Finite Group Databasebeta

← #14666203

Subgroups — #14666203

Order 2816.

484 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 59 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#13076662C211yesmaximal, characteristic, complemented
2#13067551C212yesmaximal, complemented
3#13066618C212yesmaximal, complemented
4#13066560C211yesmaximal, characteristic, complemented
5C11×#2040C211yesmaximal, characteristic, complemented
6C11×#537C2211yescharacteristic
7C2×#66928—21no—
8C2×C11×#104—21no—
9C11×#417—21no—
10C11×#382C2211yescharacteristic
11#10622649—22no—
12#10622604—21no—
13#10622604C2212yes—
14#10622286—22no—
15#10622284—22no—
16C11×#343C2211yescharacteristic
17#10622175—22no—
18#10622166C2212yes—
19C2×C11×#41—21no—
20C22×D44—21no—
21C22×D44—21no—
22C22×D44D412yes—
23C22×Dic22—21no—
24C2×C11×M16—21no—
25C11×C22⋊Q8—41no—
26C11×#121—22no—
27C11×#121—41no—
28C2×C11×C4⋊C4D411yescharacteristic
29C2×C11×C4⋊C4C2311yescharacteristic
30C2×C42×C11D411yescharacteristic
31C2×#4323—42no—
32C2×(C2×D11)⋊C4—22no—
33C2×(C2×D11)⋊C4—22no—
34C2×(C2×D11)⋊C4—22no—
35C2×(C2×D11)⋊C4—22no—
36#66928—42no—
37#66928—42no—
38C11×#104—42no—
39C11×#103—41no—
40C11×#102—41no—
41C11×#95—22no—
42C11⋊#95—21no—
43C11⋊#95D412yes—
44C22⋊(C11⋊C8)—22no—
45#66873—42no—
46#12156—111nomaximal, Sylow
47C23×D11—22no—
48C11×#41—41no—
49C11×#41—41no—
50C11×#41—41no—
51C11×#41—41no—
52C2×Q8×C11—21no—
53C2×D4×C11—21no—
54C2×D4×C11—22no—
55C2×D4×C11—41no—
56C22×C4×C11—21no—
57C22×C4×C11—21no—
58C22×C4×C11—41no—
59C22×C4×C11C2×D411yescharacteristic
60C22×C4×C11C2×D412yes—
61C22×Dic11—22no—
62C2×D44—42no—
63C2×D44—42no—
64C2×D44—82no—
65C2×D44—81no—
66C2×D44—81no—
67C2×D44—82no—
68C2×D44—81no—
69C2×Dic22—42no—
70C2×Dic22—81no—
71C2×Dic22—81no—
72C11×M16—41no—
73C11×M16—41no—
74C2×C8×C11—41no—
75C11×C4⋊C4—22no—
76C11×C4⋊C4—41no—
77C11×C4⋊C4—41no—
78C11×C22⋊C4—42no—
79C42×C11—21no—
80C42×C11D812yescomplemented
81#4323—84no—
82(C2×D11)⋊C4—44no—
83(C2×D11)⋊C4—42no—
84(C2×D11)⋊C4—42no—
85(C2×D11)⋊C4—82no—
86(C2×D11)⋊C4—82no—
87C2×C11⋊C8—42no—
88#2819—111no—
89#2040D1111yescharacteristic, complemented
90#1598—112no—
91#1345—112no—
92#1324—111no—
93C23×C11—41no—
94C23×C11#12011yescharacteristic
95C22×D11—42no—
96C22×D11—42no—
97C22×D11—42no—
98C22×D11—42no—
99C22×D11—42no—
100C22×D11—42no—
101C22×D11—42no—
102Q8×C11—41no—
103Q8×C11—41no—
104D4×C11—41no—
105D4×C11—41no—
106D4×C11—82no—
107D4×C11—81no—
108D4×C11—81no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—22no—
112C2×C4×C11—22no—
113C2×C4×C11—41no—
114C2×C4×C11—41no—
115C2×C4×C11—42no—
116C2×C4×C11—42no—
117C2×C4×C11—41no—
118C2×C4×C11—41no—
119C2×C4×C11—81no—
120C2×C4×C11—81no—
121C2×C4×C11C2×D811yescharacteristic
122C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
123C2×Dic11—42no—
124C2×Dic11—42no—
125C2×Dic11—42no—
126D44—44no—
127D44—82no—
128D44—84no—
129D44—84no—
130Dic22—84no—
131C8×C11—81no—
132C11⋊C8—82no—
133#537C2×D1111yescharacteristic
134C2×#124—221no—
135#447—222no—
136C2×#104—21no—
137#417—21no—
138#394—112no—
139#394—221no—
140#393—222no—
141#392—222no—
142#382C2×D1111yescharacteristic
143#343C2×D1111yescharacteristic
144#327—222no—
145#324—112no—
146C22×C11—21no—
147C22×C11—21no—
148C22×C11—81no—
149C22×C11—81no—
150C22×C11—81no—
151C22×C11#44711yescharacteristic
152C22×C11#45411yescharacteristic
