Finite Group Databasebeta

← #14751735

Subgroups — #14751735

Order 2816.

1110 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622732C211yesmaximal, characteristic
2C2×#10622714C211yesmaximal, characteristic
3C22×#66879C211yesmaximal, characteristic
4#13071098C211yesmaximal, characteristic
5#13068490C214yesmaximal, complemented
6#13068484C214yesmaximal, complemented
7#13068313C211yesmaximal, characteristic
8#13068309C211yesmaximal, characteristic
9C2×C11×#405C211yesmaximal, characteristic
10C22×C11×M16C2211yescharacteristic
11C23×C8×C11C2211yescharacteristic
12C2×C11×#117C2211yescharacteristic
13C2×#66979C2211yescharacteristic
14C22×C4×Dic11C2211yescharacteristic
15C22×#4318C2211yescharacteristic
16C23×C11⋊C8C2211yescharacteristic
17C11×#405—24no—
18C2×C11×#97C2212yes—
19C2×C4×C8×C11C2212yes—
20#10622732C418yescomplemented
21#10622714C418yescomplemented
22C2×#66879—24no—
23C2×#66879C2212yes—
24C2×#66879C2212yes—
25C2×#66879C2212yes—
26C2×Dic11⋊C8C2214yes—
27C2×C8×Dic11C2212yes—
28#10622586C414yes—
29#10622559C414yes—
30C4×Dic11⋊C4C2214yes—
31#10622188C2214yes—
32#10622162C2214yes—
33C23×C4×C11C2311yescharacteristic
34C23×Dic11C2×C412yes—
35C2×C11×M16—22no—
36C2×C11×M16—22no—
37C2×C11×M16C2×C414yes—
38C22×C8×C11C2×C414yes—
39C22×C8×C11D414yes—
40C22×C8×C11Q814yes—
41C22×C8×C11C2312yes—
42C22×C8×C11C2311yescharacteristic
43C22×C8×C11C2311yescharacteristic
44C11×#117—22no—
45C11×#117—22no—
46C2×C11×C4⋊C4C2×C412yes—
47C2×C11×C22⋊C4C2×C412yes—
48C2×C42×C11C2312yes—
49C2×C22⋊Dic11C2×C412yes—
50#66979C2×C414yes—
51#66979C2×C414yes—
52C2×C4⋊Dic11C2×C412yes—
53C2×Dic11⋊C4C2×C418yes—
54C2×C4×Dic11—22no—
55C2×C4×Dic11—22no—
56C2×C4×Dic11C2×C412yes—
57C2×C4×Dic11C2312yes—
58C2×C4×Dic11C2312yes—
59C2×#4318—22no—
60C2×#4318—22no—
61C2×#4318C2×C414yes—
62C22×C11⋊C8—22no—
63C22×C11⋊C8—22no—
64C22×C11⋊C8C2×C414yes—
65C22×C11⋊C8C2312yes—
66C22×C11⋊C8C2312yes—
67C11×#97—24no—
68C4×C8×C11—24no—
69C11⋊#95C2×C418yes—
70#66879—24no—
71#66879—24no—
72#66879C2×C418yescomplemented
73Dic11⋊C8C2×C4116yescomplemented
74C8×Dic11C2×C418yescomplemented
75#20436—111nomaximal, Sylow
76C24×C11C22×C411yescharacteristic
77C22×C4×C11C22×C414yes—
78C22×C4×C11C22×C411yescharacteristic
79C22×C4×C11C22×C412yes—
80C22×C4×C11C22×C412yes—
81C22×C4×C11C2×D412yes—
82C22×C4×C11C2×Q812yes—
83C22×C4×C11#4112yes—
84C22×C4×C11#4112yes—
85C22×C4×C11C2411yescharacteristic
86C22×Dic11—24no—
87C22×Dic11—44no—
88C22×Dic11C22×C414yes—
89C22×Dic11C22×C414yes—
90C11×M16—28no—
91C2×C8×C11—22no—
92C2×C8×C11—22no—
93C2×C8×C11C4⋊C4116yescomplemented
94C2×C8×C11C22×C414yes—
95C2×C8×C11C22×C412yes—
96C2×C8×C11C22×C412yes—
97C2×C8×C11C2×D412yes—
98C2×C8×C11C2×D412yes—
99C2×C8×C11C2×Q812yes—
100C2×C8×C11C2×Q812yes—
101C11×C4⋊C4—24no—
102C11×C22⋊C4—24no—
103C42×C11—22no—
104C42×C11—22no—
105C22⋊Dic11C4218yes—
106C4⋊Dic11C4218yes—
107Dic11⋊C4—48no—
108C4×Dic11—24no—
109C4×Dic11—22no—
110C4×Dic11—22no—
111C4×Dic11C22×C414yes—
112C4×Dic11C22×C414yes—
