Finite Group Databasebeta

← #21455198

Subgroups — #21455198

Order 7808.

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

normal subgroups only

This group has 704 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
1C2×#14519807C212yesmaximal, complemented
2#16840333C211yesmaximal, characteristic, complemented
3#16839945C214yesmaximal, complemented
4#16839940C214yesmaximal, complemented
5#16839779C212yesmaximal, complemented
6#16839746C211yesmaximal, characteristic, complemented
7C61×#585C211yesmaximal, characteristic
8C22×Dic122C2211yescharacteristic, complemented
9#14519807—24no—
10#14519807C2218yescomplemented
11C2×#11758202—22no—
12C2×#11758200—22no—
13C2×#11758194C2212yescomplemented
14#14519775C2212yescomplemented
15#14519764C2212yescomplemented
16#14519758—22no—
17#14519756—22no—
18#14519736C2211yescharacteristic, complemented
19#14519704C2218yescomplemented
20#14519696C2212yescomplemented
21#14519694C2212yescomplemented
222−1+4×C61—22no—
232−1+4×C61C2212yes—
24H(5,𝔽2)×C61—22no—
25H(5,𝔽2)×C61—22no—
26H(5,𝔽2)×C61C2212yes—
27C2×#41×C61—24no—
28C2×#41×C61—22no—
29C2×#41×C61C2212yes—
30C2×#41×C61C2211yescharacteristic
31#41×C61—24no—
32#41×C61—28no—
33#41×C61—24no—
34#41×C61—24no—
35#41×C61—24no—
36#41×C61—22no—
37#41×C61—22no—
38#41×C61—24no—
39#41×C61—22no—
40#41×C61—22no—
41#41×C61D414yes—
42#41×C61C2314yes—
43C2×Q8×C61—22no—
44C2×Q8×C61—24no—
45C2×Q8×C61D412yes—
46C2×Q8×C61C2311yescharacteristic
47C2×D4×C61—28no—
48C2×D4×C61—22no—
49C2×D4×C61—24no—
50C2×D4×C61—22no—
51C2×D4×C61—24no—
52C2×D4×C61D412yes—
53C2×D4×C61D412yes—
54C2×D4×C61C2311yescharacteristic
55C22×C4×C61—24no—
56C22×C4×C61—22no—
57C22×C4×C61D412yes—
58C22×C4×C61C2311yescharacteristic
59C22×Dic61—21no—
60C2×Dic122—22no—
61C2×Dic122—22no—
62C2×Dic122—21no—
63C2×Dic122C2312yes—
64C22⋊Dic61—21no—
65C22⋊Dic61—24no—
66#11758202—28no—
67#11758200—28no—
68C4⋊Dic61—21no—
69#11758196—24no—
70C4×Dic61C2312yes—
71#11758194—22no—
72#11758194C2314yes—
73C2×#92418—22no—
74C23×C61—24no—
75C23×C61—22no—
76C23×C61C2×D412yes—
77C23×C61C2×D411yescharacteristic
78Q8×C61—24no—
79Q8×C61—22no—
80Q8×C61—22no—
81Q8×C61C2×D414yes—
82D4×C61—28no—
83D4×C61—24no—
84D4×C61—24no—
85D4×C61—24no—
86D4×C61—24no—
87D4×C61—22no—
88D4×C61—22no—
89D4×C61C2×D414yes—
90C2×C4×C61—24no—
91C2×C4×C61—28no—
92C2×C4×C61—22no—
93C2×C4×C61—24no—
94C2×C4×C61—22no—
95C2×C4×C61—22no—
96C2×C4×C61—24no—
97C2×C4×C61C2×D412yes—
98C2×C4×C61C2×D411yescharacteristic
99C2×C4×C61C2×D412yes—
100C2×C4×C61C2×D412yes—
101C2×C4×C61C2411yescharacteristic
102C2×Dic61—22no—
103C2×Dic61—22no—
104C2×Dic61—42no—
105Dic122—24no—
106Dic122—41no—
107Dic122—41no—
108#92418—24no—
109C22×C61—22no—
110C22×C61—24no—
111C22×C61—41no—
112C22×C61—42no—
113C22×C61—82no—
114C22×C61—84no—
115C22×C61#12012yes—
116C22×C61C22×D411yescharacteristic
117C4×C61—24no—
118C4×C61—22no—
119C4×C61#12011yescharacteristic
120C4×C61#12011yescharacteristic
121C4×C61C22×D412yes—
122Dic61—42no—
123Dic61—42no—
124#3022—611nomaximal, Sylow
125C2×C61—21no—
126C2×C61—22no—
127C2×C61—42no—
128C2×C61—44no—
129C2×C61C2×#12011yescharacteristic
