Finite Group Databasebeta

← #14911409

Subgroups — #14911409

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#13070889C211yesmaximal, characteristic, complemented
3#13070821C212yesmaximal, complemented
4#13070796C212yesmaximal, complemented
5#13070768C211yesmaximal, characteristic, complemented
6#13070760C211yesmaximal, characteristic, complemented
7#13070731C212yesmaximal, complemented
8C4×#66892C211yesmaximal, characteristic, complemented
9#13070448C211yesmaximal, characteristic, complemented
10#13070402C212yesmaximal, complemented
11C11×#3338C211yesmaximal, characteristic, complemented
12C11×#554—21no—
13#10623094—21no—
14C11×#500C2211yescharacteristic
15C11×#484—22no—
16C11×#477—21no—
17C11×#467C2212yes—
18C4×C11×Q16C2211yescharacteristic
19C8×D4×C11C2211yescharacteristic
20C2×C11×#107C2212yes—
21C2×#66892C2211yescharacteristic
22#10622728C2212yes—
23#10622719C2212yes—
24C2×#66876C2212yes—
25#10622455—21no—
26#10622350—22no—
27C4×D88C2211yescharacteristic
28#10622295C2211yescharacteristic
29#10622202C2211yescharacteristic
30#10622202C2212yes—
31C22⋊(C11⋊C16)C2212yes—
32#10622129C2211yescharacteristic
33#10622129C2212yes—
34#10622128C2211yescharacteristic
35#10622128C2212yes—
36#10622127C2212yes—
37#10622127C2212yes—
38#10622127C2212yes—
39C4⋊(C11⋊C16)C2211yescharacteristic
40C4×C11⋊C16C2211yescharacteristic
41C2×C11×Q16C2311yescharacteristic
42C22×C8×C11C2312yes—
43C11×C4⋊Q8—21no—
44C11×#125—41no—
45C11×C22⋊Q8—22no—
46C11×C22⋊Q8—42no—
47C4×Q8×C11—21no—
48C4×D4×C11—41no—
49C4×D4×C11D411yescharacteristic
50C2×C11×C4⋊C4—22no—
51#66991—41no—
52#66983—22no—
53#66979—22no—
54C2×D88C2311yescharacteristic
55#66945—41no—
56#66938—42no—
57C4×D44—21no—
58#66922—21no—
59C11×#107—21no—
60C11×#107—22no—
61C11×#107C2312yes—
62C11×#107C2311yescharacteristic
63C11×C4⋊C8D411yescharacteristic
64C11×#103—21no—
65C11×#103—22no—
66C11×C22⋊C8D412yes—
67C4×C8×C11C2311yescharacteristic
68#66892—22no—
69#66885—22no—
70#66885—21no—
71#66882—21no—
72#66882C2312yes—
73#66882C2311yescharacteristic
74#66881—22no—
75#66876—24no—
76C2×C11⋊C16C2311yescharacteristic
77C2×C11⋊C16C2312yes—
78C2×C11⋊C16C2311yescharacteristic
79#33924—111nomaximal, Sylow
80C2×Q8×C11—21no—
81C2×Q8×C11—41no—
82C2×D4×C11D811yescharacteristic
83C22×C4×C11—42no—
84C22×C4×C11C2×D412yes—
85C2×C22⋊D11—42no—
86C2×D44—21no—
87C2×C4×D11—41no—
88C2×Dic22—41no—
89C11×Q16—21no—
90C11×Q16—21no—
91C2×C8×C11—22no—
92C2×C8×C11—22no—
93C2×C8×C11C2×D412yes—
94C2×C8×C11C2×D411yescharacteristic
95C2×C8×C11C2411yescharacteristic
96C11×C4⋊C4—21no—
97C11×C4⋊C4—22no—
98C11×C4⋊C4—42no—
99C11×C4⋊C4—41no—
100C11×C4⋊C4—41no—
101C11×C4⋊C4—42no—
102C11×C4⋊C4D811yescharacteristic
103C11×C22⋊C4—42no—
104C11×C22⋊C4D812yes—
105C42×C11—41no—
106C42×C11C2×D411yescharacteristic
107C22⋊Dic11—42no—
108(C2×D11)⋊C4—41no—
109(C2×D11)⋊C4—42no—
110C4⋊Dic11—21no—
111C4⋊Dic11—22no—
112C4⋊Dic11—41no—
113C4×Dic11—42no—
114D88—21no—
115D88—21no—
116C11⋊C16—22no—
117C11⋊C16—21no—
118C11⋊C16#4112yes—
119#3341—111no—
120#3338D1111yescharacteristic, complemented
121#2252—111no—
122#2237—112no—
123#2232—112no—
124#2227—111no—
125#2226—111no—
126#2220—112no—
127C4×SD32—111no—
128#2169—111no—
129#2159—112no—
130C23×C11C2×D812yes—
131C22×D11—41no—
132Q8×C11—41no—
133Q8×C11—41no—
134Q8×C11—161no—
135D4×C11—22no—
136C2×C4×C11—22no—
137C2×C4×C11—22no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—42no—
141C2×C4×C11—162no—
142C2×C4×C11C2×D812yes—
143C2×C4×C11C2×D811yescharacteristic
144C2×C4×C11C2×D811yescharacteristic
145C2×C4×C11C22×D411yescharacteristic
146C22⋊D11—162no—
147C2×Dic11—41no—
148C2×Dic11—42no—
149D44—41no—
150D44—41no—
151C4×D11—82no—
152Dic22—161no—
153C8×C11—22no—
154C8×C11—21no—
155C8×C11C2×#4111yescharacteristic
156C8×C112−1+411yescharacteristic
157#555—221no—
158#554—21no—
159C2×SD32—111no—
160C2×M32—112no—
161#500—111no—
162#500C2×D1111yescharacteristic
163#484—22no—
164#482—222no—
