Finite Group Databasebeta

← #14771417

Subgroups — #14771417

Order 2816.

878 conjugacy classes of subgroups.

The subgroup lattice has 312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071485C212yesmaximal
2#13069350C212yesmaximal, complemented
3#13069189C214yesmaximal, complemented
4#13068702C212yesmaximal
5#13068645C211yesmaximal, characteristic
6#107×Dic11C212yesmaximal, complemented
7C8×C22⋊Dic11C211yesmaximal, characteristic
8C22×C11×#107C211yesmaximal, characteristic
9C23×C8×C11C2211yescharacteristic
10C22×C11×C4⋊C4C2212yes—
11C2×#66979—22no—
12C2×C11×#107C418yescomplemented
13C2×C11×#107C2211yescharacteristic
14C2×C11×#107C2212yes—
15C2×C11×#107C2211yescharacteristic
16#10622825C2212yes—
17#10622824—22no—
18C4×C22⋊Dic11C2211yescharacteristic
19C2×C22⋊(C11⋊C8)C2211yescharacteristic
20C2×#66882C2212yes—
21C2×C8×Dic11C2212yes—
22#10622598C2214yes—
23#10622594—24no—
24C4⋊C4×Dic11C2214yes—
25#10622189C2212yes—
26#10622188C2212yes—
27#10622167C2214yes—
28#10622167C2214yes—
29C23×C4×C11—22no—
30C23×C4×C11C2311yescharacteristic
31C22×C8×C11—24no—
32C22×C8×C11C2×C414yes—
33C22×C8×C11C2311yescharacteristic
34C22×C8×C11C2311yescharacteristic
35C2×C11×C4⋊C4—22no—
36C2×C11×C4⋊C4—24no—
37C2×C11×C4⋊C4C2×C418yes—
38C2×C11×C4⋊C4C2312yes—
39C2×C11×C4⋊C4C2312yes—
40C2×C22⋊Dic11—22no—
41C2×C22⋊Dic11D411yescharacteristic
42C2×C22⋊Dic11D411yescharacteristic
43#66979—48no—
44C2×C4⋊Dic11—24no—
45C2×C4⋊Dic11C2314yes—
46C2×C4×Dic11—24no—
47C2×C4×Dic11C2312yes—
48C22×C11⋊C8C2312yes—
49C11×#107C2×C418yes—
50C11×#107C2×C414yes—
51C11×#107C2×C414yes—
52C11⋊#95—22no—
53C11⋊#95—24no—
54C11⋊#95—24no—
55C11⋊#95D412yes—
56C22⋊(C11⋊C8)—22no—
57#66882—24no—
58C8×Dic11—24no—
59#22611—111nomaximal, Sylow
60C24×C11C2×D411yescharacteristic
61C22×C4×C11—22no—
62C22×C4×C11—22no—
63C22×C4×C11—28no—
64C22×C4×C11—22no—
65C22×C4×C11—22no—
66C22×C4×C11—44no—
67C22×C4×C11—44no—
68C22×C4×C11C22×C412yes—
69C22×C4×C11C2×D411yescharacteristic
70C22×C4×C11#4112yes—
71C22×C4×C11C2411yescharacteristic
72C22×Dic11—24no—
73C22×Dic11C2×D412yes—
74C22×Dic11C2×D412yes—
75C2×C8×C11—28no—
76C2×C8×C11—22no—
77C2×C8×C11C22×C412yes—
78C2×C8×C11C22×C412yes—
79C2×C8×C11#4114yes—
80C11×C4⋊C4—28no—
81C11×C4⋊C4—22no—
82C11×C4⋊C4—22no—
83C11×C4⋊C4C22×C414yes—
84C11×C4⋊C4C22×C414yes—
85C22⋊Dic11—22no—
86C22⋊Dic11—44no—
87C22⋊Dic11D814yes—
88C4⋊Dic11—24no—
89C4⋊Dic11—24no—
90C4⋊Dic11—48no—
91C4×Dic11—22no—
92C4×Dic11—22no—
93C4×Dic11—48no—
94C2×C11⋊C8—22no—
95C2×C11⋊C8—22no—
96C2×C11⋊C8—22no—
97C22×#107D1111yescharacteristic
98#2344—112no—
