Finite Group Databasebeta

← #14664731

Subgroups — #14664731

Order 2816.

336 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 81 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079187C211yesmaximal, characteristic
2#13070416C211yesmaximal, characteristic, complemented
3#13068742C211yesmaximal, characteristic, complemented
4#13066628C211yesmaximal, characteristic, complemented
5#13066626C211yesmaximal, characteristic
6#13066624C211yesmaximal, characteristic
7C11×#1348C211yesmaximal, characteristic, complemented
8#10623155—21no—
9C11×#467C2211yescharacteristic
10#10622804C411yescharacteristic, complemented
11Q16×Dic11C411yescharacteristic, complemented
12#10622728C2211yescharacteristic
13C2×C8×Dic11C2211yescharacteristic
14#10622661—21no—
15#10622589—21no—
16#10622491C411yescharacteristic, complemented
17#10622485C411yescharacteristic, complemented
18#10622413—21no—
19#10622401—21no—
20C11×C22⋊C16C2211yescharacteristic
21C11×#340C2211yescharacteristic
22#10622189C2211yescharacteristic
23C22⋊(C11⋊C16)C2211yescharacteristic
24#10622167—21no—
25#10622140—21no—
26Dic11⋊C16—21no—
27C2×C11×Q16C2×C411yescharacteristic
28C22×C8×C11C2311yescharacteristic
29C11×C22⋊Q8—21no—
30C2×C11×C4⋊C4—21no—
31#67000—21no—
32Q8×Dic11—21no—
33C2×#4325—21no—
34#66983—21no—
35C2×C4⋊Dic11—21no—
36C2×Dic11⋊C4—41no—
37C2×Dic11⋊C4—41no—
38C2×C4×Dic11D411yescharacteristic
39C22×C11⋊C8D411yescharacteristic
40C2×D88C2×C411yescharacteristic
41#66951—41no—
42#66946—21no—
43#66945—41no—
44#66943—21no—
45#66939—41no—
46(C22⋊D11)⋊C4—41no—
47C2×C11×C16—21no—
48C11×#107C2×C411yescharacteristic
49C11×#103—21no—
50#66899—21no—
51#66885—21no—
52#66882C2×C411yescharacteristic
53C8×Dic11C2×C411yescharacteristic
54C8×Dic11C2×C411yescharacteristic
55C8×Dic11D411yescharacteristic
56C8×Dic11D411yescharacteristic
57C2×C11⋊C16—21no—
58#66873—21no—
59#66872—21no—
60#11860—111nomaximal, Sylow
61C2×Q8×C11—21no—
62C22×C4×C11—41no—
63C22×C4×C11C2×D411yescharacteristic
64C2×C22⋊D11—41no—
65C22×Dic11—41no—
66C22×Dic11D811yescharacteristic
67C22×Dic11D811yescharacteristic
68C2×D44—21no—
69C2×C4×D11—41no—
70C11×Q16—41no—
71C2×C8×C11—41no—
72C2×C8×C11C22×C411yescharacteristic
73C2×C8×C11C2×D411yescharacteristic
74C11×C4⋊C4—21no—
75C11×C4⋊C4—41no—
76C11×C4⋊C4—41no—
77C11×C4⋊C4—41no—
78C11×C22⋊C4—41no—
79#4325—42no—
80(C2×D11)⋊C4—41no—
81(C2×D11)⋊C4—41no—
82(C2×D11)⋊C4—41no—
83(C2×D11)⋊C4—41no—
84C4⋊Dic11—21no—
85C4⋊Dic11—41no—
86C4⋊Dic11—41no—
87C4⋊Dic11—41no—
88C4⋊Dic11—41no—
89Dic11⋊C4—41no—
90Dic11⋊C4—82no—
91Dic11⋊C4—82no—
92C4×Dic11—41no—
93C4×Dic11C22⋊C411yescharacteristic
94C4×Dic11C22⋊C411yescharacteristic
95C4×Dic11SD1611yescharacteristic
96C4×Dic11SD1611yescharacteristic
97C2×C11⋊C8—41no—
98C2×C11⋊C8C22⋊C411yescharacteristic
99C2×C11⋊C8C22⋊C411yescharacteristic
100D88—41no—
101C11×C16—41no—
102C11⋊C16—41no—
103#3168—111no—
104#2163—111no—
105#1834—111no—
106#1348—111no—
107#1348D1111yescharacteristic, complemented
108#1347—111no—
109#1347—111no—
110C23×C11C2×D811yescharacteristic
111C22×D11—41no—
112Q8×C11—41no—
113Q8×C11—41no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—41no—
117C2×C4×C11—41no—
118C2×C4×C11—81no—
119C2×C4×C11—81no—
120C2×C4×C11—81no—
121C2×C4×C11C2×C22⋊C411yescharacteristic
122C2×C4×C11C2×SD1611yescharacteristic
123C22⋊D11—81no—
124C22⋊D11—81no—
125C2×Dic11—21no—
126C2×Dic11—21no—
127C2×Dic11—22no—
128C2×Dic11—41no—
129C2×Dic11—81no—
130C2×Dic11—81no—
131C2×Dic11—81no—
132C2×Dic11#10211yescharacteristic
133C2×Dic11#10211yescharacteristic
134C2×Dic11#10211yescharacteristic
135C2×Dic11#10211yescharacteristic
136D44—41no—
137D44—41no—
138C4×D11—82no—
139C8×C11—21no—
140C8×C11—21no—
141C11⋊C8—21no—
142C11⋊C8—21no—
143#529—221no—
144#499—111no—
145#495—111no—
146#488—221no—
147#467C2×D1111yescharacteristic
148#466—111no—
149#465—221no—
150C4×Q16—111no—
151C4×SD16—221no—
152C4×D8—111no—
153C2×C4×C8—111no—
154#384—221no—
155C4⋊C16—221no—
