Finite Group Databasebeta

← #21450125

Subgroups — #21450125

Order 7808.

624 conjugacy classes of subgroups.

The subgroup lattice has 322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519762C212yesmaximal
2C2×C4×D244C211yesmaximal, characteristic
3C2×C4⋊C4×D61C211yesmaximal, characteristic, complemented
4#16839695C212yesmaximal, complemented
5#16839691C212yesmaximal, complemented
6#16839660C211yesmaximal, characteristic, complemented
7#16839624C212yesmaximal, complemented
8#16839619C211yesmaximal, characteristic, complemented
9#16839619C211yesmaximal, characteristic, complemented
10#16839619C211yesmaximal, characteristic, complemented
11C61×#389C211yesmaximal, characteristic, complemented
12C22×D244C2211yescharacteristic
13C22×C4×D61C2212yes—
14C22×C4×D61C2211yescharacteristic
15C22×C4×D61C2211yescharacteristic
16#14519762—28no—
17C4×D244—24no—
18C2×C4⋊Dic61C2211yescharacteristic
19C2×C4⋊Dic61C2211yescharacteristic
20C2×C4⋊Dic61C2211yescharacteristic
21C2×#11758196C2212yes—
22C2×#11758196C2212yes—
23C4⋊C4×D61—24no—
24C2×#11758198C2211yescharacteristic
25C2×#11758198C2212yes—
26C2×#11758198C2212yes—
27C2×#11758198C2211yescharacteristic
28C2×#11758198C2212yes—
29#14519684C2212yes—
30#14519684C2212yes—
31#14519684C2212yes—
32#14519684C2212yes—
33C2×C4⋊C4×C61C2212yes—
34C2×C4⋊C4×C61C2211yescharacteristic
35C2×C4⋊C4×C61C2211yescharacteristic
36C2×C42×C61C2211yescharacteristic
37#95×C61C2212yes—
38C23×D61C2311yescharacteristic
39C23×D61C2311yescharacteristic
40C22×C4×C61C2312yes—
41C22×C4×C61C2311yescharacteristic
42C22×C4×C61C2312yes—
43C22×C4×C61C2311yescharacteristic
44C22×C4×C61C2311yescharacteristic
45C22×Dic61C2311yescharacteristic
46C22×Dic61C2312yes—
47C22×Dic61C2312yes—
48C22×Dic61C2311yescharacteristic
49C2×D244—22no—
50C2×D244—22no—
51C2×D244D414yes—
52C2×C4×D61—22no—
53C2×C4×D61—22no—
54C2×C4×D61—24no—
55C2×C4×D61—24no—
56C2×C4×D61—24no—
57C2×C4×D61—22no—
58C2×C4×D61—22no—
59C2×C4×D61—22no—
60C2×C4×D61D414yes—
61C4⋊C4×C61—22no—
62C4⋊C4×C61—24no—
63C4⋊C4×C61—22no—
64C42×C61—22no—
65#11758198—22no—
66#11758198—24no—
67#11758198—24no—
68#11758198—24no—
69#11758198—22no—
70C4⋊Dic61—22no—
71C4⋊Dic61—22no—
72C4⋊Dic61—22no—
73#11758196—24no—
74#11758196—24no—
75C23×C61C2411yescharacteristic
76C22×D61—21no—
77C22×D61—21no—
78C22×D61—21no—
79C22×D61—21no—
80C22×D61—21no—
81C22×D61—21no—
82C22×D61—21no—
83C22×D61—21no—
84C22×D61—21no—
85C22×D61—21no—
86C22×D61C2×D412yes—
87C22×D61C2×D412yes—
88C22×D61C2×D412yes—
89C22×D61#4112yes—
90C2×C4×C61—21no—
91C2×C4×C61—21no—
92C2×C4×C61—22no—
93C2×C4×C61—21no—
94C2×C4×C61—22no—
95C2×C4×C61—22no—
96C2×C4×C61—22no—
97C2×C4×C61—22no—
98C2×C4×C61—21no—
99C2×C4×C61—21no—
100C2×C4×C61—22no—
101C2×C4×C61C2×D412yes—
102C2×C4×C61C2×D412yes—
103C2×C4×C61#4112yes—
104C2×C4×C61#4112yes—
105C2×Dic61—21no—
106C2×Dic61—21no—
107C2×Dic61—22no—
108C2×Dic61—22no—
109C2×Dic61—22no—
110C2×Dic61—21no—
111C2×Dic61—22no—
112C2×Dic61—22no—
113C2×Dic61—21no—
114C2×Dic61—21no—
115C2×Dic61—22no—
116C2×Dic61C2×D412yes—
117D244—28no—
118C4×D61—28no—
119C4×D61—48no—
120C4×D61—44no—
121C22×C61C22×D411yescharacteristic
122C22×C61C22×D411yescharacteristic
123C22×C61C2×#4111yescharacteristic
124C22×C61C2×#4111yescharacteristic
125C22×C61C2×#4111yescharacteristic
126C22×C612−1+411yescharacteristic
127C22×C612−1+411yescharacteristic
128C2×D61—22no—
129C2×D61—22no—
130C2×D61—22no—
131C2×D61—22no—
132C2×D61—22no—
133C2×D61—22no—
134C2×D61—22no—
135C2×D61—22no—
136C2×D61—22no—
137C2×D61—41no—
138C2×D61—41no—
139C2×D61—41no—
140C2×D61—41no—
141C2×D61#12114yes—
142C4×C61—22no—
143C4×C61—42no—
144C4×C61—41no—
145C4×C61—42no—
146C4×C61#12314yescomplemented
147Dic61—22no—
148Dic61—42no—
149Dic61—41no—
150Dic61—42no—
151#2486—611nomaximal, Sylow
152C2×C61C2×#12111yescharacteristic