99#1942—112no—
100#1918—114no—
101#1823—112no—
102#1808—111no—
103C4×#107—112no—
104C8×C22⋊C4—111no—
105C23×C11—22no—
106C23×C11—22no—
107C23×C11C4×D412yes—
108C23×C11C2×D812yes—
109C23×C11#13512yes—
110C23×C11C22×D411yescharacteristic
111C2×C4×C11—22no—
112C2×C4×C11—22no—
113C2×C4×C11—22no—
114C2×C4×C11—24no—
115C2×C4×C11—24no—
116C2×C4×C11—24no—
117C2×C4×C11—42no—
118C2×C4×C11—42no—
119C2×C4×C11—42no—
120C2×C4×C11—42no—
121C2×C4×C11—416no—
122C2×C4×C11C4×D412yes—
123C2×C4×C11C23×C411yescharacteristic
124C2×C4×C11C2×#4112yes—
125C2×C4×C11C2×#4111yescharacteristic
126C2×C4×C112−1+412yes—
127C2×Dic11—22no—
128C2×Dic11—22no—
129C2×Dic11—22no—
130C2×Dic11—22no—
131C2×Dic11—22no—
132C2×Dic11—44no—
133C2×Dic11—44no—
134C2×Dic11—44no—
135C2×Dic11C2×D814yes—
136C8×C11—22no—
137C8×C11#11714yescomplemented
138C11⋊C8—42no—
139C23×C8C2×D1111yescharacteristic
140C2×#117—222no—
141C22×C4⋊C4C2×D1112yes—
142C2×#107—112no—
143C2×#107Dic1118yescomplemented
144C2×#107C2×D1112yes—
145C2×#107C2×D1111yescharacteristic
146C2×#107C2×D1111yescharacteristic
147C2×C22⋊C8—111no—
148C2×C4×C8—112no—
149#389—114no—
150#387—224no—
151#381—222no—
152#380—112no—
153C4×C4⋊C4—114no—
154C4×C22⋊C4—111no—
155#340—112no—
156#340—114no—
157#340—114no—
158#336—112no—
159C22×C11—24no—
160C22×C11—24no—
161C22×C11—22no—
162C22×C11—22no—
163C22×C11C4×D814yes—
164C22×C11C2×C4×D411yescharacteristic
165C22×C11#54712yes—
166C22×C11C22×D811yescharacteristic
167C22×C11C2×#13511yescharacteristic
168C22×C11#57812yes—
169C4×C11—22no—
170C4×C11—44no—
171C4×C11—44no—
172C4×C11C2×#11711yescharacteristic
173C4×C11#51911yescharacteristic
174C4×C11#55212yes—
175Dic11—24no—
176Dic11—42no—
177Dic11—84no—
178C23×C4—22no—
179C23×C4C22×D1111yescharacteristic
180C22×C8—24no—
181C22×C8—112no—
182C22×C8C2×Dic1114yes—
183C22×C8C22×D1111yescharacteristic
184C22×C8C22×D1111yescharacteristic
185#117—448no—
186C2×C4⋊C4—22no—
187C2×C4⋊C4—24no—
188C2×C4⋊C4—114no—
189C2×C4⋊C4—224no—
190C2×C4⋊C4C2×Dic1118yes—
191C2×C4⋊C4C22×D1112yes—
192C2×C4⋊C4C22×D1112yes—
193C2×C22⋊C4—111no—
194C2×C22⋊C4—111no—
195C2×C22⋊C4—222no—
196C2×C42—112no—
197C2×C42—224no—
198#107—224no—
199#107C2×Dic1118yes—
200#107C2×Dic1114yes—
201#107C2×Dic1114yes—
202C22⋊C8—222no—
203C4×C8—224no—
204#95—112no—
205#95—224no—
206#95—224no—
207#95—222no—
208C2×C11—24no—
209C2×C11#234411yescharacteristic
210C2×C11C2×C4×D811yescharacteristic
211C2×C11#295011yescharacteristic
212C2×C11#333412yes—
213C2×C11#333612yes—
214C24D4×D1111yescharacteristic
215C22×C4—22no—
216C22×C4—22no—
217C22×C4—28no—
218C22×C4—22no—