156C22⋊C16—111no—
157C22⋊C16C2×D1111yescharacteristic
158#346—221no—
159#340—111no—
160#340—221no—
161#340C2×D1111yescharacteristic
162C22×C11—21no—
163C22×C11—21no—
164C22×C11C2×#10211yescharacteristic
165C22×C11#50911yescharacteristic
166C22×C11#51011yescharacteristic
167C2×D11—81no—
168C2×D11—81no—
169C2×D11—81no—
170C4×C11—21no—
171C4×C11—81no—
172C4×C11—81no—
173C4×C11—161no—
174C4×C11#41011yescharacteristic
175C4×C11#42111yescharacteristic
176Dic11—21no—
177Dic11—21no—
178Dic11—21no—
179Dic11—81no—
180Dic11—161no—
181Dic11#36012yes—
182C2×Q16C4×D1111yescharacteristic
183C2×SD16—221no—
184C2×D8—111no—
185C22×C8—111no—
186C22×C8C22×D1111yescharacteristic
187#126—441no—
188#125—221no—
189#124—221no—
190#123—441no—
191C22⋊Q8—21no—
192#121—221no—
193C4×Q8—221no—
194C4×D4—221no—
195C4×D4—441no—
196#117—441no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—221no—
199C2×C4⋊C4—441no—
200C2×C4⋊C4—441no—
201C2×C42—111no—
202C2×C16—21no—
203C2×C16—221no—
204#107—111no—
205#107C4×D1111yescharacteristic
206#106—221no—
207#103—21no—
208#103—221no—
209#102—221no—
210#102—221no—
211C4×C8—111no—
212C4×C8—111no—
213C4×C8—111no—
214C4×C8—111no—
215C2×C11—21no—
216C2×C11—21no—
217C2×C11#151711yescharacteristic
218C2×C11#213911yescharacteristic
219C2×C11C2×#36011yescharacteristic
220D11—161no—
221C2×Q8—21no—
222C2×D4—221no—
223C2×D4—441no—
224C22×C4—41no—
225C22×C4—111no—
226C22×C4—111no—
227C22×C4—441no—
228C22×C4—441no—
229C22×C4D4×D1111yescharacteristic
230Q16—41no—
231SD16—442no—
232D8—441no—
233C2×C8—41no—
234C2×C8—111no—
235C2×C8—111no—
236C2×C8—441no—
237C2×C8C2×C4×D1111yescharacteristic
238C2×C8D4×D1111yescharacteristic
239C4⋊C4—21no—
240C4⋊C4—41no—
241C4⋊C4—41no—
242C4⋊C4—41no—
243C4⋊C4—221no—
244C4⋊C4—441no—
245C4⋊C4—441no—
246C4⋊C4—441no—
247C4⋊C4—441no—
248C4⋊C4—441no—
249C4⋊C4—882no—
250C4⋊C4—882no—
251C22⋊C4—41no—
252C22⋊C4—441no—
253C22⋊C4—441no—
254C22⋊C4—441no—
255C22⋊C4—441no—
256C42—111no—
257C42—111no—
258C42—111no—
259C42—111no—
260C42—441no—
261C16—41no—
262C16—441no—
263C11#1186011yescharacteristic, complemented, Sylow
264C23—441no—
265C23D8×D1111yescharacteristic
266Q8—41no—
267Q8—41no—
268D4—441no—
269D4—441no—
270D4—881no—
271D4—881no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—81no—
277C2×C4—81no—
278C2×C4—81no—
279C2×C4—111no—
280C2×C4—111no—
281C2×C4—111no—
282C2×C4—111no—
283C2×C4—222no—
284C2×C4—221no—
285C2×C4—221no—
286C2×C4—441no—
287C2×C4—882no—
288C2×C4—881no—
289C2×C4—881no—
290C2×C4—881no—
291C2×C4C22⋊C4×D1111yescharacteristic
292C2×C4SD16×D1111yescharacteristic
293C8—21no—
294C8—21no—
295C8—221no—
296C8—221no—
297C22—21no—
298C22—21no—
299C22—881no—
300C22—881no—
301C22—881no—
302C22D11×#10211yescharacteristic
303C22#1062252711yescharacteristic
304C22#1062253111yescharacteristic
305C4—21no—
306C4—81no—
307C4—81no—
308C4—112no—
309C4—161no—
310C4—221no—
311C4—221no—
312C4—221no—
313C4—881no—
314C4—1761no—
315C4#1062235311yescharacteristic
316C4#1062243411yescharacteristic
317C2—21no—
318C2—21no—
319C2—1761no—
320C2#1306717411yescharacteristic
321C2#1307032711yescharacteristic
322C2D11×#36011yescharacteristic
subgroupG/H
centerC22D11×#102
commutatorC2×C8×C11C22×C4
FrattiniC22×C8C22×D11
FittingC11×#1348C2
socleC22×C11C2×#102
prime radical#10622728C22
cosocleC22×C8×C11C23
hypercenter#1348D11
hypocenterC11#11860
LCSG ▷ C2×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #1348

Complements

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

NH ≅ G/Ntype
2. #13070416C2semidirect
3. #13068742C2semidirect
4. #13066628C2semidirect
7. C11×#1348C2semidirect
10. #10622804C4semidirect
11. Q16×Dic11C4semidirect
16. #10622491C4semidirect
17. #10622485C4semidirect
107. #1348D11semidirect
263. C11#11860semidirect

Maximal subgroups

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

subgroupindex
#130791872
#130704162
#130687422
#130666282
#130666262
#130666242
C11×#13482
#1186011