Finite Group Databasebeta

← #21451519

Subgroups — #21451519

Order 7808.

476 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 141 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×#14519734C211yesmaximal, characteristic
2#16839700C211yesmaximal, characteristic, complemented
3#16839697C211yesmaximal, characteristic
4#16839693C211yesmaximal, characteristic, complemented
5#16839688C211yesmaximal, characteristic
6#16839657C212yesmaximal, complemented
7#16839652C212yesmaximal
8#16839643C212yesmaximal, complemented
9#16839633C212yesmaximal
10#16839608C211yesmaximal, characteristic, complemented
11C2×#125×C61C211yesmaximal, characteristic, complemented
12C22×C4×D61C2211yescharacteristic
13#14519734—24no—
14C2×#11758196C2211yescharacteristic
15C2×#11758196C2212yes—
16C2×#11758196C2212yes—
17C2×#11758196C2211yescharacteristic
18C2×#11758198C2211yescharacteristic
19C2×#11758198C2212yes—
20C2×#11758198C2212yes—
21C2×#11758198C2211yescharacteristic
22C2×C4×Dic61C2211yescharacteristic
23C2×C4×Dic61C2212yes—
24#14519684C2211yescharacteristic
25#14519684C2212yes—
26#14519684C2211yescharacteristic
27#14519684C2212yes—
28#14519684C2212yes—
29#14519684C2212yes—
30#14519684C2212yes—
31#125×C61—24no—
32C2×C4⋊C4×C61C2211yescharacteristic
33C2×C4⋊C4×C61C2211yescharacteristic
34C2×C4⋊C4×C61C2212yes—
35C2×C4⋊C4×C61C2212yes—
36C2×C42×C61C2211yescharacteristic
37C23×D61C2311yescharacteristic
38C22×C4×C61C2312yes—
39C22×C4×C61C2312yes—
40C22×C4×C61C2311yescharacteristic
41C22×C4×C61C2311yescharacteristic
42C22×C4×C61C2311yescharacteristic
43C22×Dic61C2312yes—
44C22×Dic61C2311yescharacteristic
45C22×Dic61C2311yescharacteristic
46C22×Dic61C2311yescharacteristic
47C22×Dic61C2312yes—
48C2×C4×D61—22no—
49C2×C4×D61—22no—
50C2×C4×D61—22no—
51C4⋊C4×C61—24no—
52C4⋊C4×C61—22no—
53C4⋊C4×C61—22no—
54C4⋊C4×C61—24no—
55C42×C61D414yes—
56#11758198—24no—
57#11758198—22no—
58#11758198—22no—
59#11758198—24no—
60#11758196—22no—
61#11758196—22no—
62#11758196—24no—
63#11758196—24no—
64C4×Dic61—22no—
65C4×Dic61—24no—
66C23×C61C2411yescharacteristic
67C22×D61—21no—
68C22×D61—22no—
69C22×D61—21no—
70C22×D61—22no—
71C22×D61#4112yes—
72C2×C4×C61—22no—
73C2×C4×C61—21no—
74C2×C4×C61—21no—
75C2×C4×C61—22no—
76C2×C4×C61—22no—
77C2×C4×C61—22no—
78C2×C4×C61—22no—
79C2×C4×C61—22no—
80C2×C4×C61—22no—
81C2×C4×C61—22no—
82C2×C4×C61C2×D412yes—
83C2×C4×C61C2×D412yes—
84C2×C4×C61C2×D412yes—
85C2×Dic61—21no—
86C2×Dic61—22no—
87C2×Dic61—21no—
88C2×Dic61—22no—
89C2×Dic61—21no—
90C2×Dic61—21no—
91C2×Dic61—22no—
92C2×Dic61—22no—
93C2×Dic61—22no—
94C2×Dic61—22no—
95C2×Dic61—22no—
96C2×Dic61#4114yes—
97C2×Dic61#4112yes—
98C4×D61—28no—
99C22×C61C22×D411yescharacteristic
100C22×C61C2×#4111yescharacteristic
101C22×C61C2×#4111yescharacteristic
102C22×C61C2×#4112yes—
103C22×C612−1+412yes—
104C2×D61—22no—
105C2×D61—24no—
106C2×D61—41no—
107C2×D61—41no—
108C2×D61—42no—
109C4×C61—22no—
110C4×C61—22no—
111C4×C61—22no—
112C4×C61—42no—
