Finite Group Databasebeta

← #21461589

Subgroups — #21461589

Order 7808.

388 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 100 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
1C2×#14519839C212yesmaximal
2#16840721C211yesmaximal, characteristic, complemented
3C4×C4⋊#6923C211yesmaximal, characteristic, complemented
4#16840635C212yesmaximal, complemented
5C4×D4×D61C211yesmaximal, characteristic
6C2×D61⋊C8C2212yes—
7C2×C4⋊#6923C2212yes—
8C2×C4×#6923—21no—
9#14519839C418yescomplemented
10#14519832—21no—
11#14519832—21no—
12(C2×#6923)⋊C4—21no—
13C2×D4×D61C2211yescharacteristic
14C22×C4×D61—21no—
15C4×D244C411yescharacteristic, complemented
16D4×Dic61C411yescharacteristic, complemented
17#14519739C411yescharacteristic, complemented
18C4×C22⋊D61—21no—
19#14519737—21no—
20C4⋊C4×D61C2211yescharacteristic
21C22⋊C4×D61—21no—
22C42×D61C2211yescharacteristic
23C4×D4×C61C411yescharacteristic, complemented
24C23×D61—21no—
25C22×#6923—22no—
26C2×D4×C61C2×C411yescharacteristic
27C22×C4×C61—21no—
28C2×C22⋊D61—21no—
29C22×Dic61—21no—
30D4×D61—22no—
31D4×D61C2×C414yes—
32C2×D244C2×C411yescharacteristic
33C2×C4×D61—21no—
34C2×C4×D61—21no—
35C2×C4×D61—21no—
36C2×C4×D61—44no—
37C2×C4×D61D411yescharacteristic
38C2×C4×D61D411yescharacteristic
39C2×C4×D61C2311yescharacteristic
40C2×#92420—22no—
41C4⋊#6923—22no—
42C4⋊#6923C2×C414yescomplemented
43C4×#6923—42no—
44D61⋊C8—22no—
45D61⋊C8C2×C414yescomplemented
46C4⋊C4×C61C2×C411yescharacteristic
47C22⋊C4×C61—21no—
48C42×C61C2×C411yescharacteristic
49C22⋊Dic61—21no—
50#11758198—21no—
51#11758198—21no—
52C4⋊Dic61C2×C411yescharacteristic
53#11758196—21no—
54C4×Dic61C2×C411yescharacteristic
55C4×Dic61D411yescharacteristic
56C4×Dic61D411yescharacteristic
57C23×C61—21no—
58C22×D61—21no—
59C22×D61—24no—
60C22×D61—42no—
61C22×D61—41no—
62C22×D61—41no—
63C22×D61C2×D411yescharacteristic
64C2×#6923—24no—
65C2×#6923—42no—
66C2×#6923—42no—
67D4×C61—21no—
68D4×C61C4212yescomplemented
69C2×C4×C61—21no—
70C2×C4×C61—42no—
71C2×C4×C61C22⋊C411yescharacteristic
72C2×C4×C61C22⋊C411yescharacteristic
73C2×C4×C61C22×C411yescharacteristic
74C22⋊D61—24no—
75C2×Dic61—21no—
76C2×Dic61—42no—
77C2×Dic61C22⋊C411yescharacteristic
78C2×Dic61C22⋊C411yescharacteristic
79C2×Dic61C2×D411yescharacteristic
80D244—21no—
81D244C4212yescomplemented
82C4×D61—21no—
83C4×D61—22no—
84C4×D61—21no—
85C4×D61—42no—
86C4×D61—42no—
87C4×D61—42no—
88C4×D61C22×C412yes—
89C4×D61#4112yes—
90#92420—24no—
91C22×C61—22no—
92C22×C61—41no—
93C22×C61—41no—
94C22×C61C2×C22⋊C411yescharacteristic
95C2×D61—22no—
96C2×D61—41no—
97C2×D61—41no—
98C2×D61—44no—
99C2×D61—44no—
100C2×D61C4×D412yes—
101C2×D61AGL(1,ℤ/8)12yes—
102C2×D61AGL(1,ℤ/8)11yescharacteristic
103C2×D61#13711yescharacteristic
104#6923—44no—
105C4×C61—21no—
106C4×C61—21no—
107C4×C61—41no—
108C4×C61C2×C4211yescharacteristic
109C4×C61#11711yescharacteristic
110Dic61—21no—
111Dic61—21no—
112Dic61—41no—
113Dic61C4×D412yes—
114#1762—611nomaximal, Sylow
115C2×C61—42no—
