Finite Group Databasebeta

← #21453196

Subgroups — #21453196

Order 7808.

520 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 121 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
1C61⋊#401C212yesmaximal, complemented
2#16839675C212yesmaximal, complemented
3#16839674C211yesmaximal, characteristic, complemented
4#16839671C211yesmaximal, characteristic
5#16839641C212yesmaximal, complemented
6#16839640C212yesmaximal, complemented
7#16839638C212yesmaximal, complemented
8#16839624C212yesmaximal, complemented
9C61×#381C211yesmaximal, characteristic, complemented
10C22×Dic122C2211yescharacteristic
11C22×D244C2211yescharacteristic
12C22×C22⋊D61C2212yes—
13C22×C4×D61C2212yes—
14C2×C22⋊Dic61C2212yes—
15C2×#11758198C2212yes—
16C2×#11758198C2212yes—
17C2×#11758198C2212yes—
18C2×#11758198C2212yes—
19#14519684C2211yescharacteristic
20#14519684C2212yes—
21#14519684C2212yes—
22#14519684C2212yes—
23#14519684C2212yes—
24#14519684C2212yes—
25#14519684C2211yescharacteristic
26C23×C4×C61C2211yescharacteristic
27C2×C22⋊C4×C61C2211yescharacteristic
28C2×C22⋊C4×C61C2211yescharacteristic
29#95×C61C2212yes—
30#95×C61C2212yes—
31C24×C61C2311yescharacteristic
32C23×D61C2312yes—
33C22×C4×C61—22no—
34C22×C4×C61—41no—
35C22×C4×C61—41no—
36C22×C4×C61C2312yes—
37C22×C4×C61C2311yescharacteristic
38C22×C4×C61C2311yescharacteristic
39C22×C4×C61C2312yes—
40C2×C22⋊D61—24no—
41C2×C22⋊D61—24no—
42C2×C22⋊D61—42no—
43C22×Dic61C2312yes—
44C22×Dic61C2312yes—
45C22×Dic61C2312yes—
46C2×D244—24no—
47C2×D244—41no—
48C2×C4×D61—24no—
49C2×C4×D61—42no—
50C2×C4×D61—42no—
51C2×Dic122—41no—
52C2×Dic122—42no—
53C22⋊C4×C61—41no—
54C22⋊C4×C61—41no—
55C22⋊Dic61—42no—
56#11758198—42no—
57#11758198—42no—
58#11758198—42no—
59#11758198—42no—
60C23×C61—22no—
61C23×C61—22no—
62C23×C61—21no—
63C23×C61—21no—
64C23×C61#4112yes—
65C23×C61C2411yescharacteristic
66C22×D61—22no—
67C22×D61—22no—
68C22×D61—22no—
69C22×D61—22no—
70C22×D61—22no—
71C22×D61—22no—
72C22×D61#4114yes—
73C2×C4×C61—22no—
74C2×C4×C61—22no—
75C2×C4×C61—22no—
76C2×C4×C61—22no—
77C2×C4×C61—22no—
78C2×C4×C61—22no—
79C2×C4×C61—22no—
80C2×C4×C61—21no—
81C2×C4×C61—22no—
82C2×C4×C61—21no—
83C2×C4×C61—44no—
84C22⋊D61—48no—
85C2×Dic61—22no—
86C2×Dic61—22no—
87C2×Dic61—22no—
88C2×Dic61—22no—
89C2×Dic61—22no—
90C2×Dic61—22no—
91C2×Dic61—22no—
92C2×Dic61—22no—
93C2×Dic61—22no—
94D244—44no—
95C4×D61—48no—
96Dic122—44no—
97C22×C61—22no—
98C22×C61—24no—
99C22×C61—42no—
100C22×C61—41no—
101C22×C61—41no—
102C22×C61C2×#4112yes—
103C22×C61C2×#4111yescharacteristic
104C22×C61H(5,𝔽2)11yescharacteristic
105C22×C61H(5,𝔽2)11yescharacteristic
106C22×C61H(5,𝔽2)12yes—
107C2×D61—24no—
108C2×D61—24no—
109C2×D61—24no—
110C2×D61—42no—
111C2×D61—42no—
112C2×D61—42no—
113C2×D61—42no—
114C4×C61—42no—
115C4×C61—42no—
116C4×C61—41no—
117C4×C61—41no—
118Dic61—42no—
119Dic61—42no—
120Dic61—42no—
