Finite Group Databasebeta

← #21461225

Subgroups — #21461225

Order 7808.

326 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 58 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, complemented
2#16840705C211yesmaximal, characteristic, complemented
3#16840614C212yesmaximal, complemented
4#16840613C212yesmaximal, complemented
5#121×D61C211yesmaximal, characteristic
6C2×#11758213—21no—
7C2×C22⋊#6923—21no—
8#14519834C2212yescomplemented
9C22⋊#92420—21no—
10(C2×#6923)⋊C4—21no—
11(C2×#6923)⋊C4C2212yescomplemented
12C2×D4×D61—21no—
13C2×D4×D61C411yescharacteristic, complemented
14C22×C4×D61C2211yescharacteristic
15#14519752C2211yescharacteristic
16#14519751C411yescharacteristic, complemented
17#14519750—21no—
18#14519749—21no—
19#14519748C2211yescharacteristic
20C4⋊C4×D61C411yescharacteristic, complemented
21C22⋊C4×D61—21no—
22#121×C61C411yescharacteristic, complemented
23C23×D61—21no—
24C23×D61D411yescharacteristic
25C22×#6923—22no—
26C2×D4×C61—21no—
27C2×D4×C61C2×C411yescharacteristic
28C22×C4×C61C2×C411yescharacteristic
29C2×C22⋊D61—21no—
30C2×C22⋊D61—21no—
31C2×C22⋊D61—21no—
32C22×Dic61D411yescharacteristic
33D4×D61—42no—
34D4×D61—44no—
35C2×D244—21no—
36C2×D244C2×C411yescharacteristic
37C2×C4×D61—21no—
38C2×C4×D61—42no—
39C2×C4×D61C2×C411yescharacteristic
40C2×C4×D61D411yescharacteristic
41C2×C4×D61D411yescharacteristic
42C2×C4×D61C2311yescharacteristic
43C22⋊#6923—42no—
44C2×#92420—22no—
45#11758213—42no—
46C4⋊C4×C61C2×C411yescharacteristic
47C22⋊C4×C61—21no—
48C22⋊Dic61—21no—
49#11758198—21no—
50#11758198—21no—
51C4⋊Dic61C2×C411yescharacteristic
52#11758196—21no—
53C23×C61—21no—
54C23×C61C22⋊C411yescharacteristic
55C22×D61—22no—
56C22×D61—22no—
57C22×D61—21no—
58C22×D61—41no—
59C22×D61—42no—
60C22×D61—42no—
61C22×D61—42no—
62C22×D61C22⋊C411yescharacteristic
63C22×D61C2×D411yescharacteristic
64C2×#6923—42no—
65C2×#6923—42no—
66C2×#6923—42no—
67D4×C61—41no—
68D4×C61—42no—
69C2×C4×C61—21no—
70C2×C4×C61—41no—
71C2×C4×C61C22⋊C411yescharacteristic
72C2×C4×C61C22×C411yescharacteristic
73C22⋊D61—42no—
74C22⋊D61—42no—
75C22⋊D61—42no—
76C2×Dic61—21no—
77C2×Dic61—41no—
78C2×Dic61C22⋊C411yescharacteristic
79C2×Dic61C2×D411yescharacteristic
80D244—41no—
81D244—42no—
82C4×D61—22no—
83C4×D61—22no—
84C4×D61—41no—
85C4×D61—41no—
86C4×D61—42no—
87#92420—42no—
88C22×C61—21no—
89C22×C61—21no—
90C22×C61—21no—
91C22×C61—41no—
92C22×C61—41no—
93C22×C61—41no—
94C22×C61C2×C22⋊C411yescharacteristic
95C2×D61—21no—
96C2×D61—21no—
97C2×D61—21no—
98C2×D61—21no—
99C2×D61—44no—
100C2×D61—41no—
101C2×D61—41no—
102C2×D61—41no—
103C2×D61—84no—
104C2×D61#9912yes—
105C2×D61AGL(1,ℤ/8)12yes—
106#6923—82no—
107C4×C61—21no—
108C4×C61—21no—
109C4×C61—41no—
110Dic61—21no—
111Dic61—21no—
112Dic61—41no—
113#1510—611nomaximal, Sylow
114C2×C61—41no—
