Finite Group Databasebeta

← D181⋊#353 #37549987

Subgroups — D181⋊#353 #37549987

Order 23168.

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

normal subgroups only

This group has 368 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
1D181⋊#99C212yesmaximal, complemented
2#26042184C212yesmaximal, complemented
3#26042183C212yesmaximal, complemented
4#127×D181C211yesmaximal, characteristic
5C2×C22⋊#10624382—22no—
6#19153875C2214yescomplemented
7#19153874—22no—
8C2×D4×D181—22no—
9C2×D4×D181C411yescharacteristic, complemented
10C2×D4×D181C2211yescharacteristic
11#19153813C2211yescharacteristic
12#19153812—22no—
13#19153812C411yescharacteristic, complemented
14#19153812C2211yescharacteristic
15C42×D181C411yescharacteristic, complemented
16#127×C181C411yescharacteristic, complemented
17C22×#10624382—42no—
18C22⋊#10624382—24no—
19C22⋊#10624382—42no—
20C23×D181—21no—
21C23×D181D412yes—
22C2×D724—22no—
23C2×D724C2×C411yescharacteristic, complemented
24C2×D724C2311yescharacteristic
25C2×C22⋊D181—22no—
26C2×C22⋊D181—21no—
27C2×C22⋊D181—22no—
28C2×C22⋊D181D412yes—
29D4×D181—41no—
30D4×D181—41no—
31D4×D181—41no—
32D4×D181—41no—
33D4×D181—48no—
34C2×C4×D181—21no—
35C2×C4×D181C2×C411yescharacteristic
36C4×Dic181—21no—
37C4×Dic181C2×C411yescharacteristic, complemented
38C2×D4×C181—22no—
39C2×D4×C181C2×C411yescharacteristic
40C2×D4×C181C2×C411yescharacteristic, complemented
41C42×C181C2×C411yescharacteristic, complemented
42C2×#10624382—44no—
43C2×#10624382—84no—
44C22×D181—22no—
45C22×D181—22no—
46C22×D181—21no—
47C22×D181—44no—
48C22×D181—44no—
49C22×D181—41no—
50C22×D181—41no—
51C22×D181C22⋊C411yescharacteristic
52C22×D181C2×D412yes—
53D724—41no—
54D724—41no—
55D724—44no—
56C22⋊D181—42no—
57C22⋊D181—44no—
58C22⋊D181—44no—
59C22⋊D181—42no—
60C2×Dic181—21no—
61C2×Dic181C22⋊C411yescharacteristic
62C4×D181—24no—
63C4×D181—21no—
64C4×D181—21no—
65C23×C181—21no—
66C23×C181C22⋊C412yes—
67D4×C181—41no—
68D4×C181—41no—
69D4×C181—44no—
70C2×C4×C181—21no—
71C2×C4×C181C22×C411yescharacteristic
72C22×C181—22no—
73C22×C181—42no—
74C22×C181—42no—
75C22×C181—41no—
76C22×C181C2×C22⋊C411yescharacteristic
77C2×D181—22no—
78C2×D181—22no—
79C2×D181—44no—
80C2×D181—42no—
81C2×D181—42no—
82C2×D181—41no—
83C2×D181—82no—
84C2×D181—82no—
85C2×D181—82no—
86C2×D181#9911yescharacteristic
87C2×D181#9911yescharacteristic
88#10624382—84no—
89C4×C181—22no—
90C4×C181—21no—
91Dic181—22no—
92Dic181—21no—
93C2×C181—21no—
94C2×C181—42no—
95C2×C181—81no—
96C2×C181C2×#9911yescharacteristic
97D181—21no—
98D181—42no—
99D181—81no—
100D181#35312yescomplemented
101C181C2×#35311yescharacteristic, complemented, Sylow
102C2×#353—1811nomaximal, Sylow
103C2×#127—1811no—
104C2×#99—1812no—
105#353—1812no—
106#353—1812no—
107C22×D4—3622no—
108C22×D4—1811no—
109C22×D4—1811no—
110#127—3622no—
111#127—1811no—
112#127—1811no—
113#127—1811no—
114#127#1062438211yescharacteristic, complemented
115C2×C22⋊C4—3622no—
116C2×C42—1811no—
117#99—3622no—
118#99—1814no—
119C24—3621no—
120C24—1812no—
121C2×D4—22no—
122C2×D4—3622no—
123C2×D4—3622no—
124C2×D4—3622no—
125C2×D4—3621no—
126C2×D4—1812no—
127C2×D4—1811no—
128C2×D4—1811no—
129C2×D4—7241no—
130C2×D4—7241no—
131C2×D4—7241no—
132C2×D4—7241no—
133C2×D4—7248no—
134C2×D4C2×#1062438211yescharacteristic
135C2×D4C2×#1062438211yescharacteristic, complemented
136C22×C4—3621no—
137C22×C4—1811no—
138C22×C4—7242no—
139C22⋊C4—3624no—
140C22⋊C4—7242no—
141C42—3621no—
142C42—1811no—
143C42C2×#1062438211yescharacteristic, complemented
144C23—21no—
145C23—3622no—
146C23—3622no—
147C23—3621no—
148C23—1811no—
149C23—1812no—
150C23—7244no—
151C23—7244no—
152C23—7241no—
153C23—7241no—
154C23C22⋊#1062438212yes—
155D4—41no—
156D4—41no—
157D4—44no—
158D4—7241no—
159D4—7241no—
160D4—7244no—
161D4—7242no—
162D4—7244no—
163D4—7244no—
164D4—7242no—
165C2×C4—21no—
166C2×C4—3624no—
167C2×C4—3621no—
168C2×C4—3621no—
169C2×C4—3621no—
170C2×C4—14484no—
171C2×C4—1811no—
172C2×C4—7244no—
173C2×C4C22×#1062438211yescharacteristic
174C22—22no—
175C22—42no—
176C22—42no—
177C22—41no—
178C22—3622no—
179C22—3622no—
180C22—14482no—
181C22—14482no—
182C22—14482no—
183C22—1811no—
184C22—1811no—
185C22—7242no—
186C22—7242no—
187C22—7244no—
188C22—7241no—
189C22C2×C22⋊#1062438211yescharacteristic
190C4—22no—
191C4—21no—
192C4—3622no—
193C4—3621no—
194C4—14484no—
195C2—21no—
196C2—42no—
197C2—81no—
198C2—3621no—
199C2—14481no—
200C2—1812no—
201C2—7242no—
202C2D181⋊#9911yescharacteristic
subgroupG/H
centerC2D181⋊#99
commutatorC2×C4×C181C22×C4
FrattiniC2×C4C22×#10624382
Fitting#127×C181C4
socleC2×C181C2×#99
prime radical#127×D181C2
cosocleC2×D724C23
hypercenter#127#10624382
hypocenterC181C2×#353
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. D181⋊#99C2semidirect
2. #26042184C2semidirect
3. #26042183C2semidirect
6. #19153875C22semidirect
9. C2×D4×D181C4semidirect
13. #19153812C4semidirect
15. C42×D181C4semidirect
16. #127×C181C4semidirect
23. C2×D724C2×C4semidirect
37. C4×Dic181C2×C4semidirect
40. C2×D4×C181C2×C4semidirect
41. C42×C181C2×C4semidirect
100. D181#353semidirect
101. C181C2×#353semidirect
114. #127#10624382semidirect
135. C2×D4C2×#10624382semidirect
143. C42C2×#10624382semidirect

Maximal subgroups

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

subgroupindex
D181⋊#992
#260421842
#260421832
#127×D1812
C2×#353181