219C22×C4—22no—
220C22×C4—44no—
221C22×C4—44no—
222C22×C4—112no—
223C22×C4—112no—
224C22×C4—224no—
225C22×C4D4×D1111yescharacteristic
226C22×C4#434112yes—
227C22×C4C22×Dic1112yes—
228C22×C4C23×D1111yescharacteristic
229C2×C8—22no—
230C2×C8—28no—
231C2×C8—222no—
232C2×C8—222no—
233C2×C8—222no—
234C2×C8#433914yes—
235C2×C8C22×Dic1112yes—
236C2×C8C22×Dic1112yes—
237C4⋊C4—28no—
238C4⋊C4—22no—
239C4⋊C4—22no—
240C4⋊C4—224no—
241C4⋊C4—224no—
242C4⋊C4—448no—
243C4⋊C4C22×Dic1114yes—
244C4⋊C4C22×Dic1114yes—
245C22⋊C4—114no—
246C22⋊C4—222no—
247C22⋊C4—444no—
248C42—222no—
249C42—222no—
250C42—448no—
251C11#2261111yescharacteristic, complemented, Sylow
252C23—22no—
253C23—22no—
254C23D8×D1112yes—
255C23#6696512yes—
256C23D4×Dic1112yes—
257C23C2×D4×D1111yescharacteristic
258C2×C4—22no—
259C2×C4—24no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—24no—
263C2×C4—24no—
264C2×C4—416no—
265C2×C4—42no—
266C2×C4—42no—
267C2×C4—42no—
268C2×C4—42no—
269C2×C4—114no—
270C2×C4—222no—
271C2×C4—222no—
272C2×C4—222no—
273C2×C4—222no—
274C2×C4—222no—
275C2×C4—444no—
276C2×C4—444no—
277C2×C4—444no—
278C2×C4D4×Dic1112yes—
279C2×C4C2×#433912yes—
280C2×C4C2×#434111yescharacteristic
281C2×C4#6704012yes—
282C2×C4C23×Dic1111yescharacteristic
283C8—22no—
284C8—442no—
285C8#6697914yescomplemented
286C22—22no—
287C22—24no—
288C22—24no—
289C22—22no—
290C22D8×Dic1114yes—
291C22#1062303812yes—
292C22C2×D8×D1111yescharacteristic
293C22C2×#6696511yescharacteristic
294C22#1062329712yes—
295C22C2×D4×Dic1111yescharacteristic
296C4—22no—
297C4—44no—
298C4—44no—
299C4—224no—
300C4—442no—
301C4—884no—
302C4#1062304412yes—
303C4C2×#6697911yescharacteristic
304C4#1062334311yescharacteristic
305C2—24no—
306C2#1307148511yescharacteristic
307C2C2×D8×Dic1111yescharacteristic
308C2#1307748411yescharacteristic
309C2#1308096112yes—
310C2#1308098012yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC22×C11×#107C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenterC22×#107D11
hypocenterC11#22611
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#107

Complements

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

NH ≅ G/Ntype
2. #13069350C2semidirect
3. #13069189C2semidirect
6. #107×Dic11C2semidirect
12. C2×C11×#107C4semidirect
137. C8×C11#117semidirect
143. C2×#107Dic11semidirect
251. C11#22611semidirect
285. C8#66979semidirect

Maximal subgroups

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

subgroupindex
#130714852
#130693502
#130691892
#130687022
#130686452
#107×Dic112
C8×C22⋊Dic112
C22×C11×#1072
#2261111