Finite Group Databasebeta

← #16840344

Subgroups — #16840344

Order 3904.

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#14519772C211yesmaximal, characteristic, complemented
2#14519770C211yesmaximal, characteristic, complemented
3#14519764C211yesmaximal, characteristic, complemented
4#14519763C211yesmaximal, characteristic, complemented
5#14519760C211yesmaximal, characteristic, complemented
6#14519758C211yesmaximal, characteristic, complemented
7#14519755C211yesmaximal, characteristic, complemented
8#14519749C211yesmaximal, characteristic, complemented
9#14519748C211yesmaximal, characteristic, complemented
10#14519745C211yesmaximal, characteristic, complemented
11#14519745C211yesmaximal, characteristic, complemented
12C4×C22⋊D61C211yesmaximal, characteristic, complemented
13#14519737C211yesmaximal, characteristic, complemented
14C22⋊C4×D61C211yesmaximal, characteristic, complemented
15#121×C61C211yesmaximal, characteristic, complemented
16C23×D61C2211yescharacteristic
17C2×D4×C61C2211yescharacteristic
18C2×D4×C61C2211yescharacteristic
19C2×D4×C61C2211yescharacteristic, complemented
20C22×C4×C61C2211yescharacteristic, complemented
21C2×C22⋊D61C2211yescharacteristic
22C2×C22⋊D61C2211yescharacteristic
23C2×C22⋊D61C2211yescharacteristic
24C2×C22⋊D61C2211yescharacteristic
25C22×Dic61C2211yescharacteristic, complemented
26C2×C4×D61C2211yescharacteristic
27C2×C4×D61C2211yescharacteristic
28C2×Dic122C2211yescharacteristic, complemented
29C4⋊C4×C61C2211yescharacteristic, complemented
30C22⋊C4×C61C2211yescharacteristic
31C22⋊C4×C61C2211yescharacteristic, complemented
32C22⋊Dic61C2211yescharacteristic
33C22⋊Dic61C2211yescharacteristic
34C22⋊Dic61C2211yescharacteristic
35C22⋊Dic61C2211yescharacteristic, complemented
36C22⋊Dic61C2211yescharacteristic, complemented
37C22⋊Dic61C2211yescharacteristic, complemented
38#11758198C2211yescharacteristic
39#11758198C2211yescharacteristic
40#11758198C2211yescharacteristic
41#11758198C2211yescharacteristic
42#11758198C2211yescharacteristic
43#11758198C2211yescharacteristic
44C4⋊Dic61C2211yescharacteristic, complemented
45#11758196C2211yescharacteristic, complemented
46#11758196C2211yescharacteristic, complemented
47#11758196C2211yescharacteristic, complemented
48#11758196C2211yescharacteristic, complemented
49C4×Dic61C2211yescharacteristic, complemented
50C4×Dic61C2211yescharacteristic, complemented
51C23×C61C2311yescharacteristic
52C23×C61C2311yescharacteristic
53C23×C61C2311yescharacteristic
54C22×D61—22no—
55C22×D61—41no—
56C22×D61—41no—
57C22×D61C2311yescharacteristic
58C22×D61C2311yescharacteristic
59D4×C61—41no—
60D4×C61—41no—
61D4×C61—41no—
62C2×C4×C61—41no—
63C2×C4×C61C2311yescharacteristic
64C2×C4×C61C2311yescharacteristic
65C2×C4×C61C2311yescharacteristic
66C2×C4×C61C2311yescharacteristic
67C22⋊D61—22no—
68C22⋊D61—22no—
69C22⋊D61—41no—
70C22⋊D61—41no—
71C2×Dic61—41no—
72C2×Dic61C2311yescharacteristic
73C2×Dic61C2311yescharacteristic
74C2×Dic61C2311yescharacteristic
75C2×Dic61C2311yescharacteristic
76C2×Dic61C2311yescharacteristic
77C2×Dic61C2311yescharacteristic
78C4×D61—41no—
79C4×D61—41no—
80Dic122—41no—
81C22×C61—21no—
82C22×C61—21no—
83C22×C61—21no—
84C22×C61—21no—
85C22×C61—21no—
86C22×C61—21no—
87C22×C61—21no—
88C22×C61—21no—
89C22×C61—21no—
90C22×C61C2411yescharacteristic
91C2×D61—21no—
92C2×D61—21no—
93C2×D61—21no—
94C2×D61—21no—
95C2×D61—21no—
96C2×D61—44no—
97C2×D61#4112yes—
98C4×C61—21no—
99C4×C61—21no—
100C4×C61—21no—
101C4×C61—21no—
102Dic61—21no—
103Dic61—21no—
104Dic61—21no—
105Dic61—21no—
106Dic61—21no—
107Dic61—21no—
108C2×C61—41no—
109C2×C61—41no—
110C2×C61—41no—
111C2×C61C2×#4111yescharacteristic
112C2×C61H(5,𝔽2)11yescharacteristic
