Finite Group Databasebeta

← #14652827

Subgroups — #14652827

Order 2816.

498 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076993C211yesmaximal, characteristic
2#13068767C211yesmaximal, characteristic
3C4⋊C8×Dic11C211yesmaximal, characteristic
4C2×#10622184C211yesmaximal, characteristic
5C2×#10622120C211yesmaximal, characteristic
6C2×#10622124C211yesmaximal, characteristic
7C2×C11×#333C211yesmaximal, characteristic
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×#66922C2211yescharacteristic
10C2×C11×C4⋊C8C2211yescharacteristic
11C2×C11×C4⋊C8C2211yescharacteristic
12#10622843C414yes—
13C2×Dic11⋊C8—22no—
14C2×C8×Dic11—21no—
15#10622590—22no—
16#10622587—21no—
17#10622587—21no—
18C42×Dic11C2211yescharacteristic
19C2×C4⋊(C11⋊C8)C2211yescharacteristic
20C2×C4⋊(C11⋊C8)C2211yescharacteristic
21C11×#333—22no—
22#10622188—21no—
23#10622184—22no—
24#10622124—22no—
25#10622120—22no—
26C22×Q8×C11C2×C412yes—
27C22×Dic22—21no—
28C22×C8×C11—21no—
29C22×C8×C11—21no—
30C11×C4⋊Q8—21no—
31C11×C4⋊Q8—21no—
32C11×C4⋊Q8—21no—
33C11×C4⋊Q8—21no—
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4—21no—
36C2×C42×C11C2311yescharacteristic
37C2×C4⋊Dic11—21no—
38C2×C4⋊Dic11C2×C412yes—
39C2×C4×Dic11C2×C412yes—
40C2×C4×Dic11D411yescharacteristic
41C2×C4×Dic11D411yescharacteristic
42C2×C4×Dic11D412yes—
43C22×C11⋊C8—21no—
44C22×C11⋊C8—21no—
45#66922—21no—
46#66922—21no—
47#66922—21no—
48#66922—21no—
49C11×C4⋊C8—21no—
50C11×C4⋊C8—21no—
51C11×C4⋊C8—21no—
52C11×C4⋊C8D412yes—
53C11⋊#95—24no—
54C11⋊#95—24no—
55Dic11⋊C8—44no—
56C8×Dic11—42no—
57C4⋊(C11⋊C8)—21no—
58C4⋊(C11⋊C8)—21no—
59C4⋊(C11⋊C8)—21no—
60C4⋊(C11⋊C8)D412yes—
61#9697—111nomaximal, Sylow
62C2×Q8×C11—22no—
63C2×Q8×C11—22no—
64C2×Q8×C11—44no—
65C22×C4×C11—22no—
66C22×C4×C11C22×C411yescharacteristic
67C22×C4×C11C2×D411yescharacteristic
68C22×C4×C11C2×D411yescharacteristic
69C22×Dic11—22no—
70C22×Dic11C22⋊C412yes—
71C22×Dic11C22⋊C412yes—
72C2×Dic22—41no—
73C2×Dic22—41no—
74C2×Dic22—41no—
75C2×Dic22—41no—
76C2×Dic22—41no—
77C2×Dic22—41no—
78C2×C8×C11—22no—
79C2×C8×C11—41no—
80C2×C8×C11—42no—
81C2×C8×C11—41no—
82C2×C8×C11—41no—
83C11×C4⋊C4—41no—
84C11×C4⋊C4—41no—
85C11×C4⋊C4—41no—
86C11×C4⋊C4—41no—
87C42×C11C2×D411yescharacteristic
88C42×C11C2×D411yescharacteristic
89C42×C11#4111yescharacteristic
90C42×C11#4111yescharacteristic
91C4⋊Dic11—22no—
92C4⋊Dic11—22no—
93C4⋊Dic11—41no—
94C4⋊Dic11—41no—
95C4×Dic11—21no—
96C4×Dic11—21no—
97C4×Dic11—21no—
98C4×Dic11—21no—
99C4×Dic11—42no—
100C4×Dic11SD1614yes—
101C4×Dic11Q1614yes—
102C2×C11⋊C8—22no—
103C2×C11⋊C8—41no—
104C2×C11⋊C8—42no—
105C2×C11⋊C8—41no—
106C2×C11⋊C8—41no—
107#2862—111no—
