Finite Group Databasebeta

← #14810449

Subgroups — #14810449

Order 2816.

1206 conjugacy classes of subgroups; only the 227 normal subgroups are shown.

normal subgroups only

This group has 1206 conjugacy classes of subgroups — too many to draw. Only its 227 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
1C2×#10622680C212yesmaximal, complemented
2#13076961C211yesmaximal, characteristic
3#13069749C214yesmaximal, complemented
4#13069586C212yesmaximal, complemented
5#13068938C214yesmaximal, complemented
6#13068378C211yesmaximal, characteristic, complemented
7C2×C11×#533C211yesmaximal, characteristic, complemented
8C11×#533—28no—
9C2×C11×C4⋊Q8C2212yes—
10C2×C11×#125C2212yes—
11C2×C11×C22⋊Q8—22no—
12C2×C4×Q8×C11—22no—
13C2×C11×#117C2212yes—
14C22×C42×C11C2211yescharacteristic
15C2×#66983—22no—
16C2×#66983C2212yes—
17C2×#66927C2211yescharacteristic
18C2×C22⋊(C11⋊C8)C2212yes—
19#10622680—28no—
20C2×#66873C2218yes—
21#10622552—22no—
22#10622552C2212yes—
23#10622548C2211yescharacteristic
24C2×#66867C2212yes—
25#10622167C2218yes—
26#10622162C2212yes—
27C22×Q8×C11—22no—
28C23×C4×C11D412yes—
29C23×C4×C11C2311yescharacteristic
30C22×C22⋊D11—22no—
31C22×D44—22no—
32C22×D44C2312yes—
33C11×C4⋊Q8—28no—
34C11×#125—24no—
35C11×#125D418yescomplemented
36C11×C22⋊Q8—216no—
37C4×Q8×C11—216no—
38C11×#117—28no—
39C2×C11×C4⋊C4—24no—
40C2×C11×C4⋊C4—22no—
41C2×C11×C4⋊C4C2314yes—
42C2×C11×C22⋊C4—22no—
43C2×C42×C11—22no—
44C2×C42×C11—24no—
45C2×C42×C11D412yes—
46C2×C42×C11C2311yescharacteristic
47C2×C42×C11C2311yescharacteristic
48#66983—28no—
49#66983—48no—
50C2×(C2×D11)⋊C4—22no—
51C2×(C2×D11)⋊C4—24no—
52C2×C4⋊Dic11—22no—
53C2×C4⋊Dic11C2312yes—
54C22×C11⋊C8C2314yes—
55#66927—24no—
56C22⋊(C11⋊C8)—24no—
57#66873—216no—
58#66867—24no—
59#25911—111nomaximal, Sylow
60C24×C11C2×D411yescharacteristic
61C23×D11—22no—
62C2×Q8×C11—28no—
63C2×Q8×C11—44no—
64C2×Q8×C11—44no—
65C22×C4×C11—22no—
66C22×C4×C11—22no—
67C22×C4×C11—24no—
68C22×C4×C11—24no—
69C22×C4×C11—24no—
70C22×C4×C11—42no—
71C22×C4×C11C2×D412yes—
72C22×C4×C11C2×D411yescharacteristic
73C22×C4×C11C2×D412yes—
74C22×C4×C11#4114yes—
75C22×C4×C11C2411yescharacteristic
76C2×C22⋊D11—48no—
77C2×C22⋊D11—44no—
78C22×Dic11—22no—
79C2×D44—24no—
80C2×D44—24no—
81C2×D44—24no—
82C2×D44—44no—
83C2×D44—44no—
84C2×D44—44no—
85C11×C4⋊C4—28no—
86C11×C4⋊C4—216no—
87C11×C4⋊C4—24no—
88C11×C4⋊C4C2×D418yes—
89C11×C22⋊C4—28no—
90C42×C11—28no—
91C42×C11—24no—
92C42×C11—22no—
93C42×C11C2×D414yes—
94(C2×D11)⋊C4—44no—
95(C2×D11)⋊C4—48no—
96C4⋊Dic11—24no—
