Finite Group Databasebeta

← #14810454

Subgroups — #14810454

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×#10622684C212yesmaximal, complemented
3#13069752C214yesmaximal, complemented
4#13069584C212yesmaximal, complemented
5#13068939C214yesmaximal, complemented
6#13068378C211yesmaximal, characteristic, complemented
7C11×#2856C211yesmaximal, characteristic
8C2×C11×#127C2211yescharacteristic
9C2×C11×#121—22no—
10C2×C11×#121C2212yes—
11C22×C42×C11C2211yescharacteristic
12C2×#66979C2212yes—
13C2×#66977—22no—
14#10623001—28no—
15C2×#66923C2212yes—
16C2×#66922C2212yes—
17C2×C4×Dic22—22no—
18C11×#390—22no—
19C11×#390C2212yes—
20C11×#384C2211yescharacteristic
21C2×#66896C2218yes—
22C2×C22⋊(C11⋊C8)C2212yes—
23#10622684—28no—
24C2×#66867C2212yes—
25#10622167C2218yes—
26#10622162C2212yes—
27C22×D4×C11—22no—
28C22×D4×C11—22no—
29C22×D4×C11C2312yes—
30C23×C4×C11D412yes—
31C23×C4×C11C2311yescharacteristic
32C22×Dic22—22no—
33C11×#127—24no—
34C11×#121—28no—
35C11×#121—48no—
36C2×C11×C4⋊C4—22no—
37C2×C11×C4⋊C4C2312yes—
38C2×C11×C22⋊C4—24no—
39C2×C11×C22⋊C4—22no—
40C2×C42×C11—24no—
41C2×C42×C11D412yes—
42C2×C42×C11C2311yescharacteristic
43C2×C42×C11C2311yescharacteristic
44C2×C22⋊Dic11—22no—
45#66979—28no—
46C2×C4⋊Dic11—22no—
47C2×C4⋊Dic11C2314yes—
48#66977—216no—
49C2×Dic11⋊C4—24no—
50C2×C4×Dic11—22no—
51C22×C11⋊C8C2314yes—
52#66923—24no—
53#66923D418yescomplemented
54#66922—28no—
55C4×Dic22—216no—
56#66896—216no—
57C22⋊(C11⋊C8)—24no—
58#66867—24no—
59#25911—111nomaximal, Sylow
60C24×C11—22no—
61C24×C11C2×D411yescharacteristic
62C2×D4×C11—24no—
63C2×D4×C11—24no—
64C2×D4×C11—24no—
65C2×D4×C11—44no—
66C2×D4×C11—44no—
67C2×D4×C11—48no—
68C2×D4×C11—44no—
69C2×D4×C11—44no—
70C22×C4×C11—22no—
71C22×C4×C11—22no—
72C22×C4×C11—24no—
73C22×C4×C11—24no—
74C22×C4×C11—22no—
75C22×C4×C11—42no—
76C22×C4×C11C2×D412yes—
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11C2×D412yes—
79C22×C4×C11#4114yes—
80C22×C4×C11C2411yescharacteristic
81C22×Dic11—24no—
82C2×Dic22—28no—
83C2×Dic22—44no—
84C2×Dic22—44no—
85C11×C4⋊C4—24no—
86C11×C4⋊C4—44no—
87C11×C22⋊C4—44no—
88C11×C22⋊C4—48no—
89C42×C11—24no—
90C42×C11—22no—
91C42×C11C2×D414yes—
92C22⋊Dic11—28no—
93C4⋊Dic11—28no—
94C4⋊Dic11—24no—
95C4⋊Dic11C2×D418yes—
96Dic11⋊C4—216no—
97C4×Dic11—28no—
98C2×C11⋊C8—24no—
99C2×C11⋊C8—24no—
100C2×C11⋊C8—24no—
101C2×#533—111no—
102C2×#490—112no—
103#2856D1111yescharacteristic
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—42no—
113C23×C11—42no—
114C23×C11—42no—
115C23×C11—44no—
116C23×C11—44no—
117C23×C11#12412yes—
118C23×C11C22×D411yescharacteristic
119D4×C11—48no—
120D4×C11—88no—
121D4×C11—88no—
122C2×C4×C11—21no—
123C2×C4×C11—22no—
124C2×C4×C11—21no—
125C2×C4×C11—22no—
126C2×C4×C11—22no—
127C2×C4×C11—22no—
128C2×C4×C11—28no—
129C2×C4×C11—48no—
130C2×C4×C11—42no—
131C2×C4×C11—44no—
132C2×C4×C11#12014yes—
133C2×C4×C11#12412yes—
134C2×C4×C11AGL(1,ℤ/8)14yes—
135C2×C4×C11C22×D412yes—
136C2×C4×C11C2×#4112yes—
137C2×C4×C112−1+412yes—
138C2×Dic11—28no—
139C2×Dic11—44no—
140C2×Dic11—44no—
141Dic22—416no—
142C11⋊C8—44no—
143#533—228no—
144C2×C4⋊Q8—112no—
145C2×#127C2×D1111yescharacteristic
146C2×#125—112no—
147C2×C22⋊Q8—222no—
148C2×#121—22no—
149C2×#121C2×D1112yes—
150C2×C4×Q8—222no—
151C2×#117—112no—
152C22×C42C2×D1111yescharacteristic
153#490—228no—
154C2×#102—118no—
155C2×C22⋊C8—112no—
156C2×#97—112no—
157#390—22no—
158#390C2×D1112yes—
159#384C2×D1111yescharacteristic
160#340—118no—
161#336—112no—
162C22×C11—22no—
163C22×C11—22no—
164C22×C11—22no—
165C22×C11—42no—
166C22×C11—42no—
167C22×C11—82no—
168C22×C11—82no—
