Finite Group Databasebeta

← #14911403

Subgroups — #14911403

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#13081009C211yesmaximal, characteristic, complemented
2#13070889C211yesmaximal, characteristic, complemented
3#13070824C212yesmaximal, complemented
4#13070794C212yesmaximal, complemented
5#13070765C211yesmaximal, characteristic, complemented
6#13070763C211yesmaximal, characteristic, complemented
7#13070727C212yesmaximal, complemented
8C4×#66891C211yesmaximal, characteristic, complemented
9#13070448C211yesmaximal, characteristic, complemented
10#13070405C212yesmaximal, complemented
11C11×#3341C211yesmaximal, characteristic
12C11×#555—21no—
13#10623074—21no—
14C11×#500C2211yescharacteristic
15C11×#482—22no—
16C11×#476—21no—
17C11×#466C2212yes—
18C4×C11×D8C2211yescharacteristic
19C8×D4×C11C2211yescharacteristic
20C11×#427C2212yes—
21C2×#66891C2211yescharacteristic
22#10622729C2212yes—
23C2×#66882C2212yes—
24C2×#66876C2212yes—
25#10622463—21no—
26#10622335—22no—
27C4×Dic44C2211yescharacteristic
28#10622295C2211yescharacteristic
29#10622200C2211yescharacteristic
30#10622200C2212yes—
31C22⋊(C11⋊C16)C2212yes—
32#10622130C2211yescharacteristic
33#10622130C2212yes—
34#10622128C2211yescharacteristic
35#10622128C2212yes—
36#10622127C2212yes—
37#10622127C2212yes—
38#10622127C2212yes—
39C4⋊(C11⋊C16)C2211yescharacteristic
40C4×C11⋊C16C2211yescharacteristic
41C2×C11×D8C2311yescharacteristic
42C22×C8×C11C2312yes—
43C11×C4⋊Q8—21no—
44C11×#124—42no—
45C11×#121—22no—
46C11×#121—41no—
47C4×D4×C11—21no—
48C4×D4×C11D411yescharacteristic
49C11×#117—22no—
50C11×#117—41no—
51D4×Dic11—41no—
52C2×C4⋊Dic11—22no—
53#66977—22no—
54C2×Dic44C2311yescharacteristic
55#66943—41no—
56#66931—42no—
57#66922—21no—
58C4×Dic22—21no—
59C11×#107—21no—
60C11×#107C2312yes—
61C11×#107C2311yescharacteristic
62C11×#106—22no—
63C11×C4⋊C8D411yescharacteristic
64C11×#102—21no—
65C11×#102—22no—
66C11×C22⋊C8D412yes—
67C4×C8×C11C2311yescharacteristic
68#66891—22no—
69#66882—21no—
70#66882—22no—
71#66882C2312yes—
72#66882C2311yescharacteristic
73#66880—22no—
74#66880—21no—
75#66876—24no—
76C2×C11⋊C16C2311yescharacteristic
77C2×C11⋊C16C2312yes—
78C2×C11⋊C16C2311yescharacteristic
79#33924—111nomaximal, Sylow
80C2×Q8×C11—41no—
81C2×D4×C11—21no—
82C2×D4×C11—42no—
83C2×D4×C11D811yescharacteristic
84C22×C4×C11—41no—
85C22×C4×C11C2×D412yes—
86C22×Dic11—42no—
87C2×Dic22—21no—
88C2×Dic22—41no—
89C11×D8—21no—
90C11×D8—21no—
91C2×C8×C11—22no—
92C2×C8×C11—22no—
93C2×C8×C11C2×D411yescharacteristic
94C2×C8×C11C2×D412yes—
95C2×C8×C11C2411yescharacteristic
96C11×C4⋊C4—21no—
97C11×C4⋊C4—22no—
98C11×C4⋊C4—41no—
99C11×C4⋊C4D811yescharacteristic
100C11×C22⋊C4—42no—
101C11×C22⋊C4—42no—
102C11×C22⋊C4—41no—
103C11×C22⋊C4D812yes—
104C42×C11—42no—
105C42×C11C2×D411yescharacteristic
106C22⋊Dic11—42no—
107C4⋊Dic11—21no—
108C4⋊Dic11—22no—
109C4⋊Dic11—41no—
110C4⋊Dic11—42no—
111Dic11⋊C4—41no—
112Dic11⋊C4—42no—
113C4×Dic11—41no—
114Dic44—21no—
115Dic44—21no—
116C11⋊C16—22no—
117C11⋊C16—21no—
118C11⋊C16#4112yes—
119#3341D1111yescharacteristic
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#2169—111no—
129#2159—112no—
130C23×C11—41no—
131C23×C11C2×D812yes—
132Q8×C11—161no—
133D4×C11—22no—
134D4×C11—41no—
135D4×C11—41no—
136D4×C11—162no—
137C2×C4×C11—22no—
138C2×C4×C11—22no—
139C2×C4×C11—41no—
140C2×C4×C11—42no—
141C2×C4×C11—82no—
142C2×C4×C11C2×D812yes—
143C2×C4×C11C2×D811yescharacteristic
144C2×C4×C11C2×D811yescharacteristic
145C2×C4×C11C22×D411yescharacteristic
146C2×Dic11—41no—
147C2×Dic11—41no—
148C2×Dic11—42no—
149C2×Dic11—162no—
150Dic22—41no—
151Dic22—41no—
152Dic22—161no—
153C8×C11—22no—
154C8×C11—21no—
155C8×C11C2×#4111yescharacteristic