97C4⋊Dic11—44no—
98C2×C11⋊C8—24no—
99C2×C11⋊C8—24no—
100C2×C11⋊C8—24no—
101C2×#533D1111yescharacteristic, complemented
102C2×#490—112no—
103#2856—111no—
104#2023—114no—
105#1992—112no—
106#1875—114no—
107#1749—111no—
108C23×C11—21no—
109C23×C11—21no—
110C23×C11—22no—
111C23×C11—22no—
112C23×C11#12412yes—
113C23×C11C22×D411yescharacteristic
114C22×D11—42no—
115C22×D11—42no—
116C22×D11—42no—
117C22×D11—44no—
118C22×D11—44no—
119Q8×C11—416no—
120C2×C4×C11—21no—
121C2×C4×C11—22no—
122C2×C4×C11—21no—
123C2×C4×C11—22no—
124C2×C4×C11—22no—
125C2×C4×C11—22no—
126C2×C4×C11—28no—
127C2×C4×C11—28no—
128C2×C4×C11—48no—
129C2×C4×C11—44no—
130C2×C4×C11—44no—
131C2×C4×C11#12014yes—
132C2×C4×C11#12412yes—
133C2×C4×C11AGL(1,ℤ/8)14yes—
134C2×C4×C11C22×D412yes—
135C2×C4×C11C2×#4112yes—
136C2×C4×C112−1+412yes—
137C22⋊D11—88no—
138C2×Dic11—42no—
139C2×Dic11—44no—
140D44—48no—
141D44—88no—
142C11⋊C8—44no—
143#533—28no—
144C2×C4⋊Q8C2×D1112yes—
145C2×#127—111no—
146C2×#125C2×D1112yes—
147C2×C22⋊Q8—22no—
148C2×#121—112no—
149C2×#121—222no—
150C2×C4×Q8—22no—
151C2×#117C2×D1112yes—
152C22×C42C2×D1111yescharacteristic
153#490—228no—
154C2×#102—118no—
155C2×C22⋊C8—112no—
156C2×#97—112no—
157#390—112no—
158#390—222no—
159#384—111no—
160#340—118no—
161#336—112no—
162C22×C11—22no—
163C22×C11—22no—
164C22×C11—22no—
165C22×C11—42no—
166C22×C11—42no—
167C22×C11C2×#12011yescharacteristic
168C22×C11C2×#12411yescharacteristic
169C22×C11#53611yescharacteristic
170C22×C11C2×AGL(1,ℤ/8)12yes—
171C22×C11#57512yes—
172C2×D11—82no—
173C2×D11—82no—
174C2×D11—82no—
175C2×D11—84no—
176C2×D11—84no—
177C4×C11—22no—
178C4×C11—24no—
179C4×C11—24no—
180C4×C11—48no—
181C4×C11#54814yes—
182Dic11—82no—
183C22×Q8—22no—
184C22×D4—112no—
185C22×D4—222no—
186C22×D4—222no—
187C23×C4C22⋊D1112yes—
188C23×C4C22×D1111yescharacteristic
189C22×C8—114no—
190C4⋊Q8—28no—
191#127—224no—
192#125—24no—
193#125C22⋊D1118yescomplemented
194C22⋊Q8—216no—
195#121—228no—
196#121—448no—
197C4×Q8—216no—
198#117—28no—
199C2×C4⋊C4—24no—
200C2×C4⋊C4—22no—
201C2×C4⋊C4—112no—
202C2×C4⋊C4—222no—
203C2×C4⋊C4C22×D1114yes—
204C2×C22⋊C4—22no—
205C2×C22⋊C4—222no—
206C2×C22⋊C4—224no—
207C2×C42—22no—
208C2×C42—24no—
209C2×C42C22⋊D1112yes—
210C2×C42C22×D1111yescharacteristic
211C2×C42C22×D1111yescharacteristic
212#102—2216no—
213C22⋊C8—224no—
214#97—224no—
215C2×C11—42no—
216C2×C11#243611yescharacteristic
217C2×C11#300612yes—
218C2×C11#313511yescharacteristic
219C2×C11#313811yescharacteristic
220C2×C11#323512yes—
221D11—162no—
222C24—222no—
223C24C2×C22⋊D1111yescharacteristic