113C4×C61—42no—
114Dic61—22no—
115Dic61—24no—
116Dic61—41no—
117Dic61—41no—
118Dic61—42no—
119#2611—611nomaximal, Sylow
120C2×C61#52511yescharacteristic
121C2×C61#53211yescharacteristic
122C2×C61#53611yescharacteristic
123C2×C61#55212yes—
124C2×C61#55212yes—
125D61—42no—
126C2×#125D6111yescharacteristic, complemented
127C2×#117—611no—
128#400—611no—
129#399—611no—
130#398—611no—
131#397—611no—
132#389—612no—
133#388—612no—
134#387—612no—
135#385—612no—
136#376—611no—
137C61#261111yescharacteristic, complemented, Sylow
138C23×C4—611no—
139#125—24no—
140#117—1224no—
141C2×C4⋊C4—611no—
142C2×C4⋊C4—611no—
143C2×C4⋊C4—612no—
144C2×C4⋊C4—612no—
145C2×C4⋊C4C2×D6112yes—
146C2×C4⋊C4C2×D6112yes—
147C2×C4⋊C4C2×D6111yescharacteristic
148C2×C4⋊C4C2×D6111yescharacteristic
149C2×C22⋊C4—611no—
150C2×C22⋊C4—611no—
151C2×C22⋊C4—612no—
152C2×C22⋊C4—612no—
153C2×C42—611no—
154C2×C42—612no—
155C2×C42C2×D6111yescharacteristic
156#95—612no—
157#95—611no—
158#95—611no—
159#95—612no—
160#95—612no—
161#95—612no—
162#95—612no—
163C24—611no—
164C22×C4—612no—
165C22×C4—611no—
166C22×C4—612no—
167C22×C4—611no—
168C22×C4—611no—
169C22×C4—1222no—
170C22×C4—1222no—
171C22×C4—1222no—
172C22×C4C22×D6112yes—
173C22×C4C22×D6112yes—
174C22×C4C22×D6111yescharacteristic
175C22×C4C22×D6111yescharacteristic
176C22×C4C22×D6111yescharacteristic
177C4⋊C4—24no—
178C4⋊C4—24no—
179C4⋊C4—22no—
180C4⋊C4—22no—
181C4⋊C4—1224no—
182C4⋊C4—1224no—
183C4⋊C4—1222no—
184C4⋊C4—1222no—
185C22⋊C4—1224no—
186C22⋊C4—1224no—
187C22⋊C4—1222no—
188C22⋊C4—1222no—
189C42—1224no—
190C42—1222no—
191C42C22⋊D6114yes—
192C23—612no—
193C23—1221no—
194C23—1222no—
195C23—1221no—
196C23—1222no—
197C23C23×D6111yescharacteristic
198C2×C4—22no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—614no—
209C2×C4—612no—
210C2×C4—1228no—
211C2×C4—1221no—
212C2×C4—1222no—
213C2×C4—1221no—
214C2×C4—1222no—
215C2×C4—1221no—
216C2×C4—1221no—
217C2×C4—1222no—
218C2×C4—1222no—
219C2×C4—1222no—
220C2×C4—1222no—
221C2×C4—1222no—
222C2×C4C2×C22⋊D6112yes—
223C2×C4C2×C22⋊D6112yes—
224C2×C4C2×C22⋊D6112yes—
225C22—1222no—
226C22—1224no—
227C22—2441no—
228C22—2441no—
229C22—2442no—
230C22C22×C22⋊D6111yescharacteristic
231C22#41×D6111yescharacteristic
232C22#41×D6111yescharacteristic
233C22#41×D6112yes—
234C22#1451982512yes—
235C4—22no—
236C4—22no—
237C4—22no—
238C4—42no—
239C4—42no—
240C4—1222no—
241C4—1224no—
242C4—2441no—
243C4—2441no—
244C4—2442no—
245C2—2442no—
246C2#1684026911yescharacteristic
247C2#1684030811yescharacteristic
248C2#1684033611yescharacteristic
249C2#1684044412yes—
250C2#1684044412yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC2×#125×C61C2
hypercenterC2×#125D61
hypocenterC61#2611
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
2. #16839700C2semidirect
4. #16839693C2semidirect
6. #16839657C2semidirect
8. #16839643C2semidirect
10. #16839608C2semidirect
11. C2×#125×C61C2semidirect
126. C2×#125D61semidirect
137. C61#2611semidirect