Finite Group Databasebeta

← #26041865

Subgroups — #26041865

Order 11584.

250 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 93 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#19153811C211yesmaximal, characteristic, complemented
2#19153809C211yesmaximal, characteristic, complemented
3#19153802C211yesmaximal, characteristic, complemented
4#19153802C211yesmaximal, characteristic, complemented
5#19153801C211yesmaximal, characteristic, complemented
6#19153796C211yesmaximal, characteristic, complemented
7#19153790C211yesmaximal, characteristic, complemented
8#19153789C211yesmaximal, characteristic, complemented
9#19153787C211yesmaximal, characteristic, complemented
10#19153786C211yesmaximal, characteristic, complemented
11#19153784C211yesmaximal, characteristic, complemented
12#19153778C211yesmaximal, characteristic, complemented
13C4×C22⋊D181C211yesmaximal, characteristic, complemented
14C22⋊C4×D181C211yesmaximal, characteristic, complemented
15#123×C181C211yesmaximal, characteristic, complemented
16C23×D181C2211yescharacteristic
17C2×Dic362C2211yescharacteristic, complemented
18C2×D724C2211yescharacteristic
19C2×D724C2211yescharacteristic
20C2×C22⋊D181C2211yescharacteristic
21C2×C22⋊D181C2211yescharacteristic
22C2×C22⋊D181C2211yescharacteristic
23C2×C22⋊D181C2211yescharacteristic, complemented
24C2×C4×D181C2211yescharacteristic
25C2×C4×D181C2211yescharacteristic
26C2×C4×D181C2211yescharacteristic, complemented
27C4⋊Dic181C2211yescharacteristic, complemented
28C4⋊Dic181C2211yescharacteristic, complemented
29#15668428C2211yescharacteristic, complemented
30#15668428C2211yescharacteristic, complemented
31C22⋊Dic181C2211yescharacteristic
32C22⋊Dic181C2211yescharacteristic
33C22⋊Dic181C2211yescharacteristic, complemented
34#15668426C2211yescharacteristic
35#15668426C2211yescharacteristic
36#15668426C2211yescharacteristic
37#15668426C2211yescharacteristic
38#15668426C2211yescharacteristic
39#15668426C2211yescharacteristic
40#15668426C2211yescharacteristic, complemented
41#15668426C2211yescharacteristic, complemented
42C4×Dic181C2211yescharacteristic, complemented
43C4×Dic181C2211yescharacteristic, complemented
44C2×D4×C181C2211yescharacteristic
45C22×C4×C181C2211yescharacteristic, complemented
46C4⋊C4×C181C2211yescharacteristic, complemented
47C4⋊C4×C181C2211yescharacteristic, complemented
48C22⋊C4×C181C2211yescharacteristic
49C22⋊C4×C181C2211yescharacteristic
50C22⋊C4×C181C2211yescharacteristic, complemented
51C22×D181—22no—
52C22×D181—41no—
53C22×D181—41no—
54C22×D181C2311yescharacteristic
55C22×D181C2311yescharacteristic
56C22×D181C2311yescharacteristic
57Dic362—41no—
58D724—22no—
59D724—41no—
60C22⋊D181—22no—
61C22⋊D181—41no—
62C22⋊D181—41no—
63C22⋊D181—41no—
64C2×Dic181C2311yescharacteristic
65C2×Dic181C2311yescharacteristic
66C2×Dic181C2311yescharacteristic
67C2×Dic181C2311yescharacteristic
68C2×Dic181C2311yescharacteristic
69C4×D181—41no—
70C4×D181—41no—
71C4×D181—41no—
72C23×C181C2311yescharacteristic
73C23×C181C2311yescharacteristic
74D4×C181—41no—
75C2×C4×C181—41no—
76C2×C4×C181C2311yescharacteristic
77C2×C4×C181C2311yescharacteristic
78C2×C4×C181C2311yescharacteristic
79C2×C4×C181C2311yescharacteristic
80C2×C4×C181C2311yescharacteristic
81C22×C181—21no—
82C22×C181—21no—
83C22×C181—21no—
84C22×C181—21no—
85C22×C181—21no—
86C22×C181—21no—
87C22×C181C2411yescharacteristic
88C2×D181—21no—
89C2×D181—21no—
90C2×D181—21no—
91C2×D181—21no—
92C2×D181—21no—
93C2×D181—21no—
94C2×D181—21no—
95C2×D181—21no—
96C2×D181—44no—
97C2×D181#4112yes—
98C4×C181—21no—
99C4×C181—21no—
100C4×C181—21no—
101C4×C181—21no—
102C4×C181—21no—
103Dic181—21no—
104Dic181—21no—
105Dic181—21no—
106Dic181—21no—
107Dic181—21no—
108C2×C181—41no—
109C2×C181—41no—
110C2×C181C2×#4111yescharacteristic
111C2×C181H(5,𝔽2)11yescharacteristic
112C2×C181H(5,𝔽2)11yescharacteristic
113D181—22no—
114D181—41no—
115D181—41no—
116C181#53811yescharacteristic, complemented, Sylow
117#538—1811nomaximal, Sylow
118#126—1811no—
119#126—1811no—
120#124—1811no—
121#124—1811no—
122#123—1811no—
123#123D18111yescharacteristic, complemented
124C22⋊Q8—1811no—
125#121—1811no—
126#121—1811no—
127#121—1811no—
128#120—1811no—
129#120—1811no—
130C4×D4—1811no—
131C4×D4—1811no—
132C2×C22⋊C4—1811no—
133C24—1811no—
134C2×Q8—1811no—
135C2×D4—1811no—
136C2×D4—1811no—
137C2×D4—1811no—
138C2×D4—1811no—
139C2×D4—1811no—
140C2×D4—1811no—
141C2×D4C2×D18111yescharacteristic
142C22×C4—1811no—
143C22×C4—1811no—
144C22×C4—1811no—
145C22×C4C2×D18111yescharacteristic, complemented
146C4⋊C4—1811no—
147C4⋊C4—1811no—
148C4⋊C4—1811no—
149C4⋊C4—1811no—
150C4⋊C4C2×D18111yescharacteristic, complemented
151C4⋊C4C2×D18111yescharacteristic, complemented
152C22⋊C4—1811no—
153C22⋊C4—1811no—
154C22⋊C4—1811no—
155C22⋊C4—1811no—
156C22⋊C4—1811no—
157C22⋊C4—1811no—
158C22⋊C4—1811no—
159C22⋊C4—1811no—
160C22⋊C4—1811no—
161C22⋊C4—1811no—
162C22⋊C4—1811no—
163C22⋊C4C2×D18111yescharacteristic
164C22⋊C4C2×D18111yescharacteristic
165C22⋊C4C2×D18111yescharacteristic, complemented
166C42—1811no—
167C42—1811no—
168C23—3622no—
169C23—1811no—
170C23—1811no—
171C23—1811no—
172C23—7241no—
173C23—7241no—
174C23C22×D18111yescharacteristic
175C23C22×D18111yescharacteristic
176Q8—7241no—
177D4—41no—
178D4—3622no—
179D4—3622no—
180D4—7241no—
181D4—7241no—
182D4—7241no—
183D4—7241no—
184C2×C4—41no—
185C2×C4—1811no—
186C2×C4—1811no—
187C2×C4—1811no—
188C2×C4—1811no—
189C2×C4—1811no—
190C2×C4—7241no—
191C2×C4—7241no—
192C2×C4—7241no—
193C2×C4C22×D18111yescharacteristic
194C2×C4C22×D18111yescharacteristic
195C2×C4C22×D18111yescharacteristic
196C2×C4C22×D18111yescharacteristic
197C2×C4C22×D18111yescharacteristic
198C22—21no—
199C22—21no—
200C22—21no—
201C22—21no—
202C22—21no—
203C22—21no—
204C22—3621no—
205C22—3621no—
206C22—3621no—
207C22—3621no—
208C22—3621no—
209C22—3621no—
210C22—3621no—
211C22—3621no—
212C22—1812no—
213C22—7244no—
214C22C23×D18111yescharacteristic
215C4—21no—
216C4—21no—
217C4—21no—
218C4—21no—
219C4—21no—
220C4—3621no—
221C4—3621no—
222C4—3621no—
223C4—3621no—
224C4—3621no—
225C2—41no—
226C2—41no—
227C2—3622no—
228C2—7241no—
229C2—7241no—
230C2#41×D18111yescharacteristic
231C2#1915386111yescharacteristic
232C2#1915386211yescharacteristic
subgroupG/H
center, FrattiniC22C23×D181
commutator, socle, cosocleC22×C181C24
Fitting#123×C181C2
hypercenter#123D181
hypocenterC181#538
LCSG ▷ C22×C181 ▷ C181
UCSC1 ◁ C22 ◁ #123

