Finite Group Databasebeta

← #37550021

Subgroups — #37550021

Order 23168.

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

normal subgroups only

This group has 262 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#26042188C212yesmaximal, complemented
3#26042187C212yesmaximal, complemented
4#26041842C211yesmaximal, characteristic
5C2×#15668458—22no—
6#19153877C2214yescomplemented
7#19153876—22no—
8C2×#15668448C2211yescharacteristic
9C2×D4×D181C411yescharacteristic
10#19153812C411yescharacteristic
11#19153804C2211yescharacteristic
12#19153803C2211yescharacteristic
13#19153788—22no—
14#19153784—22no—
15#19153773C411yescharacteristic
16#127×C181C411yescharacteristic
17#15668458—24no—
18#15668458—42no—
19C2×#13089685—42no—
20C23×D181—21no—
21#15668448—42no—
22C2×Dic362C2311yescharacteristic
23C2×D724C2×C411yescharacteristic
24C2×C22⋊D181—21no—
25C2×C22⋊D181—22no—
26C2×C22⋊D181D412yes—
27D4×D181—42no—
28C22×Dic181D412yes—
29C2×C4×D181C2×C411yescharacteristic
30#15668428—21no—
31C22⋊Dic181—22no—
32#15668426—21no—
33#15668426—22no—
34C4×Dic181C2×C411yescharacteristic
35C2×D4×C181—22no—
36C2×D4×C181C2×C411yescharacteristic
37C2×D4×C181C2×C411yescharacteristic
38C42×C181C2×C411yescharacteristic
39#13089685—44no—
40C22×D181—21no—
41C22×D181—42no—
42C22×D181—82no—
43C22×D181C22⋊C411yescharacteristic
44Dic362—41no—
45D724—41no—
46C22⋊D181—42no—
47C22⋊D181—42no—
48C22⋊D181—82no—
49C2×Dic181—22no—
50C2×Dic181—22no—
51C2×Dic181—21no—
52C2×Dic181C22⋊C411yescharacteristic
53C2×Dic181C2×D412yes—
54C4×D181—22no—
55C23×C181—21no—
56C23×C181C22⋊C412yes—
57D4×C181—41no—
58D4×C181—41no—
59D4×C181—82no—
60C2×C4×C181—21no—
61C2×C4×C181C22×C411yescharacteristic
62C22×C181—22no—
63C22×C181—42no—
64C22×C181—42no—
65C22×C181—41no—
66C22×C181C2×C22⋊C411yescharacteristic
67C2×D181—21no—
68C2×D181—41no—
69C2×D181—42no—
70C2×D181—41no—
71C2×D181—84no—
72C4×C181—21no—
73C4×C181—41no—
74Dic181—22no—
75Dic181—41no—
76Dic181#9912yes—
77C2×C181—21no—
78C2×C181—42no—
79C2×C181—81no—
80C2×C181C2×#9911yescharacteristic
81D181—41no—
82D181—81no—
83C181#213411yescharacteristic, complemented, Sylow
84#2134—1811nomaximal, Sylow
85#535—1811no—
86#413—1812no—
87#355—1812no—
88#355—1812no—
89C2×#41—1811no—
90C22×D4—1811no—
91C2×M16—3622no—
92#127—1811no—
93#127#1062438211yescharacteristic
94#124—1811no—
95#124—1811no—
96#121—3622no—
97#120—3622no—
98#117—1811no—
99#101—1814no—
100#100—3622no—
101C24—3621no—
102#41—7242no—
103C2×Q8—1811no—
104C2×D4—22no—
105C2×D4—3622no—
106C2×D4—3621no—
107C2×D4—1812no—
108C2×D4—1811no—
109C2×D4—7242no—
110C2×D4C2×#1062438211yescharacteristic
111C2×D4C2×#1062438211yescharacteristic
112C22×C4—1812no—
113C22×C4—1811no—
114M16—3624no—
115M16—7242no—
116C2×C8—7242no—
117C4⋊C4—3621no—
118C22⋊C4—3621no—
119C22⋊C4—3622no—
120C22⋊C4—3622no—
121C42—1811no—
122C42C2×#1062438211yescharacteristic
123C23—21no—
124C23—3621no—
125C23—14482no—
126C23—1811no—
127C23—7242no—
128C23C22⋊#1062438212yes—
129Q8—7241no—
130D4—41no—
131D4—41no—
132D4—82no—
133D4—14482no—
134D4—7241no—
135D4—7242no—
136D4—7242no—
137C2×C4—21no—
138C2×C4—3622no—
139C2×C4—3622no—
140C2×C4—3622no—
141C2×C4—3621no—
142C2×C4—1812no—
143C2×C4—1811no—
144C2×C4C22×#1062438211yescharacteristic
145C8—7244no—
146C22—22no—
147C22—42no—
148C22—42no—
149C22—41no—
150C22—3621no—
151C22—14484no—
152C22—7242no—
153C22—7241no—
154C22—7241no—
155C22C2×C22⋊#1062438211yescharacteristic
156C4—21no—
157C4—41no—
158C4—3622no—
159C4—1812no—
160C4—7241no—
161C2—21no—
162C2—42no—
163C2—81no—
164C2—14481no—
165C2—7241no—
166C2D181⋊#9911yescharacteristic
subgroupG/H
centerC2D181⋊#99
commutatorC2×C4×C181C22×C4
FrattiniC2×C4C22×#10624382
Fitting#127×C181C4
socleC2×C181C2×#99
prime radical#26041842C2
cosocleC2×Dic362C23
hypercenter#127#10624382
hypocenterC181#2134
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. #26042188C2semidirect
3. #26042187C2semidirect
6. #19153877C22semidirect
83. C181#2134semidirect

Maximal subgroups

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

subgroupindex
#260422662
#260421882
#260421872
#260418422
#2134181