Finite Group Databasebeta

← #37549225

Subgroups — #37549225

Order 23168.

246 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 60 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#26042297C212yesmaximal, complemented
2#26042139C212yesmaximal, complemented
3#26042137C212yesmaximal, complemented
4#26041828C211yesmaximal, characteristic
5#19153883C2214yes—
6#19153873—22no—
7C4×#13089685—22no—
8C2×#15668450C411yescharacteristic
9C2×#15668448C411yescharacteristic
10#19153814C2211yescharacteristic
11#19153812C2211yescharacteristic
12#19153804C411yescharacteristic
13#19153789—22no—
14#19153776—22no—
15C42×D181C2211yescharacteristic
16#124×C181C411yescharacteristic
17C2×#13089685—24no—
18#15668450—42no—
19#15668448—42no—
20C2×Dic362C2×C411yescharacteristic
21C2×D724—21no—
22C2×D724C2×C411yescharacteristic
23C2×C22⋊D181—21no—
24C2×C22⋊D181—22no—
25C22×Dic181—21no—
26C2×C4×D181—21no—
27C2×C4×D181C2×C411yescharacteristic
28C2×C4×D181D412yes—
29#15668428—22no—
30#15668426—22no—
31C4×Dic181D412yes—
32C4×Dic181C2311yescharacteristic
33C2×Q8×C181C2×C411yescharacteristic
34C2×D4×C181C2×C411yescharacteristic
35C22⋊C4×C181—22no—
36C42×C181C2×C411yescharacteristic
37#13089685—44no—
38C22×D181—21no—
39C22×D181C22⋊C411yescharacteristic
40Dic362—41no—
41D724—41no—
42D724—42no—
43C22⋊D181—42no—
44C22⋊D181—44no—
45C2×Dic181—21no—
46C2×Dic181—42no—
47C2×Dic181C22⋊C411yescharacteristic
48C2×Dic181C2×D412yes—
49C4×D181—22no—
50C4×D181—24no—
51C4×D181—42no—
52C23×C181—21no—
53Q8×C181—41no—
54D4×C181—41no—
55C2×C4×C181—21no—
56C2×C4×C181C22⋊C412yes—
57C2×C4×C181C22×C411yescharacteristic
58C22×C181—41no—
59C22×C181—42no—
60C22×C181C2×C22⋊C411yescharacteristic
61C2×D181—21no—
62C2×D181—22no—
63C2×D181—41no—
64C2×D181—42no—
65C4×C181—21no—
66C4×C181—22no—
67C4×C181—41no—
68Dic181—41no—
69Dic181#10012yes—
70Dic181#13514yes—
71C2×C181—81no—
72C2×C181C2×#10011yescharacteristic
73C2×C181#41612yes—
74D181—41no—
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—1811no—
84C4⋊Q8—1811no—
85#127—1811no—
86#124—1811no—
87#124#1062438211yescharacteristic
88#121—3622no—
89C4×D4—3622no—
90C2×C42—1811no—
91C4⋊C8—1814no—
92C22⋊C8—3622no—
93C4×C8—3622no—
94#41—7242no—
95#41—7242no—
96C2×Q8—1811no—
97C2×Q8C2×#1062438211yescharacteristic
98C2×D4—3621no—
99C2×D4—3621no—
100C2×D4—3622no—
101C2×D4—1811no—
102C2×D4C2×#1062438211yescharacteristic
103C22×C4—3621no—
104C22×C4—3621no—
105C22×C4—1812no—
106C22×C4—1811no—
107C2×C8—3624no—
108C4⋊C4—3622no—
109C22⋊C4—22no—
110C22⋊C4—3622no—
111C42—1812no—
112C42—1811no—
113C42C2×#1062438211yescharacteristic
114C23—21no—
115C23—3621no—
116C23—1811no—
117Q8—41no—
118Q8—7241no—
119D4—41no—
120D4—7241no—
121D4—7242no—
122D4—7244no—
123D4—7242no—
124C2×C4—21no—
125C2×C4—3622no—
126C2×C4—3624no—
127C2×C4—3621no—
128C2×C4—1812no—
129C2×C4—1811no—
130C2×C4—7242no—
131C2×C4—7242no—
132C2×C4C22⋊#1062438212yes—
133C2×C4C22×#1062438211yescharacteristic
134C8—7244no—
135C22—41no—
136C22—42no—
137C22—3621no—
138C22—3622no—
139C22—7241no—
140C22—7242no—
141C22C2×C22⋊#1062438211yescharacteristic
142C4—21no—
143C4—22no—
144C4—41no—
145C4—1812no—
146C4—1814no—
147C4—7241no—
148C2—81no—
149C2—14481no—
150C2—7241no—
151C2D181⋊#10011yescharacteristic
152C2#2604226912yes—
subgroupG/H
centerC22C2×C22⋊#10624382
commutatorC2×C4×C181C22×C4
FrattiniC2×C4C22×#10624382
Fitting#124×C181C4
socleC22×C181C2×C22⋊C4
prime radical#26041828C2
cosocleC4×Dic181C23
hypercenter#124#10624382
hypocenterC181#1543
LCSG ▷ C2×C4×C181 ▷ C22×C181 ▷ C181
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
1. #26042297C2semidirect
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
#260422972
#260421392
#260421372
#260418282
#1543181