Finite Group Databasebeta

← #14718909

Subgroups — #14718909

Order 2816.

1426 conjugacy classes of subgroups; only the 243 normal subgroups are shown.

normal subgroups only

This group has 1426 conjugacy classes of subgroups — too many to draw. Only its 243 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13066874C214yesmaximal, complemented
2#13066859C214yesmaximal, complemented
3#13066859C214yesmaximal, complemented
4#13066857C212yesmaximal
5C11×#1438C211yesmaximal, characteristic
6C23×D4×C11C2211yescharacteristic
7C22×C11×C22⋊C4C2214yes—
8C22×C22⋊Dic11C2212yes—
9C22×C22⋊Dic11C2214yes—
10C22×C22⋊Dic11C2212yes—
11C22×Dic11⋊C4C2214yes—
12C2×C11×#95C2212yes—
13C2×C11⋊#95C2214yes—
14C2×C11⋊#95C2214yes—
15C2×C11⋊#95C2214yes—
16C2×C11⋊#95C2214yes—
17C25×C11C2312yes—
18C22×D4×C11—44no—
19C22×D4×C11—42no—
20C22×D4×C11Q814yes—
21C23×C4×C11C2314yes—
22C23×C4×C11C2311yescharacteristic
23C23×Dic11C2314yes—
24C23×Dic11C2314yes—
25C2×C11×C22⋊C4—44no—
26C2×C11×C22⋊C4—44no—
27C2×C11×C22⋊C4—44no—
28C2×C22⋊Dic11—28no—
29C2×C22⋊Dic11—28no—
30C2×C22⋊Dic11—42no—
31C2×C22⋊Dic11—44no—
32C2×C22⋊Dic11—44no—
33C2×C22⋊Dic11—44no—
34C2×C22⋊Dic11—42no—
35C2×Dic11⋊C4—44no—
36C2×Dic11⋊C4—44no—
37C2×Dic11⋊C4—44no—
38C11×#95—42no—
39C11⋊#95—28no—
40C11⋊#95—44no—
41C11⋊#95—44no—
42C11⋊#95—44no—
43#17271—111nomaximal, Sylow
44C24×C11—24no—
45C24×C11—24no—
46C24×C11—24no—
47C24×C11—24no—
48C24×C11—24no—
49C24×C11—22no—
50C24×C11—22no—
51C24×C11—24no—
52C24×C11C2×Q814yes—
53C24×C11C2411yescharacteristic
54C2×D4×C11—44no—
55C2×D4×C11—48no—
56C2×D4×C11—416no—
57C22×C4×C11—24no—
58C22×C4×C11—22no—
59C22×C4×C11—24no—
60C22×C4×C11—24no—
61C22×C4×C11—24no—
62C22×C4×C11—24no—
63C22×C4×C11—24no—
64C22×C4×C11—24no—
65C22×C4×C11—24no—
66C22×C4×C11C2×Q812yes—
67C22×Dic11—24no—
68C22×Dic11—24no—
69C22×Dic11—24no—
70C22×Dic11—24no—
71C22×Dic11—24no—
72C22×Dic11—24no—
73C22×Dic11—24no—
74C22×Dic11—24no—
75C22×Dic11—24no—
76C22×Dic11—24no—
77C22×Dic11—24no—
78C22×Dic11—24no—
79C22×Dic11—24no—
80C22×Dic11#4118yes—
81C11×C22⋊C4—416no—
82C22⋊Dic11—48no—
83C22⋊Dic11—416no—
84C22⋊Dic11—48no—
85Dic11⋊C4—416no—
86#1442—114no—
87#1439—114no—
88#1439—114no—
89#1438—112no—
90#1438D1111yescharacteristic
91C23×C11—24no—
92C23×C11—24no—
93C23×C11—24no—
94C23×C11—28no—
95C23×C11—28no—
96C23×C11—44no—
97C23×C11—44no—
98C23×C11—44no—
99C23×C11—44no—
100C23×C11—44no—
101C23×C11—44no—
102C23×C11—42no—
103C23×C11—42no—
104C23×C11—44no—
105C23×C11—44no—
106C23×C11—42no—
107C23×C11—44no—
108C23×C11—42no—
109C23×C11—44no—
110C23×C11—44no—
111C23×C11—44no—
112C23×C11C22×Q811yescharacteristic
113C23×C11C2×#4114yes—
114C23×C11H(5,𝔽2)14yes—
115C23×C11H(5,𝔽2)14yes—
116C23×C11H(5,𝔽2)12yes—
117D4×C11—416no—
118C2×C4×C11—22no—
119C2×C4×C11—24no—
120C2×C4×C11—44no—
121C2×C4×C11—44no—
122C2×C4×C11—44no—
123C2×C4×C11—44no—
124C2×C4×C11—44no—
125C2×C4×C11—44no—
126C2×C4×C11—44no—
127C2×C4×C11—44no—
128C2×Dic11—28no—
129C2×Dic11—28no—
130C2×Dic11—28no—
131C2×Dic11—44no—
132C2×Dic11—44no—
133C2×Dic11—44no—
134C2×Dic11—44no—
135C2×Dic11—44no—
136C2×Dic11—44no—
137C2×Dic11—44no—
138C2×Dic11—44no—
139C2×Dic11—44no—
140C2×Dic11—44no—
141C2×Dic11—44no—
142C23×D4C2×D1111yescharacteristic
143C22×C4⋊C4—114no—
144C22×C22⋊C4—112no—
145C22×C22⋊C4—114no—
146C22×C22⋊C4—112no—
147C22×C22⋊C4C2×D1114yes—
148C2×#95—114no—
149C2×#95—114no—
150C2×#95—114no—
151C2×#95—114no—
152C2×#95C2×D1112yes—
153C22×C11—44no—
154C22×C11—44no—
155C22×C11—44no—
156C22×C11—48no—
157C22×C11—48no—
158C22×C11—84no—
159C22×C11—84no—
160C22×C11—84no—
161C22×C11—84no—
162C22×C11#53814yes—
