Finite Group Databasebeta

← #14911199

Subgroups — #14911199

Order 2816.

480 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081048C211yesmaximal, characteristic, complemented
2#13081038C211yesmaximal, characteristic
3#13070896C211yesmaximal, characteristic, complemented
4#13070823C212yesmaximal, complemented
5#13070810C212yesmaximal, complemented
6#13070754C211yesmaximal, characteristic, complemented
7#13070715C212yesmaximal, complemented
8C4×#66892C211yesmaximal, characteristic, complemented
9#13070435C211yesmaximal, characteristic, complemented
10#13070397C212yesmaximal, complemented
11C11×#2227C211yesmaximal, characteristic, complemented
12#10623265—21no—
13#10623115—21no—
14C11×#500C2211yescharacteristic
15C4×C11×Q16C2211yescharacteristic
16#10622801C2212yes—
17C2×#66892C2211yescharacteristic
18#10622697—21no—
19#10622633—21no—
20C2×C16×D11C2212yes—
21#10622498—22no—
22#10622496C2212yes—
23#10622493C2212yes—
24#10622493C2212yes—
25#10622427—22no—
26C4×D88C2211yescharacteristic
27C8×D44C2211yescharacteristic
28#10622295C2211yescharacteristic
29C11×#366C2212yes—
30C11×C4⋊C16C2211yescharacteristic
31C11×#358C2212yes—
32#10622202C2211yescharacteristic
33#10622147C2212yes—
34(C2×D11)⋊C16C2212yes—
35#10622142C2212yes—
36#10622129C2211yescharacteristic
37#10622128C2212yes—
38#10622128C2212yes—
39#10622128C2211yescharacteristic
40C4×C11⋊C16C2211yescharacteristic
41C2×C11×Q16C2311yescharacteristic
42C11×C4⋊Q8—21no—
43C4×Q8×C11—21no—
44#67000—42no—
45#66999—22no—
46C2×D88C2311yescharacteristic
47C2×C8×D11C2312yes—
48#66951—42no—
49#66948—22no—
50#66948—41no—
51#66945—22no—
52#66945—22no—
53#66945—41no—
54#66928—41no—
55C4×D44—21no—
56C4×D44D411yescharacteristic
57#66922—21no—
58C4×Dic22—41no—
59C2×C11×C16C2312yes—
60C11×#107—21no—
61C11×#107C2312yes—
62C11×#107C2311yescharacteristic
63C11×#103—21no—
64C4×C8×C11C2311yescharacteristic
65#66899—22no—
66#66892—22no—
67#66885—21no—
68(C2×D11)⋊C8D412yes—
69#66882—21no—
70#66882C2311yescharacteristic
71#66882C2312yes—
72C2×C11⋊C16C2311yescharacteristic
73C2×C11⋊C16C2311yescharacteristic
74#66873—22no—
75#66872—22no—
76#66872—22no—
77C4⋊(C11⋊C8)D411yescharacteristic
78C16×D11—24no—
79#33907—111nomaximal, Sylow
80C2×Q8×C11—21no—
81C2×Q8×C11—41no—
82C2×D44—21no—
83C2×D44—42no—
84C2×D44D811yescharacteristic
85C2×C4×D11—41no—
86C2×C4×D11C2×D412yes—
87C2×Dic22—41no—
88C11×Q16—21no—
89C11×Q16—21no—
90C2×C8×C11C2×D411yescharacteristic
91C2×C8×C11C2411yescharacteristic
92C11×C4⋊C4—21no—
93C11×C4⋊C4—22no—
94C11×C4⋊C4—41no—
95C11×C4⋊C4—41no—
96C42×C11—41no—
97C42×C11C2×D411yescharacteristic
98(C2×D11)⋊C4—42no—
99(C2×D11)⋊C4—42no—
100(C2×D11)⋊C4—42no—
101(C2×D11)⋊C4—42no—
102(C2×D11)⋊C4—41no—
103(C2×D11)⋊C4D812yes—
104C4⋊Dic11—21no—
105C4⋊Dic11—22no—
106C4⋊Dic11—41no—
107C4⋊Dic11D811yescharacteristic
108Dic11⋊C4—42no—
109C4×Dic11—42no—
110C4×Dic11—42no—
111C2×C11⋊C8C2×D412yes—
112D88—21no—
113D88—21no—
114C8×D11—22no—
115C8×D11—22no—
116C11×C16—22no—
117C11⋊C16—21no—
118C11⋊C16#4112yes—
119#3342—111no—
120#3341—111no—
121#2254—111no—
122#2237—112no—
123#2234—112no—
124#2227D1111yescharacteristic, complemented
125#2224—111no—
126#2217—112no—
127C4×SD32—111no—
128D4×C16—111no—
129#2158—112no—
130C22×D11—41no—
131C22×D11C2×D812yes—
132Q8×C11—41no—
133Q8×C11—41no—
134Q8×C11—161no—
135C2×C4×C11—41no—
136C2×C4×C11—42no—
137C2×C4×C11—41no—
138C2×C4×C11C2×D811yescharacteristic
139C2×C4×C11C2×D811yescharacteristic
140C2×C4×C11C22×D411yescharacteristic
141C2×Dic11—41no—
142C2×Dic11—42no—
143C2×Dic11C2×D812yes—
144D44—22no—
145D44—41no—
146D44—41no—
147D44—162no—
148C4×D11—22no—
149C4×D11—22no—
150C4×D11—82no—
151Dic22—82no—
152C8×C11—21no—
153C8×C11C2×#4111yescharacteristic
154C8×C112−1+411yescharacteristic
155C11⋊C8—22no—
156#556—221no—
157#555—221no—
158C2×SD32—111no—
159C22×C16—112no—
160#500—111no—
161#500C2×D1111yescharacteristic
162#485—222no—
163#482—222no—
164#476—221no—
