Finite Group Databasebeta

← #14763693

Subgroups — #14763693

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
1C2×#10623001C211yesmaximal, characteristic
2#13071014C211yesmaximal, characteristic
3#13069567C212yesmaximal, complemented
4#13069538C212yesmaximal, complemented
5#13069039C214yesmaximal
6#13068632C214yesmaximal, complemented
7C22×C11×C4⋊C8C211yesmaximal, characteristic
8C23×C8×C11C2212yes—
9C22×C42×C11C2211yescharacteristic
10C2×#66979—21no—
11C2×#66977—21no—
12C2×#66977C2212yes—
13#10623001—24no—
14#10623001C418yescomplemented
15C2×#66923—21no—
16C2×#66922C2211yescharacteristic
17C2×#66922C2211yescharacteristic
18C2×C4×Dic22—21no—
19C2×C4×Dic22C2212yes—
20C2×C11×C4⋊C8—24no—
21C2×C11×C4⋊C8C2212yes—
22C2×C11×C4⋊C8C2212yes—
23#10622825C2212yes—
24#10622824—21no—
25C4×C22⋊Dic11—21no—
26C2×#66880C2218yes—
27#10622550—21no—
28#10622549C2212yes—
29C4×C4⋊Dic11C2212yes—
30#10622545—21no—
31#10622189C2218yes—
32C23×C4×C11D411yescharacteristic
33C23×C4×C11D411yescharacteristic
34C23×C4×C11C2311yescharacteristic
35C22×Dic22—21no—
36C22×Dic22C2312yes—
37C22×C8×C11—24no—
38C22×C8×C11—44no—
39C22×C8×C11C2314yes—
40C2×C42×C11C2×C414yes—
41C2×C42×C11D411yescharacteristic
42C2×C42×C11D411yescharacteristic
43C2×C42×C11D414yes—
44C2×C42×C11C2311yescharacteristic
45C2×C42×C11C2311yescharacteristic
46C2×C22⋊Dic11—22no—
47C2×C22⋊Dic11—22no—
48#66979—28no—
49C2×C4⋊Dic11—21no—
50C2×C4⋊Dic11—21no—
51C2×C4⋊Dic11—21no—
52C2×C4⋊Dic11C2314yes—
53C2×C4⋊Dic11C2312yes—
54#66977—28no—
55#66977—24no—
56#66977C2×C418yes—
57C2×Dic11⋊C4—22no—
58C2×Dic11⋊C4—22no—
59C2×C4×Dic11—22no—
60C2×C4×Dic11—22no—
61#66923—28no—
62#66922—22no—
63#66922—22no—
64#66922C2×C414yes—
65#66922C2×C414yes—
66C4×Dic22—28no—
67C4×Dic22—24no—
68C4×Dic22C2×C418yes—
69C11×C4⋊C8—24no—
70C11×C4⋊C8—24no—
71C11⋊#95—22no—
72C11⋊#95—22no—
73C11⋊#95—22no—
74C11⋊#95—22no—
75#66880—48no—
76#21889—111nomaximal, Sylow
77C24×C11C2×D411yescharacteristic
78C22×C4×C11—24no—
79C22×C4×C11—24no—
80C22×C4×C11—22no—
81C22×C4×C11—22no—
82C22×C4×C11C22⋊C414yes—
83C22×C4×C11C22⋊C414yes—
84C22×C4×C11C22×C412yes—
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11C2×D412yes—
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11C2411yescharacteristic
92C22×Dic11—22no—
93C22×Dic11—22no—
94C22×Dic11—24no—
95C2×Dic22—24no—
96C2×Dic22—22no—
97C2×Dic22—24no—
98C2×Dic22—24no—
99C2×Dic22—44no—
100C2×Dic22C22×C414yes—
101C2×C8×C11—24no—
102C2×C8×C11—28no—
103C2×C8×C11—48no—
104C42×C11C22⋊C414yes—
105C42×C11C22⋊C414yes—
106C42×C11C22×C412yes—
107C42×C11C22×C412yes—
108C42×C11C2×D412yes—
109C42×C11C2×D412yes—
110C22⋊Dic11—28no—
