Finite Group Databasebeta

← #14581009

Subgroups — #14581009

Order 2624.

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#13050159C211yesmaximal, characteristic, complemented
2#13050159C211yesmaximal, characteristic, complemented
3#13050150C211yesmaximal, characteristic, complemented
4#13050148C211yesmaximal, characteristic, complemented
5#13050146C211yesmaximal, characteristic, complemented
6#13050144C211yesmaximal, characteristic, complemented
7#13050141C211yesmaximal, characteristic, complemented
8#13050132C211yesmaximal, characteristic
9D4×Dic41C211yesmaximal, characteristic, complemented
10#13050124C211yesmaximal, characteristic, complemented
11#13050123C211yesmaximal, characteristic, complemented
12#13050122C211yesmaximal, characteristic, complemented
13C2×#10620281C211yesmaximal, characteristic, complemented
14C22⋊C4×D41C211yesmaximal, characteristic, complemented
15#123×C41C211yesmaximal, characteristic, complemented
16C23×D41C2211yescharacteristic
17C2×D4×C41C2211yescharacteristic
18C22×C4×C41C2211yescharacteristic
19C2×C22⋊D41C2211yescharacteristic
20C2×C22⋊D41C2211yescharacteristic
21C22×Dic41C2211yescharacteristic
22C22×Dic41C2211yescharacteristic, complemented
23C2×C4×D41C2211yescharacteristic
24C2×C4×D41C2211yescharacteristic
25C2×Dic82C2211yescharacteristic, complemented
26C4⋊C4×C41C2211yescharacteristic, complemented
27C4⋊C4×C41C2211yescharacteristic, complemented
28C22⋊C4×C41C2211yescharacteristic
29C22⋊C4×C41C2211yescharacteristic, complemented
30C22⋊C4×C41C2211yescharacteristic, complemented
31C22⋊Dic41C2211yescharacteristic
32C22⋊Dic41C2211yescharacteristic
33C22⋊Dic41C2211yescharacteristic, complemented
34#10620281C2211yescharacteristic
35#10620281C2211yescharacteristic
36#10620281C2211yescharacteristic
37#10620281C2211yescharacteristic
38#10620281C2211yescharacteristic
39#10620281C2211yescharacteristic
40#10620281C2211yescharacteristic
41#10620281C2211yescharacteristic
42C4⋊Dic41C2211yescharacteristic, complemented
43C4⋊Dic41C2211yescharacteristic, complemented
44C4⋊Dic41C2211yescharacteristic, complemented
45C4⋊Dic41C2211yescharacteristic, complemented
46#10620279C2211yescharacteristic, complemented
47#10620279C2211yescharacteristic, complemented
48C4×Dic41C2211yescharacteristic, complemented
49C4×Dic41C2211yescharacteristic, complemented
50C4×Dic41C2211yescharacteristic, complemented
51C23×C41C2311yescharacteristic
52C23×C41C2311yescharacteristic
53C22×D41—22no—
54C22×D41—22no—
55C22×D41—41no—
56C22×D41C2311yescharacteristic
57C22×D41C2311yescharacteristic
58D4×C41—22no—
59C2×C4×C41—22no—
60C2×C4×C41C2311yescharacteristic
61C2×C4×C41C2311yescharacteristic
62C2×C4×C41C2311yescharacteristic
63C2×C4×C41C2311yescharacteristic
64C2×C4×C41C2311yescharacteristic
65C22⋊D41—22no—
66C22⋊D41—41no—
67C2×Dic41—41no—
68C2×Dic41—41no—
69C2×Dic41C2311yescharacteristic
70C2×Dic41C2311yescharacteristic
71C2×Dic41C2311yescharacteristic
72C2×Dic41C2311yescharacteristic
73C2×Dic41C2311yescharacteristic
74C2×Dic41C2311yescharacteristic
75C4×D41—22no—
76C4×D41—41no—
77Dic82—41no—
78C22×C41—21no—
79C22×C41—21no—
80C22×C41—21no—
81C22×C41—21no—
82C22×C41—21no—
83C22×C41#4112yes—
84C22×C41C2411yescharacteristic
85C2×D41—21no—
86C2×D41—21no—
87C2×D41—21no—
88C2×D41—21no—
89C2×D41—21no—
90C2×D41—44no—
91C2×D41#4112yes—
92C4×C41—21no—
93C4×C41—21no—
94C4×C41—21no—
95C4×C41—21no—
96C4×C41—21no—
97Dic41—21no—
98Dic41—21no—
99Dic41—21no—
100Dic41—21no—
101Dic41—21no—
102Dic41—21no—
103C2×C41—22no—
104C2×C41—41no—
105C2×C41C2×#4111yescharacteristic
106C2×C41C2×#4111yescharacteristic
107C2×C41H(5,𝔽2)11yescharacteristic
108D41—22no—
109D41—41no—
110#551—411nomaximal, Sylow
111C41#55111yescharacteristic, complemented, Sylow
112#126—411no—
113#126—411no—
114#124—411no—
115#123—411no—
116#123—411no—
117#123D4111yescharacteristic, complemented
118C22⋊Q8—411no—
119C22⋊Q8—411no—
120#120—411no—
121C4×D4—411no—
122C4×D4—411no—
123#117—411no—
124#117—411no—
125C2×C22⋊C4—411no—
126C2×C22⋊C4—411no—
127C24—411no—
128C2×Q8—411no—
129C2×D4—411no—
130C2×D4—411no—
131C2×D4C2×D4111yescharacteristic
132C22×C4—411no—
133C22×C4—411no—
134C22×C4—411no—
135C22×C4—411no—
136C22×C4C2×D4111yescharacteristic
137C4⋊C4—411no—
138C4⋊C4—411no—
139C4⋊C4—411no—
140C4⋊C4—411no—
141C4⋊C4—411no—
142C4⋊C4—411no—
143C4⋊C4C2×D4111yescharacteristic, complemented
144C4⋊C4C2×D4111yescharacteristic, complemented
145C22⋊C4—411no—
146C22⋊C4—411no—
147C22⋊C4—411no—
148C22⋊C4—411no—
149C22⋊C4—411no—
150C22⋊C4—411no—
151C22⋊C4—411no—
152C22⋊C4—411no—
153C22⋊C4—411no—
154C22⋊C4—411no—
155C22⋊C4—411no—
156C22⋊C4C2×D4111yescharacteristic
157C22⋊C4C2×D4111yescharacteristic, complemented
158C22⋊C4C2×D4111yescharacteristic, complemented
159C42—411no—
160C42—411no—
161C42—411no—
162C23—411no—
163C23—411no—
164C23—822no—
165C23—822no—
166C23—1641no—
167C23C22×D4111yescharacteristic
168C23C22×D4111yescharacteristic
169Q8—1641no—
170D4—22no—
171D4—822no—
172D4—1641no—
173C2×C4—22no—
174C2×C4—411no—
175C2×C4—411no—
176C2×C4—411no—
177C2×C4—411no—
178C2×C4—411no—
179C2×C4—411no—
180C2×C4—822no—
181C2×C4—1641no—
182C2×C4—1641no—
183C2×C4—1641no—
184C2×C4C22×D4111yescharacteristic
185C2×C4C22×D4111yescharacteristic
186C2×C4C22×D4111yescharacteristic
187C2×C4C22×D4111yescharacteristic
188C2×C4C22×D4111yescharacteristic
189C22—21no—
190C22—21no—
191C22—21no—
192C22—21no—
193C22—21no—
194C22—412no—
195C22—821no—
196C22—821no—
197C22—821no—
198C22—821no—
199C22—821no—
200C22—1644no—
201C22#1062030812yes—
202C22C23×D4111yescharacteristic
203C4—21no—
204C4—21no—
205C4—21no—
206C4—21no—
207C4—21no—
208C4—821no—
209C4—821no—
210C4—821no—
211C4—821no—
212C4—821no—
213C4—821no—
214C2—22no—
215C2—41no—
216C2—822no—
217C2—1641no—
218C2#41×D4111yescharacteristic
219C2C2×#1062030811yescharacteristic
220C2#1305021011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D41
commutator, socle, cosocleC22×C41C24
Fitting#123×C41C2
prime radical#13050132C2
hypercenter#123D41
hypocenterC41#551
LCSG ▷ C22×C41 ▷ C41
UCSC1 ◁ C22 ◁ #123

