Finite Group Databasebeta

← #14911174

Subgroups — #14911174

Order 2816.

484 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081010C211yesmaximal, characteristic
2#13081008C211yesmaximal, characteristic
3#13070889C211yesmaximal, characteristic, complemented
4#13070820C212yesmaximal, complemented
5#13070817C212yesmaximal, complemented
6#13070769C211yesmaximal, characteristic, complemented
7#13070706C212yesmaximal, complemented
8C4×#66893C211yesmaximal, characteristic, complemented
9#13070435C211yesmaximal, characteristic
10D11×#366C212yesmaximal, complemented
11C11×#2227C211yesmaximal, characteristic, complemented
12#10623261—21no—
13#10623110—21no—
14C11×#500C2211yescharacteristic
15C4×C11×Q16C2211yescharacteristic
16#10622801C2212yes—
17C2×#66893C2211yescharacteristic
18#10622704—21no—
19#10622634—21no—
20C2×C16×D11C2212yes—
21#10622500C2212yes—
22#10622497—22no—
23D11×#107C2212yes—
24D11×#107C2212yes—
25#10622422—22no—
26C4×Dic44C2211yescharacteristic
27C8×D44C2211yescharacteristic
28#10622295C2211yescharacteristic
29C11×#366C2212yes—
30C11×C4⋊C16C2211yescharacteristic
31C11×#358C2212yes—
32#10622202C2211yescharacteristic
33(C2×D11)⋊C16C2212yes—
34#10622142C2212yes—
35#10622141C2212yes—
36#10622130C2211yescharacteristic
37#10622127C2212yes—
38#10622127C2212yes—
39#10622127C2211yescharacteristic
40C4×C11⋊C16C2211yescharacteristic
41C2×C11×Q16C2311yescharacteristic
42C11×C4⋊Q8—21no—
43C4×Q8×C11—21no—
44#66999—22no—
45#66999—42no—
46C2×Dic44C2311yescharacteristic
47C2×C8×D11C2312yes—
48#66950—22no—
49#66949—42no—
50#66946—41no—
51C4⋊C4×D11—22no—
52C4⋊C4×D11—22no—
53#66943—41no—
54C4×D44—41no—
55C4×D44D411yescharacteristic
56#66923—41no—
57#66922—21no—
58C4×Dic22—21no—
59C2×C11×C16C2312yes—
60C11×#107—21no—
61C11×#107C2312yes—
62C11×#107C2311yescharacteristic
63C11×#103—21no—
64C4×C8×C11C2311yescharacteristic
65#66899—22no—
66#66893—22no—
67(C2×D11)⋊C8D412yes—
68#66882—21no—
69#66882C2311yescharacteristic
70#66882C2312yes—
71#66880—21no—
72C2×C11⋊C16C2311yescharacteristic
73C2×C11⋊C16C2311yescharacteristic
74#66874—22no—
75#66871—22no—
76#66871—22no—
77C4⋊(C11⋊C8)D411yescharacteristic
78C16×D11—24no—
79#33905—111nomaximal, Sylow
80C2×Q8×C11—21no—
81C2×Q8×C11—41no—
82C2×D44D811yescharacteristic
83C2×C4×D11—42no—
84C2×C4×D11—42no—
85C2×C4×D11C2×D412yes—
86C2×Dic22—21no—
87C2×Dic22—41no—
88C11×Q16—21no—
89C11×Q16—21no—
90C2×C8×C11C2×D411yescharacteristic
91C2×C8×C11C2411yescharacteristic
92C11×C4⋊C4—21no—
93C11×C4⋊C4—22no—
94C11×C4⋊C4—41no—
95C11×C4⋊C4—41no—
96C42×C11—41no—
97C42×C11C2×D411yescharacteristic
98(C2×D11)⋊C4—42no—
99(C2×D11)⋊C4—42no—
100(C2×D11)⋊C4D812yes—
101C4⋊Dic11—21no—
102C4⋊Dic11—22no—
103C4⋊Dic11—42no—
104C4⋊Dic11—41no—
105C4⋊Dic11D811yescharacteristic
106Dic11⋊C4—42no—
107Dic11⋊C4—42no—
108Dic11⋊C4—42no—
109Dic11⋊C4—41no—
110C4×Dic11—41no—
111C2×C11⋊C8C2×D412yes—
112Dic44—21no—
113Dic44—21no—
114C8×D11—22no—
115C8×D11—22no—
116C11×C16—22no—
117C11⋊C16—21no—
118C11⋊C16#4112yes—
119#3338—111no—
120#3338—111no—
121#2252—111no—
122#2236—112no—
123#2236—112no—
124#2227—111no—
125#2227D1111yescharacteristic, complemented
126#2216—112no—
127C4×Q32—111no—
128D4×C16—111no—
129C2×#366—112no—
130C22×D11C2×D812yes—
131Q8×C11—41no—
132Q8×C11—41no—
133Q8×C11—161no—
134C2×C4×C11—41no—
135C2×C4×C11—41no—
136C2×C4×C11—42no—
137C2×C4×C11C2×D811yescharacteristic
138C2×C4×C11C2×D811yescharacteristic
139C2×C4×C11C22×D411yescharacteristic
140C2×Dic11—41no—
141C2×Dic11—41no—
142C2×Dic11—42no—
143C2×Dic11C2×D812yes—
144D44Q3214yescomplemented
145C4×D11—22no—
146C4×D11—22no—
147C4×D11—162no—
148C4×D11—162no—
149Dic22—41no—
150Dic22—41no—
151Dic22—161no—
152C8×C11—21no—
153C8×C11C2×#4111yescharacteristic
154C8×C112−1+411yescharacteristic
155C11⋊C8—22no—
156#554—221no—
157#554—221no—
158C2×Q32—111no—
159C22×C16—112no—
160#500—111no—
