Finite Group Databasebeta

← #21453942

Subgroups — #21453942

Order 7808.

508 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 508 conjugacy classes of subgroups — too many to draw. Only its 117 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#16839701C211yesmaximal, characteristic, complemented
2#16839689C212yesmaximal, complemented
3#16839678C212yesmaximal, complemented
4#16839678C212yesmaximal, complemented
5#16839671C212yesmaximal, complemented
6#16839670C212yesmaximal, complemented
7#16839663C211yesmaximal, characteristic, complemented
8#16839655C212yesmaximal, complemented
9C61×#394C211yesmaximal, characteristic, complemented
10C22×D244C2211yescharacteristic
11C22×C22⋊D61C2212yes—
12C22×C22⋊D61C2212yes—
13C2×C4⋊Dic61C2212yes—
14C2×C4⋊Dic61C2211yescharacteristic
15C2×C22⋊Dic61C2212yes—
16C2×C22⋊Dic61C2212yes—
17C2×#11758198C2212yes—
18C2×#11758198C2212yes—
19C2×#11758198C2212yes—
20C2×#11758198C2212yes—
21C2×C4×Dic61C2211yescharacteristic
22#14519684C2212yes—
23#14519684C2212yes—
24#14519684C2212yes—
25#14519684C2211yescharacteristic
26C22×D4×C61C2211yescharacteristic
27C2×C4⋊C4×C61C2211yescharacteristic
28C2×C22⋊C4×C61C2212yes—
29C2×C22⋊C4×C61C2212yes—
30#95×C61C2211yescharacteristic
31C24×C61C2312yes—
32C23×D61C2312yes—
33C2×D4×C61—42no—
34C2×D4×C61—41no—
35C22×C4×C61C2312yes—
36C22×C4×C61C2311yescharacteristic
37C22×C4×C61C2311yescharacteristic
38C22×C4×C61C2311yescharacteristic
39C2×C22⋊D61—42no—
40C2×C22⋊D61—42no—
41C2×C22⋊D61—42no—
42C2×C22⋊D61—42no—
43C2×C22⋊D61—42no—
44C2×C22⋊D61—42no—
45C22×Dic61C2312yes—
46C22×Dic61C2312yes—
47C22×Dic61C2312yes—
48C2×D244—22no—
49C2×D244—41no—
50C2×D244—41no—
51C4⋊C4×C61—41no—
52C22⋊C4×C61—24no—
53C22⋊C4×C61—42no—
54C22⋊Dic61—42no—
55C22⋊Dic61—42no—
56#11758198—42no—
57#11758198—42no—
58#11758198—42no—
59#11758198—42no—
60C4⋊Dic61—42no—
61C4⋊Dic61—41no—
62C4×Dic61—41no—
63C23×C61—22no—
64C23×C61—22no—
65C23×C61—22no—
66C23×C61—22no—
67C23×C61—22no—
68C23×C61—22no—
69C23×C61—22no—
70C23×C61C2411yescharacteristic
71C22×D61—22no—
72C22×D61—22no—
73C22×D61—22no—
74C22×D61—22no—
75C22×D61—22no—
76C22×D61—22no—
77C22×D61—22no—
78D4×C61—44no—
79C2×C4×C61—21no—
80C2×C4×C61—21no—
81C2×C4×C61—22no—
82C2×C4×C61—22no—
83C2×C4×C61—21no—
84C2×C4×C61—22no—
85C2×C4×C61—22no—
86C2×C4×C61—22no—
87C2×C4×C61—21no—
88C2×C4×C61#4112yes—
89C22⋊D61—48no—
90C22⋊D61—48no—
91C2×Dic61—22no—
92C2×Dic61—22no—
93C2×Dic61—22no—
94C2×Dic61—22no—
95C2×Dic61—22no—
96C2×Dic61—22no—
97C2×Dic61—22no—
98C2×Dic61—22no—
99C2×Dic61—22no—
100D244—44no—
101C22×C61—42no—
102C22×C61—42no—
103C22×C61—42no—
104C22×C61—42no—
105C22×C61—42no—
106C22×C61—42no—
107C22×C61—42no—
108C22×C61C2×#4111yescharacteristic
109C22×C61H(5,𝔽2)11yescharacteristic
110C22×C61H(5,𝔽2)12yes—
111C22×C61H(5,𝔽2)11yescharacteristic
112C22×C61H(5,𝔽2)12yes—
113C2×D61—42no—
114C2×D61—42no—
115C2×D61—42no—
116C2×D61—42no—
117C2×D61—42no—
118C2×D61—42no—
119C2×D61—42no—
120C4×C61—22no—
121C4×C61—42no—
122C4×C61—41no—
123C4×C61—41no—
124Dic61—42no—
125Dic61—42no—