163C22×C11#54014yes—
164C22×C11#54014yes—
165C22×C11#54311yescharacteristic
166C22×C11#54312yes—
167C22×C11#55112yes—
168C22×C11#55314yes—
169C22×C11#55414yes—
170C22×C11#56012yes—
171C22×C11#56014yes—
172C22×C11H(3,𝔽4)14yes—
173C4×C11—42no—
174C4×C11—84no—
175Dic11—48no—
176Dic11—84no—
177C25C22×D1112yes—
178C22×D4—42no—
179C22×D4—44no—
180C22×D4Dic2214yes—
181C23×C4—114no—
182C23×C4—114no—
183C23×C4C22×D1114yes—
184C23×C4C22×D1111yescharacteristic
185C2×C4⋊C4—444no—
186C2×C4⋊C4—444no—
187C2×C4⋊C4—444no—
188C2×C22⋊C4—44no—
189C2×C22⋊C4—44no—
190C2×C22⋊C4—44no—
191C2×C22⋊C4—228no—
192C2×C22⋊C4—228no—
193C2×C22⋊C4—442no—
194C2×C22⋊C4—444no—
195C2×C22⋊C4—444no—
196C2×C22⋊C4—444no—
197C2×C22⋊C4—442no—
198#95—42no—
199#95—228no—
200#95—444no—
201#95—444no—
202#95—444no—
203C2×C11—84no—
204C2×C11#274812yes—
205C2×C11#275314yes—
206C2×C11#278014yes—
207C2×C11#282814yes—
208C2×C11#284011yescharacteristic
209C24—24no—
210C24—24no—
211C24—24no—
212C24—22no—
213C24—22no—
214C24—24no—
215C24—24no—
216C24—24no—
217C24C2×Dic2214yes—
218C24C23×D1111yescharacteristic
219C2×D4—48no—
220C2×D4—44no—
221C2×D4—416no—
222C22×C4—22no—
223C22×C4—24no—
224C22×C4—24no—
225C22×C4—24no—
226C22×C4—24no—
227C22×C4—24no—
228C22×C4—24no—
229C22×C4—24no—
230C22×C4—24no—
231C22×C4—118no—
232C22×C4—224no—
233C22×C4—224no—
234C22×C4—224no—
235C22×C4—224no—
236C22×C4—224no—
237C22×C4—224no—
238C22×C4—224no—
239C22×C4—224no—
240C22×C4—224no—
241C22×C4—224no—
242C22×C4—224no—
243C22×C4—224no—
244C22×C4—224no—
245C22×C4C2×Dic2212yes—
246C4⋊C4—4416no—
247C22⋊C4—416no—
248C22⋊C4—448no—
249C22⋊C4—4416no—
250C22⋊C4—448no—
251C11#1727111yescharacteristic, complemented, Sylow
252C23—24no—
253C23—24no—
254C23—24no—
255C23—28no—
256C23—28no—
257C23—42no—
258C23—42no—
259C23—44no—
260C23—44no—
261C23—44no—
262C23—44no—
263C23—44no—
264C23—44no—
265C23—44no—
266C23—44no—
267C23—44no—
268C23—44no—
269C23—44no—
270C23—44no—
271C23—42no—
272C23—42no—
273C23C22×Dic2211yescharacteristic
274C23#6703712yes—
275C23#6703714yes—
276C23#6703714yes—
277C23#41×D1114yes—
278D4—416no—
279C2×C4—24no—
280C2×C4—22no—
281C2×C4—44no—
282C2×C4—44no—
283C2×C4—44no—
284C2×C4—44no—
285C2×C4—44no—
286C2×C4—44no—
287C2×C4—44no—
288C2×C4—44no—
289C2×C4—228no—
290C2×C4—228no—
291C2×C4—228no—
292C2×C4—444no—
293C2×C4—444no—
294C2×C4—444no—
295C2×C4—444no—
296C2×C4—444no—
297C2×C4—444no—
298C2×C4—444no—
299C2×C4—444no—
300C2×C4—444no—
301C2×C4—444no—
302C2×C4—444no—
303C22—48no—
304C22—48no—
305C22—44no—
306C22—44no—
307C22—44no—
308C22—84no—
309C22—84no—
310C22—84no—
311C22—84no—
312C22#1062301412yes—
313C22#1062301411yescharacteristic
314C22#1062307014yes—
315C22#1062312514yes—
316C22#1062312614yes—
317C22#1062314414yes—
318C22#1062314614yes—
319C22#1062314614yes—
320C22#1062319214yes—
321C22#1062321012yes—
322C22#1062325112yes—
323C4—42no—
324C4—84no—
325C4—448no—
326C4—884no—
327C2—84no—
328C2#1307582912yes—
329C2#1307589214yes—
330C2#1307626114yes—
331C2#1307673414yes—
332C2#1307686911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutator, socle, cosocleC24×C11C24
FittingC11×#1438C2
prime radicalC23×D4×C11C22
hypercenter#1438D11
hypocenterC11#17271
LCSG ▷ C24×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1438

Complements

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

NH ≅ G/Ntype
1. #13066874C2semidirect
2. #13066859C2semidirect
3. #13066859C2semidirect
251. C11#17271semidirect

Maximal subgroups

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

subgroupindex
#130668742
#130668592
#130668572
C11×#14382
#1727111