Finite Group Databasebeta

← #21461727

Subgroups — #21461727

Order 7808.

306 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 68 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#16840733C211yesmaximal, characteristic
2C4×C22⋊#6923C211yesmaximal, characteristic
3#16840632C212yesmaximal, complemented
4#16840632C212yesmaximal, complemented
5#117×D61C211yesmaximal, characteristic
6C2×#11758213C2212yes—
7C2×C22⋊#6923—21no—
8C2×C4×#6923C2212yes—
9#14519834—21no—
10C22⋊#92420—21no—
11(C2×#6923)⋊C4—21no—
12C22×C4×D61C2211yescharacteristic
13#14519736C411yescharacteristic, complemented
14#14519735C2211yescharacteristic
15#14519735C2211yescharacteristic
16#14519734—21no—
17#14519733—21no—
18C4⋊C4×D61C411yescharacteristic, complemented
19C4⋊C4×D61C411yescharacteristic, complemented
20C22⋊C4×D61—21no—
21C42×D61—21no—
22#117×C61C411yescharacteristic, complemented
23C23×D61D411yescharacteristic
24C22×#6923—22no—
25C22×C4×C61C2×C411yescharacteristic
26C22×Dic61D411yescharacteristic
27C2×C4×D61—24no—
28C2×C4×D61—21no—
29C2×C4×D61—21no—
30C2×C4×D61C2×C411yescharacteristic
31C2×C4×D61D411yescharacteristic
32C2×C4×D61D411yescharacteristic
33C2×C4×D61C2311yescharacteristic
34C22⋊#6923—24no—
35C2×#92420—22no—
36C4×#6923—24no—
37#11758213—24no—
38C4⋊C4×C61C2×C411yescharacteristic
39C4⋊C4×C61C2×C411yescharacteristic
40C22⋊C4×C61—21no—
41C42×C61—21no—
42C22⋊Dic61—21no—
43#11758198—21no—
44#11758198—21no—
45C4⋊Dic61C2×C411yescharacteristic
46C4⋊Dic61C2×C411yescharacteristic
47#11758196—21no—
48#11758196—21no—
49C4×Dic61—21no—
50C4×Dic61—21no—
51C4×Dic61—21no—
52C23×C61C22⋊C411yescharacteristic
53C22×D61—22no—
54C22×D61—22no—
55C22×D61—41no—
56C22×D61C22⋊C411yescharacteristic
57C22×D61C2×D411yescharacteristic
58C2×#6923—24no—
59C2×#6923—42no—
60C2×#6923—42no—
61C2×C4×C61—22no—
62C2×C4×C61—21no—
63C2×C4×C61—21no—
64C2×C4×C61C22⋊C411yescharacteristic
65C2×C4×C61C22×C411yescharacteristic
66C2×Dic61—22no—
67C2×Dic61—21no—
68C2×Dic61—21no—
69C2×Dic61C22⋊C411yescharacteristic
70C2×Dic61C2×D411yescharacteristic
71C4×D61—22no—
72C4×D61—22no—
73C4×D61—22no—
74C4×D61—42no—
75C4×D61—42no—
76C4×D61#4114yes—
77#92420—42no—
78C22×C61—21no—
79C22×C61—21no—
80C22×C61—21no—
81C22×C61C2×C22⋊C411yescharacteristic
82C2×D61—21no—
83C2×D61—21no—
84C2×D61—21no—
85C2×D61—21no—
86C2×D61—44no—
87C2×D61#10412yes—
88C2×D61#12312yes—
89#6923—44no—
90C4×C61—21no—
91C4×C61—41no—
92C4×C61—41no—
93C4×C61#11712yes—
94Dic61—21no—
95Dic61—41no—
96Dic61—41no—
97Dic61#12312yes—
98#1826—611nomaximal, Sylow
99C2×C61—41no—
100C2×C61#38111yescharacteristic
101C2×C61C2×#10411yescharacteristic
102C2×C61#42111yescharacteristic
103D61—22no—
104D61—22no—
105C2×#117—611no—
106#407—611no—
107C4×C22⋊C4—611no—
108#339—612no—
109#339—612no—
110C61#182611yescharacteristic, complemented, Sylow
111C23×C4—611no—
112C2×M16—612no—
113#117—611no—
114#117—611no—
115#117—611no—
116#117—1221no—
117#117—1221no—
118#117#692311yescharacteristic, complemented
119C2×C4⋊C4—611no—
120C2×C4⋊C4—611no—
121C2×C22⋊C4—1221no—
122C2×C22⋊C4—1221no—
123C2×C42—612no—
124C2×C42—1221no—
125C22⋊C8—1221no—
126C22⋊C8—1221no—
127#95—1221no—
128C24—611no—
129C22×C4—611no—
130C22×C4—611no—
131C22×C4—611no—
132C22×C4—611no—
133C22×C4—611no—
134C22×C4—1224no—
135C22×C4—1221no—
136C22×C4—1221no—
137C22×C4—1222no—
138C22×C4C2×#692311yescharacteristic
139M16—1224no—
140C2×C8—1222no—
141C4⋊C4—611no—
142C4⋊C4—611no—
143C4⋊C4—1221no—
144C4⋊C4—1221no—
145C4⋊C4C2×#692311yescharacteristic
146C4⋊C4C2×#692311yescharacteristic
147C22⋊C4—21no—
148C22⋊C4—1221no—
149C22⋊C4—1221no—
150C22⋊C4—1224no—
151C22⋊C4—1221no—
152C42—21no—
153C42—1221no—
154C42—1221no—
155C42—1224no—
156C42—1221no—
157C23—611no—
158C23—611no—
159C23—1222no—
160C23—1222no—
161C23—2441no—
162C23C22⋊#692311yescharacteristic
163C2×C4—22no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—611no—
167C2×C4—614no—
168C2×C4—611no—
169C2×C4—1222no—
170C2×C4—1222no—
171C2×C4—1222no—
172C2×C4—1222no—
173C2×C4—1224no—
174C2×C4—1221no—
175C2×C4—1221no—
176C2×C4—2442no—
177C2×C4—2442no—
178C2×C4—2442no—
179C2×C4—2442no—
180C2×C4C22⋊#692311yescharacteristic
181C2×C4C22×#692311yescharacteristic
182C8—2442no—
183C22—21no—
184C22—21no—
185C22—21no—
186C22—612no—
187C22—612no—
188C22—1221no—
189C22—1221no—
190C22—1221no—
191C22—1221no—
192C22—2444no—
193C22C2×C22⋊#692311yescharacteristic
194C4—21no—
195C4—41no—
196C4—41no—
197C4—612no—
198C4—1221no—
199C4—2444no—
200C4—2441no—
201C4—2441no—
202C4#1451985612yes—
203C2—41no—
204C2—1222no—
205C2—1222no—
206C2#1684070511yescharacteristic
207C2D61⋊#10411yescharacteristic
208C2#1684075911yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
Fitting#117×C61C4
socleC22×C61C2×C22⋊C4
hypercenter#117#6923
hypocenterC61#1826
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
3. #16840632C2semidirect
4. #16840632C2semidirect
13. #14519736C4semidirect
18. C4⋊C4×D61C4semidirect
19. C4⋊C4×D61C4semidirect
22. #117×C61C4semidirect
110. C61#1826semidirect
118. #117#6923semidirect