Complements

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

NH ≅ G/Ntype
1. #19153811C2semidirect
2. #19153809C2semidirect
3. #19153802C2semidirect
4. #19153802C2semidirect
5. #19153801C2semidirect
6. #19153796C2semidirect
7. #19153790C2semidirect
8. #19153789C2semidirect
9. #19153787C2semidirect
10. #19153786C2semidirect
11. #19153784C2semidirect
12. #19153778C2semidirect
13. C4×C22⋊D181C2semidirect
14. C22⋊C4×D181C2semidirect
15. #123×C181C2semidirect
17. C2×Dic362C22semidirect
23. C2×C22⋊D181C22semidirect
26. C2×C4×D181C22semidirect
27. C4⋊Dic181C22semidirect
28. C4⋊Dic181C22semidirect
29. #15668428C22semidirect
30. #15668428C22semidirect
33. C22⋊Dic181C22semidirect
40. #15668426C22semidirect
41. #15668426C22semidirect
42. C4×Dic181C22semidirect
43. C4×Dic181C22semidirect
45. C22×C4×C181C22semidirect
46. C4⋊C4×C181C22semidirect
47. C4⋊C4×C181C22semidirect
50. C22⋊C4×C181C22semidirect
116. C181#538semidirect
123. #123D181semidirect
145. C22×C4C2×D181semidirect
150. C4⋊C4C2×D181semidirect
151. C4⋊C4C2×D181semidirect
165. C22⋊C4C2×D181semidirect

Maximal subgroups

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

subgroupindex
#191538112
#191538092
#191538022
#191538012
#191537962
#191537902
#191537892
#191537872
#191537862
#191537842
#191537782
C4×C22⋊D1812
C22⋊C4×D1812
#123×C1812
#538181