Finite Group Databasebeta

← #14666180

Subgroups — #14666180

Order 2816.

588 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 588 conjugacy classes of subgroups — too many to draw. Only its 63 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#13069840C211yesmaximal, characteristic, complemented
2#13067550C212yesmaximal, complemented
3#13066619C212yesmaximal, complemented
4#13066562C211yesmaximal, characteristic, complemented
5C11×#2537C211yesmaximal, characteristic, complemented
6C2×C11×#121—22no—
7C2×C4×D4×C11—21no—
8#10623041C2211yescharacteristic
9C11×#394—21no—
10C11×#394C2212yes—
11C11×#384C2211yescharacteristic
12C11×#380—22no—
13#10622830—22no—
14#10622579—21no—
15C2×#66869—21no—
16#10622168C2211yescharacteristic
17#10622166C2212yes—
18#10622089—22no—
19C22×D4×C11—21no—
20C22×D4×C11—21no—
21C22×D4×C11D412yes—
22C23×C4×C11—22no—
23C2×#4339—21no—
24C11×#121—48no—
25C4×D4×C11—42no—
26C4×D4×C11—42no—
27C2×C11×C4⋊C4—21no—
28C2×C11×C4⋊C4—22no—
29C2×C11×C4⋊C4D411yescharacteristic
30C2×C11×C4⋊C4C2311yescharacteristic
31C2×C11×C22⋊C4—22no—
32C2×C11×C22⋊C4—22no—
33C2×C11×C22⋊C4—22no—
34C2×C42×C11D411yescharacteristic
35C2×#4323—42no—
36#66983—22no—
37C2×#4318—21no—
38#66950—41no—
39#66948—41no—
40C11×#95—21no—
41C11×#95D412yes—
42#66896—42no—
43C22⋊(C11⋊C8)—22no—
44#66874—41no—
45#66873—41no—
46#66869—42no—
47#12152—111nomaximal, Sylow
48C24×C11—22no—
49C2×D4×C11—24no—
50C2×D4×C11—42no—
51C2×D4×C11—42no—
52C2×D4×C11—42no—
53C2×D4×C11—44no—
54C2×D4×C11—44no—
55C2×D4×C11—81no—
56C22×C4×C11—21no—
57C22×C4×C11—22no—
58C22×C4×C11—21no—
59C22×C4×C11—44no—
60C22×C4×C11—44no—
61C22×C4×C11—44no—
62C22×C4×C11C2×D411yescharacteristic
63C22×C4×C11C2×D412yes—
64C2×C22⋊D11—41no—
65#4339—41no—
66#4339—41no—
67#4339—41no—
68#4339—41no—
69C2×D44—21no—
70C2×D44—22no—
71C2×C4×D11—41no—
72C2×Dic22—21no—
73C11×C4⋊C4—41no—
74C11×C4⋊C4—42no—
75C11×C4⋊C4—44no—
76C11×C4⋊C4—41no—
77C11×C22⋊C4—44no—
78C11×C22⋊C4—44no—
79C11×C22⋊C4—42no—
80C11×C22⋊C4—42no—
81C42×C11—21no—
82C42×C11D812yescomplemented
83#4323—84no—
84(C2×D11)⋊C4—42no—
85C4⋊Dic11—22no—
86#4318—41no—
87#4318—41no—
88C2×C11⋊C8—41no—
89C2×C11⋊C8—42no—
90#2537D1111yescharacteristic, complemented
91#2039—111no—
92#1598—112no—
93#1345—112no—
94#1325—111no—
95C23×C11—24no—
96C23×C11—42no—
97C23×C11—42no—
98C23×C11—42no—
99C23×C11—42no—
100C23×C11—42no—
101C23×C11—42no—
102C23×C11#12011yescharacteristic
103C22×D11—41no—
104D4×C11—48no—
105D4×C11—44no—
106D4×C11—82no—
107D4×C11—84no—
108C2×C4×C11—22no—
109C2×C4×C11—22no—
110C2×C4×C11—22no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—22no—
114C2×C4×C11—42no—
115C2×C4×C11—42no—
116C2×C4×C11—42no—
117C2×C4×C11—42no—
118C2×C4×C11—42no—
119C2×C4×C11—41no—
120C2×C4×C11—88no—
121C2×C4×C11C2×D811yescharacteristic
122C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
123C22⋊D11—81no—
124C22⋊D11—81no—
125C2×Dic11—41no—
126D44—41no—
127D44—41no—
128D44—82no—
129C4×D11—81no—
130C4×D11—81no—
131Dic22—41no—
132Dic22—41no—
133C11⋊C8—81no—
134C11⋊C8—82no—
135#537—111no—
136C2×#121—22no—
137C2×C4×D4—21no—
138#447—222no—
139C2×#104—221no—
140#417—221no—
141#394—21no—
142#394C2×D1112yes—
143#384C2×D1111yescharacteristic
144#380—22no—
145#343—111no—
146#327—222no—
147#324—112no—
148C22×C11—21no—
149C22×C11—21no—
150C22×C11—44no—
151C22×C11—44no—
152C22×C11—44no—
153C22×C11—82no—
154C22×C11—82no—
155C22×C11—82no—
156C22×C11—82no—
157C22×C11#44711yescharacteristic
158C22×C11#45411yescharacteristic