111C22⋊Dic11—44no—
112C4⋊Dic11—24no—
113C4⋊Dic11—24no—
114C4⋊Dic11—24no—
115C4⋊Dic11—22no—
116C4⋊Dic11—24no—
117C4⋊Dic11—24no—
118C4⋊Dic11C22×C414yes—
119Dic11⋊C4—28no—
120Dic11⋊C4—28no—
121C4×Dic11—28no—
122C4×Dic11—44no—
123C2×#533—111no—
124C22×C4⋊C8D1111yescharacteristic
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
135C2×C4×C11—22no—
136C2×C4×C11—22no—
137C2×C4×C11—22no—
138C2×C4×C11—22no—
139C2×C4×C11—28no—
140C2×C4×C11—24no—
141C2×C4×C11—22no—
142C2×C4×C11—22no—
143C2×C4×C11—28no—
144C2×C4×C11C2×C22⋊C412yes—
145C2×C4×C11C2×C22⋊C412yes—
146C2×C4×C11C2×C22⋊C412yes—
147C2×C4×C11C2×C22⋊C412yes—
148C2×C4×C11C2×C22⋊C412yes—
149C2×C4×C11#13514yes—
150C2×C4×C11C23×C411yescharacteristic
151C2×C4×C11C22×D411yescharacteristic
152C2×C4×C11H(5,𝔽2)12yes—
153C2×C4×C112−1+412yes—
154C2×Dic11—24no—
155C2×Dic11—24no—
156C2×Dic11—44no—
157C2×Dic11—44no—
158C2×Dic11—44no—
159C2×Dic11—44no—
160C2×Dic11—44no—
161Dic22—28no—
162Dic22—42no—
163Dic22—42no—
164Dic22—48no—
165C8×C11—44no—
166C23×C8C2×D1112yes—
167#533—118no—
168#533—224no—
169C2×C4⋊Q8—111no—
170C2×C4⋊Q8—111no—
171C2×#125—221no—
172C2×C22⋊Q8—112no—
173C2×C22⋊Q8—221no—
174C2×C4×Q8—112no—
175C2×C4×Q8—221no—
176C2×#117—221no—
177C22×C42C2×D1111yescharacteristic
178C2×C4⋊C8—24no—
179C2×C4⋊C8C2×D1112yes—
180C2×C4⋊C8C2×D1112yes—
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#41614yes—
203C4×C11#52012yes—
204C4×C11#53511yescharacteristic
205C4×C11#53611yescharacteristic
206Dic11—44no—
207Dic11—44no—
208Dic11—84no—
209C22×Q8—112no—
210C22×Q8—221no—
211C23×C4D4411yescharacteristic
212C23×C4D4411yescharacteristic
213C23×C4C22×D1111yescharacteristic
214C22×C8—24no—
215C22×C8—44no—
216C22×C8C22×D1114yes—
217C4⋊Q8—114no—
218C4⋊Q8—114no—
219C4⋊Q8—222no—
220C4⋊Q8—222no—
221#125—228no—
222C22⋊Q8—118no—
223C22⋊Q8—228no—
224C22⋊Q8—224no—
225C4×Q8—118no—
226C4×Q8—228no—
227C4×Q8—224no—
228#117—228no—
229C2×C4⋊C4—112no—
230C2×C4⋊C4—114no—
231C2×C4⋊C4—221no—
232C2×C4⋊C4—221no—
233C2×C4⋊C4—222no—
234C2×C4⋊C4—222no—
235C2×C4⋊C4—221no—
236C2×C22⋊C4—222no—
237C2×C22⋊C4—222no—
238C2×C42—222no—
239C2×C42—222no—
240C2×C42C4×D1114yes—
241C2×C42D4411yescharacteristic
242C2×C42D4411yescharacteristic
243C2×C42C22⋊D1114yes—
244C2×C42C22×D1111yescharacteristic
245C2×C42C22×D1111yescharacteristic
246C4⋊C8—24no—
247C4⋊C8—24no—
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×D4411yescharacteristic
259C2×Q8—114no—
260C2×Q8—224no—
261C2×Q8—222no—
262C2×Q8—224no—
263C2×Q8—224no—
264C2×Q8—444no—
265C22×C4—24no—
266C22×C4—24no—
267C22×C4—22no—
268C22×C4—22no—
269C22×C4—222no—
270C22×C4—222no—
271C22×C4—224no—
