Finite Group Databasebeta

← #14911400

Subgroups — #14911400

Order 2816.

470 conjugacy classes of subgroups.

The subgroup lattice has 326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081048C211yesmaximal, characteristic
2#13081010C211yesmaximal, characteristic
3#13070898C211yesmaximal, characteristic, complemented
4#13070822C212yesmaximal, complemented
5#13070812C212yesmaximal, complemented
6#13070768C211yesmaximal, characteristic, complemented
7#13070758C211yesmaximal, characteristic, complemented
8#13070721C212yesmaximal, complemented
9#13070449C211yesmaximal, characteristic
10#13070401C212yesmaximal, complemented
11C4×C11×Q32C211yesmaximal, characteristic, complemented
12#10623115—21no—
13#10623110—21no—
14C2×C11×Q32C2211yescharacteristic
15C4×C11×Q16C2211yescharacteristic
16C4×C11×Q16C2211yescharacteristic
17#10622801C2212yes—
18#10622801C2212yes—
19#10622634—21no—
20#10622633—21no—
21C2×#66862C2212yes—
22#10622493C2212yes—
23D11×#107C2212yes—
24#10622427—22no—
25#10622422—22no—
26C8×D44C2211yescharacteristic
27#10622295C2211yescharacteristic
28#10622295C2211yescharacteristic
29C11×#366C2211yescharacteristic
30C11×#358C2211yescharacteristic
31C11×#358C2211yescharacteristic
32C4×C11×C16C2211yescharacteristic
33#10622202C2212yes—
34#10622202C2212yes—
35(C2×D11)⋊C16C2212yes—
36#10622143C2212yes—
37#10622143C2212yes—
38#10622128C2212yes—
39#10622127C2212yes—
40C4⋊(C11⋊C16)C2211yescharacteristic
41C2×C11×Q16C2311yescharacteristic
42C2×C11×Q16C2311yescharacteristic
43C4×Q8×C11—21no—
44C4×Q8×C11—21no—
45#66999—22no—
46#66999—22no—
47C2×C8×D11C2312yes—
48#66951—42no—
49#66949—42no—
50#66945—22no—
51C4⋊C4×D11—22no—
52#66928—41no—
53C4×D44—41no—
54C4×D44D411yescharacteristic
55#66923—41no—
56#66922—21no—
57#66922—21no—
58C4×Dic22—41no—
59C11×Q32—22no—
60C2×C11×C16C2311yescharacteristic
61C2×C11×C16C2311yescharacteristic
62C11×#107C2311yescharacteristic
63C11×#107C2311yescharacteristic
64C11×#103—21no—
65C11×#103—21no—
66C4×C8×C11C2311yescharacteristic
67#66899—22no—
68#66899—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#33923—111nomaximal, Sylow
80C2×Q8×C11—21no—
81C2×Q8×C11—21no—
82C2×D44D811yescharacteristic
83C2×C4×D11—42no—
84C2×C4×D11C2×D412yes—
85C2×Dic22—41no—
86C2×Dic22—41no—
87C11×Q16—21no—
88C11×Q16—21no—
89C11×Q16—21no—
90C11×Q16—21no—
91C2×C8×C11C2×D411yescharacteristic
92C2×C8×C11C2411yescharacteristic
93C11×C4⋊C4—21no—
94C11×C4⋊C4—21no—
95C11×C4⋊C4—41no—
96C11×C4⋊C4—41no—
97C42×C11—41no—
98C42×C11—41no—
99C42×C11C2×D411yescharacteristic
100(C2×D11)⋊C4—42no—
101(C2×D11)⋊C4—42no—
102(C2×D11)⋊C4—42no—
103(C2×D11)⋊C4D812yes—
104C4⋊Dic11—22no—
105C4⋊Dic11—22no—
106C4⋊Dic11—41no—
107C4⋊Dic11—41no—
108C4⋊Dic11D811yescharacteristic
109Dic11⋊C4—42no—
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#3342—111no—
120#3338—111no—
121#2254—111no—
122#2237—112no—
123#2235—112no—
124#2227—111no—
125#2225—111no—
126#2219—112no—
127C4×Q32D1111yescharacteristic, complemented
128#2169—111no—
129#2159—112no—
130C22×D11C2×D812yes—
131Q8×C11—41no—
132Q8×C11—41no—
133Q8×C11—41no—
134Q8×C11—41no—
135C2×C4×C11—41no—
136C2×C4×C11—41no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11C2×D811yescharacteristic
140C2×C4×C11C2×D811yescharacteristic
141C2×C4×C11C22×D411yescharacteristic
142C2×Dic11—42no—
143C2×Dic11—42no—
144C2×Dic11C2×D812yes—
145D44—22no—
146C4×D11—22no—
147C4×D11—22no—
148C4×D11—162no—
149Dic22—82no—
150Dic22—161no—
151C8×C11—21no—
152C8×C11C2×#4111yescharacteristic
153C8×C112−1+411yescharacteristic
154C11⋊C8—22no—
155#556—221no—
156#554—221no—
157C2×Q32C2×D1111yescharacteristic
158C2×M32—112no—
159#500—111no—
160#500—111no—
161#485—222no—
162#484—222no—
163#477—221no—
164#475—221no—
165#467—112no—
166#467—112no—
167C4×Q16C2×D1111yescharacteristic
