Finite Group Databasebeta

← #14911410

Subgroups — #14911410

Order 2816.

482 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081039C211yesmaximal, characteristic
2#13081009C211yesmaximal, characteristic, complemented
3#13070891C211yesmaximal, characteristic, complemented
4#13070825C212yesmaximal, complemented
5#13070797C212yesmaximal, complemented
6#13070769C211yesmaximal, characteristic, complemented
7#13070764C211yesmaximal, characteristic, complemented
8#13070729C212yesmaximal, complemented
9C4×#66864C211yesmaximal, characteristic, complemented
10#13070404C212yesmaximal, complemented
11C11×#2169C211yesmaximal, characteristic, complemented
12#10623094—21no—
13#10623074—21no—
14C2×C11×M32C2212yes—
15C8×D4×C11C2211yescharacteristic
16#10622729C2212yes—
17#10622728C2212yes—
18#10622719C2212yes—
19C2×#66882C2212yes—
20C2×#66864C2211yescharacteristic
21#10622463—21no—
22#10622455—21no—
23#10622350—22no—
24#10622335—22no—
25C4×Dic44C2211yescharacteristic
26C4×D88C2211yescharacteristic
27#10622295C2211yescharacteristic
28#10622295C2211yescharacteristic
29C11×C4⋊C16C2211yescharacteristic
30C11×C22⋊C16C2212yes—
31C4×C11×C16C2211yescharacteristic
32#10622147C2211yescharacteristic
33#10622147C2212yes—
34#10622143C2211yescharacteristic
35#10622143C2212yes—
36#10622142C2212yes—
37#10622142C2212yes—
38#10622142C2212yes—
39#10622141C2211yescharacteristic
40#10622141C2212yes—
41C22×C8×C11C2312yes—
42C4×D4×C11D411yescharacteristic
43#66991—41no—
44D4×Dic11—41no—
45#66983—22no—
46#66979—22no—
47C2×C4⋊Dic11—22no—
48#66977—22no—
49C2×Dic44C2311yescharacteristic
50C2×D88C2311yescharacteristic
51#66945—41no—
52#66943—41no—
53#66938—42no—
54#66931—42no—
55C4×D44—21no—
56#66922—21no—
57#66922—21no—
58C4×Dic22—21no—
59C11×M32—24no—
60C2×C11×C16C2312yes—
61C2×C11×C16C2311yescharacteristic
62C2×C11×C16C2311yescharacteristic
63C11×C4⋊C8D411yescharacteristic
64C11×C22⋊C8D412yes—
65C4×C8×C11C2311yescharacteristic
66#66885—22no—
67#66885—21no—
68#66882—21no—
69#66882—21no—
70#66882—22no—
71#66882C2312yes—
72#66882C2312yes—
73#66882C2311yescharacteristic
74#66882C2311yescharacteristic
75#66881—22no—
76#66880—22no—
77#66880—21no—
78#66864—22no—
79#33924—111nomaximal, Sylow
80C2×D4×C11D811yescharacteristic
81C22×C4×C11C2×D412yes—
82C2×C22⋊D11—42no—
83C22×Dic11—42no—
84C2×D44—21no—
85C2×C4×D11—41no—
86C2×Dic22—21no—
87C2×Dic22—41no—
88C2×Dic22—41no—
89C2×C8×C11—22no—
90C2×C8×C11—22no—
91C2×C8×C11C2×D412yes—
92C2×C8×C11C2×D411yescharacteristic
93C2×C8×C11C2411yescharacteristic
94C11×C4⋊C4D811yescharacteristic
95C11×C22⋊C4D812yes—
96C42×C11C2×D411yescharacteristic
97C22⋊Dic11—42no—
98C22⋊Dic11—42no—
99(C2×D11)⋊C4—41no—
100(C2×D11)⋊C4—42no—
101C4⋊Dic11—21no—
102C4⋊Dic11—22no—
103C4⋊Dic11—21no—
104C4⋊Dic11—22no—
105C4⋊Dic11—41no—
106C4⋊Dic11—41no—
107C4⋊Dic11—42no—
108Dic11⋊C4—41no—
109Dic11⋊C4—42no—
110C4×Dic11—41no—
111C4×Dic11—42no—
112Dic44—21no—
113Dic44—21no—
114D88—21no—
115D88—21no—
116C11×C16—22no—
117C11×C16—21no—
118C11×C16#4112yes—
119#3341—111no—
120#3338—111no—
121#2252—111no—
122#2237—112no—
123#2232—112no—
124#2227—111no—
125#2226—111no—
126#2220—112no—
127C4×SD32—111no—
128#2169D1111yescharacteristic, complemented
129#2159—112no—
130C23×C11C2×D812yes—
131C22×D11—41no—
132D4×C11—22no—
133C2×C4×C11—22no—
134C2×C4×C11—22no—
135C2×C4×C11C2×D812yes—
136C2×C4×C11C2×D811yescharacteristic
137C2×C4×C11C2×D811yescharacteristic
138C2×C4×C11C22×D411yescharacteristic
139C22⋊D11—162no—
140C2×Dic11—41no—
141C2×Dic11—41no—
142C2×Dic11—41no—
143C2×Dic11—42no—
144C2×Dic11—42no—
145C2×Dic11—162no—
146D44—41no—
147D44—41no—
148C4×D11—82no—
149Dic22—41no—
150Dic22—41no—
151Dic22—161no—
152Dic22—161no—
153C8×C11—22no—
154C8×C11—21no—
155C8×C11C2×#4111yescharacteristic
156C8×C112−1+411yescharacteristic
157#555—221no—
158#554—221no—
159C2×SD32—111no—
160C2×M32C2×D1112yes—
161#500—111no—
162#500—111no—
163#484—222no—
164#482—222no—
165#477—221no—
166#476—221no—
167#467—112no—
168#466—112no—
169C4×Q16—111no—
170C4×D8—111no—
