Finite Group Databasebeta

← #21450132

Subgroups — #21450132

Order 7808.

584 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C22⋊D61C211yesmaximal, characteristic
2C2×C4⋊C4×D61C211yesmaximal, characteristic, complemented
3#16839703C212yesmaximal, complemented
4#16839698C212yesmaximal, complemented
5#16839661C211yesmaximal, characteristic, complemented
6#16839658C211yesmaximal, characteristic, complemented
7#16839638C212yesmaximal
8#16839636C212yesmaximal, complemented
9#16839622C211yesmaximal, characteristic, complemented
10#16839619C211yesmaximal, characteristic, complemented
11C61×#380C211yesmaximal, characteristic, complemented
12C22×C22⋊D61C2211yescharacteristic
13C22×C4×D61C2211yescharacteristic
14C22×C4×D61C2212yes—
15C4×C22⋊D61—24no—
16C2×C4⋊Dic61C2211yescharacteristic
17C2×C4⋊Dic61C2211yescharacteristic
18C2×C4⋊Dic61C2212yes—
19C2×#11758196C2212yes—
20C2×#11758196C2211yescharacteristic
21C2×#11758196C2212yes—
22C4⋊C4×D61—24no—
23C2×C22⋊Dic61C2211yescharacteristic
24C2×C22⋊Dic61C2212yes—
25C2×#11758198C2211yescharacteristic
26C2×#11758198C2212yes—
27C2×C4×Dic61C2211yescharacteristic
28#14519684C2212yes—
29#14519684C2212yes—
30#14519684C2212yes—
31#14519684C2212yes—
32C23×C4×C61C2211yescharacteristic
33C2×C4⋊C4×C61C2211yescharacteristic
34C2×C4⋊C4×C61C2211yescharacteristic
35C2×C22⋊C4×C61C2212yes—
36#95×C61C2212yes—
37C24×C61C2311yescharacteristic
38C23×D61C2311yescharacteristic
39C22×C4×C61—22no—
40C22×C4×C61—22no—
41C22×C4×C61—22no—
42C22×C4×C61C2312yes—
43C22×C4×C61C2311yescharacteristic
44C22×C4×C61C2312yes—
45C22×C4×C61C2311yescharacteristic
46C2×C22⋊D61—22no—
47C2×C22⋊D61—22no—
48C2×C22⋊D61Q814yes—
49C22×Dic61C2312yes—
50C22×Dic61C2312yes—
51C22×Dic61C2311yescharacteristic
52C22×Dic61C2311yescharacteristic
53C22×Dic61C2311yescharacteristic
54C2×C4×D61—22no—
55C2×C4×D61—22no—
56C2×C4×D61—24no—
57C2×C4×D61—42no—
58C2×C4×D61—42no—
59C2×C4×D61D414yes—
60C4⋊C4×C61—22no—
61C4⋊C4×C61—22no—
62C22⋊C4×C61—42no—
63C22⋊Dic61—22no—
64C22⋊Dic61—42no—
65#11758198—22no—
66#11758198—24no—
67C4⋊Dic61—22no—
68C4⋊Dic61—22no—
69C4⋊Dic61—42no—
70#11758196—24no—
71#11758196—22no—
72#11758196—42no—
73C4×Dic61—22no—
74C23×C61—21no—
75C23×C61—21no—
76C23×C61—21no—
77C23×C61—21no—
78C23×C61—21no—
79C23×C61—21no—
80C23×C61C2×Q812yes—
81C23×C61C2411yescharacteristic
82C22×D61—21no—
83C22×D61—21no—
84C22×D61—21no—
85C22×D61—21no—
86C22×D61C2×D412yes—
87C22×D61C2×Q812yes—
88C22×D61#4112yes—
89C2×C4×C61—21no—
90C2×C4×C61—22no—
91C2×C4×C61—22no—
92C2×C4×C61—22no—
93C2×C4×C61—21no—
94C2×C4×C61—21no—
95C2×C4×C61—22no—
96C2×C4×C61—22no—
97C2×C4×C61—22no—
98C2×C4×C61—44no—
99C2×C4×C61C2×D412yes—
100C2×C4×C61#4112yes—
101C2×C4×C61#4112yes—
102C22⋊D61—28no—
103C2×Dic61—21no—
104C2×Dic61—21no—
105C2×Dic61—21no—
106C2×Dic61—21no—
107C2×Dic61—21no—
108C2×Dic61—22no—
109C2×Dic61—22no—
110C2×Dic61—22no—
111C2×Dic61—21no—
112C2×Dic61—22no—
113C2×Dic61—21no—
114C2×Dic61—22no—
115C2×Dic61—22no—
116C2×Dic61C2×D412yes—
117C2×Dic61C2×Q812yes—
118C4×D61—28no—
119C4×D61—48no—
120C22×C61—22no—
121C22×C61—22no—
122C22×C61—22no—
123C22×C61—41no—
124C22×C61—41no—
125C22×C61—41no—
126C22×C61—41no—
127C22×C61C22×D411yescharacteristic
128C22×C61C22×Q811yescharacteristic
129C22×C61C2×#4111yescharacteristic
130C22×C61C2×#4111yescharacteristic
131C22×C61C2×#4111yescharacteristic
132C22×C61H(5,𝔽2)11yescharacteristic
133C22×C61H(5,𝔽2)11yescharacteristic
134C2×D61—22no—
135C2×D61—22no—
136C2×D61—22no—
137C2×D61—22no—
138C2×D61—22no—
139C2×D61—22no—
140C2×D61C22⋊Q814yes—
141C4×C61—41no—
142C4×C61—42no—
143C4×C61—42no—
144C4×C61#12314yes—
145Dic61—22no—
146Dic61—22no—
147Dic61—42no—
148Dic61—41no—
149Dic61—42no—
150#2487—611nomaximal, Sylow
151C2×C61—42no—
152C2×C61C2×C22⋊Q811yescharacteristic
