C₇₃	C₂×D₄	1	2	yes	—
52	C₂²×C₇₃	—	2	1	no	—
53	C₂²×C₇₃	—	2	1	no	—
54	C₂²×C₇₃	SD₃₂	1	2	yes	complemented
55	C₂²×C₇₃	C₂×D₈	1	1	yes	characteristic
56	C₂×D₇₃	—	8	1	no	—
57	C₂×D₇₃	—	8	1	no	—
58	C₂×D₇₃	—	8	1	no	—
59	C₄×C₇₃	—	2	1	no	—
60	C₄×C₇₃	—	4	4	no	—
61	C₄×C₇₃	#120	1	1	yes	characteristic
62	C₄×C₇₃	AGL(1,ℤ/8)	1	1	yes	characteristic
63	Dic₇₃	—	8	1	no	—
64	C₂×C₇₃	—	2	2	no	—
65	C₂×C₇₃	#447	1	1	yes	characteristic
66	C₂×C₇₃	C₂×SD₃₂	1	1	yes	characteristic
67	C₂×C₇₃	#510	1	1	yes	characteristic
68	D₇₃	—	16	1	no	—
69	#2185	—	73	1	no	maximal, Sylow
70	C₇₃	#2185	1	1	yes	characteristic, complemented, Sylow
71	C₂²×Q₁₆	D₇₃	1	1	yes	characteristic, complemented
72	C₂×SD₃₂	—	73	2	no	—
73	#466	—	73	1	no	—
74	#358	—	73	2	no	—
75	C₂²⋊C₁₆	—	73	1	no	—
76	C₂²×Q₈	—	2	1	no	—
77	C₂×Q₁₆	—	2	4	no	—
78	C₂×Q₁₆	—	2	1	no	—
79	C₂×Q₁₆	C₂×D₇₃	1	2	yes	—
80	C₂×D₈	—	73	1	no	—
81	C₂²×C₈	C₂×D₇₃	1	1	yes	characteristic
82	#121	—	146	1	no	—
83	SD₃₂	—	146	4	no	—
84	C₂×C₁₆	—	73	2	no	—
85	#107	—	73	1	no	—
86	#102	—	146	1	no	—
87	C₂×Q₈	—	2	4	no	—
88	C₂×Q₈	—	2	2	no	—
89	C₂×Q₈	—	4	2	no	—
90	C₂×Q₈	—	4	1	no	—
91	C₂×D₄	—	292	1	no	—
92	C₂×D₄	—	146	1	no	—
93	C₂²×C₄	—	4	1	no	—
94	C₂²×C₄	C₂²⋊D₇₃	1	1	yes	characteristic
95	Q₁₆	—	2	4	no	—
96	Q₁₆	—	2	2	no	—
97	Q₁₆	C₂²⋊D₇₃	1	4	yes	complemented
98	D₈	—	146	2	no	—
99	C₂×C₈	—	2	2	no	—
100	C₂×C₈	C₂²⋊D₇₃	1	1	yes	characteristic
101	C₂×C₈	C₂²×D₇₃	1	1	yes	characteristic
102	C₄⋊C₄	—	146	1	no	—
103	C₂²⋊C₄	—	292	1	no	—
104	C₁₆	—	146	2	no	—
105	C₂³	—	292	1	no	—
106	C₂³	#11924013	1	1	yes	characteristic
107	Q₈	—	2	4	no	—
108	Q₈	—	4	4	no	—
109	Q₈	—	4	2	no	—
110	D₄	—	292	1	no	—
111	D₄	—	292	1	no	—
112	D₄	—	584	2	no	—
113	C₂×C₄	—	2	1	no	—
114	C₂×C₄	—	2	1	no	—
115	C₂×C₄	—	4	4	no	—
116	C₂×C₄	—	4	2	no	—
117	C₂×C₄	—	292	1	no	—
118	C₂×C₄	#11924013	1	1	yes	characteristic
119	C₂×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
120	C₈	—	2	1	no	—
121	C₈	C₂×C₂²⋊D₇₃	1	2	yes	—
122	C₂²	—	2	1	no	—
123	C₂²	—	2	1	no	—
124	C₂²	—	584	1	no	—
125	C₂²	—	584	1	no	—
126	C₂²	—	584	1	no	—
127	C₂²	#14556534	1	2	yes	complemented
128	C₂²	C₂×#11924013	1	1	yes	characteristic
129	C₄	—	2	1	no	—
130	C₄	—	4	4	no	—
131	C₄	—	584	1	no	—
132	C₄	#14556560	1	1	yes	characteristic
133	C₄	#14556617	1	1	yes	characteristic
134	C₂	—	2	2	no	—
135	C₂	—	1168	1	no	—
136	C₂	#17988721	1	1	yes	characteristic
137	C₂	C₂×#14556534	1	1	yes	characteristic
138	C₂	#17989028	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14556534

