Finite Group Databasebeta

← #21450110

Subgroups — #21450110

Order 7808.

540 conjugacy classes of subgroups.

The subgroup lattice has 314 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C22⋊D61C211yesmaximal, characteristic
2#16839690C212yesmaximal, complemented
3#16839677C212yesmaximal
4#16839658C211yesmaximal, characteristic, complemented
5#16839658C211yesmaximal, characteristic, complemented
6#16839653C212yesmaximal, complemented
7#16839646C212yesmaximal, complemented
8#16839622C211yesmaximal, characteristic, complemented
9#16839619C211yesmaximal, characteristic, complemented
10#16839619C211yesmaximal, characteristic, complemented
11C2×#117×C61C211yesmaximal, characteristic, complemented
12C22×C22⋊D61C2211yescharacteristic
13C22×C4×D61C2211yescharacteristic
14C4×C22⋊D61—24no—
15C2×C4⋊Dic61C2211yescharacteristic
16C2×C4⋊Dic61C2211yescharacteristic
17C2×#11758196C2211yescharacteristic
18C2×#11758196C2212yes—
19C2×#11758196C2212yes—
20C2×C22⋊Dic61C2211yescharacteristic
21C2×C22⋊Dic61C2212yes—
22C2×#11758198C2211yescharacteristic
23C2×#11758198C2212yes—
24C2×#11758198C2212yes—
25C2×C4×Dic61C2211yescharacteristic
26#14519684C2212yes—
27#14519684C2212yes—
28#14519684C2212yes—
29#14519684C2212yes—
30#14519684C2212yes—
31C23×C4×C61C2211yescharacteristic
32#117×C61—24no—
33C2×C4⋊C4×C61C2211yescharacteristic
34C2×C4⋊C4×C61C2211yescharacteristic
35C2×C22⋊C4×C61C2212yes—
36C2×C42×C61C2212yes—
37C24×C61C2311yescharacteristic
38C23×D61C2311yescharacteristic
39C22×C4×C61—22no—
40C22×C4×C61—22no—
41C22×C4×C61D414yes—
42C22×C4×C61C2312yes—
43C22×C4×C61C2312yes—
44C22×C4×C61C2311yescharacteristic
45C22×C4×C61C2311yescharacteristic
46C2×C22⋊D61—22no—
47C2×C22⋊D61—22no—
48C2×C22⋊D61—22no—
49C22×Dic61C2311yescharacteristic
50C22×Dic61C2312yes—
51C22×Dic61C2312yes—
52C22×Dic61C2311yescharacteristic
53C22×Dic61C2311yescharacteristic
54C2×C4×D61—22no—
55C2×C4×D61—22no—
56C2×C4×D61—22no—
57C4⋊C4×C61—22no—
58C4⋊C4×C61—22no—
59C22⋊C4×C61—24no—
60C42×C61—24no—
61C22⋊Dic61—22no—
62C22⋊Dic61—42no—
63#11758198—24no—
64#11758198—22no—
65#11758198—42no—
66C4⋊Dic61—22no—
67C4⋊Dic61—22no—
68#11758196—22no—
69#11758196—24no—
70#11758196—42no—
71C4×Dic61—22no—
72C23×C61—21no—
73C23×C61—21no—
74C23×C61—21no—
75C23×C61—21no—
76C23×C61—21no—
77C23×C61—21no—
78C23×C61C2×D412yes—
79C23×C61C2411yescharacteristic
80C22×D61—21no—
81C22×D61—21no—
82C22×D61—21no—
83C22×D61—21no—
84C22×D61—21no—
85C22×D61—21no—
86C22×D61#4112yes—
87C2×C4×C61—21no—
88C2×C4×C61—21no—
89C2×C4×C61—28no—
90C2×C4×C61—22no—
91C2×C4×C61—22no—
92C2×C4×C61—22no—
93C2×C4×C61—22no—
94C2×C4×C61—22no—
95C2×C4×C61—22no—
96C2×C4×C61C2×D412yes—
97C2×C4×C61C2×D412yes—
98C2×C4×C61#4112yes—
99C2×C4×C61#4112yes—
100C22⋊D61—28no—
101C2×Dic61—21no—
102C2×Dic61—21no—
103C2×Dic61—21no—
104C2×Dic61—21no—
105C2×Dic61—22no—
106C2×Dic61—22no—
107C2×Dic61—22no—
108C2×Dic61—22no—
109C2×Dic61—21no—
110C2×Dic61—21no—
111C2×Dic61—21no—
112C2×Dic61—22no—
113C2×Dic61—22no—
114C2×Dic61—21no—
115C2×Dic61#4112yes—
116C4×D61—44no—
117C22×C61—22no—
118C22×C61—22no—
119C22×C61—22no—
120C22×C61—41no—
121C22×C61—41no—
122C22×C61—41no—
123C22×C61—41no—
124C22×C61C22×D411yescharacteristic
125C22×C61C2×#4111yescharacteristic
126C22×C61C2×#4111yescharacteristic
127C22×C61C2×#4111yescharacteristic
128C22×C61C2×#4111yescharacteristic
129C22×C61H(5,𝔽2)11yescharacteristic
130C22×C612−1+411yescharacteristic
131C2×D61—22no—
132C2×D61—22no—
133C2×D61—22no—
134C2×D61—41no—
135C2×D61—41no—
136C2×D61—41no—
137C2×D61—41no—
138C4×C61—22no—
139C4×C61—42no—
140C4×C61—42no—
141C4×C61#12314yes—
142Dic61—22no—
143Dic61—41no—
144Dic61—41no—
145Dic61—42no—
146Dic61—42no—
147#2485—611nomaximal, Sylow
