Finite Group Databasebeta

← #14810453

Subgroups — #14810453

Order 2816.

1206 conjugacy classes of subgroups; only the 211 normal subgroups are shown.

normal subgroups only

This group has 1206 conjugacy classes of subgroups — too many to draw. Only its 211 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×#10623001C211yesmaximal, characteristic, complemented
2C2×#10622326C212yesmaximal, complemented
3#13076961C211yesmaximal, characteristic
4#13069753C214yesmaximal, complemented
5#13069585C212yesmaximal, complemented
6#13068936C214yesmaximal, complemented
7C11×#1749C211yesmaximal, characteristic, complemented
8C22×C42×C11C2211yescharacteristic
9C2×#66983—22no—
10C2×#66983C2212yes—
11C2×#66979C2212yes—
12C2×#66977—22no—
13C2×#66927C2211yescharacteristic
14#10623001—28no—
15C2×#66923C2212yes—
16C2×#66922C2212yes—
17C2×C4×Dic22—22no—
18C2×C11×C22⋊C8C2212yes—
19C2×C11×#97C2212yes—
20C2×#66885C2218yes—
21#10622552—22no—
22#10622552C2212yes—
23#10622548C2211yescharacteristic
24#10622326—28no—
25C11×#336C2212yes—
26#10622189C2218yes—
27C23×C4×C11D412yes—
28C23×C4×C11C2311yescharacteristic
29C22×C22⋊D11—22no—
30C22×D44—22no—
31C22×D44C2312yes—
32C22×Dic22—22no—
33C22×C8×C11C2314yes—
34C2×C42×C11—24no—
35C2×C42×C11D412yes—
36C2×C42×C11C2311yescharacteristic
37C2×C42×C11C2311yescharacteristic
38C2×C22⋊Dic11—22no—
39#66983—28no—
40#66983—48no—
41C2×(C2×D11)⋊C4—22no—
42C2×(C2×D11)⋊C4—24no—
43#66979—28no—
44C2×C4⋊Dic11—22no—
45C2×C4⋊Dic11—22no—
46C2×C4⋊Dic11C2312yes—
47C2×C4⋊Dic11C2314yes—
48#66977—216no—
49C2×Dic11⋊C4—24no—
50C2×C4×Dic11—22no—
51#66927—24no—
52#66923—24no—
53#66923D418yescomplemented
54#66922—28no—
55C4×Dic22—216no—
56C11×C22⋊C8—24no—
57C11×#97—24no—
58#66885—216no—
59#25911—111nomaximal, Sylow
60C24×C11C2×D411yescharacteristic
61C23×D11—22no—
62C22×C4×C11—22no—
63C22×C4×C11—22no—
64C22×C4×C11—24no—
65C22×C4×C11—24no—
66C22×C4×C11—42no—
67C22×C4×C11C2×D412yes—
68C22×C4×C11C2×D411yescharacteristic
69C22×C4×C11C2×D412yes—
70C22×C4×C11#4114yes—
71C22×C4×C11C2411yescharacteristic
72C2×C22⋊D11—48no—
73C2×C22⋊D11—44no—
74C22×Dic11—24no—
75C22×Dic11—22no—
76C2×D44—24no—
77C2×D44—24no—
78C2×D44—24no—
79C2×D44—44no—
80C2×D44—44no—
81C2×D44—44no—
82C2×Dic22—28no—
83C2×Dic22—44no—
84C2×Dic22—44no—
85C2×C8×C11—24no—
86C2×C8×C11—24no—
87C2×C8×C11—24no—
88C42×C11—24no—
89C42×C11—22no—
90C42×C11C2×D414yes—
91C22⋊Dic11—28no—
92(C2×D11)⋊C4—44no—
93(C2×D11)⋊C4—48no—
94C4⋊Dic11—28no—
95C4⋊Dic11—24no—
96C4⋊Dic11—24no—
97C4⋊Dic11—44no—
98C4⋊Dic11C2×D418yes—
99Dic11⋊C4—216no—
100C4×Dic11—28no—
101C2×#533—111no—
102C2×#490—112no—
103#2856—111no—
104#2023—114no—
105#1992—112no—
106#1875—114no—
107#1749D1111yescharacteristic, complemented
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—
119C2×C4×C11—21no—
120C2×C4×C11—22no—
121C2×C4×C11—21no—
122C2×C4×C11—22no—
123C2×C4×C11—22no—
124C2×C4×C11—22no—
125C2×C4×C11—28no—
126C2×C4×C11—48no—
127C2×C4×C11#12014yes—
128C2×C4×C11#12412yes—
129C2×C4×C11AGL(1,ℤ/8)14yes—
130C2×C4×C11C22×D412yes—
131C2×C4×C11C2×#4112yes—
132C2×C4×C112−1+412yes—
133C22⋊D11—88no—
134C2×Dic11—28no—
135C2×Dic11—44no—
136C2×Dic11—44no—
137C2×Dic11—42no—
138C2×Dic11—44no—
139D44—48no—
140D44—88no—
141Dic22—416no—
142C8×C11—44no—
143#533—228no—
144C2×C4⋊Q8—112no—
145C2×#127—111no—
146C2×#125—112no—
147C2×C22⋊Q8—222no—
148C2×#121—112no—
149C2×#121—222no—
150C2×C4×Q8—222no—
151C2×#117—112no—
152C22×C42C2×D1111yescharacteristic
153#490—228no—
154C2×#102—118no—
