Finite Group Databasebeta

← #14657243

Subgroups — #14657243

Order 2816.

534 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 534 conjugacy classes of subgroups — too many to draw. Only its 91 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
2#13069430C212yesmaximal, complemented
3C2×#10622102C212yesmaximal, complemented
4#13066497C211yesmaximal, characteristic, complemented
5C11×#1847C211yesmaximal, characteristic, complemented
6C2×#66928C2212yes—
7C2×C11×#107—21no—
8C2×C11×#106—21no—
9C2×C11×#97C2211yescharacteristic
10C11×#384C2211yescharacteristic
11C11×#382C2211yescharacteristic
12#10622604—21no—
13#10622604—21no—
14C2×#66874—22no—
15C2×#66873—22no—
16C2×#66867C2212yes—
17#10622286—22no—
18#10622284—22no—
19#10622102—24no—
20C22×D44—21no—
21C22×D44—21no—
22C22×D44D412yes—
23C22×Dic22D412yes—
24C22×C8×C11—21no—
25C2×C11×C4⋊C4—22no—
26C2×C11×C4⋊C4—21no—
27C2×C11×C4⋊C4D411yescharacteristic
28C2×C11×C4⋊C4D411yescharacteristic
29C2×C42×C11C2311yescharacteristic
30C2×(C2×D11)⋊C4—22no—
31C2×(C2×D11)⋊C4—22no—
32C2×(C2×D11)⋊C4—22no—
33C2×(C2×D11)⋊C4—22no—
34C22×C11⋊C8—22no—
35#66928—22no—
36#66928—22no—
37#66928—22no—
38#66928—22no—
39C11×#107—42no—
40C11×#106—42no—
41C11×#97—21no—
42C11×#97D412yescomplemented
43C11×#95—22no—
44C11⋊#95—21no—
45C11⋊#95—21no—
46#66874—44no—
47#66873—44no—
48#66867—22no—
49#66867—22no—
50#10424—111nomaximal, Sylow
51C23×D11—22no—
52C22×C4×C11—21no—
53C22×C4×C11—21no—
54C22×C4×C11—41no—
55C22×C4×C11C2×D412yes—
56C22×C4×C11C2×D411yescharacteristic
57C22×Dic11—22no—
58C2×D44—22no—
59C2×D44—22no—
60C2×D44—42no—
61C2×D44—42no—
62C2×D44—82no—
63C2×D44—81no—
64C2×D44—81no—
65C2×D44—82no—
66C2×Dic22—22no—
67C2×Dic22—22no—
68C2×Dic22—42no—
69C2×Dic22—42no—
70C2×C8×C11—22no—
71C2×C8×C11—22no—
72C2×C8×C11—22no—
73C11×C4⋊C4—41no—
74C11×C4⋊C4—41no—
75C11×C4⋊C4—42no—
76C11×C4⋊C4—42no—
77C11×C4⋊C4—41no—
78C11×C4⋊C4—41no—
79C42×C11C2×D411yescharacteristic
80C42×C11#4111yescharacteristic
81C42×C11#4112yes—
82(C2×D11)⋊C4—42no—
83(C2×D11)⋊C4—42no—
84(C2×D11)⋊C4—42no—
85(C2×D11)⋊C4—42no—
86(C2×D11)⋊C4—82no—
87(C2×D11)⋊C4—82no—
88C2×C11⋊C8—24no—
89C2×C11⋊C8—42no—
90C2×C11⋊C8—42no—
91#2819—111no—
92#1959—112no—
93#1847D1111yescharacteristic, complemented
94C2×#329—112no—
95#1295—111no—
96C23×C11#12011yescharacteristic
97C22×D11—42no—
98C22×D11—42no—
99C22×D11—42no—
100C22×D11—42no—
101C22×D11—42no—
102C22×D11—42no—
103C22×D11—42no—
104C2×C4×C11—22no—
105C2×C4×C11—21no—
106C2×C4×C11—22no—
107C2×C4×C11—21no—
108C2×C4×C11—42no—
109C2×C4×C11—41no—
110C2×C4×C11—41no—
111C2×C4×C11—42no—
112C2×C4×C11—82no—
113C2×C4×C11—81no—
114C2×C4×C11#12112yes—
115C2×C4×C11#12111yescharacteristic
116C2×C4×C11#12312yes—
117C2×C4×C11#12411yescharacteristic
118C2×Dic11—42no—
119C2×Dic11—42no—
120C2×Dic11—42no—
121D44—44no—
122D44—82no—
123D44—84no—
124D44—84no—
125Dic22—44no—
126Dic22—82no—
127C8×C11—24no—
128C11⋊C8—44no—
129C2×#124—112no—
130C2×#107—21no—
131C2×#106—21no—
132C2×#103—222no—
133C2×#102—222no—
134C2×#97—112no—
135C2×#97C2×D1111yescharacteristic
136#394—221no—
137#394—221no—
138#393—222no—
139#392—222no—
140#384C2×D1111yescharacteristic
141#382C2×D1111yescharacteristic
142#329—224no—
143C22×C11#39411yescharacteristic
144C22×C11#45312yes—
145C22×C11#45311yescharacteristic
146C22×C11#45512yes—
147C22×C11#45611yescharacteristic
