Finite Group Databasebeta

← #37534788

Subgroups — #37534788

Order 23168.

394 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 69 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26042079C211yesmaximal, characteristic, complemented
2#26041790C212yesmaximal, complemented
3#26041295C212yesmaximal, complemented
4#26041036C211yesmaximal, characteristic, complemented
5#407×C181C211yesmaximal, characteristic, complemented
6C2×#15668449C2212yes—
7#19153849—22no—
8#19153844—22no—
9#19153838—22no—
10#19153799—22no—
11#19153795—22no—
12#19153790—22no—
13#19153785—22no—
14C4×C22⋊D181—24no—
15#19153775C2212yes—
16#19153742—24no—
17C23×C4×C181C2211yescharacteristic
18C2×M16×C181C2211yescharacteristic
19C2×M16×C181C2211yescharacteristic
20C22⋊C8×C181—22no—
21#15668449—22no—
22#15668449—22no—
23#15668449—22no—
24#15668449—22no—
25C2×Dic362D412yescomplemented
26C2×D724D412yescomplemented
27C2×C22⋊D181—24no—
28C2×C22⋊D181—22no—
29C2×C4×D181—22no—
30Dic724—22no—
31#15668438—24no—
32D1448—22no—
33C4⋊Dic181—22no—
34#15668428—24no—
35C22⋊Dic181—24no—
36C22⋊Dic181—22no—
37#15668426—24no—
38C4×Dic181D414yescomplemented
39C24×C181D411yescharacteristic
40C22×C4×C181—21no—
41C22×C4×C181—22no—
42C22×C4×C181—22no—
43C22×C4×C181—21no—
44C22×C4×C181D411yescharacteristic
45C22×C4×C181C2311yescharacteristic
46M16×C181—22no—
47M16×C181—22no—
48C2×C8×C181—21no—
49C2×C8×C181D412yescomplemented
50C22×D181—22no—
51Dic362—22no—
52Dic362—22no—
53D724—22no—
54D724—22no—
55C22⋊D181—48no—
56C22⋊D181—42no—
57C22⋊D181—42no—
58C2×Dic181—24no—
59C2×Dic181—22no—
60C4×D181—42no—
61C4×D181—42no—
62C23×C181—22no—
63C23×C181—21no—
64C23×C181—42no—
65C23×C181C2×D411yescharacteristic
66C2×C4×C181—22no—
67C2×C4×C181—21no—
68C2×C4×C181—41no—
69C2×C4×C181—42no—
70C2×C4×C181—41no—
71C2×C4×C181C2×D412yes—
72C2×C4×C181C2×D412yes—
73C2×C4×C181C2×D411yescharacteristic
74C2×C4×C181#4111yescharacteristic
75C8×C181—22no—
76C8×C181—41no—
77C22×C181—22no—
78C22×C181—24no—
79C22×C181—41no—
80C22×C181—42no—
81C22×C181—41no—
82C22×C181—41no—
83C22×C181#12012yes—
84C22×C181#12111yescharacteristic
85C2×D181—44no—
86C2×D181—42no—
87C4×C181—41no—
88C4×C181#12011yescharacteristic
89C4×C181#12112yes—
90C4×C181#12711yescharacteristic
91Dic181—44no—
92Dic181—42no—
93C2×C181—22no—
94C2×C181—21no—
95C2×C181—42no—
96C2×C181#39211yescharacteristic
97D181—82no—
98C181#201011yescharacteristic, complemented, Sylow
99#2010—1811nomaximal, Sylow
100#575—1811no—
101#525—1812no—
102#421—1812no—
103#407D18111yescharacteristic, complemented
104H(3,ℤ/4)—1811no—
105C2×#41—1812no—
106C23×C4C2×D18111yescharacteristic
107#137—3622no—
108AGL(1,ℤ/8)—3622no—
109#135—3622no—
110C2×M16C2×D18111yescharacteristic
111C2×M16C2×D18111yescharacteristic
112#123—3622no—
113C22⋊Q8—3622no—
114#121—3622no—
115#120—3622no—
116C4×D4—3624no—
117#117—1812no—
118#104—3624no—
119C22⋊C8—22no—
120C24D72411yescharacteristic
121#41—3622no—
122#41—3622no—
123#41—3622no—
124#41—3622no—
125C2×Q8—1812no—
126C2×D4—3624no—
127C2×D4—3622no—
128C2×D4—1812no—
129C22×C4—22no—
130C22×C4—22no—
131C22×C4—21no—
132C22×C4—21no—
133C22×C4—3622no—
134C22×C4D72411yescharacteristic
135C22×C4C22×D18111yescharacteristic
136Q16—3622no—
137SD16—3624no—
138D8—3622no—
139M16—22no—
140M16—22no—
141C2×C8—21no—
142C2×C8C22⋊D18112yescomplemented
143C4⋊C4—3624no—
144C4⋊C4—3622no—
145C22⋊C4—3624no—
146C22⋊C4—3624no—
147C22⋊C4—3622no—
148C42—1814no—
149C23—22no—
150C23—21no—
151C23—42no—
152C23—3622no—
153C23C2×D72411yescharacteristic
154Q8—3622no—
155Q8—3622no—
156D4—3622no—
157D4—3622no—
158D4—7248no—
159D4—7242no—
160D4—7242no—
161C2×C4—22no—
162C2×C4—21no—
163C2×C4—41no—
164C2×C4—42no—
165C2×C4—41no—
166C2×C4—3624no—
167C2×C4—3622no—
168C2×C4—7242no—
169C2×C4—7242no—
170C2×C4D4×D18112yes—
171C2×C4D4×D18112yes—
172C2×C4C2×C22⋊D18111yescharacteristic
173C2×C4#1566844911yescharacteristic
174C8—22no—
175C8—41no—
176C22—24no—
177C22—22no—
178C22—41no—
179C22—42no—
180C22—41no—
181C22—41no—
182C22—7244no—
183C22—7242no—
184C22#1915378612yes—
185C22#1915379011yescharacteristic
186C4—41no—
187C4—7244no—
188C4—7242no—
189C4#1915378411yescharacteristic
190C4#1915378912yes—
191C4#1915381211yescharacteristic
192C2—22no—
193C2—21no—
194C2—42no—
195C2—14482no—
196C2#2604118811yescharacteristic
subgroupG/H
centerC4#19153812
commutator, cosocleC22×C4×C181C23
FrattiniC22×C4C22×D181
Fitting#407×C181C2
socleC2×C181#392
hypercenter#407D181
hypocenterC181#2010
LCSG ▷ C22×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C4 ◁ C22×C4 ◁ #407

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #26042079C2semidirect
2. #26041790C2semidirect
3. #26041295C2semidirect
4. #26041036C2semidirect
5. #407×C181C2semidirect
25. C2×Dic362D4semidirect
26. C2×D724D4semidirect
38. C4×Dic181D4semidirect
49. C2×C8×C181D4semidirect
98. C181#2010semidirect
103. #407D181semidirect
142. C2×C8C22⋊D181semidirect

Maximal subgroups

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

subgroupindex
#260420792
#260417902
#260412952
#260410362
#407×C1812
#2010181