Finite Group Databasebeta

← #14657244

Subgroups — #14657244

Order 2816.

534 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 534 conjugacy classes of subgroups — too many to draw. Only its 89 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#13069432C212yesmaximal, complemented
3#13068785C211yesmaximal, characteristic, complemented
4C2×#10622102C212yesmaximal, complemented
5C11×#1295C211yesmaximal, characteristic, complemented
6C2×#66928C2212yes—
7C2×C11×#97C2212yes—
8C11×#382C2211yescharacteristic
9C2×#66885—22no—
10C2×#66880—22no—
11#10622604—21no—
12#10622604—21no—
13C2×#66872—21no—
14C2×#66871—21no—
15#10622548C2211yescharacteristic
16C2×#66867C2211yescharacteristic
17#10622286—22no—
18#10622284—22no—
19#10622102—24no—
20C22×D44—21no—
21C22×D44—21no—
22C22×D44D412yes—
23C22×Dic22D412yes—
24C22×C8×C11—22no—
25C2×C11×C4⋊C4D411yescharacteristic
26C2×C11×C4⋊C4D411yescharacteristic
27C2×C42×C11C2311yescharacteristic
28C2×(C2×D11)⋊C4—22no—
29C2×(C2×D11)⋊C4—22no—
30C2×(C2×D11)⋊C4—22no—
31C2×(C2×D11)⋊C4—22no—
32C2×C4⋊Dic11—22no—
33C2×C4⋊Dic11—21no—
34C22×C11⋊C8—21no—
35#66928—22no—
36#66928—22no—
37#66928—22no—
38#66928—22no—
39C11×#97—22no—
40C11×#97—22no—
41C11×#95—22no—
42C11⋊#95—21no—
43C11⋊#95—21no—
44#66885—44no—
45#66880—44no—
46#66872—42no—
47#66871—42no—
48#66867—21no—
49#66867D412yescomplemented
50#10424—111nomaximal, Sylow
51C23×D11—22no—
52C22×C4×C11—21no—
53C22×C4×C11—21no—
54C22×C4×C11C2×D412yes—
55C22×C4×C11C2×D411yescharacteristic
56C22×Dic11—22no—
57C22×Dic11—41no—
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—24no—
71C2×C8×C11—42no—
72C2×C8×C11—42no—
73C11×C4⋊C4—41no—
74C11×C4⋊C4—41no—
75C42×C11C2×D411yescharacteristic
76C42×C11#4111yescharacteristic
77C42×C11#4112yes—
78(C2×D11)⋊C4—42no—
79(C2×D11)⋊C4—42no—
80(C2×D11)⋊C4—42no—
81(C2×D11)⋊C4—42no—
82(C2×D11)⋊C4—82no—
83(C2×D11)⋊C4—82no—
84C4⋊Dic11—41no—
85C4⋊Dic11—41no—
86C4⋊Dic11—42no—
87C4⋊Dic11—42no—
88C2×C11⋊C8—22no—
89C2×C11⋊C8—22no—
90C2×C11⋊C8—22no—
91#2819—111no—
92#1959—112no—
93#1847—111no—
94C2×#329—112no—
95#1295D1111yescharacteristic, complemented
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—21no—
105C2×C4×C11—22no—
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#12112yes—
113C2×C4×C11#12111yescharacteristic
114C2×C4×C11#12312yes—
115C2×C4×C11#12411yescharacteristic
116C2×Dic11—42no—
117C2×Dic11—42no—
118C2×Dic11—42no—
119C2×Dic11—81no—
120C2×Dic11—82no—
121D44—44no—
122D44—82no—
123D44—84no—
124D44—84no—
125Dic22—44no—
126Dic22—82no—
127C8×C11—44no—
128C11⋊C8—24no—
129C2×#124—112no—
130C2×#107—221no—
131C2×#106—221no—
132C2×#103—222no—
133C2×#102—222no—
134C2×#97—111no—
135C2×#97C2×D1112yes—
136#394—221no—
137#394—221no—
138#393—222no—
139#392—222no—
140#384—111no—
141#382C2×D1111yescharacteristic
142#329—224no—
143C22×C11#39411yescharacteristic
144C22×C11#45311yescharacteristic
