Finite Group Databasebeta

← #26041956

Subgroups — #26041956

Order 11584.

248 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 97 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#19153811C211yesmaximal, characteristic, complemented
3#19153805C211yesmaximal, characteristic, complemented
4#19153801C211yesmaximal, characteristic, complemented
5#19153801C211yesmaximal, characteristic, complemented
6#19153800C211yesmaximal, characteristic, complemented
7#19153792C211yesmaximal, characteristic, complemented
8#19153786C211yesmaximal, characteristic
9#19153778C211yesmaximal, characteristic, complemented
10C4×C22⋊D181C211yesmaximal, characteristic, complemented
11#19153774C211yesmaximal, characteristic, complemented
12#19153772C211yesmaximal, characteristic, complemented
13C2×#15668426C211yesmaximal, characteristic, complemented
14C22⋊C4×D181C211yesmaximal, characteristic, complemented
15C22⋊Q8×C181C211yesmaximal, characteristic, complemented
16C23×D181C2211yescharacteristic
17C2×D724C2211yescharacteristic
18C2×D724C2211yescharacteristic
19C2×C22⋊D181C2211yescharacteristic
20C22×Dic181C2211yescharacteristic
21C2×C4×D181C2211yescharacteristic
22C2×C4×D181C2211yescharacteristic
23C2×C4×D181C2211yescharacteristic, complemented
24C4⋊Dic181C2211yescharacteristic, complemented
25C4⋊Dic181C2211yescharacteristic, complemented
26#15668428C2211yescharacteristic, complemented
27#15668428C2211yescharacteristic, complemented
28#15668428C2211yescharacteristic, complemented
29C22⋊Dic181C2211yescharacteristic
30#15668426C2211yescharacteristic
31#15668426C2211yescharacteristic
32#15668426C2211yescharacteristic
33#15668426C2211yescharacteristic
34#15668426C2211yescharacteristic
35#15668426C2211yescharacteristic
36#15668426C2211yescharacteristic
37#15668426C2211yescharacteristic
38#15668426C2211yescharacteristic, complemented
39#15668426C2211yescharacteristic, complemented
40#15668426C2211yescharacteristic, complemented
41C4×Dic181C2211yescharacteristic, complemented
42C4×Dic181C2211yescharacteristic, complemented
43C4×Dic181C2211yescharacteristic, complemented
44C2×Q8×C181C2211yescharacteristic, complemented
45C22×C4×C181C2211yescharacteristic
46C4⋊C4×C181C2211yescharacteristic, complemented
47C4⋊C4×C181C2211yescharacteristic, complemented
48C4⋊C4×C181C2211yescharacteristic, complemented
49C22⋊C4×C181C2211yescharacteristic
50C22⋊C4×C181C2211yescharacteristic
51C22×D181—22no—
52C22×D181—22no—
53C22×D181—41no—
54C22×D181C2311yescharacteristic
55C22×D181C2311yescharacteristic
56C22×D181C2311yescharacteristic
57D724—22no—
58D724—41no—
59C22⋊D181—22no—
60C2×Dic181—22no—
61C2×Dic181C2311yescharacteristic
62C2×Dic181C2311yescharacteristic
63C2×Dic181C2311yescharacteristic
64C2×Dic181C2311yescharacteristic
65C2×Dic181C2311yescharacteristic
66C4×D181—22no—
67C4×D181—41no—
68C4×D181—41no—
69C23×C181C2311yescharacteristic
70Q8×C181—41no—
71C2×C4×C181—41no—
72C2×C4×C181C2311yescharacteristic
73C2×C4×C181C2311yescharacteristic
74C2×C4×C181C2311yescharacteristic
75C2×C4×C181C2311yescharacteristic
76C2×C4×C181C2311yescharacteristic
77C2×C4×C181C2311yescharacteristic
78C22×C181—21no—
79C22×C181—21no—
80C22×C181#4112yes—
81C22×C181C2411yescharacteristic
82C2×D181—21no—
83C2×D181—21no—
84C2×D181—21no—
85C2×D181—21no—
86C2×D181—21no—
87C2×D181—21no—
88C2×D181—21no—
89C2×D181—21no—
90C2×D181—44no—
91C2×D181#4112yes—
92C4×C181—21no—
93C4×C181—21no—
94C4×C181—21no—
95C4×C181—21no—
96C4×C181—21no—
97C4×C181—21no—
98Dic181—21no—
99Dic181—21no—
100Dic181—21no—
101Dic181—21no—
102Dic181—21no—
103C2×C181—22no—
104C2×C181C2×#4111yescharacteristic
105C2×C181C2×#4111yescharacteristic
106C2×C181H(5,𝔽2)11yescharacteristic
107D181—22no—
108D181—41no—
109D181—41no—
