Finite Group Databasebeta

← #14651602

Subgroups — #14651602

Order 2816.

614 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 614 conjugacy classes of subgroups — too many to draw. Only its 103 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#13072890C211yesmaximal, characteristic
2#13068716C212yesmaximal, complemented
3#13066943C211yesmaximal, characteristic
4#13066469C212yesmaximal, complemented
5C11×#2312C211yesmaximal, characteristic
6C22×C11×C22⋊C4C2211yescharacteristic
7C2×#66979C2211yescharacteristic
8C11×#388—24no—
9C11×#380—21no—
10C11×#379—21no—
11C4×C11×C22⋊C4C2212yes—
12#10622860—21no—
13#10622824C2211yescharacteristic
14#10622823—21no—
15#10622820C2212yes—
16#10622566C412yescomplemented
17#10622562C412yescomplemented
18#10622557—22no—
19#10622163—22no—
20#10622161—24no—
21C25×C11D411yescharacteristic
22C23×C4×C11D411yescharacteristic
23C23×C4×C11C2311yescharacteristic
24C2×C11×C4⋊C4—22no—
25C2×C11×C22⋊C4—22no—
26C2×C11×C22⋊C4—22no—
27C2×C11×C22⋊C4—22no—
28C2×C11×C22⋊C4—22no—
29C2×C11×C22⋊C4—22no—
30C2×C11×C22⋊C4C2×C412yes—
31C2×C11×C22⋊C4D412yes—
32C2×C42×C11D414yes—
33C2×C22⋊Dic11—22no—
34C2×C22⋊Dic11—21no—
35C2×C22⋊Dic11—21no—
36C2×C22⋊Dic11—22no—
37#66979—22no—
38#66979—22no—
39C2×C4⋊Dic11C2×C411yescharacteristic
40C2×C4⋊Dic11C2×C411yescharacteristic
41C2×Dic11⋊C4—22no—
42C2×C4×Dic11—21no—
43C2×#4318—22no—
44C11×#95—22no—
45C11×#95—22no—
46C11⋊#95—22no—
47C11⋊#95—21no—
48C11⋊#95C2×C412yes—
49C22⋊(C11⋊C8)—22no—
50C22⋊(C11⋊C8)—22no—
51#9481—111nomaximal, Sylow
52C24×C11—21no—
53C24×C11—21no—
54C24×C11—42no—
55C24×C11—42no—
56C24×C11—81no—
57C24×C11C22⋊C412yes—
58C24×C11C2×D411yescharacteristic
59C22×C4×C11—21no—
60C22×C4×C11—21no—
61C22×C4×C11—24no—
62C22×C4×C11—42no—
63C22×C4×C11—81no—
64C22×C4×C11C22⋊C412yes—
65C22×C4×C11C22×C411yescharacteristic
66C22×C4×C11C2×D412yes—
67C22×C4×C11C2×D411yescharacteristic
68C22×C4×C11#4112yes—
69C22×Dic11—22no—
70C22×Dic11—21no—
71C22×Dic11—21no—
72C11×C4⋊C4—82no—
73C11×C22⋊C4—24no—
74C11×C22⋊C4—24no—
75C11×C22⋊C4—44no—
76C11×C22⋊C4—82no—
77C11×C22⋊C4—82no—
78C42×C11—44no—
79C22⋊Dic11—42no—
80C22⋊Dic11—44no—
81C22⋊Dic11—41no—
82C22⋊Dic11—41no—
83C22⋊Dic11—82no—
84C4⋊Dic11—22no—
85C4⋊Dic11—22no—
86Dic11⋊C4—82no—
87C4×Dic11—42no—
88#4318—44no—
89C2×C11⋊C8—42no—
90#2482—111no—
91#2312D1111yescharacteristic
92#1826—112no—
93#1462—111no—
94#1284—112no—
95C23×C11—22no—
96C23×C11—22no—
97C23×C11—22no—
98C23×C11—22no—
99C23×C11—22no—
100C23×C11—41no—
101C23×C11—42no—
102C23×C11—42no—
103C23×C11—42no—
104C23×C11—42no—
105C23×C11—42no—
106C23×C11—42no—
107C23×C11—81no—
108C23×C11—81no—
109C23×C11—88no—
110C23×C11C2×C22⋊C411yescharacteristic
111C23×C11#12011yescharacteristic
112C23×C11#12311yescharacteristic
113C2×C4×C11—24no—
114C2×C4×C11—22no—
115C2×C4×C11—41no—
116C2×C4×C11—41no—
117C2×C4×C11—42no—
118C2×C4×C11—42no—
119C2×C4×C11—42no—
120C2×C4×C11—44no—
121C2×C4×C11—44no—
122C2×C4×C11—44no—
123C2×C4×C11—81no—
124C2×C4×C11C4×D412yes—
125C2×C4×C11#12112yes—
126C2×Dic11—42no—
127C2×Dic11—42no—
128C2×Dic11—42no—
129C2×Dic11—41no—
130C2×Dic11—41no—
131C2×Dic11—42no—
132C2×Dic11—42no—
133C11⋊C8—82no—
134C2×#117—111no—
135C22×C22⋊C4C2×D1111yescharacteristic
136#407—112no—
137#399—112no—
138#397—112no—
139#388—24no—
140#388—222no—
141#385—221no—
142#381—111no—
143#380—21no—
144#379—21no—
145#379—221no—
146C4×C22⋊C4C2×D1112yes—
147#339—224no—
148#323—222no—
149C22×C11—21no—
150C22×C11—21no—
151C22×C11—21no—
152C22×C11—21no—
153C22×C11—21no—
154C22×C11—21no—
155C22×C11—21no—
156C22×C11—44no—
157C22×C11—44no—
158C22×C11—42no—
