Finite Group Databasebeta

← #14666204

Subgroups — #14666204

Order 2816.

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

normal subgroups only

This group has 484 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#13069845C211yesmaximal, characteristic, complemented
2#13067550C212yesmaximal, complemented
3#13066619C212yesmaximal, complemented
4#13066560C211yesmaximal, characteristic, complemented
5C11×#2819C211yesmaximal, characteristic, complemented
6C2×C11×#124—21no—
7#10623041C2211yescharacteristic
8C11×#394—21no—
9C11×#394C2212yes—
10C11×#393—22no—
11C11×#392—22no—
12C11×#382C2211yescharacteristic
13#10622830—22no—
14#10622579—21no—
15C2×#66869—21no—
16#10622168C2211yescharacteristic
17#10622166C2212yes—
18#10622089—22no—
19C22×Q8×C11—21no—
20C22×D4×C11—21no—
21C22×D4×C11—21no—
22C22×D4×C11D412yes—
23C2×#4339—21no—
24C11×#124—42no—
25C11×#124—42no—
26C2×C11×C4⋊C4D411yescharacteristic
27C2×C11×C4⋊C4C2311yescharacteristic
28C2×C11×C22⋊C4—22no—
29C2×C11×C22⋊C4—22no—
30C2×C11×C22⋊C4—22no—
31C2×C11×C22⋊C4—22no—
32C2×C42×C11D411yescharacteristic
33C2×#4323—42no—
34#66983—22no—
35C2×#4318—21no—
36#66950—41no—
37#66948—41no—
38C11×#95—21no—
39C11×#95—22no—
40C11×#95D412yes—
41#66896—42no—
42C22⋊(C11⋊C8)—22no—
43#66874—41no—
44#66873—41no—
45#66869—42no—
46#12156—111nomaximal, Sylow
47C24×C11—22no—
48C2×Q8×C11—42no—
49C2×Q8×C11—81no—
50C2×Q8×C11—81no—
51C2×D4×C11—42no—
52C2×D4×C11—42no—
53C2×D4×C11—82no—
54C2×D4×C11—81no—
55C2×D4×C11—81no—
56C2×D4×C11—82no—
57C2×D4×C11—81no—
58C22×C4×C11—21no—
59C22×C4×C11—21no—
60C22×C4×C11—22no—
61C22×C4×C11C2×D411yescharacteristic
62C22×C4×C11C2×D412yes—
63C2×C22⋊D11—41no—
64#4339—41no—
65#4339—41no—
66#4339—41no—
67#4339—41no—
68C2×D44—21no—
69C2×D44—22no—
70C2×C4×D11—41no—
71C2×Dic22—21no—
72C11×C4⋊C4—41no—
73C11×C4⋊C4—41no—
74C11×C22⋊C4—44no—
75C11×C22⋊C4—42no—
76C11×C22⋊C4—42no—
77C11×C22⋊C4—82no—
78C11×C22⋊C4—82no—
79C42×C11—21no—
80C42×C11D812yescomplemented
81#4323—84no—
82(C2×D11)⋊C4—42no—
83C4⋊Dic11—22no—
84#4318—41no—
85#4318—41no—
86C2×C11⋊C8—41no—
87C2×C11⋊C8—42no—
88#2819D1111yescharacteristic, complemented
89#2040—111no—
90#1598—112no—
91#1345—112no—
92#1324—111no—
93C23×C11—42no—
94C23×C11—42no—
95C23×C11—42no—
96C23×C11—42no—
97C23×C11—42no—
98C23×C11—42no—
99C23×C11—42no—
100C23×C11#12011yescharacteristic
101C22×D11—41no—
102Q8×C11—84no—
103D4×C11—44no—
104D4×C11—82no—
105D4×C11—84no—
106D4×C11—84no—
107C2×C4×C11—21no—
108C2×C4×C11—21no—
109C2×C4×C11—22no—
110C2×C4×C11—22no—
111C2×C4×C11—41no—
112C2×C4×C11—41no—
113C2×C4×C11—42no—
114C2×C4×C11—42no—
115C2×C4×C11—42no—
116C2×C4×C11—42no—
117C2×C4×C11—42no—
118C2×C4×C11—41no—
119C2×C4×C11C2×D811yescharacteristic
120C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
121C22⋊D11—81no—
122C22⋊D11—81no—
123C2×Dic11—41no—
124D44—41no—
125D44—41no—
126D44—82no—
127C4×D11—81no—
128C4×D11—81no—
129Dic22—41no—
130Dic22—41no—
131C11⋊C8—81no—
132C11⋊C8—82no—
133#537—111no—
134C2×#124—21no—
135#447—222no—
136C2×#104—221no—
137#417—221no—
138#394—21no—
139#394C2×D1112yes—
140#393—22no—
141#392—22no—
142#382C2×D1111yescharacteristic
143#343—111no—
144#327—222no—
145#324—112no—
146C22×C11—21no—
147C22×C11—21no—
148C22×C11—82no—
149C22×C11—82no—
150C22×C11—82no—
151C22×C11—82no—
152C22×C11—82no—
153C22×C11—82no—
154C22×C11—82no—
155C22×C11#44711yescharacteristic
156C22×C11#45411yescharacteristic
157C22×C11B(4,𝔽2)11yescharacteristic
