Finite Group Databasebeta

← #14652894

Subgroups — #14652894

Order 2816.

716 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076968C211yesmaximal, characteristic
2C2×#10622105C214yesmaximal
3C4×C11⋊#95C211yesmaximal, characteristic
4C11×#1797C211yesmaximal, characteristic
5C22×C42×C11C2211yescharacteristic
6C2×#66977C2212yes—
7C22×C4×Dic11—21no—
8C2×#66922C411yescharacteristic, complemented
9C2×C11×C4⋊C8—21no—
10C2×C11×C22⋊C8C2212yes—
11#10622825—21no—
12#10622825—21no—
13C2×C11⋊#95—21no—
14C2×C11⋊#95C2212yes—
15#10622548C411yescharacteristic, complemented
16#10622542C412yescomplemented
17#10622541—21no—
18#10622541—21no—
19C11×#336—21no—
20#10622105—28no—
21C23×C4×C11D411yescharacteristic
22C23×C4×C11D411yescharacteristic
23C23×C4×C11C2311yescharacteristic
24C23×Dic11—22no—
25C22×Dic22C2×C412yes—
26C22×C8×C11—22no—
27C2×C42×C11—42no—
28C2×C42×C11C2×C411yescharacteristic
29C2×C42×C11C2×C411yescharacteristic
30C2×C42×C11D411yescharacteristic
31C2×C42×C11D411yescharacteristic
32C2×C22⋊Dic11—22no—
33C2×C4⋊Dic11—21no—
34C2×C4⋊Dic11—21no—
35C2×C4⋊Dic11—21no—
36C2×C4⋊Dic11—21no—
37C2×C4⋊Dic11C2×C412yes—
38#66977—24no—
39#66977—24no—
40C2×Dic11⋊C4—22no—
41C2×C4×Dic11—24no—
42C2×C4×Dic11—42no—
43C2×C4×Dic11—42no—
44#66922—42no—
45C11×C4⋊C8—42no—
46C11×C22⋊C8—24no—
47C11⋊#95—24no—
48C11⋊#95—22no—
49C11⋊#95—22no—
50C11⋊#95—22no—
51C11⋊#95D414yes—
52#9711—111nomaximal, Sylow
53C24×C11C2×D411yescharacteristic
54C22×C4×C11—22no—
55C22×C4×C11—22no—
56C22×C4×C11—22no—
57C22×C4×C11—22no—
58C22×C4×C11—41no—
59C22×C4×C11—41no—
60C22×C4×C11—41no—
61C22×C4×C11C22⋊C411yescharacteristic
62C22×C4×C11C22⋊C411yescharacteristic
63C22×C4×C11C22⋊C411yescharacteristic
64C22×C4×C11C22⋊C411yescharacteristic
65C22×C4×C11SD1612yes—
66C22×C4×C11Q1612yes—
67C22×C4×C11C22×C411yescharacteristic
68C22×C4×C11C2×D411yescharacteristic
69C22×C4×C11C2×D412yes—
70C22×C4×C11#4112yes—
71C22×Dic11—24no—
72C22×Dic11—24no—
73C22×Dic11—22no—
74C22×Dic11—22no—
75C22×Dic11—24no—
76C22×Dic11—42no—
77C22×Dic11—42no—
78C22×Dic11—42no—
79C22×Dic11—42no—
80C2×Dic22—24no—
81C2×Dic22—42no—
82C2×Dic22—42no—
83C2×C8×C11—42no—
84C2×C8×C11—42no—
85C2×C8×C11—42no—
86C42×C11—22no—
87C42×C11—22no—
88C42×C11—41no—
89C42×C11—41no—
90C22⋊Dic11—44no—
91C4⋊Dic11—24no—
92C4⋊Dic11—42no—
93C4⋊Dic11—42no—
94C4⋊Dic11—42no—
95C4⋊Dic11—42no—
96Dic11⋊C4—42no—
97Dic11⋊C4—42no—
98C4×Dic11—48no—
99#2857—111no—
100#1797D1111yescharacteristic
101C2×#328—114no—
102C4×#95—111no—
103C23×C11—21no—
104C23×C11—21no—
105C23×C11—21no—
106C23×C11—21no—
107C23×C11C2×C22⋊C411yescharacteristic
108C23×C11#12112yes—
109C23×C11C2×SD1611yescharacteristic
110C23×C11C2×Q1611yescharacteristic
111C23×C11#13712yes—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—24no—
