Finite Group Databasebeta

← #21451389

Subgroups — #21451389

Order 7808.

492 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 139 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×Q8×Dic61C211yesmaximal, characteristic, complemented
2C2×#14519733C211yesmaximal, characteristic
3#16839694C211yesmaximal, characteristic, complemented
4#16839687C211yesmaximal, characteristic
5#16839681C211yesmaximal, characteristic, complemented
6#16839656C212yesmaximal
7#16839649C212yesmaximal, complemented
8#16839645C212yesmaximal, complemented
9#16839637C212yesmaximal
10#16839629C211yesmaximal, characteristic, complemented
11C61×#393C211yesmaximal, characteristic
12C23×Dic61C2211yescharacteristic
13Q8×Dic61—24no—
14#14519733—24no—
15C2×C4⋊Dic61C2211yescharacteristic
16C2×C4⋊Dic61C2212yes—
17C2×C4⋊Dic61C2212yes—
18C2×#11758196C2211yescharacteristic
19C2×#11758196C2212yes—
20C2×#11758196C2211yescharacteristic
21C2×C22⋊Dic61C2212yes—
22C2×C22⋊Dic61C2211yescharacteristic
23C2×C4×Dic61C2211yescharacteristic
24C2×C4×Dic61C2212yes—
25C2×C4×Dic61C2211yescharacteristic
26#14519684C2211yescharacteristic
27#14519684C2212yes—
28#14519684C2212yes—
29#14519684C2212yes—
30#14519684C2212yes—
31#14519684C2212yes—
32C22×Q8×C61C2211yescharacteristic
33C2×C22⋊C4×C61C2211yescharacteristic
34C2×C22⋊C4×C61C2212yes—
35#95×C61C2211yescharacteristic
36#95×C61C2212yes—
37C24×C61C2311yescharacteristic
38C2×Q8×C61—22no—
39C2×Q8×C61—24no—
40C22×C4×C61C2312yes—
41C22×C4×C61C2311yescharacteristic
42C22×C4×C61C2311yescharacteristic
43C22×C4×C61C2312yes—
44C22×Dic61—22no—
45C22×Dic61—22no—
46C22×Dic61—22no—
47C22×Dic61C2312yes—
48C22×Dic61C2311yescharacteristic
49C22×Dic61C2312yes—
50C22×Dic61C2311yescharacteristic
51C22×Dic61C2311yescharacteristic
52C22×Dic61C2311yescharacteristic
53C22⋊C4×C61—22no—
54C22⋊C4×C61—24no—
55C22⋊Dic61—24no—
56C22⋊Dic61—22no—
57C4⋊Dic61—22no—
58C4⋊Dic61—24no—
59C4⋊Dic61—24no—
60#11758196—22no—
61#11758196—24no—
62#11758196—22no—
63C4×Dic61—22no—
64C4×Dic61—24no—
65C4×Dic61D414yes—
66C23×C61—21no—
67C23×C61—22no—
68C23×C61—21no—
69C23×C61—22no—
70C23×C61#4112yes—
71C23×C61C2411yescharacteristic
72Q8×C61—28no—
73C2×C4×C61—22no—
74C2×C4×C61—22no—
75C2×C4×C61—22no—
76C2×C4×C61—21no—
77C2×C4×C61—22no—
78C2×C4×C61—22no—
79C2×C4×C61—22no—
80C2×C4×C61—22no—
81C2×C4×C61C2×D412yes—
82C2×C4×C61#4114yes—
83C2×Dic61—28no—
84C2×Dic61—21no—
85C2×Dic61—21no—
86C2×Dic61—21no—
87C2×Dic61—21no—
88C2×Dic61—22no—
89C2×Dic61—21no—
90C2×Dic61—22no—
91C2×Dic61—22no—
92C2×Dic61—22no—
93C2×Dic61—22no—
94C2×Dic61—22no—
95C2×Dic61—22no—
96C2×Dic61—22no—
97C2×Dic61C2×D412yes—
98C2×Dic61C2×D412yes—
99C2×Dic61#4112yes—
100C22×C61—22no—
101C22×C61—24no—
102C22×C61—41no—
103C22×C61—41no—
104C22×C61—42no—
105C22×C61C22×D411yescharacteristic
106C22×C61C2×#4111yescharacteristic
107C22×C61C2×#4112yes—
108C22×C61C2×#4111yescharacteristic
109C22×C612−1+412yes—
110C4×C61—22no—
111C4×C61—24no—
112C4×C61—41no—
113C4×C61—42no—