148C2×C61—42no—
149C2×C61C2×#12311yescharacteristic
150C2×C61#52511yescharacteristic
151C2×C61#53711yescharacteristic
152C2×C61#55211yescharacteristic
153C2×C61#55311yescharacteristic
154C2×C61#55511yescharacteristic
155C2×C61#55611yescharacteristic
156D61—42no—
157C2×C4×D4—611no—
158C2×#117D6111yescharacteristic, complemented
159#397—612no—
160#394—612no—
161#389—611no—
162#389—611no—
163#388—612no—
164#387—612no—
165#380—611no—
166#380—611no—
167#380—611no—
168C61#248511yescharacteristic, complemented, Sylow
169C22×D4—611no—
170C23×C4—611no—
171C23×C4C2×D6111yescharacteristic
172C4×D4—1224no—
173#117—24no—
174C2×C4⋊C4—611no—
175C2×C4⋊C4—611no—
176C2×C4⋊C4—611no—
177C2×C4⋊C4—612no—
178C2×C4⋊C4—612no—
179C2×C4⋊C4C2×D6111yescharacteristic
180C2×C4⋊C4C2×D6111yescharacteristic
181C2×C22⋊C4—611no—
182C2×C22⋊C4—611no—
183C2×C22⋊C4—612no—
184C2×C22⋊C4—612no—
185C2×C22⋊C4—612no—
186C2×C22⋊C4C2×D6112yes—
187C2×C42—611no—
188C2×C42C2×D6112yes—
189#95—612no—
190#95—612no—
191#95—612no—
192#95—612no—
193#95—612no—
194C24—611no—
195C24C22×D6111yescharacteristic
196C2×D4—1222no—
197C2×D4—1222no—
198C2×D4—1222no—
199C22×C4—22no—
200C22×C4—22no—
201C22×C4—611no—
202C22×C4—611no—
203C22×C4—612no—
204C22×C4—612no—
205C22×C4—611no—
206C22×C4—1222no—
207C22×C4—1222no—
208C22×C4—1222no—
209C22×C4C22⋊D6114yes—
210C22×C4C22×D6112yes—
211C22×C4C22×D6112yes—
212C22×C4C22×D6111yescharacteristic
213C22×C4C22×D6111yescharacteristic
214C4⋊C4—22no—
215C4⋊C4—22no—
216C4⋊C4—1224no—
217C4⋊C4—1222no—
218C4⋊C4—1222no—
219C4⋊C4—1222no—
220C4⋊C4—2442no—
221C22⋊C4—24no—
222C22⋊C4—1224no—
223C22⋊C4—1222no—
224C22⋊C4—1222no—
225C22⋊C4—2442no—
226C22⋊C4—2442no—
227C42—24no—
228C42—1222no—
229C23—21no—
230C23—21no—
231C23—21no—
232C23—21no—
233C23—21no—
234C23—21no—
235C23—612no—
236C23—1221no—
237C23—1221no—
238C23—1221no—
239C23—1221no—
240C23—1221no—
241C23—1221no—
242C23C2×C22⋊D6112yes—
243C23C23×D6111yescharacteristic
244D4—1228no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—28no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—612no—
255C2×C4—1221no—
256C2×C4—1221no—
257C2×C4—1221no—
258C2×C4—1221no—
259C2×C4—1222no—
260C2×C4—1222no—
261C2×C4—1222no—
262C2×C4—1222no—
263C2×C4—1221no—
264C2×C4—1221no—
265C2×C4—1222no—
266C2×C4—1222no—
267C2×C4—1221no—
268C2×C4—1221no—
269C2×C4—2444no—
270C2×C4#1175822212yes—
271C2×C4#1175822212yes—
272C2×C4C2×C22⋊D6112yes—
273C2×C4C2×C22⋊D6112yes—
274C22—22no—
275C22—22no—
276C22—22no—
277C22—41no—
278C22—41no—
279C22—41no—
280C22—41no—
281C22—1222no—
282C22—1222no—
283C22—1222no—
284C22—2441no—
285C22—2441no—
286C22—2441no—
287C22—2441no—
288C22C22×C22⋊D6111yescharacteristic
289C22#41×D6111yescharacteristic
290C22#41×D6111yescharacteristic
291C22C2×#1175822211yescharacteristic
292C22C2×#1175822211yescharacteristic
293C22#1451982311yescharacteristic
294C22#1451982411yescharacteristic
295C4—22no—
296C4—42no—
297C4—42no—
298C4—1222no—
299C4—2442no—
300C4—2442no—
301C4—2441no—
302C4—2441no—
303C4#1451976014yes—
304C2—42no—
305C2—2442no—
306C2C2×#1451976011yescharacteristic
307C2#1684026911yescharacteristic
308C2#1684034011yescharacteristic
309C2#1684045111yescharacteristic
310C2#1684045611yescharacteristic
311C2#1684047511yescharacteristic
312C2#1684048011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC2×#117×C61C2
hypercenterC2×#117D61
hypocenterC61#2485
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. #16839690C2semidirect
4. #16839658C2semidirect
5. #16839658C2semidirect
6. #16839653C2semidirect
7. #16839646C2semidirect
8. #16839622C2semidirect
9. #16839619C2semidirect
10. #16839619C2semidirect
11. C2×#117×C61C2semidirect
158. C2×#117D61semidirect
168. C61#2485semidirect