Finite Group Databasebeta

← #14647168

Subgroups — #14647168

Order 2816.

588 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#13068684C211yesmaximal, characteristic
2#13066843C211yesmaximal, characteristic
3#13066494C214yesmaximal
4C11×#2285C211yesmaximal, characteristic
5C2×C11×#117—21no—
6C22×C42×C11C2211yescharacteristic
7C11×#384C411yescharacteristic, complemented
8C11×#384C411yescharacteristic, complemented
9C11×#382—21no—
10C11×#380—21no—
11C11×#380C2212yes—
12C4×C11×C4⋊C4—21no—
13C4×C11×C4⋊C4C412yescomplemented
14C2×C11⋊#95—21no—
15C2×C11⋊#95—21no—
16C2×C11⋊#95C2212yes—
17C2×C22⋊(C11⋊C8)C2212yes—
18#10622162—21no—
19#10622162—21no—
20C23×C4×C11D411yescharacteristic
21C23×C4×C11D411yescharacteristic
22C23×C4×C11C2311yescharacteristic
23C23×Dic11—22no—
24C11×#117—44no—
25C2×C11×C4⋊C4—21no—
26C2×C11×C4⋊C4—21no—
27C2×C11×C4⋊C4—21no—
28C2×C11×C4⋊C4—21no—
29C2×C11×C4⋊C4C2×C412yes—
30C2×C11×C4⋊C4C2×C412yes—
31C2×C11×C22⋊C4—22no—
32C2×C42×C11—24no—
33C2×C42×C11—22no—
34C2×C42×C11C2×C411yescharacteristic
35C2×C42×C11C2×C411yescharacteristic
36C2×C42×C11D411yescharacteristic
37C2×C42×C11D411yescharacteristic
38C22×C11⋊C8—22no—
39C11×#95—22no—
40C11×#95—22no—
41C11⋊#95—24no—
42C11⋊#95—24no—
43C11⋊#95—42no—
44C22⋊(C11⋊C8)—24no—
45#8717—111nomaximal, Sylow
46C24×C11C2×D411yescharacteristic
47C22×C4×C11—22no—
48C22×C4×C11—22no—
49C22×C4×C11—22no—
50C22×C4×C11—22no—
51C22×C4×C11—22no—
52C22×C4×C11—22no—
53C22×C4×C11—41no—
54C22×C4×C11—41no—
55C22×C4×C11—41no—
56C22×C4×C11C22⋊C411yescharacteristic
57C22×C4×C11C22⋊C411yescharacteristic
58C22×C4×C11C22⋊C411yescharacteristic
59C22×C4×C11C22⋊C411yescharacteristic
60C22×C4×C11SD1612yes—
61C22×C4×C11Q1612yes—
62C22×C4×C11C22×C411yescharacteristic
63C22×C4×C11C2×D411yescharacteristic
64C22×C4×C11#4114yes—
65C22×Dic11—24no—
66C22×Dic11—42no—
67C22×Dic11—42no—
68C22×Dic11—42no—
69C22×Dic11—42no—
70C22×Dic11—42no—
71C22×Dic11—42no—
72C11×C4⋊C4—42no—
73C11×C4⋊C4—42no—
74C11×C4⋊C4—42no—
75C11×C4⋊C4—42no—
76C11×C4⋊C4—42no—
77C11×C4⋊C4—42no—
78C11×C22⋊C4—44no—
79C42×C11—22no—
80C42×C11—22no—
81C42×C11—22no—
82C42×C11—22no—
83C42×C11—44no—
84C2×C11⋊C8—42no—
85C2×C11⋊C8—42no—
86C2×C11⋊C8—42no—
87#2285D1111yescharacteristic
88#1817—111no—
89#1434—111no—
90#1294—114no—
91C23×C11—21no—
92C23×C11—21no—
93C23×C11—21no—
94C23×C11—21no—
95C23×C11C2×C22⋊C411yescharacteristic
96C23×C11#12312yes—
97C23×C11C2×SD1611yescharacteristic
98C23×C11C2×Q1611yescharacteristic
99C23×C11AGL(1,ℤ/8)12yes—
100C2×C4×C11—21no—
101C2×C4×C11—21no—
102C2×C4×C11—21no—
103C2×C4×C11—21no—
104C2×C4×C11—21no—
105C2×C4×C11—21no—
106C2×C4×C11—21no—
107C2×C4×C11—21no—
108C2×C4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11—24no—
111C2×C4×C11—24no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—44no—
116C2×C4×C11—44no—
117C2×C4×C11—42no—
118C2×C4×C11—42no—
119C2×C4×C11—42no—
120C2×C4×C11—42no—
121C2×C4×C11—42no—
122C2×C4×C11—42no—
123C2×C4×C11#10312yes—
124C2×C4×C11#10312yes—
125C2×C4×C11#10412yes—
126C2×C4×C11#11712yes—
127C2×C4×C11#12312yes—
128C2×Dic11—44no—
129C2×Dic11—44no—
130C2×Dic11—44no—
131C2×Dic11—82no—
132C2×Dic11—82no—
133C2×Dic11—82no—
134C2×Dic11—82no—
135C11⋊C8—82no—
136C2×#117—21no—
137C22×C42C2×D1111yescharacteristic
138C2×C22⋊C8—112no—
139#384Dic1111yescharacteristic, complemented
140#384Dic1111yescharacteristic, complemented
141#382—21no—
142#380—21no—
143#380C2×D1112yes—
144C4×C4⋊C4—21no—
145C4×C4⋊C4Dic1112yescomplemented
146C2×#95—112no—
147C2×#95—221no—
148C2×#95—221no—
149#336—221no—
150#336—221no—
151C22×C11—22no—
152C22×C11—22no—
153C22×C11—21no—
154C22×C11—21no—
155C22×C11—22no—
156C22×C11—22no—
157C22×C11—21no—
158C22×C11—21no—
159C22×C11#38111yescharacteristic
160C22×C11#41011yescharacteristic
161C22×C11#41011yescharacteristic
162C22×C11C2×#10311yescharacteristic
163C22×C11#41811yescharacteristic
164C22×C11C2×#10411yescharacteristic
165C22×C11#42111yescharacteristic
166C22×C11#48112yes—
167C22×C11#48412yes—
168C4×C11—22no—