114Dic61—22no—
115Dic61—22no—
116Dic61—22no—
117Dic61—41no—
118Dic61—42no—
119Dic61—42no—
120#2599—611nomaximal, Sylow
121C2×C61—42no—
122C2×C61#52511yescharacteristic
123C2×C61#52511yescharacteristic
124C2×C61#53611yescharacteristic
125C2×C61#55212yes—
126C2×C61#55612yes—
127C2×C4×Q8—611no—
128C2×#117—611no—
129#398—611no—
130#397—611no—
131#395—611no—
132#393D6111yescharacteristic
133#388—612no—
134#387—612no—
135#387—612no—
136#385—612no—
137#383—611no—
138C61#259911yescharacteristic, complemented, Sylow
139C22×Q8C2×D6111yescharacteristic
140C23×C4—611no—
141C4×Q8—1224no—
142#117—1224no—
143C2×C4⋊C4—611no—
144C2×C4⋊C4—611no—
145C2×C4⋊C4—612no—
146C2×C4⋊C4—611no—
147C2×C4⋊C4—612no—
148C2×C4⋊C4—612no—
149C2×C22⋊C4—611no—
150C2×C22⋊C4—612no—
151C2×C22⋊C4C2×D6111yescharacteristic
152C2×C22⋊C4C2×D6112yes—
153C2×C42—611no—
154C2×C42—611no—
155C2×C42—612no—
156#95—612no—
157#95—612no—
158#95—611no—
159#95—612no—
160#95—612no—
161#95—612no—
162#95C2×D6111yescharacteristic
163#95C2×D6112yes—
164C24C22×D6111yescharacteristic
165C2×Q8—22no—
166C2×Q8—24no—
167C22×C4—611no—
168C22×C4—611no—
169C22×C4—611no—
170C22×C4—612no—
171C22×C4—611no—
172C22×C4—612no—
173C22×C4—1222no—
174C22×C4—1222no—
175C22×C4—1222no—
176C22×C4C22×D6112yes—
177C22×C4C22×D6111yescharacteristic
178C22×C4C22×D6111yescharacteristic
179C22×C4C22×D6112yes—
180C4⋊C4—1222no—
181C4⋊C4—1224no—
182C4⋊C4—1224no—
183C4⋊C4—1222no—
184C4⋊C4—1222no—
185C4⋊C4—1224no—
186C22⋊C4—22no—
187C22⋊C4—24no—
188C22⋊C4—1222no—
189C22⋊C4—1224no—
190C42—614no—
191C42—1222no—
192C42—1224no—
193C23—21no—
194C23—21no—
195C23—22no—
196C23—22no—
197C23#1175822612yes—
198C23C23×D6111yescharacteristic
199Q8—28no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—21no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—612no—
209C2×C4—612no—
210C2×C4—612no—
211C2×C4—1228no—
212C2×C4—1221no—
213C2×C4—1221no—
214C2×C4—1221no—
215C2×C4—1221no—
216C2×C4—1222no—
217C2×C4—1221no—
218C2×C4—1222no—
219C2×C4—1222no—
220C2×C4—1222no—
221C2×C4—1222no—
222C2×C4—1222no—
223C2×C4—1222no—
224C2×C4—1222no—
225C2×C4D4×D6112yes—
226C2×C4#1175822414yes—
227C22—24no—
228C22—22no—
229C22—42no—
230C22—41no—
231C22—41no—
232C22C2×D4×D6111yescharacteristic
233C22#41×D6111yescharacteristic
234C22C2×#1175822412yes—
235C22C2×#1175822611yescharacteristic
236C22#1451982412yes—
237C4—22no—
238C4—24no—
239C4—42no—
240C4—41no—
241C4—1222no—
242C4—1222no—
243C4—1222no—
244C4—2442no—
245C4—2441no—
246C4—2442no—
247C2—42no—
248C2#1684026811yescharacteristic
249C2#1684027511yescharacteristic
250C2#1684033211yescharacteristic
251C2#1684045412yes—
252C2#1684048112yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#393C2
hypercenter#393D61
hypocenterC61#2599
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
1. C2×Q8×Dic61C2semidirect
3. #16839694C2semidirect
5. #16839681C2semidirect
7. #16839649C2semidirect
8. #16839645C2semidirect
10. #16839629C2semidirect
138. C61#2599semidirect