Finite Group Databasebeta

← #21453799

Subgroups — #21453799

Order 7808.

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

normal subgroups only

This group has 428 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#16839687C212yesmaximal, complemented
2#16839676C212yesmaximal
3#16839674C212yesmaximal, complemented
4#16839668C211yesmaximal, characteristic, complemented
5#16839660C211yesmaximal, characteristic, complemented
6#16839655C212yesmaximal, complemented
7#16839655C212yesmaximal, complemented
8#16839643C212yesmaximal, complemented
9C61×#390C211yesmaximal, characteristic
10C22×Dic122C2211yescharacteristic
11C2×C4⋊Dic61C2211yescharacteristic
12C2×C4⋊Dic61C2211yescharacteristic
13C2×C4⋊Dic61C2211yescharacteristic
14C2×#11758196C2212yes—
15C2×C22⋊Dic61C2212yes—
16C2×C22⋊Dic61C2212yes—
17C2×C22⋊Dic61C2212yes—
18C2×C22⋊Dic61C2212yes—
19C2×C4×Dic61C2212yes—
20#14519684C2212yes—
21#14519684C2212yes—
22#14519684C2212yes—
23#14519684C2212yes—
24#14519684C2212yes—
25#14519684C2212yes—
26C22×D4×C61C2211yescharacteristic
27C2×C4⋊C4×C61C2211yescharacteristic
28C2×C22⋊C4×C61C2212yes—
29C2×C22⋊C4×C61C2212yes—
30C2×C42×C61C2211yescharacteristic
31C24×C61C2312yes—
32C2×D4×C61—22no—
33C2×D4×C61—41no—
34C2×D4×C61—41no—
35C22×C4×C61C2312yes—
36C22×C4×C61C2311yescharacteristic
37C22×C4×C61C2311yescharacteristic
38C22×C4×C61C2311yescharacteristic
39C22×Dic61C2312yes—
40C22×Dic61C2312yes—
41C22×Dic61C2312yes—
42C22×Dic61C2312yes—
43C2×Dic122—22no—
44C2×Dic122—41no—
45C2×Dic122—41no—
46C4⋊C4×C61—41no—
47C22⋊C4×C61—24no—
48C22⋊C4×C61—24no—
49C42×C61—41no—
50C22⋊Dic61—42no—
51C22⋊Dic61—42no—
52C22⋊Dic61—42no—
53C22⋊Dic61—42no—
54C4⋊Dic61—22no—
55C4⋊Dic61—41no—
56C4⋊Dic61—41no—
57#11758196—24no—
58C4×Dic61—42no—
59C23×C61—22no—
60C23×C61—22no—
61C23×C61—22no—
62C23×C61—22no—
63C23×C61—22no—
64C23×C61—22no—
65C23×C61—22no—
66C23×C61C2411yescharacteristic
67D4×C61—44no—
68C2×C4×C61—21no—
69C2×C4×C61—21no—
70C2×C4×C61—21no—
71C2×C4×C61—21no—
72C2×C4×C61—21no—
73C2×C4×C61—21no—
74C2×C4×C61—22no—
75C2×C4×C61—22no—
76C2×C4×C61—22no—
77C2×C4×C61#4112yes—
78C2×C4×C61#4112yes—
79C2×C4×C61#4112yes—
80C2×Dic61—22no—
81C2×Dic61—22no—
82C2×Dic61—22no—
83C2×Dic61—22no—
84C2×Dic61—22no—
85C2×Dic61—22no—
86C2×Dic61—22no—
87C2×Dic61—22no—
88C2×Dic61—22no—
89C2×Dic61—22no—
90C2×Dic61—22no—
91C2×Dic61—22no—
92Dic122—44no—
93C22×C61—42no—
94C22×C61—42no—
95C22×C61—42no—
96C22×C61—42no—
97C22×C61—42no—
98C22×C61—42no—
99C22×C61—42no—
100C22×C61C2×#4111yescharacteristic
101C22×C61C2×#4111yescharacteristic
102C22×C61C2×#4111yescharacteristic
103C22×C61H(5,𝔽2)11yescharacteristic
104C22×C61H(5,𝔽2)11yescharacteristic
105C22×C61H(5,𝔽2)11yescharacteristic
106C22×C612−1+411yescharacteristic
107C4×C61—22no—
108C4×C61—22no—
109C4×C61—22no—
110C4×C61—42no—
111Dic61—42no—
112Dic61—42no—
113Dic61—42no—
114Dic61—42no—
115#2808—611nomaximal, Sylow
116C2×C61—82no—
