Finite Group Databasebeta

← #14763692

Subgroups — #14763692

Order 2816.

1118 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
1C22×C4⋊(C11⋊C8)C211yesmaximal, characteristic
2#13071014C211yesmaximal, characteristic
3#13069569C212yesmaximal, complemented
4#13069540C212yesmaximal, complemented
5#13069040C214yesmaximal
6#13068631C214yesmaximal, complemented
7C2×C11×#533C211yesmaximal, characteristic
8C11×#533—24no—
9C11×#533C418yescomplemented
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×C11×C4⋊Q8C2211yescharacteristic
12C2×C11×#125—21no—
13C2×C11×C22⋊Q8—21no—
14C2×C11×C22⋊Q8C2212yes—
15C2×C4×Q8×C11—21no—
16C2×C4×Q8×C11C2212yes—
17C2×C11×#117—21no—
18C22×C42×C11C2211yescharacteristic
19C23×C11⋊C8C2212yes—
20C2×#66899C2218yes—
21#10622825C2212yes—
22#10622824—21no—
23C4×C22⋊Dic11—21no—
24#10622550—21no—
25#10622549C2212yes—
26C4×C4⋊Dic11C2212yes—
27#10622545—21no—
28C2×C4⋊(C11⋊C8)—24no—
29C2×C4⋊(C11⋊C8)C2212yes—
30C2×C4⋊(C11⋊C8)C2212yes—
31#10622167C2218yes—
32C22×Q8×C11—21no—
33C22×Q8×C11C2312yes—
34C23×C4×C11D411yescharacteristic
35C23×C4×C11D411yescharacteristic
36C23×C4×C11C2311yescharacteristic
37C11×C4⋊Q8—22no—
38C11×C4⋊Q8—22no—
39C11×C4⋊Q8C2×C414yes—
40C11×C4⋊Q8C2×C414yes—
41C11×#125—28no—
42C11×C22⋊Q8—28no—
43C11×C22⋊Q8—24no—
44C11×C22⋊Q8C2×C418yes—
45C4×Q8×C11—28no—
46C4×Q8×C11—24no—
47C4×Q8×C11C2×C418yes—
48C11×#117—28no—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—22no—
53C2×C11×C4⋊C4—22no—
54C2×C11×C4⋊C4C2312yes—
55C2×C11×C22⋊C4—22no—
56C2×C42×C11—22no—
57C2×C42×C11C2×C414yes—
58C2×C42×C11D411yescharacteristic
59C2×C42×C11D411yescharacteristic
60C2×C42×C11D414yes—
61C2×C42×C11C2311yescharacteristic
62C2×C42×C11C2311yescharacteristic
63C2×C22⋊Dic11—22no—
64C2×C4⋊Dic11C2314yes—
65C2×C4×Dic11—22no—
66C22×C11⋊C8—24no—
67C22×C11⋊C8—44no—
68C22×C11⋊C8C2314yes—
69#66899—48no—
70C11⋊#95—22no—
71C11⋊#95—22no—
72C11⋊#95—22no—
73C11⋊#95—22no—
74C4⋊(C11⋊C8)—24no—
75C4⋊(C11⋊C8)—24no—
76#21889—111nomaximal, Sylow
77C24×C11C2×D411yescharacteristic
78C2×Q8×C11—24no—
79C2×Q8×C11—22no—
80C2×Q8×C11—24no—
81C2×Q8×C11—24no—
82C2×Q8×C11—44no—
83C2×Q8×C11C22×C414yes—
84C22×C4×C11—24no—
85C22×C4×C11—24no—
86C22×C4×C11—22no—
87C22×C4×C11—22no—
88C22×C4×C11—22no—
89C22×C4×C11—22no—
90C22×C4×C11C22⋊C414yes—
91C22×C4×C11C22⋊C414yes—
92C22×C4×C11C22×C412yes—
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2×D412yes—
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2411yescharacteristic
100C22×Dic11—24no—
101C11×C4⋊C4—24no—
102C11×C4⋊C4—24no—
103C11×C4⋊C4—24no—
104C11×C4⋊C4—28no—
105C11×C4⋊C4—28no—
106C11×C4⋊C4—22no—
107C11×C4⋊C4C22×C414yes—
108C11×C22⋊C4—28no—
109C42×C11—28no—
110C42×C11C22⋊C414yes—
111C42×C11C22⋊C414yes—
112C42×C11C22×C412yes—
113C42×C11C22×C412yes—
114C42×C11C2×D412yes—
115C42×C11C2×D412yes—
116C22⋊Dic11—44no—
117C4⋊Dic11—24no—
118C4⋊Dic11—24no—
