Finite Group Databasebeta

← #14911412

Subgroups — #14911412

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#13081040C211yesmaximal, characteristic
2#13081008C211yesmaximal, characteristic, complemented
3#13070889C211yesmaximal, characteristic, complemented
4#13070827C212yesmaximal, complemented
5#13070795C212yesmaximal, complemented
6#13070769C211yesmaximal, characteristic, complemented
7#13070728C212yesmaximal, complemented
8C4×#66891C211yesmaximal, characteristic, complemented
9#13070447C211yesmaximal, characteristic, complemented
10#13070403C212yesmaximal, complemented
11C11×#2226C211yesmaximal, characteristic, complemented
12#10623261—21no—
13#10623094—21no—
14C11×#500C2211yescharacteristic
15C4×C11×D8C2211yescharacteristic
16#10622770C2212yes—
17C2×#66891C2211yescharacteristic
18#10622704—21no—
19#10622621—21no—
20C2×#66862C2212yes—
21#10622500C2212yes—
22#10622497—22no—
23#10622493C2212yes—
24D11×#107C2212yes—
25#10622397—22no—
26C4×Dic44C2211yescharacteristic
27C8×D44C2211yescharacteristic
28#10622295C2211yescharacteristic
29C11×#367C2212yes—
30C11×C4⋊C16C2211yescharacteristic
31C11×#357C2212yes—
32#10622200C2211yescharacteristic
33(C2×D11)⋊C16C2212yes—
34#10622142C2212yes—
35#10622141C2212yes—
36#10622130C2211yescharacteristic
37#10622128C2211yescharacteristic
38#10622127C2212yes—
39#10622127C2212yes—
40C4×C11⋊C16C2211yescharacteristic
41C2×C11×D8C2311yescharacteristic
42C11×C4⋊Q8—21no—
43C4×D4×C11—21no—
44#66999—42no—
45#66991—22no—
46#66983—41no—
47#66979—41no—
48C2×Dic44C2311yescharacteristic
49C2×C8×D11C2312yes—
50#66950—22no—
51#66946—41no—
52#66945—22no—
53C4⋊C4×D11—22no—
54#66943—41no—
55#66938—42no—
56C4×D44D411yescharacteristic
57#66922—21no—
58C4×Dic22—21no—
59C2×C11×C16C2312yes—
60C11×#107—21no—
61C11×#107C2312yes—
62C11×#107C2311yescharacteristic
63C11×#102—21no—
64C4×C8×C11C2311yescharacteristic
65#66896—22no—
66#66891—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#66872—22no—
76#66871—22no—
77C4⋊(C11⋊C8)D411yescharacteristic
78#66862—24no—
79#33924—111nomaximal, Sylow
80C2×Q8×C11—41no—
81C2×D4×C11—21no—
82C22×C4×C11—41no—
83C2×C22⋊D11—42no—
84C2×D44D811yescharacteristic
85C2×C4×D11—42no—
86C2×C4×D11C2×D412yes—
87C2×Dic22—21no—
88C2×Dic22—41no—
89C11×D8—21no—
90C11×D8—21no—
91C2×C8×C11C2×D411yescharacteristic
92C2×C8×C11C2411yescharacteristic
93C11×C4⋊C4—22no—
94C11×C4⋊C4—21no—
95C11×C4⋊C4—41no—
96C11×C22⋊C4—41no—
97C42×C11C2×D411yescharacteristic
98C22⋊Dic11—42no—
99(C2×D11)⋊C4—42no—
100(C2×D11)⋊C4—42no—
101(C2×D11)⋊C4D812yes—
102C4⋊Dic11—21no—
103C4⋊Dic11—22no—
104C4⋊Dic11—42no—
105C4⋊Dic11—41no—
106C4⋊Dic11D811yescharacteristic
107Dic11⋊C4—42no—
108Dic11⋊C4—41no—
109C4×Dic11—42no—
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#3341—111no—
120#3338—111no—
121#2252—111no—
122#2237—112no—
123#2232—112no—
124#2227—111no—
125#2226D1111yescharacteristic, complemented
126#2220—112no—
127C4×SD32—111no—
128#2169—111no—
129#2159—112no—
130C23×C11—41no—
131C22×D11C2×D812yes—
132Q8×C11—161no—
133D4×C11—41no—
134D4×C11—41no—
135C2×C4×C11—41no—
136C2×C4×C11—42no—
137C2×C4×C11—82no—
138C2×C4×C11C2×D811yescharacteristic
139C2×C4×C11C2×D811yescharacteristic
140C2×C4×C11C22×D411yescharacteristic
141C22⋊D11—162no—
142C2×Dic11—41no—
143C2×Dic11—41no—
144C2×Dic11—42no—
145C2×Dic11C2×D812yes—
146D44—22no—
147C4×D11—22no—
148C4×D11—22no—
149C4×D11—162no—
150Dic22—41no—
151Dic22—41no—
152Dic22—161no—
153C8×C11—21no—
154C8×C11C2×#4111yescharacteristic
155C8×C112−1+411yescharacteristic
156C11⋊C8—22no—
157#555—221no—
158#554—221no—
159C2×SD32—111no—
160C2×M32—112no—
161#500—111no—
162#500C2×D1111yescharacteristic
163#484—222no—
164#482—222no—
165#477—221no—
166#476—221no—
167#467—112no—
168#466—112no—
169C4×Q16—111no—
170C4×D8C2×D1111yescharacteristic