148C2×D11—82no—
149C2×D11—82no—
150C2×D11—82no—
151C2×D11—82no—
152C2×D11—82no—
153C2×D11—82no—
154C2×D11—82no—
155C4×C11—22no—
156C4×C11—22no—
157C4×C11—21no—
158C4×C11—21no—
159C4×C11—81no—
160C4×C11—81no—
161C4×C11—161no—
162Dic11—82no—
163C22×Q8—112no—
164C22×D4—112no—
165C22×D4—221no—
166C22×D4—221no—
167C22×C8—21no—
168C22×C8—222no—
169#124—222no—
170#124—222no—
171#124—222no—
172#124—222no—
173C2×C4⋊C4—22no—
174C2×C4⋊C4—21no—
175C2×C4⋊C4C22⋊D1111yescharacteristic
176C2×C4⋊C4C22⋊D1111yescharacteristic
177C2×C22⋊C4—222no—
178C2×C22⋊C4—222no—
179C2×C22⋊C4—222no—
180C2×C22⋊C4—222no—
181C2×C42C22×D1111yescharacteristic
182#107—42no—
183#106—42no—
184#103—444no—
185#102—444no—
186#97—21no—
187#97—222no—
188#97—222no—
189#97D4412yescomplemented
190#95—22no—
191#95—221no—
192#95—221no—
193C2×C11#165511yescharacteristic
194C2×C11#165911yescharacteristic
195C2×C11#166112yes—
196C2×C11#203712yes—
197C2×C11#203911yescharacteristic
198D11—162no—
199C24—222no—
200C2×Q8—222no—
201C2×Q8—222no—
202C2×Q8—442no—
203C2×Q8—442no—
204C2×D4—222no—
205C2×D4—222no—
206C2×D4—442no—
207C2×D4—442no—
208C2×D4—882no—
209C2×D4—882no—
210C2×D4—881no—
211C2×D4—881no—
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—41no—
215C22×C4—222no—
216C22×C4D4×D1112yes—
217C22×C4C2×C22⋊D1111yescharacteristic
218C2×C8—22no—
219C2×C8—22no—
220C2×C8—22no—
221C2×C8—224no—
222C2×C8—442no—
223C2×C8—442no—
224C4⋊C4—41no—
225C4⋊C4—41no—
226C4⋊C4—42no—
227C4⋊C4—42no—
228C4⋊C4—41no—
229C4⋊C4—41no—
230C22⋊C4—442no—
231C22⋊C4—442no—
232C22⋊C4—442no—
233C22⋊C4—442no—
234C22⋊C4—882no—
235C22⋊C4—882no—
236C42C2×D4411yescharacteristic
237C42#433911yescharacteristic
238C42#434312yes—
239C11#1042411yescharacteristic, complemented, Sylow
240C23—442no—
241C23—442no—
242C23—442no—
243C23—442no—
244C23—442no—
245C23—442no—
246C23—442no—
247C23#6699011yescharacteristic
248Q8—444no—
249Q8—882no—
250D4—444no—
251D4—882no—
252D4—884no—
253D4—884no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—82no—
263C2×C4—81no—
264C2×C4—442no—
265C2×C4—442no—
266C2×C4—442no—
267C2×C4#6694712yes—
268C2×C4#6694812yes—
269C2×C4#6698311yescharacteristic
270C2×C4#6700011yescharacteristic
271C8—24no—
272C8—444no—
273C22—882no—
274C22—882no—
275C22—882no—
276C22—882no—
277C22—882no—
278C22—882no—
279C22—882no—
280C22#1062260411yescharacteristic
281C22#1062269011yescharacteristic
282C22#1062270811yescharacteristic
283C22#1062281112yes—
284C22#1062281512yes—
285C4—22no—
286C4—22no—
287C4—21no—
288C4—21no—
289C4—81no—
290C4—81no—
291C4—161no—
292C4—882no—
293C2—1762no—
294C2#1306790411yescharacteristic
295C2#1306792011yescharacteristic
296C2#1306793112yes—
297C2#1306982812yes—
298C2#1306984011yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1847C2
socleC23×C11#120
prime radical#13076662C2
hypercenter#1847D11
hypocenterC11#10424
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1847

Complements

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

NH ≅ G/Ntype
2. #13069430C2semidirect
3. C2×#10622102C2semidirect
4. #13066497C2semidirect
5. C11×#1847C2semidirect
42. C11×#97D4semidirect
93. #1847D11semidirect
189. #97D44semidirect
239. C11#10424semidirect

Maximal subgroups

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

subgroupindex
#130766622
#130694302
C2×#106221022
#130664972
C11×#18472
#1042411