121C2×C4×C11—24no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—42no—
126C2×C4×C11—42no—
127C2×C4×C11—44no—
128C2×C4×C11#9912yes—
129C2×C4×C11#10312yes—
130C2×C4×C11#10312yes—
131C2×C4×C11#10412yes—
132C2×C4×C11#10412yes—
133C2×C4×C11C4×D412yes—
134C2×C4×C11#12411yescharacteristic
135C2×C4×C11#12711yescharacteristic
136C2×Dic11—28no—
137C2×Dic11—44no—
138C2×Dic11—44no—
139C2×Dic11—44no—
140C2×Dic11—44no—
141C2×Dic11—44no—
142C2×Dic11—44no—
143C2×Dic11—42no—
144C2×Dic11—42no—
145C2×Dic11—42no—
146C2×Dic11—42no—
147C2×Dic11—42no—
148C2×Dic11—42no—
149Dic22—84no—
150C8×C11—82no—
151C2×C4⋊Q8—111no—
152C2×C22⋊Q8—112no—
153C22×C42—221no—
154C22×C42C2×D1111yescharacteristic
155C2×C4⋊C8—21no—
156C2×C22⋊C8C2×D1112yes—
157#391—112no—
158#389—221no—
159#389—221no—
160#384—111no—
161#380—221no—
162#380—221no—
163C2×#95—112no—
164C2×#95—221no—
165#336—21no—
166#328—228no—
167C22×C11—22no—
168C22×C11—22no—
169C22×C11—21no—
170C22×C11—21no—
171C22×C11—21no—
172C22×C11—21no—
173C22×C11—22no—
174C22×C11—22no—
175C22×C11#39011yescharacteristic
176C22×C11C2×#9911yescharacteristic
177C22×C11#41011yescharacteristic
178C22×C11C2×#10311yescharacteristic
179C22×C11#41911yescharacteristic
180C22×C11C2×#10411yescharacteristic
181C22×C11C2×#10411yescharacteristic
182C22×C11#46112yes—
183C22×C11#46212yes—
184C4×C11—22no—
185C4×C11—21no—
186C4×C11—21no—
187C4×C11—22no—
188C4×C11—22no—
189C4×C11—41no—
190C4×C11#32814yescomplemented
191Dic11—48no—
192Dic11—82no—
193Dic11—82no—
194C22×Q8—112no—
195C23×C4—222no—
196C23×C4D4411yescharacteristic
197C23×C4D4411yescharacteristic
198C23×C4C22×D1111yescharacteristic
199C22×C8—22no—
200C4⋊Q8—442no—
201C22⋊Q8—224no—
202C22⋊Q8—224no—
203C2×C4⋊C4—112no—
204C2×C4⋊C4—221no—
205C2×C4⋊C4—221no—
206C2×C4⋊C4—221no—
207C2×C4⋊C4—221no—
208C2×C4⋊C4—222no—
209C2×C22⋊C4—222no—
210C2×C42—42no—
211C2×C42—224no—
212C2×C42—442no—
213C2×C42—442no—
214C2×C42C4×D1111yescharacteristic
215C2×C42C4×D1111yescharacteristic
216C2×C42C22⋊D1111yescharacteristic
217C2×C42C22⋊D1111yescharacteristic
218C4⋊C8—42no—
219C22⋊C8—24no—
220#95—114no—
221#95—224no—
222#95—222no—
223#95—222no—
224#95—222no—
225C2×C11—22no—
226C2×C11—22no—
227C2×C11C2×#32811yescharacteristic
228C2×C11#150311yescharacteristic
229C2×C11#150611yescharacteristic
230C2×C11#150811yescharacteristic
231C2×C11#196211yescharacteristic
232C2×C11#196411yescharacteristic
233C2×C11#198111yescharacteristic
234C24C2×D4411yescharacteristic
235C2×Q8—224no—
236C2×Q8—442no—
237C2×Q8—442no—
238C22×C4—22no—
239C22×C4—22no—
240C22×C4—22no—
241C22×C4—22no—
242C22×C4—41no—
243C22×C4—41no—
244C22×C4—41no—
245C22×C4—224no—
246C22×C4—224no—
247C22×C4—224no—
248C22×C4—222no—
249C22×C4—222no—
250C22×C4—442no—
251C22×C4—442no—
252C22×C4—442no—
253C22×C4—442no—
254C22×C4#431412yes—
255C22×C4Dic4412yes—
