Finite Group Databasebeta

← #14664170

Subgroups — #14664170

Order 2816.

358 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 83 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#13074492C211yesmaximal, characteristic
2#13066940C211yesmaximal, characteristic
3#13066642C212yesmaximal
4#13066621C212yesmaximal
5C4×C11×#101C211yesmaximal, characteristic
6C2×C4×Q8×C11C2211yescharacteristic
7C2×#66923C411yescharacteristic
8C2×C11×#101—21no—
9C4×C11×M16—21no—
10#10622842—21no—
11#10622599C411yescharacteristic
12#10622599C2211yescharacteristic
13#10622596C411yescharacteristic
14#10622596C2211yescharacteristic
15#10622595—21no—
16#10622550C411yescharacteristic
17#10622546—21no—
18#10622546—21no—
19#10622538—21no—
20C11×#343C2212yes—
21#10622166—21no—
22#10622166C2212yes—
23C22×Q8×C11D411yescharacteristic
24C2×C11×M16—22no—
25C4×Q8×C11—41no—
26C4×Q8×C11—41no—
27C2×C11×C4⋊C4C2×C411yescharacteristic
28C2×C11×C4⋊C4D411yescharacteristic
29C2×C11×C4⋊C4C2311yescharacteristic
30C2×C42×C11C2×C411yescharacteristic
31C2×C42×C11D411yescharacteristic
32C2×C42×C11D411yescharacteristic
33C2×C4⋊Dic11C2×C411yescharacteristic
34C2×C4⋊Dic11C2×C411yescharacteristic
35C2×Dic11⋊C4—21no—
36C2×Dic11⋊C4—21no—
37C2×Dic11⋊C4—21no—
38C2×Dic11⋊C4—21no—
39#66923—41no—
40#66923—41no—
41C11×#101—24no—
42C11×#97—41no—
43C4×C8×C11—41no—
44C11⋊#95—21no—
45C11⋊#95—21no—
46C11⋊#95—21no—
47C11⋊#95—21no—
48C11⋊#95—21no—
49C11⋊#95—21no—
50C11⋊#95—21no—
51C11⋊#95—21no—
52C11⋊#95C2×C411yescharacteristic
53C11⋊#95C2×C411yescharacteristic
54C22⋊(C11⋊C8)—22no—
55C4⋊(C11⋊C8)—41no—
56C4×C11⋊C8—41no—
57#11740—111nomaximal, Sylow
58C2×Q8×C11—22no—
59C2×Q8×C11—22no—
60C2×Q8×C11—41no—
61C22×C4×C11C22⋊C411yescharacteristic
62C22×C4×C11C22⋊C411yescharacteristic
63C22×C4×C11C22⋊C411yescharacteristic
64C22×C4×C11C22⋊C411yescharacteristic
65C22×C4×C11C22×C411yescharacteristic
66C22×C4×C11C2×D411yescharacteristic
67C22×C4×C11C2×D411yescharacteristic
68C22×Dic11—21no—
69C22×Dic11—21no—
70C22×Dic11—21no—
71C22×Dic11—21no—
72C11×M16—24no—
73C11×M16—42no—
74C2×C8×C11—42no—
75C11×C4⋊C4—41no—
76C11×C4⋊C4—41no—
77C11×C4⋊C4—41no—
78C42×C11—21no—
79C42×C11—21no—
80C42×C11—21no—
81C42×C11—21no—
82C42×C11—21no—
83C42×C11—21no—
84C4⋊Dic11—41no—
85C4⋊Dic11—41no—
86Dic11⋊C4—42no—
87Dic11⋊C4—41no—
88Dic11⋊C4—41no—
89Dic11⋊C4—42no—
90Dic11⋊C4—42no—
91C2×C11⋊C8—42no—
92#2634—111no—
93C4×#101D1111yescharacteristic
94#1461—111no—
95#1353—112no—
96#1346—112no—
97C23×C11C2×C22⋊C411yescharacteristic
98Q8×C11—44no—
99C2×C4×C11—21no—
100C2×C4×C11—21no—
101C2×C4×C11—21no—
102C2×C4×C11—21no—
103C2×C4×C11—21no—
104C2×C4×C11—21no—
105C2×C4×C11—21no—
106C2×C4×C11—21no—
107C2×C4×C11—21no—
108C2×C4×C11—21no—
109C2×C4×C11—41no—
110C2×C4×C11—41no—
111C2×C4×C11—41no—
112C2×C4×C11—41no—
113C2×C4×C11#9911yescharacteristic
114C2×C4×C11#9911yescharacteristic
115C2×C4×C11#10412yes—
116C2×C4×C11#13512yes—
117C2×Dic11—41no—
118C2×Dic11—41no—
119C2×Dic11—41no—
120C2×Dic11—41no—
121C2×Dic11—42no—
122C2×Dic11—41no—
123C2×Dic11—41no—
124C2×Dic11—41no—
125C2×Dic11—41no—
126C2×Dic11—41no—
127C2×Dic11—41no—
128C8×C11—44no—
129C11⋊C8—82no—
130C2×#125—111no—
131C2×C4×Q8C2×D1111yescharacteristic
132#431—221no—
133C2×#101—21no—
134C4×M16—21no—
135#400—111no—
136#400—111no—
137#400—221no—
138#398—111no—
139#398—111no—
