Finite Group Databasebeta

← #14764017

Subgroups — #14764017

Order 2816.

1074 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622339C212yesmaximal
2#13070995C211yesmaximal, characteristic
3#13068800C214yesmaximal, complemented
4#13068797C214yesmaximal, complemented
5#13068600C211yesmaximal, characteristic, complemented
6#13068598C212yesmaximal, complemented
7C11×#1798C211yesmaximal, characteristic, complemented
8C23×C4×D11C2211yescharacteristic
9C2×C11×#117C2211yescharacteristic
10C2×#66979C2211yescharacteristic
11C22×#4313C2214yes—
12C2×C11×C4⋊C8C2212yescomplemented
13C2×C11×C22⋊C8C2212yes—
14C2×C22⋊(C11⋊C8)C2212yes—
15C2×(C2×D11)⋊C8C2214yes—
16C2×Dic11⋊C8C2214yescomplemented
17#10622600C414yes—
18#10622568C412yes—
19#10622556C412yes—
20C4×(C2×D11)⋊C4C2212yes—
21C4×(C2×D11)⋊C4C2212yes—
22C2×C4⋊(C11⋊C8)C2212yescomplemented
23#10622339—28no—
24C11×#336C2212yescomplemented
25#10622188C2214yescomplemented
26#10622162C2212yescomplemented
27C24×D11C2×C411yescharacteristic
28C23×C4×C11C2311yescharacteristic
29C23×Dic11C2×C411yescharacteristic
30C22×C4×D11—42no—
31C22×C4×D11—42no—
32C22×C4×D11C2×C412yes—
33C22×C4×D11D414yes—
34C22×C4×D11Q814yes—
35C22×C4×D11C2312yes—
36C22×C8×C11C2314yes—
37C11×#117—42no—
38C2×C11×C4⋊C4C2×C412yes—
39C2×C11×C22⋊C4C2×C412yes—
40C2×C42×C11C2311yescharacteristic
41C2×C42×C11C2311yescharacteristic
42C2×C22⋊Dic11C2×C412yes—
43C2×(C2×D11)⋊C4C2×C414yes—
44C2×(C2×D11)⋊C4C2×C414yes—
45#66979—42no—
46C2×C4⋊Dic11C2×C412yes—
47C2×C4×Dic11C2312yes—
48C22×C11⋊C8C2314yes—
49C2×#4313—28no—
50C2×#4313—44no—
51C2×#4313—44no—
52C11×C4⋊C8—42no—
53C11×C22⋊C8—24no—
54C11⋊#95C2×C414yes—
55C11⋊#95C2×C414yes—
56C22⋊(C11⋊C8)—24no—
57(C2×D11)⋊C8—28no—
58Dic11⋊C8—44no—
59C4⋊(C11⋊C8)—42no—
60#21935—111nomaximal, Sylow
61C24×C11C22×C411yescharacteristic
62C23×D11—41no—
63C23×D11—41no—
64C23×D11—44no—
65C23×D11C4⋊C414yes—
66C23×D11C22×C412yes—
67C22×C4×C11—22no—
68C22×C4×C11—22no—
69C22×C4×C11C22×C412yes—
70C22×C4×C11C22×C412yes—
71C22×C4×C11C22×C411yescharacteristic
72C22×C4×C11C2×D412yes—
73C22×C4×C11C2×Q812yes—
74C22×C4×C11C2411yescharacteristic
75C22×Dic11—41no—
76C22×Dic11—41no—
77C22×Dic11C4⋊C414yes—
78C22×Dic11C22×C414yes—
79C22×Dic11C22×C412yes—
80C2×C4×D11—24no—
81C2×C4×D11—24no—
82C2×C4×D11—42no—
83C2×C4×D11—42no—
84C2×C4×D11—48no—
85C2×C4×D11—48no—
86C2×C4×D11C4⋊C418yes—
87C2×C4×D11C2×D414yes—
88C2×C4×D11C2×Q814yes—
89C2×C8×C11—24no—
90C2×C8×C11—24no—
91C2×C8×C11—24no—
92C11×C4⋊C4—42no—
93C11×C22⋊C4—42no—
94C42×C11—22no—
95C42×C11—22no—
96C22⋊Dic11—42no—
97(C2×D11)⋊C4—44no—
98(C2×D11)⋊C4—44no—
99C4⋊Dic11—42no—
100C4×Dic11—24no—
101C2×C11⋊C8—24no—
102C2×C11⋊C8—24no—
103C2×C11⋊C8—24no—
104#4313—416no—
105C2×#407—112no—
