Finite Group Databasebeta

← #21455176

Subgroups — #21455176

Order 7808.

762 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 762 conjugacy classes of subgroups — too many to draw. Only its 161 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#16840560C212yesmaximal, complemented
2#16840329C211yesmaximal, characteristic, complemented
3#16839940C214yesmaximal, complemented
4#16839930C214yesmaximal, complemented
5#16839779C212yesmaximal, complemented
6C2×#14519694C211yesmaximal, characteristic, complemented
7C2×H(5,𝔽2)×C61C211yesmaximal, characteristic, complemented
8C2×#11758222C2211yescharacteristic, complemented
9#14519808—22no—
10#14519807C2214yescomplemented
11#14519803—22no—
12#14519802C2214yescomplemented
13#14519797—24no—
14C2×#11758194C2212yescomplemented
15#14519773C2212yescomplemented
16#14519764C2212yescomplemented
17#14519748—22no—
18#14519746—22no—
19#14519736C2211yescharacteristic, complemented
20#14519704C2218yescomplemented
21#14519694C2214yescomplemented
22H(5,𝔽2)×C61—24no—
23H(5,𝔽2)×C61—22no—
24H(5,𝔽2)×C61C2214yes—
25C2×#41×C61—22no—
26C2×#41×C61C2212yes—
27C22×D4×C61—22no—
28C22×D4×C61—22no—
29C22×D4×C61C2211yescharacteristic
30C24×C61—22no—
31C24×C61D412yes—
32#41×C61—28no—
33#41×C61—28no—
34#41×C61—22no—
35#41×C61—22no—
36#41×C61D414yescomplemented
37#41×C61C2314yes—
38C2×Q8×C61D412yescomplemented
39C2×D4×C61—24no—
40C2×D4×C61—28no—
41C2×D4×C61—28no—
42C2×D4×C61—22no—
43C2×D4×C61—28no—
44C2×D4×C61—28no—
45C2×D4×C61—22no—
46C2×D4×C61—22no—
47C2×D4×C61D412yes—
48C2×D4×C61D412yescomplemented
49C2×D4×C61C2312yes—
50C22×C4×C61—22no—
51C22×C4×C61—22no—
52C22×C4×C61C2311yescharacteristic
53C2×C22⋊D61—21no—
54C2×C22⋊D61—24no—
55#11758222—22no—
56#11758222—22no—
57C2×D244C2311yescharacteristic, complemented
58C2×C4×D61—21no—
59C2×Dic122C2311yescharacteristic, complemented
60C22⋊Dic61—21no—
61C22⋊Dic61—24no—
62#11758202—24no—
63#11758201—24no—
64#11758200—24no—
65#11758199—24no—
66C4⋊Dic61—21no—
67C4×Dic61C2312yescomplemented
68#11758194—22no—
69#11758194C2314yescomplemented
70C2×#92418—22no—
71C23×C61—28no—
72C23×C61—22no—
73C23×C61—22no—
74C23×C61—22no—
75C23×C61—82no—
76C23×C61—84no—
77C23×C61C2×D414yes—
78C23×C61C2×D411yescharacteristic
79C22×D61—21no—
80Q8×C61—22no—
81Q8×C61C2×D414yes—
82D4×C61—216no—
83D4×C61—24no—
84D4×C61—24no—
85D4×C61—24no—
86D4×C61—22no—
87D4×C61—24no—
88D4×C61C2×D414yes—
89C2×C4×C61—28no—
90C2×C4×C61—22no—
91C2×C4×C61—24no—
92C2×C4×C61—24no—
93C2×C4×C61C2×D411yescharacteristic
94C2×C4×C61C2×D412yes—
95C2×C4×C61C2×D412yes—
96C2×C4×C61C2411yescharacteristic
97C22⋊D61—41no—
98C22⋊D61—41no—
99C22⋊D61—84no—
100C2×Dic61—22no—
101C2×Dic61—21no—
102D244—22no—
103C4×D61—42no—
104Dic122—22no—
105#92418—24no—
106C22×C61—24no—
107C22×C61—24no—
108C22×C61—41no—
109C22×C61—44no—
110C22×C61—44no—
111C22×C61—44no—
112C22×C61—82no—
113C22×C61—88no—
114C22×C61#12011yescharacteristic
115C22×C61#12011yescharacteristic
116C22×C61C22×D411yescharacteristic
117C2×D61—42no—
118C2×D61—41no—
119C4×C61—24no—
120C4×C61#12012yes—
121C4×C61C22×D412yes—
122Dic61—42no—
123Dic61—41no—
124#3019—611nomaximal, Sylow
125C2×C61—21no—
126C2×C61—21no—
127C2×C61—21no—
128C2×C61—44no—
129C2×C61—44no—
130C2×C61C2×#12011yescharacteristic
131D61—81no—
132C2×H(5,𝔽2)D6111yescharacteristic, complemented
133#575—612no—
134#535—611no—
135#455—614no—
