Finite Group Databasebeta

← #37549765

Subgroups — #37549765

Order 23168.

344 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 66 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#26042359C211yesmaximal, characteristic, complemented
2#26042271C212yesmaximal, complemented
3#26042260C211yesmaximal, characteristic, complemented
4#26042146C212yesmaximal, complemented
5#26041847C211yesmaximal, characteristic
6#19153904—24no—
7D181⋊M16—22no—
8D181⋊M16C2212yes—
9#19153895C2212yes—
10#19153878—24no—
11#19153875—22no—
12C2×#15668450C2211yescharacteristic
13C2×D4×D181C2211yescharacteristic
14#19153813C411yescharacteristic, complemented
15#19153812C411yescharacteristic, complemented
16#19153805C411yescharacteristic, complemented
17#19153789—22no—
18#19153786—22no—
19#19153773C2211yescharacteristic
20#124×C181C411yescharacteristic, complemented
21#15668459—24no—
22#15668459—22no—
23#15668458—22no—
24D181⋊C8—24no—
25D181⋊C8D414yescomplemented
26C4⋊#10624382—22no—
27C22⋊#10624382—22no—
28C4×#10624382—22no—
29C23×D181—21no—
30#15668450—22no—
31#15668450—22no—
32C2×D724—22no—
33C2×D724C2×C411yescharacteristic
34C2×D724C2×C411yescharacteristic
35C2×D724D412yes—
36C2×C22⋊D181—22no—
37C2×C22⋊D181—21no—
38D4×D181—22no—
39D4×D181—22no—
40C2×C4×D181D412yes—
41C2×C4×D181C2311yescharacteristic
42#15668428—21no—
43#15668426—21no—
44#15668426—22no—
45C4×Dic181C2×C411yescharacteristic
46C2×Q8×C181C2×C411yescharacteristic
47C2×D4×C181C2×C411yescharacteristic
48C22⋊C4×C181—22no—
49C42×C181C2×C411yescharacteristic
50C2×#10624382—42no—
51#13089685—24no—
52C22×D181—21no—
53C22×D181—42no—
54C22×D181—82no—
55C22×D181C22⋊C412yes—
56C22×D181C2×D411yescharacteristic
57D724—24no—
58D724—22no—
59D724—22no—
60D724—82no—
61C22⋊D181—41no—
62C22⋊D181—41no—
63C22⋊D181—82no—
64C2×Dic181—21no—
65C2×Dic181C2×D411yescharacteristic
66C4×D181—22no—
67C4×D181—22no—
68C4×D181C2×D412yes—
69C4×D181#4112yes—
70C23×C181—21no—
71Q8×C181—22no—
72D4×C181—22no—
73C2×C4×C181—21no—
74C2×C4×C181C22⋊C412yes—
75C2×C4×C181C22×C411yescharacteristic
76C22×C181—42no—
77C22×C181—41no—
78C22×C181C2×C22⋊C411yescharacteristic
79C2×D181—22no—
80C2×D181—41no—
81C2×D181—42no—
82C2×D181—42no—
83C2×D181—41no—
84C2×D181—84no—
85C2×D181#12112yes—
86#10624382—82no—
87C4×C181—22no—
88C4×C181—41no—
89C4×C181C4×D412yes—
90Dic181—41no—
91Dic181#12011yescharacteristic
92Dic181#12311yescharacteristic
93C2×C181—21no—
94C2×C181—81no—
95C2×C181#38611yescharacteristic
96D181—22no—
97D181—42no—
98D181—81no—
99C181#191011yescharacteristic, complemented, Sylow
100#1910—1811nomaximal, Sylow
101#568—1811no—
102#535—1811no—
103#418—1812no—
104#410—1811no—
105H(3,ℤ/4)—1812no—
106C2×#41—1811no—
107C22×D4—1811no—
108#131—3624no—
109C2×M16—3622no—
110C2×M16—1812no—
111#127—1811no—
112#127—1811no—
113#124—1811no—
114#124#1062438211yescharacteristic, complemented
115#121—3622no—
116#120—3622no—
117#117—1812no—
118#117—1811no—
119#102—3624no—
120#99—3622no—
121C24—3621no—
122#41—3622no—
123#41—3622no—
124C2×Q8C2×#1062438211yescharacteristic
125C2×D4—3622no—
126C2×D4—3622no—
127C2×D4—3622no—
128C2×D4—3622no—
129C2×D4—3621no—
130C2×D4—1812no—
131C2×D4—1811no—
132C2×D4—1811no—
133C2×D4C2×#1062438211yescharacteristic
134C22×C4—1812no—
135C22×C4—1811no—
136M16—3624no—
137M16—3622no—
138M16—3622no—
139C2×C8—3624no—
140C2×C8—1814no—
141C4⋊C4—3621no—
142C4⋊C4—3622no—
143C22⋊C4—22no—
144C22⋊C4—3621no—
145C22⋊C4—3622no—
146C22⋊C4—3622no—
147C42—3622no—
148C42—1811no—
149C42C2×#1062438211yescharacteristic
150C23—21no—
151C23—3621no—
152C23—14482no—
153C23—1812no—
154C23—1811no—
155C23—7242no—
156Q8—22no—
157D4—22no—
158D4—3624no—
159D4—3622no—
160D4—3622no—
161D4—14482no—
162D4—14482no—
163D4—7241no—
164D4—7241no—
165C2×C4—21no—
166C2×C4—3622no—
167C2×C4—3622no—
168C2×C4—3621no—
169C2×C4—1811no—
170C2×C4—1812no—
171C2×C4—1812no—
172C2×C4—7242no—
173C2×C4C22⋊#1062438212yes—
174C2×C4C22×#1062438211yescharacteristic
175C8—3624no—
176C22—42no—
177C22—41no—
178C22—3622no—
179C22—14484no—
180C22—1812no—
181C22—7241no—
182C22—7242no—
183C22—7242no—
184C22—7241no—
185C22C2×C22⋊#1062438211yescharacteristic
186C4—22no—
187C4—41no—
188C4—14482no—
189C4—1811no—
190C4—1811no—
191C4—7241no—
192C4D4×#1062438212yes—
193C2—21no—
194C2—81no—
195C2—3622no—
196C2—14481no—
197C2—7242no—
198C2#2604222711yescharacteristic
subgroupG/H
centerC2#26042227
commutatorC2×C4×C181C22×C4
FrattiniC2×C4C22×#10624382
Fitting#124×C181C4
socleC2×C181#386
prime radical#26041847C2
cosocleC2×C4×D181C23
hypercenter#124#10624382
hypocenterC181#1910
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C2 ◁ C2×C4 ◁ #124

Complements

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

NH ≅ G/Ntype
1. #26042359C2semidirect
2. #26042271C2semidirect
3. #26042260C2semidirect
4. #26042146C2semidirect
14. #19153813C4semidirect
15. #19153812C4semidirect
16. #19153805C4semidirect
20. #124×C181C4semidirect
25. D181⋊C8D4semidirect
99. C181#1910semidirect
114. #124#10624382semidirect

Maximal subgroups

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

subgroupindex
#260423592
#260422712
#260422602
#260421462
#260418472
#1910181