Finite Group Databasebeta

← #37549224

Subgroups — #37549224

Order 23168.

246 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 62 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#26042296C212yesmaximal, complemented
2#26042139C212yesmaximal, complemented
3#26042137C212yesmaximal, complemented
4#26041825C211yesmaximal, characteristic
5#19153883C2214yes—
6C22⋊#13089685—22no—
7C4×#13089685—22no—
8C2×#15668449C411yescharacteristic
9#19153814C2211yescharacteristic
10#19153812C2211yescharacteristic
11#19153805C411yescharacteristic
12#19153803C411yescharacteristic
13#19153788—22no—
14C4×C22⋊D181—22no—
15C2×C4×Dic181C2211yescharacteristic
16C2×#41×C181C411yescharacteristic
17C2×#13089685—24no—
18#15668449—42no—
19C2×Dic362C2×C411yescharacteristic
20C2×D724C2×C411yescharacteristic
21C2×C22⋊D181—22no—
22C2×C22⋊D181—21no—
23C22×Dic181D412yes—
24C2×C4×D181—21no—
25#15668428—22no—
26C22⋊Dic181—22no—
27#15668426—22no—
28C4×Dic181C2×C411yescharacteristic
29C4×Dic181D412yes—
30C4×Dic181C2311yescharacteristic
31#41×C181—42no—
32C2×Q8×C181C2×C411yescharacteristic
33C2×D4×C181—21no—
34C2×D4×C181C2×C411yescharacteristic
35C22×C4×C181—21no—
36C22×C4×C181C2×C411yescharacteristic
37#13089685—44no—
38C22×D181—21no—
39Dic362—41no—
40D724—41no—
41C22⋊D181—42no—
42C22⋊D181—44no—
43C2×Dic181—24no—
44C2×Dic181—21no—
45C2×Dic181C22⋊C412yes—
46C2×Dic181C2×D412yes—
47C4×D181—42no—
48C23×C181—21no—
49C23×C181C22⋊C411yescharacteristic
50Q8×C181—41no—
51D4×C181—41no—
52D4×C181—42no—
53C2×C4×C181—22no—
54C2×C4×C181—21no—
55C2×C4×C181—42no—
56C2×C4×C181C22⋊C411yescharacteristic
57C2×C4×C181C22×C411yescharacteristic
58C22×C181—21no—
59C22×C181—22no—
60C22×C181—41no—
61C22×C181—42no—
62C22×C181C2×C22⋊C411yescharacteristic
63C2×D181—41no—
64C2×D181—42no—
65C4×C181—21no—
66C4×C181—41no—
67C4×C181#10012yes—
68Dic181—22no—
69Dic181—41no—
70Dic181#13514yes—
71C2×C181—41no—
72C2×C181—81no—
73C2×C181C2×#10011yescharacteristic
74C2×C181#41612yes—
75D181—81no—
76C181#154311yescharacteristic, complemented, Sylow
77#1543—1811nomaximal, Sylow
78#532—1811no—
79#431—1812no—
80#333—1812no—
81#331—1812no—
82C2×#41—1811no—
83C2×#41#1062438211yescharacteristic
84C4⋊Q8—1811no—
85#127—1811no—
86#124—1811no—
87#124—1811no—
88#121—3622no—
89C4×D4—3622no—
90C2×C42—1811no—
91C4⋊C8—1814no—
92C22⋊C8—3622no—
93C4×C8—3622no—
94#41—42no—
95#41—7242no—
96C2×Q8—1811no—
97C2×Q8C2×#1062438211yescharacteristic
98C2×D4—21no—
99C2×D4—3621no—
100C2×D4—3622no—
101C2×D4—1811no—
102C2×D4C2×#1062438211yescharacteristic
103C22×C4—21no—
104C22×C4—3621no—
105C22×C4—1812no—
106C22×C4C2×#1062438211yescharacteristic
107C2×C8—3624no—
108C4⋊C4—3622no—
109C22⋊C4—3622no—
110C22⋊C4—3622no—
111C42—1812no—
112C42—1811no—
113C42—1811no—
114C23—21no—
115C23—3621no—
116C23C22⋊#1062438211yescharacteristic
117Q8—41no—
118Q8—7241no—
119D4—41no—
120D4—42no—
121D4—7241no—
122D4—7244no—
123D4—7242no—
124C2×C4—22no—
125C2×C4—21no—
126C2×C4—42no—
127C2×C4—3624no—
128C2×C4—3621no—
129C2×C4—1812no—
130C2×C4—1812no—
131C2×C4—7242no—
132C2×C4C22⋊#1062438211yescharacteristic
133C2×C4C22×#1062438211yescharacteristic
134C8—7244no—
135C22—21no—
136C22—22no—
137C22—41no—
138C22—42no—
139C22—7241no—
140C22—7242no—
141C22C2×C22⋊#1062438211yescharacteristic
142C4—21no—
143C4—41no—
144C4—3622no—
145C4—1814no—
146C4—7241no—
147C4#1915387612yes—
148C2—41no—
149C2—81no—
150C2—14481no—
151C2C2×#1915387611yescharacteristic
152C2#2604226912yes—
subgroupG/H
centerC2×C4C22⋊#10624382
commutatorC2×C4×C181C22×C4
FrattiniC2×C4C22×#10624382
FittingC2×#41×C181C4
socleC22×C181C2×C22⋊C4
prime radical#26041825C2
cosocleC4×Dic181C23
hypercenterC2×#41#10624382
hypocenterC181#1543
LCSG ▷ C2×C4×C181 ▷ C22×C181 ▷ C181
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #26042296C2semidirect
2. #26042139C2semidirect
3. #26042137C2semidirect
76. C181#1543semidirect

Maximal subgroups

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

subgroupindex
#260422962
#260421392
#260421372
#260418252
#1543181