106#2280—111no—
107#1851—114no—
108#1851—114no—
109#1798—112no—
110#1798—111no—
111#1798D1111yescharacteristic, complemented
112C23×C11—21no—
113C23×C11—21no—
114C23×C11—24no—
115C23×C11C2×C4⋊C412yes—
116C23×C11C23×C411yescharacteristic
117C22×D11—22no—
118C22×D11—22no—
119C22×D11—24no—
120C22×D11—24no—
121C22×D11—44no—
122C22×D11—48no—
123C22×D11—48no—
124C22×D11—48no—
125C22×D11C2×C4⋊C414yes—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—24no—
129C2×C4×C11—24no—
130C2×C4×C11—22no—
131C2×C4×C11—22no—
132C2×C4×C11—24no—
133C2×C4×C11—24no—
134C2×C4×C11C2×C4⋊C412yes—
135C2×C4×C11C22×D411yescharacteristic
136C2×C4×C11C22×Q811yescharacteristic
137C2×C4×C11H(5,𝔽2)12yes—
138C2×C4×C11H(5,𝔽2)12yes—
139C2×Dic11—22no—
140C2×Dic11—22no—
141C2×Dic11—24no—
142C2×Dic11—24no—
143C2×Dic11—24no—
144C2×Dic11—44no—
145C2×Dic11C2×C4⋊C414yes—
146C4×D11—28no—
147C4×D11—28no—
148C4×D11—48no—
149C8×C11—44no—
150C11⋊C8—44no—
151C24×C4—111no—
152C22×M16—114no—
153C2×#117—111no—
154C2×#117C2×D1111yescharacteristic
155C2×C4⋊C8—114no—
156C2×C4⋊C8—112no—
157C2×C4⋊C8C2×D1112yescomplemented
158#407—228no—
159C2×C22⋊C8—112no—
160C2×C22⋊C8—114no—
161C2×C22⋊C8C2×D1112yes—
162#381—112no—
163#380—114no—
164#379—112no—
165C4×C22⋊C4—112no—
166C4×C22⋊C4—112no—
167#336—114no—
168#336—112no—
169#336C2×D1112yescomplemented
170C22×C11—22no—
171C22×C11—24no—
172C22×C11—42no—
173C22×C11—42no—
174C22×C11C22×C4⋊C411yescharacteristic
175C22×C11#51811yescharacteristic
176C22×C11#51811yescharacteristic
177C22×C11#56814yes—
178C2×D11—24no—
179C2×D11—24no—
180C2×D11—24no—
181C2×D11—416no—
182C2×D11—44no—
183C2×D11—44no—
184C4×C11—22no—
185C4×C11—42no—
186C4×C11—42no—
187C4×C11#53412yes—
188C4×C11#54312yes—
189Dic11—24no—
190Dic11—44no—
191C25—111no—
192C23×C4—111no—
193C23×C4—112no—
194C23×C4—112no—
195C23×C4—114no—
196C23×C4—114no—
197C23×C4—442no—
198C23×C4—442no—
199C23×C4C22×D1111yescharacteristic
200C2×M16—228no—
201C2×M16—444no—
202C2×M16—444no—
203C22×C8—114no—
204C22×C8C22×D1114yes—
205#117—42no—
206#117—442no—
207C2×C4⋊C4—112no—
208C2×C4⋊C4C4×D1112yes—
209C2×C22⋊C4—112no—
210C2×C22⋊C4—114no—
211C2×C22⋊C4—114no—
212C2×C22⋊C4C4×D1112yes—
213C2×C42—112no—
214C2×C42C22×D1111yescharacteristic
215C2×C42C22×D1111yescharacteristic
216C4⋊C8—42no—
217C4⋊C8—442no—
218C4⋊C8—444no—
219C22⋊C8—24no—
220C22⋊C8—228no—
221C22⋊C8—224no—
222#95—114no—
223#95—114no—
224C2×C11—42no—
225C2×C11#231511yescharacteristic
226C2×C11#290512yes—
227C2×C11#297812yes—
228C2×C11#297812yes—
229D11—44no—
230C24—112no—
231C24—114no—
232C24—441no—
233C24—441no—
234C24—444no—
235C24C2×C4×D1111yescharacteristic
236C22×C4—22no—
237C22×C4—22no—
238C22×C4—112no—
239C22×C4—114no—
240C22×C4—114no—
241C22×C4—114no—
