Finite Group Databasebeta

← #14664717

Subgroups — #14664717

Order 2816.

334 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 89 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#13079197C211yesmaximal, characteristic
2#13070412C211yesmaximal, characteristic
3#13068742C211yesmaximal, characteristic
4#13066629C211yesmaximal, characteristic
5#13066628C211yesmaximal, characteristic
6#13066627C211yesmaximal, characteristic
7C11×#1348C211yesmaximal, characteristic
8#10623153—21no—
9C11×#467C2211yescharacteristic
10Q16×Dic11C411yescharacteristic, complemented
11#10622794C411yescharacteristic, complemented
12#10622729C2211yescharacteristic
13C2×C8×Dic11C2211yescharacteristic
14#10622664—21no—
15#10622589—21no—
16#10622487C411yescharacteristic, complemented
17#10622486C411yescharacteristic, complemented
18#10622405—21no—
19#10622403—21no—
20C11×C22⋊C16C2211yescharacteristic
21C11×#340C2211yescharacteristic
22#10622189C2211yescharacteristic
23C22⋊(C11⋊C16)C2211yescharacteristic
24#10622167—21no—
25Dic11⋊C16—21no—
26C16×Dic11—21no—
27C2×C11×Q16C2×C411yescharacteristic
28C22×C8×C11C2311yescharacteristic
29C11×C22⋊Q8—21no—
30C2×C11×C4⋊C4—21no—
31Q8×Dic11—21no—
32#66997—21no—
33C2×#4326—21no—
34C2×C4⋊Dic11—21no—
35#66977—21no—
36C2×Dic11⋊C4—41no—
37C2×Dic11⋊C4—41no—
38C2×C4×Dic11D411yescharacteristic
39C22×C11⋊C8D411yescharacteristic
40C2×Dic44C2×C411yescharacteristic
41#66942—41no—
42#66941—21no—
43#66940—21no—
44#66940—41no—
45#66931—41no—
46#66930—41no—
47C2×C11×C16—21no—
48C11×#107C2×C411yescharacteristic
49C11×#103—21no—
50#66899—21no—
51#66882C2×C411yescharacteristic
52#66880—21no—
53C8×Dic11C2×C411yescharacteristic
54C8×Dic11C2×C411yescharacteristic
55C8×Dic11D411yescharacteristic
56C8×Dic11D411yescharacteristic
57C2×C11⋊C16—21no—
58#66874—21no—
59#66871—21no—
60#11857—111nomaximal, Sylow
61C2×Q8×C11—21no—
62C22×C4×C11—41no—
63C22×C4×C11C2×D411yescharacteristic
64C22×Dic11—41no—
65C22×Dic11D811yescharacteristic
66C22×Dic11D811yescharacteristic
67C2×Dic22—21no—
68C2×Dic22—41no—
69C11×Q16—41no—
70C2×C8×C11—41no—
71C2×C8×C11C22×C411yescharacteristic
72C2×C8×C11C2×D411yescharacteristic
73C11×C4⋊C4—21no—
74C11×C4⋊C4—41no—
75C11×C4⋊C4—41no—
76C11×C4⋊C4—41no—
77C11×C22⋊C4—41no—
78C22⋊Dic11—41no—
79#4326—42no—
80C4⋊Dic11—21no—
81C4⋊Dic11—41no—
82C4⋊Dic11—41no—
83C4⋊Dic11—41no—
84Dic11⋊C4—41no—
85Dic11⋊C4—41no—
86Dic11⋊C4—41no—
87Dic11⋊C4—41no—
88Dic11⋊C4—41no—
89Dic11⋊C4—82no—
90Dic11⋊C4—82no—
91C4×Dic11—41no—
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
100Dic44—41no—
101C11×C16—41no—
102C11⋊C16—41no—
103#3170—111no—
104#2162—111no—
105#1834—111no—
106#1348—111no—
107#1348—111no—
108#1348—111no—
109#1348D1111yescharacteristic
110C23×C11C2×D811yescharacteristic
111Q8×C11—41no—
112Q8×C11—41no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—41no—
116C2×C4×C11—41no—
117C2×C4×C11—81no—
118C2×C4×C11—81no—
119C2×C4×C11—81no—
120C2×C4×C11C2×C22⋊C411yescharacteristic
121C2×C4×C11C2×SD1611yescharacteristic
122C2×Dic11—22no—
123C2×Dic11—41no—
124C2×Dic11—41no—
125C2×Dic11—81no—
126C2×Dic11—81no—
127C2×Dic11—81no—
128C2×Dic11#10211yescharacteristic
129C2×Dic11#10211yescharacteristic
130C2×Dic11#10211yescharacteristic
131C2×Dic11#10211yescharacteristic
132C2×Dic11SD3212yes—
133C2×Dic11Q3212yes—
134Dic22—41no—
135Dic22—41no—
136Dic22—82no—
137C8×C11—21no—
138C8×C11—21no—
139C11⋊C8—21no—
140C11⋊C8—21no—
141#533—221no—
142#500—111no—
143#494—111no—
144#487—221no—
145#467—111no—
146#467—221no—
147#467C2×D1111yescharacteristic
148C4×Q16—111no—
149C4×Q16—111no—
150C4×Q16—221no—
151C2×C4×C8—111no—
152#384—221no—
