Finite Group Databasebeta

← #14651309

Subgroups — #14651309

Order 2816.

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

normal subgroups only

This group has 534 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#13078991C211yesmaximal, characteristic
2#13071792C211yesmaximal, characteristic
3#13067329C211yesmaximal, characteristic
4#13067168C211yesmaximal, characteristic, complemented
5#13067166C211yesmaximal, characteristic, complemented
6#13066481C211yesmaximal, characteristic, complemented
7C11×#1288C211yesmaximal, characteristic, complemented
8C2×#66927C2211yescharacteristic
9#10623001C2211yescharacteristic
10C11×#432C2211yescharacteristic
11C4×C11×M16C2211yescharacteristic
12C11×#383C2211yescharacteristic
13#10622744—22no—
14#10622550C2211yescharacteristic
15#10622539C2211yescharacteristic
16#10622326—22no—
17#10622307C412yescomplemented
18#10622307C412yescomplemented
19#10622278—22no—
20#10622278—22no—
21#10622278—22no—
22#10622123—22no—
23#10622105—22no—
24#10622090—22no—
25C22×D44—21no—
26C22×D44—21no—
27C22×D44D412yes—
28C22×C4×D11—22no—
29C2×C11×M16—21no—
30C2×C42×C11C2311yescharacteristic
31C2×(C2×D11)⋊C4—22no—
32C2×(C2×D11)⋊C4—22no—
33C2×(C2×D11)⋊C4—22no—
34#66979—21no—
35#66977—21no—
36#66977—21no—
37#66927—21no—
38#66927—21no—
39#66927C2×C412yes—
40#66927D412yes—
41#66923—21no—
42#66922C2×C411yescharacteristic, complemented
43#66922C2×C411yescharacteristic, complemented
44C4×Dic22—21no—
45C4×Dic22—21no—
46C11×C4⋊C8—21no—
47C11×C22⋊C8—21no—
48C11×#97—21no—
49C11×#97—21no—
50C4×C8×C11C2×C412yescomplemented
51C11×#95—21no—
52C11×#95—21no—
53C11×#95D412yes—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95D412yes—
57C22⋊(C11⋊C8)—21no—
58#66885—24no—
59#66885—24no—
60C4⋊(C11⋊C8)—21no—
61#66867—21no—
62#9425—111nomaximal, Sylow
63C23×D11—22no—
64C22×C4×C11—22no—
65C22×C4×C11C2×D411yescharacteristic
66C22×C4×C11C2×D411yescharacteristic
67C22×C4×C11C2×D411yescharacteristic
68C22×Dic11—22no—
69C2×D44—22no—
70C2×D44—22no—
71C2×D44—22no—
72C2×D44—22no—
73C2×D44—22no—
74C2×D44—42no—
75C2×D44—42no—
76C2×D44—81no—
77C2×D44—81no—
78C2×D44—81no—
79C2×D44—81no—
80C2×D44C22⋊C414yes—
81C2×C4×D11—82no—
82C2×C4×D11—82no—
83C2×C4×D11—82no—
84C2×Dic22—21no—
85C2×Dic22—21no—
86C11×M16—42no—
87C2×C8×C11—22no—
88C2×C8×C11—41no—
89C42×C11C22×C411yescharacteristic
90C42×C11C2×D411yescharacteristic
91C42×C11#4111yescharacteristic
92C42×C11#4111yescharacteristic
93C22⋊Dic11—41no—
94(C2×D11)⋊C4—82no—
95(C2×D11)⋊C4—82no—
96(C2×D11)⋊C4—82no—
97C4⋊Dic11—21no—
98C4⋊Dic11—21no—
99C4⋊Dic11—21no—
100C4⋊Dic11—21no—
101Dic11⋊C4—41no—
102Dic11⋊C4—41no—
103C4×Dic11—41no—
104C2×C11⋊C8—41no—
105#3138—111no—
106#2380—111no—
107#1555—111no—
108#1515—111no—
109#1515—111no—
110#1288—111no—
111#1288D1111yescharacteristic, complemented
112C23×C11#12011yescharacteristic
113C22×D11—24no—
114C22×D11—42no—
115C22×D11—42no—
116C22×D11—42no—
117C22×D11—42no—
118C22×D11—42no—
119C22×D11—42no—
120C2×C4×C11—22no—
121C2×C4×C11—41no—
122C2×C4×C11—41no—
123C2×C4×C11—42no—
124C2×C4×C11—42no—
125C2×C4×C11—42no—
126C2×C4×C11C2×C22⋊C411yescharacteristic
127C2×C4×C11C4×D411yescharacteristic
128C2×C4×C11C4×D411yescharacteristic
129C2×C4×C11#12111yescharacteristic
130C2×C4×C11#12111yescharacteristic
131C2×C4×C11#12311yescharacteristic
132C2×Dic11—42no—
133C2×Dic11—42no—
134C2×Dic11—41no—
135C2×Dic11—41no—
136C2×Dic11—42no—
137D44—44no—
138D44—82no—
139D44—82no—
140D44—82no—
141D44—82no—
142D44—82no—
143C4×D11—88no—
144Dic22—81no—
145Dic22—81no—
146C8×C11—42no—
147C8×C11—81no—
148C11⋊C8—81no—
149#533—111no—
150C2×#127—111no—
151#490—222no—
152#486—112no—
153#486—112no—
154#432—111no—
155#432C2×D1111yescharacteristic
156#418—222no—
157C4×M16C2×D1111yescharacteristic
158#386—222no—
159#386—222no—
160#386—222no—
161#383—111no—
162#383C2×D1111yescharacteristic
163#331—222no—
164#328—222no—
165#328—222no—
