Finite Group Databasebeta

← #14650481

Subgroups — #14650481

Order 2816.

470 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071336C211yesmaximal, characteristic
2#13069598C211yesmaximal, characteristic
3#13067288C211yesmaximal, characteristic
4#13067180C211yesmaximal, characteristic
5#13066475C211yesmaximal, characteristic
6#13066444C211yesmaximal, characteristic
7C11×#3229C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×Q8×Dic11—21no—
11C11×#498C412yescomplemented
12C11×#487C412yescomplemented
13C11×#483—22no—
14C11×#475—22no—
15C11×#431C2211yescharacteristic
16#10622843—21no—
17#10622594—22no—
18#10622594—22no—
19#10622549C2211yescharacteristic
20#10622545C2211yescharacteristic
21#10622538C2211yescharacteristic
22#10622537C2211yescharacteristic
23#10622185—22no—
24#10622176—22no—
25#10622170—21no—
26#10622170—21no—
27C22×Q8×C11—21no—
28C11×C4⋊Q8—21no—
29C11×C4⋊Q8—21no—
30C11×C4⋊Q8C2×C411yescharacteristic
31C11×C4⋊Q8C2×C411yescharacteristic
32C11×C4⋊Q8C2×C412yes—
33C11×C4⋊Q8D412yes—
34C11×#125—21no—
35C11×C22⋊Q8—21no—
36C11×C22⋊Q8—21no—
37C4×Q8×C11—21no—
38C4×Q8×C11—21no—
39C11×#117—21no—
40C2×C11×C4⋊C4—21no—
41C2×C11×C4⋊C4D412yes—
42C2×C42×C11C2311yescharacteristic
43Q8×Dic11—42no—
44Q8×Dic11—42no—
45C2×C4⋊Dic11—22no—
46C2×C4⋊Dic11—21no—
47C2×C4×Dic11—22no—
48C2×C4×Dic11D411yescharacteristic
49C2×C4×Dic11D411yescharacteristic
50C2×#4318—21no—
51C11×#106—24no—
52C11×C4⋊C8—21no—
53C11×#103—24no—
54C11×C22⋊C8—21no—
55C4×C8×C11C2×C412yes—
56C11⋊#95—24no—
57C11⋊#95—21no—
58C11⋊#95—21no—
59C11⋊#95—21no—
60C11⋊#95D412yes—
61C22⋊(C11⋊C8)—21no—
62C4⋊(C11⋊C8)—21no—
63C4⋊(C11⋊C8)—21no—
64C4⋊(C11⋊C8)—21no—
65C4×C11⋊C8—21no—
66#9296—111nomaximal, Sylow
67C2×Q8×C11—22no—
68C2×Q8×C11—22no—
69C2×Q8×C11—21no—
70C2×Q8×C11—21no—
71C2×Q8×C11—41no—
72C2×Q8×C11—41no—
73C2×Q8×C11—41no—
74C2×Q8×C11—41no—
75C22×C4×C11—22no—
76C22×C4×C11C2×D411yescharacteristic
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11C2×D411yescharacteristic
79C22×Dic11—21no—
80C22×Dic11—21no—
81C22×Dic11—22no—
82C2×C8×C11—22no—
83C11×C4⋊C4—22no—
84C11×C4⋊C4—22no—
85C11×C4⋊C4—22no—
86C11×C4⋊C4—21no—
87C11×C4⋊C4—21no—
88C11×C4⋊C4—21no—
89C11×C4⋊C4—21no—
90C11×C4⋊C4—41no—
91C11×C4⋊C4—41no—
92C11×C4⋊C4C22⋊C414yes—
93C11×C22⋊C4—41no—
94C42×C11—41no—
95C42×C11C22×C411yescharacteristic
96C42×C11C2×D411yescharacteristic
97C42×C11#4111yescharacteristic
98C42×C11#4111yescharacteristic
99C4⋊Dic11—44no—
100C4⋊Dic11—41no—
101C4⋊Dic11—41no—
102C4×Dic11—21no—
103C4×Dic11—21no—
104C4×Dic11—21no—
105C4×Dic11—44no—
106C4×Dic11SD1612yes—
107#4318—41no—
108#4318—41no—
109C2×C11⋊C8—41no—
110C2×C11⋊C8—41no—
111#3229D1111yescharacteristic
112#2327—111no—