272C22×C4(C2×D11)⋊C414yes—
273C22×C4(C2×D11)⋊C414yes—
274C22×C4C2×C4×D1112yes—
275C22×C4C2×D4411yescharacteristic
276C22×C4C2×D4411yescharacteristic
277C22×C4C2×D4411yescharacteristic
278C22×C4C2×D4411yescharacteristic
279C22×C4C2×D4411yescharacteristic
280C22×C4C2×C22⋊D1112yes—
281C22×C4C23×D1111yescharacteristic
282C2×C8—28no—
283C2×C8—24no—
284C2×C8—48no—
285C4⋊C4—114no—
286C4⋊C4—224no—
287C4⋊C4—224no—
288C4⋊C4—228no—
289C4⋊C4—228no—
290C4⋊C4—224no—
291C4⋊C4—222no—
292C4⋊C4—224no—
293C4⋊C4—224no—
294C22⋊C4—228no—
295C22⋊C4—444no—
296C42—228no—
297C42—444no—
298C42(C2×D11)⋊C414yes—
299C42(C2×D11)⋊C414yes—
300C42C2×C4×D1112yes—
301C42C2×C4×D1112yes—
302C42C2×C22⋊D1112yes—
303C42C2×C22⋊D1112yes—
304C11#2188911yescharacteristic, complemented, Sylow
305C23—22no—
306C23—22no—
307C23#6696214yes—
308C23C2×(C2×D11)⋊C412yes—
309C23C22×D4411yescharacteristic
310Q8—228no—
311Q8—448no—
312Q8—442no—
313Q8—442no—
314C2×C4—28no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—28no—
320C2×C4—24no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—224no—
324C2×C4—224no—
325C2×C4—444no—
326C2×C4—444no—
327C2×C4—444no—
328C2×C4—444no—
329C2×C4—444no—
330C2×C4#6695714yes—
331C2×C4C2×(C2×D11)⋊C412yes—
332C2×C4C2×(C2×D11)⋊C412yes—
333C2×C4C2×(C2×D11)⋊C412yes—
334C2×C4C2×(C2×D11)⋊C412yes—
335C2×C4C2×(C2×D11)⋊C412yes—
336C2×C4C22×C4×D1111yescharacteristic
337C2×C4#6703712yes—
338C2×C4#6704012yes—
339C2×C4C22×C22⋊D1111yescharacteristic
340C8—44no—
341C22—22no—
342C22—22no—
343C22—28no—
344C22#1062273314yes—
345C22#1062304112yes—
346C22C2×#6695712yes—
347C22C2×#6696212yes—
348C22C22×(C2×D11)⋊C411yescharacteristic
349C4—22no—
350C4—22no—
351C4—22no—
352C4—22no—
353C4—444no—
354C4—444no—
355C4—884no—
356C4#1062272614yes—
357C4#1062303512yes—
358C4#1062333611yescharacteristic
359C4#1062334711yescharacteristic
360C2—24no—
361C2#1307120911yescharacteristic
362C2C2×#1062272611yescharacteristic
363C2C2×#1062273311yescharacteristic
364C2#1307995414yes—
subgroupG/H
centerC23C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC22×C11×C4⋊C8C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenterC22×C4⋊C8D11
hypocenterC11#21889
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C22×C4⋊C8

Complements

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

NH ≅ G/Ntype
3. #13069567C2semidirect
4. #13069538C2semidirect
6. #13068632C2semidirect
14. #10623001C4semidirect
304. C11#21889semidirect

Maximal subgroups

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

subgroupindex
C2×#106230012
#130710142
#130695672
#130695382
#130690392
#130686322
C22×C11×C4⋊C82
#2188911