Finite Group Databasebeta

← #21456991

Subgroups — #21456991

Order 7808.

334 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#16840299C211yesmaximal, characteristic
2#125×D61C211yesmaximal, characteristic, complemented
3#16840163C211yesmaximal, characteristic, complemented
4#16840162C211yesmaximal, characteristic, complemented
5#16840118C211yesmaximal, characteristic, complemented
6#16840118C211yesmaximal, characteristic, complemented
7#16840096C211yesmaximal, characteristic, complemented
8#16840091C211yesmaximal, characteristic, complemented
9#16840082C211yesmaximal, characteristic
10#16840077C211yesmaximal, characteristic
11#16840069C211yesmaximal, characteristic, complemented
12#16840063C211yesmaximal, characteristic, complemented
13#16840059C211yesmaximal, characteristic, complemented
14#16839814C211yesmaximal, characteristic, complemented
15C61×#479C211yesmaximal, characteristic, complemented
16#14519772—21no—
17#14519769C2211yescharacteristic
18#14519768C2211yescharacteristic
19#14519768C2211yescharacteristic
20#14519768C2211yescharacteristic
21#14519767—21no—
22#14519767—21no—
23#14519766C2211yescharacteristic
24#14519762—21no—
25#14519753C2211yescharacteristic
26#14519752C2211yescharacteristic
27C4×D244—21no—
28C4×D244C2211yescharacteristic
29#14519734—21no—
30C4⋊C4×D61—21no—
31C4⋊C4×D61—21no—
32C4⋊C4×D61C2211yescharacteristic
33C4⋊C4×D61C2211yescharacteristic
34C42×D61C2211yescharacteristic
35#14519711C2211yescharacteristic
36#14519710C2211yescharacteristic
37#14519710C2211yescharacteristic
38#14519709C2211yescharacteristic
39#14519708C2211yescharacteristic
40#14519708C2211yescharacteristic
41C4⋊#92418C2211yescharacteristic
42#14519701C2211yescharacteristic
43#14519701C2211yescharacteristic
44#14519699C2211yescharacteristic
45#14519699C2211yescharacteristic
46#14519697C2211yescharacteristic
47#14519697C2211yescharacteristic
48#14519689C2211yescharacteristic
49#14519689C2211yescharacteristic
50C8×Dic61C2211yescharacteristic
51C8×Dic61C2211yescharacteristic
52#125×C61C2211yescharacteristic
53C4×Q8×C61C2211yescharacteristic
54#107×C61C2211yescharacteristic
55#106×C61C2211yescharacteristic
56C4⋊C8×C61C2211yescharacteristic
57#103×C61C2211yescharacteristic
58#103×C61C2211yescharacteristic
59C2×Q8×C61C2311yescharacteristic
60C2×D244—21no—
61C2×D244C2311yescharacteristic
62C2×C4×D61—21no—
63C2×C4×D61—21no—
64C2×C4×D61—21no—
65C2×C4×D61D411yescharacteristic
66C2×C4×D61D411yescharacteristic
67C2×C4×D61C2311yescharacteristic
68C2×C8×C61C2311yescharacteristic
69C2×C8×C61C2311yescharacteristic
70C4⋊C4×C61—21no—
71C4⋊C4×C61—21no—
72C4⋊C4×C61—21no—
73C4⋊C4×C61C2311yescharacteristic
74C4⋊C4×C61C2311yescharacteristic
75C4⋊C4×C61C2311yescharacteristic
76C42×C61—21no—
77C42×C61C2311yescharacteristic
78#11758198—21no—
79#11758198—21no—
80#11758198—21no—
81#11758198—21no—
82#11758198—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—
94#11758196—21no—
95#11758196—21no—
96#11758196—21no—
97C4×Dic61D411yescharacteristic
98C4×Dic61D411yescharacteristic
99C4×Dic61C2311yescharacteristic
100C2×#92418C2311yescharacteristic
101C2×#92418C2311yescharacteristic
102C22×D61—21no—
103C22×D61C2×D411yescharacteristic
104Q8×C61—21no—
105Q8×C61—21no—
106C2×C4×C61—21no—
107C2×C4×C61—21no—
108C2×C4×C61—21no—
109C2×C4×C61—21no—
110C2×C4×C61C2×D411yescharacteristic
111C2×C4×C61C2×D411yescharacteristic
112C2×C4×C61C2411yescharacteristic
113C2×Dic61—21no—
114C2×Dic61—21no—
115C2×Dic61—21no—
116C2×Dic61C2×D411yescharacteristic
117C2×Dic61C2×D411yescharacteristic
118C2×Dic61C2×D411yescharacteristic
119D244—21no—
120D244—21no—
121D244—42no—
122C4×D61—22no—
123C4×D61—21no—
124C4×D61—21no—
125C4×D61—41no—
126C4×D61—42no—
127C4×D61—42no—
128C4×D61—42no—
129C8×C61—21no—
130C8×C61—21no—
131#92418—21no—