153C2×C61C2×#12311yescharacteristic
154C2×C61#53611yescharacteristic
155C2×C61#54711yescharacteristic
156C2×C61#54711yescharacteristic
157C2×C61#55211yescharacteristic
158C2×C61#55211yescharacteristic
159D61—24no—
160D61—42no—
161C2×#123—612no—
162C2×C4×D4—611no—
163C22×C4⋊C4—611no—
164#398—612no—
165#397—612no—
166#389—611no—
167#389D6111yescharacteristic, complemented
168#381—612no—
169#380—611no—
170#380—611no—
171#380—611no—
172C61#248611yescharacteristic, complemented, Sylow
173C22×D4—611no—
174C23×C4—611no—
175C23×C4—612no—
176C23×C4—611no—
177#123—1228no—
178C4×D4—1224no—
179C2×C4⋊C4—611no—
180C2×C4⋊C4—612no—
181C2×C4⋊C4—611no—
182C2×C4⋊C4—612no—
183C2×C4⋊C4—611no—
184C2×C4⋊C4—1224no—
185C2×C4⋊C4C2×D6111yescharacteristic
186C2×C4⋊C4C2×D6112yes—
187C2×C4⋊C4C2×D6111yescharacteristic
188C2×C22⋊C4—611no—
189C2×C22⋊C4—611no—
190C2×C22⋊C4—612no—
191C2×C22⋊C4—612no—
192C2×C22⋊C4—612no—
193C2×C42C2×D6111yescharacteristic
194#95—612no—
195#95—612no—
196#95—612no—
197#95—612no—
198#95C2×D6112yes—
199C24—611no—
200C24—611no—
201C2×D4—614no—
202C2×D4—1222no—
203C2×D4—1222no—
204C22×C4—611no—
205C22×C4—614no—
206C22×C4—611no—
207C22×C4—612no—
208C22×C4—612no—
209C22×C4—1224no—
210C22×C4—1224no—
211C22×C4—1224no—
212C22×C4—1222no—
213C22×C4—1222no—
214C22×C4—1222no—
215C22×C4—1222no—
216C22×C4—1222no—
217C22×C4C22×D6111yescharacteristic
218C22×C4C22×D6112yes—
219C22×C4C22×D6112yes—
220C22×C4C22×D6111yescharacteristic
221C22×C4C22×D6111yescharacteristic
222C4⋊C4—22no—
223C4⋊C4—22no—
224C4⋊C4—24no—
225C4⋊C4—1224no—
226C4⋊C4—1222no—
227C4⋊C4—1222no—
228C4⋊C4—1224no—
229C4⋊C4—1222no—
230C22⋊C4—1222no—
231C22⋊C4—1222no—
232C22⋊C4—1224no—
233C22⋊C4—1224no—
234C22⋊C4—1224no—
235C42—22no—
236C23—612no—
237C23—612no—
238C23—612no—
239C23—612no—
240C23—1221no—
241C23—1221no—
242C23—1221no—
243C23—1221no—
244C23—1221no—
245C23—1221no—
246C23—1221no—
247C23—1221no—
248C23—1221no—
249C23—1221no—
250C23C23×D6111yescharacteristic
251D4—1228no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—22no—
256C2×C4—22no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—21no—
261C2×C4—22no—
262C2×C4—21no—
263C2×C4—612no—
264C2×C4—1221no—
265C2×C4—1221no—
266C2×C4—1228no—
267C2×C4—1222no—
268C2×C4—1222no—
269C2×C4—1221no—
270C2×C4—1222no—
271C2×C4—1222no—
272C2×C4—1221no—
273C2×C4—1222no—
274C2×C4—1221no—
275C2×C4—1222no—
276C2×C4—2448no—
277C2×C4—2444no—
278C2×C4#1175822212yes—
279C2×C4D4×D6112yes—
280C2×C4D4×D6112yes—
281C2×C4#1175822612yes—
282C22—614no—
283C22—1222no—
284C22—1222no—
285C22—1222no—
286C22—1222no—
287C22—1222no—
288C22—1222no—
289C22—1222no—
290C22—1222no—
291C22—1222no—
292C22—2441no—
293C22—2441no—
294C22—2441no—
295C22—2441no—
296C22C2×D4×D6111yescharacteristic
297C22C2×D4×D6111yescharacteristic
298C22#41×D6111yescharacteristic
299C22C2×#1175822211yescharacteristic
300C22C2×#1175822611yescharacteristic
301C22#1451982411yescharacteristic
302C22#1451982511yescharacteristic
303C4—22no—
304C4—42no—
305C4—41no—
306C4—42no—
307C4—1222no—
308C4—2442no—
309C4—2441no—
310C4—2442no—
311C4#1451976214yescomplemented
312C2—1224no—
313C2—2442no—
314C2#121×D6111yescharacteristic
315C2C2×#1451976211yescharacteristic
316C2#1684033511yescharacteristic
317C2#1684041511yescharacteristic
318C2#1684041711yescharacteristic
319C2#1684045011yescharacteristic
320C2#1684045311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#389C2
hypercenter#389D61
hypocenterC61#2486
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
3. C2×C4⋊C4×D61C2semidirect
4. #16839695C2semidirect
5. #16839691C2semidirect
6. #16839660C2semidirect
7. #16839624C2semidirect
8. #16839619C2semidirect
9. #16839619C2semidirect
10. #16839619C2semidirect
11. C61×#389C2semidirect
146. C4×C61#123semidirect
167. #389D61semidirect
172. C61#2486semidirect
311. C4#14519762semidirect