136#453—614no—
137#421—612no—
138C2×#100—611no—
139C61#301911yescharacteristic, complemented, Sylow
140H(5,𝔽2)—24no—
141H(5,𝔽2)—22no—
142H(5,𝔽2)C2×D6114yes—
143C2×#41—22no—
144C2×#41—611no—
145C2×#41C2×D6112yes—
146C22×D4—22no—
147C22×D4—22no—
148C22×D4C2×D6111yescharacteristic
149#137—614no—
150#137—1222no—
151AGL(1,ℤ/8)—614no—
152AGL(1,ℤ/8)—1222no—
153#135—1224no—
154C2×M16—612no—
155#127—612no—
156#124—612no—
157#121—1222no—
158#120—1222no—
159#117—611no—
160#104—618no—
161#100—614no—
162C24—22no—
163C24C22⋊D6112yes—
164#41—28no—
165#41—28no—
166#41—22no—
167#41—22no—
168#41—1222no—
169#41—1222no—
170#41C22⋊D6114yescomplemented
171#41C22×D6114yes—
172C2×Q8—611no—
173C2×Q8C22⋊D6112yescomplemented
174C2×D4—24no—
175C2×D4—28no—
176C2×D4—28no—
177C2×D4—22no—
178C2×D4—28no—
179C2×D4—28no—
180C2×D4—22no—
181C2×D4—22no—
182C2×D4—611no—
183C2×D4—1224no—
184C2×D4—1221no—
185C2×D4C22⋊D6112yes—
186C2×D4C22⋊D6112yescomplemented
187C2×D4C22×D6112yes—
188C22×C4—22no—
189C22×C4—22no—
190C22×C4—1221no—
191C22×C4C22×D6111yescharacteristic
192Q16—1224no—
193SD16—1224no—
194SD16—1224no—
195D8—1224no—
196M16—614no—
197M16—1222no—
198C2×C8—1222no—
199C4⋊C4—1221no—
200C22⋊C4—1221no—
201C22⋊C4—1224no—
202C42—612no—
203C23—28no—
204C23—22no—
205C23—22no—
206C23—22no—
207C23—82no—
208C23—84no—
209C23—1221no—
210C23C2×C22⋊D6114yes—
211C23C2×C22⋊D6111yescharacteristic
212Q8—22no—
213Q8—1222no—
214Q8C2×C22⋊D6114yes—
215D4—216no—
216D4—24no—
217D4—24no—
218D4—24no—
219D4—24no—
220D4—22no—
221D4—1222no—
222D4—4884no—
223D4—2441no—
224D4—2441no—
225D4C2×C22⋊D6114yes—
226C2×C4—28no—
227C2×C4—22no—
228C2×C4—24no—
229C2×C4—24no—
230C2×C4—1222no—
231C2×C4—1221no—
232C2×C4—2442no—
233C2×C4C2×C22⋊D6112yes—
234C2×C4C2×C22⋊D6112yes—
235C2×C4C2×C22⋊D6111yescharacteristic
236C2×C4C23×D6111yescharacteristic
237C8—1224no—
238C22—24no—
239C22—24no—
240C22—41no—
241C22—44no—
242C22—44no—
243C22—44no—
244C22—82no—
245C22—88no—
246C22—2442no—
247C22—2441no—
248C22#1451974611yescharacteristic
249C22#1451974611yescharacteristic
250C22C22×C22⋊D6111yescharacteristic
251C4—24no—
252C4—2442no—
253C4—2441no—
254C4#1451974612yes—
255C4C22×C22⋊D6112yes—
256C2—21no—
257C2—21no—
258C2—21no—
259C2—44no—
260C2—44no—
261C2—4881no—
262C2C2×#1451974611yescharacteristic
subgroupG/H
centerC2C2×#14519746
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC2×H(5,𝔽2)×C61C2
socleC2×C61C2×#120
hypercenterC2×H(5,𝔽2)D61
hypocenterC61#3019
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×H(5,𝔽2)

Complements

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

NH ≅ G/Ntype
1. #16840560C2semidirect
2. #16840329C2semidirect
3. #16839940C2semidirect
4. #16839930C2semidirect
5. #16839779C2semidirect
6. C2×#14519694C2semidirect
7. C2×H(5,𝔽2)×C61C2semidirect
8. C2×#11758222C22semidirect
10. #14519807C22semidirect
12. #14519802C22semidirect
14. C2×#11758194C22semidirect
15. #14519773C22semidirect
16. #14519764C22semidirect
19. #14519736C22semidirect
20. #14519704C22semidirect
21. #14519694C22semidirect
36. #41×C61D4semidirect
38. C2×Q8×C61D4semidirect
48. C2×D4×C61D4semidirect
57. C2×D244C23semidirect
59. C2×Dic122C23semidirect
67. C4×Dic61C23semidirect
69. #11758194C23semidirect
132. C2×H(5,𝔽2)D61semidirect
139. C61#3019semidirect
170. #41C22⋊D61semidirect
173. C2×Q8C22⋊D61semidirect
186. C2×D4C22⋊D61semidirect