140#395—221no—
141#387—221no—
142#387—221no—
143#383—111no—
144#343C2×D1112yes—
145#324—112no—
146#324—221no—
147C22×C11—21no—
148C22×C11—21no—
149C22×C11C2×#9911yescharacteristic
150C22×C11#41611yescharacteristic
151C22×C11C2×#10411yescharacteristic
152C4×C11—21no—
153C4×C11—21no—
154C4×C11—22no—
155C4×C11—22no—
156C4×C11—41no—
157C4×C11—41no—
158C4×C11—41no—
159C4×C11—41no—
160Dic11—81no—
161Dic11—81no—
162Dic11—81no—
163Dic11—81no—
164C22×Q8C22⋊D1111yescharacteristic
165C2×M16—22no—
166#125—441no—
167#125—441no—
168C4×Q8—41no—
169C4×Q8—41no—
170C2×C4⋊C4—111no—
171C2×C4⋊C4—111no—
172C2×C4⋊C4—221no—
173C2×C4⋊C4—221no—
174C2×C4⋊C4—221no—
175C2×C4⋊C4—221no—
176C2×C4⋊C4C4×D1111yescharacteristic
177C2×C4⋊C4D4411yescharacteristic
178C2×C4⋊C4C22×D1111yescharacteristic
179C2×C42C4×D1111yescharacteristic
180C2×C42D4411yescharacteristic
181C2×C42C22⋊D1111yescharacteristic
182C4⋊C8—441no—
183#101—24no—
184C22⋊C8—222no—
185#97—41no—
186C4×C8—41no—
187C4×C8—441no—
188#95—111no—
189#95—111no—
190#95—221no—
191#95—221no—
192#95—221no—
193#95—221no—
194#95—221no—
195#95—221no—
196#95—221no—
197#95—221no—
198C2×C11—21no—
199C2×C11—21no—
200C2×C11#150111yescharacteristic
201C2×C11#212311yescharacteristic
202C2×C11#213311yescharacteristic
203C2×Q8—22no—
204C2×Q8—22no—
205C2×Q8—41no—
206C22×C4—221no—
207C22×C4—221no—
208C22×C4—221no—
209C22×C4—221no—
210C22×C4(C2×D11)⋊C411yescharacteristic
211C22×C4(C2×D11)⋊C411yescharacteristic
212C22×C4(C2×D11)⋊C411yescharacteristic
213C22×C4(C2×D11)⋊C411yescharacteristic
214C22×C4C2×C4×D1111yescharacteristic
215C22×C4C2×D4411yescharacteristic
216C22×C4C2×C22⋊D1111yescharacteristic
217M16—24no—
218M16—42no—
219C2×C8—42no—
220C2×C8—442no—
221C4⋊C4—41no—
222C4⋊C4—41no—
223C4⋊C4—41no—
224C4⋊C4—441no—
225C4⋊C4—441no—
226C4⋊C4—442no—
227C4⋊C4—442no—
228C4⋊C4—441no—
229C4⋊C4—441no—
230C4⋊C4—442no—
231C42—21no—
232C42—21no—
233C42—21no—
234C42—21no—
235C42—21no—
236C42—21no—
237C11#1174011yescharacteristic, complemented, Sylow
238C23C2×(C2×D11)⋊C411yescharacteristic
239Q8—44no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—441no—
255C2×C4—441no—
256C2×C4—441no—
257C2×C4—441no—
258C2×C4—442no—
259C2×C4—441no—
260C2×C4—441no—
261C2×C4—441no—
262C2×C4—441no—
263C2×C4—441no—
264C2×C4—441no—
265C2×C4#6686912yes—
266C2×C4#6687011yescharacteristic
267C2×C4#6687011yescharacteristic
268C2×C4#6700312yes—
269C8—44no—
270C8—882no—
271C22—21no—
272C22—21no—
273C22C2×#6686911yescharacteristic
274C22C2×#6687011yescharacteristic
275C22#1062261511yescharacteristic
276C4—22no—
277C4—22no—
278C4—21no—
279C4—21no—
280C4—41no—
281C4—41no—
282C4—41no—
283C4—41no—
284C4—881no—
285C4—881no—
286C4—881no—
287C4—881no—
288C2—21no—
289C2—21no—
290C2#1306710511yescharacteristic
291C2#1307027111yescharacteristic
292C2#1307030311yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC4×C11×#101C2
socleC22×C11C2×#99
prime radicalC23×C11C2×C22⋊C4
cosocleC2×C11×C4⋊C4C23
hypercenterC4×#101D11
hypocenterC11#11740
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ C4×#101

Complements

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

NH ≅ G/Ntype
237. C11#11740semidirect

Maximal subgroups

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

subgroupindex
#130744922
#130669402
#130666422
#130666212
C4×C11×#1012
#1174011