Finite Group Databasebeta

← #14651450

Subgroups — #14651450

Order 2816.

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

normal subgroups only

This group has 518 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#13077645C211yesmaximal, characteristic
2#13073608C211yesmaximal, characteristic
3#13067341C212yesmaximal, complemented
4#13066471C212yesmaximal, complemented
5C11×#1466C211yesmaximal, characteristic
6C2×C4×D4×C11C2211yescharacteristic
7C2×#66989C412yes—
8C2×#66922C2211yescharacteristic
9C11×#432C2212yes—
10#10622825—21no—
11#10622825—21no—
12#10622820—21no—
13C2×C22⋊(C11⋊C8)—21no—
14#10622624—24no—
15#10622587C412yes—
16#10622566—21no—
17#10622566—21no—
18C4×C4⋊Dic11C2211yescharacteristic
19#10622539C2212yes—
20C11×#323—21no—
21C11×#323—21no—
22#10622119—24no—
23C22×D4×C11C2×C411yescharacteristic
24C23×C4×C11D411yescharacteristic
25C23×C4×C11D411yescharacteristic
26C22×Dic22C2×C412yes—
27C4×D4×C11—22no—
28C4×D4×C11—22no—
29C2×C11×C4⋊C4C2×C411yescharacteristic
30C2×C11×C22⋊C4D411yescharacteristic
31C2×C11×C22⋊C4D411yescharacteristic
32C2×C42×C11C2311yescharacteristic
33C2×C22⋊Dic11—22no—
34C2×C22⋊Dic11—22no—
35#66989—44no—
36C2×C4⋊Dic11—21no—
37C2×C4⋊Dic11—21no—
38C2×C4⋊Dic11—21no—
39C2×C4×Dic11C2×C412yes—
40C2×#4318—22no—
41C22×C11⋊C8—22no—
42#66922—22no—
43#66922—22no—
44C11×C4⋊C8—22no—
45C11×C22⋊C8—22no—
46C11×#97—22no—
47C11⋊#95—22no—
48C11⋊#95—22no—
49C11⋊#95—21no—
50C22⋊(C11⋊C8)—22no—
51C22⋊(C11⋊C8)—22no—
52C22⋊(C11⋊C8)—22no—
53C4⋊(C11⋊C8)D414yes—
54#66867—22no—
55#9451—111nomaximal, Sylow
56C24×C11C22⋊C411yescharacteristic
57C24×C11C22⋊C411yescharacteristic
58C2×D4×C11—22no—
59C2×D4×C11—22no—
60C2×D4×C11—41no—
61C22×C4×C11—21no—
62C22×C4×C11—21no—
63C22×C4×C11—21no—
64C22×C4×C11—21no—
65C22×C4×C11—42no—
66C22×C4×C11—42no—
67C22×C4×C11C22⋊C411yescharacteristic
68C22×C4×C11C22⋊C411yescharacteristic
69C22×C4×C11C22×C411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C22×Dic11—22no—
73C22×Dic11—22no—
74C2×Dic22—24no—
75C2×Dic22—42no—
76C2×Dic22—42no—
77C2×C8×C11—42no—
78C11×C4⋊C4—22no—
79C11×C22⋊C4—22no—
80C11×C22⋊C4—22no—
81C42×C11C2×D412yes—
82C42×C11#4112yes—
83C22⋊Dic11—44no—
84C22⋊Dic11—44no—
85C4⋊Dic11—42no—
86C4⋊Dic11—41no—
87C4⋊Dic11—42no—
88C4⋊Dic11—41no—
89C4×Dic11—42no—
90#4318—82no—
91C2×C11⋊C8—24no—
92C2×C11⋊C8—82no—
93#2973—111no—
94#2547—111no—
95#1558—112no—
96#1466D1111yescharacteristic
97#1285—112no—
98C23×C11—21no—
99C23×C11—21no—
100C23×C11—21no—
101C23×C11—21no—
102C23×C11—21no—
103C23×C11—41no—
104C23×C11—41no—
105C23×C11—41no—
106C23×C11—41no—
107C23×C11#10012yes—
108C23×C11C2×C22⋊C411yescharacteristic
109D4×C11—44no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—22no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—41no—
116C2×C4×C11—42no—
117C2×C4×C11—42no—
118C2×C4×C11—41no—
119C2×C4×C11—41no—
120C2×C4×C11—81no—
121C2×C4×C11—81no—
122C2×C4×C11C4×D412yes—
123C2×C4×C11#12011yescharacteristic
124C2×C4×C11#12112yes—
125C2×C4×C11#12311yescharacteristic
126C2×Dic11—42no—
127C2×Dic11—42no—
128C2×Dic11—42no—
129C2×Dic11—42no—
130C2×Dic11—42no—
131C2×Dic11—42no—
132Dic22—84no—
133C8×C11—82no—
134C11⋊C8—44no—
135C2×C4⋊Q8—111no—
136C2×#124—112no—
137C2×C4×D4C2×D1111yescharacteristic
138#435—224no—
139#432—112no—
140#432C2×D1112yes—
141#407—221no—
142C2×C22⋊C8—221no—
143#397—221no—
144#397—221no—
145#391—112no—
146#380—221no—
147#380—221no—
148C4×C4⋊C4—111no—
149#333—224no—
150#323—21no—
151#323—21no—
152C22×C11—21no—
153C22×C11—21no—
154C22×C11—22no—
155C22×C11—42no—
156C22×C11—42no—
157C22×C11—41no—
158C22×C11—41no—