155C2×C22⋊C8C2×D1112yes—
156C2×#97C2×D1112yes—
157#390—112no—
158#390—222no—
159#384—111no—
160#340—118no—
161#336C2×D1112yes—
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#54814yes—
181Dic11—48no—
182Dic11—82no—
183C22×Q8—222no—
184C22×D4—112no—
185C22×D4—222no—
186C22×D4—222no—
187C23×C4D4412yes—
188C23×C4C22×D1111yescharacteristic
189C22×C8C22×D1114yes—
190C4⋊Q8—228no—
191#127—224no—
192#125—118no—
193#125—224no—
194C22⋊Q8—2216no—
195#121—228no—
196#121—448no—
197C4×Q8—2216no—
198#117—228no—
199C2×C4⋊C4—114no—
200C2×C4⋊C4—112no—
201C2×C4⋊C4—224no—
202C2×C4⋊C4—222no—
203C2×C4⋊C4—222no—
204C2×C22⋊C4—222no—
205C2×C22⋊C4—222no—
206C2×C22⋊C4—224no—
207C2×C42—24no—
208C2×C42—222no—
209C2×C42D4412yes—
210C2×C42C22×D1111yescharacteristic
211C2×C42C22×D1111yescharacteristic
212#102—2216no—
213C22⋊C8—24no—
214#97—24no—
215C2×C11—42no—
216C2×C11#243611yescharacteristic
217C2×C11#300612yes—
218C2×C11#313511yescharacteristic
219C2×C11#313811yescharacteristic
220C2×C11#323512yes—
221D11—162no—
222C24—222no—
223C24C2×D4411yescharacteristic
224C2×Q8—228no—
225C2×Q8—444no—
226C2×Q8—444no—
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—42no—
240C22×C4—224no—
241C22×C4—222no—
242C22×C4C2×D4411yescharacteristic
243C22×C4C2×D4412yes—
244C22×C4C2×D4412yes—
245C22×C4#433914yes—
246C22×C4C23×D1111yescharacteristic
247C2×C8—24no—
248C2×C8—24no—
249C2×C8—24no—
250C4⋊C4—118no—
251C4⋊C4—228no—
252C4⋊C4—2216no—
253C4⋊C4—224no—
254C4⋊C4—224no—
255C4⋊C4—444no—
256C22⋊C4—228no—
257C22⋊C4—444no—
258C22⋊C4—448no—
259C42—24no—
260C42—22no—
261C42—228no—
262C42D4×D1114yes—
263C11#2591111yescharacteristic, complemented, Sylow
264C23—21no—
265C23—22no—
266C23—22no—
267C23—21no—
268C23—442no—
269C23—442no—
270C23—444no—
271C23—444no—
272C23—442no—
273C23#6692812yes—
274C23C22×D4411yescharacteristic
275Q8—4416no—
276D4—448no—
277D4—888no—
278D4—888no—
279C2×C4—21no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—21no—
285C2×C4—28no—
286C2×C4—48no—
287C2×C4—228no—
288C2×C4—444no—
289C2×C4—444no—
290C2×C4—442no—
291C2×C4—444no—
292C2×C4#6692812yes—
293C2×C4#6693514yes—
294C2×C4#6696114yes—
295C2×C4C2×#433912yes—
296C2×C4C2×D4×D1112yes—
297C2×C4#6704312yes—
298C8—44no—
299C22—22no—
300C22—22no—
301C22—22no—
302C22—42no—
303C22—42no—
304C22—884no—
305C22—884no—
306C22—882no—
307C22—882no—
308C22—882no—
309C22C2×#6692811yescharacteristic
310C22C2×#6693511yescharacteristic
311C22#1062305711yescharacteristic
312C22C2×#6696112yes—
313C22#1062327912yes—
314C4—24no—
315C4—24no—
316C4—22no—
317C4—448no—
318C4—882no—
319C4#1062308314yes—
320C2—42no—
321C2—1762no—
322C2#1307227411yescharacteristic
323C2#1307787012yes—
324C2#1307896211yescharacteristic
325C2#1307899111yescharacteristic
326C2#1307981612yes—
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1749C2
socleC23×C11C22×D4
prime radical#13076961C2
hypercenter#1749D11
hypocenterC11#25911
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1749

Complements

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

NH ≅ G/Ntype
1. C2×#10623001C2semidirect
2. C2×#10622326C2semidirect
4. #13069753C2semidirect
5. #13069585C2semidirect
6. #13068936C2semidirect
7. C11×#1749C2semidirect
53. #66923D4semidirect
107. #1749D11semidirect
263. C11#25911semidirect

Maximal subgroups

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

subgroupindex
C2×#106230012
C2×#106223262
#130769612
#130697532
#130695852
#130689362
C11×#17492
#2591111