113#4318—28no—
114C2×C11⋊C8—28no—
115C2×C11⋊C8—22no—
116C2×C11⋊C8—22no—
117C2×C11⋊C8—22no—
118C2×C11⋊C8—22no—
119C2×C11⋊C8C22×C414yes—
120C2×C11⋊C8C22×C414yes—
121C2×#424—111no—
122C2×#405—111no—
123C2×#405D1111yescharacteristic
124C22×#97—111no—
125#2296—111no—
126#1771—114no—
127#1770—114no—
128#1729—111no—
129#1728—111no—
130C23×C11—24no—
131C23×C11C2×C4212yes—
132C23×C11C4×D412yes—
133C23×C11C4×Q812yes—
134C23×C11C23×C411yescharacteristic
135C2×C4×C11—24no—
136C2×C4×C11—28no—
137C2×C4×C11C2×C4212yes—
138C2×C4×C11C2×C4⋊C414yes—
139C2×C4×C11#11714yes—
140C2×C4×C11C4×D414yes—
141C2×C4×C11C4×D412yes—
142C2×C4×C11C4×Q814yes—
143C2×C4×C11C4×Q812yes—
144C2×C4×C11C23×C411yescharacteristic
145C2×C4×C11C23×C411yescharacteristic
146C2×C4×C11C22×D411yescharacteristic
147C2×C4×C11C22×Q811yescharacteristic
148C2×C4×C11C2×#4111yescharacteristic
149C2×C4×C11C2×#4111yescharacteristic
150C2×Dic11—28no—
151C2×Dic11—24no—
152C2×Dic11—24no—
153C2×Dic11—24no—
154C2×Dic11—48no—
155C2×Dic11C2×C4218yes—
156C8×C11—24no—
157C8×C11C2×C4⋊C414yes—
158C8×C11C2×C4⋊C414yes—
159C11⋊C8—24no—
160C11⋊C8—24no—
161C22×M16—111no—
162C22×M16C2×D1111yescharacteristic
163C23×C8—111no—
164C23×C8C2×D1111yescharacteristic
165C2×#117—111no—
166C2×#117C2×D1111yescharacteristic
167C22×C42—111no—
168#424—118no—
169C2×C4⋊C8—114no—
170#405—24no—
171#405—118no—
172C2×#97—112no—
173C2×#97—112no—
174C2×#97—112no—
175C2×#97—224no—
176C2×#97C2×D1112yes—
177C2×C4×C8—112no—
178C2×C4×C8C2×D1112yes—
179#389—114no—
180#385—114no—
181C4×C4⋊C4—114no—
182#336—114no—
183#336—114no—
184C22×C11—24no—
185C22×C11—24no—
186C22×C11—24no—
187C22×C11C4×C4⋊C414yes—
188C22×C11C22×C4211yescharacteristic
189C22×C11C2×C4×D411yescharacteristic
190C22×C11C2×C4×Q811yescharacteristic
191C22×C11#56814yes—
192C4×C11—44no—
193C4×C11C4×C4⋊C414yes—
194C4×C11C22×C4⋊C411yescharacteristic
195C4×C11C2×#11711yescharacteristic
196C4×C11C2×C4×D411yescharacteristic
197C4×C11C2×C4×Q811yescharacteristic
198Dic11—28no—
199Dic11—44no—
200C23×C4—112no—
201C23×C4C22×D1111yescharacteristic
202C2×M16—22no—
203C2×M16—22no—
204C2×M16—114no—
205C2×M16—222no—
206C2×M16—222no—
207C2×M16C4×D1114yes—
208C22×C8—114no—
209C22×C8—112no—
210C22×C8—112no—
211C22×C8—222no—
212C22×C8—222no—
213C22×C8Dic2214yes—
214C22×C8C4×D1114yes—
215C22×C8C22⋊D1114yes—
216C22×C8C22×D1112yes—
217C22×C8C22×D1111yescharacteristic
218C22×C8C22×D1111yescharacteristic
219#117—22no—
220#117—22no—
221#117—114no—
222#117—114no—
223C2×C4⋊C4—112no—
224C2×C4⋊C4—118no—
225C2×C4⋊C4C4×D1112yes—
226C2×C22⋊C4—112no—
227C2×C22⋊C4C4×D1112yes—
228C2×C42—112no—
229C2×C42—112no—
230C2×C42—112no—
231C2×C42—222no—
232C2×C42—222no—
233C2×C42C22×D1112yes—
234C4⋊C8—1116no—
235#97—24no—
236#97—118no—
237#97—224no—
238#97—224no—
239C4×C8—24no—
240C4×C8—118no—
241#95—118no—
242C2×C11—24no—
243C2×C11C2×C4×C4⋊C411yescharacteristic
244C2×C11#287512yes—
245C2×C11#293012yes—
246C2×C11#296112yes—
247C24C2×C4×D1111yescharacteristic
248C22×C4—114no—
