Finite Group Databasebeta

← #14580920

Subgroups — #14580920

Order 2624.

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#13050158C211yesmaximal, characteristic, complemented
2#13050157C211yesmaximal, characteristic, complemented
3#13050153C211yesmaximal, characteristic, complemented
4#13050148C211yesmaximal, characteristic, complemented
5#13050146C211yesmaximal, characteristic, complemented
6#13050140C211yesmaximal, characteristic, complemented
7#13050137C211yesmaximal, characteristic, complemented
8#13050137C211yesmaximal, characteristic, complemented
9#13050136C211yesmaximal, characteristic, complemented
10#13050134C211yesmaximal, characteristic, complemented
11#13050132C211yesmaximal, characteristic, complemented
12C4×D164C211yesmaximal, characteristic, complemented
13#13050124C211yesmaximal, characteristic, complemented
14C22⋊C4×D41C211yesmaximal, characteristic, complemented
15#124×C41C211yesmaximal, characteristic, complemented
16C23×D41C2211yescharacteristic
17C2×Q8×C41C2211yescharacteristic, complemented
18C2×D4×C41C2211yescharacteristic
19C2×C22⋊D41C2211yescharacteristic
20C2×C22⋊D41C2211yescharacteristic
21C2×C22⋊D41C2211yescharacteristic
22C2×C22⋊D41C2211yescharacteristic, complemented
23C22×Dic41C2211yescharacteristic, complemented
24C2×D164C2211yescharacteristic
25C2×D164C2211yescharacteristic
26C2×C4×D41C2211yescharacteristic
27C2×C4×D41C2211yescharacteristic
28C2×C4×D41C2211yescharacteristic, complemented
29C22⋊C4×C41C2211yescharacteristic
30C22⋊C4×C41C2211yescharacteristic
31C22⋊C4×C41C2211yescharacteristic, complemented
32C22⋊C4×C41C2211yescharacteristic, complemented
33C42×C41C2211yescharacteristic, complemented
34C22⋊Dic41C2211yescharacteristic
35C22⋊Dic41C2211yescharacteristic
36#10620281C2211yescharacteristic
37#10620281C2211yescharacteristic
38#10620281C2211yescharacteristic
39#10620281C2211yescharacteristic
40#10620281C2211yescharacteristic
41#10620281C2211yescharacteristic
42#10620281C2211yescharacteristic, complemented
43#10620281C2211yescharacteristic, complemented
44C4⋊Dic41C2211yescharacteristic, complemented
45C4⋊Dic41C2211yescharacteristic, complemented
46#10620279C2211yescharacteristic, complemented
47#10620279C2211yescharacteristic, complemented
48#10620279C2211yescharacteristic, complemented
49#10620279C2211yescharacteristic, complemented
50C4×Dic41C2211yescharacteristic, complemented
51C23×C41C2311yescharacteristic
52C23×C41C2311yescharacteristic
53C22×D41—22no—
54C22×D41—41no—
55C22×D41—41no—
56C22×D41C2311yescharacteristic
57C22×D41C2311yescharacteristic
58C22×D41C2311yescharacteristic
59Q8×C41—41no—
60D4×C41—41no—
61C2×C4×C41C2311yescharacteristic
62C2×C4×C41C2311yescharacteristic
63C2×C4×C41C2311yescharacteristic
64C2×C4×C41C2311yescharacteristic
65C2×C4×C41C2311yescharacteristic
66C22⋊D41—22no—
67C22⋊D41—41no—
68C22⋊D41—41no—
69C22⋊D41—41no—
70C2×Dic41—41no—
71C2×Dic41C2311yescharacteristic
72C2×Dic41C2311yescharacteristic
73C2×Dic41C2311yescharacteristic
74C2×Dic41C2311yescharacteristic
75C2×Dic41C2311yescharacteristic
76D164—22no—
77D164—41no—
78C4×D41—41no—
79C4×D41—41no—
80C4×D41—41no—
81C22×C41—21no—
82C22×C41—21no—
83C22×C41—21no—
84C22×C41—21no—
85C22×C41—21no—
86C22×C41—21no—
87C22×C41C2411yescharacteristic
88C2×D41—21no—
89C2×D41—21no—
90C2×D41—21no—
91C2×D41—21no—
92C2×D41—21no—
93C2×D41—21no—
94C2×D41—21no—
95C2×D41—21no—
96C2×D41—44no—
97C2×D41#4112yes—
98C4×C41—21no—
99C4×C41—21no—
100C4×C41—21no—
101C4×C41—21no—
102C4×C41—21no—
103Dic41—21no—
104Dic41—21no—
105Dic41—21no—
106Dic41—21no—
107Dic41—21no—
108C2×C41—41no—
109C2×C41—41no—
110C2×C41C2×#4111yescharacteristic
111C2×C41H(5,𝔽2)11yescharacteristic
112C2×C41H(5,𝔽2)11yescharacteristic
113D41—22no—
114D41—41no—
115D41—41no—
116#538—411nomaximal, Sylow
117C41#53811yescharacteristic, complemented, Sylow
118#126—411no—
119#126—411no—
120#124—411no—
121#124D4111yescharacteristic, complemented
122#123—411no—
123#123—411no—
124C22⋊Q8—411no—
125#121—411no—
126#121—411no—
127#121—411no—
128#120—411no—
129#120—411no—
130C4×D4—411no—
131C4×D4—411no—
132C2×C22⋊C4—411no—
133C24—411no—
134C2×Q8C2×D4111yescharacteristic, complemented
135C2×D4—411no—
136C2×D4—411no—
137C2×D4—411no—
138C2×D4—411no—
139C2×D4—411no—
140C2×D4—411no—
141C2×D4C2×D4111yescharacteristic
142C22×C4—411no—
143C22×C4—411no—
144C22×C4—411no—
145C22×C4—411no—
146C4⋊C4—411no—
147C4⋊C4—411no—
148C4⋊C4—411no—
149C4⋊C4—411no—
150C4⋊C4—411no—
151C4⋊C4—411no—
152C22⋊C4—411no—
153C22⋊C4—411no—
154C22⋊C4—411no—
155C22⋊C4—411no—
156C22⋊C4—411no—
157C22⋊C4—411no—
158C22⋊C4—411no—
159C22⋊C4—411no—
160C22⋊C4—411no—
161C22⋊C4—411no—
162C22⋊C4C2×D4111yescharacteristic
163C22⋊C4C2×D4111yescharacteristic
164C22⋊C4C2×D4111yescharacteristic, complemented
165C22⋊C4C2×D4111yescharacteristic, complemented
166C42—411no—
167C42C2×D4111yescharacteristic, complemented
168C23—411no—
169C23—411no—
170C23—411no—
171C23—822no—
172C23—1641no—
173C23—1641no—
174C23C22×D4111yescharacteristic
175C23C22×D4111yescharacteristic
176Q8—41no—
177D4—41no—
178D4—822no—
179D4—822no—
180D4—1641no—
181D4—1641no—
182D4—1641no—
183D4—1641no—
184C2×C4—411no—
185C2×C4—411no—
186C2×C4—411no—
187C2×C4—411no—
188C2×C4—411no—
189C2×C4—1641no—
190C2×C4—1641no—
191C2×C4—1641no—
192C2×C4—1641no—
193C2×C4C22×D4111yescharacteristic
194C2×C4C22×D4111yescharacteristic
195C2×C4C22×D4111yescharacteristic
196C2×C4C22×D4111yescharacteristic
197C2×C4C22×D4111yescharacteristic
198C22—21no—
199C22—21no—
200C22—21no—
201C22—21no—
202C22—21no—
203C22—21no—
204C22—412no—
205C22—821no—
206C22—821no—
207C22—821no—
208C22—821no—
209C22—821no—
210C22—821no—
211C22—821no—
212C22—821no—
213C22—1644no—
214C22C23×D4111yescharacteristic
215C4—21no—
216C4—21no—
217C4—21no—
218C4—21no—
219C4—21no—
220C4—821no—
221C4—821no—
222C4—821no—
223C4—821no—
224C4—821no—
225C2—41no—
226C2—41no—
227C2—822no—
228C2—1641no—
229C2—1641no—
230C2#41×D4111yescharacteristic
231C2#1305020911yescharacteristic
232C2#1305021011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D41
commutator, socle, cosocleC22×C41C24
Fitting#124×C41C2
hypercenter#124D41
hypocenterC41#538
LCSG ▷ C22×C41 ▷ C41
UCSC1 ◁ C22 ◁ #124

