Finite Group Databasebeta

← #21457063

Subgroups — #21457063

Order 7808.

328 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
1#16840315C211yesmaximal, characteristic, complemented
2#16840298C211yesmaximal, characteristic
3#16840170C211yesmaximal, characteristic, complemented
4#16840169C211yesmaximal, characteristic, complemented
5#16840123C211yesmaximal, characteristic, complemented
6#16840123C211yesmaximal, characteristic, complemented
7#16840100C211yesmaximal, characteristic, complemented
8#16840087C211yesmaximal, characteristic
9#16840086C211yesmaximal, characteristic
10#16840071C211yesmaximal, characteristic, complemented
11#16840067C211yesmaximal, characteristic, complemented
12#16840065C211yesmaximal, characteristic, complemented
13#16840061C211yesmaximal, characteristic, complemented
14#16839816C211yesmaximal, characteristic, complemented
15C61×#485C211yesmaximal, characteristic, complemented
16#14519776C2211yescharacteristic
17#14519776C2211yescharacteristic
18#14519772—21no—
19#14519768C2211yescharacteristic
20#14519768C2211yescharacteristic
21#14519768C2211yescharacteristic
22#14519766C2211yescharacteristic
23#14519761—21no—
24#14519754—21no—
25#14519754—21no—
26#14519751C2211yescharacteristic
27Q8×Dic61C2211yescharacteristic
28C4×Dic122—21no—
29C4×Dic122—21no—
30#14519739C2211yescharacteristic
31#14519737—21no—
32#14519736C2211yescharacteristic
33#14519735—21no—
34C2×C4×Dic61C2211yescharacteristic
35#14519711C2211yescharacteristic
36#14519710C2211yescharacteristic
37#14519710C2211yescharacteristic
38#14519709C2211yescharacteristic
39#14519708C2211yescharacteristic
40#14519708C2211yescharacteristic
41#14519706C2211yescharacteristic
42#14519706C2211yescharacteristic
43#14519701C2211yescharacteristic
44#14519701C2211yescharacteristic
45#14519699C2211yescharacteristic
46#14519699C2211yescharacteristic
47#14519697C2211yescharacteristic
48#14519697C2211yescharacteristic
49C22⋊#92418C2211yescharacteristic
50#14519687C2211yescharacteristic
51#14519687C2211yescharacteristic
52C22⋊Q8×C61C2211yescharacteristic
53#117×C61C2211yescharacteristic
54#107×C61C2211yescharacteristic
55#106×C61C2211yescharacteristic
56#103×C61C2211yescharacteristic
57#103×C61C2211yescharacteristic
58C22⋊C8×C61C2211yescharacteristic
59C2×Q8×C61C2311yescharacteristic
60C22×C4×C61C2311yescharacteristic
61C2×C22⋊D61—21no—
62C22×Dic61D411yescharacteristic
63C22×Dic61D411yescharacteristic
64C2×D244C2311yescharacteristic
65C2×C4×D61—21no—
66C2×Dic122—21no—
67C2×Dic122—21no—
68C2×C8×C61C2311yescharacteristic
69C2×C8×C61C2311yescharacteristic
70C4⋊C4×C61—21no—
71C4⋊C4×C61C2311yescharacteristic
72C4⋊C4×C61C2311yescharacteristic
73C4⋊C4×C61C2311yescharacteristic
74C22⋊C4×C61—21no—
75C22⋊C4×C61—21no—
76C42×C61—21no—
77C22⋊Dic61—21no—
78#11758198—21no—
79#11758198—21no—
80#11758198—21no—
81#11758198—21no—
82C4⋊Dic61—21no—
83C4⋊Dic61—21no—
84C4⋊Dic61—21no—
85C4⋊Dic61—21no—
86C4⋊Dic61C2311yescharacteristic
87C4⋊Dic61C2311yescharacteristic
88C4⋊Dic61C2311yescharacteristic
89#11758196—21no—
90#11758196—21no—
91#11758196—21no—
92#11758196—21no—
93#11758196—21no—
94C4×Dic61—21no—
95C4×Dic61—21no—
96C4×Dic61D411yescharacteristic
97C4×Dic61D411yescharacteristic
98C4×Dic61C2311yescharacteristic
99C4×Dic61C2311yescharacteristic
100C2×#92418C2311yescharacteristic
101C2×#92418C2311yescharacteristic
102C23×C61C2×D411yescharacteristic
103C22×D61—21no—
104Q8×C61—21no—
105Q8×C61—21no—
106C2×C4×C61—21no—
107C2×C4×C61—21no—
108C2×C4×C61—21no—
109C2×C4×C61—21no—
110C2×C4×C61—21no—
111C2×C4×C61—21no—
112C2×C4×C61C2×D411yescharacteristic
113C2×C4×C61C2411yescharacteristic
114C22⋊D61—42no—
115C2×Dic61—21no—
116C2×Dic61—21no—
117C2×Dic61—21no—
118C2×Dic61—41no—
119C2×Dic61—41no—
120C2×Dic61C2×D411yescharacteristic
121C2×Dic61C2×D411yescharacteristic
122C2×Dic61C2×D411yescharacteristic
123C2×Dic61C2×D411yescharacteristic
124D244—21no—
125D244—21no—
126C4×D61—42no—
127Dic122—42no—
128Dic122—42no—
129C8×C61—21no—
130C8×C61—21no—