171C8×D4C2×D1111yescharacteristic
172#427—112no—
173C2×#107—112no—
174#367—111no—
175#367—112no—
176#366—112no—
177#366—112no—
178#366—112no—
179C4⋊C16C2×D1111yescharacteristic
180#358—111no—
181#358—112no—
182#357—111no—
183#357—112no—
184C22⋊C16C2×D1112yes—
185C4×C16C2×D1111yescharacteristic
186C22×C11—22no—
187C22×C11—22no—
188C22×C11—22no—
189C22×C11C22×D811yescharacteristic
190C2×D11—81no—
191C2×D11—81no—
192C2×D11—81no—
193C4×C11—22no—
194C4×C11—21no—
195C4×C11#51012yes—
196C4×C11#54711yescharacteristic
197C4×C11#57811yescharacteristic
198Dic11—81no—
199Dic11—81no—
200Dic11—82no—
201Dic11—82no—
202Dic11—81no—
203C2×Q16—111no—
204C2×D8—111no—
205C22×C8C22×D1112yes—
206C4⋊Q8—221no—
207C4⋊Q8—221no—
208#125—441no—
209#124—442no—
210C22⋊Q8—222no—
211C22⋊Q8—442no—
212#121—222no—
213#121—441no—
214C4×Q8—221no—
215C4×D4—221no—
216C4×D4—441no—
217C4×D4D4411yescharacteristic
218#117—222no—
219#117—441no—
220C2×C4⋊C4—222no—
221SD32—222no—
222M32—24no—
223C2×C16C22×D1111yescharacteristic
224C2×C16C22×D1112yes—
225C2×C16C22×D1111yescharacteristic
226#107—111no—
227#107—112no—
228#107—112no—
229#107—111no—
230#107—222no—
231#107—221no—
232#107—221no—
233#106—222no—
234C4⋊C8D4411yescharacteristic
235#103—221no—
236#103—222no—
237#102—221no—
238#102—222no—
239C22⋊C8D4412yes—
240C4×C8C22×D1111yescharacteristic
241C2×C11—42no—
242C2×C11#333411yescharacteristic
243C2×C11C2×#51011yescharacteristic
244C2×C11#341511yescharacteristic
245D11—161no—
246C2×Q8—221no—
247C2×Q8—441no—
248C2×Q8—441no—
249C2×D4—221no—
250C2×D4—442no—
251C2×D4D8811yescharacteristic
252C22×C4—442no—
253C22×C4—441no—
254C22×C4C2×D4412yes—
255Q16—221no—
256Q16—221no—
257D8—221no—
258D8—221no—
259C2×C8—22no—
260C2×C8—22no—
261C2×C8C2×D4411yescharacteristic
262C2×C8C2×D4412yes—
263C2×C8C23×D1111yescharacteristic
264C4⋊C4—221no—
265C4⋊C4—222no—
266C4⋊C4—221no—
267C4⋊C4—222no—
268C4⋊C4—442no—
269C4⋊C4—441no—
270C4⋊C4—441no—
271C4⋊C4—441no—
272C4⋊C4—442no—
273C4⋊C4D8811yescharacteristic
274C22⋊C4—442no—
275C22⋊C4—442no—
276C22⋊C4—442no—
277C22⋊C4—441no—
278C22⋊C4D8812yes—
279C42—442no—
280C42—441no—
281C42C2×D4411yescharacteristic
282C16—22no—
283C16—21no—
284C16#434112yes—
285C11#3392411yescharacteristic, complemented, Sylow
286C23—441no—
287C23C2×D8812yes—
288Q8—441no—
289Q8—441no—
290Q8—1761no—
291Q8—1761no—
292D4—22no—
293D4—441no—
294D4—441no—
295D4—1762no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—441no—
299C2×C4—442no—
300C2×C4—441no—
301C2×C4—441no—
302C2×C4—442no—
303C2×C4—882no—
304C2×C4—1762no—
305C2×C4C2×D8812yes—
306C2×C4C2×D8811yescharacteristic
307C2×C4C2×D8811yescharacteristic
308C2×C4C22×D4411yescharacteristic
309C8—21no—
310C8—22no—
311C8C2×#434111yescharacteristic
312C8#6704311yescharacteristic
313C22—22no—
314C22—22no—
315C22—22no—
316C22—881no—
317C22—881no—
318C22—881no—
319C22C22×D8811yescharacteristic
320C4—22no—
321C4—21no—
322C4—881no—
323C4—881no—
324C4—881no—
325C4—882no—
326C4—882no—
327C4#1062252212yes—
328C4#1062308611yescharacteristic
329C4#1062328411yescharacteristic
330C2—42no—
331C2—1761no—
332C2#1308096411yescharacteristic
333C2C2×#1062252211yescharacteristic
334C2#1308175711yescharacteristic
subgroupG/H
centerC22C22×D88
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2169C2
socleC22×C11C22×D8
prime radical#13081039C2
hypercenter#2169D11
hypocenterC11#33924
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #2169

Complements

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

NH ≅ G/Ntype
2. #13081009C2semidirect
3. #13070891C2semidirect
4. #13070825C2semidirect
5. #13070797C2semidirect
6. #13070769C2semidirect
7. #13070764C2semidirect
8. #13070729C2semidirect
9. C4×#66864C2semidirect
10. #13070404C2semidirect
11. C11×#2169C2semidirect
128. #2169D11semidirect
285. C11#33924semidirect

Maximal subgroups

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

subgroupindex
#130810392
#130810092
#130708912
#130708252
#130707972
#130707692
#130707642
#130707292
C4×#668642
#130704042
C11×#21692
#3392411