130#585D6111yescharacteristic
131C2×#137—612no—
132#536—611no—
133#456—614no—
134#455—614no—
135#421—612no—
136#413—611no—
137C61#302211yescharacteristic, complemented, Sylow
1382−1+4—22no—
1392−1+4C2×D6112yes—
140H(5,𝔽2)—22no—
141H(5,𝔽2)—22no—
142H(5,𝔽2)C2×D6112yes—
143C2×#41—24no—
144C2×#41—22no—
145C2×#41C2×D6112yes—
146C2×#41C2×D6111yescharacteristic
147C22×Q8—611no—
148#137—618no—
149#137—1224no—
150C2×Q16—1222no—
151C2×SD16—1222no—
152C2×M16—612no—
153C4⋊Q8—612no—
154#124—612no—
155#123—1222no—
156C22⋊Q8—1222no—
157#117—611no—
158#104—618no—
159#101—612no—
160#100—612no—
161#41—24no—
162#41—28no—
163#41—24no—
164#41—24no—
165#41—24no—
166#41—22no—
167#41—22no—
168#41—24no—
169#41—22no—
170#41—22no—
171#41C22⋊D6114yes—
172#41C22×D6114yes—
173C2×Q8—22no—
174C2×Q8—24no—
175C2×Q8—612no—
176C2×Q8—1221no—
177C2×Q8—1222no—
178C2×Q8—1222no—
179C2×Q8C22⋊D6112yes—
180C2×Q8C22×D6111yescharacteristic
181C2×D4—28no—
182C2×D4—22no—
183C2×D4—24no—
184C2×D4—22no—
185C2×D4—24no—
186C2×D4C22⋊D6112yes—
187C2×D4C22⋊D6112yes—
188C2×D4C22×D6111yescharacteristic
189C22×C4—24no—
190C22×C4—22no—
191C22×C4—1221no—
192C22×C4C22⋊D6112yes—
193C22×C4C22×D6111yescharacteristic
194Q16—1228no—
195SD16—1228no—
196M16—614no—
197M16—1222no—
198C2×C8—1222no—
199C4⋊C4—1224no—
200C4⋊C4—1221no—
201C22⋊C4—1221no—
202C22⋊C4—1224no—
203C42—612no—
204C23—24no—
205C23—22no—
206C23C2×C22⋊D6112yes—
207C23C2×C22⋊D6111yescharacteristic
208Q8—24no—
209Q8—22no—
210Q8—22no—
211Q8—1224no—
212Q8—2441no—
213Q8—2441no—
214Q8C2×C22⋊D6114yes—
215D4—28no—
216D4—24no—
217D4—24no—
218D4—24no—
219D4—24no—
220D4—22no—
221D4—22no—
222D4C2×C22⋊D6114yes—
223C2×C4—24no—
224C2×C4—28no—
225C2×C4—22no—
226C2×C4—24no—
227C2×C4—24no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—1222no—
231C2×C4—1222no—
232C2×C4—2442no—
233C2×C4C2×C22⋊D6112yes—
234C2×C4C2×C22⋊D6112yes—
235C2×C4C2×C22⋊D6112yes—
236C2×C4C2×C22⋊D6111yescharacteristic
237C2×C4C23×D6111yescharacteristic
238C8—1224no—
239C22—22no—
240C22—24no—
241C22—41no—
242C22—42no—
243C22—82no—
244C22—84no—
245C22#1451974612yes—
246C22C22×C22⋊D6111yescharacteristic
247C4—24no—
248C4—22no—
249C4—2442no—
250C4—2442no—
251C4#1451974611yescharacteristic
252C4#1451974611yescharacteristic
253C4C22×C22⋊D6112yes—
254C2—21no—
255C2—22no—
256C2—42no—
257C2—44no—
258C2C2×#1451974611yescharacteristic
subgroupG/H
centerC2C2×#14519746
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#585C2
socleC2×C61C2×#120
hypercenter#585D61
hypocenterC61#3022
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22×C4 ◁ #585

Complements

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

NH ≅ G/Ntype
1. C2×#14519807C2semidirect
2. #16840333C2semidirect
3. #16839945C2semidirect
4. #16839940C2semidirect
5. #16839779C2semidirect
6. #16839746C2semidirect
8. C22×Dic122C22semidirect
10. #14519807C22semidirect
13. C2×#11758194C22semidirect
14. #14519775C22semidirect
15. #14519764C22semidirect
18. #14519736C22semidirect
19. #14519704C22semidirect
20. #14519696C22semidirect
21. #14519694C22semidirect
137. C61#3022semidirect