169C22×C11—82no—
170C22×C11—84no—
171C22×C11—84no—
172C22×C11C2×#12011yescharacteristic
173C22×C11C2×#12411yescharacteristic
174C22×C11#53611yescharacteristic
175C22×C11C2×AGL(1,ℤ/8)12yes—
176C22×C11#57512yes—
177C4×C11—22no—
178C4×C11—24no—
179C4×C11—24no—
180C4×C11—82no—
181C4×C11#54814yes—
182Dic11—48no—
183C22×Q8—222no—
184C22×D4—22no—
185C22×D4—22no—
186C22×D4C22×D1112yes—
187C23×C4C22⋊D1112yes—
188C23×C4C22×D1111yescharacteristic
189C22×C8—114no—
190C4⋊Q8—228no—
191#127—24no—
192#125—118no—
193#125—224no—
194C22⋊Q8—2216no—
195#121—28no—
196#121—48no—
197C4×Q8—2216no—
198#117—228no—
199C2×C4⋊C4—22no—
200C2×C4⋊C4—114no—
201C2×C4⋊C4—224no—
202C2×C4⋊C4—222no—
203C2×C4⋊C4C22×D1112yes—
204C2×C22⋊C4—24no—
205C2×C22⋊C4—22no—
206C2×C22⋊C4—222no—
207C2×C42—24no—
208C2×C42—222no—
209C2×C42C22⋊D1112yes—
210C2×C42C22×D1111yescharacteristic
211C2×C42C22×D1111yescharacteristic
212#102—2216no—
213C22⋊C8—224no—
214#97—224no—
215C2×C11—42no—
216C2×C11—162no—
217C2×C11#243611yescharacteristic
218C2×C11#300612yes—
219C2×C11#313511yescharacteristic
220C2×C11#313811yescharacteristic
221C2×C11#323512yes—
222C24—22no—
223C24C2×C22⋊D1111yescharacteristic
224C2×Q8—228no—
225C2×Q8—444no—
226C2×Q8—444no—
227C2×D4—24no—
228C2×D4—24no—
229C2×D4—24no—
230C2×D4—44no—
231C2×D4—44no—
232C2×D4—48no—
233C2×D4—44no—
234C2×D4—44no—
235C22×C4—22no—
236C22×C4—22no—
237C22×C4—24no—
238C22×C4—24no—
239C22×C4—22no—
240C22×C4—42no—
241C22×C4—224no—
242C22×C4#434114yes—
243C22×C4C2×C22⋊D1112yes—
244C22×C4C2×C22⋊D1111yescharacteristic
245C22×C4C2×C22⋊D1112yes—
246C22×C4C23×D1111yescharacteristic
247C2×C8—224no—
248C2×C8—224no—
249C2×C8—224no—
250C4⋊C4—24no—
251C4⋊C4—44no—
252C4⋊C4—118no—
253C4⋊C4—228no—
254C4⋊C4—2216no—
255C4⋊C4—224no—
256C22⋊C4—48no—
257C22⋊C4—44no—
258C22⋊C4—228no—
259C42—24no—
260C42—22no—
261C42—228no—
262C42D4×D1114yes—
263C11#2591111yescharacteristic, complemented, Sylow
264C23—22no—
265C23—21no—
266C23—22no—
267C23—21no—
268C23—44no—
269C23—42no—
270C23—42no—
271C23—44no—
272C23—42no—
273C23#6698912yes—
274C23C22×C22⋊D1111yescharacteristic
275Q8—4416no—
276D4—48no—
277D4—88no—
278D4—88no—
279C2×C4—22no—
280C2×C4—21no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—21no—
285C2×C4—28no—
286C2×C4—48no—
287C2×C4—44no—
288C2×C4—42no—
289C2×C4—228no—
290C2×C4—444no—
291C2×C4—444no—
292C2×C4#6698514yes—
293C2×C4#6698912yes—
294C2×C4#6699014yes—
295C2×C4C2×D4×D1112yes—
296C2×C4C2×#434112yes—
297C2×C4#6704312yes—
298C8—444no—
299C22—22no—
300C22—22no—
301C22—22no—
302C22—42no—
303C22—42no—
304C22—84no—
305C22—84no—
306C22—82no—
307C22—82no—
308C22—82no—
309C22C2×#6698512yes—
310C22C2×#6698911yescharacteristic
311C22C2×#6699011yescharacteristic
312C22#1062335312yes—
313C22#1062335611yescharacteristic
314C4—24no—
315C4—24no—
316C4—22no—
317C4—82no—
318C4—448no—
319C4#1062312914yes—
320C2—42no—
321C2—162no—
322C2#1307227511yescharacteristic
323C2#1307786612yes—
324C2#1307896111yescharacteristic
325C2#1307899011yescharacteristic
326C2#1307981012yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC11×#2856C2
socleC23×C11C22×D4
hypercenter#2856D11
hypocenterC11#25911
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2856

Complements

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

NH ≅ G/Ntype
1. C2×#10623001C2semidirect
2. C2×#10622684C2semidirect
3. #13069752C2semidirect
4. #13069584C2semidirect
5. #13068939C2semidirect
6. #13068378C2semidirect
53. #66923D4semidirect
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×#106226842
#130697522
#130695842
#130689392
#130683782
C11×#28562
#2591111