249C22×C4—114no—
250C22×C4—224no—
251C22×C4—444no—
252C22×C4C2×Dic2212yes—
253C22×C4C2×C4×D1114yes—
254C22×C4C2×C4×D1111yescharacteristic
255C22×C4C2×C4×D1112yes—
256C22×C4C2×C4×D1112yes—
257C22×C4#433912yes—
258C22×C4#433912yes—
259C22×C4C2×C22⋊D1112yes—
260C22×C4C23×D1111yescharacteristic
261M16—28no—
262M16—228no—
263C2×C8—22no—
264C2×C8—22no—
265C2×C8—114no—
266C2×C8—114no—
267C2×C8—228no—
268C2×C8—222no—
269C2×C8—222no—
270C2×C8—222no—
271C2×C8—222no—
272C2×C8Dic11⋊C4116yescomplemented
273C2×C8C2×Dic2212yes—
274C2×C8C2×Dic2212yes—
275C2×C8C2×C4×D1114yes—
276C2×C8C2×C4×D1112yes—
277C2×C8C2×C4×D1112yes—
278C2×C8C2×C22⋊D1112yes—
279C2×C8C2×C22⋊D1112yes—
280C4⋊C4—24no—
281C4⋊C4—118no—
282C4⋊C4—448no—
283C22⋊C4—24no—
284C22⋊C4—118no—
285C42—22no—
286C42—22no—
287C42—114no—
288C42—114no—
289C42—224no—
290C42—222no—
291C42—222no—
292C11#2043611yescharacteristic, complemented, Sylow
293C23—24no—
294C23C4×Dic2212yes—
295C23C42×D1112yes—
296C23C4×C22⋊D1112yes—
297C23C22×C4×D1111yescharacteristic
298C2×C4—28no—
299C2×C4—24no—
300C2×C4—118no—
301C2×C4—228no—
302C2×C4—224no—
303C2×C4—224no—
304C2×C4—224no—
305C2×C4—448no—
306C2×C4C4×Dic2214yes—
307C2×C4C4×Dic2212yes—
308C2×C4C42×D1112yes—
309C2×C4#6692514yes—
310C2×C4C2×Dic11⋊C414yes—
311C2×C4C4×C22⋊D1112yes—
312C2×C4C4×C22⋊D1114yes—
313C2×C4C22×Dic2211yescharacteristic
314C2×C4C22×C4×D1111yescharacteristic
315C2×C4C22×C4×D1111yescharacteristic
316C2×C4C2×#433911yescharacteristic
317C2×C4C2×#433911yescharacteristic
318C2×C4C22×C22⋊D1111yescharacteristic
319C8—24no—
320C8—224no—
321C8—224no—
322C8C2×Dic11⋊C414yes—
323C8C2×Dic11⋊C414yes—
324C22—24no—
325C22—24no—
326C22—24no—
327C22C4×Dic11⋊C414yes—
328C22C2×C4×Dic2211yescharacteristic
329C22C2×C42×D1111yescharacteristic
330C22#1062328114yes—
331C22C2×C4×C22⋊D1111yescharacteristic
332C4—44no—
333C4—228no—
334C4—444no—
335C4C4×Dic11⋊C414yes—
336C4C2×C4×Dic2211yescharacteristic
337C4C2×#6692511yescharacteristic
338C4C22×Dic11⋊C411yescharacteristic
339C4C2×C4×C22⋊D1111yescharacteristic
340C2—24no—
341C2C2×C4×Dic11⋊C411yescharacteristic
342C2#1307704312yes—
343C2#1307731712yes—
344C2#1307755412yes—
subgroupG/H
center, FrattiniC22×C4C23×D11
commutatorC22×C11C22×C42
FittingC2×C11×#405C2
socleC23×C11C23×C4
prime radicalC24×C11C22×C4
cosocleC22×C4×C11C24
hypercenterC2×#405D11
hypocenterC11#20436
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×#405

Complements

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

NH ≅ G/Ntype
5. #13068490C2semidirect
6. #13068484C2semidirect
20. #10622732C4semidirect
21. #10622714C4semidirect
72. #66879C2×C4semidirect
73. Dic11⋊C8C2×C4semidirect
74. C8×Dic11C2×C4semidirect
93. C2×C8×C11C4⋊C4semidirect
272. C2×C8Dic11⋊C4semidirect
292. C11#20436semidirect

Maximal subgroups

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

subgroupindex
C2×#106227322
C2×#106227142
C22×#668792
#130710982
#130684902
#130684842
#130683132
#130683092
C2×C11×#4052
#2043611