Finite Group Databasebeta

← #21456190

Subgroups — #21456190

Order 7808.

484 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 125 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#16840317C211yesmaximal, characteristic, complemented
2#127×D61C211yesmaximal, characteristic
3#16840125C214yesmaximal, complemented
4#16840110C211yesmaximal, characteristic, complemented
5#16840109C211yesmaximal, characteristic, complemented
6#16840108C211yesmaximal, characteristic, complemented
7#16839765C214yesmaximal, complemented
8C4×#11758189C211yesmaximal, characteristic, complemented
9C61×#486C211yesmaximal, characteristic, complemented
10C2×D4×D61—21no—
11C2×D4×D61—21no—
12C2×D4×D61C2212yes—
13C2×#11758189C2212yes—
14#14519777C2211yescharacteristic, complemented
15#14519774C2211yescharacteristic
16#14519773—21no—
17#14519773—21no—
18#14519773C2212yes—
19#14519768C2212yescomplemented
20#14519757—21no—
21#14519753—21no—
22Q8×Dic61—21no—
23#14519742—21no—
24#14519735C2212yes—
25C42×D61C2211yescharacteristic
26#14519699C2214yescomplemented
27#14519698C2214yescomplemented
28#14519697C2214yescomplemented
29#14519687C2212yescomplemented
30C4×#92418C2211yescharacteristic, complemented
31C4⋊Q8×C61C2211yescharacteristic, complemented
32#127×C61C2211yescharacteristic
33#102×C61C2214yescomplemented
34C4×C8×C61C2211yescharacteristic, complemented
35C23×D61—22no—
36C2×Q8×C61—21no—
37C2×D4×C61—21no—
38C2×D4×C61—21no—
39C2×D4×C61C2312yes—
40C2×C22⋊D61—22no—
41C2×C22⋊D61—22no—
42C2×C22⋊D61—22no—
43D4×D61—28no—
44D4×D61—44no—
45D4×D61—44no—
46C2×D244—21no—
47C2×D244—21no—
48C2×D244C2312yes—
49C2×C4×D61D411yescharacteristic
50C2×C4×D61D411yescharacteristic
51C2×C4×D61C2311yescharacteristic
52C2×Dic122—21no—
53C2×C8×C61C2312yes—
54C4⋊C4×C61—21no—
55C4⋊C4×C61C2312yes—
56C42×C61C2311yescharacteristic
57#11758198—22no—
58C4⋊Dic61—21no—
59C4⋊Dic61—22no—
60C4⋊Dic61C2312yes—
61#11758196—22no—
62C4×Dic61—22no—
63C4×Dic61D411yescharacteristic
64C4×Dic61D411yescharacteristic
65C4×Dic61C2311yescharacteristic
66C2×#92418C2312yes—
67#11758189—24no—
68C23×C61—22no—
69C22×D61—22no—
70C22×D61—44no—
71C22×D61—44no—
72C22×D61—44no—
73C22×D61C2×D411yescharacteristic
74Q8×C61—42no—
75D4×C61—24no—
76D4×C61—42no—
77D4×C61—42no—
78C2×C4×C61—22no—
79C2×C4×C61C2×D411yescharacteristic
80C2×C4×C61C2×D411yescharacteristic
81C2×C4×C61C2411yescharacteristic
82C22⋊D61—44no—
83C22⋊D61—44no—
84C22⋊D61—44no—
85C2×Dic61—22no—
86C2×Dic61C2×D411yescharacteristic
87C2×Dic61C2×D411yescharacteristic
88C2×Dic61C2×D411yescharacteristic
89D244—24no—
90D244—42no—
91D244—42no—
92C4×D61—22no—
93C4×D61—22no—
94C4×D61#4114yes—
95Dic122—42no—
96C8×C61—22no—
97#92418—22no—
98C22×C61—42no—
99C22×C61—42no—
100C22×C61—42no—
101C22×C61C22×D411yescharacteristic
102C2×D61—21no—
103C2×D61—21no—
104C2×D61—42no—
105C2×D61—42no—
106C2×D61—42no—
107C2×D61—88no—
108C2×D61#12412yes—
109C4×C61—42no—
110C4×C61AGL(1,ℤ/8)12yes—
111C4×C61AGL(1,ℤ/8)12yes—
112C4×C61C2×#4112yes—
113Dic61—21no—
114Dic61—21no—
115Dic61—42no—
116Dic61#12412yes—
117#3138—611nomaximal, Sylow
118C2×C61—82no—
119C2×C61C2×#12411yescharacteristic