116C2×C61C4×C22⋊C411yescharacteristic
117C2×C61#41711yescharacteristic
118C2×C61#41811yescharacteristic
119D61—42no—
120D61#44012yes—
121D61#44212yes—
122C2×C4×D4—611no—
123C2×#102—612no—
124C2×#97—611no—
125C4×C4⋊C4—611no—
126#340—612no—
127C61#176211yescharacteristic, complemented, Sylow
128C22×D4—611no—
129C23×C4—1221no—
130C22×C8—612no—
131C4×D4—611no—
132C4×D4—611no—
133C4×D4—611no—
134C4×D4—1221no—
135C4×D4—1221no—
136C4×D4#692311yescharacteristic, complemented
137C2×C4⋊C4—612no—
138C2×C4⋊C4—611no—
139C2×C22⋊C4—1221no—
140C2×C42—611no—
141C2×C42—1221no—
142#102—618no—
143#97—1221no—
144#97—1221no—
145#95—1221no—
146C24—1221no—
147C2×D4—614no—
148C2×D4—611no—
149C2×D4—1222no—
150C2×D4—1221no—
151C2×D4C2×#692311yescharacteristic
152C22×C4—21no—
153C22×C4—611no—
154C22×C4—611no—
155C22×C4—611no—
156C22×C4—1221no—
157C22×C4—1221no—
158C22×C4—1221no—
159C22×C4—1222no—
160C22×C4—1221no—
161C22×C4—2444no—
162C2×C8—614no—
163C2×C8—1222no—
164C2×C8—1222no—
165C4⋊C4—614no—
166C4⋊C4—611no—
167C4⋊C4—1221no—
168C4⋊C4—1222no—
169C4⋊C4C2×#692311yescharacteristic
170C22⋊C4—21no—
171C22⋊C4—1221no—
172C22⋊C4—1221no—
173C22⋊C4—1221no—
174C42—611no—
175C42—611no—
176C42—611no—
177C42—2442no—
178C42C2×#692311yescharacteristic
179C23—21no—
180C23—611no—
181C23—1224no—
182C23—1221no—
183C23—2442no—
184C23—2441no—
185C23—2441no—
186D4—21no—
187D4—612no—
188D4—1224no—
189D4—1221no—
190D4C4×#692312yescomplemented
191C2×C4—21no—
192C2×C4—42no—
193C2×C4—611no—
194C2×C4—612no—
195C2×C4—612no—
196C2×C4—611no—
197C2×C4—611no—
198C2×C4—1221no—
199C2×C4—1221no—
200C2×C4—1222no—
201C2×C4—1224no—
202C2×C4—1221no—
203C2×C4—2442no—
204C2×C4—2442no—
205C2×C4—2442no—
206C2×C4—2442no—
207C2×C4—2442no—
208C2×C4—2442no—
209C2×C4C22⋊#692311yescharacteristic
210C2×C4C22⋊#692311yescharacteristic
211C2×C4C22×#692311yescharacteristic
212C8—1224no—
213C22—22no—
214C22—41no—
215C22—41no—
216C22—611no—
217C22—611no—
218C22—612no—
219C22—612no—
220C22—1222no—
221C22—2444no—
222C22—2444no—
223C22—2441no—
224C22—2441no—
225C22C2×C22⋊#692311yescharacteristic
226C4—21no—
227C4—21no—
228C4—41no—
229C4—612no—
230C4—1221no—
231C4—1221no—
232C4—2444no—
233C4—2441no—
234C4C2×C4×#692311yescharacteristic
235C4#1451985611yescharacteristic
236C2—42no—
237C2—612no—
238C2—612no—
239C2—2442no—
240C2C4×C22⋊#692311yescharacteristic
241C2#1684075311yescharacteristic
242C2#1684075411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC4×C61C2×C42
FrattiniC2×C4C22×#6923
FittingC4×D4×C61C4
socleC22×C61C2×C22⋊C4
hypercenterC4×D4#6923
hypocenterC61#1762
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. #16840721C2semidirect
3. C4×C4⋊#6923C2semidirect
4. #16840635C2semidirect
9. #14519839C4semidirect
15. C4×D244C4semidirect
16. D4×Dic61C4semidirect
17. #14519739C4semidirect
23. C4×D4×C61C4semidirect
42. C4⋊#6923C2×C4semidirect
45. D61⋊C8C2×C4semidirect
68. D4×C61C42semidirect
81. D244C42semidirect
127. C61#1762semidirect
136. C4×D4#6923semidirect
190. D4C4×#6923semidirect