Finite Group Databasebeta

← #21453943

Subgroups — #21453943

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#16839691C212yesmaximal, complemented
2#16839680C212yesmaximal, complemented
3#16839679C211yesmaximal, characteristic, complemented
4#16839679C212yesmaximal, complemented
5#16839672C212yesmaximal, complemented
6#16839672C212yesmaximal, complemented
7#16839663C211yesmaximal, characteristic, complemented
8#16839651C212yesmaximal, complemented
9C61×#400C211yesmaximal, characteristic, complemented
10C22×D244C2211yescharacteristic
11C22×D244C2212yes—
12C22×D244C2211yescharacteristic
13C22×D244C2212yes—
14C2×#11758196C2212yes—
15C2×#11758198C2212yes—
16C2×#11758198C2212yes—
17C2×#11758198C2212yes—
18C2×#11758198C2212yes—
19C2×#11758198C2212yes—
20C2×#11758198C2212yes—
21C2×#11758198C2212yes—
22C2×#11758198C2212yes—
23C2×C4×Dic61C2211yescharacteristic
24#14519684C2211yescharacteristic
25#14519684C2212yes—
26C2×C4⋊C4×C61C2211yescharacteristic
27C2×C4⋊C4×C61C2211yescharacteristic
28#95×C61C2211yescharacteristic
29#95×C61C2212yes—
30#95×C61C2212yes—
31C23×D61C2312yes—
32C23×D61C2312yes—
33C22×C4×C61C2312yes—
34C22×C4×C61C2311yescharacteristic
35C22×C4×C61C2312yes—
36C22×C4×C61C2311yescharacteristic
37C22×C4×C61C2311yescharacteristic
38C22×Dic61C2312yes—
39C22×Dic61C2312yes—
40C2×D244—22no—
41C2×D244—41no—
42C2×D244—41no—
43C2×D244—42no—
44C2×D244—42no—
45C2×D244—42no—
46C2×D244—42no—
47C2×D244—42no—
48C2×D244—42no—
49C2×D244—41no—
50C2×D244—42no—
51C4⋊C4×C61—41no—
52C4⋊C4×C61—41no—
53#11758198—24no—
54#11758198—42no—
55#11758198—42no—
56#11758198—42no—
57#11758198—42no—
58#11758198—42no—
59#11758198—42no—
60#11758198—42no—
61#11758196—42no—
62C4×Dic61—41no—
63C23×C61C2411yescharacteristic
64C22×D61—22no—
65C22×D61—22no—
66C22×D61—22no—
67C22×D61—22no—
68C22×D61—22no—
69C22×D61—22no—
70C22×D61—22no—
71C22×D61—22no—
72C22×D61—22no—
73C22×D61—22no—
74C22×D61—22no—
75C22×D61—22no—
76C22×D61—22no—
77C22×D61—22no—
78C2×C4×C61—21no—
79C2×C4×C61—21no—
80C2×C4×C61—22no—
81C2×C4×C61—22no—
82C2×C4×C61—22no—
83C2×C4×C61—22no—
84C2×C4×C61—22no—
85C2×C4×C61—22no—
86C2×C4×C61—22no—
87C2×C4×C61—21no—
88C2×C4×C61—21no—
89C2×C4×C61—22no—
90C2×C4×C61#4112yes—
91C2×Dic61—22no—
92C2×Dic61—22no—
93C2×Dic61—22no—
94C2×Dic61—22no—
95C2×Dic61—22no—
96C2×Dic61—22no—
97D244—44no—
98D244—44no—
99D244—48no—
100D244—48no—
101C22×C61C2×#4111yescharacteristic
102C22×C61H(5,𝔽2)11yescharacteristic
103C22×C61H(5,𝔽2)11yescharacteristic
104C22×C61H(5,𝔽2)12yes—
105C22×C61H(5,𝔽2)12yes—
106C2×D61—42no—
107C2×D61—42no—
108C2×D61—42no—
109C2×D61—42no—
110C2×D61—42no—
111C2×D61—42no—
112C2×D61—42no—
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—41no—
122C4×C61—42no—
123C4×C61—41no—
124C4×C61—42no—
125Dic61—42no—
126Dic61—42no—
