Finite Group Databasebeta

← #21457080

Subgroups — #21457080

Order 7808.

308 conjugacy classes of subgroups.

The subgroup lattice has 308 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840389C211yesmaximal, characteristic
2#16840373C211yesmaximal, characteristic
3#16840168C211yesmaximal, characteristic, complemented
4#16840164C211yesmaximal, characteristic, complemented
5#16840130C211yesmaximal, characteristic, complemented
6#16840102C211yesmaximal, characteristic
7#16840101C211yesmaximal, characteristic
8#16840096C211yesmaximal, characteristic
9#16840091C211yesmaximal, characteristic
10#16840071C211yesmaximal, characteristic, complemented
11#16840067C211yesmaximal, characteristic, complemented
12#16840055C211yesmaximal, characteristic, complemented
13#16840045C211yesmaximal, characteristic, complemented
14#16839821C211yesmaximal, characteristic
15C61×#487C211yesmaximal, characteristic, complemented
16#14519776C2211yescharacteristic
17#14519775—21no—
18#14519772—21no—
19#14519772—21no—
20#14519769C2211yescharacteristic
21#14519769C2211yescharacteristic
22#14519768C2211yescharacteristic
23#14519767—21no—
24#14519767—21no—
25#14519767—21no—
26#14519755—21no—
27#14519753—21no—
28#14519753C2211yescharacteristic
29#14519753C2211yescharacteristic
30Q8×Dic61C2211yescharacteristic
31Q8×Dic61C2211yescharacteristic
32#14519735C2211yescharacteristic
33#14519734C2211yescharacteristic
34C4⋊C4×D61C2211yescharacteristic
35#14519711C2211yescharacteristic
36#14519711C2211yescharacteristic
37#14519710C2211yescharacteristic
38#14519710C2211yescharacteristic
39#14519709C2211yescharacteristic
40#14519709C2211yescharacteristic
41#14519708C2211yescharacteristic
42#14519708C2211yescharacteristic
43#14519706C2211yescharacteristic
44#14519706C2211yescharacteristic
45#14519701C2211yescharacteristic
46#14519701C2211yescharacteristic
47#14519701C2211yescharacteristic
48#14519701C2211yescharacteristic
49#14519689C2211yescharacteristic
50#14519689C2211yescharacteristic
51#14519688C2211yescharacteristic
52C4⋊Q8×C61C2211yescharacteristic
53C4⋊Q8×C61C2211yescharacteristic
54#103×C61C2211yescharacteristic
55#103×C61C2211yescharacteristic
56#103×C61C2211yescharacteristic
57#103×C61C2211yescharacteristic
58C4×C8×C61C2211yescharacteristic
59C2×Q8×C61—21no—
60C2×Q8×C61C2311yescharacteristic
61C2×Q8×C61C2311yescharacteristic
62C2×C4×D61—21no—
63C2×C4×D61C2311yescharacteristic
64C2×Dic122—21no—
65C2×C8×C61C2311yescharacteristic
66C2×C8×C61C2311yescharacteristic
67C4⋊C4×C61—21no—
68C4⋊C4×C61—21no—
69C4⋊C4×C61—21no—
70C4⋊C4×C61C2311yescharacteristic
71C4⋊C4×C61C2311yescharacteristic
72C42×C61C2311yescharacteristic
73#11758198—21no—
74#11758198—21no—
75#11758198—21no—
76#11758198D411yescharacteristic
77#11758198D411yescharacteristic
78C4⋊Dic61—21no—
79C4⋊Dic61—21no—
80C4⋊Dic61—21no—
81C4⋊Dic61C2311yescharacteristic
82C4⋊Dic61C2311yescharacteristic
83C4⋊Dic61C2311yescharacteristic
84C4⋊Dic61C2311yescharacteristic
85#11758196—21no—
86#11758196—21no—
87#11758196—21no—
88#11758196—21no—
89#11758196—21no—
90#11758196—21no—
91#11758196—21no—
92#11758196—21no—
93#11758196—21no—
94#11758196D411yescharacteristic
95#11758196D411yescharacteristic
96C4×Dic61—21no—
97C4×Dic61—21no—
98C4×Dic61—21no—
99C4×Dic61C2311yescharacteristic
100C2×#92418C2311yescharacteristic
101C2×#92418C2311yescharacteristic
102C22×D61C2×D411yescharacteristic
103Q8×C61—21no—
104Q8×C61—21no—
105Q8×C61—21no—
106Q8×C61—21no—
107Q8×C61—81no—
108C2×C4×C61—21no—
109C2×C4×C61—21no—
110C2×C4×C61—21no—
111C2×C4×C61—21no—
112C2×C4×C61C2×D411yescharacteristic
113C2×C4×C61C2×D411yescharacteristic
114C2×C4×C61C2411yescharacteristic
115C2×Dic61—21no—
116C2×Dic61—21no—
117C2×Dic61—21no—
118C2×Dic61—21no—
119C2×Dic61C2×D411yescharacteristic
120C2×Dic61C2×D411yescharacteristic
121C2×Dic61C2×D411yescharacteristic