119C4×Dic11—44no—
120C2×C11⋊C8—24no—
121C2×C11⋊C8—28no—
122C2×C11⋊C8—48no—
123C2×#533D1111yescharacteristic
124C22×C4⋊C8—111no—
125#2283—111no—
126#1988—112no—
127#1981—112no—
128#1892—114no—
129#1805—114no—
130C23×C11—22no—
131C23×C11—22no—
132C23×C11C2×C22⋊C412yes—
133C23×C11#13714yes—
134C23×C11C22×D411yescharacteristic
135Q8×C11—28no—
136Q8×C11—42no—
137Q8×C11—42no—
138Q8×C11—48no—
139C2×C4×C11—22no—
140C2×C4×C11—22no—
141C2×C4×C11—22no—
142C2×C4×C11—22no—
143C2×C4×C11—28no—
144C2×C4×C11—24no—
145C2×C4×C11—22no—
146C2×C4×C11—22no—
147C2×C4×C11—28no—
148C2×C4×C11—24no—
149C2×C4×C11—24no—
150C2×C4×C11—44no—
151C2×C4×C11—44no—
152C2×C4×C11C2×C22⋊C412yes—
153C2×C4×C11C2×C22⋊C412yes—
154C2×C4×C11C2×C22⋊C412yes—
155C2×C4×C11C2×C22⋊C412yes—
156C2×C4×C11C2×C22⋊C412yes—
157C2×C4×C11#13514yes—
158C2×C4×C11C23×C411yescharacteristic
159C2×C4×C11C22×D411yescharacteristic
160C2×C4×C11H(5,𝔽2)12yes—
161C2×C4×C112−1+412yes—
162C2×Dic11—44no—
163C2×Dic11—44no—
164C2×Dic11—44no—
165C11⋊C8—44no—
166C23×C8—112no—
167#533—24no—
168#533Dic1118yescomplemented
169C2×C4⋊Q8C2×D1111yescharacteristic
170C2×C4⋊Q8C2×D1111yescharacteristic
171C2×#125—21no—
172C2×C22⋊Q8—21no—
173C2×C22⋊Q8C2×D1112yes—
174C2×C4×Q8—21no—
175C2×C4×Q8C2×D1112yes—
176C2×#117—21no—
177C22×C42C2×D1111yescharacteristic
178C2×C4⋊C8—112no—
179C2×C4⋊C8—112no—
180C2×C4⋊C8—224no—
181C2×#103—118no—
182#383—221no—
183#382—112no—
184#381—221no—
185#380—112no—
186C4×C4⋊C4—112no—
187C4×C22⋊C4—221no—
188#376—221no—
189#340—118no—
190C22×C11—22no—
191C22×C11—22no—
192C22×C11—28no—
193C22×C11#41914yes—
194C22×C11C22×C22⋊C411yescharacteristic
195C22×C11#53712yes—
196C22×C11C2×#13512yes—
197C22×C11C2×#13712yes—
198C4×C11—22no—
199C4×C11—22no—
200C4×C11—22no—
201C4×C11—22no—
202C4×C11—44no—
203C4×C11—44no—
204C4×C11#41614yes—
205C4×C11#52012yes—
206C4×C11#53511yescharacteristic
207C4×C11#53611yescharacteristic
208Dic11—84no—
209C22×Q8—21no—
210C22×Q8C22×D1112yes—
211C23×C4C22⋊D1111yescharacteristic
212C23×C4C22⋊D1111yescharacteristic
213C23×C4C22×D1111yescharacteristic
214C22×C8—114no—
215C22×C8—224no—
216C22×C8—444no—
217C4⋊Q8—22no—
218C4⋊Q8—22no—
219C4⋊Q8C2×Dic1114yes—
220C4⋊Q8C2×Dic1114yes—
221#125—28no—
222C22⋊Q8—28no—
223C22⋊Q8—24no—
224C22⋊Q8C2×Dic1118yes—
225C4×Q8—28no—
226C4×Q8—24no—
227C4×Q8C2×Dic1118yes—
228#117—28no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—22no—
233C2×C4⋊C4—22no—
234C2×C4⋊C4—114no—
235C2×C4⋊C4C22×D1112yes—
236C2×C22⋊C4—22no—
237C2×C22⋊C4—222no—
238C2×C42—22no—
239C2×C42—222no—
240C2×C42C2×Dic1114yes—
241C2×C42C22⋊D1111yescharacteristic
242C2×C42C22⋊D1111yescharacteristic
243C2×C42C22⋊D1114yes—
244C2×C42C22×D1111yescharacteristic
245C2×C42C22×D1111yescharacteristic
246C4⋊C8—224no—
247C4⋊C8—224no—
248#103—448no—
249#95—222no—
250#95—222no—
251#95—222no—
252#95—222no—
253C2×C11—24no—