113C2×C61H(5,𝔽2)11yescharacteristic
114D61—22no—
115D61—41no—
116#538—611nomaximal, Sylow
117C61#53811yescharacteristic, complemented, Sylow
118#126—611no—
119#126—611no—
120#124—611no—
121#124—611no—
122#123—611no—
123#123—611no—
124C22⋊Q8—611no—
125#121—611no—
126#121—611no—
127#121D6111yescharacteristic, complemented
128#120—611no—
129#120—611no—
130C4×D4—611no—
131C4×D4—611no—
132C2×C22⋊C4—611no—
133C24—611no—
134C2×Q8—611no—
135C2×D4—611no—
136C2×D4—611no—
137C2×D4—611no—
138C2×D4—611no—
139C2×D4C2×D6111yescharacteristic
140C2×D4C2×D6111yescharacteristic
141C2×D4C2×D6111yescharacteristic, complemented
142C22×C4—611no—
143C22×C4—611no—
144C22×C4—611no—
145C22×C4C2×D6111yescharacteristic, complemented
146C4⋊C4—611no—
147C4⋊C4—611no—
148C4⋊C4—611no—
149C4⋊C4—611no—
150C4⋊C4—611no—
151C4⋊C4C2×D6111yescharacteristic, complemented
152C22⋊C4—611no—
153C22⋊C4—611no—
154C22⋊C4—611no—
155C22⋊C4—611no—
156C22⋊C4—611no—
157C22⋊C4—611no—
158C22⋊C4—611no—
159C22⋊C4—611no—
160C22⋊C4—611no—
161C22⋊C4—611no—
162C22⋊C4—611no—
163C22⋊C4—611no—
164C22⋊C4C2×D6111yescharacteristic
165C22⋊C4C2×D6111yescharacteristic, complemented
166C42—611no—
167C42—611no—
168C23—611no—
169C23—611no—
170C23—1222no—
171C23—2441no—
172C23—2441no—
173C23C22×D6111yescharacteristic
174C23C22×D6111yescharacteristic
175C23C22×D6111yescharacteristic
176Q8—2441no—
177D4—41no—
178D4—41no—
179D4—41no—
180D4—1222no—
181D4—1222no—
182D4—2441no—
183D4—2441no—
184C2×C4—41no—
185C2×C4—611no—
186C2×C4—611no—
187C2×C4—611no—
188C2×C4—611no—
189C2×C4—611no—
190C2×C4—611no—
191C2×C4—2441no—
192C2×C4—2441no—
193C2×C4—2441no—
194C2×C4C22×D6111yescharacteristic
195C2×C4C22×D6111yescharacteristic
196C2×C4C22×D6111yescharacteristic
197C2×C4C22×D6111yescharacteristic
198C22—21no—
199C22—21no—
200C22—21no—
201C22—21no—
202C22—21no—
203C22—21no—
204C22—21no—
205C22—21no—
206C22—21no—
207C22—612no—
208C22—1221no—
209C22—1221no—
210C22—1221no—
211C22—1221no—
212C22—1221no—
213C22—2444no—
214C22C23×D6111yescharacteristic
215C4—21no—
216C4—21no—
217C4—21no—
218C4—21no—
219C4—1221no—
220C4—1221no—
221C4—1221no—
222C4—1221no—
223C4—1221no—
224C4—1221no—
225C2—41no—
226C2—41no—
227C2—41no—
228C2—1222no—
229C2—2441no—
230C2#41×D6111yescharacteristic
231C2#1451982211yescharacteristic
232C2#1451982211yescharacteristic
subgroupG/H
center, FrattiniC22C23×D61
commutator, socle, cosocleC22×C61C24
Fitting#121×C61C2
hypercenter#121D61
hypocenterC61#538
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. #14519772C2semidirect
2. #14519770C2semidirect
3. #14519764C2semidirect
4. #14519763C2semidirect
5. #14519760C2semidirect
6. #14519758C2semidirect
7. #14519755C2semidirect
8. #14519749C2semidirect
9. #14519748C2semidirect
10. #14519745C2semidirect
11. #14519745C2semidirect
12. C4×C22⋊D61C2semidirect
13. #14519737C2semidirect
14. C22⋊C4×D61C2semidirect
15. #121×C61C2semidirect
19. C2×D4×C61C22semidirect
20. C22×C4×C61C22semidirect
25. C22×Dic61C22semidirect
28. C2×Dic122C22semidirect
29. C4⋊C4×C61C22semidirect
31. C22⋊C4×C61C22semidirect
35. C22⋊Dic61C22semidirect
36. C22⋊Dic61C22semidirect
37. C22⋊Dic61C22semidirect
44. C4⋊Dic61C22semidirect
45. #11758196C22semidirect
46. #11758196C22semidirect
47. #11758196C22semidirect
48. #11758196C22semidirect
49. C4×Dic61C22semidirect
50. C4×Dic61C22semidirect
117. C61#538semidirect
127. #121D61semidirect
141. C2×D4C2×D61semidirect
145. C22×C4C2×D61semidirect
151. C4⋊C4C2×D61semidirect
165. C22⋊C4C2×D61semidirect

Maximal subgroups

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

subgroupindex
#145197722
#145197702
#145197642
#145197632
#145197602
#145197582
#145197552
#145197492
#145197482
#145197452
C4×C22⋊D612
#145197372
C22⋊C4×D612
#121×C612
#53861