Finite Group Databasebeta

← #14911411

Subgroups — #14911411

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#13081010C211yesmaximal, characteristic, complemented
3#13070891C211yesmaximal, characteristic, complemented
4#13070823C212yesmaximal, complemented
5#13070795C212yesmaximal, complemented
6#13070768C211yesmaximal, characteristic, complemented
7#13070763C211yesmaximal, characteristic, complemented
8#13070726C212yesmaximal, complemented
9#13070449C211yesmaximal, characteristic, complemented
10#13070403C212yesmaximal, complemented
11C4×C11×SD32C211yesmaximal, characteristic, complemented
12#10623110—21no—
13#10623094—21no—
14C2×C11×SD32C2211yescharacteristic
15C4×C11×Q16C2211yescharacteristic
16C4×C11×D8C2211yescharacteristic
17#10622801C2212yes—
18#10622770C2212yes—
19#10622634—21no—
20#10622621—21no—
21C2×#66862C2212yes—
22#10622493C2212yes—
23D11×#107C2212yes—
24#10622422—22no—
25#10622397—22no—
26C8×D44C2211yescharacteristic
27#10622295C2211yescharacteristic
28#10622295C2211yescharacteristic
29C11×#367C2211yescharacteristic
30C11×#358C2211yescharacteristic
31C11×#357C2211yescharacteristic
32C4×C11×C16C2211yescharacteristic
33#10622202C2212yes—
34#10622200C2212yes—
35(C2×D11)⋊C16C2212yes—
36#10622142C2212yes—
37#10622142C2212yes—
38#10622128C2212yes—
39#10622127C2212yes—
40C4⋊(C11⋊C16)C2211yescharacteristic
41C2×C11×Q16C2311yescharacteristic
42C2×C11×D8C2311yescharacteristic
43C4×Q8×C11—21no—
44C4×D4×C11—21no—
45#66999—22no—
46#66991—22no—
47#66983—41no—
48#66979—41no—
49C2×C8×D11C2312yes—
50#66949—42no—
51#66945—22no—
52C4⋊C4×D11—22no—
53#66938—42no—
54C4×D44—41no—
55C4×D44D411yescharacteristic
56#66923—41no—
57#66922—21no—
58#66922—21no—
59C11×SD32—22no—
60C2×C11×C16C2311yescharacteristic
61C2×C11×C16C2311yescharacteristic
62C11×#107C2311yescharacteristic
63C11×#107C2311yescharacteristic
64C11×#103—21no—
65C11×#102—21no—
66C4×C8×C11C2311yescharacteristic
67#66899—22no—
68#66896—22no—
69(C2×D11)⋊C8D412yes—
70#66882—21no—
71#66882—21no—
72#66882C2312yes—
73#66882C2312yes—
74C2×C11⋊C16C2312yes—
75#66872—22no—
76#66871—22no—
77C4⋊(C11⋊C8)D411yescharacteristic
78#66862—24no—
79#33924—111nomaximal, Sylow
80C2×Q8×C11—21no—
81C2×D4×C11—21no—
82C22×C4×C11—41no—
83C2×C22⋊D11—42no—
84C2×D44D811yescharacteristic
85C2×C4×D11—42no—
86C2×C4×D11C2×D412yes—
87C2×Dic22—41no—
88C2×Dic22—41no—
89C11×Q16—21no—
90C11×Q16—21no—
91C11×D8—21no—
92C11×D8—21no—
93C2×C8×C11C2×D411yescharacteristic
94C2×C8×C11C2411yescharacteristic
95C11×C4⋊C4—21no—
96C11×C4⋊C4—21no—
97C11×C4⋊C4—41no—
98C11×C22⋊C4—41no—
99C42×C11—41no—
100C42×C11C2×D411yescharacteristic
101C22⋊Dic11—42no—
102(C2×D11)⋊C4—42no—
103(C2×D11)⋊C4—42no—
104(C2×D11)⋊C4D812yes—
105C4⋊Dic11—22no—
106C4⋊Dic11—22no—
107C4⋊Dic11—41no—
108C4⋊Dic11—41no—
109C4⋊Dic11D811yescharacteristic
110Dic11⋊C4—42no—
111Dic11⋊C4—42no—
112C4×Dic11—42no—
113C2×C11⋊C8C2×D412yes—
114C8×D11—22no—
115C8×D11—22no—
116C11×C16—21no—
117C11×C16#4112yes—
118C11⋊C16—22no—
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×SD32D1111yescharacteristic, complemented
128#2169—111no—
129#2159—112no—
130C23×C11—41no—
131C22×D11C2×D812yes—
132Q8×C11—41no—
133Q8×C11—41no—
134D4×C11—41no—
135D4×C11—41no—
136C2×C4×C11—41no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—82no—
140C2×C4×C11C2×D811yescharacteristic
141C2×C4×C11C2×D811yescharacteristic
142C2×C4×C11C22×D411yescharacteristic
143C22⋊D11—162no—
144C2×Dic11—42no—
145C2×Dic11—42no—
146C2×Dic11C2×D812yes—
147D44—22no—
148C4×D11—22no—
149C4×D11—22no—
150C4×D11—162no—
151Dic22—161no—
152Dic22—161no—
153C8×C11—21no—
154C8×C11C2×#4111yescharacteristic
155C8×C112−1+411yescharacteristic
156C11⋊C8—22no—
157#555—221no—