132#92418—21no—
133C22×C61C22×D411yescharacteristic
134C2×D61—21no—
135C2×D61—21no—
136C2×D61—41no—
137C2×D61—41no—
138C2×D61—41no—
139C2×D61#13512yes—
140C4×C61—21no—
141C4×C61—21no—
142C4×C61—41no—
143C4×C61—41no—
144C4×C61—41no—
145C4×C61—41no—
146C4×C612−1+411yescharacteristic
147C4×C612−1+411yescharacteristic
148Dic61—21no—
149Dic61—21no—
150Dic61—21no—
151Dic61—41no—
152Dic61—41no—
153Dic61—41no—
154#3232—611nomaximal, Sylow
155C2×C61#53611yescharacteristic
156C2×C61C2×#13511yescharacteristic
157C2×C61#57511yescharacteristic
158D61—22no—
159D61—81no—
160#529—611no—
161C2×#125—611no—
162#499—611no—
163#499—611no—
164#488—611no—
165#488—611no—
166#484—611no—
167#483—611no—
168#481—611no—
169#480—611no—
170#479—611no—
171#479D6111yescharacteristic, complemented
172#478—611no—
173#478—611no—
174#431—611no—
175C61#323211yescharacteristic, complemented, Sylow
176#126—1221no—
177#125—611no—
178#125—611no—
179#125—611no—
180#125—611no—
181#125—1221no—
182#125—1221no—
183#125C2×D6111yescharacteristic
184#124—611no—
185#123—1221no—
186C22⋊Q8—611no—
187#121—611no—
188C4×Q8C2×D6111yescharacteristic
189C4×D4—611no—
190C4×D4—1221no—
191#117—1221no—
192C2×C4⋊C4—611no—
193C2×C4⋊C4—611no—
194C2×C4⋊C4—1221no—
195C2×C4⋊C4—1221no—
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⋊C8C2×D6111yescharacteristic
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⋊C8—611no—
217C4×C8—611no—
218C4×C8—611no—
219C2×Q8C22×D6111yescharacteristic
220C2×D4—611no—
221C2×D4—1221no—
222C22×C4—611no—
223C22×C4—611no—
224C22×C4—611no—
225C22×C4—1221no—
226C22×C4—1221no—
227C22×C4—1221no—
228C2×C8—611no—
229C2×C8—611no—
230C2×C8C22×D6111yescharacteristic
231C2×C8C22×D6111yescharacteristic
232C4⋊C4—21no—
233C4⋊C4—21no—
234C4⋊C4—21no—
235C4⋊C4—611no—
236C4⋊C4—611no—
237C4⋊C4—611no—
238C4⋊C4—1221no—
239C4⋊C4—1221no—
240C4⋊C4—1221no—
241C4⋊C4—1221no—
242C4⋊C4—1221no—
243C4⋊C4—1221no—
244C4⋊C4—1221no—
245C4⋊C4—1221no—
246C4⋊C4—1221no—
247C4⋊C4—1221no—
248C4⋊C4—1221no—
249C4⋊C4C22×D6111yescharacteristic
250C4⋊C4C22×D6111yescharacteristic
251C4⋊C4C22×D6111yescharacteristic
252C22⋊C4—1221no—
253C22⋊C4—1221no—
254C22⋊C4—1221no—
255C22⋊C4—1221no—
256C22⋊C4—1221no—
257C42—21no—
258C42—611no—
259C42—611no—
260C42—611no—
261C42C22×D6111yescharacteristic
262C23—611no—
263C23—1221no—
264Q8—21no—
265Q8—21no—
266D4—1221no—
267D4—1221no—
268D4—2442no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—611no—
274C2×C4—611no—
275C2×C4—611no—
276C2×C4—1222no—
277C2×C4—1221no—
278C2×C4—1221no—
279C2×C4—1221no—
280C2×C4—1221no—
281C2×C4—1221no—
282C2×C4—2441no—
283C2×C4—2442no—
284C2×C4—2442no—
285C2×C4—2442no—
286C2×C4D4×D6111yescharacteristic
287C2×C4D4×D6111yescharacteristic
288C2×C4C23×D6111yescharacteristic
289C8—21no—
290C8—21no—
291C8—1221no—
292C8—1221no—
293C22—612no—
294C22—1221no—
295C22—1221no—
296C22—2441no—
297C22—2441no—
298C22—2441no—
299C22C2×D4×D6111yescharacteristic
300C4—21no—
301C4—21no—
302C4—41no—
303C4—41no—
304C4—41no—
305C4—41no—
306C4—1221no—
307C4—1221no—
308C4—1221no—
309C4—2441no—
310C4—2441no—
311C4—2441no—
312C4#1451982411yescharacteristic
313C4#1451982511yescharacteristic
314C2—1222no—
315C2—4881no—
316C2#1684033511yescharacteristic
317C2#135×D6111yescharacteristic
318C2#1684056111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#479C2
socleC22×C61C22×D4
hypercenter#479D61
hypocenterC61#3232
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
2. #125×D61C2semidirect
3. #16840163C2semidirect
4. #16840162C2semidirect
5. #16840118C2semidirect
6. #16840118C2semidirect
7. #16840096C2semidirect
8. #16840091C2semidirect
11. #16840069C2semidirect
12. #16840063C2semidirect
13. #16840059C2semidirect
14. #16839814C2semidirect
15. C61×#479C2semidirect
171. #479D61semidirect
175. C61#3232semidirect