224C2×Q8—28no—
225C2×Q8—44no—
226C2×Q8—44no—
227C2×D4—224no—
228C2×D4—224no—
229C2×D4—224no—
230C2×D4—444no—
231C2×D4—444no—
232C2×D4—448no—
233C2×D4—444no—
234C2×D4—444no—
235C22×C4—22no—
236C22×C4—22no—
237C22×C4—24no—
238C22×C4—24no—
239C22×C4—24no—
240C22×C4—42no—
241C22×C4—222no—
242C22×C4#434314yes—
243C22×C4C2×C22⋊D1111yescharacteristic
244C22×C4C2×C22⋊D1112yes—
245C22×C4C2×C22⋊D1112yes—
246C22×C4C23×D1111yescharacteristic
247C2×C8—224no—
248C2×C8—224no—
249C2×C8—224no—
250C4⋊C4—28no—
251C4⋊C4—216no—
252C4⋊C4—24no—
253C4⋊C4—224no—
254C4⋊C4—444no—
255C4⋊C4C2×C22⋊D1118yes—
256C22⋊C4—28no—
257C22⋊C4—444no—
258C22⋊C4—448no—
259C42—28no—
260C42—24no—
261C42—22no—
262C42C2×C22⋊D1114yes—
263C11#2591111yescharacteristic, complemented, Sylow
264C23—21no—
265C23—22no—
266C23—22no—
267C23—21no—
268C23—442no—
269C23—442no—
270C23—444no—
271C23—444no—
272C23—442no—
273C23#6700012yes—
274C23C22×C22⋊D1111yescharacteristic
275Q8—416no—
276D4—448no—
277D4—888no—
278D4—888no—
279C2×C4—21no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—21no—
284C2×C4—22no—
285C2×C4—28no—
286C2×C4—28no—
287C2×C4—48no—
288C2×C4—44no—
289C2×C4—44no—
290C2×C4—442no—
291C2×C4—444no—
292C2×C4#6700012yes—
293C2×C4#6700214yes—
294C2×C4#6700614yes—
295C2×C4C2×#434312yes—
296C2×C4#6704012yes—
297C2×C4C22×C22⋊D1112yes—
298C8—444no—
299C22—22no—
300C22—22no—
301C22—22no—
302C22—42no—
303C22—42no—
304C22—884no—
305C22—884no—
306C22—882no—
307C22—882no—
308C22—882no—
309C22C2×#6700011yescharacteristic
310C22#1062334711yescharacteristic
311C22C2×#6700212yes—
312C22#1062335312yes—
313C22C2×#6700611yescharacteristic
314C4—24no—
315C4—24no—
316C4—22no—
317C4—48no—
318C4—882no—
319C4#1062334814yes—
320C2—42no—
321C2—1762no—
322C2#1307227011yescharacteristic
323C2#1307786812yes—
324C2#1307896411yescharacteristic
325C2#1307899211yescharacteristic
326C2#1307981412yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#533C2
socleC23×C11C22×D4
prime radical#13076961C2
hypercenterC2×#533D11
hypocenterC11#25911
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
1. C2×#10622680C2semidirect
3. #13069749C2semidirect
4. #13069586C2semidirect
5. #13068938C2semidirect
6. #13068378C2semidirect
7. C2×C11×#533C2semidirect
35. C11×#125D4semidirect
101. C2×#533D11semidirect
193. #125C22⋊D11semidirect
263. C11#25911semidirect

Maximal subgroups

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

subgroupindex
C2×#106226802
#130769612
#130697492
#130695862
#130689382
#130683782
C2×C11×#5332
#2591111