254C2×C11#231111yescharacteristic
255C2×C11C2×#41611yescharacteristic
256C2×C11C2×#41911yescharacteristic
257C2×C11#324814yes—
258C24C2×C22⋊D1111yescharacteristic
259C2×Q8—24no—
260C2×Q8—22no—
261C2×Q8—24no—
262C2×Q8—24no—
263C2×Q8—44no—
264C2×Q8C22×Dic1114yes—
265C22×C4—24no—
266C22×C4—24no—
267C22×C4—22no—
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—22no—
271C22×C4—224no—
272C22×C4C22⋊Dic1114yes—
273C22×C4C22⋊Dic1114yes—
274C22×C4C22×Dic1112yes—
275C22×C4C2×C22⋊D1111yescharacteristic
276C22×C4C2×C22⋊D1111yescharacteristic
277C22×C4C2×C22⋊D1111yescharacteristic
278C22×C4C2×C22⋊D1111yescharacteristic
279C22×C4C2×C22⋊D1112yes—
280C22×C4C2×C22⋊D1111yescharacteristic
281C22×C4C23×D1111yescharacteristic
282C2×C8—228no—
283C2×C8—224no—
284C2×C8—448no—
285C4⋊C4—24no—
286C4⋊C4—24no—
287C4⋊C4—24no—
288C4⋊C4—28no—
289C4⋊C4—28no—
290C4⋊C4—22no—
291C4⋊C4—224no—
292C4⋊C4—224no—
293C4⋊C4C22×Dic1114yes—
294C22⋊C4—28no—
295C22⋊C4—444no—
296C42—28no—
297C42—444no—
298C42C22⋊Dic1114yes—
299C42C22⋊Dic1114yes—
300C42C22×Dic1112yes—
301C42C22×Dic1112yes—
302C42C2×C22⋊D1112yes—
303C42C2×C22⋊D1112yes—
304C11#2188911yescharacteristic, complemented, Sylow
305C23—22no—
306C23—22no—
307C23#6699514yes—
308C23C2×C22⋊Dic1112yes—
309C23C22×C22⋊D1111yescharacteristic
310Q8—28no—
311Q8—42no—
312Q8—48no—
313Q8—42no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—28no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—28no—
321C2×C4—24no—
322C2×C4—22no—
323C2×C4—24no—
324C2×C4—24no—
325C2×C4—44no—
326C2×C4—44no—
327C2×C4—444no—
328C2×C4—444no—
329C2×C4—444no—
330C2×C4#6700314yes—
331C2×C4C2×C22⋊Dic1112yes—
332C2×C4C2×C22⋊Dic1112yes—
333C2×C4C2×C22⋊Dic1112yes—
334C2×C4C2×C22⋊Dic1112yes—
335C2×C4C2×C22⋊Dic1112yes—
336C2×C4#6704212yes—
337C2×C4#6704312yes—
338C2×C4C23×Dic1111yescharacteristic
339C2×C4C22×C22⋊D1111yescharacteristic
340C8—444no—
341C22—22no—
342C22—22no—
343C22—28no—
344C22#1062283814yes—
345C22C2×#6699512yes—
346C22C2×#6700312yes—
347C22#1062336412yes—
348C22C22×C22⋊Dic1111yescharacteristic
349C4—22no—
350C4—22no—
351C4—22no—
352C4—22no—
353C4—44no—
354C4—44no—
355C4—884no—
356C4#1062284614yes—
357C4#1062335611yescharacteristic
358C4#1062335812yes—
359C4#1062336111yescharacteristic
360C2—24no—
361C2#1307120811yescharacteristic
362C2C2×#1062284611yescharacteristic
363C2C2×#1062283811yescharacteristic
364C2#1307994714yes—
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#533C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenterC2×#533D11
hypocenterC11#21889
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
3. #13069569C2semidirect
4. #13069540C2semidirect
6. #13068631C2semidirect
9. C11×#533C4semidirect
168. #533Dic11semidirect
304. C11#21889semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊(C11⋊C8)2
#130710142
#130695692
#130695402
#130690402
#130686312
C2×C11×#5332
#2188911