126Dic61—42no—
127#2828—611nomaximal, Sylow
128C2×C61—82no—
129C2×C61#53811yescharacteristic
130C2×C61#54012yes—
131C2×C61#56011yescharacteristic
132C2×C61#56012yes—
133C2×C61H(3,𝔽4)11yescharacteristic
134D61—82no—
135#400—611no—
136#397—612no—
137#394—612no—
138#394—612no—
139#394D6111yescharacteristic, complemented
140#392—612no—
141#392—612no—
142#390—611no—
143#388—612no—
144C61#282811yescharacteristic, complemented, Sylow
145C22×D4—612no—
146C22×D4—612no—
147C22×D4—611no—
148C22×D4C2×D6111yescharacteristic
149C2×C4⋊C4—612no—
150C2×C4⋊C4—611no—
151C2×C4⋊C4C2×D6111yescharacteristic
152C2×C22⋊C4—612no—
153C2×C22⋊C4—612no—
154C2×C22⋊C4—612no—
155C2×C22⋊C4—612no—
156C2×C22⋊C4—612no—
157C2×C22⋊C4—612no—
158C2×C22⋊C4C2×D6112yes—
159C2×C22⋊C4C2×D6112yes—
160C2×C42—611no—
161#95—612no—
162#95—612no—
163#95—612no—
164#95—611no—
165#95C2×D6111yescharacteristic
166C24—612no—
167C24C22×D6112yes—
168C2×D4—42no—
169C2×D4—41no—
170C2×D4—1222no—
171C2×D4—2441no—
172C2×D4—2441no—
173C2×D4—2442no—
174C2×D4—2442no—
175C2×D4—2442no—
176C2×D4—2442no—
177C2×D4—2442no—
178C2×D4—2442no—
179C22×C4—612no—
180C22×C4—612no—
181C22×C4—612no—
182C22×C4C22×D6111yescharacteristic
183C22×C4C22×D6112yes—
184C22×C4C22×D6111yescharacteristic
185C22×C4C22×D6111yescharacteristic
186C4⋊C4—41no—
187C4⋊C4—2441no—
188C4⋊C4—2442no—
189C22⋊C4—24no—
190C22⋊C4—42no—
191C22⋊C4—2442no—
192C22⋊C4—2442no—
193C22⋊C4—2442no—
194C22⋊C4—2442no—
195C22⋊C4—2442no—
196C22⋊C4—2442no—
197C42—2441no—
198C23—22no—
199C23—22no—
200C23—22no—
201C23—22no—
202C23—22no—
203C23—22no—
204C23—22no—
205C23—1222no—
206C23—1222no—
207C23—1222no—
208C23—1222no—
209C23—1222no—
210C23—1222no—
211C23—1222no—
212C23C23×D6111yescharacteristic
213D4—44no—
214D4—2444no—
215D4—2448no—
216D4—2448no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—22no—
226C2×C4—1222no—
227C2×C4—1222no—
228C2×C4—1222no—
229C2×C4—1222no—
230C2×C4—1222no—
231C2×C4—1222no—
232C2×C4—1222no—
233C2×C4—1222no—
234C2×C4—1222no—
235C2×C4#1175822412yes—
236C22—42no—
237C22—42no—
238C22—42no—
239C22—42no—
240C22—42no—
241C22—42no—
242C22—42no—
243C22—2442no—
244C22—2442no—
245C22—2442no—
246C22—2442no—
247C22—2442no—
248C22—2442no—
249C22—2442no—
250C22C2×#1175822411yescharacteristic
251C22#1451982212yes—
252C22#1451982211yescharacteristic
253C22#1451982311yescharacteristic
254C22#1451982312yes—
255C4—22no—
256C4—41no—
257C4—41no—
258C4—42no—
259C4—2442no—
260C4—2442no—
261C4—2442no—
262C2—82no—
263C2—4882no—
264C2#1684034911yescharacteristic
265C2#1684036512yes—
266C2#1684050111yescharacteristic
267C2#1684050212yes—
268C2#1684050411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#394C2
hypercenter#394D61
hypocenterC61#2828
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. #16839701C2semidirect
2. #16839689C2semidirect
3. #16839678C2semidirect
4. #16839678C2semidirect
5. #16839671C2semidirect
6. #16839670C2semidirect
7. #16839663C2semidirect
8. #16839655C2semidirect
9. C61×#394C2semidirect
139. #394D61semidirect
144. C61#2828semidirect