153C2×C61C2×#12311yescharacteristic
154C2×C61#53511yescharacteristic
155C2×C61#55311yescharacteristic
156C2×C61#55311yescharacteristic
157C2×C61#55411yescharacteristic
158C2×C61#55411yescharacteristic
159D61—24no—
160C2×C4×D4—611no—
161C22×C4⋊C4—611no—
162#400—612no—
163#399—612no—
164#389—611no—
165#389—611no—
166#386—612no—
167#385—612no—
168#380—611no—
169#380—611no—
170#380D6111yescharacteristic, complemented
171C61#248711yescharacteristic, complemented, Sylow
172C22×D4—611no—
173C23×C4—611no—
174C23×C4—612no—
175C23×C4C2×D6111yescharacteristic
176C4×D4—1224no—
177C2×C4⋊C4—611no—
178C2×C4⋊C4—612no—
179C2×C4⋊C4—611no—
180C2×C4⋊C4—611no—
181C2×C4⋊C4—612no—
182C2×C4⋊C4—612no—
183C2×C4⋊C4—1224no—
184C2×C4⋊C4C2×D6111yescharacteristic
185C2×C4⋊C4C2×D6111yescharacteristic
186C2×C22⋊C4—611no—
187C2×C22⋊C4—611no—
188C2×C22⋊C4—612no—
189C2×C22⋊C4—612no—
190C2×C22⋊C4C2×D6112yes—
191C2×C42—611no—
192#95—612no—
193#95—612no—
194#95—612no—
195#95—612no—
196#95C2×D6112yes—
197C24—611no—
198C24C22×D6111yescharacteristic
199C2×D4—614no—
200C2×D4—1222no—
201C2×D4—1222no—
202C22×C4—22no—
203C22×C4—22no—
204C22×C4—22no—
205C22×C4—611no—
206C22×C4—611no—
207C22×C4—614no—
208C22×C4—612no—
209C22×C4—612no—
210C22×C4—611no—
211C22×C4—1224no—
212C22×C4—1222no—
213C22×C4—1222no—
214C22×C4—2442no—
215C22×C4—2442no—
216C22×C4C22×D6111yescharacteristic
217C22×C4C22×D6112yes—
218C22×C4C22×D6112yes—
219C22×C4C22×D6111yescharacteristic
220C4⋊C4—22no—
221C4⋊C4—22no—
222C4⋊C4—1224no—
223C4⋊C4—1222no—
224C4⋊C4—1222no—
225C4⋊C4—1222no—
226C4⋊C4—2442no—
227C4⋊C4—2442no—
228C22⋊C4—42no—
229C22⋊C4—1222no—
230C22⋊C4—1224no—
231C22⋊C4—1222no—
232C22⋊C4—2442no—
233C42—1222no—
234C23—21no—
235C23—21no—
236C23—21no—
237C23—21no—
238C23—21no—
239C23—21no—
240C23—612no—
241C23—612no—
242C23—612no—
243C23—1221no—
244C23—1221no—
245C23—1221no—
246C23—1221no—
247C23Q8×D6112yes—
248C23C23×D6111yescharacteristic
249D4—1228no—
250C2×C4—21no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—22no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—44no—
260C2×C4—612no—
261C2×C4—612no—
262C2×C4—1221no—
263C2×C4—1221no—
264C2×C4—1221no—
265C2×C4—1221no—
266C2×C4—1228no—
267C2×C4—1221no—
268C2×C4—1222no—
269C2×C4—1222no—
270C2×C4—1222no—
271C2×C4—1221no—
272C2×C4—1222no—
273C2×C4—1222no—
274C2×C4—1222no—
275C2×C4—1221no—
276C2×C4—2448no—
277C2×C4#1175822212yes—
278C2×C4D4×D6112yes—
279C2×C4#1175822412yes—
280C22—22no—
281C22—22no—
282C22—22no—
283C22—41no—
284C22—41no—
285C22—41no—
286C22—41no—
287C22—614no—
288C22—1222no—
289C22—1222no—
290C22—1222no—
291C22—1222no—
292C22—1222no—
293C22—1222no—
294C22C2×D4×D6111yescharacteristic
295C22C2×Q8×D6111yescharacteristic
296C22#41×D6111yescharacteristic
297C22C2×#1175822411yescharacteristic
298C22C2×#1175822211yescharacteristic
299C22#1451982211yescharacteristic
300C22#1451982311yescharacteristic
301C4—42no—
302C4—41no—
303C4—42no—
304C4—1222no—
305C4—1222no—
306C4—2442no—
307C4—2441no—
308C4—2442no—
309C4#1451975914yes—
310C2—42no—
311C2—1224no—
312C2C22⋊Q8×D6111yescharacteristic
313C2C2×#1451975911yescharacteristic
314C2#1684032811yescharacteristic
315C2#1684045611yescharacteristic
316C2#1684045911yescharacteristic
317C2#1684046711yescharacteristic
318C2#1684047011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#380C2
hypercenter#380D61
hypocenterC61#2487
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #380

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×D61C2semidirect
3. #16839703C2semidirect
4. #16839698C2semidirect
5. #16839661C2semidirect
6. #16839658C2semidirect
8. #16839636C2semidirect
9. #16839622C2semidirect
10. #16839619C2semidirect
11. C61×#380C2semidirect
170. #380D61semidirect
171. C61#2487semidirect