169C4×C11—22no—
170C4×C11—22no—
171C4×C11—22no—
172C4×C11—22no—
173C4×C11—41no—
174C4×C11—82no—
175C4×C11—82no—
176Dic11—84no—
177C23×C4—222no—
178C23×C4C22⋊D1111yescharacteristic
179C23×C4C22⋊D1111yescharacteristic
180C23×C4C22×D1111yescharacteristic
181C22×C8—222no—
182#117—44no—
183C2×C4⋊C4—21no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—21no—
186C2×C4⋊C4—21no—
187C2×C4⋊C4C2×Dic1112yes—
188C2×C4⋊C4C2×Dic1112yes—
189C2×C22⋊C4—22no—
190C2×C42—24no—
191C2×C42—22no—
192C2×C42C2×Dic1111yescharacteristic
193C2×C42C2×Dic1111yescharacteristic
194C2×C42C22⋊D1111yescharacteristic
195C2×C42C22⋊D1111yescharacteristic
196C22⋊C8—224no—
197#95—22no—
198#95—22no—
199#95—224no—
200#95—224no—
201#95—442no—
202C2×C11—22no—
203C2×C11—22no—
204C2×C11#150311yescharacteristic
205C2×C11#150511yescharacteristic
206C2×C11#151411yescharacteristic
207C2×C11#151811yescharacteristic
208C2×C11#182011yescharacteristic
209C2×C11#182411yescharacteristic
210C2×C11#182611yescharacteristic
211C24C2×C22⋊D1111yescharacteristic
212C22×C4—22no—
213C22×C4—22no—
214C22×C4—22no—
215C22×C4—22no—
216C22×C4—22no—
217C22×C4—22no—
218C22×C4—41no—
219C22×C4—41no—
220C22×C4—41no—
221C22×C4—224no—
222C22×C4—442no—
223C22×C4—442no—
224C22×C4—442no—
225C22×C4—442no—
226C22×C4—442no—
227C22×C4—442no—
228C22×C4#432512yes—
229C22×C4#432612yes—
230C22×C4C22⋊Dic1111yescharacteristic
231C22×C4C22⋊Dic1111yescharacteristic
232C22×C4C22⋊Dic1111yescharacteristic
233C22×C4C22⋊Dic1111yescharacteristic
234C22×C4#433914yes—
235C22×C4C22×Dic1111yescharacteristic
236C22×C4C2×C22⋊D1111yescharacteristic
237C2×C8—442no—
238C2×C8—442no—
239C2×C8—442no—
240C4⋊C4—42no—
241C4⋊C4—42no—
242C4⋊C4—42no—
243C4⋊C4—42no—
244C4⋊C4—42no—
245C4⋊C4—42no—
246C22⋊C4—44no—
247C42—22no—
248C42—22no—
249C42—22no—
250C42—22no—
251C42—44no—
252C11#871711yescharacteristic, complemented, Sylow
253C23—21no—
254C23—21no—
255C23—21no—
256C23—21no—
257C23#6698212yes—
258C23#6698512yes—
259C23C2×#432511yescharacteristic
260C23C2×#432611yescharacteristic
261C23C2×C22⋊Dic1111yescharacteristic
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—24no—
268C2×C4—24no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—44no—
278C2×C4—44no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4—42no—
285C2×C4—444no—
286C2×C4—444no—
287C2×C4—444no—
288C2×C4—882no—
289C2×C4—882no—
290C2×C4—882no—
291C2×C4—882no—
292C2×C4#6689912yes—
293C2×C4#6689912yes—
294C2×C4#6690112yes—
295C2×C4#6697912yes—
296C2×C4#6698212yes—
297C8—882no—
298C22—21no—
299C22—21no—
300C22—22no—
301C22—22no—
302C22—22no—
303C22—22no—
304C22—21no—
305C22—21no—
306C22#1062258112yes—
307C22#1062258312yes—
308C22#1062282411yescharacteristic
309C22#1062282811yescharacteristic
310C22C2×#6689911yescharacteristic
311C22C2×#6690111yescharacteristic
312C22#1062284911yescharacteristic
313C22#1062285311yescharacteristic
314C22#1062285311yescharacteristic
315C4—22no—
316C4—22no—
317C4—22no—
318C4—22no—
319C4—22no—
320C4—41no—
321C4—82no—
322C4—82no—
323C4—884no—
324C2—22no—
325C2—22no—
326C2#1306711511yescharacteristic
327C2#1306712411yescharacteristic
328C2#1306716311yescharacteristic
329C2#1306718011yescharacteristic
330C2#1306869311yescharacteristic
331C2#1306870611yescharacteristic
332C2#1306871511yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic11
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#2285C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C2×D4
cosocleC23×C4×C11C23
hypercenter#2285D11
hypocenterC11#8717
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2285

Complements

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

NH ≅ G/Ntype
7. C11×#384C4semidirect
8. C11×#384C4semidirect
13. C4×C11×C4⋊C4C4semidirect
139. #384Dic11semidirect
140. #384Dic11semidirect
145. C4×C4⋊C4Dic11semidirect
252. C11#8717semidirect

Maximal subgroups

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

subgroupindex
#130686842
#130668432
#130664942
C11×#22852
#871711