110C181#55111yescharacteristic, complemented, Sylow
111#551—1811nomaximal, Sylow
112#126—1811no—
113#126—1811no—
114#124—1811no—
115#123—1811no—
116#123—1811no—
117#123—1811no—
118C22⋊Q8—1811no—
119C22⋊Q8D18111yescharacteristic, complemented
120#120—1811no—
121C4×D4—1811no—
122C4×D4—1811no—
123#117—1811no—
124#117—1811no—
125C2×C22⋊C4—1811no—
126C2×C22⋊C4—1811no—
127C24—1811no—
128C2×Q8C2×D18111yescharacteristic, complemented
129C2×D4—1811no—
130C2×D4—1811no—
131C2×D4—1811no—
132C22×C4—1811no—
133C22×C4—1811no—
134C22×C4—1811no—
135C22×C4—1811no—
136C22×C4C2×D18111yescharacteristic
137C4⋊C4—1811no—
138C4⋊C4—1811no—
139C4⋊C4—1811no—
140C4⋊C4—1811no—
141C4⋊C4—1811no—
142C4⋊C4C2×D18111yescharacteristic, complemented
143C4⋊C4C2×D18111yescharacteristic, complemented
144C4⋊C4C2×D18111yescharacteristic, complemented
145C22⋊C4—1811no—
146C22⋊C4—1811no—
147C22⋊C4—1811no—
148C22⋊C4—1811no—
149C22⋊C4—1811no—
150C22⋊C4—1811no—
151C22⋊C4—1811no—
152C22⋊C4—1811no—
153C22⋊C4—1811no—
154C22⋊C4—1811no—
155C22⋊C4—1811no—
156C22⋊C4—1811no—
157C22⋊C4C2×D18111yescharacteristic
158C22⋊C4C2×D18111yescharacteristic
159C42—1811no—
160C42—1811no—
161C42—1811no—
162C23—3622no—
163C23—3622no—
164C23—1811no—
165C23—1811no—
166C23—1811no—
167C23—7241no—
168C23C22×D18111yescharacteristic
169Q8—41no—
170D4—3622no—
171D4—3622no—
172D4—7241no—
173C2×C4—41no—
174C2×C4—3622no—
175C2×C4—3622no—
176C2×C4—1811no—
177C2×C4—1811no—
178C2×C4—1811no—
179C2×C4—1811no—
180C2×C4—1811no—
181C2×C4—7241no—
182C2×C4—7241no—
183C2×C4C22×D18111yescharacteristic
184C2×C4C22×D18111yescharacteristic
185C2×C4C22×D18111yescharacteristic
186C2×C4C22×D18111yescharacteristic
187C2×C4C22×D18111yescharacteristic
188C2×C4C22×D18111yescharacteristic
189C22—21no—
190C22—21no—
191C22—3621no—
192C22—3621no—
193C22—3621no—
194C22—3621no—
195C22—3621no—
196C22—3621no—
197C22—3621no—
198C22—3621no—
199C22—1812no—
200C22—7244no—
201C22#1566845012yes—
202C22C23×D18111yescharacteristic
203C4—21no—
204C4—21no—
205C4—21no—
206C4—21no—
207C4—21no—
208C4—21no—
209C4—3621no—
210C4—3621no—
211C4—3621no—
212C4—3621no—
213C4—3621no—
214C2—22no—
215C2—3622no—
216C2—7241no—
217C2—7241no—
218C2#41×D18111yescharacteristic
219C2C2×#1566845011yescharacteristic
220C2#1915386111yescharacteristic
subgroupG/H
center, FrattiniC22C23×D181
commutator, socle, cosocleC22×C181C24
FittingC22⋊Q8×C181C2
prime radical#19153786C2
hypercenterC22⋊Q8D181
hypocenterC181#551
LCSG ▷ C22×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. #19153811C2semidirect
2. #19153811C2semidirect
3. #19153805C2semidirect
4. #19153801C2semidirect
5. #19153801C2semidirect
6. #19153800C2semidirect
7. #19153792C2semidirect
9. #19153778C2semidirect
10. C4×C22⋊D181C2semidirect
11. #19153774C2semidirect
12. #19153772C2semidirect
13. C2×#15668426C2semidirect
14. C22⋊C4×D181C2semidirect
15. C22⋊Q8×C181C2semidirect
23. C2×C4×D181C22semidirect
24. C4⋊Dic181C22semidirect
25. C4⋊Dic181C22semidirect
26. #15668428C22semidirect
27. #15668428C22semidirect
28. #15668428C22semidirect
38. #15668426C22semidirect
39. #15668426C22semidirect
40. #15668426C22semidirect
41. C4×Dic181C22semidirect
42. C4×Dic181C22semidirect
43. C4×Dic181C22semidirect
44. C2×Q8×C181C22semidirect
46. C4⋊C4×C181C22semidirect
47. C4⋊C4×C181C22semidirect
48. C4⋊C4×C181C22semidirect
110. C181#551semidirect
119. C22⋊Q8D181semidirect
128. C2×Q8C2×D181semidirect
142. C4⋊C4C2×D181semidirect
143. C4⋊C4C2×D181semidirect
144. C4⋊C4C2×D181semidirect

Maximal subgroups

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

subgroupindex
#191538112
#191538052
#191538012
#191538002
#191537922
#191537862
#191537782
C4×C22⋊D1812
#191537742
#191537722
C2×#156684262
C22⋊C4×D1812
C22⋊Q8×C1812
#551181