131#92418—21no—
132#92418—21no—
133C22×C61—21no—
134C22×C61—21no—
135C22×C61—21no—
136C22×C61C22×D411yescharacteristic
137C2×D61—41no—
138C2×D61—41no—
139C2×D61—41no—
140C4×C61—21no—
141C4×C61—41no—
142C4×C61—41no—
143C4×C61—41no—
144C4×C61—41no—
145C4×C612−1+411yescharacteristic
146C4×C612−1+411yescharacteristic
147Dic61—21no—
148Dic61—21no—
149Dic61—21no—
150Dic61—21no—
151Dic61—41no—
152Dic61—41no—
153Dic61—41no—
154#3240—611nomaximal, Sylow
155C2×C61—41no—
156C2×C61#53611yescharacteristic
157C2×C61#57511yescharacteristic
158C2×C61#57511yescharacteristic
159D61—81no—
160#533—611no—
161#529—611no—
162#501—611no—
163#501—611no—
164#489—611no—
165#489—611no—
166#485—611no—
167#485D6111yescharacteristic, complemented
168#482—611no—
169#482—611no—
170#479—611no—
171#479—611no—
172#478—611no—
173#478—611no—
174#432—611no—
175C61#324011yescharacteristic, complemented, Sylow
176C4⋊Q8—611no—
177C4⋊Q8—611no—
178#126—1221no—
179#125—611no—
180#125—611no—
181#125—611no—
182#124—611no—
183#123—1221no—
184C22⋊Q8—1221no—
185C22⋊Q8—1221no—
186C22⋊Q8C2×D6111yescharacteristic
187#121—611no—
188C4×Q8—611no—
189C4×Q8—1221no—
190C4×Q8—1221no—
191C4×D4—611no—
192C4×D4—1221no—
193#117—611no—
194#117—1221no—
195#117C2×D6111yescharacteristic
196C2×C42—611no—
197#107—611no—
198#107—611no—
199#107—611no—
200#107C2×D6111yescharacteristic
201#106—611no—
202#106—611no—
203#106—611no—
204#106C2×D6111yescharacteristic
205C4⋊C8—611no—
206C4⋊C8—611no—
207#103—611no—
208#103—611no—
209#103C2×D6111yescharacteristic
210#103C2×D6111yescharacteristic
211#102—611no—
212#102—611no—
213#102—611no—
214#102—611no—
215C22⋊C8—611no—
216C22⋊C8C2×D6111yescharacteristic
217#97—611no—
218#97—611no—
219C2×Q8—1221no—
220C2×Q8—1221no—
221C2×Q8C22×D6111yescharacteristic
222C2×D4—611no—
223C2×D4—1221no—
224C22×C4—611no—
225C22×C4—611no—
226C22×C4—1221no—
227C22×C4C22×D6111yescharacteristic
228C2×C8—611no—
229C2×C8—611no—
230C2×C8C22×D6111yescharacteristic
231C2×C8C22×D6111yescharacteristic
232C4⋊C4—21no—
233C4⋊C4—611no—
234C4⋊C4—611no—
235C4⋊C4—611no—
236C4⋊C4—1221no—
237C4⋊C4—1221no—
238C4⋊C4—1221no—
239C4⋊C4—1221no—
240C4⋊C4—1221no—
241C4⋊C4—1221no—
242C4⋊C4—1221no—
243C4⋊C4—1221no—
244C4⋊C4—1221no—
245C4⋊C4C22×D6111yescharacteristic
246C4⋊C4C22×D6111yescharacteristic
247C4⋊C4C22×D6111yescharacteristic
248C22⋊C4—21no—
249C22⋊C4—21no—
250C22⋊C4—1221no—
251C22⋊C4—1221no—
252C22⋊C4—1221no—
253C22⋊C4—1221no—
254C22⋊C4—1221no—
255C42—21no—
256C42—611no—
257C42—611no—
258C42—611no—
259C42—611no—
260C42—1221no—
261C42—1221no—
262C23—1221no—
263C23D4×D6111yescharacteristic
264Q8—21no—
265Q8—21no—
266Q8—2442no—
267Q8—2442no—
268D4—1221no—
269D4—1221no—
270D4—2442no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—611no—
278C2×C4—611no—
279C2×C4—611no—
280C2×C4—611no—
281C2×C4—1221no—
282C2×C4—1221no—
283C2×C4—1221no—
284C2×C4—2442no—
285C2×C4—2441no—
286C2×C4—2441no—
287C2×C4D4×D6111yescharacteristic
288C2×C4C23×D6111yescharacteristic
289C8—21no—
290C8—21no—
291C8—1221no—
292C8—1221no—
293C22—21no—
294C22—21no—
295C22—21no—
296C22—2441no—
297C22—2441no—
298C22—2441no—
299C22C2×D4×D6111yescharacteristic
300C4—21no—
301C4—41no—
302C4—41no—
303C4—41no—
304C4—41no—
305C4—1221no—
306C4—1221no—
307C4—1221no—
308C4—1221no—
309C4—2441no—
310C4—2441no—
311C4—2441no—
312C4#1451982411yescharacteristic
313C4#1451982411yescharacteristic
314C2—41no—
315C2—4881no—
316C2#1684033411yescharacteristic
317C2#1684055911yescharacteristic
318C2#1684056111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#485C2
socleC22×C61C22×D4
hypercenter#485D61
hypocenterC61#3240
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
1. #16840315C2semidirect
3. #16840170C2semidirect
4. #16840169C2semidirect
5. #16840123C2semidirect
6. #16840123C2semidirect
7. #16840100C2semidirect
10. #16840071C2semidirect
11. #16840067C2semidirect
12. #16840065C2semidirect
13. #16840061C2semidirect
14. #16839816C2semidirect
15. C61×#485C2semidirect
167. #485D61semidirect
175. C61#3240semidirect