165#475—221no—
166#467—112no—
167#466—112no—
168C4×Q16C2×D1111yescharacteristic
169C4×D8—111no—
170C8×D4—111no—
171#427—112no—
172#427—112no—
173#367—111no—
174#367—112no—
175#367—112no—
176#366—112no—
177#366C2×D1112yes—
178C4⋊C16C2×D1111yescharacteristic
179#358—111no—
180#358C2×D1112yes—
181#357—112no—
182#357—111no—
183C22⋊C16—112no—
184C4×C16—111no—
185C22×C11C22×D811yescharacteristic
186C2×D11—22no—
187C2×D11—22no—
188C2×D11—22no—
189C2×D11—81no—
190C2×D11—81no—
191C2×D11—81no—
192C4×C11—21no—
193C4×C11—81no—
194C4×C11—81no—
195C4×C11—82no—
196C4×C11#50812yes—
197C4×C11#54711yescharacteristic
198C4×C11#57811yescharacteristic
199Dic11—22no—
200Dic11—82no—
201Dic11—81no—
202C2×Q16C22×D1111yescharacteristic
203C2×D8—111no—
204C22×C8—112no—
205C4⋊Q8—21no—
206C4⋊Q8—221no—
207#126—442no—
208#124—441no—
209#124—442no—
210C22⋊Q8—222no—
211#121—222no—
212#121—441no—
213C4×Q8—21no—
214C4×Q8—441no—
215C4×D4—111no—
216C4×D4—221no—
217#117—222no—
218#117—222no—
219#117—441no—
220SD32—222no—
221C2×C16—111no—
222C2×C16—111no—
223C2×C16—224no—
224C2×C16C22×D1112yes—
225#107—21no—
226#107—112no—
227#107—111no—
228#107—221no—
229#107C22×D1111yescharacteristic
230#107C22×D1112yes—
231#106—222no—
232#106—222no—
233C4⋊C8—111no—
234#103—21no—
235#103—222no—
236#102—222no—
237#102—221no—
238C22⋊C8—112no—
239C4×C8C22×D1111yescharacteristic
240C2×C11#333411yescharacteristic
241C2×C11C2×#50811yescharacteristic
242C2×C11#341611yescharacteristic
243D11—42no—
244D11—161no—
245C2×Q8—21no—
246C2×Q8—41no—
247C2×Q8—441no—
248C2×D4—111no—
249C2×D4—221no—
250C2×D4—442no—
251C22×C4—112no—
252C22×C4—441no—
253Q16—21no—
254Q16—21no—
255D8—221no—
256D8—221no—
257C2×C8—112no—
258C2×C8—222no—
259C2×C8—222no—
260C2×C8D4×D1111yescharacteristic
261C2×C8C23×D1111yescharacteristic
262C4⋊C4—22no—
263C4⋊C4—21no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—111no—
267C4⋊C4—221no—
268C4⋊C4—222no—
269C4⋊C4—442no—
270C4⋊C4—441no—
271C22⋊C4—112no—
272C22⋊C4—442no—
273C22⋊C4—442no—
274C22⋊C4—442no—
275C22⋊C4—442no—
276C22⋊C4—441no—
277C42—41no—
278C42—442no—
279C42—442no—
280C42D4×D1111yescharacteristic
281C16—22no—
282C16—112no—
283C16—221no—
284C11#3390711yescharacteristic, complemented, Sylow
285C23—112no—
286C23—441no—
287Q8—41no—
288Q8—41no—
289Q8—161no—
290Q8—882no—
291D4—222no—
292D4—441no—
293D4—441no—
294D4—1762no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—42no—
298C2×C4—112no—
299C2×C4—222no—
300C2×C4—222no—
301C2×C4—441no—
302C2×C4—442no—
303C2×C4—882no—
304C2×C4D8×D1111yescharacteristic
305C2×C4D8×D1111yescharacteristic
306C2×C4C2×D4×D1111yescharacteristic
307C8—21no—
308C8—222no—
309C8#6704011yescharacteristic
310C8#41×D1111yescharacteristic
311C22—222no—
312C22—222no—
313C22—222no—
314C22—881no—
315C22—881no—
316C22—881no—
317C22C2×D8×D1111yescharacteristic
318C4—21no—
319C4—81no—
320C4—82no—
321C4—81no—
322C4—222no—
323C4—881no—
324C4—882no—
325C4#1062253212yes—
326C4#1062316211yescharacteristic
327C4#1062331011yescharacteristic
328C2—442no—
329C2—1761no—
330C2#1308096211yescharacteristic
331C2C2×#1062253211yescharacteristic
332C2#1308176211yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2227C2
socleC22×C11C22×D8
prime radical#13081038C2
hypercenter#2227D11
hypocenterC11#33907
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2227

Complements

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

NH ≅ G/Ntype
1. #13081048C2semidirect
3. #13070896C2semidirect
4. #13070823C2semidirect
5. #13070810C2semidirect
6. #13070754C2semidirect
7. #13070715C2semidirect
8. C4×#66892C2semidirect
9. #13070435C2semidirect
10. #13070397C2semidirect
11. C11×#2227C2semidirect
124. #2227D11semidirect
284. C11#33907semidirect

Maximal subgroups

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

subgroupindex
#130810482
#130810382
#130708962
#130708232
#130708102
#130707542
#130707152
C4×#668922
#130704352
#130703972
C11×#22272
#3390711