161#500C2×D1111yescharacteristic
162#484—222no—
163#484—222no—
164#477—221no—
165#477—221no—
166#467—112no—
167#467—112no—
168C4×Q16—111no—
169C4×Q16C2×D1111yescharacteristic
170C8×D4—111no—
171C2×#107—112no—
172C2×#107—112no—
173#366—112no—
174#366—111no—
175#366—112no—
176#366—112no—
177#366C2×D1112yes—
178C4⋊C16C2×D1111yescharacteristic
179#358—111no—
180#358—112no—
181#358—111no—
182#358C2×D1112yes—
183C22⋊C16—112no—
184C4×C16—111no—
185C22×C11C22×D811yescharacteristic
186C2×D11—22no—
187C2×D11—22no—
188C2×D11C2×Q3214yes—
189C4×C11—21no—
190C4×C11—81no—
191C4×C11—82no—
192C4×C11—81no—
193C4×C11C2×Q3212yes—
194C4×C11#54711yescharacteristic
195C4×C11#57811yescharacteristic
196Dic11—22no—
197Dic11—81no—
198Dic11—82no—
199Dic11—81no—
200C2×Q16—111no—
201C2×Q16C22×D1111yescharacteristic
202C22×C8—112no—
203C4⋊Q8—21no—
204C4⋊Q8—221no—
205#125—441no—
206#125—441no—
207C22⋊Q8—222no—
208C22⋊Q8—222no—
209C22⋊Q8—442no—
210C22⋊Q8—442no—
211C4×Q8—21no—
212C4×Q8—221no—
213C4×D4—111no—
214C4×D4—441no—
215C4×D4—441no—
216C2×C4⋊C4—222no—
217C2×C4⋊C4—222no—
218Q32—222no—
219C2×C16—111no—
220C2×C16—111no—
221C2×C16—224no—
222C2×C16C22×D1112yes—
223#107—21no—
224#107—111no—
225#107—112no—
226#107—222no—
227#107—222no—
228#107—221no—
229#107C22×D1111yescharacteristic
230#107C22×D1112yes—
231C4⋊C8—111no—
232#103—21no—
233#103—222no—
234#103—222no—
235#103—221no—
236C22⋊C8—112no—
237C4×C8C22×D1111yescharacteristic
238C2×C11#333411yescharacteristic
239C2×C11C22×Q3211yescharacteristic
240C2×C11#341511yescharacteristic
241D11—24no—
242C2×Q8—21no—
243C2×Q8—41no—
244C2×Q8—221no—
245C2×Q8—441no—
246C2×D4—111no—
247C22×C4—112no—
248C22×C4—442no—
249C22×C4—442no—
250Q16—21no—
251Q16—21no—
252Q16—221no—
253Q16—221no—
254C2×C8—112no—
255C2×C8—222no—
256C2×C8—222no—
257C2×C8D4×D1111yescharacteristic
258C2×C8C23×D1111yescharacteristic
259C4⋊C4—21no—
260C4⋊C4—22no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—111no—
264C4⋊C4—221no—
265C4⋊C4—222no—
266C4⋊C4—442no—
267C4⋊C4—442no—
268C4⋊C4—442no—
269C4⋊C4—442no—
270C4⋊C4—441no—
271C4⋊C4—441no—
272C22⋊C4—112no—
273C22⋊C4—442no—
274C22⋊C4—442no—
275C42—41no—
276C42—441no—
277C42D4×D1111yescharacteristic
278C16—22no—
279C16—112no—
280C16—221no—
281C11#3390511yescharacteristic, complemented, Sylow
282C23—112no—
283Q8—41no—
284Q8—41no—
285Q8—161no—
286Q8—441no—
287Q8—441no—
288Q8—1761no—
289D4—114no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—42no—
293C2×C4—112no—
294C2×C4—222no—
295C2×C4—222no—
296C2×C4—441no—
297C2×C4—441no—
298C2×C4—442no—
299C2×C4—1762no—
300C2×C4—1762no—
301C2×C4D8×D1111yescharacteristic
302C2×C4D8×D1111yescharacteristic
303C2×C4C2×D4×D1111yescharacteristic
304C8—21no—
305C8—222no—
306C8#6704011yescharacteristic
307C8#41×D1111yescharacteristic
308C22—114no—
309C22—222no—
310C22—222no—
311C22C2×D8×D1111yescharacteristic
312C4—21no—
313C4—81no—
314C4—81no—
315C4—82no—
316C4—222no—
317C4—881no—
318C4—881no—
319C4—882no—
320C4D11×Q3212yes—
321C4#1062316211yescharacteristic
322C4#1062331011yescharacteristic
323C2—224no—
324C2#1308096211yescharacteristic
325C2C2×D11×Q3211yescharacteristic
326C2#1308175611yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2227C2
socleC22×C11C22×D8
prime radicalC2×D44D8
hypercenter#2227D11
hypocenterC11#33905
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2227

Complements

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

NH ≅ G/Ntype
3. #13070889C2semidirect
4. #13070820C2semidirect
5. #13070817C2semidirect
6. #13070769C2semidirect
7. #13070706C2semidirect
8. C4×#66893C2semidirect
10. D11×#366C2semidirect
11. C11×#2227C2semidirect
125. #2227D11semidirect
144. D44Q32semidirect
281. C11#33905semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#130810102
#130810082
#130708892
#130708202
#130708172
#130707692
#130707062
C4×#668932
#130704352
D11×#3662
C11×#22272
#3390511