108#1842—111no—
109C4×C4⋊C8—111no—
110C2×#333—111no—
111C2×#333D1111yescharacteristic
112C2×#332—111no—
113C2×#332—111no—
114C23×C11C2×C22⋊C411yescharacteristic
115Q8×C11—82no—
116Q8×C11—82no—
117C2×C4×C11—22no—
118C2×C4×C11—42no—
119C2×C4×C11—44no—
120C2×C4×C11C4×D411yescharacteristic
121C2×C4×C11C4×D411yescharacteristic
122C2×C4×C11#12111yescharacteristic
123C2×C4×C11#12111yescharacteristic
124C2×C4×C11#12411yescharacteristic
125C2×C4×C11#12711yescharacteristic
126C2×C4×C11C2×SD1612yes—
127C2×C4×C11C2×Q1612yes—
128C2×C4×C11#13511yescharacteristic
129C2×C4×C11#13511yescharacteristic
130C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
131C2×C4×C11#13711yescharacteristic
132C2×Dic11—22no—
133C2×Dic11—22no—
134C2×Dic11—22no—
135C2×Dic11—22no—
136C2×Dic11—42no—
137C2×Dic11—42no—
138C2×Dic11—42no—
139C2×Dic11#10314yes—
140C2×Dic11#10314yes—
141Dic22—81no—
142Dic22—81no—
143Dic22—81no—
144Dic22—81no—
145C8×C11—42no—
146C8×C11—81no—
147C11⋊C8—42no—
148C11⋊C8—81no—
149C2×C4⋊Q8—111no—
150C2×C4⋊Q8C2×D1111yescharacteristic
151C2×C4⋊C8—111no—
152C2×C4⋊C8—111no—
153C2×C4⋊C8—222no—
154C2×C4⋊C8C2×D1111yescharacteristic
155C2×C4⋊C8C2×D1111yescharacteristic
156C2×C4×C8—221no—
157#391—114no—
158#391—221no—
159#391—221no—
160#382—222no—
161C43—111no—
162#336—221no—
163#333—22no—
164#333—222no—
165#332—222no—
166#332—222no—
167C22×C11#39011yescharacteristic
168C22×C11#41312yes—
169C22×C11C2×#10312yes—
170C22×C11#41611yescharacteristic
171C22×C11#41711yescharacteristic
172C4×C11—21no—
173C4×C11—21no—
174C4×C11—82no—
175C4×C11#46311yescharacteristic
176C4×C11#46311yescharacteristic
177C4×C11#46411yescharacteristic
178C4×C11#46411yescharacteristic
179C4×C11#48712yes—
180C4×C11#49211yescharacteristic
181C4×C11#49411yescharacteristic
182Dic11—24no—
183Dic11—24no—
184Dic11—82no—
185C22×Q8—221no—
186C22×Q8C4×D1112yes—
187C22×C8—21no—
188C22×C8—21no—
189C22×C8—221no—
190C22×C8—221no—
191C4⋊Q8—21no—
192C4⋊Q8—21no—
193C4⋊Q8—21no—
194C4⋊Q8—21no—
195C4⋊Q8—221no—
196C4⋊Q8—221no—
197C4⋊Q8—221no—
198C4⋊Q8—221no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—112no—
202C2×C4⋊C4—221no—
203C2×C42—112no—
204C2×C42—111no—
205C2×C42—111no—
206C2×C42—112no—
207C2×C42C22×D1111yescharacteristic
208C4⋊C8—21no—
209C4⋊C8—21no—
210C4⋊C8—21no—
211C4⋊C8—112no—
212C4⋊C8—221no—
213C4⋊C8—221no—
214C4⋊C8—221no—
215C4⋊C8—444no—
216C4⋊C8C22⋊D1112yes—
217C4×C8—442no—
218#95—224no—
219#95—224no—
220C2×C11#154212yes—
221C2×C11#155012yes—
222C2×C11#195611yescharacteristic
223C2×C11#196711yescharacteristic
224C2×C11#198311yescharacteristic
225C2×Q8—22no—
226C2×Q8—22no—
227C2×Q8—44no—
228C2×Q8—441no—
229C2×Q8—441no—