159C22×C11B(4,𝔽2)11yescharacteristic
160C2×D11—81no—
161C2×D11—81no—
162C2×D11—81no—
163C4×C11—24no—
164C4×C11—21no—
165C4×C11—21no—
166C4×C11—42no—
167C4×C11—82no—
168C4×C11—81no—
169Dic11—81no—
170C2×#41—221no—
171C22×D4—21no—
172C22×D4—21no—
173C22×D4C22⋊D1112yes—
174C23×C4—22no—
175C2×D8—442no—
176C2×M16—221no—
177C22⋊Q8—441no—
178#121—48no—
179#121—222no—
180#121—441no—
181C4×D4—42no—
182C4×D4—42no—
183C2×C4⋊C4—21no—
184C2×C4⋊C4—22no—
185C2×C4⋊C4C22⋊D1111yescharacteristic
186C2×C4⋊C4C22×D1111yescharacteristic
187C2×C22⋊C4—22no—
188C2×C22⋊C4—22no—
189C2×C22⋊C4—22no—
190C2×C42C22⋊D1111yescharacteristic
191#104—442no—
192#103—441no—
193#102—441no—
194#102—442no—
195C22⋊C8—222no—
196#95—21no—
197#95C22⋊D1112yes—
198C2×C11—21no—
199C2×C11—21no—
200C2×C11—84no—
201C2×C11#159811yescharacteristic
202C2×C11#219611yescharacteristic
203C2×C11#220411yescharacteristic
204D11—161no—
205C24—22no—
206#41—441no—
207#41—441no—
208#41—441no—
209#41—441no—
210C2×Q8—221no—
211C2×D4—24no—
212C2×D4—42no—
213C2×D4—42no—
214C2×D4—42no—
215C2×D4—44no—
216C2×D4—44no—
217C2×D4—81no—
218C2×D4—221no—
219C2×D4—222no—
220C2×D4—441no—
221C22×C4—21no—
222C22×C4—22no—
223C22×C4—21no—
224C22×C4—44no—
225C22×C4—44no—
226C22×C4—44no—
227C22×C4—441no—
228C22×C4C2×C22⋊D1111yescharacteristic
229C22×C4C2×C22⋊D1112yes—
230D8—884no—
231M16—441no—
232M16—441no—
233C2×C8—442no—
234C2×C8—441no—
235C4⋊C4—41no—
236C4⋊C4—41no—
237C4⋊C4—42no—
238C4⋊C4—44no—
239C4⋊C4—222no—
240C22⋊C4—44no—
241C22⋊C4—44no—
242C22⋊C4—42no—
243C22⋊C4—42no—
244C22⋊C4—442no—
245C42—21no—
246C42#432312yescomplemented
247C11#1215211yescharacteristic, complemented, Sylow
248C23—24no—
249C23—42no—
250C23—42no—
251C23—42no—
252C23—42no—
253C23—42no—
254C23—42no—
255C23—441no—
256C23#6700611yescharacteristic
257Q8—441no—
258Q8—441no—
259D4—48no—
260D4—44no—
261D4—82no—
262D4—84no—
263D4—441no—
264D4—441no—
265D4—882no—
266D4—881no—
267D4—881no—
268C2×C4—22no—
269C2×C4—22no—
270C2×C4—22no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—22no—
274C2×C4—42no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—41no—
280C2×C4—88no—
281C2×C4—441no—
282C2×C4—881no—
283C2×C4—881no—
284C2×C4C2×#432311yescharacteristic
285C2×C4#6698511yescharacteristic
286C8—881no—
287C8—882no—
288C22—21no—
289C22—21no—
290C22—44no—
291C22—44no—
292C22—44no—
293C22—82no—
294C22—82no—
295C22—82no—
296C22—82no—
297C22—881no—
298C22—881no—
299C22—881no—
300C22#1062283011yescharacteristic
301C22#1062285711yescharacteristic
302C22#1062285811yescharacteristic
303C4—24no—
304C4—21no—
305C4—21no—
306C4—42no—
307C4—82no—
308C4—81no—
309C4—881no—
310C2—21no—
311C2—21no—
312C2—84no—
313C2—1761no—
314C2#1306755111yescharacteristic
315C2#1307060011yescharacteristic
316C2#1307064211yescharacteristic
subgroupG/H
centerC22#10622857
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
FittingC11×#2537C2
socleC22×C11B(4,𝔽2)
hypercenter#2537D11
hypocenterC11#12152
LCSG ▷ C2×C11×C4⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2537

Complements

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

NH ≅ G/Ntype
1. #13069840C2semidirect
2. #13067550C2semidirect
3. #13066619C2semidirect
4. #13066562C2semidirect
5. C11×#2537C2semidirect
82. C42×C11D8semidirect
90. #2537D11semidirect
246. C42#4323semidirect
247. C11#12152semidirect

Maximal subgroups

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

subgroupindex
#130698402
#130675502
#130666192
#130665622
C11×#25372
#1215211