Finite Group Databasebeta

← #14670331

Subgroups — #14670331

Order 2816.

458 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 117 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
1C2×D11×#106C211yesmaximal, characteristic
2C2×#10622151C211yesmaximal, characteristic, complemented
3C2×#10622125C211yesmaximal, characteristic, complemented
4#13070226C211yesmaximal, characteristic
5#13068651C211yesmaximal, characteristic
6#13066716C211yesmaximal, characteristic, complemented
7C11×#1383C211yesmaximal, characteristic, complemented
8C22×C8×D11C2211yescharacteristic
9C2×C4⋊C4×D11—21no—
10C2×C11×M32C2211yescharacteristic
11C2×C11×#108C2211yescharacteristic
12C2×C11×#106C2211yescharacteristic
13#10622739—21no—
14C2×#66883C2211yescharacteristic
15C2×#66881C2211yescharacteristic
16C2×#66876C2211yescharacteristic
17C2×#66872—21no—
18D11×#106—22no—
19D11×#106—22no—
20#10622196—21no—
21#10622151—22no—
22(C2×D11)⋊C16C414yescomplemented
23#10622125—22no—
24C22×C4×D11—41no—
25C22×C4×D11D411yescharacteristic
26C2×C11×M16—21no—
27C22×C8×C11C2311yescharacteristic
28C2×C11×C4⋊C4—21no—
29C2×C4⋊Dic11—21no—
30C2×Dic11⋊C4—41no—
31C2×#4318—21no—
32C22×C11⋊C8D411yescharacteristic
33C2×C8×D11—21no—
34C2×C8×D11—21no—
35C2×C8×D11—21no—
36C2×C8×D11—21no—
37C2×C8×D11C2×C412yes—
38C2×C8×D11Q812yes—
39C4⋊C4×D11—24no—
40C4⋊C4×D11—42no—
41C11×M32—21no—
42C11×M32—21no—
43C2×C11×C16C2×C412yescomplemented
44C11×#108—21no—
45C11×#108—21no—
46C11×#106—21no—
47C11×#106D412yes—
48(C2×D11)⋊C8—42no—
49#66883—21no—
50#66883—21no—
51#66881—21no—
52#66881D412yes—
53#66876—21no—
54#66876—21no—
55C2×C11⋊C16C2×C412yescomplemented
56#66872—24no—
57#12929—111nomaximal, Sylow
58C23×D11SD1611yescharacteristic
59C22×C4×C11—41no—
60C22×C4×C11C2×D411yescharacteristic
61C22×Dic11—41no—
62C22×Dic11SD1611yescharacteristic
63C2×C4×D11—21no—
64C2×C4×D11—21no—
65C2×C4×D11—21no—
66C2×C4×D11—21no—
67C2×C4×D11—44no—
68C2×C4×D11—84no—
69C2×C4×D11C4⋊C412yes—
70C2×C4×D11SD1612yes—
71C11×M16—41no—
72C11×M16—41no—
73C2×C8×C11—41no—
74C2×C8×C11C22×C411yescharacteristic
75C2×C8×C11C2×D411yescharacteristic
76C2×C8×C11C2×D411yescharacteristic
77C2×C8×C11C2×Q811yescharacteristic
78C2×C8×C11#4111yescharacteristic
79C2×C8×C11#4111yescharacteristic
80C11×C4⋊C4—22no—
81C11×C4⋊C4—41no—
82C4⋊Dic11—22no—
83C4⋊Dic11—41no—
84Dic11⋊C4—44no—
85#4318—41no—
86#4318—41no—
87C2×C11⋊C8—21no—
88C2×C11⋊C8—21no—
89C2×C11⋊C8—41no—
90C2×C11⋊C8C4⋊C412yes—
91C8×D11—22no—
92C8×D11—22no—
93C8×D11—22no—
94C8×D11—22no—
95C11×C16—22no—
96C11⋊C16—22no—
97C22×#106—111no—
98C2×#365—111no—
99C2×#365—111no—
100#2112—111no—
101#1810—111no—
102#1383—111no—
103#1383D1111yescharacteristic, complemented
104C23×C11C2×SD1611yescharacteristic
105C22×D11—21no—
106C22×D11—21no—
107C22×D11—24no—
108C22×D11#10612yes—
109C2×C4×C11—42no—
110C2×C4×C11—82no—
111C2×C4×C11C2×C4⋊C411yescharacteristic
112C2×C4×C11#12011yescharacteristic
113C2×C4×C11#12311yescharacteristic
114C2×C4×C11C2×SD1611yescharacteristic
115C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
116C2×C4×C11#13711yescharacteristic
117C2×Dic11—21no—
118C2×Dic11—21no—
119C2×Dic11—42no—
120C2×Dic11—82no—
121C2×Dic11#10612yes—
122C4×D11—22no—
123C4×D11—22no—
124C4×D11—22no—
125C4×D11—22no—
126C4×D11—88no—
127C8×C11—81no—
128C8×C11C4×D411yescharacteristic
129C8×C11C4×D411yescharacteristic
130C8×C11C22⋊Q811yescharacteristic
131C8×C11C22⋊Q811yescharacteristic
132C11⋊C8—22no—
133C11⋊C8—81no—
134C23×C8—111no—
135C22×C4⋊C4—221no—
136C2×M32—111no—
137C2×M32C2×D1111yescharacteristic
138C2×#108—111no—
139C2×#108C2×D1111yescharacteristic
140C2×#106—111no—
141C2×#106—222no—
142C2×#106—221no—
143C2×#106—222no—
144C2×#106C2×D1111yescharacteristic
145#407—221no—
146#365—222no—
147#365—222no—
148C22⋊C16—114no—
149#341—221no—
150C22×C11—22no—
