Finite Group Databasebeta

← #14911408

Subgroups — #14911408

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#13081038C211yesmaximal, characteristic
2#13081008C211yesmaximal, characteristic, complemented
3#13070826C212yesmaximal, complemented
4#13070798C212yesmaximal, complemented
5#13070765C211yesmaximal, characteristic, complemented
6#13070760C211yesmaximal, characteristic, complemented
7#13070730C212yesmaximal, complemented
8C4×#66864C211yesmaximal, characteristic, complemented
9#13070449C211yesmaximal, characteristic, complemented
10#13070401C212yesmaximal, complemented
11C11×#2252C211yesmaximal, characteristic, complemented
12#10623265—21no—
13#10623261—21no—
14C11×#500C2211yescharacteristic
15C11×#500C2211yescharacteristic
16#10622704—21no—
17#10622697—21no—
18C2×#66864C2211yescharacteristic
19C2×#66862C2212yes—
20#10622500C2212yes—
21#10622498—22no—
22#10622497—22no—
23#10622496C2212yes—
24#10622493C2212yes—
25D11×#107C2212yes—
26C4×Dic44C2211yescharacteristic
27C4×D88C2211yescharacteristic
28C8×D44C2211yescharacteristic
29C11×#366C2212yes—
30C11×#366C2212yes—
31C4×C11×C16C2211yescharacteristic
32#10622147C2211yescharacteristic
33(C2×D11)⋊C16C2212yes—
34#10622143C2211yescharacteristic
35#10622141C2211yescharacteristic
36#10622130C2212yes—
37#10622129C2212yes—
38#10622128C2212yes—
39#10622127C2212yes—
40C4⋊(C11⋊C16)C2211yescharacteristic
41C11×C4⋊Q8—21no—
42C11×C4⋊Q8—21no—
43#67000—42no—
44#66999—42no—
45C2×Dic44C2311yescharacteristic
46C2×D88C2311yescharacteristic
47C2×C8×D11C2312yes—
48#66950—22no—
49#66948—22no—
50#66948—41no—
51#66946—41no—
52#66945—22no—
53#66945—41no—
54C4⋊C4×D11—22no—
55#66943—41no—
56C4×D44—21no—
57C4×D44D411yescharacteristic
58C4×Dic22—21no—
59C2×C11×C16C2311yescharacteristic
60C2×C11×C16C2311yescharacteristic
61C11×#107—21no—
62C11×#107—21no—
63C11×#107C2312yes—
64C11×#107C2312yes—
65C4×C8×C11C2311yescharacteristic
66#66885—21no—
67(C2×D11)⋊C8D412yes—
68#66882C2311yescharacteristic
69#66882C2311yescharacteristic
70#66880—21no—
71C2×C11⋊C16C2312yes—
72#66874—22no—
73#66873—22no—
74#66872—22no—
75#66871—22no—
76C4⋊(C11⋊C8)D411yescharacteristic
77#66864—22no—
78#66862—24no—
79#33924—111nomaximal, Sylow
80C2×Q8×C11—41no—
81C2×Q8×C11—41no—
82C2×D44—21no—
83C2×D44—42no—
84C2×D44D811yescharacteristic
85C2×C4×D11—42no—
86C2×C4×D11—41no—
87C2×C4×D11C2×D412yes—
88C2×Dic22—21no—
89C2×C8×C11C2×D411yescharacteristic
90C2×C8×C11C2411yescharacteristic
91C11×C4⋊C4—22no—
92C11×C4⋊C4—22no—
93C11×C4⋊C4—41no—
94C11×C4⋊C4—41no—
95C42×C11C2×D411yescharacteristic
96(C2×D11)⋊C4—42no—
97(C2×D11)⋊C4—42no—
98(C2×D11)⋊C4—42no—
99(C2×D11)⋊C4—41no—
100(C2×D11)⋊C4D812yes—
101C4⋊Dic11—21no—
102C4⋊Dic11—21no—
103C4⋊Dic11—42no—
104C4⋊Dic11D811yescharacteristic
105Dic11⋊C4—42no—
106Dic11⋊C4—41no—
107C4×Dic11—42no—
108C4×Dic11—41no—
109C2×C11⋊C8C2×D412yes—
110Dic44—21no—
111Dic44—21no—
112D88—21no—
113D88—21no—
114C8×D11—22no—
115C8×D11—22no—
116C11×C16—21no—
117C11×C16#4112yes—
118C11⋊C16—22no—
119#3341—111no—
120#3338—111no—
121#2252D1111yescharacteristic, complemented
122#2237—112no—
123#2232—112no—
124#2227—111no—
125#2226—111no—
126#2220—112no—
127C4×SD32—111no—
128#2169—111no—
129#2159—112no—
130C22×D11—41no—
131C22×D11C2×D812yes—
132Q8×C11—161no—
133Q8×C11—161no—
134C2×C4×C11—42no—
135C2×C4×C11—42no—
136C2×C4×C11C2×D811yescharacteristic
137C2×C4×C11C2×D811yescharacteristic
138C2×C4×C11C22×D411yescharacteristic
139C2×Dic11—41no—
140C2×Dic11—41no—
141C2×Dic11—41no—
142C2×Dic11C2×D812yes—
143D44—22no—
144D44—41no—
145D44—41no—
146D44—162no—
147C4×D11—22no—
148C4×D11—22no—
149C4×D11—82no—
150C4×D11—162no—
151Dic22—41no—
152Dic22—41no—
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#500C2×D1111yescharacteristic
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×D8—111no—
171C8×D4—111no—
172#427—112no—