166C22×C11—21no—
167C22×C11—21no—
168C22×C11#38611yescharacteristic
169C22×C11#45512yes—
170C2×D11—44no—
171C2×D11—44no—
172C2×D11—44no—
173C2×D11—82no—
174C2×D11—82no—
175C2×D11—82no—
176C2×D11—82no—
177C4×C11—21no—
178C4×C11—21no—
179C4×C11—21no—
180C4×C11—21no—
181C4×C11—21no—
182C4×C11—21no—
183C4×C11—82no—
184Dic11—82no—
185Dic11—81no—
186Dic11—81no—
187C22×D4—112no—
188C22×D4—221no—
189C22×D4—221no—
190C23×C4—222no—
191C2×M16—21no—
192C4⋊Q8—111no—
193C4⋊Q8—111no—
194#127—112no—
195#127—112no—
196#127—221no—
197#127—221no—
198#125—221no—
199C22⋊Q8—221no—
200C22⋊Q8—221no—
201C4×Q8—221no—
202C4×Q8—221no—
203#117—221no—
204C2×C22⋊C4—222no—
205C2×C22⋊C4—222no—
206C2×C22⋊C4—222no—
207C2×C42C22×D1111yescharacteristic
208C4⋊C8—21no—
209C4⋊C8—221no—
210#102—224no—
211#102—224no—
212C22⋊C8—21no—
213C22⋊C8—221no—
214#97—21no—
215#97—21no—
216#97—221no—
217C4×C8C4×D1112yescomplemented
218#95—21no—
219#95—21no—
220#95—112no—
221#95—221no—
222#95—221no—
223#95D4412yes—
224C2×C11—22no—
225C2×C11#188511yescharacteristic
226C2×C11#190411yescharacteristic
227C2×C11#190411yescharacteristic
228D11—84no—
229C24—222no—
230C2×Q8—221no—
231C2×Q8—221no—
232C2×D4—114no—
233C2×D4—222no—
234C2×D4—222no—
235C2×D4—222no—
236C2×D4—222no—
237C2×D4—222no—
238C2×D4—442no—
239C2×D4—442no—
240C2×D4—881no—
241C2×D4—881no—
242C2×D4—881no—
243C2×D4—881no—
244C22×C4—22no—
245C22×C4—222no—
246C22×C4—882no—
247C22×C4—882no—
248C22×C4—882no—
249C22×C4C2×D4411yescharacteristic
250C22×C4D4×D1111yescharacteristic
251C22×C4D4×D1111yescharacteristic
252M16—42no—
253C2×C8—22no—
254C2×C8—41no—
255C2×C8—441no—
256C4⋊C4—221no—
257C4⋊C4—221no—
258C4⋊C4—221no—
259C4⋊C4—221no—
260C4⋊C4—441no—
261C4⋊C4—441no—
262C22⋊C4—441no—
263C22⋊C4—882no—
264C22⋊C4—882no—
265C22⋊C4—882no—
266C42—441no—
267C42C2×C4×D1111yescharacteristic
268C42#433911yescharacteristic
269C42D4×D1111yescharacteristic
270C42#434311yescharacteristic
271C11#942511yescharacteristic, complemented, Sylow
272C23—224no—
273C23—442no—
274C23—442no—
275C23—442no—
276C23—442no—
277C23—442no—
278C23—442no—
279C23#6693511yescharacteristic
280Q8—881no—
281Q8—881no—
282D4—444no—
283D4—882no—
284D4—882no—
285D4—882no—
286D4—882no—
287D4—882no—
288C2×C4—22no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—42no—
294C2×C4—442no—
295C2×C4—442no—
296C2×C4—441no—
297C2×C4—441no—
298C2×C4—442no—
299C2×C4—888no—
300C2×C4C4×D4411yescharacteristic
301C2×C4C22⋊C4×D1111yescharacteristic
302C2×C4#6693711yescharacteristic
303C2×C4#6694611yescharacteristic
304C2×C4#6694711yescharacteristic
305C2×C4#6694811yescharacteristic
306C8—42no—
307C8—81no—
308C8—881no—
309C22—21no—
310C22—21no—
311C22—444no—
312C22—444no—
313C22—444no—
314C22—882no—
315C22—882no—
316C22—882no—
317C22—882no—
318C22#1062227811yescharacteristic
319C22#1062243812yes—
320C4—21no—
321C4—21no—
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—82no—
327C4—882no—
328C4—881no—
329C4—881no—
330C2—22no—
331C2—884no—
332C2#1306900311yescharacteristic
333C2#1306910211yescharacteristic
334C2#1306910411yescharacteristic
subgroupG/H
centerC22#10622278
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1288C2
socleC22×C11#386
prime radicalC2×#66927C22
cosocleC2×C42×C11C23
hypercenter#1288D11
hypocenterC11#9425
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1288

Complements

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

NH ≅ G/Ntype
4. #13067168C2semidirect
5. #13067166C2semidirect
6. #13066481C2semidirect
7. C11×#1288C2semidirect
17. #10622307C4semidirect
18. #10622307C4semidirect
42. #66922C2×C4semidirect
43. #66922C2×C4semidirect
50. C4×C8×C11C2×C4semidirect
111. #1288D11semidirect
217. C4×C8C4×D11semidirect
271. C11#9425semidirect

Maximal subgroups

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

subgroupindex
#130789912
#130717922
#130673292
#130671682
#130671662
#130664812
C11×#12882
#942511