Finite Group Databasebeta

← #14580921

Subgroups — #14580921

Order 2624.

250 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 95 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#13050157C211yesmaximal, characteristic, complemented
2#13050157C211yesmaximal, characteristic, complemented
3#13050151C211yesmaximal, characteristic, complemented
4#13050150C211yesmaximal, characteristic, complemented
5#13050146C211yesmaximal, characteristic, complemented
6#13050145C211yesmaximal, characteristic, complemented
7#13050141C211yesmaximal, characteristic, complemented
8#13050136C211yesmaximal, characteristic, complemented
9#13050136C211yesmaximal, characteristic, complemented
10#13050135C211yesmaximal, characteristic, complemented
11#13050133C211yesmaximal, characteristic, complemented
12D4×Dic41C211yesmaximal, characteristic, complemented
13#13050124C211yesmaximal, characteristic, complemented
14C2×C22⋊Dic41C211yesmaximal, characteristic, complemented
15#120×C41C211yesmaximal, characteristic, complemented
16C24×C41C2211yescharacteristic
17C2×D4×C41C2211yescharacteristic
18C2×D4×C41C2211yescharacteristic
19C2×D4×C41C2211yescharacteristic
20C2×C22⋊D41C2211yescharacteristic
21C2×C22⋊D41C2211yescharacteristic
22C2×C22⋊D41C2211yescharacteristic
23C2×C22⋊D41C2211yescharacteristic, complemented
24C22×Dic41C2211yescharacteristic
25C22×Dic41C2211yescharacteristic
26C22×Dic41C2211yescharacteristic, complemented
27C2×C4×D41C2211yescharacteristic, complemented
28C2×Dic82C2211yescharacteristic, complemented
29C22⋊C4×C41C2211yescharacteristic
30C22⋊C4×C41C2211yescharacteristic
31C22⋊C4×C41C2211yescharacteristic
32C22⋊Dic41C2211yescharacteristic
33C22⋊Dic41C2211yescharacteristic
34C22⋊Dic41C2211yescharacteristic
35C22⋊Dic41C2211yescharacteristic
36C22⋊Dic41C2211yescharacteristic
37C22⋊Dic41C2211yescharacteristic
38C22⋊Dic41C2211yescharacteristic
39C22⋊Dic41C2211yescharacteristic, complemented
40C22⋊Dic41C2211yescharacteristic, complemented
41#10620281C2211yescharacteristic, complemented
42#10620281C2211yescharacteristic, complemented
43C4⋊Dic41C2211yescharacteristic, complemented
44C4⋊Dic41C2211yescharacteristic, complemented
45#10620279C2211yescharacteristic, complemented
46#10620279C2211yescharacteristic, complemented
47#10620279C2211yescharacteristic, complemented
48#10620279C2211yescharacteristic, complemented
49C4×Dic41C2211yescharacteristic, complemented
50C4×Dic41C2211yescharacteristic, complemented
51C23×C41—22no—
52C23×C41—41no—
53C23×C41—41no—
54C23×C41C2311yescharacteristic
55C23×C41C2311yescharacteristic
56C23×C41C2311yescharacteristic
57C23×C41C2311yescharacteristic
58C22×D41C2311yescharacteristic
59D4×C41—22no—
60D4×C41—41no—
61D4×C41—41no—
62C2×C4×C41C2311yescharacteristic
63C2×C4×C41C2311yescharacteristic
64C2×C4×C41C2311yescharacteristic
65C22⋊D41—22no—
66C22⋊D41—41no—
67C22⋊D41—41no—
68C22⋊D41—41no—
69C2×Dic41—41no—
70C2×Dic41—41no—
71C2×Dic41—41no—
72C2×Dic41C2311yescharacteristic
73C2×Dic41C2311yescharacteristic
74C2×Dic41C2311yescharacteristic
75C2×Dic41C2311yescharacteristic
76C2×Dic41C2311yescharacteristic
77C2×Dic41C2311yescharacteristic
78C2×Dic41C2311yescharacteristic
79C4×D41—41no—
80Dic82—41no—
81C22×C41—21no—
82C22×C41—21no—
83C22×C41—21no—
84C22×C41—21no—
85C22×C41—21no—
86C22×C41—21no—
87C22×C41—21no—
88C22×C41—21no—
89C22×C41—21no—
90C22×C41—21no—
91C22×C41—21no—
92C22×C41—44no—
93C22×C41#4112yes—
94C22×C41C2411yescharacteristic
95C2×D41—21no—
96C2×D41—21no—
97C2×D41—21no—
98C4×C41—21no—
99C4×C41—21no—
100C4×C41—21no—
101Dic41—21no—
102Dic41—21no—
103Dic41—21no—
104Dic41—21no—
105Dic41—21no—
106Dic41—21no—
107Dic41—21no—
108C2×C41—22no—
109C2×C41—41no—
110C2×C41—41no—
111C2×C41—41no—
112C2×C41C2×#4111yescharacteristic
113C2×C41H(5,𝔽2)11yescharacteristic
114C2×C41H(5,𝔽2)11yescharacteristic
115D41—41no—
116#538—411nomaximal, Sylow
117C41#53811yescharacteristic, complemented, Sylow
118#126—411no—
119#126—411no—
120#124—411no—
121#124—411no—
122#123—411no—
123#123—411no—
124C22⋊Q8—411no—
125#121—411no—
126#121—411no—
127#121—411no—
128#120—411no—
129#120D4111yescharacteristic, complemented
130C4×D4—411no—
131C4×D4—411no—
132C2×C22⋊C4—411no—
133C24C2×D4111yescharacteristic
134C2×Q8—411no—
135C2×D4—411no—
136C2×D4—411no—
137C2×D4—411no—
138C2×D4—411no—
139C2×D4C2×D4111yescharacteristic
140C2×D4C2×D4111yescharacteristic
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⋊C4—411no—
163C22⋊C4C2×D4111yescharacteristic
164C22⋊C4C2×D4111yescharacteristic
165C22⋊C4C2×D4111yescharacteristic
166C42—411no—
167C42—411no—
168C23—22no—
169C23—41no—
170C23—41no—
171C23—411no—
172C23C22×D4111yescharacteristic
173C23C22×D4111yescharacteristic
174C23C22×D4111yescharacteristic
175C23C22×D4111yescharacteristic
176Q8—1641no—
177D4—22no—
178D4—41no—
179D4—41no—
180D4—822no—
181D4—1641no—
182D4—1641no—
183D4—1641no—
184C2×C4—411no—
185C2×C4—411no—
186C2×C4—411no—
187C2×C4—411no—
188C2×C4—411no—
189C2×C4—411no—
190C2×C4—411no—
191C2×C4—1641no—
192C2×C4—1641no—
193C2×C4—1641no—
194C2×C4—1641no—
195C2×C4C22×D4111yescharacteristic
196C2×C4C22×D4111yescharacteristic
197C2×C4C22×D4111yescharacteristic
198C22—21no—
199C22—21no—
200C22—21no—
201C22—21no—
202C22—21no—
203C22—21no—
204C22—21no—
205C22—21no—
206C22—21no—
207C22—21no—
208C22—21no—
209C22—44no—
210C22—821no—
211C22—821no—
212C22—821no—
213C22#1062030812yes—
214C22C23×D4111yescharacteristic
215C4—21no—
216C4—21no—
217C4—21no—
218C4—821no—
219C4—821no—
220C4—821no—
221C4—821no—
222C4—821no—
223C4—821no—
224C4—821no—
225C2—22no—
226C2—41no—
227C2—41no—
228C2—41no—
229C2—1641no—
230C2C2×#1062030811yescharacteristic
231C2#1305020911yescharacteristic
232C2#1305020911yescharacteristic
subgroupG/H
center, FrattiniC22C23×D41
commutator, socle, cosocleC22×C41C24
Fitting#120×C41C2
hypercenter#120D41
hypocenterC41#538
LCSG ▷ C22×C41 ▷ C41
UCSC1 ◁ C22 ◁ #120

