Finite Group Databasebeta

← #37550013

Subgroups — #37550013

Order 23168.

250 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 52 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#26042266C212yesmaximal, complemented
2#26042190C212yesmaximal, complemented
3#26042187C212yesmaximal, complemented
4#26041827C211yesmaximal, characteristic
5C2×#15668458—22no—
6#19153877C2214yes—
7#19153876—22no—
8C2×#15668448C411yescharacteristic
9C2×#15668448C2211yescharacteristic
10#19153816C2211yescharacteristic
11#19153803C411yescharacteristic
12#19153803C2211yescharacteristic
13#19153787—22no—
14D4×Dic181—22no—
15C42×D181C411yescharacteristic
16#127×C181C411yescharacteristic
17#15668458—24no—
18#15668458—42no—
19C2×#13089685—42no—
20#15668448—41no—
21#15668448—41no—
22#15668448—41no—
23#15668448—41no—
24C2×Dic362C2×C411yescharacteristic
25C2×Dic362C2311yescharacteristic
26C2×C22⋊D181—21no—
27C2×C22⋊D181D412yes—
28C22×Dic181—21no—
29C22×Dic181D412yes—
30C2×C4×D181—21no—
31C2×C4×D181C2×C411yescharacteristic
32C4⋊Dic181—22no—
33C22⋊Dic181—22no—
34C22⋊Dic181—22no—
35C4×Dic181—21no—
36C4×Dic181C2×C411yescharacteristic
37C2×D4×C181—22no—
38C2×D4×C181C2×C411yescharacteristic
39C2×D4×C181C2×C411yescharacteristic
40C42×C181C2×C411yescharacteristic
41#13089685—44no—
42C22×D181C22⋊C411yescharacteristic
43Dic362—41no—
44Dic362—41no—
45C22⋊D181—42no—
46C22⋊D181—42no—
47C2×Dic181—22no—
48C2×Dic181—22no—
49C2×Dic181—21no—
50C2×Dic181—21no—
51C2×Dic181—41no—
52C2×Dic181—41no—
53C2×Dic181C22⋊C411yescharacteristic
54C2×Dic181C2×D412yes—
55C4×D181—21no—
56C4×D181—21no—
57C4×D181—42no—
58C23×C181—21no—
59C23×C181C22⋊C412yes—
60D4×C181—41no—
61D4×C181—41no—
62D4×C181—44no—
63C2×C4×C181—21no—
64C2×C4×C181C22×C411yescharacteristic
65C22×C181—22no—
66C22×C181—42no—
67C22×C181—42no—
68C22×C181—41no—
69C22×C181C2×C22⋊C411yescharacteristic
70C2×D181—21no—
71C2×D181—41no—
72C4×C181—22no—
73C4×C181—21no—
74Dic181—22no—
75Dic181—41no—
76Dic181—41no—
77Dic181#9911yescharacteristic
78Dic181#9911yescharacteristic
79C2×C181—21no—
80C2×C181—42no—
81C2×C181—81no—
82C2×C181C2×#9911yescharacteristic
83D181—41no—
84C181#213211yescharacteristic, complemented, Sylow
85#2132—1811nomaximal, Sylow
86#532—1811no—
87#413—1812no—
88#356—1812no—
89#355—1812no—
90C2×#41—1811no—
91C2×#41—1811no—
92C2×M16—3622no—
93C4⋊Q8—1811no—
94#127#1062438211yescharacteristic
95#124—1811no—
96#124—1811no—
97#121—3622no—
98C4×D4—3622no—
99C2×C42—1811no—
100#101—1814no—
101#100—3622no—
102#41—7241no—
103#41—7241no—
104#41—7241no—
105#41—7241no—
106C2×Q8—1811no—
107C2×Q8—1811no—
108C2×D4—22no—
109C2×D4—3621no—
110C2×D4—1812no—
111C2×D4C2×#1062438211yescharacteristic
112C2×D4C2×#1062438211yescharacteristic
113C22×C4—3621no—
114C22×C4—3621no—
115C22×C4—1812no—
116C22×C4—1811no—
117M16—3624no—
118M16—7242no—
119C2×C8—7242no—
120C4⋊C4—3622no—
121C22⋊C4—3622no—
122C22⋊C4—3622no—
123C42—3621no—
124C42—1811no—
125C42C2×#1062438211yescharacteristic
126C23—21no—
127C23—1811no—
128C23C22⋊#1062438212yes—
129Q8—7241no—
130Q8—7241no—
131D4—41no—
132D4—41no—
133D4—44no—
134D4—7242no—
135D4—7242no—
136C2×C4—21no—
137C2×C4—3621no—
138C2×C4—3621no—
139C2×C4—3622no—
140C2×C4—3622no—
141C2×C4—3621no—
142C2×C4—3621no—
143C2×C4—1812no—
144C2×C4—1811no—
145C2×C4—7242no—
146C2×C4—7241no—
147C2×C4—7241no—
148C2×C4C22×#1062438211yescharacteristic
149C8—7244no—
150C22—22no—
151C22—42no—
152C22—42no—
153C22—41no—
154C22—3621no—
155C22—7241no—
156C22C2×C22⋊#1062438211yescharacteristic
157C4—22no—
158C4—21no—
159C4—3622no—
160C4—1811no—
161C4—1811no—
162C4—7241no—
163C4—7241no—
164C2—21no—
165C2—42no—
166C2—81no—
167C2—7241no—
168C2D181⋊#9911yescharacteristic
subgroupG/H
centerC2D181⋊#99
commutatorC2×C4×C181C22×C4
FrattiniC2×C4C22×#10624382
Fitting#127×C181C4
socleC2×C181C2×#99
prime radical#26041827C2
cosocleC2×Dic362C23
hypercenter#127#10624382
hypocenterC181#2132
LCSG ▷ C2×C4×C181 ▷ C22×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #127

Complements

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

NH ≅ G/Ntype
1. #26042266C2semidirect
2. #26042190C2semidirect
3. #26042187C2semidirect
84. C181#2132semidirect

Maximal subgroups

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

subgroupindex
#260422662
#260421902
#260421872
#260418272
#2132181