159C22×C11—41no—
160C22×C11—41no—
161C22×C11—41no—
162C22×C11—81no—
163C22×C11—81no—
164C22×C11#38611yescharacteristic
165C22×C11C2×#10011yescharacteristic
166C22×C11#41311yescharacteristic
167C4×C11—21no—
168C4×C11—22no—
169C4×C11—22no—
170C4×C11—41no—
171C4×C11—41no—
172C4×C11#45512yes—
173Dic11—82no—
174Dic11—82no—
175C22×Q8—112no—
176C22×D4C4×D1111yescharacteristic
177C23×C4D4411yescharacteristic
178C23×C4D4411yescharacteristic
179C2×M16—222no—
180C22×C8—222no—
181C4⋊Q8—222no—
182C4⋊Q8—222no—
183#124—444no—
184C4×D4—22no—
185C4×D4—22no—
186C2×C4⋊C4—221no—
187C2×C4⋊C4—221no—
188C2×C4⋊C4—221no—
189C2×C4⋊C4C4×D1111yescharacteristic
190C2×C22⋊C4—222no—
191C2×C22⋊C4—222no—
192C2×C22⋊C4C22⋊D1111yescharacteristic
193C2×C22⋊C4C22⋊D1111yescharacteristic
194C2×C42—112no—
195C2×C42C22×D1111yescharacteristic
196C4⋊C8—22no—
197C4⋊C8—114no—
198C22⋊C8—22no—
199C22⋊C8—222no—
200C22⋊C8—222no—
201C22⋊C8—222no—
202#97—22no—
203#97—222no—
204#95—222no—
205#95—222no—
206#95—221no—
207C2×C11—21no—
208C2×C11—21no—
209C2×C11—42no—
210C2×C11—81no—
211C2×C11#188511yescharacteristic
212C2×C11#190011yescharacteristic
213C2×C11#190911yescharacteristic
214C24(C2×D11)⋊C411yescharacteristic
215C24(C2×D11)⋊C411yescharacteristic
216C2×Q8—224no—
217C2×Q8—442no—
218C2×Q8—442no—
219C2×D4—22no—
220C2×D4—22no—
221C2×D4—41no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—42no—
227C22×C4—42no—
228C22×C4—222no—
229C22×C4—222no—
230C22×C4(C2×D11)⋊C411yescharacteristic
231C22×C4(C2×D11)⋊C411yescharacteristic
232C22×C4C2×C4×D1111yescharacteristic
233C22×C4C2×D4411yescharacteristic
234C22×C4C2×C22⋊D1111yescharacteristic
235M16—882no—
236C2×C8—42no—
237C2×C8—224no—
238C2×C8—882no—
239C4⋊C4—22no—
240C4⋊C4—442no—
241C4⋊C4—441no—
242C4⋊C4—441no—
243C4⋊C4—442no—
244C22⋊C4—22no—
245C22⋊C4—22no—
246C22⋊C4—444no—
247C22⋊C4—444no—
248C42—442no—
249C42D4×D1112yes—
250C42#434112yes—
251C11#945111yescharacteristic, complemented, Sylow
252C23—21no—
253C23—21no—
254C23—21no—
255C23—21no—
256C23—21no—
257C23—41no—
258C23—41no—
259C23—41no—
260C23—41no—
261C23#6688712yes—
262C23C2×(C2×D11)⋊C411yescharacteristic
263Q8—884no—
264D4—44no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—22no—
268C2×C4—21no—
269C2×C4—21no—
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×C4—442no—
281C2×C4—442no—
282C2×C4—442no—
283C2×C4(C22⋊D11)⋊C412yes—
284C2×C4#6693511yescharacteristic
285C2×C4#6693911yescharacteristic
286C2×C4#6699212yes—
287C8—82no—
288C8—444no—
289C22—21no—
290C22—21no—
291C22—22no—
292C22—42no—
293C22—42no—
294C22—41no—
295C22—41no—
296C22—41no—
297C22—41no—
298C22—41no—
299C22—81no—
300C22—81no—
301C22#1062257111yescharacteristic
302C22C2×#6688711yescharacteristic
303C22#1062274511yescharacteristic
304C4—22no—
305C4—22no—
306C4—21no—
307C4—41no—
308C4—41no—
309C4—882no—
310C4—882no—
311C4#1062235912yes—
312C2—21no—
313C2—21no—
314C2—42no—
315C2—81no—
316C2#1306900211yescharacteristic
317C2#1306907711yescharacteristic
318C2#1306913611yescharacteristic
subgroupG/H
centerC22#10622571
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1466C2
socleC22×C11#386
prime radicalC22×D4×C11C2×C4
cosocleC2×C42×C11C23
hypercenter#1466D11
hypocenterC11#9451
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1466

Complements

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

NH ≅ G/Ntype
3. #13067341C2semidirect
4. #13066471C2semidirect
251. C11#9451semidirect

Maximal subgroups

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

subgroupindex
#130776452
#130736082
#130673412
#130664712
C11×#14662
#945111