Complements

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

NH ≅ G/Ntype
1. #13050157C2semidirect
2. #13050157C2semidirect
3. #13050151C2semidirect
4. #13050150C2semidirect
5. #13050146C2semidirect
6. #13050145C2semidirect
7. #13050141C2semidirect
8. #13050136C2semidirect
9. #13050136C2semidirect
10. #13050135C2semidirect
11. #13050133C2semidirect
12. D4×Dic41C2semidirect
13. #13050124C2semidirect
14. C2×C22⋊Dic41C2semidirect
15. #120×C41C2semidirect
23. C2×C22⋊D41C22semidirect
26. C22×Dic41C22semidirect
27. C2×C4×D41C22semidirect
28. C2×Dic82C22semidirect
39. C22⋊Dic41C22semidirect
40. C22⋊Dic41C22semidirect
41. #10620281C22semidirect
42. #10620281C22semidirect
43. C4⋊Dic41C22semidirect
44. C4⋊Dic41C22semidirect
45. #10620279C22semidirect
46. #10620279C22semidirect
47. #10620279C22semidirect
48. #10620279C22semidirect
49. C4×Dic41C22semidirect
50. C4×Dic41C22semidirect
117. C41#538semidirect
129. #120D41semidirect

Maximal subgroups

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

subgroupindex
#130501572
#130501512
#130501502
#130501462
#130501452
#130501412
#130501362
#130501352
#130501332
D4×Dic412
#130501242
C2×C22⋊Dic412
#120×C412
#53841