Finite Group Databasebeta

← #37550012

Subgroups — #37550012

Order 23168.

250 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 54 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#26042265C212yesmaximal, complemented
2#26042189C212yesmaximal, complemented
3#26042187C212yesmaximal, complemented
4#26041825C211yesmaximal, characteristic
5D181⋊M16—22no—
6#19153877C2214yes—
7#19153876—22no—
8C2×#15668449C2211yescharacteristic
9#19153814C2211yescharacteristic
10#19153812C411yescharacteristic
11#19153805C411yescharacteristic
12#19153803C2211yescharacteristic
13#19153788—22no—
14C4×C22⋊D181—22no—
15C2×C4×Dic181C411yescharacteristic
16C2×#41×C181C411yescharacteristic
17#15668459—42no—
18#15668458—24no—
19D181⋊C8—42no—
20#15668449—41no—
21#15668449—41no—
22C2×Dic362C2311yescharacteristic
23C2×D724C2×C411yescharacteristic
24C2×C22⋊D181—22no—
25C2×C22⋊D181D412yes—
26C22×Dic181—21no—
27C2×C4×D181D412yes—
28#15668428—22no—
29C22⋊Dic181—22no—
30#15668426—22no—
31C4×Dic181—21no—
32C4×Dic181C2×C411yescharacteristic
33C4×Dic181C2×C411yescharacteristic
34#41×C181—41no—
35#41×C181—41no—
36C2×Q8×C181C2×C411yescharacteristic
37C2×D4×C181—21no—
38C2×D4×C181C2×C411yescharacteristic
39C22×C4×C181—21no—
40C22×C4×C181C2×C411yescharacteristic
41#13089685—44no—
42C22×D181C22⋊C412yes—
43Dic362—41no—
44D724—41no—
45C22⋊D181—42no—
46C22⋊D181—44no—
47C2×Dic181—21no—
48C2×Dic181—21no—
49C2×Dic181—42no—
50C2×Dic181C2×D412yes—
51C4×D181—22no—
52C4×D181—22no—
53C23×C181—21no—
54C23×C181C22⋊C411yescharacteristic
55Q8×C181—41no—
56D4×C181—41no—
57D4×C181—42no—
58C2×C4×C181—21no—
59C2×C4×C181—21no—
60C2×C4×C181—21no—
61C2×C4×C181—41no—
62C2×C4×C181—41no—
63C2×C4×C181C22⋊C411yescharacteristic
64C2×C4×C181C22×C411yescharacteristic
65C22×C181—21no—
66C22×C181—41no—
67C22×C181—42no—
68C22×C181—41no—
69C22×C181C2×C22⋊C411yescharacteristic
70C2×D181—22no—
71C2×D181—42no—
72C4×C181—21no—
73C4×C181—41no—
74C4×C181#9911yescharacteristic
75C4×C181#9911yescharacteristic
76Dic181—22no—
77Dic181—22no—
78Dic181—41no—
79C2×C181—21no—
80C2×C181—41no—
81C2×C181—81no—
82C2×C181C2×#9911yescharacteristic
83D181—42no—
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#1062438211yescharacteristic
92C2×M16—3622no—
93C4⋊Q8—1811no—
94#127—1811no—
95#124—1811no—
96#124—1811no—
97#121—3622no—
98C4×D4—3622no—
99C2×C42—1811no—
100#101—1814no—
101#100—3622no—
102#41—41no—
103#41—41no—
104#41—7241no—
105#41—7241no—
106C2×Q8—1811no—
107C2×Q8C2×#1062438211yescharacteristic
108C2×D4—21no—
109C2×D4—3622no—
110C2×D4—1812no—
111C2×D4—1811no—
112C2×D4C2×#1062438211yescharacteristic
113C22×C4—21no—
114C22×C4—3621no—
115C22×C4—1812no—
116C22×C4C2×#1062438211yescharacteristic
117M16—3624no—
118M16—7242no—
119C2×C8—7242no—
120C4⋊C4—3622no—
121C22⋊C4—3622no—
122C22⋊C4—3622no—
123C42—3621no—
124C42—1811no—
125C42—1811no—
126C23—21no—
127C23—1812no—
128C23C22⋊#1062438211yescharacteristic
129Q8—41no—
130Q8—7241no—
131D4—41no—
132D4—42no—
133D4—7241no—
134D4—7242no—
135D4—7244no—
136C2×C4—21no—
137C2×C4—21no—
138C2×C4—21no—
139C2×C4—41no—
140C2×C4—41no—
141C2×C4—3621no—
142C2×C4—3622no—
143C2×C4—3622no—
144C2×C4—3621no—
145C2×C4—1812no—
146C2×C4—7242no—
147C2×C4C22⋊#1062438211yescharacteristic
148C2×C4C22×#1062438211yescharacteristic
149C8—7244no—
150C22—21no—
151C22—41no—
152C22—42no—
153C22—41no—
154C22—3622no—
155C22—7242no—
156C22C2×C22⋊#1062438211yescharacteristic
157C4—21no—
158C4—41no—
159C4—3622no—
160C4—3622no—
161C4—7241no—
162C4#1915387411yescharacteristic
163C4#1915387411yescharacteristic
164C2—21no—
165C2—41no—
166C2—81no—
167C2—7242no—
168C2C2×#1915387411yescharacteristic
subgroupG/H
centerC4#19153874
commutatorC2×C4×C181C22×C4
FrattiniC2×C4C22×#10624382
FittingC2×#41×C181C4
socleC2×C181C2×#99
prime radical#26041825C2
cosocleC2×Dic362C23
hypercenterC2×#41#10624382
hypocenterC181#2132
LCSG ▷ C2×C4×C181 ▷ C22×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #26042265C2semidirect
2. #26042189C2semidirect
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
#260422652
#260421892
#260421872
#260418252
#2132181