Finite Group Databasebeta

← #16840441

Subgroups — #16840441

Order 3904.

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#14519772C211yesmaximal, characteristic, complemented
2#14519771C211yesmaximal, characteristic, complemented
3#14519763C211yesmaximal, characteristic, complemented
4#14519760C211yesmaximal, characteristic, complemented
5#14519759C211yesmaximal, characteristic, complemented
6#14519758C211yesmaximal, characteristic, complemented
7#14519756C211yesmaximal, characteristic, complemented
8#14519755C211yesmaximal, characteristic, complemented
9#14519745C211yesmaximal, characteristic
10C4×C22⋊D61C211yesmaximal, characteristic, complemented
11#14519734C211yesmaximal, characteristic, complemented
12#14519733C211yesmaximal, characteristic, complemented
13C2×#11758198C211yesmaximal, characteristic, complemented
14C22⋊C4×D61C211yesmaximal, characteristic, complemented
15C4×D4×C61C211yesmaximal, characteristic, complemented
16C23×D61C2211yescharacteristic
17C2×D4×C61C2211yescharacteristic
18C22×C4×C61C2211yescharacteristic
19C22×C4×C61C2211yescharacteristic, complemented
20C2×C22⋊D61C2211yescharacteristic
21C2×C22⋊D61C2211yescharacteristic
22C22×Dic61C2211yescharacteristic
23C2×C4×D61C2211yescharacteristic
24C2×C4×D61C2211yescharacteristic
25C2×Dic122C2211yescharacteristic, complemented
26C4⋊C4×C61C2211yescharacteristic, complemented
27C22⋊C4×C61C2211yescharacteristic
28C22⋊C4×C61C2211yescharacteristic, complemented
29C42×C61C2211yescharacteristic, complemented
30C22⋊Dic61C2211yescharacteristic
31C22⋊Dic61C2211yescharacteristic
32C22⋊Dic61C2211yescharacteristic, complemented
33C22⋊Dic61C2211yescharacteristic, complemented
34#11758198C2211yescharacteristic
35#11758198C2211yescharacteristic
36#11758198C2211yescharacteristic
37#11758198C2211yescharacteristic
38#11758198C2211yescharacteristic
39#11758198C2211yescharacteristic
40#11758198C2211yescharacteristic
41#11758198C2211yescharacteristic
42C4⋊Dic61C2211yescharacteristic, complemented
43#11758196C2211yescharacteristic, complemented
44#11758196C2211yescharacteristic, complemented
45#11758196C2211yescharacteristic, complemented
46#11758196C2211yescharacteristic, complemented
47#11758196C2211yescharacteristic, complemented
48#11758196C2211yescharacteristic, complemented
49C4×Dic61C2211yescharacteristic, complemented
50C4×Dic61C2211yescharacteristic, complemented
51C23×C61C2311yescharacteristic
52C23×C61C2311yescharacteristic
53C22×D61—22no—
54C22×D61—22no—
55C22×D61—41no—
56C22×D61C2311yescharacteristic
57C22×D61C2311yescharacteristic
58D4×C61—22no—
59C2×C4×C61—41no—
60C2×C4×C61—41no—
61C2×C4×C61C2311yescharacteristic
62C2×C4×C61C2311yescharacteristic
63C2×C4×C61C2311yescharacteristic
64C2×C4×C61C2311yescharacteristic
65C2×C4×C61C2311yescharacteristic
66C22⋊D61—22no—
67C22⋊D61—41no—
68C2×Dic61—22no—
69C2×Dic61C2311yescharacteristic
70C2×Dic61C2311yescharacteristic
71C2×Dic61C2311yescharacteristic
72C2×Dic61C2311yescharacteristic
73C2×Dic61C2311yescharacteristic
74C2×Dic61C2311yescharacteristic
75C4×D61—22no—
76C4×D61—41no—
77Dic122—41no—
78C22×C61—21no—
79C22×C61—21no—
80C22×C61—21no—
81C22×C61—21no—
82C22×C61—21no—
83C22×C61#4112yes—
84C22×C61C2411yescharacteristic
85C2×D61—21no—
86C2×D61—21no—
87C2×D61—21no—
88C2×D61—21no—
89C2×D61—21no—
90C2×D61—44no—
91C2×D61#4112yes—
92C4×C61—21no—
93C4×C61—21no—
94C4×C61—21no—
95C4×C61—21no—
96C4×C61—21no—
97Dic61—21no—
98Dic61—21no—
99Dic61—21no—
100Dic61—21no—
101Dic61—21no—
102Dic61—21no—
103C2×C61—22no—
104C2×C61—41no—
105C2×C61C2×#4111yescharacteristic
106C2×C61C2×#4111yescharacteristic
107C2×C61H(5,𝔽2)11yescharacteristic
108D61—22no—
