Finite Group Databasebeta

← #14649558

Subgroups — #14649558

Order 2816.

648 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 648 conjugacy classes of subgroups — too many to draw. Only its 131 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#13076947C211yesmaximal, characteristic
2#13068684C211yesmaximal, characteristic, complemented
3C2×#10622089C212yesmaximal
4#13066495C212yesmaximal, complemented
5C2×C11×#383C211yesmaximal, characteristic, complemented
6C22×C42×C11C2211yescharacteristic
7C2×#66983C2211yescharacteristic
8C2×#66982—21no—
9C11×#383—24no—
10C2×C11×#95—21no—
11C2×C11×#95—21no—
12C2×C11×#95C2212yes—
13#10622826—21no—
14#10622825C2211yescharacteristic
15C2×C22⋊(C11⋊C8)C2212yes—
16#10622553—22no—
17#10622552C412yescomplemented
18#10622541C412yescomplemented
19#10622162—22no—
20#10622089—24no—
21C23×C4×C11—22no—
22C23×C4×C11D411yescharacteristic
23C23×C4×C11D411yescharacteristic
24C23×C4×C11C2311yescharacteristic
25C22×C22⋊D11—21no—
26C22×D44C2×C411yescharacteristic
27C2×C42×C11—22no—
28C2×C42×C11—22no—
29C2×C42×C11C2×C412yes—
30C2×C42×C11D412yes—
31C2×C22⋊Dic11—21no—
32#66983—22no—
33#66983—22no—
34#66982—44no—
35C2×(C2×D11)⋊C4—22no—
36C2×(C2×D11)⋊C4—22no—
37C2×(C2×D11)⋊C4—21no—
38C2×C4⋊Dic11C2×C411yescharacteristic
39C2×C4⋊Dic11C2×C412yes—
40C2×Dic11⋊C4—22no—
41C22×C11⋊C8—22no—
42C11×#95—24no—
43C11×#95—24no—
44C11×#95—22no—
45C11×#95D414yes—
46C11⋊#95—22no—
47C11⋊#95—21no—
48C22⋊(C11⋊C8)—22no—
49C22⋊(C11⋊C8)—22no—
50#9157—111nomaximal, Sylow
51C24×C11C2×D411yescharacteristic
52C23×D11—21no—
53C22×C4×C11—21no—
54C22×C4×C11—21no—
55C22×C4×C11—21no—
56C22×C4×C11—21no—
57C22×C4×C11—22no—
58C22×C4×C11—22no—
59C22×C4×C11—24no—
60C22×C4×C11—42no—
61C22×C4×C11—42no—
62C22×C4×C11—44no—
63C22×C4×C11—44no—
64C22×C4×C11—42no—
65C22×C4×C11—42no—
66C22×C4×C11C22⋊C412yes—
67C22×C4×C11C22⋊C412yes—
68C22×C4×C11C22×C411yescharacteristic
69C22×C4×C11C2×D411yescharacteristic
70C22×C4×C11C2×D412yes—
71C22×C4×C11#4112yes—
72C2×C22⋊D11—41no—
73C2×C22⋊D11—41no—
74C2×C22⋊D11—42no—
75C2×C22⋊D11—42no—
76C22×Dic11—21no—
77C22×Dic11—22no—
78C2×D44—22no—
79C2×D44—42no—
80C42×C11—24no—
81C42×C11—24no—
82C22⋊Dic11—42no—
83(C2×D11)⋊C4—44no—
84(C2×D11)⋊C4—44no—
85(C2×D11)⋊C4—42no—
86C4⋊Dic11—22no—
87C4⋊Dic11—42no—
88Dic11⋊C4—44no—
89C2×C11⋊C8—44no—
90C2×C11⋊C8—42no—
91#2854—111no—
92C2×#383D1111yescharacteristic, complemented
93#1817—111no—
94C2×#327—112no—
95#1294—112no—
96C23×C11—22no—
97C23×C11—22no—
98C23×C11C2×C22⋊C411yescharacteristic
99C23×C11#12011yescharacteristic
100C23×C11#12311yescharacteristic
101C23×C11#13512yes—
102C23×C11AGL(1,ℤ/8)12yes—
103C22×D11—41no—
104C22×D11—42no—
105C22×D11—41no—
106C22×D11—41no—
107C22×D11—42no—
108C2×C4×C11—22no—
109C2×C4×C11—22no—
110C2×C4×C11—22no—
111C2×C4×C11—22no—
112C2×C4×C11—22no—
113C2×C4×C11—22no—
114C2×C4×C11—22no—
115C2×C4×C11—22no—
116C2×C4×C11—42no—
117C2×C4×C11—42no—
118C2×C4×C11—42no—
119C2×C4×C11—42no—
120C2×C4×C11—42no—
121C2×C4×C11—42no—
122C2×C4×C11—44no—
123C2×C4×C11—44no—
124C2×C4×C11—44no—
125C2×C4×C11—84no—
126C2×C4×C11—84no—
127C2×C4×C11C4×D412yes—
128C2×C4×C11#12112yes—
129C22⋊D11—82no—
130C22⋊D11—82no—
131C2×Dic11—41no—
132C2×Dic11—42no—
133C2×Dic11—41no—
134C2×Dic11—41no—
135C2×Dic11—42no—
136C2×Dic11—42no—
137D44—82no—
138C11⋊C8—82no—
139C2×#123—221no—
140C2×#121—111no—
141C22×C42C2×D1111yescharacteristic
142C2×C22⋊C8—112no—
143#390—112no—
144#389—112no—
145#388—222no—
146#386—221no—
147#383—24no—
148#380—111no—
149C2×#95—21no—
150C2×#95—21no—
151C2×#95C2×D1112yes—
152#336—222no—
153#327—224no—
154C22×C11—21no—
155C22×C11—21no—
156C22×C11—21no—
157C22×C11—21no—
158C22×C11—24no—
159C22×C11—24no—
160C22×C11#38611yescharacteristic
161C22×C11#41012yes—
162C22×C11#41611yescharacteristic
163C22×C11#41811yescharacteristic
