Finite Group Databasebeta

← #14647395

Subgroups — #14647395

Order 2816.

384 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 95 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#13071581C211yesmaximal, characteristic
2#13066960C211yesmaximal, characteristic
3#13066510C212yesmaximal
4#13066481C212yesmaximal
5C4×C11×#101C211yesmaximal, characteristic
6C2×C4×Q8×C11C2211yescharacteristic
7C2×C11×#101—21no—
8C4×C11×M16C2212yes—
9#10622843—21no—
10#10622594—21no—
11#10622594—21no—
12C4⋊C4×Dic11—21no—
13#10622550C411yescharacteristic
14#10622550C2211yescharacteristic
15#10622549C411yescharacteristic
16C4×C4⋊Dic11C411yescharacteristic
17#10622545C411yescharacteristic
18#10622545C2211yescharacteristic
19#10622539C2212yes—
20C11×#343—21no—
21#10622166—21no—
22#10622166—21no—
23C22×Q8×C11D411yescharacteristic
24C2×C11×M16—22no—
25C4×Q8×C11—22no—
26C4×Q8×C11—22no—
27C2×C11×C4⋊C4D411yescharacteristic
28C2×C11×C4⋊C4D411yescharacteristic
29C2×C11×C4⋊C4D411yescharacteristic
30C2×C42×C11C2×C411yescharacteristic
31C2×C42×C11C2×C411yescharacteristic
32C2×C42×C11C2311yescharacteristic
33C2×C4⋊Dic11—21no—
34C2×C4⋊Dic11—21no—
35C2×C4×Dic11—21no—
36C2×C4×Dic11—21no—
37C2×C4×Dic11—21no—
38C11×#101—24no—
39C11×#97—22no—
40C4×C8×C11—22no—
41C11⋊#95—21no—
42C11⋊#95—21no—
43C11⋊#95—21no—
44C11⋊#95—21no—
45C11⋊#95—21no—
46C11⋊#95—21no—
47C11⋊#95—21no—
48C11⋊#95C2×C411yescharacteristic
49C11⋊#95C2×C411yescharacteristic
50C11⋊#95C2×C411yescharacteristic
51C11⋊#95C2×C411yescharacteristic
52C22⋊(C11⋊C8)—22no—
53C4⋊(C11⋊C8)—22no—
54#66867—22no—
55#8775—111nomaximal, Sylow
56C2×Q8×C11—22no—
57C2×Q8×C11—22no—
58C2×Q8×C11—41no—
59C22×C4×C11C22⋊C411yescharacteristic
60C22×C4×C11C22⋊C411yescharacteristic
61C22×C4×C11C22⋊C411yescharacteristic
62C22×C4×C11C22⋊C411yescharacteristic
63C22×C4×C11C22×C411yescharacteristic
64C22×C4×C11C2×D411yescharacteristic
65C22×C4×C11C2×D411yescharacteristic
66C22×Dic11—21no—
67C22×Dic11—21no—
68C22×Dic11—21no—
69C22×Dic11—21no—
70C11×M16—24no—
71C11×M16—42no—
72C2×C8×C11—42no—
73C11×C4⋊C4—22no—
74C11×C4⋊C4—22no—
75C11×C4⋊C4—22no—
76C42×C11—21no—
77C42×C11—21no—
78C42×C11—21no—
79C42×C11—21no—
80C42×C11#4112yes—
81C42×C11#4112yes—
82C4⋊Dic11—42no—
83C4⋊Dic11—42no—
84C4×Dic11—42no—
85C4×Dic11—42no—
86C4×Dic11—42no—
87C2×C11⋊C8—42no—
88#2356—111no—
89C4×#101D1111yescharacteristic
90#1467—111no—
91#1300—112no—
92#1288—112no—
93C23×C11C2×C22⋊C411yescharacteristic
94Q8×C11—44no—
95C2×C4×C11—21no—
96C2×C4×C11—21no—
97C2×C4×C11—21no—
98C2×C4×C11—21no—
99C2×C4×C11—21no—
100C2×C4×C11—21no—
101C2×C4×C11—21no—
102C2×C4×C11—21no—
103C2×C4×C11—21no—
104C2×C4×C11—41no—
105C2×C4×C11—41no—
106C2×C4×C11—41no—
107C2×C4×C11—41no—
108C2×C4×C11#10412yes—
109C2×C4×C11#11711yescharacteristic
110C2×C4×C11#11711yescharacteristic
111C2×C4×C11#12312yes—
112C2×C4×C11#12312yes—
113C2×Dic11—22no—
114C2×Dic11—41no—
115C2×Dic11—41no—
116C2×Dic11—41no—
117C2×Dic11—41no—
118C2×Dic11—41no—
119C2×Dic11—41no—
120C2×Dic11—41no—
121C2×Dic11—41no—
122C2×Dic11—41no—
123C2×Dic11—41no—
124C2×Dic11—41no—
125C8×C11—44no—
126C11⋊C8—82no—
127C2×C4×Q8C2×D1111yescharacteristic
128#432—112no—
129C2×#101—21no—
130C4×M16C2×D1112yes—
131#391—221no—
132#387—221no—
133#387—221no—
134#383—111no—
135#383—111no—
136#382—111no—
137C4×C4⋊C4—111no—