122C4×D61—21no—
123C4×D61—21no—
124C4×D61—81no—
125Dic122—81no—
126C8×C61—21no—
127C8×C61—21no—
128#92418—21no—
129#92418—21no—
130C22×C61C22×D411yescharacteristic
131C2×D61—21no—
132C2×D61—21no—
133C2×D61—21no—
134C4×C61—21no—
135C4×C61—21no—
136C4×C61—41no—
137C4×C61—41no—
138C4×C61—41no—
139C4×C61—41no—
140C4×C612−1+411yescharacteristic
141C4×C612−1+411yescharacteristic
142Dic61—21no—
143Dic61—21no—
144Dic61—21no—
145Dic61—41no—
146Dic61—41no—
147Dic61—41no—
148Dic61—41no—
149#3242—611nomaximal, Sylow
150C2×C61#53611yescharacteristic
151C2×C61#57711yescharacteristic
152C2×C61#57811yescharacteristic
153D61—41no—
154#544—611no—
155#541—611no—
156#501—611no—
157#499—611no—
158#491—611no—
159#487D6111yescharacteristic, complemented
160#485—611no—
161#485—611no—
162#484—611no—
163#483—611no—
164#479—611no—
165#479—611no—
166#477—611no—
167#475—611no—
168#433—611no—
169C61#324211yescharacteristic, complemented, Sylow
170C4⋊Q8—611no—
171C4⋊Q8—1221no—
172C4⋊Q8C2×D6111yescharacteristic
173C4⋊Q8C2×D6111yescharacteristic
174#126—1221no—
175#126—1221no—
176#125—611no—
177#125—611no—
178#125—611no—
179#125—1221no—
180#125—1221no—
181#125—1221no—
182C22⋊Q8—611no—
183C22⋊Q8—611no—
184C22⋊Q8—1221no—
185C22⋊Q8—1221no—
186C4×Q8—611no—
187C4×Q8—611no—
188#117—611no—
189#117—611no—
190C2×C4⋊C4—611no—
191#107—611no—
192#107—611no—
193#107—611no—
194#107—611no—
195#106—611no—
196#106—611no—
197#106—611no—
198#106—611no—
199C4⋊C8—611no—
200C4⋊C8—611no—
201#103—611no—
202#103—611no—
203#103—611no—
204#103—611no—
205#103C2×D6111yescharacteristic
206#103C2×D6111yescharacteristic
207#103C2×D6111yescharacteristic
208#103C2×D6111yescharacteristic
209C22⋊C8—611no—
210C22⋊C8—611no—
211#97—611no—
212C4×C8C2×D6111yescharacteristic
213C2×Q8—21no—
214C2×Q8—1221no—
215C2×Q8C22×D6111yescharacteristic
216C2×Q8C22×D6111yescharacteristic
217C22×C4—611no—
218C22×C4—1221no—
219C2×C8—611no—
220C2×C8—611no—
221C2×C8C22×D6111yescharacteristic
222C2×C8C22×D6111yescharacteristic
223C4⋊C4—21no—
224C4⋊C4—21no—
225C4⋊C4—21no—
226C4⋊C4—611no—
227C4⋊C4—611no—
228C4⋊C4—611no—
229C4⋊C4—611no—
230C4⋊C4—611no—
231C4⋊C4—611no—
232C4⋊C4—1221no—
233C4⋊C4—1221no—
234C4⋊C4—1221no—
235C4⋊C4—1221no—
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⋊C4C22×D6111yescharacteristic
245C4⋊C4C22×D6111yescharacteristic
246C22⋊C4—611no—
247C22⋊C4—611no—
248C22⋊C4—1221no—
249C22⋊C4—1221no—
250C22⋊C4—1221no—
251C42—611no—
252C42—1221no—
253C42—1221no—
254C42—1221no—
255C42C22×D6111yescharacteristic
256C23—611no—
257Q8—21no—
258Q8—21no—
259Q8—21no—
260Q8—21no—
261Q8—81no—
262Q8—4881no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—611no—
268C2×C4—611no—
269C2×C4—611no—
270C2×C4—1221no—
271C2×C4—1221no—
272C2×C4—1221no—
273C2×C4—1221no—
274C2×C4—1221no—
275C2×C4—1221no—
276C2×C4—4881no—
277C2×C4D4×D6111yescharacteristic
278C2×C4D4×D6111yescharacteristic
279C2×C4C23×D6111yescharacteristic
280C8—21no—
281C8—21no—
282C8—1221no—
283C8—1221no—
284C22—1221no—
285C22—1221no—
286C22—1221no—
287C22C2×D4×D6111yescharacteristic
288C4—21no—
289C4—21no—
290C4—41no—
291C4—41no—
292C4—41no—
293C4—41no—
294C4—1221no—
295C4—1221no—
296C4—1221no—
297C4—2441no—
298C4—2441no—
299C4—2441no—
300C4—2441no—
301C4#1451982411yescharacteristic
302C4#1451982411yescharacteristic
303C2—2441no—
304C2#1684033211yescharacteristic
305C2#1684056811yescharacteristic
306C2#1684057511yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#487C2
socleC22×C61C22×D4
hypercenter#487D61
hypocenterC61#3242
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
3. #16840168C2semidirect
4. #16840164C2semidirect
5. #16840130C2semidirect
10. #16840071C2semidirect
11. #16840067C2semidirect
12. #16840055C2semidirect
13. #16840045C2semidirect
15. C61×#487C2semidirect
159. #487D61semidirect
169. C61#3242semidirect