164C22×C11#42112yes—
165C22×C11#44912yes—
166C22×C11#48212yes—
167C2×D11—81no—
168C2×D11—81no—
169C2×D11—81no—
170C2×D11—82no—
171C2×D11—82no—
172C4×C11—22no—
173C4×C11—22no—
174C4×C11—42no—
175C4×C11—42no—
176C4×C11—84no—
177Dic11—81no—
178Dic11—82no—
179C22×D4—111no—
180C22×D4—221no—
181C23×C4—22no—
182C23×C4C22⋊D1111yescharacteristic
183C23×C4C22⋊D1111yescharacteristic
184C23×C4C22×D1111yescharacteristic
185C22×C8—222no—
186#123—444no—
187#121—222no—
188#121—222no—
189C2×C4⋊C4—111no—
190C2×C4⋊C4—112no—
191C2×C4⋊C4—222no—
192C2×C22⋊C4—221no—
193C2×C22⋊C4—222no—
194C2×C22⋊C4—222no—
195C2×C22⋊C4—221no—
196C2×C42—22no—
197C2×C42—22no—
198C2×C42C4×D1112yes—
199C2×C42D4412yes—
200C22⋊C8—222no—
201C22⋊C8—222no—
202#95—24no—
203#95—24no—
204#95—22no—
205#95—222no—
206#95—221no—
207#95C22⋊D1114yes—
208C2×C11—22no—
209C2×C11—22no—
210C2×C11#151412yes—
211C2×C11#152112yes—
212C2×C11#187511yescharacteristic
213C2×C11#189711yescharacteristic
214C2×C11#189911yescharacteristic
215D11—161no—
216C24—221no—
217C24C2×C22⋊D1111yescharacteristic
218C2×D4—222no—
219C2×D4—442no—
220C2×D4—441no—
221C2×D4—442no—
222C2×D4—442no—
223C2×D4—441no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—22no—
227C22×C4—22no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—24no—
231C22×C4—42no—
232C22×C4—42no—
233C22×C4—44no—
234C22×C4—44no—
235C22×C4—42no—
236C22×C4—42no—
237C22×C4—222no—
238C22×C4—221no—
239C22×C4(C2×D11)⋊C412yes—
240C22×C4(C2×D11)⋊C412yes—
241C22×C4C2×C4×D1111yescharacteristic
242C22×C4C2×D4411yescharacteristic
243C22×C4#433912yes—
244C22×C4C2×C22⋊D1112yes—
245C2×C8—444no—
246C2×C8—442no—
247C4⋊C4—222no—
248C4⋊C4—442no—
249C4⋊C4—444no—
250C22⋊C4—444no—
251C22⋊C4—444no—
252C22⋊C4—442no—
253C22⋊C4—442no—
254C42—24no—
255C42—24no—
256C11#915711yescharacteristic, complemented, Sylow
257C23—22no—
258C23—22no—
259C23—441no—
260C23—441no—
261C23—441no—
262C23—442no—
263C23—442no—
264C23C2×(C2×D11)⋊C411yescharacteristic
265C23#6698211yescharacteristic
266C23#6700212yes—
267C23#6700312yes—
268C23#6700611yescharacteristic
269D4—882no—
270D4—882no—
271D4—882no—
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—22no—
276C2×C4—22no—
277C2×C4—22no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4—42no—
285C2×C4—42no—
286C2×C4—44no—
287C2×C4—44no—
288C2×C4—44no—
289C2×C4—84no—
290C2×C4—84no—
291C2×C4—441no—
292C2×C4—442no—
293C2×C4—441no—
294C2×C4—441no—
295C2×C4—442no—
296C2×C4—442no—
297C2×C4C4×C22⋊D1112yes—
298C2×C4#6698312yes—
299C8—882no—
300C22—21no—
301C22—21no—
302C22—21no—
303C22—21no—
304C22—24no—
305C22—24no—
306C22—881no—
307C22—881no—
308C22—881no—
309C22—882no—
310C22—882no—
311C22#1062261411yescharacteristic
312C22#1062261511yescharacteristic
313C22#1062261612yes—
314C22#1062261812yes—
315C22#1062261912yes—
316C22#1062282611yescharacteristic
317C22#1062285112yes—
318C4—22no—
319C4—22no—
320C4—42no—
321C4—42no—
322C4—84no—
323C4—881no—
324C4—882no—
325C2—22no—
326C2—22no—
327C2—1761no—
328C2#1306716212yes—
329C2#1306719112yes—
330C2#1306893811yescharacteristic
331C2#1306906411yescharacteristic
332C2#1306907411yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC2×C11×#383C2
socleC23×C11C2×C22⋊C4
prime radicalC2×#66983C22
cosocleC23×C4×C11C23
hypercenterC2×#383D11
hypocenterC11#9157
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#383

Complements

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

NH ≅ G/Ntype
2. #13068684C2semidirect
4. #13066495C2semidirect
5. C2×C11×#383C2semidirect
17. #10622552C4semidirect
18. #10622541C4semidirect
92. C2×#383D11semidirect
256. C11#9157semidirect

Maximal subgroups

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

subgroupindex
#130769472
#130686842
C2×#106220892
#130664952
C2×C11×#3832
#915711