156C8×C112−1+411yescharacteristic
157#555—21no—
158#554—221no—
159C2×SD32—111no—
160C2×M32—112no—
161#500—111no—
162#500C2×D1111yescharacteristic
163#484—222no—
164#482—22no—
165#477—221no—
166#476—21no—
167#467—112no—
168#466C2×D1112yes—
169C4×Q16—111no—
170C4×D8C2×D1111yescharacteristic
171C8×D4C2×D1111yescharacteristic
172#427C2×D1112yes—
173C2×#107—112no—
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×C11—81no—
190C22×C11—81no—
191C22×C11—81no—
192C22×C11C22×D811yescharacteristic
193C4×C11—22no—
194C4×C11—21no—
195C4×C11—81no—
196C4×C11—82no—
197C4×C11#51012yes—
198C4×C11#54711yescharacteristic
199C4×C11#57811yescharacteristic
200Dic11—81no—
201Dic11—82no—
202Dic11—81no—
203C2×Q16—111no—
204C2×D8C22×D1111yescharacteristic
205C22×C8C22×D1112yes—
206C4⋊Q8—21no—
207C4⋊Q8—221no—
208#125—441no—
209#124—42no—
210C22⋊Q8—222no—
211C22⋊Q8—442no—
212#121—22no—
213#121—41no—
214C4×Q8—221no—
215C4×D4—21no—
216C4×D4—441no—
217C4×D4C22⋊D1111yescharacteristic
218#117—22no—
219#117—41no—
220C2×C4⋊C4—222no—
221SD32—222no—
222M32—224no—
223C2×C16—111no—
224C2×C16—111no—
225C2×C16—112no—
226#107—21no—
227#107—111no—
228#107—112no—
229#107—222no—
230#107—221no—
231#107C22×D1112yes—
232#107C22×D1111yescharacteristic
233#106—22no—
234C4⋊C8C22⋊D1111yescharacteristic
235#103—221no—
236#103—222no—
237#102—21no—
238#102—22no—
239C22⋊C8C22⋊D1112yes—
240C4×C8C22×D1111yescharacteristic
241C2×C11—42no—
242C2×C11—161no—
243C2×C11#333411yescharacteristic
244C2×C11C2×#51011yescharacteristic
245C2×C11#341511yescharacteristic
246C2×Q8—41no—
247C2×Q8—221no—
248C2×Q8—441no—
249C2×D4—21no—
250C2×D4—42no—
251C2×D4#432311yescharacteristic
252C22×C4—41no—
253C22×C4—442no—
254C22×C4C2×C22⋊D1112yes—
255Q16—221no—
256Q16—221no—
257D8—21no—
258D8—21no—
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—41no—
267C4⋊C4—221no—
268C4⋊C4—222no—
269C4⋊C4—442no—
270C4⋊C4—441no—
271C4⋊C4—441no—
272C4⋊C4—442no—
273C4⋊C4#432311yescharacteristic
274C22⋊C4—42no—
275C22⋊C4—42no—
276C22⋊C4—41no—
277C22⋊C4—442no—
278C22⋊C4#432312yes—
279C42—42no—
280C42—441no—
281C42C2×C22⋊D1111yescharacteristic
282C16—112no—
283C16—222no—
284C16—221no—
285C11#3392411yescharacteristic, complemented, Sylow
286C23—41no—
287C23C2×#432312yes—
288Q8—161no—
289Q8—441no—
290Q8—441no—
291Q8—1761no—
292D4—22no—
293D4—41no—
294D4—41no—
295D4—162no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—41no—
299C2×C4—42no—
300C2×C4—82no—
301C2×C4—441no—
302C2×C4—441no—
303C2×C4—442no—
304C2×C4—1762no—
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—81no—
317C22—81no—
318C22—81no—
319C22C22×#432311yescharacteristic
320C4—22no—
321C4—21no—
322C4—81no—
323C4—82no—
324C4—881no—
325C4—881no—
326C4—882no—
327C4#1062280812yes—
328C4#1062335511yescharacteristic
329C4#1062336911yescharacteristic
330C2—42no—
331C2—161no—
332C2#1308095911yescharacteristic
333C2C2×#1062280811yescharacteristic
334C2#1308175511yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
Fitting, prime radicalC11×#3341C2
socleC22×C11C22×D8
hypercenter#3341D11
hypocenterC11#33924
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #3341

Complements

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

NH ≅ G/Ntype
1. #13081009C2semidirect
2. #13070889C2semidirect
3. #13070824C2semidirect
4. #13070794C2semidirect
5. #13070765C2semidirect
6. #13070763C2semidirect
7. #13070727C2semidirect
8. C4×#66891C2semidirect
9. #13070448C2semidirect
10. #13070405C2semidirect
285. C11#33924semidirect

Maximal subgroups

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

subgroupindex
#130810092
#130708892
#130708242
#130707942
#130707652
#130707632
#130707272
C4×#668912
#130704482
#130704052
C11×#33412
#3392411