Finite Group Databasebeta

← #21461724

Subgroups — #21461724

Order 7808.

300 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 300 conjugacy classes of subgroups — too many to draw. Only its 74 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
1D61⋊(C22⋊C8)C211yesmaximal, characteristic
2#16840704C211yesmaximal, characteristic
3#16840635C212yesmaximal, complemented
4#16840635C212yesmaximal, complemented
5#117×D61C211yesmaximal, characteristic
6C2×D61⋊C8C2212yes—
7C2×C4⋊#6923C2212yes—
8C2×C22⋊#6923—21no—
9#14519834—21no—
10C22⋊#92420—21no—
11(C2×#6923)⋊C4—21no—
12C22×C4×D61C2211yescharacteristic
13#14519736C411yescharacteristic, complemented
14#14519735C411yescharacteristic, complemented
15#14519735C411yescharacteristic, complemented
16#14519734—21no—
17#14519733—21no—
18C4⋊C4×D61C2211yescharacteristic
19C4⋊C4×D61C2211yescharacteristic
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—42no—
35C2×#92420—22no—
36C4⋊#6923—24no—
37D61⋊C8—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—21no—
56C22×D61—21no—
57C22×D61C22⋊C411yescharacteristic
58C22×D61C2×D411yescharacteristic
59C2×#6923—42no—
60C2×#6923—42no—
61C2×#6923—42no—
62C2×C4×C61—22no—
63C2×C4×C61—21no—
64C2×C4×C61—21no—
65C2×C4×C61C22⋊C411yescharacteristic
66C2×C4×C61C22×C411yescharacteristic
67C2×Dic61—22no—
68C2×Dic61—21no—
69C2×Dic61—21no—
70C2×Dic61C22⋊C411yescharacteristic
71C2×Dic61C2×D411yescharacteristic
72C4×D61—22no—
73C4×D61—22no—
74C4×D61—22no—
75C4×D61—42no—
76C4×D61—41no—
77C4×D61—41no—
78C4×D61#4114yes—
79#92420—42no—
80C22×C61—21no—
81C22×C61—21no—
82C22×C61—21no—
83C22×C61C2×C22⋊C411yescharacteristic
84C2×D61—21no—
85C2×D61—21no—
86C2×D61—21no—
87C2×D61—42no—
88C2×D61—42no—
89C2×D61#12312yes—
90C2×D61#13512yes—
91C2×D61AGL(1,ℤ/8)11yescharacteristic
92C2×D61#13711yescharacteristic
93#6923—82no—
94C4×C61—21no—
95C4×C61—41no—
96C4×C61—41no—
97C4×C61#11712yes—
98Dic61—21no—
99Dic61—41no—
100Dic61—41no—
101Dic61#12312yes—
102#1825—611nomaximal, Sylow
103C2×C61—41no—
104C2×C61#38111yescharacteristic
105C2×C61#41611yescharacteristic
106C2×C61#41711yescharacteristic
107D61—41no—
108D61#48212yes—
109D61#48512yes—
110C2×#117—611no—
111C2×C22⋊C8—611no—
112#380—611no—
113#340—612no—
114#340—612no—
115C61#182511yescharacteristic, complemented, Sylow
116C23×C4—611no—
117C22×C8—612no—
118#117—611no—
119#117—611no—
120#117—611no—
121#117—1221no—
122#117—1221no—
123#117#692311yescharacteristic, complemented
124C2×C4⋊C4—611no—
125C2×C4⋊C4—611no—
126C2×C4⋊C4—612no—
127C2×C22⋊C4—1221no—
128C2×C22⋊C4—1221no—
129C2×C42—1221no—
130C22⋊C8—1221no—
131C22⋊C8—1221no—
132#95—1221no—
133C24—611no—
134C22×C4—611no—
135C22×C4—611no—
136C22×C4—611no—
137C22×C4—611no—
138C22×C4—611no—
139C22×C4—1224no—
140C22×C4—1221no—
141C22×C4—1221no—
142C22×C4—1222no—
143C22×C4C2×#692311yescharacteristic
144C2×C8—1222no—
145C2×C8—1224no—
146C4⋊C4—611no—
147C4⋊C4—611no—
148C4⋊C4—1221no—
149C4⋊C4—1221no—
150C4⋊C4—1224no—
151C4⋊C4C2×#692311yescharacteristic
152C4⋊C4C2×#692311yescharacteristic
153C22⋊C4—21no—
154C22⋊C4—1221no—
155C22⋊C4—1221no—
156C22⋊C4—1221no—
157C22⋊C4—2442no—
158C42—21no—
159C42—1221no—
160C42—1221no—
161C42—1221no—
162C23—611no—
163C23—611no—
164C23—1221no—
165C23—1222no—
166C23—1222no—
167C23—1221no—
168C23C22⋊#692311yescharacteristic
169C2×C4—22no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—611no—
173C2×C4—614no—
174C2×C4—611no—
175C2×C4—1222no—
176C2×C4—1222no—
177C2×C4—1222no—
178C2×C4—1222no—
179C2×C4—1221no—
180C2×C4—1221no—
181C2×C4—2442no—
182C2×C4—2441no—
183C2×C4—2441no—
184C2×C4—2442no—
185C2×C4—2442no—
186C2×C4—2442no—
187C2×C4C22⋊#692311yescharacteristic
188C2×C4C22×#692311yescharacteristic
189C8—2442no—
190C22—21no—
191C22—21no—
192C22—21no—
193C22—612no—
194C22—612no—
195C22—611no—
196C22—611no—
197C22—1221no—
198C22—1221no—
199C22—1221no—
200C22—2442no—
201C22—2442no—
202C22C2×C22⋊#692311yescharacteristic
203C4—21no—
204C4—41no—
205C4—41no—
206C4—612no—
207C4—1221no—
208C4—4882no—
209C4—2441no—
210C4—2441no—
211C4#1451985612yes—
212C2—41no—
213C2—612no—
214C2—612no—
215C2—2441no—
216C2#1684070511yescharacteristic
217C2#1684075211yescharacteristic
218C2#1684075311yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
Fitting#117×C61C4
socleC22×C61C2×C22⋊C4
hypercenter#117#6923
hypocenterC61#1825
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. #16840635C2semidirect
4. #16840635C2semidirect
13. #14519736C4semidirect
14. #14519735C4semidirect
15. #14519735C4semidirect
22. #117×C61C4semidirect
115. C61#1825semidirect
123. #117#6923semidirect