Complements

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

NH ≅ G/Ntype
1. #13050158C2semidirect
2. #13050157C2semidirect
3. #13050153C2semidirect
4. #13050148C2semidirect
5. #13050146C2semidirect
6. #13050140C2semidirect
7. #13050137C2semidirect
8. #13050137C2semidirect
9. #13050136C2semidirect
10. #13050134C2semidirect
11. #13050132C2semidirect
12. C4×D164C2semidirect
13. #13050124C2semidirect
14. C22⋊C4×D41C2semidirect
15. #124×C41C2semidirect
17. C2×Q8×C41C22semidirect
22. C2×C22⋊D41C22semidirect
23. C22×Dic41C22semidirect
28. C2×C4×D41C22semidirect
31. C22⋊C4×C41C22semidirect
32. C22⋊C4×C41C22semidirect
33. C42×C41C22semidirect
42. #10620281C22semidirect
43. #10620281C22semidirect
44. C4⋊Dic41C22semidirect
45. C4⋊Dic41C22semidirect
46. #10620279C22semidirect
47. #10620279C22semidirect
48. #10620279C22semidirect
49. #10620279C22semidirect
50. C4×Dic41C22semidirect
117. C41#538semidirect
121. #124D41semidirect
134. C2×Q8C2×D41semidirect
164. C22⋊C4C2×D41semidirect
165. C22⋊C4C2×D41semidirect
167. C42C2×D41semidirect

Maximal subgroups

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

subgroupindex
#130501582
#130501572
#130501532
#130501482
#130501462
#130501402
#130501372
#130501362
#130501342
#130501322
C4×D1642
#130501242
C22⋊C4×D412
#124×C412
#53841