121#2760—611nomaximal, Sylow
122C2×C61—42no—
123C2×C61#53812yes—
124C2×C61#53811yescharacteristic
125C2×C61#55112yes—
126C2×C61#55111yescharacteristic
127C2×C61#56011yescharacteristic
128D61—44no—
129#401—612no—
130#393—611no—
131#393—612no—
132#392—611no—
133#386—612no—
134#386—612no—
135#386—612no—
136#381—612no—
137#381D6111yescharacteristic, complemented
138C61#276011yescharacteristic, complemented, Sylow
139C22×Q8—611no—
140C22×D4—612no—
141C22×D4—611no—
142C23×C4—612no—
143C23×C4C2×D6111yescharacteristic
144C2×C22⋊C4—612no—
145C2×C22⋊C4—612no—
146C2×C22⋊C4—612no—
147C2×C22⋊C4—612no—
148C2×C22⋊C4—612no—
149C2×C22⋊C4C2×D6111yescharacteristic
150C2×C22⋊C4C2×D6111yescharacteristic
151#95—611no—
152#95—612no—
153#95—612no—
154#95—612no—
155#95—612no—
156#95—612no—
157#95—611no—
158#95C2×D6112yes—
159#95C2×D6112yes—
160C24—612no—
161C24C22×D6111yescharacteristic
162C2×Q8—2441no—
163C2×Q8—2442no—
164C2×D4—1224no—
165C2×D4—1224no—
166C2×D4—1224no—
167C2×D4—2441no—
168C2×D4—2442no—
169C22×C4—22no—
170C22×C4—41no—
171C22×C4—41no—
172C22×C4—612no—
173C22×C4—612no—
174C22×C4—612no—
175C22×C4—1224no—
176C22×C4—2442no—
177C22×C4—2442no—
178C22×C4C22×D6111yescharacteristic
179C22×C4C22×D6112yes—
180C22×C4C22×D6112yes—
181C22×C4C22×D6111yescharacteristic
182C22⋊C4—41no—
183C22⋊C4—41no—
184C22⋊C4—2442no—
185C22⋊C4—2442no—
186C22⋊C4—2442no—
187C22⋊C4—2442no—
188C22⋊C4—2442no—
189C23—22no—
190C23—21no—
191C23—21no—
192C23—22no—
193C23—614no—
194C23—1222no—
195C23—1222no—
196C23—1222no—
197C23—1222no—
198C23—1222no—
199C23—1222no—
200C23#1175822212yes—
201C23C23×D6111yescharacteristic
202Q8—2444no—
203D4—2444no—
204D4—2448no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—44no—
216C2×C4—1222no—
217C2×C4—1222no—
218C2×C4—1222no—
219C2×C4—1222no—
220C2×C4—1222no—
221C2×C4—1222no—
222C2×C4—1222no—
223C2×C4—1222no—
224C2×C4—1222no—
225C2×C4—2448no—
226C22—22no—
227C22—24no—
228C22—41no—
229C22—42no—
230C22—41no—
231C22—1224no—
232C22—1224no—
233C22—1224no—
234C22—2442no—
235C22—2442no—
236C22—2442no—
237C22—2442no—
238C22#41×D6112yes—
239C22C2×#1175822211yescharacteristic
240C22#1451982211yescharacteristic
241C22#1451982211yescharacteristic
242C22#1451982312yes—
243C4—41no—
244C4—42no—
245C4—42no—
246C4—41no—
247C4—2442no—
248C4—2442no—
249C4—2442no—
250C2—42no—
251C2—2444no—
252C2#1684034812yes—
253C2#1684035011yescharacteristic
254C2#1684043612yes—
255C2#1684044011yescharacteristic
256C2#1684050211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#381C2
hypercenter#381D61
hypocenterC61#2760
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
1. C61⋊#401C2semidirect
2. #16839675C2semidirect
3. #16839674C2semidirect
5. #16839641C2semidirect
6. #16839640C2semidirect
7. #16839638C2semidirect
8. #16839624C2semidirect
9. C61×#381C2semidirect
137. #381D61semidirect
138. C61#2760semidirect