158C2×D11—81no—
159C2×D11—81no—
160C2×D11—81no—
161C4×C11—21no—
162C4×C11—21no—
163C4×C11—42no—
164C4×C11—42no—
165C4×C11—82no—
166C4×C11—81no—
167Dic11—81no—
168C2×#41—221no—
169C22×Q8—21no—
170C22×D4—21no—
171C22×D4—21no—
172C22×D4C22⋊D1112yes—
173C2×D8—442no—
174C2×M16—221no—
175#124—42no—
176#124—42no—
177C22⋊Q8—441no—
178#121—222no—
179#121—441no—
180C2×C4⋊C4C22⋊D1111yescharacteristic
181C2×C4⋊C4C22×D1111yescharacteristic
182C2×C22⋊C4—22no—
183C2×C22⋊C4—22no—
184C2×C22⋊C4—22no—
185C2×C22⋊C4—22no—
186C2×C42C22⋊D1111yescharacteristic
187#104—442no—
188#103—441no—
189#102—441no—
190#102—442no—
191C22⋊C8—222no—
192#95—21no—
193#95—22no—
194#95C22⋊D1112yes—
195C2×C11—21no—
196C2×C11—21no—
197C2×C11—162no—
198C2×C11#159811yescharacteristic
199C2×C11#219911yescharacteristic
200C2×C11#220211yescharacteristic
201D11—161no—
202C24—22no—
203#41—441no—
204#41—441no—
205#41—441no—
206#41—441no—
207C2×Q8—42no—
208C2×Q8—81no—
209C2×Q8—81no—
210C2×Q8—221no—
211C2×D4—42no—
212C2×D4—42no—
213C2×D4—82no—
214C2×D4—81no—
215C2×D4—81no—
216C2×D4—82no—
217C2×D4—81no—
218C2×D4—221no—
219C2×D4—222no—
220C2×D4—441no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—22no—
224C22×C4—441no—
225C22×C4C2×C22⋊D1111yescharacteristic
226C22×C4C2×C22⋊D1112yes—
227D8—884no—
228M16—441no—
229M16—441no—
230C2×C8—442no—
231C2×C8—441no—
232C4⋊C4—41no—
233C4⋊C4—41no—
234C4⋊C4—222no—
235C22⋊C4—44no—
236C22⋊C4—42no—
237C22⋊C4—42no—
238C22⋊C4—82no—
239C22⋊C4—82no—
240C22⋊C4—442no—
241C42—21no—
242C42#432312yescomplemented
243C11#1215611yescharacteristic, complemented, Sylow
244C23—42no—
245C23—42no—
246C23—42no—
247C23—42no—
248C23—42no—
249C23—42no—
250C23—42no—
251C23—441no—
252C23#6700611yescharacteristic
253Q8—84no—
254Q8—441no—
255Q8—441no—
256D4—44no—
257D4—82no—
258D4—84no—
259D4—84no—
260D4—441no—
261D4—441no—
262D4—882no—
263D4—881no—
264D4—881no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—22no—
268C2×C4—22no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—42no—
272C2×C4—42no—
273C2×C4—42no—
274C2×C4—42no—
275C2×C4—42no—
276C2×C4—41no—
277C2×C4—441no—
278C2×C4—881no—
279C2×C4—881no—
280C2×C4C2×#432311yescharacteristic
281C2×C4#6698511yescharacteristic
282C8—881no—
283C8—882no—
284C22—21no—
285C22—21no—
286C22—82no—
287C22—82no—
288C22—82no—
289C22—82no—
290C22—82no—
291C22—82no—
292C22—82no—
293C22—881no—
294C22—881no—
295C22—881no—
296C22#1062283011yescharacteristic
297C22#1062285711yescharacteristic
298C22#1062285811yescharacteristic
299C4—21no—
300C4—21no—
301C4—42no—
302C4—42no—
303C4—82no—
304C4—81no—
305C4—881no—
306C2—21no—
307C2—21no—
308C2—162no—
309C2—1761no—
310C2#1306755111yescharacteristic
311C2#1307061711yescharacteristic
312C2#1307063311yescharacteristic
subgroupG/H
centerC22#10622857
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
FittingC11×#2819C2
socleC22×C11B(4,𝔽2)
hypercenter#2819D11
hypocenterC11#12156
LCSG ▷ C2×C11×C4⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2819

Complements

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

NH ≅ G/Ntype
1. #13069845C2semidirect
2. #13067550C2semidirect
3. #13066619C2semidirect
4. #13066560C2semidirect
5. C11×#2819C2semidirect
80. C42×C11D8semidirect
88. #2819D11semidirect
242. C42#4323semidirect
243. C11#12156semidirect

Maximal subgroups

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

subgroupindex
#130698452
#130675502
#130666192
#130665602
C11×#28192
#1215611