153C4⋊C16—221no—
154C22⋊C16—111no—
155C22⋊C16C2×D1111yescharacteristic
156C4×C16—221no—
157#340—111no—
158#340—221no—
159#340C2×D1111yescharacteristic
160C22×C11—21no—
161C22×C11—21no—
162C22×C11C2×#10211yescharacteristic
163C22×C11C2×SD3211yescharacteristic
164C22×C11C2×Q3211yescharacteristic
165C4×C11—21no—
166C4×C11—81no—
167C4×C11—81no—
168C4×C11—161no—
169C4×C11#41011yescharacteristic
170C4×C11#42111yescharacteristic
171Dic11—21no—
172Dic11—81no—
173Dic11—81no—
174Dic11—161no—
175Dic11#35812yes—
176Dic11#35812yes—
177Dic11#36012yes—
178C2×Q16—111no—
179C2×Q16—221no—
180C2×Q16C4×D1111yescharacteristic
181C22×C8—111no—
182C22×C8C22×D1111yescharacteristic
183C4⋊Q8—221no—
184C4⋊Q8—221no—
185#125—441no—
186C22⋊Q8—21no—
187C22⋊Q8—221no—
188C22⋊Q8—441no—
189C4×Q8—221no—
190C4×Q8—221no—
191C4×Q8—441no—
192#117—441no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4—221no—
195C2×C4⋊C4—441no—
196C2×C4⋊C4—441no—
197C2×C42—111no—
198C2×C16—21no—
199C2×C16—221no—
200#107—111no—
201#107—221no—
202#107C4×D1111yescharacteristic
203#103—21no—
204#103—221no—
205#103—221no—
206#103—221no—
207C4×C8—111no—
208C4×C8—111no—
209C4×C8—111no—
210C4×C8—111no—
211C2×C11—21no—
212C2×C11—21no—
213C2×C11#151711yescharacteristic
214C2×C11C2×#35811yescharacteristic
215C2×C11C2×#36011yescharacteristic
216C2×Q8—21no—
217C2×Q8—221no—
218C2×Q8—441no—
219C22×C4—41no—
220C22×C4—111no—
221C22×C4—111no—
222C22×C4—441no—
223C22×C4D4×D1111yescharacteristic
224Q16—41no—
225Q16—441no—
226Q16—442no—
227C2×C8—41no—
228C2×C8—111no—
229C2×C8—111no—
230C2×C8—441no—
231C2×C8C2×C4×D1111yescharacteristic
232C2×C8D4×D1111yescharacteristic
233C4⋊C4—21no—
234C4⋊C4—41no—
235C4⋊C4—41no—
236C4⋊C4—41no—
237C4⋊C4—221no—
238C4⋊C4—441no—
239C4⋊C4—441no—
240C4⋊C4—441no—
241C4⋊C4—441no—
242C4⋊C4—441no—
243C4⋊C4—441no—
244C4⋊C4—441no—
245C4⋊C4—441no—
246C4⋊C4—882no—
247C4⋊C4—882no—
248C22⋊C4—41no—
249C22⋊C4—441no—
250C42—111no—
251C42—111no—
252C42—111no—
253C42—111no—
254C42—441no—
255C42—441no—
256C16—41no—
257C16—441no—
258C11#1185711yescharacteristic, complemented, Sylow
259C23D8×D1111yescharacteristic
260Q8—41no—
261Q8—41no—
262Q8—441no—
263Q8—441no—
264Q8—882no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—81no—
270C2×C4—81no—
271C2×C4—81no—
272C2×C4—112no—
273C2×C4—112no—
274C2×C4—111no—
275C2×C4—111no—
276C2×C4—111no—
277C2×C4—111no—
278C2×C4—222no—
279C2×C4—441no—
280C2×C4—441no—
281C2×C4—881no—
282C2×C4—881no—
283C2×C4—881no—
284C2×C4C22⋊C4×D1111yescharacteristic
285C2×C4SD16×D1111yescharacteristic
286C8—21no—
287C8—21no—
288C8—221no—
289C8—221no—
290C22—21no—
291C22—21no—
292C22D11×#10211yescharacteristic
293C22D11×SD3211yescharacteristic
294C22D11×Q3211yescharacteristic
295C4—21no—
296C4—81no—
297C4—81no—
298C4—112no—
299C4—112no—
300C4—112no—
301C4—161no—
302C4—221no—
303C4—881no—
304C4—881no—
305C4—1761no—
306C4#1062235311yescharacteristic
307C4#1062243411yescharacteristic
308C2—21no—
309C2—21no—
310C2#1306717411yescharacteristic
311C2D11×#35811yescharacteristic
312C2D11×#36011yescharacteristic
subgroupG/H
centerC22D11×#102
commutatorC2×C8×C11C22×C4
FrattiniC22×C8C22×D11
FittingC11×#1348C2
socleC22×C11C2×#102
prime radicalC23×C11C2×D8
cosocleC22×C8×C11C23
hypercenter#1348D11
hypocenterC11#11857
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
10. Q16×Dic11C4semidirect
11. #10622794C4semidirect
16. #10622487C4semidirect
17. #10622486C4semidirect
258. C11#11857semidirect

Maximal subgroups

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

subgroupindex
#130791972
#130704122
#130687422
#130666292
#130666282
#130666272
C11×#13482
#1185711