173C2×#107—112no—
174#367—111no—
175#367—112no—
176#366—112no—
177#366C2×D1112yes—
178#366C2×D1112yes—
179C4⋊C16—111no—
180#358—111no—
181#358—112no—
182#357—111no—
183#357—112no—
184C22⋊C16—112no—
185C4×C16C2×D1111yescharacteristic
186C22×C11C22×D811yescharacteristic
187C2×D11—22no—
188C2×D11—22no—
189C2×D11—22no—
190C2×D11—81no—
191C2×D11—81no—
192C2×D11—81no—
193C4×C11—21no—
194C4×C11—82no—
195C4×C11—82no—
196C4×C11#51012yes—
197C4×C11#54711yescharacteristic
198C4×C11#57811yescharacteristic
199Dic11—22no—
200Dic11—81no—
201Dic11—81no—
202Dic11—81no—
203C2×Q16—111no—
204C2×D8—111no—
205C22×C8—112no—
206C4⋊Q8—21no—
207C4⋊Q8—21no—
208#125—441no—
209#124—442no—
210C22⋊Q8—222no—
211C22⋊Q8—442no—
212#121—222no—
213#121—441no—
214C4×Q8—221no—
215C4×D4—111no—
216C4×D4—221no—
217C4×D4—441no—
218#117—222no—
219#117—441no—
220C2×C4⋊C4—222no—
221SD32—222no—
222M32—224no—
223C2×C16—112no—
224C2×C16C22×D1111yescharacteristic
225C2×C16C22×D1111yescharacteristic
226#107—21no—
227#107—21no—
228#107—111no—
229#107—111no—
230#107—222no—
231#107C22×D1112yes—
232#107C22×D1112yes—
233#106—222no—
234C4⋊C8—111no—
235#103—222no—
236#103—221no—
237#102—222no—
238#102—221no—
239C22⋊C8—112no—
240C4×C8C22×D1111yescharacteristic
241C2×C11#333411yescharacteristic
242C2×C11C2×#51011yescharacteristic
243C2×C11#341511yescharacteristic
244D11—42no—
245D11—161no—
246C2×Q8—41no—
247C2×Q8—41no—
248C2×Q8—221no—
249C2×D4—111no—
250C2×D4—221no—
251C2×D4—442no—
252C22×C4—112no—
253C22×C4—442no—
254C22×C4—441no—
255Q16—221no—
256Q16—221no—
257D8—221no—
258D8—221no—
259C2×C8—112no—
260C2×C8—222no—
261C2×C8—222no—
262C2×C8D4×D1111yescharacteristic
263C2×C8C23×D1111yescharacteristic
264C4⋊C4—22no—
265C4⋊C4—22no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—111no—
269C4⋊C4—221no—
270C4⋊C4—221no—
271C4⋊C4—442no—
272C4⋊C4—442no—
273C4⋊C4—441no—
274C22⋊C4—112no—
275C22⋊C4—442no—
276C22⋊C4—442no—
277C22⋊C4—442no—
278C22⋊C4—441no—
279C42—442no—
280C42—441no—
281C42D4×D1111yescharacteristic
282C16—21no—
283C16—222no—
284C16#434312yes—
285C11#3392411yescharacteristic, complemented, Sylow
286C23—112no—
287C23—441no—
288Q8—161no—
289Q8—161no—
290Q8—441no—
291Q8—441no—
292D4—222no—
293D4—441no—
294D4—441no—
295D4—1762no—
296C2×C4—42no—
297C2×C4—42no—
298C2×C4—112no—
299C2×C4—222no—
300C2×C4—222no—
301C2×C4—441no—
302C2×C4—441no—
303C2×C4—441no—
304C2×C4—882no—
305C2×C4—1762no—
306C2×C4D8×D1111yescharacteristic
307C2×C4D8×D1111yescharacteristic
308C2×C4C2×D4×D1111yescharacteristic
309C8—21no—
310C8—222no—
311C8C2×#434311yescharacteristic
312C8#6704011yescharacteristic
313C22—222no—
314C22—222no—
315C22—222no—
316C22—881no—
317C22—881no—
318C22—881no—
319C22C2×D8×D1111yescharacteristic
320C4—21no—
321C4—82no—
322C4—82no—
323C4—222no—
324C4—881no—
325C4—881no—
326C4—881no—
327C4#1062253112yes—
328C4#1062325711yescharacteristic
329C4#1062329711yescharacteristic
330C2—442no—
331C2—1761no—
332C2#1308096311yescharacteristic
333C2C2×#1062253111yescharacteristic
334C2#1308175311yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2252C2
socleC22×C11C22×D8
prime radical#13081038C2
hypercenter#2252D11
hypocenterC11#33924
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2252

Complements

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

NH ≅ G/Ntype
2. #13081008C2semidirect
3. #13070826C2semidirect
4. #13070798C2semidirect
5. #13070765C2semidirect
6. #13070760C2semidirect
7. #13070730C2semidirect
8. C4×#66864C2semidirect
9. #13070449C2semidirect
10. #13070401C2semidirect
11. C11×#2252C2semidirect
121. #2252D11semidirect
285. C11#33924semidirect

Maximal subgroups

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

subgroupindex
#130810382
#130810082
#130708262
#130707982
#130707652
#130707602
#130707302
C4×#668642
#130704492
#130704012
C11×#22522
#3392411