165#477—21no—
166#476—221no—
167#467C2×D1112yes—
168#466—112no—
169C4×Q16C2×D1111yescharacteristic
170C4×D8—111no—
171C8×D4C2×D1111yescharacteristic
172#427—112no—
173C2×#107C2×D1112yes—
174#367—111no—
175#367—112no—
176#366—112no—
177#366—112no—
178#366—112no—
179C4⋊C16—111no—
180#358—111no—
181#358—112no—
182#357—111no—
183#357—112no—
184C22⋊C16—112no—
185C4×C16—111no—
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—81no—
196C4×C11—81no—
197C4×C11—82no—
198C4×C11#51012yes—
199C4×C11#54711yescharacteristic
200C4×C11#57811yescharacteristic
201Dic11—81no—
202Dic11—82no—
203C2×Q16C22×D1111yescharacteristic
204C2×D8—111no—
205C22×C8C22×D1112yes—
206C4⋊Q8—21no—
207C4⋊Q8—221no—
208#125—41no—
209#124—442no—
210C22⋊Q8—22no—
211C22⋊Q8—42no—
212#121—222no—
213#121—441no—
214C4×Q8—21no—
215C4×D4—41no—
216C4×D4—221no—
217C4×D4C22⋊D1111yescharacteristic
218#117—222no—
219#117—441no—
220C2×C4⋊C4—22no—
221SD32—222no—
222M32—224no—
223C2×C16—111no—
224C2×C16—111no—
225C2×C16—112no—
226#107—22no—
227#107—21no—
228#107—112no—
229#107—111no—
230#107—221no—
231#107C22×D1111yescharacteristic
232#107C22×D1112yes—
233#106—222no—
234C4⋊C8C22⋊D1111yescharacteristic
235#103—21no—
236#103—22no—
237#102—221no—
238#102—222no—
239C22⋊C8C22⋊D1112yes—
240C4×C8C22×D1111yescharacteristic
241C2×C11—42no—
242C2×C11#333411yescharacteristic
243C2×C11C2×#51011yescharacteristic
244C2×C11#341511yescharacteristic
245D11—161no—
246C2×Q8—21no—
247C2×Q8—41no—
248C2×Q8—441no—
249C2×D4—221no—
250C2×D4—442no—
251C2×D4#432311yescharacteristic
252C22×C4—42no—
253C22×C4—441no—
254C22×C4C2×C22⋊D1112yes—
255Q16—21no—
256Q16—21no—
257D8—221no—
258D8—221no—
259C2×C8—22no—
260C2×C8—22no—
261C2×C8C2×C22⋊D1111yescharacteristic
262C2×C8C2×C22⋊D1112yes—
263C2×C8C23×D1111yescharacteristic
264C4⋊C4—21no—
265C4⋊C4—22no—
266C4⋊C4—42no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—42no—
270C4⋊C4—221no—
271C4⋊C4—222no—
272C4⋊C4—441no—
273C4⋊C4#432311yescharacteristic
274C22⋊C4—42no—
275C22⋊C4—442no—
276C22⋊C4—442no—
277C22⋊C4—441no—
278C22⋊C4#432312yes—
279C42—41no—
280C42—442no—
281C42C2×C22⋊D1111yescharacteristic
282C16—112no—
283C16—222no—
284C16—221no—
285C11#3392411yescharacteristic, complemented, Sylow
286C23—441no—
287C23C2×#432312yes—
288Q8—41no—
289Q8—41no—
290Q8—161no—
291Q8—1761no—
292D4—22no—
293D4—441no—
294D4—441no—
295D4—1762no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—42no—
301C2×C4—162no—
302C2×C4—441no—
303C2×C4—442no—
304C2×C4—882no—
305C2×C4C2×#432312yes—
306C2×C4C2×#432311yescharacteristic
307C2×C4C2×#432311yescharacteristic
308C2×C4C22×C22⋊D1111yescharacteristic
309C8—22no—
310C8—21no—
311C8#41×D1111yescharacteristic
312C8#6704311yescharacteristic
313C22—22no—
314C22—22no—
315C22—22no—
316C22—881no—
317C22—881no—
318C22—881no—
319C22C22×#432311yescharacteristic
320C4—22no—
321C4—21no—
322C4—81no—
323C4—81no—
324C4—82no—
325C4—881no—
326C4—882no—
327C4#1062279212yes—
328C4#1062335511yescharacteristic
329C4#1062336911yescharacteristic
330C2—42no—
331C2—1761no—
332C2#1308095911yescharacteristic
333C2C2×#1062279211yescharacteristic
334C2#1308175511yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3338C2
socleC22×C11C22×D8
prime radical#13081039C2
hypercenter#3338D11
hypocenterC11#33924
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #3338

Complements

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

NH ≅ G/Ntype
2. #13070889C2semidirect
3. #13070821C2semidirect
4. #13070796C2semidirect
5. #13070768C2semidirect
6. #13070760C2semidirect
7. #13070731C2semidirect
8. C4×#66892C2semidirect
9. #13070448C2semidirect
10. #13070402C2semidirect
11. C11×#3338C2semidirect
120. #3338D11semidirect
285. C11#33924semidirect

Maximal subgroups

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

subgroupindex
#130810392
#130708892
#130708212
#130707962
#130707682
#130707602
#130707312
C4×#668922
#130704482
#130704022
C11×#33382
#3392411