256C22×C4(C2×D11)⋊C411yescharacteristic
257C22×C4(C2×D11)⋊C411yescharacteristic
258C22×C4(C2×D11)⋊C411yescharacteristic
259C22×C4(C2×D11)⋊C411yescharacteristic
260C22×C4C2×C4×D1111yescharacteristic
261C22×C4D4×D1112yes—
262C22×C4#434312yes—
263C22×C4C2×C22⋊D1111yescharacteristic
264C2×C8—42no—
265C2×C8—42no—
266C2×C8—42no—
267C4⋊C4—224no—
268C4⋊C4—442no—
269C4⋊C4—442no—
270C4⋊C4—442no—
271C4⋊C4—442no—
272C4⋊C4—442no—
273C4⋊C4—442no—
274C22⋊C4—444no—
275C42—22no—
276C42—22no—
277C42—41no—
278C42—41no—
279C42—448no—
280C11#971111yescharacteristic, complemented, Sylow
281C23—21no—
282C23—21no—
283C23—21no—
284C23—21no—
285C23#6694812yes—
286C23C2×#431411yescharacteristic
287C23C2×Dic4411yescharacteristic
288C23#6696212yes—
289C23C2×(C2×D11)⋊C411yescharacteristic
290Q8—884no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—24no—
300C2×C4—24no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—42no—
305C2×C4—42no—
306C2×C4—44no—
307C2×C4—228no—
308C2×C4—444no—
309C2×C4—444no—
310C2×C4—444no—
311C2×C4—444no—
312C2×C4—444no—
313C2×C4—444no—
314C2×C4—442no—
315C2×C4—442no—
316C2×C4—442no—
317C2×C4—442no—
318C2×C4—442no—
319C2×C4—442no—
320C2×C4#6687012yes—
321C2×C4#6688012yes—
322C2×C4#6688012yes—
323C2×C4#6688912yes—
324C2×C4#6688912yes—
325C2×C4#6694612yes—
326C2×C4#6699311yescharacteristic
327C2×C4#6700011yescharacteristic
328C8—82no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—22no—
334C22—22no—
335C22—22no—
336C22—22no—
337C22#1062245412yes—
338C22#1062246212yes—
339C22C2×#6687011yescharacteristic
340C22#1062260111yescharacteristic
341C22#1062261911yescharacteristic
342C22C2×#6688011yescharacteristic
343C22#1062273311yescharacteristic
344C22C2×#6688911yescharacteristic
345C22C2×#6688911yescharacteristic
346C4—22no—
347C4—22no—
348C4—21no—
349C4—22no—
350C4—21no—
351C4—41no—
352C4—448no—
353C4—882no—
354C4—882no—
355C4#1062210514yescomplemented
356C2—22no—
357C2—22no—
358C2C2×#1062210511yescharacteristic
359C2#1306711611yescharacteristic
360C2#1306712911yescharacteristic
361C2#1306713711yescharacteristic
362C2#1306944311yescharacteristic
363C2#1306945111yescharacteristic
364C2#1306953811yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1797C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C2×D4
cosocleC23×C4×C11C23
hypercenter#1797D11
hypocenterC11#9711
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1797

Complements

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

NH ≅ G/Ntype
8. C2×#66922C4semidirect
15. #10622548C4semidirect
16. #10622542C4semidirect
190. C4×C11#328semidirect
280. C11#9711semidirect
355. C4#10622105semidirect

Maximal subgroups

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

subgroupindex
#130769682
C2×#106221052
C4×C11⋊#952
C11×#17972
#971111