C₂

yes

maximal, complemented

#17988823

C₂

yes

maximal, characteristic

#17988391

C₂

yes

maximal, complemented

C₂²⋊#11924003

C₂

yes

maximal, characteristic, complemented

C₂²×Q₁₆×C₇₃

C₂

yes

maximal, characteristic, complemented

C₂×D₅₈₄

C₂²

yes

—

—

C₂²

yes

—

#14556525

C₂²

yes

characteristic

#14556513

—

C₂²×Q₈×C₇₃

—

C₂×Q₁₆×C₇₃

—

C₂×Q₁₆×C₇₃

—

C₂×Q₁₆×C₇₃

C₂²

yes

—

C₂²×C₈×C₇₃

C₂²

yes

characteristic

C₂×D₂₉₂

—

C₂×C₂²⋊D₇₃

—

D₅₈₄

—

C₄⋊Dic₇₃

—

#11924005

—

#11924003

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

D₄

yes

characteristic

Q₁₆×C₇₃

—

Q₁₆×C₇₃

—

Q₁₆×C₇₃

D₄

yes

complemented

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

D₄

yes

characteristic

C₂×C₈×C₇₃

C₂³

yes

characteristic

C₂³×C₇₃

D₈

yes

characteristic

C₂²×D₇₃

—

Q₈×C₇₃

—

Q₈×C₇₃

—

Q₈×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

D₈

yes

characteristic

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂²⋊D₇₃

—

C₂×Dic₇₃

—

D₂₉₂

—

D₂₉₂

—

C₈×C₇₃

—

C₈×C₇₃

C₂×D₄

yes

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

SD₃₂

yes

complemented

C₂²×C₇₃

C₂×D₈

yes

characteristic

C₂×D₇₃

—

C₂×D₇₃

—

C₂×D₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

yes

C₄×C₇₃

yes

Dic₇₃

—

C₂×C₇₃

—

C₂×C₇₃

#447

yes

characteristic

C₂×C₇₃

C₂×SD₃₂

yes

characteristic

C₂×C₇₃

#510

yes

characteristic

D₇₃

—

#2185

—

maximal, Sylow

C₇₃

#2185

yes

characteristic, complemented, Sylow

C₂²×Q₁₆

D₇₃

yes

characteristic, complemented

C₂×SD₃₂

—

#466

—

#358

—

C₂²⋊C₁₆

—

C₂²×Q₈

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×Q₁₆

C₂×D₇₃

yes

—

C₂×D₈

—

C₂²×C₈

C₂×D₇₃

yes

characteristic

#121

—

146

—

SD₃₂

—

146

—

C₂×C₁₆

—

#107

—

#102

—

146

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×D₄

—

292

—

C₂×D₄

—

146

—

C₂²×C₄

—

C₂²×C₄

C₂²⋊D₇₃

yes

characteristic

Q₁₆

—

Q₁₆

—

Q₁₆

C₂²⋊D₇₃

yes

complemented

D₈

—

146

—

C₂×C₈

—

100

C₂×C₈

C₂²⋊D₇₃

yes

characteristic

101

C₂×C₈

C₂²×D₇₃

yes

characteristic

102

C₄⋊C₄

—

146

—

103

C₂²⋊C₄

—

292

—

104

C₁₆

—

146

—

105

C₂³

—

292

—

106

C₂³

#11924013

yes

characteristic

107

Q₈

—

108

Q₈

—

109

Q₈

—

110

D₄

—

292

—

111

D₄

—

292

—

112

D₄

—

584

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

292

—

118

C₂×C₄

#11924013

yes

characteristic

119

C₂×C₄

C₂×C₂²⋊D₇₃

yes

characteristic

120

C₈

—

121

C₈

C₂×C₂²⋊D₇₃

yes

—

122

C₂²

—

123

C₂²

—

124

C₂²

—

584

—

125

C₂²

—

584

—

126

C₂²

—

584

—

127

C₂²

#14556534

yes

complemented

128

C₂²

C₂×#11924013

yes

characteristic

129

C₄

—

130

C₄

—

131

C₄

—

584

—

132

C₄

#14556560

yes

characteristic

133

C₄

#14556617

yes

characteristic

134

C₂

—

135

C₂

—

1168

—

136

C₂

#17988721

yes

characteristic

137

C₂

C₂×#14556534

yes

characteristic

138

C₂

#17989028

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×#11924013
commutator	C₂×C₈×C₇₃	C₂³
Frattini	C₂×C₈	C₂²×D₇₃
Fitting	C₂²×Q₁₆×C₇₃	C₂
socle	C₂²×C₇₃	C₂×D₈
hypercenter	C₂²×Q₁₆	D₇₃
hypocenter	C₇₃	#2185
LCS	G ▷ C₂×C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×Q₁₆

subgroup

G/H

center

C₂²

C₂×#11924013

commutator

C₂×C₈×C₇₃

C₂³

Frattini

C₂×C₈

C₂²×D₇₃

Fitting

C₂²×Q₁₆×C₇₃

C₂

socle

C₂²×C₇₃

C₂×D₈

hypercenter

C₂²×Q₁₆

D₇₃

hypocenter

C₇₃

#2185

LCS

G ▷ C₂×C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×Q₁₆

N	H ≅ G/N	type
1. C₂×#14556534	C₂	semidirect
3. #17988391	C₂	semidirect
4. C₂²⋊#11924003	C₂	semidirect
5. C₂²×Q₁₆×C₇₃	C₂	semidirect
31. Q₁₆×C₇₃	D₄	semidirect
54. C₂²×C₇₃	SD₃₂	semidirect
70. C₇₃	#2185	semidirect
71. C₂²×Q₁₆	D₇₃	semidirect
97. Q₁₆	C₂²⋊D₇₃	semidirect
127. C₂²	#14556534	semidirect

H ≅ G/N

type

1. C₂×#14556534

C₂

semidirect

3. #17988391

C₂

semidirect

4. C₂²⋊#11924003

C₂

semidirect

5. C₂²×Q₁₆×C₇₃

C₂

semidirect

31. Q₁₆×C₇₃

D₄

semidirect

54. C₂²×C₇₃

SD₃₂

semidirect

70. C₇₃

#2185

semidirect

71. C₂²×Q₁₆

D₇₃

semidirect

97. Q₁₆

C₂²⋊D₇₃

semidirect

127. C₂²

#14556534

semidirect

Subgroups — #22611848

Conjugacy classes of subgroups

Complements