138C4×C4⋊C4—221no—
139#376—111no—
140#376—111no—
141#343—21no—
142#324—221no—
143#324—221no—
144C22×C11—21no—
145C22×C11—21no—
146C22×C11#38111yescharacteristic
147C22×C11C2×#10411yescharacteristic
148C22×C11#42111yescharacteristic
149C4×C11—22no—
150C4×C11—22no—
151C4×C11—22no—
152C4×C11—21no—
153C4×C11—21no—
154C4×C11—41no—
155C4×C11—41no—
156C4×C11—41no—
157Dic11—42no—
158Dic11—81no—
159Dic11—81no—
160Dic11—81no—
161C22×Q8C22⋊D1111yescharacteristic
162C2×M16—22no—
163C4×Q8—22no—
164C4×Q8—22no—
165C2×C4⋊C4—221no—
166C2×C4⋊C4—221no—
167C2×C4⋊C4D4411yescharacteristic
168C2×C4⋊C4D4411yescharacteristic
169C2×C4⋊C4C22⋊D1111yescharacteristic
170C2×C42—221no—
171C2×C42—221no—
172C2×C42—221no—
173C2×C42C4×D1111yescharacteristic
174C2×C42C4×D1111yescharacteristic
175C2×C42C22×D1111yescharacteristic
176C4⋊C8—222no—
177#101—24no—
178C22⋊C8—222no—
179#97—22no—
180#97—222no—
181C4×C8—22no—
182#95—111no—
183#95—111no—
184#95—111no—
185#95—111no—
186#95—221no—
187#95—221no—
188#95—221no—
189#95—221no—
190#95—221no—
191#95—221no—
192#95—221no—
193C2×C11—21no—
194C2×C11—21no—
195C2×C11#182611yescharacteristic
196C2×C11#182711yescharacteristic
197C2×C11#183011yescharacteristic
198C2×Q8—22no—
199C2×Q8—22no—
200C2×Q8—41no—
201C22×C4—221no—
202C22×C4—221no—
203C22×C4—221no—
204C22×C4—221no—
205C22×C4(C2×D11)⋊C411yescharacteristic
206C22×C4(C2×D11)⋊C411yescharacteristic
207C22×C4(C2×D11)⋊C411yescharacteristic
208C22×C4(C2×D11)⋊C411yescharacteristic
209C22×C4C2×C4×D1111yescharacteristic
210C22×C4C2×D4411yescharacteristic
211C22×C4C2×C22⋊D1111yescharacteristic
212M16—24no—
213M16—42no—
214C2×C8—42no—
215C2×C8—442no—
216C4⋊C4—22no—
217C4⋊C4—22no—
218C4⋊C4—22no—
219C4⋊C4—442no—
220C4⋊C4—442no—
221C42—21no—
222C42—21no—
223C42—21no—
224C42—21no—
225C42—442no—
226C42—442no—
227C42—442no—
228C42#434112yes—
229C42#434112yes—
230C11#877511yescharacteristic, complemented, Sylow
231C23C2×(C2×D11)⋊C411yescharacteristic
232Q8—44no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—222no—
247C2×C4—441no—
248C2×C4—441no—
249C2×C4—441no—
250C2×C4—441no—
251C2×C4—441no—
252C2×C4—441no—
253C2×C4—441no—
254C2×C4—441no—
255C2×C4—441no—
256C2×C4—441no—
257C2×C4—441no—
258C2×C4#6686912yes—
259C2×C4#6693011yescharacteristic
260C2×C4#6693011yescharacteristic
261C2×C4#6693912yes—
262C2×C4#6698812yes—
263C8—44no—
264C8—882no—
265C22—21no—
266C22—21no—
267C22C2×#6686911yescharacteristic
268C22#1062255611yescharacteristic
269C22#1062261811yescharacteristic
270C4—22no—
271C4—22no—
272C4—22no—
273C4—21no—
274C4—21no—
275C4—41no—
276C4—41no—
277C4—41no—
278C4—442no—
279C4—881no—
280C4—881no—
281C4—881no—
282C2—21no—
283C2—21no—
284C2#1306871611yescharacteristic
285C2#1306872111yescharacteristic
286C2#1306872811yescharacteristic
subgroupG/H
centerC22#10622556
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC4×C11×#101C2
socleC22×C11#381
prime radicalC23×C11C2×C22⋊C4
cosocleC2×C42×C11C23
hypercenterC4×#101D11
hypocenterC11#8775
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×#101

Complements

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

NH ≅ G/Ntype
230. C11#8775semidirect

Maximal subgroups

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

subgroupindex
#130715812
#130669602
#130665102
#130664812
C4×C11×#1012
#877511