Complements

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

NH ≅ G/Ntype
1. #13050159C2semidirect
2. #13050159C2semidirect
3. #13050150C2semidirect
4. #13050148C2semidirect
5. #13050146C2semidirect
6. #13050144C2semidirect
7. #13050141C2semidirect
9. D4×Dic41C2semidirect
10. #13050124C2semidirect
11. #13050123C2semidirect
12. #13050122C2semidirect
13. C2×#10620281C2semidirect
14. C22⋊C4×D41C2semidirect
15. #123×C41C2semidirect
22. C22×Dic41C22semidirect
25. C2×Dic82C22semidirect
26. C4⋊C4×C41C22semidirect
27. C4⋊C4×C41C22semidirect
29. C22⋊C4×C41C22semidirect
30. C22⋊C4×C41C22semidirect
33. C22⋊Dic41C22semidirect
42. C4⋊Dic41C22semidirect
43. C4⋊Dic41C22semidirect
44. C4⋊Dic41C22semidirect
45. C4⋊Dic41C22semidirect
46. #10620279C22semidirect
47. #10620279C22semidirect
48. C4×Dic41C22semidirect
49. C4×Dic41C22semidirect
50. C4×Dic41C22semidirect
111. C41#551semidirect
117. #123D41semidirect
143. C4⋊C4C2×D41semidirect
144. C4⋊C4C2×D41semidirect
157. C22⋊C4C2×D41semidirect
158. C22⋊C4C2×D41semidirect

Maximal subgroups

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

subgroupindex
#130501592
#130501502
#130501482
#130501462
#130501442
#130501412
#130501322
D4×Dic412
#130501242
#130501232
#130501222
C2×#106202812
C22⋊C4×D412
#123×C412
#55141