113#1995—111no—
114#1546—111no—
115#1518—111no—
116#1286—111no—
117#1274—111no—
118C23×C11#12011yescharacteristic
119Q8×C11—42no—
120Q8×C11—42no—
121Q8×C11—42no—
122Q8×C11—42no—
123Q8×C11—42no—
124Q8×C11—81no—
125C2×C4×C11—24no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11—42no—
129C2×C4×C11—42no—
130C2×C4×C11—41no—
131C2×C4×C11—41no—
132C2×C4×C11C2×C22⋊C411yescharacteristic
133C2×C4×C11C4×D411yescharacteristic
134C2×C4×C11C4×D411yescharacteristic
135C2×C4×C11#12111yescharacteristic
136C2×C4×C11#12111yescharacteristic
137C2×C4×C11#12311yescharacteristic
138C2×C4×C11C2×SD1611yescharacteristic
139C2×C4×C11#13511yescharacteristic
140C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
141C2×C4×C11#13711yescharacteristic
142C2×Dic11—22no—
143C2×Dic11—41no—
144C2×Dic11—41no—
145C2×Dic11—41no—
146C2×Dic11—42no—
147C2×Dic11—41no—
148C2×Dic11—42no—
149C2×Dic11—42no—
150C2×Dic11—41no—
151C8×C11—42no—
152C11⋊C8—81no—
153C11⋊C8—81no—
154#533C2×D1111yescharacteristic
155C2×C4⋊Q8C2×D1111yescharacteristic
156C2×C4×Q8—221no—
157#498Dic1112yescomplemented
158#487Dic1112yescomplemented
159#483—22no—
160#475—22no—
161#431—111no—
162#431C2×D1111yescharacteristic
163#423—111no—
164#391—221no—
165#387—222no—
166#387—222no—
167#382—111no—
168#376—111no—
169#339—221no—
170#339—221no—
171#332—222no—
172#328—222no—
173C22×C11—21no—
174C22×C11—21no—
175C22×C11#38611yescharacteristic
176C22×C11#45011yescharacteristic
177C22×C11#45211yescharacteristic
178C4×C11—21no—
179C4×C11—21no—
180C4×C11—21no—
181C4×C11—21no—
182C4×C11—44no—
183C4×C11—81no—
184C4×C11—81no—
185C4×C11C4×SD1611yescharacteristic
186C4×C11#44011yescharacteristic
187C4×C11#46111yescharacteristic
188C4×C11#46311yescharacteristic
189Dic11—42no—
190Dic11—82no—
191Dic11—81no—
192C22×Q8—21no—
193C2×M16—221no—
194C4⋊Q8—21no—
195C4⋊Q8—21no—
196C4⋊Q8C2×Dic1111yescharacteristic
197C4⋊Q8C2×Dic1111yescharacteristic
198C4⋊Q8C2×Dic1112yes—
199C4⋊Q8C22⋊D1112yes—
200#125—21no—
201C22⋊Q8—21no—
202C22⋊Q8—21no—
203C4×Q8—21no—
204C4×Q8—21no—
205C4×Q8—442no—
206C4×Q8—442no—
207#117—21no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—222no—
210C2×C4⋊C4—221no—
211C2×C4⋊C4C22⋊D1112yes—
212C2×C42—111no—
213C2×C42—111no—
214C2×C42—222no—
215C2×C42C22×D1111yescharacteristic
216#106—24no—
217C4⋊C8—21no—
218C4⋊C8—221no—
219C4⋊C8—221no—
220C4⋊C8—221no—
221#103—24no—
222C22⋊C8—21no—
223C22⋊C8—221no—
224C4×C8—221no—
225C4×C8C2×Dic1112yes—
226#95—112no—
227#95—224no—
228#95—221no—
229#95—221no—
230#95—221no—
231C2×C11—21no—
232C2×C11—21no—
233C2×C11#187711yescharacteristic
234C2×C11#190511yescharacteristic
235C2×C11#191211yescharacteristic
236C2×Q8—22no—
237C2×Q8—22no—
238C2×Q8—21no—
239C2×Q8—21no—
