Finite Group Databasebeta

← #14763531

Subgroups — #14763531

Order 2816.

1086 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623001C211yesmaximal, characteristic
2#13071023C211yesmaximal, characteristic
3#13069589C212yesmaximal, complemented
4#13069436C212yesmaximal, complemented
5#13068926C214yesmaximal
6#13068622C214yesmaximal, complemented
7C2×C11×#432C211yesmaximal, characteristic
8C22×C42×C11C2211yescharacteristic
9C2×#66979—21no—
10C2×#66979C2212yes—
11C2×#66977—21no—
12C2×#66977C2212yes—
13#10623001—24no—
14#10623001C418yescomplemented
15C2×#66923—21no—
16C2×#66922C2211yescharacteristic
17C2×#66922C2211yescharacteristic
18C2×C4×Dic22—21no—
19C2×C4×Dic22C2212yes—
20C11×#432—24no—
21C2×C11×C4⋊C8C2212yes—
22C2×C11×C22⋊C8C2212yes—
23C2×C11×#97C2212yes—
24#10622825—21no—
25#10622825—21no—
26C2×#66880C2218yes—
27#10622549C2212yes—
28#10622548C2212yes—
29C4×C4⋊Dic11—21no—
30C4×C4⋊Dic11—21no—
31#10622189C2218yes—
32C23×C4×C11D411yescharacteristic
33C23×C4×C11D411yescharacteristic
34C23×C4×C11C2311yescharacteristic
35C22×Dic22—21no—
36C22×Dic22C2312yes—
37C22×C8×C11C2314yes—
38C2×C42×C11C2×C414yes—
39C2×C42×C11D411yescharacteristic
40C2×C42×C11D411yescharacteristic
41C2×C42×C11D414yes—
42C2×C42×C11C2311yescharacteristic
43C2×C42×C11C2311yescharacteristic
44C2×C22⋊Dic11—22no—
45C2×C22⋊Dic11—22no—
46#66979—28no—
47#66979—44no—
48C2×C4⋊Dic11—21no—
49C2×C4⋊Dic11—21no—
50C2×C4⋊Dic11—21no—
51C2×C4⋊Dic11—22no—
52C2×C4⋊Dic11—22no—
53C2×C4⋊Dic11C2314yes—
54C2×C4⋊Dic11C2312yes—
55#66977—28no—
56#66977—24no—
57#66977C2×C418yes—
58C2×Dic11⋊C4—22no—
59C2×Dic11⋊C4—22no—
60C2×C4×Dic11—22no—
61C2×C4×Dic11—22no—
62#66923—28no—
63#66922—22no—
64#66922—22no—
65#66922C2×C414yes—
66#66922C2×C414yes—
67C4×Dic22—28no—
68C4×Dic22—24no—
69C4×Dic22C2×C418yes—
70C11×C4⋊C8—24no—
71C11×C22⋊C8—24no—
72C11×#97—24no—
73C11⋊#95—22no—
74C11⋊#95—22no—
75#66880—48no—
76#21870—111nomaximal, Sylow
77C24×C11C2×D411yescharacteristic
78C22×C4×C11—24no—
79C22×C4×C11—22no—
80C22×C4×C11—22no—
81C22×C4×C11—42no—
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—24no—
103C2×C8×C11—24no—
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—28no—
117C4⋊Dic11—44no—
118C4⋊Dic11—44no—
119C4⋊Dic11C22×C414yes—
120Dic11⋊C4—28no—
121Dic11⋊C4—28no—
122C4×Dic11—28no—
123C4×Dic11—44no—
124C2×#533—111no—
125C2×#432D1111yescharacteristic
126#2285—111no—
127#1993—112no—
128#1960—112no—
129#1873—114no—
130#1803—114no—
131C23×C11—21no—
132C23×C11—21no—
133C23×C11—22no—
134C23×C11—22no—
135C23×C11C2×C22⋊C412yes—
136C23×C11C22×D411yescharacteristic
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—22no—
140C2×C4×C11—22no—
141C2×C4×C11—22no—