117C2×C61#53811yescharacteristic
118C2×C61#53811yescharacteristic
119C2×C61#53911yescharacteristic
120C2×C61#55511yescharacteristic
121C2×C61#55611yescharacteristic
122C2×C61#55911yescharacteristic
123C2×C61#56211yescharacteristic
124#397—612no—
125#394—612no—
126#393—612no—
127#391—611no—
128#390D6111yescharacteristic
129#389—611no—
130#388—612no—
131#388—612no—
132#387—612no—
133C61#280811yescharacteristic, complemented, Sylow
134C22×Q8—611no—
135C22×D4C2×D6111yescharacteristic
136C2×C4⋊C4—612no—
137C2×C4⋊C4—611no—
138C2×C4⋊C4—611no—
139C2×C4⋊C4—611no—
140C2×C4⋊C4C2×D6111yescharacteristic
141C2×C22⋊C4—612no—
142C2×C22⋊C4—612no—
143C2×C22⋊C4—612no—
144C2×C22⋊C4—612no—
145C2×C22⋊C4C2×D6112yes—
146C2×C22⋊C4C2×D6112yes—
147C2×C42—612no—
148C2×C42C2×D6111yescharacteristic
149#95—612no—
150#95—612no—
151#95—612no—
152#95—612no—
153#95—612no—
154#95—612no—
155C24C22×D6112yes—
156C2×Q8—1222no—
157C2×Q8—2441no—
158C2×Q8—2441no—
159C2×D4—22no—
160C2×D4—41no—
161C2×D4—41no—
162C22×C4—612no—
163C22×C4—612no—
164C22×C4—612no—
165C22×C4—612no—
166C22×C4C22×D6112yes—
167C22×C4C22×D6111yescharacteristic
168C22×C4C22×D6111yescharacteristic
169C22×C4C22×D6111yescharacteristic
170C4⋊C4—41no—
171C4⋊C4—1224no—
172C4⋊C4—1222no—
173C4⋊C4—2441no—
174C4⋊C4—2441no—
175C22⋊C4—24no—
176C22⋊C4—24no—
177C22⋊C4—2442no—
178C22⋊C4—2442no—
179C22⋊C4—2442no—
180C22⋊C4—2442no—
181C42—41no—
182C42—2442no—
183C23—22no—
184C23—22no—
185C23—22no—
186C23—22no—
187C23—22no—
188C23—22no—
189C23—22no—
190C23C23×D6111yescharacteristic
191Q8—2444no—
192D4—44no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—1222no—
203C2×C4—1222no—
204C2×C4—1222no—
205C2×C4—1222no—
206C2×C4—1222no—
207C2×C4—1222no—
208C2×C4—1222no—
209C2×C4—1222no—
210C2×C4—1222no—
211C2×C4—1222no—
212C2×C4—1222no—
213C2×C4—1222no—
214C2×C4#1175822212yes—
215C2×C4#1175822412yes—
216C2×C4#1175822412yes—
217C22—42no—
218C22—42no—
219C22—42no—
220C22—42no—
221C22—42no—
222C22—42no—
223C22—42no—
224C22C2×#1175822411yescharacteristic
225C22C2×#1175822411yescharacteristic
226C22C2×#1175822211yescharacteristic
227C22#1451982211yescharacteristic
228C22#1451982211yescharacteristic
229C22#1451982311yescharacteristic
230C22#1451982411yescharacteristic
231C4—22no—
232C4—22no—
233C4—22no—
234C4—42no—
235C4—2442no—
236C4—2442no—
237C4—2442no—
238C4—2442no—
239C2—82no—
240C2#1684034911yescharacteristic
241C2#1684035011yescharacteristic
242C2#1684035711yescharacteristic
243C2#1684047711yescharacteristic
244C2#1684048211yescharacteristic
245C2#1684049811yescharacteristic
246C2#1684050611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#390C2
hypercenter#390D61
hypocenterC61#2808
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
1. #16839687C2semidirect
3. #16839674C2semidirect
4. #16839668C2semidirect
5. #16839660C2semidirect
6. #16839655C2semidirect
7. #16839655C2semidirect
8. #16839643C2semidirect
133. C61#2808semidirect