230C2×Q8—441no—
231C2×Q8—441no—
232C2×Q8—441no—
233C2×Q8—441no—
234C22×C4—22no—
235C22×C4—112no—
236C22×C4—112no—
237C22×C4—222no—
238C22×C4C2×C4×D1111yescharacteristic
239C22×C4D4×D1111yescharacteristic
240C22×C4D4×D1111yescharacteristic
241C2×C8—22no—
242C2×C8—41no—
243C2×C8—41no—
244C2×C8—42no—
245C2×C8—41no—
246C2×C8—222no—
247C2×C8—441no—
248C2×C8—441no—
249C2×C8—442no—
250C2×C8—441no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—222no—
256C4⋊C4—222no—
257C4⋊C4—441no—
258C4⋊C4—441no—
259C42—114no—
260C42—114no—
261C42—221no—
262C42—221no—
263C42—221no—
264C42—221no—
265C42—442no—
266C42#433911yescharacteristic
267C42D4×D1111yescharacteristic
268C42#434111yescharacteristic
269C42C2×C22⋊D1111yescharacteristic
270C11#969711yescharacteristic, complemented, Sylow
271C23C22⋊C4×D1111yescharacteristic
272Q8—82no—
273Q8—82no—
274Q8—881no—
275Q8—881no—
276Q8—881no—
277Q8—881no—
278C2×C4—22no—
279C2×C4—42no—
280C2×C4—44no—
281C2×C4—114no—
282C2×C4—114no—
283C2×C4—222no—
284C2×C4—222no—
285C2×C4—222no—
286C2×C4—222no—
287C2×C4—442no—
288C2×C4—442no—
289C2×C4—442no—
290C2×C4(C22⋊D11)⋊C411yescharacteristic
291C2×C4#6693711yescharacteristic
292C2×C4#6693811yescharacteristic
293C2×C4SD16×D1112yes—
294C2×C4#6696711yescharacteristic
295C2×C4#6696911yescharacteristic
296C2×C4Q16×D1112yes—
297C2×C4#6697111yescharacteristic
298C2×C4#6697211yescharacteristic
299C2×C4C4×C22⋊D1111yescharacteristic
300C2×C4#6699211yescharacteristic
301C2×C4#6699311yescharacteristic
302C8—42no—
303C8—81no—
304C8—442no—
305C8—881no—
306C22#1062235812yes—
307C22D11×#10312yes—
308C22#1062241611yescharacteristic
309C22#1062241711yescharacteristic
310C22#1062257011yescharacteristic
311C4—21no—
312C4—21no—
313C4—82no—
314C4—224no—
315C4—224no—
316C4—882no—
317C4#1062240512yes—
318C4#1062241111yescharacteristic
319C4#1062243211yescharacteristic
320C4#1062277811yescharacteristic
321C4#1062278811yescharacteristic
322C4#1062279411yescharacteristic
323C4#1062279811yescharacteristic
324C2#1306727012yes—
325C2#1306730312yes—
326C2#1306941611yescharacteristic
327C2#1306946211yescharacteristic
328C2#1306954511yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC2×C11×#333C2
socle, prime radicalC23×C11C2×C22⋊C4
cosocleC2×C42×C11C23
hypercenterC2×#333D11
hypocenterC11#9697
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#333

Complements

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

NH ≅ G/Ntype
270. C11#9697semidirect

Maximal subgroups

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

subgroupindex
#130769932
#130687672
C4⋊C8×Dic112
C2×#106221842
C2×#106221202
C2×#106221242
C2×C11×#3332
#969711