145C22×C11#45312yes—
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—
161Dic11—82no—
162Dic11—161no—
163C22×Q8—112no—
164C22×D4—112no—
165C22×D4—221no—
166C22×D4—221no—
167C22×C8—22no—
168C22×C8—221no—
169#124—222no—
170#124—222no—
171#124—222no—
172#124—222no—
173C2×C4⋊C4—221no—
174C2×C4⋊C4—222no—
175C2×C4⋊C4D4411yescharacteristic
176C2×C4⋊C4D4411yescharacteristic
177C2×C22⋊C4—222no—
178C2×C22⋊C4—222no—
179C2×C22⋊C4—222no—
180C2×C22⋊C4—222no—
181C2×C42C22×D1111yescharacteristic
182#107—442no—
183#106—442no—
184#103—444no—
185#102—444no—
186#97—22no—
187#97—22no—
188#97—112no—
189#97—221no—
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—881no—
209C2×D4—881no—
210C2×D4—882no—
211C2×D4—882no—
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—222no—
215C22×C4—441no—
216C22×C4C2×D4411yescharacteristic
217C22×C4D4×D1112yes—
218C2×C8—24no—
219C2×C8—42no—
220C2×C8—42no—
221C2×C8—222no—
222C2×C8—222no—
223C2×C8—222no—
224C4⋊C4—41no—
225C4⋊C4—41no—
226C4⋊C4—442no—
227C4⋊C4—442no—
228C4⋊C4—441no—
229C4⋊C4—441no—
230C22⋊C4—442no—
231C22⋊C4—442no—
232C22⋊C4—442no—
233C22⋊C4—442no—
234C22⋊C4—882no—
235C22⋊C4—882no—
236C42#433912yes—
237C42D4×D1111yescharacteristic
238C42#434311yescharacteristic
239C11#1042411yescharacteristic, complemented, Sylow
240C23—442no—
241C23—442no—
242C23—442no—
243C23—442no—
244C23—442no—
245C23—442no—
246C23—442no—
247C23#6693511yescharacteristic
248Q8—444no—
249Q8—882no—
250D4—444no—
251D4—882no—
252D4—884no—
253D4—884no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—22no—
257C2×C4—22no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—42no—
261C2×C4—42no—
262C2×C4—442no—
263C2×C4—442no—
264C2×C4—442no—
265C2×C4—881no—
266C2×C4—882no—
267C2×C4#6692811yescharacteristic
268C2×C4#6693712yes—
269C2×C4#6694712yes—
270C2×C4#6694811yescharacteristic
271C8—44no—
272C8—224no—
273C22—882no—
274C22—882no—
275C22—882no—
276C22—882no—
277C22—882no—
278C22—882no—
279C22—882no—
280C22#1062228511yescharacteristic
281C22#1062236011yescharacteristic
282C22#1062236511yescharacteristic
283C22#1062243512yes—
284C22#1062243812yes—
285C4—22no—
286C4—22no—
287C4—21no—
288C4—21no—
289C4—81no—
290C4—81no—
291C4—882no—
292C4—1761no—
293C2—1762no—
294C2#1306790611yescharacteristic
295C2#1306792311yescharacteristic
296C2#1306793512yes—
297C2#1306982912yes—
298C2#1306984111yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1295C2
socleC23×C11#120
prime radical#13076662C2
hypercenter#1295D11
hypocenterC11#10424
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
2. #13069432C2semidirect
3. #13068785C2semidirect
4. C2×#10622102C2semidirect
5. C11×#1295C2semidirect
49. #66867D4semidirect
95. #1295D11semidirect
239. C11#10424semidirect

Maximal subgroups

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

subgroupindex
#130766622
#130694322
#130687852
C2×#106221022
C11×#12952
#1042411