142C2×C4×C11—24no—
143C2×C4×C11—24no—
144C2×C4×C11—28no—
145C2×C4×C11—44no—
146C2×C4×C11C2×C22⋊C412yes—
147C2×C4×C11C2×C22⋊C412yes—
148C2×C4×C11C2×C22⋊C412yes—
149C2×C4×C11C2×C22⋊C412yes—
150C2×C4×C11C2×C22⋊C412yes—
151C2×C4×C11#13714yes—
152C2×C4×C11C23×C411yescharacteristic
153C2×C4×C11C22×D411yescharacteristic
154C2×C4×C11H(5,𝔽2)12yes—
155C2×C4×C112−1+412yes—
156C2×Dic11—24no—
157C2×Dic11—24no—
158C2×Dic11—42no—
159C2×Dic11—42no—
160C2×Dic11—44no—
161C2×Dic11—44no—
162C2×Dic11—44no—
163C2×Dic11—44no—
164Dic22—28no—
165Dic22—48no—
166Dic22—44no—
167C8×C11—44no—
168#533—118no—
169#533—224no—
170C2×C4⋊Q8—111no—
171C2×C4⋊Q8—111no—
172C2×#125—221no—
173C2×C22⋊Q8—112no—
174C2×C22⋊Q8—221no—
175C2×C4×Q8—112no—
176C2×C4×Q8—221no—
177C2×#117—112no—
178C2×#117—221no—
179C22×C42C2×D1111yescharacteristic
180#432—24no—
181C2×C4⋊C8C2×D1112yes—
182C2×#103—118no—
183C2×C22⋊C8C2×D1112yes—
184C2×#97C2×D1112yes—
185#384—112no—
186#382—112no—
187#380—221no—
188#380—221no—
189C4×C4⋊C4—221no—
190C4×C4⋊C4—221no—
191#340—118no—
192C22×C11—22no—
193C22×C11—22no—
194C22×C11—22no—
195C22×C11—42no—
196C22×C11—42no—
197C22×C11C22×C22⋊C411yescharacteristic
198C22×C11#53511yescharacteristic
199C22×C11#53611yescharacteristic
200C22×C11C2×#13712yes—
201C22×C11#57512yes—
202C4×C11—22no—
203C4×C11—22no—
204C4×C11—22no—
205C4×C11—22no—
206C4×C11#41914yes—
207C4×C11#52012yes—
208C4×C11#53712yes—
209Dic11—44no—
210Dic11—44no—
211Dic11—84no—
212C22×Q8—112no—
213C22×Q8—221no—
214C23×C4D4411yescharacteristic
215C23×C4D4411yescharacteristic
216C23×C4C22×D1111yescharacteristic
217C22×C8C22×D1114yes—
218C4⋊Q8—114no—
219C4⋊Q8—114no—
220C4⋊Q8—222no—
221C4⋊Q8—222no—
222#125—228no—
223C22⋊Q8—118no—
224C22⋊Q8—228no—
225C22⋊Q8—224no—
226C4×Q8—118no—
227C4×Q8—228no—
228C4×Q8—224no—
229#117—228no—
230#117—444no—
231C2×C4⋊C4—112no—
232C2×C4⋊C4—114no—
233C2×C4⋊C4—221no—
234C2×C4⋊C4—221no—
235C2×C4⋊C4—222no—
236C2×C4⋊C4—222no—
237C2×C4⋊C4—221no—
238C2×C4⋊C4—222no—
239C2×C4⋊C4—222no—
240C2×C22⋊C4—222no—
241C2×C22⋊C4—222no—
242C2×C42—222no—
243C2×C42—222no—
244C2×C42C4×D1114yes—
245C2×C42D4411yescharacteristic
246C2×C42D4411yescharacteristic
247C2×C42C22⋊D1114yes—
248C2×C42C22×D1111yescharacteristic
249C2×C42C22×D1111yescharacteristic
250C4⋊C8—24no—
251#103—448no—
252C22⋊C8—24no—
253#97—24no—
254#95—222no—
255#95—222no—
256C2×C11—42no—
257C2×C11#231111yescharacteristic
258C2×C11C2×#41911yescharacteristic
259C2×C11#289611yescharacteristic
260C2×C11#321612yes—
261C2×C11#323712yes—
262C24C2×D4411yescharacteristic
263C2×Q8—114no—
264C2×Q8—224no—
265C2×Q8—222no—
266C2×Q8—224no—
267C2×Q8—224no—
268C2×Q8—444no—
269C22×C4—24no—
270C22×C4—22no—
271C22×C4—22no—
272C22×C4—42no—