158#554—221no—
159C2×SD32C2×D1111yescharacteristic
160C2×M32—112no—
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×Q16C2×D1111yescharacteristic
170C4×D8C2×D1111yescharacteristic
171C8×D4—111no—
172#427—112no—
173C2×#107—112no—
174#367—112no—
175#367C2×D1111yescharacteristic
176#366—112no—
177#366—112no—
178#366—112no—
179C4⋊C16—111no—
180#358—112no—
181#358C2×D1111yescharacteristic
182#357—112no—
183#357C2×D1111yescharacteristic
184C22⋊C16—112no—
185C4×C16C2×D1111yescharacteristic
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—81no—
196C4×C11—81no—
197C4×C11#51012yes—
198C4×C11#54711yescharacteristic
199C4×C11#57811yescharacteristic
200Dic11—22no—
201Dic11—82no—
202Dic11—82no—
203C2×Q16C22×D1111yescharacteristic
204C2×D8C22×D1111yescharacteristic
205C22×C8—112no—
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—21no—
215C4×D4—21no—
216C4×D4—111no—
217C4×D4—441no—
218#117—222no—
219#117—441no—
220C2×C4⋊C4—222no—
221SD32—22no—
222M32—224no—
223C2×C16—112no—
224C2×C16C22×D1111yescharacteristic
225C2×C16C22×D1111yescharacteristic
226#107—112no—
227#107—112no—
228#107—222no—
229#107—221no—
230#107—221no—
231#107C22×D1111yescharacteristic
232#107C22×D1111yescharacteristic
233#106—222no—
234C4⋊C8—111no—
235#103—21no—
236#103—222no—
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—21no—
247C2×Q8—441no—
248C2×Q8—441no—
249C2×D4—21no—
250C2×D4—111no—
251C2×D4—442no—
252C22×C4—41no—
253C22×C4—112no—
254C22×C4—442no—
255Q16—21no—
256Q16—21no—
257D8—21no—
258D8—21no—
259C2×C8—112no—
260C2×C8—222no—
261C2×C8—222no—
262C2×C8D4×D1111yescharacteristic
263C2×C8C23×D1111yescharacteristic
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—41no—
267C4⋊C4—111no—
268C4⋊C4—222no—
269C4⋊C4—222no—
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—41no—
280C42—442no—
281C42D4×D1111yescharacteristic
282C16—21no—
283C16—222no—
284C16#433912yes—
285C11#3392411yescharacteristic, complemented, Sylow
286C23—41no—
287C23—112no—
288Q8—41no—
289Q8—41no—
290Q8—1761no—
291Q8—1761no—
292D4—41no—
293D4—41no—
294D4—222no—
295D4—1762no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—82no—
300C2×C4—112no—
301C2×C4—222no—
302C2×C4—222no—
303C2×C4—442no—
304C2×C4—442no—
305C2×C4—1762no—
306C2×C4D8×D1111yescharacteristic
307C2×C4D8×D1111yescharacteristic
308C2×C4C2×D4×D1111yescharacteristic
309C8—21no—
310C8—222no—
311C8C2×#433911yescharacteristic
312C8#6704311yescharacteristic
313C22—81no—
314C22—81no—
315C22—81no—
316C22—222no—
317C22—222no—
318C22—222no—
319C22C2×D8×D1111yescharacteristic
320C4—21no—
321C4—81no—
322C4—81no—
323C4—81no—
324C4—222no—
325C4—882no—
326C4—882no—
327C4#1062252812yes—
328C4#1062308211yescharacteristic
329C4#1062330211yescharacteristic
330C2—161no—
331C2—442no—
332C2#1308096511yescharacteristic
333C2C2×#1062252811yescharacteristic
334C2#1308175411yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC4×C11×SD32C2
socleC22×C11C22×D8
prime radical#13081040C2
hypercenterC4×SD32D11
hypocenterC11#33924
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ C4×SD32

Complements

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

NH ≅ G/Ntype
2. #13081010C2semidirect
3. #13070891C2semidirect
4. #13070823C2semidirect
5. #13070795C2semidirect
6. #13070768C2semidirect
7. #13070763C2semidirect
8. #13070726C2semidirect
9. #13070449C2semidirect
10. #13070403C2semidirect
11. C4×C11×SD32C2semidirect
127. C4×SD32D11semidirect
285. C11#33924semidirect

Maximal subgroups

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

subgroupindex
#130810402
#130810102
#130708912
#130708232
#130707952
#130707682
#130707632
#130707262
#130704492
#130704032
C4×C11×SD322
#3392411