168C4×Q16C2×D1111yescharacteristic
169C8×D4—111no—
170#427—112no—
171C2×#107—112no—
172#367—112no—
173#367—112no—
174#367—112no—
175#366—112no—
176#366C2×D1111yescharacteristic
177C4⋊C16—111no—
178#358—112no—
179#358—112no—
180#358C2×D1111yescharacteristic
181#358C2×D1111yescharacteristic
182C22⋊C16—112no—
183C4×C16C2×D1111yescharacteristic
184C22×C11C22×D811yescharacteristic
185C2×D11—22no—
186C2×D11—22no—
187C2×D11—22no—
188C4×C11—21no—
189C4×C11—81no—
190C4×C11—81no—
191C4×C11—81no—
192C4×C11—81no—
193C4×C11#51012yes—
194C4×C11#54711yescharacteristic
195C4×C11#57811yescharacteristic
196Dic11—22no—
197Dic11—82no—
198Dic11—82no—
199C2×Q16C22×D1111yescharacteristic
200C2×Q16C22×D1111yescharacteristic
201C22×C8—112no—
202C4⋊Q8—221no—
203C4⋊Q8—221no—
204#126—442no—
205#125—441no—
206#124—441no—
207C22⋊Q8—222no—
208C22⋊Q8—222no—
209C22⋊Q8—442no—
210C4×Q8—21no—
211C4×Q8—21no—
212C4×Q8—441no—
213C4×D4—111no—
214C4×D4—441no—
215#117—222no—
216C2×C4⋊C4—222no—
217Q32—22no—
218M32—224no—
219C2×C16—112no—
220C2×C16C22×D1111yescharacteristic
221C2×C16C22×D1111yescharacteristic
222#107—112no—
223#107—112no—
224#107—222no—
225#107—221no—
226#107—221no—
227#107C22×D1111yescharacteristic
228#107C22×D1111yescharacteristic
229#106—222no—
230C4⋊C8—111no—
231#103—21no—
232#103—21no—
233#103—222no—
234#103—222no—
235C22⋊C8—112no—
236C4×C8C22×D1111yescharacteristic
237C2×C11#333411yescharacteristic
238C2×C11C2×#51011yescharacteristic
239C2×C11#341611yescharacteristic
240D11—42no—
241C2×Q8—21no—
242C2×Q8—21no—
243C2×Q8—441no—
244C2×Q8—441no—
245C2×D4—111no—
246C22×C4—112no—
247C22×C4—442no—
248Q16—21no—
249Q16—21no—
250Q16—21no—
251Q16—21no—
252C2×C8—112no—
253C2×C8—222no—
254C2×C8—222no—
255C2×C8D4×D1111yescharacteristic
256C2×C8C23×D1111yescharacteristic
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—111no—
262C4⋊C4—222no—
263C4⋊C4—222no—
264C4⋊C4—442no—
265C4⋊C4—442no—
266C4⋊C4—442no—
267C4⋊C4—441no—
268C4⋊C4—441no—
269C22⋊C4—112no—
270C22⋊C4—442no—
271C22⋊C4—442no—
272C22⋊C4—442no—
273C42—41no—
274C42—41no—
275C42—442no—
276C42D4×D1111yescharacteristic
277C16—21no—
278C16—222no—
279C16#433912yes—
280C11#3392311yescharacteristic, complemented, Sylow
281C23—112no—
282Q8—41no—
283Q8—41no—
284Q8—41no—
285Q8—41no—
286Q8—882no—
287Q8—1761no—
288D4—222no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—112no—
294C2×C4—222no—
295C2×C4—222no—
296C2×C4—442no—
297C2×C4—442no—
298C2×C4—1762no—
299C2×C4D8×D1111yescharacteristic
300C2×C4D8×D1111yescharacteristic
301C2×C4C2×D4×D1111yescharacteristic
302C8—21no—
303C8—222no—
304C8C2×#433911yescharacteristic
305C8#6704311yescharacteristic
306C22—222no—
307C22—222no—
308C22—222no—
309C22C2×D8×D1111yescharacteristic
310C4—21no—
311C4—81no—
312C4—81no—
313C4—81no—
314C4—81no—
315C4—222no—
316C4—882no—
317C4—882no—
318C4#1062253112yes—
319C4#1062308211yescharacteristic
320C4#1062330211yescharacteristic
321C2—442no—
322C2#1308096511yescharacteristic
323C2C2×#1062253111yescharacteristic
324C2#1308175911yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC4×C11×Q32C2
socleC22×C11C22×D8
prime radicalC2×D44D8
hypercenterC4×Q32D11
hypocenterC11#33923
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ C4×Q32

Complements

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

NH ≅ G/Ntype
3. #13070898C2semidirect
4. #13070822C2semidirect
5. #13070812C2semidirect
6. #13070768C2semidirect
7. #13070758C2semidirect
8. #13070721C2semidirect
10. #13070401C2semidirect
11. C4×C11×Q32C2semidirect
127. C4×Q32D11semidirect
280. C11#33923semidirect

Maximal subgroups

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

subgroupindex
#130810482
#130810102
#130708982
#130708222
#130708122
#130707682
#130707582
#130707212
#130704492
#130704012
C4×C11×Q322
#3392311