240C2×Q8—41no—
241C2×Q8—41no—
242C2×Q8—41no—
243C2×Q8—41no—
244C22×C4—22no—
245C22×C4—221no—
246C22×C4—222no—
247C22×C4—221no—
248C22×C4D4×D1111yescharacteristic
249C22×C4D4×D1111yescharacteristic
250C22×C4C2×C22⋊D1111yescharacteristic
251M16—441no—
252M16—441no—
253C2×C8—22no—
254C2×C8—441no—
255C2×C8—441no—
256C4⋊C4—22no—
257C4⋊C4—22no—
258C4⋊C4—22no—
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4—21no—
262C4⋊C4—21no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—444no—
266C4⋊C4—441no—
267C4⋊C4—441no—
268C4⋊C4C22⋊Dic1114yes—
269C22⋊C4—41no—
270C42—41no—
271C42—112no—
272C42—221no—
273C42—221no—
274C42—221no—
275C42—444no—
276C42#434111yescharacteristic
277C42#434111yescharacteristic
278C42C22×Dic1111yescharacteristic
279C42C2×C22⋊D1111yescharacteristic
280C11#929611yescharacteristic, complemented, Sylow
281C23#6699011yescharacteristic
282Q8—42no—
283Q8—42no—
284Q8—42no—
285Q8—42no—
286Q8—42no—
287Q8—81no—
288C2×C4—24no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—222no—
296C2×C4—441no—
297C2×C4—441no—
298C2×C4—442no—
299C2×C4—441no—
300C2×C4—442no—
301C2×C4—441no—
302C2×C4—442no—
303C2×C4—441no—
304C2×C4SD16×D1111yescharacteristic
305C2×C4#6696711yescharacteristic
306C2×C4#6696811yescharacteristic
307C2×C4#6696911yescharacteristic
308C2×C4D4×Dic1111yescharacteristic
309C2×C4D4×Dic1111yescharacteristic
310C2×C4#6698811yescharacteristic
311C2×C4#6699211yescharacteristic
312C2×C4#6699211yescharacteristic
313C2×C4C2×C22⋊Dic1111yescharacteristic
314C8—42no—
315C8—881no—
316C8—881no—
317C22—21no—
318C22—21no—
319C22#1062278211yescharacteristic
320C22#1062278611yescharacteristic
321C22#1062283311yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—44no—
327C4—81no—
328C4—81no—
329C4—442no—
330C4—882no—
331C4—881no—
332C4SD16×Dic1111yescharacteristic
333C4#1062277511yescharacteristic
334C4#1062277711yescharacteristic
335C4#1062277811yescharacteristic
336C2—21no—
337C2—21no—
338C2#1306895211yescharacteristic
339C2#1306911211yescharacteristic
340C2#1306915411yescharacteristic
subgroupG/H
centerC22#10622833
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#3229C2
socleC22×C11#386
prime radicalC23×C11#120
cosocleC2×C42×C11C23
hypercenter#3229D11
hypocenterC11#9296
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3229

Complements

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

NH ≅ G/Ntype
11. C11×#498C4semidirect
12. C11×#487C4semidirect
157. #498Dic11semidirect
158. #487Dic11semidirect
280. C11#9296semidirect

Maximal subgroups

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

subgroupindex
#130713362
#130695982
#130672882
#130671802
#130664752
#130664442
C11×#32292
#929611