109D61—41no—
110#551—611nomaximal, Sylow
111C61#55111yescharacteristic, complemented, Sylow
112#126—611no—
113#126—611no—
114#124—611no—
115#123—611no—
116#123—611no—
117#123—611no—
118C22⋊Q8—611no—
119C22⋊Q8—611no—
120#120—611no—
121C4×D4—611no—
122C4×D4D6111yescharacteristic, complemented
123#117—611no—
124#117—611no—
125C2×C22⋊C4—611no—
126C2×C22⋊C4—611no—
127C24—611no—
128C2×Q8—611no—
129C2×D4—611no—
130C2×D4—611no—
131C2×D4C2×D6111yescharacteristic
132C22×C4—611no—
133C22×C4—611no—
134C22×C4—611no—
135C22×C4C2×D6111yescharacteristic
136C22×C4C2×D6111yescharacteristic, complemented
137C4⋊C4—611no—
138C4⋊C4—611no—
139C4⋊C4—611no—
140C4⋊C4—611no—
141C4⋊C4—611no—
142C4⋊C4—611no—
143C4⋊C4—611no—
144C4⋊C4C2×D6111yescharacteristic, complemented
145C22⋊C4—611no—
146C22⋊C4—611no—
147C22⋊C4—611no—
148C22⋊C4—611no—
149C22⋊C4—611no—
150C22⋊C4—611no—
151C22⋊C4—611no—
152C22⋊C4—611no—
153C22⋊C4—611no—
154C22⋊C4—611no—
155C22⋊C4—611no—
156C22⋊C4—611no—
157C22⋊C4C2×D6111yescharacteristic
158C22⋊C4C2×D6111yescharacteristic, complemented
159C42—611no—
160C42—611no—
161C42C2×D6111yescharacteristic, complemented
162C23—611no—
163C23—611no—
164C23—1222no—
165C23—1222no—
166C23—2441no—
167C23C22×D6111yescharacteristic
168C23C22×D6111yescharacteristic
169Q8—2441no—
170D4—22no—
171D4—1222no—
172D4—2441no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—611no—
176C2×C4—611no—
177C2×C4—611no—
178C2×C4—611no—
179C2×C4—611no—
180C2×C4—611no—
181C2×C4—1222no—
182C2×C4—1222no—
183C2×C4—2441no—
184C2×C4C22×D6111yescharacteristic
185C2×C4C22×D6111yescharacteristic
186C2×C4C22×D6111yescharacteristic
187C2×C4C22×D6111yescharacteristic
188C2×C4C22×D6111yescharacteristic
189C22—21no—
190C22—21no—
191C22—21no—
192C22—21no—
193C22—21no—
194C22—612no—
195C22—1221no—
196C22—1221no—
197C22—1221no—
198C22—1221no—
199C22—1221no—
200C22—2444no—
201C22#1175822212yes—
202C22C23×D6111yescharacteristic
203C4—21no—
204C4—21no—
205C4—21no—
206C4—21no—
207C4—21no—
208C4—1221no—
209C4—1221no—
210C4—1221no—
211C4—1221no—
212C4—1221no—
213C4—1221no—
214C2—22no—
215C2—41no—
216C2—1222no—
217C2—2441no—
218C2#41×D6111yescharacteristic
219C2C2×#1175822211yescharacteristic
220C2#1451982211yescharacteristic
subgroupG/H
center, FrattiniC22C23×D61
commutator, socle, cosocleC22×C61C24
FittingC4×D4×C61C2
prime radical#14519745C2
hypercenterC4×D4D61
hypocenterC61#551
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #14519772C2semidirect
2. #14519771C2semidirect
3. #14519763C2semidirect
4. #14519760C2semidirect
5. #14519759C2semidirect
6. #14519758C2semidirect
7. #14519756C2semidirect
8. #14519755C2semidirect
10. C4×C22⋊D61C2semidirect
11. #14519734C2semidirect
12. #14519733C2semidirect
13. C2×#11758198C2semidirect
14. C22⋊C4×D61C2semidirect
15. C4×D4×C61C2semidirect
19. C22×C4×C61C22semidirect
25. C2×Dic122C22semidirect
26. C4⋊C4×C61C22semidirect
28. C22⋊C4×C61C22semidirect
29. C42×C61C22semidirect
32. C22⋊Dic61C22semidirect
33. C22⋊Dic61C22semidirect
42. C4⋊Dic61C22semidirect
43. #11758196C22semidirect
44. #11758196C22semidirect
45. #11758196C22semidirect
46. #11758196C22semidirect
47. #11758196C22semidirect
48. #11758196C22semidirect
49. C4×Dic61C22semidirect
50. C4×Dic61C22semidirect
111. C61#551semidirect
122. C4×D4D61semidirect
136. C22×C4C2×D61semidirect
144. C4⋊C4C2×D61semidirect
158. C22⋊C4C2×D61semidirect
161. C42C2×D61semidirect

Maximal subgroups

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

subgroupindex
#145197722
#145197712
#145197632
#145197602
#145197592
#145197582
#145197562
#145197552
#145197452
C4×C22⋊D612
#145197342
#145197332
C2×#117581982
C22⋊C4×D612
C4×D4×C612
#55161