171C8×D4—111no—
172#427—112no—
173C2×#107—112no—
174#367—111no—
175#367C2×D1112yes—
176#366—112no—
177#366—112no—
178#366—112no—
179C4⋊C16C2×D1111yescharacteristic
180#358—112no—
181#358—111no—
182#357—111no—
183#357C2×D1112yes—
184C22⋊C16—112no—
185C4×C16—111no—
186C22×C11—81no—
187C22×C11—81no—
188C22×C11—81no—
189C22×C11C22×D811yescharacteristic
190C2×D11—22no—
191C2×D11—22no—
192C2×D11—22no—
193C4×C11—21no—
194C4×C11—81no—
195C4×C11—82no—
196C4×C11#51012yes—
197C4×C11#54711yescharacteristic
198C4×C11#57811yescharacteristic
199Dic11—22no—
200Dic11—81no—
201Dic11—82no—
202Dic11—81no—
203C2×Q16—111no—
204C2×D8C22×D1111yescharacteristic
205C22×C8—112no—
206C4⋊Q8—21no—
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—21no—
216C4×D4—111no—
217C4×D4—441no—
218#117—222no—
219#117—441no—
220C2×C4⋊C4—222no—
221SD32—222no—
222M32—224no—
223C2×C16—111no—
224C2×C16—111no—
225C2×C16C22×D1112yes—
226#107—21no—
227#107—111no—
228#107—112no—
229#107—222no—
230#107—221no—
231#107C22×D1112yes—
232#107C22×D1111yescharacteristic
233#106—222no—
234C4⋊C8—111no—
235#103—222no—
236#103—221no—
237#102—21no—
238#102—222no—
239C22⋊C8—112no—
240C4×C8C22×D1111yescharacteristic
241C2×C11—161no—
242C2×C11#333411yescharacteristic
243C2×C11C2×#51011yescharacteristic
244C2×C11#341511yescharacteristic
245D11—42no—
246C2×Q8—41no—
247C2×Q8—221no—
248C2×Q8—441no—
249C2×D4—21no—
250C2×D4—111no—
251C2×D4—442no—
252C22×C4—41no—
253C22×C4—112no—
254C22×C4—442no—
255Q16—221no—
256Q16—221no—
257D8—21no—
258D8—21no—
259C2×C8—112no—
260C2×C8—222no—
261C2×C8—222no—
262C2×C8D4×D1111yescharacteristic
263C2×C8C23×D1111yescharacteristic
264C4⋊C4—21no—
265C4⋊C4—22no—
266C4⋊C4—41no—
267C4⋊C4—111no—
268C4⋊C4—222no—
269C4⋊C4—221no—
270C4⋊C4—442no—
271C4⋊C4—442no—
272C4⋊C4—441no—
273C4⋊C4—441no—
274C22⋊C4—41no—
275C22⋊C4—112no—
276C22⋊C4—442no—
277C22⋊C4—442no—
278C22⋊C4—442no—
279C42—442no—
280C42—441no—
281C42D4×D1111yescharacteristic
282C16—22no—
283C16—112no—
284C16—221no—
285C11#3392411yescharacteristic, complemented, Sylow
286C23—41no—
287C23—112no—
288Q8—161no—
289Q8—441no—
290Q8—441no—
291Q8—1761no—
292D4—41no—
293D4—41no—
294D4—222no—
295D4—1762no—
296C2×C4—41no—
297C2×C4—42no—
298C2×C4—82no—
299C2×C4—112no—
300C2×C4—222no—
301C2×C4—222no—
302C2×C4—442no—
303C2×C4—441no—
304C2×C4—441no—
305C2×C4—1762no—
306C2×C4D8×D1111yescharacteristic
307C2×C4D8×D1111yescharacteristic
308C2×C4C2×D4×D1111yescharacteristic
309C8—21no—
310C8—222no—
311C8#6704011yescharacteristic
312C8#41×D1111yescharacteristic
313C22—81no—
314C22—81no—
315C22—81no—
316C22—222no—
317C22—222no—
318C22—222no—
319C22C2×D8×D1111yescharacteristic
320C4—21no—
321C4—81no—
322C4—82no—
323C4—222no—
324C4—881no—
325C4—881no—
326C4—882no—
327C4#1062252812yes—
328C4#1062316211yescharacteristic
329C4#1062331011yescharacteristic
330C2—161no—
331C2—442no—
332C2#1308096211yescharacteristic
333C2C2×#1062252811yescharacteristic
334C2#1308175611yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2226C2
socleC22×C11C22×D8
prime radical#13081040C2
hypercenter#2226D11
hypocenterC11#33924
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2226

Complements

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

NH ≅ G/Ntype
2. #13081008C2semidirect
3. #13070889C2semidirect
4. #13070827C2semidirect
5. #13070795C2semidirect
6. #13070769C2semidirect
7. #13070728C2semidirect
8. C4×#66891C2semidirect
9. #13070447C2semidirect
10. #13070403C2semidirect
11. C11×#2226C2semidirect
125. #2226D11semidirect
285. C11#33924semidirect

Maximal subgroups

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

subgroupindex
#130810402
#130810082
#130708892
#130708272
#130707952
#130707692
#130707282
C4×#668912
#130704472
#130704032
C11×#22262
#3392411