159C22×C11—42no—
160C22×C11—42no—
161C22×C11—82no—
162C22×C11—84no—
163C22×C11—84no—
164C22×C11#38611yescharacteristic
165C22×C11#42112yes—
166C22×C11#45812yes—
167C4×C11—22no—
168C4×C11—22no—
169C4×C11—42no—
170C4×C11—84no—
171Dic11—82no—
172Dic11—81no—
173Dic11—81no—
174C25C22⋊D1111yescharacteristic
175C23×C4C22⋊D1111yescharacteristic
176C23×C4C22×D1111yescharacteristic
177C2×M16—222no—
178#117—222no—
179#117—222no—
180C2×C4⋊C4—22no—
181C2×C4⋊C4—111no—
182C2×C4⋊C4—111no—
183C2×C4⋊C4—222no—
184C2×C22⋊C4—22no—
185C2×C22⋊C4—22no—
186C2×C22⋊C4—22no—
187C2×C22⋊C4—22no—
188C2×C22⋊C4—22no—
189C2×C22⋊C4—222no—
190C2×C22⋊C4—221no—
191C2×C22⋊C4—221no—
192C2×C22⋊C4—222no—
193C2×C22⋊C4C4×D1112yes—
194C2×C22⋊C4D4412yes—
195C2×C42—221no—
196C2×C42C22⋊D1114yes—
197C22⋊C8—222no—
198C22⋊C8—222no—
199#95—22no—
200#95—22no—
201#95—112no—
202#95—222no—
203#95—221no—
204C2×C11—22no—
205C2×C11—22no—
206C2×C11—41no—
207C2×C11—82no—
208C2×C11#189011yescharacteristic
209C2×C11#189711yescharacteristic
210C2×C11#191111yescharacteristic
211C24—21no—
212C24—21no—
213C24—42no—
214C24—42no—
215C24—81no—
216C24(C2×D11)⋊C412yes—
217C24C2×C22⋊D1111yescharacteristic
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—24no—
221C22×C4—42no—
222C22×C4—81no—
223C22×C4—222no—
224C22×C4—221no—
225C22×C4—221no—
226C22×C4(C2×D11)⋊C412yes—
227C22×C4C2×C4×D1111yescharacteristic
228C22×C4C2×D4411yescharacteristic
229C22×C4#433912yes—
230C22×C4C2×C22⋊D1112yes—
231M16—444no—
232C2×C8—442no—
233C4⋊C4—82no—
234C4⋊C4—222no—
235C4⋊C4—222no—
236C4⋊C4—882no—
237C22⋊C4—24no—
238C22⋊C4—24no—
239C22⋊C4—44no—
240C22⋊C4—82no—
241C22⋊C4—82no—
242C22⋊C4—442no—
243C22⋊C4—444no—
244C22⋊C4—441no—
245C22⋊C4—441no—
246C22⋊C4—882no—
247C42—44no—
248C42—442no—
249C11#948111yescharacteristic, complemented, Sylow
250C23—22no—
251C23—22no—
252C23—22no—
253C23—22no—
254C23—22no—
255C23—41no—
256C23—42no—
257C23—42no—
258C23—42no—
259C23—42no—
260C23—42no—
261C23—42no—
262C23—81no—
263C23—81no—
264C23—88no—
265C23C2×(C2×D11)⋊C411yescharacteristic
266C23#6698211yescharacteristic
267C23#6700611yescharacteristic
268C2×C4—24no—
269C2×C4—22no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—42no—
273C2×C4—42no—
274C2×C4—42no—
275C2×C4—44no—
276C2×C4—44no—
277C2×C4—44no—
278C2×C4—81no—
279C2×C4—442no—
280C2×C4—442no—
281C2×C4—442no—
282C2×C4—441no—
283C2×C4—441no—
284C2×C4—442no—
285C2×C4—442no—
286C2×C4C4×C22⋊D1112yes—
287C2×C4#6698312yes—
288C8—882no—
289C22—21no—
290C22—21no—
291C22—21no—
292C22—21no—
293C22—21no—
294C22—21no—
295C22—21no—
296C22—44no—
297C22—44no—
298C22—42no—
299C22—42no—
300C22—42no—
301C22—82no—
302C22—84no—
303C22—84no—
304C22#1062261812yes—
305C22#1062282611yescharacteristic
306C22#1062285612yes—
307C4—22no—
308C4—22no—
309C4—42no—
310C4—84no—
311C4—882no—
312C4—881no—
313C4—881no—
314C2—22no—
315C2—22no—
316C2—41no—
317C2—82no—
318C2#1306902911yescharacteristic
319C2#1306906411yescharacteristic
320C2#1306914811yescharacteristic
subgroupG/H
centerC22#10622826
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#2312C2
socleC22×C11#386
prime radicalC25×C11D4
cosocleC23×C4×C11C23
hypercenter#2312D11
hypocenterC11#9481
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2312

Complements

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

NH ≅ G/Ntype
2. #13068716C2semidirect
4. #13066469C2semidirect
16. #10622566C4semidirect
17. #10622562C4semidirect
249. C11#9481semidirect

Maximal subgroups

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

subgroupindex
#130728902
#130687162
#130669432
#130664692
C11×#23122
#948111