115C2×C61—81no—
116C2×C61C2×#9911yescharacteristic
117C2×C61#41811yescharacteristic
118C2×C61#42111yescharacteristic
119D61—22no—
120D61—22no—
121D61—81no—
122C2×#121—611no—
123#407—611no—
124#381—611no—
125#327—612no—
126#327—612no—
127C61#151011yescharacteristic, complemented, Sylow
128C22×D4—611no—
129C22×D4—1221no—
130C23×C4—611no—
131C2×M16—1221no—
132#121—611no—
133#121—611no—
134#121—611no—
135#121—1221no—
136#121—1221no—
137#121#692311yescharacteristic, complemented
138C2×C4⋊C4—611no—
139C2×C22⋊C4—1221no—
140C2×C22⋊C4—1221no—
141C22⋊C8—612no—
142C22⋊C8—1221no—
143#95—612no—
144#95—1221no—
145C24—611no—
146C24—1221no—
147C2×D4—21no—
148C2×D4—611no—
149C2×D4—1221no—
150C2×D4—1221no—
151C2×D4—1221no—
152C2×D4—1221no—
153C2×D4—2442no—
154C2×D4—2444no—
155C2×D4C2×#692311yescharacteristic
156C22×C4—611no—
157C22×C4—611no—
158C22×C4—611no—
159C22×C4—611no—
160C22×C4—611no—
161C22×C4—1221no—
162C22×C4—1222no—
163C22×C4—2442no—
164C22×C4C2×#692311yescharacteristic
165M16—2442no—
166C2×C8—1222no—
167C4⋊C4—611no—
168C4⋊C4—1221no—
169C4⋊C4C2×#692311yescharacteristic
170C22⋊C4—21no—
171C22⋊C4—1221no—
172C22⋊C4—1221no—
173C22⋊C4—1221no—
174C22⋊C4—2442no—
175C23—21no—
176C23—611no—
177C23—611no—
178C23—1222no—
179C23—1222no—
180C23—1221no—
181C23—2441no—
182C23—2442no—
183C23—2442no—
184C23—2442no—
185C23C22⋊#692311yescharacteristic
186D4—41no—
187D4—42no—
188D4—2441no—
189D4—2442no—
190D4—2442no—
191D4—2442no—
192D4—2442no—
193C2×C4—21no—
194C2×C4—41no—
195C2×C4—611no—
196C2×C4—611no—
197C2×C4—1222no—
198C2×C4—1222no—
199C2×C4—1221no—
200C2×C4—2441no—
201C2×C4—2441no—
202C2×C4—2442no—
203C2×C4—2441no—
204C2×C4—2442no—
205C2×C4—2442no—
206C2×C4—2442no—
207C2×C4C22⋊#692311yescharacteristic
208C2×C4C22×#692311yescharacteristic
209C8—2442no—
210C22—21no—
211C22—21no—
212C22—21no—
213C22—41no—
214C22—41no—
215C22—41no—
216C22—612no—
217C22—612no—
218C22—1221no—
219C22—1221no—
220C22—1221no—
221C22—1221no—
222C22—4884no—
223C22—2444no—
224C22—2441no—
225C22—2441no—
226C22—2441no—
227C22C2×C22⋊#692311yescharacteristic
228C4—21no—
229C4—21no—
230C4—41no—
231C4—1221no—
232C4—1221no—
233C4—4882no—
234C4—2441no—
235C2—41no—
236C2—81no—
237C2—1222no—
238C2—1222no—
239C2—4881no—
240C2D61⋊#9911yescharacteristic
241C2#1684075411yescharacteristic
242C2#1684075911yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
Fitting#121×C61C4
socleC22×C61C2×C22⋊C4
hypercenter#121#6923
hypocenterC61#1510
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. #16840733C2semidirect
2. #16840705C2semidirect
3. #16840614C2semidirect
4. #16840613C2semidirect
8. #14519834C22semidirect
11. (C2×#6923)⋊C4C22semidirect
13. C2×D4×D61C4semidirect
16. #14519751C4semidirect
20. C4⋊C4×D61C4semidirect
22. #121×C61C4semidirect
127. C61#1510semidirect
137. #121#6923semidirect