242C22×C4—118no—
243C22×C4—114no—
244C22×C4—224no—
245C22×C4—224no—
246C22×C4—448no—
247C22×C4—448no—
248C22×C4—442no—
249C22×C4—442no—
250C22×C4—441no—
251C22×C4—441no—
252C22×C4C2×C4×D1112yes—
253C22×C4C2×C4×D1112yes—
254C22×C4C2×C4×D1111yescharacteristic
255C22×C4D4×D1112yes—
256C22×C4Q8×D1112yes—
257C22×C4C23×D1111yescharacteristic
258M16—4416no—
259C2×C8—24no—
260C2×C8—24no—
261C2×C8—24no—
262C2×C8—224no—
263C2×C8—224no—
264C2×C8—224no—
265C4⋊C4—42no—
266C4⋊C4—442no—
267C22⋊C4—42no—
268C22⋊C4—444no—
269C22⋊C4—444no—
270C22⋊C4—442no—
271C42—22no—
272C42—22no—
273C42—224no—
274C11#2193511yescharacteristic, complemented, Sylow
275C23—21no—
276C23—24no—
277C23—21no—
278C23—114no—
279C23—222no—
280C23—224no—
281C23—224no—
282C23—222no—
283C23—444no—
284C23—448no—
285C23—448no—
286C23—448no—
287C23C4⋊C4×D1112yes—
288C23C22×C4×D1111yescharacteristic
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—24no—
292C2×C4—24no—
293C2×C4—22no—
294C2×C4—22no—
295C2×C4—24no—
296C2×C4—24no—
297C2×C4—114no—
298C2×C4—222no—
299C2×C4—222no—
300C2×C4—228no—
301C2×C4—228no—
302C2×C4—224no—
303C2×C4—224no—
304C2×C4—224no—
305C2×C4—448no—
306C2×C4—444no—
307C2×C4C4⋊C4×D1112yes—
308C2×C4C2×D4×D1111yescharacteristic
309C2×C4#6703712yes—
310C2×C4C2×Q8×D1111yescharacteristic
311C2×C4#6704212yes—
312C8—44no—
313C8—444no—
314C22—22no—
315C22—24no—
316C22—42no—
317C22—42no—
318C22—224no—
319C22—224no—
320C22—224no—
321C22—4416no—
322C22—444no—
323C22—444no—
324C22#1062301711yescharacteristic
325C22C2×C4⋊C4×D1111yescharacteristic
326C22#1062305211yescharacteristic
327C22#1062328114yes—
328C4—22no—
329C4—42no—
330C4—42no—
331C4—224no—
332C4—444no—
333C4#1062313612yes—
334C4#1062316512yes—
335C2—42no—
336C2—444no—
337C2#1307122911yescharacteristic
338C2#1307717712yes—
339C2#1307767412yes—
340C2#1307767712yes—
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1798C2
prime radicalC24×D11C2×C4
cosocleC22×C4×C11C24
hypercenter#1798D11
hypocenterC11#21935
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1798

Complements

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

NH ≅ G/Ntype
3. #13068800C2semidirect
4. #13068797C2semidirect
5. #13068600C2semidirect
6. #13068598C2semidirect
7. C11×#1798C2semidirect
12. C2×C11×C4⋊C8C22semidirect
16. C2×Dic11⋊C8C22semidirect
22. C2×C4⋊(C11⋊C8)C22semidirect
24. C11×#336C22semidirect
25. #10622188C22semidirect
26. #10622162C22semidirect
111. #1798D11semidirect
157. C2×C4⋊C8C2×D11semidirect
169. #336C2×D11semidirect
274. C11#21935semidirect

Maximal subgroups

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

subgroupindex
C2×#106223392
#130709952
#130688002
#130687972
#130686002
#130685982
C11×#17982
#2193511