151C22×C11C2×#10611yescharacteristic
152C22×C11#45011yescharacteristic
153C22×C11#48311yescharacteristic
154C2×D11—24no—
155C2×D11—24no—
156C2×D11—22no—
157C2×D11—22no—
158C2×D11#36514yescomplemented
159C4×C11—82no—
160C4×C11#38511yescharacteristic
161C4×C11#42811yescharacteristic
162C4×C11#44811yescharacteristic
163C4×C11#48111yescharacteristic
164Dic11—22no—
165Dic11—82no—
166C23×C4—111no—
167C23×C4—441no—
168C2×M16—21no—
169C2×M16—221no—
170C22×C8—111no—
171C22×C8—112no—
172C22×C8—112no—
173C22×C8—221no—
174C22×C8—221no—
175C22×C8—221no—
176C22×C8—221no—
177C22×C8C22×D1111yescharacteristic
178C2×C4⋊C4—21no—
179C2×C4⋊C4—224no—
180C2×C4⋊C4—221no—
181C2×C4⋊C4—442no—
182C2×C4⋊C4—441no—
183M32—21no—
184M32—21no—
185M32—221no—
186M32—221no—
187C2×C16—112no—
188C2×C16C4×D1112yescomplemented
189#108—21no—
190#108—21no—
191#108—221no—
192#108—221no—
193#106—21no—
194#106—112no—
195#106—224no—
196#106—221no—
197#106D4412yes—
198C22⋊C8—442no—
199C2×C11—21no—
200C2×C11—21no—
201C2×C11#185311yescharacteristic
202C2×C11C2×#36512yes—
203D11—24no—
204C24—111no—
205C22×C4—41no—
206C22×C4—111no—
207C22×C4—112no—
208C22×C4—112no—
209C22×C4—221no—
210C22×C4—221no—
211C22×C4—221no—
212C22×C4—221no—
213C22×C4—444no—
214C22×C4—441no—
215C22×C4—884no—
216C22×C4D4×D1111yescharacteristic
217M16—41no—
218M16—41no—
219M16—441no—
220M16—441no—
221C2×C8—41no—
222C2×C8—112no—
223C2×C8—221no—
224C2×C8—221no—
225C2×C8—222no—
226C2×C8—222no—
227C2×C8—222no—
228C2×C8—222no—
229C2×C8—441no—
230C2×C8C2×C4×D1111yescharacteristic
231C2×C8C2×D4411yescharacteristic
232C2×C8#433911yescharacteristic
233C2×C8D4×D1111yescharacteristic
234C2×C8#434111yescharacteristic
235C2×C8Q8×D1111yescharacteristic
236C4⋊C4—22no—
237C4⋊C4—41no—
238C4⋊C4—222no—
239C4⋊C4—444no—
240C4⋊C4—441no—
241C16—22no—
242C16—222no—
243C11#1292911yescharacteristic, complemented, Sylow
244C23—112no—
245C23—224no—
246C23—221no—
247C23—221no—
248C23SD16×D1111yescharacteristic
249C2×C4—42no—
250C2×C4—82no—
251C2×C4—112no—
252C2×C4—221no—
253C2×C4—221no—
254C2×C4—222no—
255C2×C4—222no—
256C2×C4—222no—
257C2×C4—222no—
258C2×C4—442no—
259C2×C4—888no—
260C2×C4—882no—
261C2×C4#6693511yescharacteristic
262C2×C4#6693611yescharacteristic
263C2×C4C4⋊C4×D1111yescharacteristic
264C2×C4#6696411yescharacteristic
265C2×C4SD16×D1111yescharacteristic
266C2×C4#6697111yescharacteristic
267C8—81no—
268C8—222no—
269C8—881no—
270C8C4×D4411yescharacteristic
271C8(C22⋊D11)⋊C411yescharacteristic
272C8#6694911yescharacteristic
273C8#6695011yescharacteristic
274C22—22no—
275C22—114no—
276C22—224no—
277C22—224no—
278C22—222no—
279C22—222no—
280C22#1062238911yescharacteristic
281C22#1062241811yescharacteristic
282C22D11×#10611yescharacteristic
283C4—82no—
284C4—222no—
285C4—882no—
286C4#1062228111yescharacteristic
287C4#1062239011yescharacteristic
288C4#1062241911yescharacteristic
289C4#1062249411yescharacteristic
290C2—21no—
291C2—21no—
292C2—224no—
293C2#1306881011yescharacteristic
294C2D11×#36512yes—
subgroupG/H
centerC22D11×#106
commutatorC2×C8×C11C22×C4
FrattiniC22×C8C22×D11
FittingC11×#1383C2
socleC22×C11C2×#106
prime radicalC23×D11SD16
cosocleC22×C8×C11C23
hypercenter#1383D11
hypocenterC11#12929
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #1383

Complements

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

NH ≅ G/Ntype
2. C2×#10622151C2semidirect
3. C2×#10622125C2semidirect
6. #13066716C2semidirect
7. C11×#1383C2semidirect
22. (C2×D11)⋊C16C4semidirect
43. C2×C11×C16C2×C4semidirect
55. C2×C11⋊C16C2×C4semidirect
103. #1383D11semidirect
158. C2×D11#365semidirect
188. C2×C16C4×D11semidirect
243. C11#12929semidirect

Maximal subgroups

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

subgroupindex
C2×D11×#1062
C2×#106221512
C2×#106221252
#130702262
#130686512
#130667162
C11×#13832
#1292911