120C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
121C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
122D61—22no—
123D61—82no—
124#533—611no—
125C2×#127—611no—
126#490—614no—
127#486—611no—
128#486—611no—
129#486—611no—
130#486D6111yescharacteristic, complemented
131#418—614no—
132C4×M16—611no—
133C61#313811yescharacteristic, complemented, Sylow
134C22×D4—612no—
135C22×D4—1221no—
136C22×D4—1221no—
137C2×M16—612no—
138C4⋊Q8—611no—
139C4⋊Q8C2×D6111yescharacteristic, complemented
140#127—612no—
141#127—611no—
142#127—1221no—
143#127—1221no—
144#127C2×D6111yescharacteristic
145#125—612no—
146C22⋊Q8—1221no—
147C22⋊Q8—1221no—
148C4×Q8—1221no—
149C4×Q8—1221no—
150#117—612no—
151C2×C42—611no—
152#102—614no—
153#102—614no—
154#102—614no—
155#102C2×D6114yescomplemented
156#97—612no—
157C4×C8—611no—
158C4×C8C2×D6111yescharacteristic, complemented
159C24—1222no—
160C2×Q8—21no—
161C2×Q8—1221no—
162C2×D4—21no—
163C2×D4—21no—
164C2×D4—612no—
165C2×D4—1228no—
166C2×D4—1222no—
167C2×D4—1222no—
168C2×D4—1222no—
169C2×D4—1221no—
170C2×D4—1221no—
171C2×D4—2444no—
172C2×D4—2444no—
173C2×D4C22×D6112yes—
174C22×C4—611no—
175C22×C4—611no—
176C22×C4—611no—
177M16—1224no—
178C2×C8—612no—
179C2×C8C22×D6112yes—
180C4⋊C4—21no—
181C4⋊C4—612no—
182C4⋊C4—1222no—
183C4⋊C4—1222no—
184C4⋊C4—1221no—
185C4⋊C4C22×D6112yes—
186C22⋊C4—1222no—
187C42—611no—
188C42—611no—
189C42—611no—
190C42—1222no—
191C42C22×D6111yescharacteristic
192C23—22no—
193C23—611no—
194C23—1222no—
195C23—2444no—
196C23—2444no—
197C23—2444no—
198Q8—42no—
199Q8—2442no—
200D4—24no—
201D4—42no—
202D4—42no—
203D4—1224no—
204D4—2444no—
205D4—2444no—
206D4—2444no—
207D4—2442no—
208D4—2442no—
209C2×C4—22no—
210C2×C4—611no—
211C2×C4—614no—
212C2×C4—611no—
213C2×C4—611no—
214C2×C4—1222no—
215C2×C4—1222no—
216C2×C4—1222no—
217C2×C4D4×D6111yescharacteristic
218C2×C4D4×D6111yescharacteristic
219C2×C4C23×D6111yescharacteristic
220C8—22no—
221C8—1222no—
222C22—42no—
223C22—42no—
224C22—42no—
225C22—612no—
226C22—1221no—
227C22—1221no—
228C22—4888no—
229C22—2442no—
230C22—2442no—
231C22—2442no—
232C22C2×D4×D6111yescharacteristic
233C4—42no—
234C4—612no—
235C4—1221no—
236C4—1221no—
237C4—2442no—
238C4#1451980112yes—
239C4#1451980412yes—
240C4#41×D6112yes—
241C2—82no—
242C2—1222no—
243C2—4882no—
244C2#124×D6111yescharacteristic
245C2C2×#1451980111yescharacteristic
246C2C2×#1451980411yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#486C2
socleC22×C61C22×D4
hypercenter#486D61
hypocenterC61#3138
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #16840317C2semidirect
3. #16840125C2semidirect
4. #16840110C2semidirect
5. #16840109C2semidirect
6. #16840108C2semidirect
7. #16839765C2semidirect
8. C4×#11758189C2semidirect
9. C61×#486C2semidirect
14. #14519777C22semidirect
19. #14519768C22semidirect
26. #14519699C22semidirect
27. #14519698C22semidirect
28. #14519697C22semidirect
29. #14519687C22semidirect
30. C4×#92418C22semidirect
31. C4⋊Q8×C61C22semidirect
33. #102×C61C22semidirect
34. C4×C8×C61C22semidirect
130. #486D61semidirect
133. C61#3138semidirect
139. C4⋊Q8C2×D61semidirect
155. #102C2×D61semidirect
158. C4×C8C2×D61semidirect