127#2828—611nomaximal, Sylow
128C2×C61#53811yescharacteristic
129C2×C61#54012yes—
130C2×C61#56011yescharacteristic
131C2×C61#56012yes—
132C2×C61H(3,𝔽4)11yescharacteristic
133D61—82no—
134D61—82no—
135#400D6111yescharacteristic, complemented
136#397—612no—
137#394—612no—
138#394—611no—
139#394—612no—
140#392—612no—
141#392—612no—
142#390—611no—
143#388—612no—
144C61#282811yescharacteristic, complemented, Sylow
145C22×D4—611no—
146C22×D4—612no—
147C22×D4—611no—
148C22×D4—612no—
149C2×C4⋊C4—612no—
150C2×C4⋊C4C2×D6111yescharacteristic
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⋊C4—612no—
159C2×C22⋊C4—612no—
160C2×C42—611no—
161#95—612no—
162#95—611no—
163#95C2×D6112yes—
164#95C2×D6112yes—
165#95C2×D6111yescharacteristic
166C24—612no—
167C24—612no—
168C2×D4—1222no—
169C2×D4—2441no—
170C2×D4—2441no—
171C2×D4—2441no—
172C2×D4—2442no—
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×C4C22×D6112yes—
182C22×C4C22×D6111yescharacteristic
183C22×C4C22×D6112yes—
184C22×C4C22×D6111yescharacteristic
185C22×C4C22×D6111yescharacteristic
186C4⋊C4—41no—
187C4⋊C4—41no—
188C4⋊C4—2442no—
189C22⋊C4—1224no—
190C22⋊C4—2442no—
191C22⋊C4—2442no—
192C22⋊C4—2442no—
193C22⋊C4—2442no—
194C22⋊C4—2442no—
195C22⋊C4—2442no—
196C22⋊C4—2442no—
197C42—2441no—
198C23—1222no—
199C23—1222no—
200C23—1222no—
201C23—1222no—
202C23—1222no—
203C23—1222no—
204C23—1222no—
205C23—1222no—
206C23—1222no—
207C23—1222no—
208C23—1222no—
209C23—1222no—
210C23—1222no—
211C23—1222no—
212C23C23×D6111yescharacteristic
213D4—2444no—
214D4—2444no—
215D4—2448no—
216D4—2448no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—1222no—
230C2×C4—1222no—
231C2×C4—1222no—
232C2×C4—1222no—
233C2×C4—1222no—
234C2×C4—1222no—
235C2×C4#1175822612yes—
236C22—2442no—
237C22—2442no—
238C22—2442no—
239C22—2442no—
240C22—2442no—
241C22—2442no—
242C22—2442no—
243C22—2442no—
244C22—2442no—
245C22—2442no—
246C22—2442no—
247C22—2442no—
248C22—2442no—
249C22—2442no—
250C22C2×#1175822611yescharacteristic
251C22#1451982211yescharacteristic
252C22#1451982312yes—
253C22#1451982311yescharacteristic
254C22#1451982312yes—
255C4—22no—
256C4—41no—
257C4—41no—
258C4—42no—
259C4—42no—
260C4—2442no—
261C4—2442no—
262C2—4882no—
263C2—4882no—
264C2#1684035211yescharacteristic
265C2#1684036812yes—
266C2#1684050211yescharacteristic
267C2#1684050312yes—
268C2#1684050411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#400C2
hypercenter#400D61
hypocenterC61#2828
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
1. #16839691C2semidirect
2. #16839680C2semidirect
3. #16839679C2semidirect
4. #16839679C2semidirect
5. #16839672C2semidirect
6. #16839672C2semidirect
7. #16839663C2semidirect
8. #16839651C2semidirect
9. C61×#400C2semidirect
135. #400D61semidirect
144. C61#2828semidirect