153C22×C11B(4,𝔽2)11yescharacteristic
154C2×D11—82no—
155C2×D11—82no—
156C2×D11—82no—
157C2×D11—82no—
158C2×D11—82no—
159C2×D11—82no—
160C2×D11—82no—
161C4×C11—21no—
162C4×C11—21no—
163C4×C11—42no—
164C4×C11—42no—
165C4×C11—81no—
166C4×C11—81no—
167Dic11—82no—
168C2×#41—21no—
169C22×Q8—221no—
170C22×D4—112no—
171C22×D4—221no—
172C22×D4—221no—
173C2×D8—442no—
174C2×M16—21no—
175#124—442no—
176#124—442no—
177C22⋊Q8—41no—
178#121—22no—
179#121—41no—
180C2×C4⋊C4C22⋊D1111yescharacteristic
181C2×C4⋊C4C22×D1111yescharacteristic
182C2×C22⋊C4—222no—
183C2×C22⋊C4—222no—
184C2×C22⋊C4—222no—
185C2×C22⋊C4—222no—
186C2×C42C22⋊D1111yescharacteristic
187#104—42no—
188#103—41no—
189#102—41no—
190#102—442no—
191C22⋊C8—222no—
192#95—22no—
193#95—112no—
194#95—221no—
195C2×C11—21no—
196C2×C11—21no—
197C2×C11—161no—
198C2×C11#159811yescharacteristic
199C2×C11#219911yescharacteristic
200C2×C11#220211yescharacteristic
201D11—162no—
202C24—222no—
203#41—41no—
204#41—41no—
205#41—41no—
206#41—41no—
207C2×Q8—21no—
208C2×Q8—442no—
209C2×Q8—881no—
210C2×Q8—881no—
211C2×D4—21no—
212C2×D4—22no—
213C2×D4—41no—
214C2×D4—442no—
215C2×D4—442no—
216C2×D4—882no—
217C2×D4—881no—
218C2×D4—881no—
219C2×D4—882no—
220C2×D4—881no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—41no—
224C22×C4—222no—
225C22×C4D4×D1112yes—
226C22×C4C2×C22⋊D1111yescharacteristic
227D8—884no—
228M16—41no—
229M16—41no—
230C2×C8—41no—
231C2×C8—442no—
232C4⋊C4—22no—
233C4⋊C4—41no—
234C4⋊C4—41no—
235C22⋊C4—42no—
236C22⋊C4—444no—
237C22⋊C4—442no—
238C22⋊C4—442no—
239C22⋊C4—882no—
240C22⋊C4—882no—
241C42—21no—
242C42#432312yescomplemented
243C11#1215611yescharacteristic, complemented, Sylow
244C23—41no—
245C23—442no—
246C23—442no—
247C23—442no—
248C23—442no—
249C23—442no—
250C23—442no—
251C23—442no—
252C23#6699011yescharacteristic
253Q8—41no—
254Q8—41no—
255Q8—884no—
256D4—41no—
257D4—41no—
258D4—82no—
259D4—81no—
260D4—81no—
261D4—444no—
262D4—882no—
263D4—884no—
264D4—884no—
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—41no—
274C2×C4—41no—
275C2×C4—81no—
276C2×C4—81no—
277C2×C4—442no—
278C2×C4—442no—
279C2×C4—442no—
280C2×C4C2×#432311yescharacteristic
281C2×C4#6700211yescharacteristic
282C8—81no—
283C8—882no—
284C22—21no—
285C22—21no—
286C22—81no—
287C22—81no—
288C22—81no—
289C22—882no—
290C22—882no—
291C22—882no—
292C22—882no—
293C22—882no—
294C22—882no—
295C22—882no—
296C22#1062264511yescharacteristic
297C22#1062264911yescharacteristic
298C22#1062267511yescharacteristic
299C4—21no—
300C4—21no—
301C4—42no—
302C4—42no—
303C4—81no—
304C4—81no—
305C4—882no—
306C2—21no—
307C2—21no—
308C2—161no—
309C2—1762no—
310C2#1306755011yescharacteristic
311C2#1307061611yescharacteristic
312C2#1307063211yescharacteristic
subgroupG/H
centerC22#10622645
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
FittingC11×#2040C2
socleC22×C11B(4,𝔽2)
hypercenter#2040D11
hypocenterC11#12156
LCSG ▷ C2×C11×C4⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2040

Complements

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

NH ≅ G/Ntype
1. #13076662C2semidirect
2. #13067551C2semidirect
3. #13066618C2semidirect
4. #13066560C2semidirect
5. C11×#2040C2semidirect
80. C42×C11D8semidirect
89. #2040D11semidirect
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
#130766622
#130675512
#130666182
#130665602
C11×#20402
#1215611