273C22×C4—222no—
274C22×C4—222no—
275C22×C4—224no—
276C22×C4(C2×D11)⋊C414yes—
277C22×C4(C2×D11)⋊C414yes—
278C22×C4C2×C4×D1112yes—
279C22×C4C2×D4411yescharacteristic
280C22×C4C2×D4411yescharacteristic
281C22×C4C2×D4411yescharacteristic
282C22×C4C2×D4411yescharacteristic
283C22×C4C2×D4411yescharacteristic
284C22×C4C2×C22⋊D1112yes—
285C22×C4C23×D1111yescharacteristic
286C2×C8—24no—
287C2×C8—24no—
288C2×C8—24no—
289C4⋊C4—114no—
290C4⋊C4—224no—
291C4⋊C4—224no—
292C4⋊C4—228no—
293C4⋊C4—228no—
294C4⋊C4—224no—
295C4⋊C4—222no—
296C4⋊C4—228no—
297C4⋊C4—444no—
298C4⋊C4—444no—
299C22⋊C4—228no—
300C22⋊C4—444no—
301C42—228no—
302C42—444no—
303C42(C2×D11)⋊C414yes—
304C42(C2×D11)⋊C414yes—
305C42C2×C4×D1112yes—
306C42C2×C4×D1112yes—
307C42C2×C22⋊D1112yes—
308C42C2×C22⋊D1112yes—
309C11#2187011yescharacteristic, complemented, Sylow
310C23—22no—
311C23—22no—
312C23—21no—
313C23—21no—
314C23C2×(C2×D11)⋊C412yes—
315C23C22×D4411yescharacteristic
316Q8—228no—
317Q8—448no—
318Q8—444no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—28no—
325C2×C4—24no—
326C2×C4—24no—
327C2×C4—44no—
328C2×C4—224no—
329C2×C4—224no—
330C2×C4—444no—
331C2×C4—442no—
332C2×C4—442no—
333C2×C4—444no—
334C2×C4—444no—
335C2×C4—444no—
336C2×C4#6696214yes—
337C2×C4C2×(C2×D11)⋊C412yes—
338C2×C4C2×(C2×D11)⋊C412yes—
339C2×C4C2×(C2×D11)⋊C412yes—
340C2×C4C2×(C2×D11)⋊C412yes—
341C2×C4C2×(C2×D11)⋊C412yes—
342C2×C4C22×C4×D1111yescharacteristic
343C2×C4#6704212yes—
344C2×C4#6704312yes—
345C2×C4C22×C22⋊D1111yescharacteristic
346C8—44no—
347C22—22no—
348C22—22no—
349C22—22no—
350C22—42no—
351C22—42no—
352C22#1062305611yescharacteristic
353C22#1062305711yescharacteristic
354C22C2×#6696212yes—
355C22#1062327912yes—
356C22C22×(C2×D11)⋊C411yescharacteristic
357C4—22no—
358C4—22no—
359C4—22no—
360C4—22no—
361C4—444no—
362C4—444no—
363C4—884no—
364C4#1062273314yes—
365C4#1062305412yes—
366C4#1062336412yes—
367C2—42no—
368C2#1307120411yescharacteristic
369C2C2×#1062273311yescharacteristic
370C2#1307713611yescharacteristic
371C2#1307962912yes—
372C2#1307983212yes—
subgroupG/H
centerC23C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#432C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenterC2×#432D11
hypocenterC11#21870
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#432

Complements

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

NH ≅ G/Ntype
3. #13069589C2semidirect
4. #13069436C2semidirect
6. #13068622C2semidirect
14. #10623001C4semidirect
309. C11#21870semidirect

Maximal subgroups

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

subgroupindex
C2×#106230012
#130710232
#130695892
#130694362
#130689262
#130686222
C2×C11×#4322
#2187011