Finite Group Databasebeta

← C11×#11790 #14588983

Subgroups — C11×#11790 #14588983

Order 2816.

444 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 106 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
1C11×#2487C211yesmaximal, characteristic
2C4×C11×#100C211yesmaximal, characteristic
3C11×#1465C211yesmaximal, characteristic
4C11×#1353C214yesmaximal, complemented
5C2×C4×D4×C11C2211yescharacteristic
6C22×C11×C4⋊C4C411yescharacteristic
7C2×C11×#100—21no—
8C11×#407—21no—
9C4×C11×M16—21no—
10C11×#400C2212yes—
11C11×#399C412yes—
12C11×#389—21no—
13C11×#386—21no—
14C11×#385—21no—
15C11×#380—21no—
16C11×#380C411yescharacteristic
17C11×#343C2212yes—
18C11×#324C2212yes—
19C11×#323—21no—
20C22×D4×C11D411yescharacteristic
21C23×C4×C11—21no—
22C23×C4×C11C2×C411yescharacteristic
23C23×C4×C11D411yescharacteristic
24C2×C11×M16—22no—
25C2×C11×M16—41no—
26C4×D4×C11—41no—
27C4×D4×C11—41no—
28C2×C11×C4⋊C4—21no—
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4—22no—
31C2×C11×C4⋊C4—41no—
32C2×C11×C4⋊C4—41no—
33C2×C11×C4⋊C4C2×C412yes—
34C2×C11×C4⋊C4C2311yescharacteristic
35C2×C11×C22⋊C4—21no—
36C2×C11×C22⋊C4—22no—
37C2×C11×C22⋊C4C2×C411yescharacteristic
38C2×C11×C22⋊C4D411yescharacteristic
39C2×C42×C11D411yescharacteristic
40C11×#100—24no—
41C11×C22⋊C8—22no—
42C11×C22⋊C8—41no—
43C11×#97—41no—
44C4×C8×C11—41no—
45C11×#95—22no—
46C11×#95—22no—
47C11×#95C2×C412yes—
48#11790C1111yesmaximal, characteristic, direct product factor, Sylow
49C24×C11C22⋊C411yescharacteristic
50C24×C11C22⋊C411yescharacteristic
51C2×D4×C11—22no—
52C2×D4×C11—22no—
53C2×D4×C11—41no—
54C22×C4×C11—21no—
55C22×C4×C11—21no—
56C22×C4×C11—21no—
57C22×C4×C11—21no—
58C22×C4×C11—22no—
59C22×C4×C11—22no—
60C22×C4×C11—42no—
61C22×C4×C11—42no—
62C22×C4×C11—42no—
63C22×C4×C11—82no—
64C22×C4×C11C22⋊C411yescharacteristic
65C22×C4×C11C22⋊C411yescharacteristic
66C22×C4×C11C22×C411yescharacteristic
67C22×C4×C11C2×D411yescharacteristic
68C22×C4×C11C2×D411yescharacteristic
69C11×M16—24no—
70C11×M16—42no—
71C11×M16—82no—
72C2×C8×C11—42no—
73C2×C8×C11—42no—
74C11×C4⋊C4—41no—
75C11×C4⋊C4—42no—
76C11×C4⋊C4—42no—
77C11×C4⋊C4—41no—
78C11×C4⋊C4—41no—
79C11×C4⋊C4—82no—
80C11×C22⋊C4—41no—
81C11×C22⋊C4—41no—
82C11×C22⋊C4—42no—
83C11×C22⋊C4—82no—
84C42×C11—21no—
85C42×C11—21no—
86#2487C2×C1111yescharacteristic
87C4×#100C2×C1111yescharacteristic
88#1465C2×C1111yescharacteristic
89#1353C2×C1114yescomplemented
90C23×C11—21no—
91C23×C11—21no—
92C23×C11—21no—
93C23×C11—21no—
94C23×C11—21no—
95C23×C11—41no—
96C23×C11—41no—
97C23×C11—41no—
98C23×C11—41no—
99C23×C11#10412yes—
100C23×C11C2×C22⋊C411yescharacteristic
101D4×C11—44no—
102C2×C4×C11—21no—
103C2×C4×C11—21no—
104C2×C4×C11—22no—
105C2×C4×C11—21no—
106C2×C4×C11—21no—
107C2×C4×C11—21no—
108C2×C4×C11—42no—
109C2×C4×C11—42no—
110C2×C4×C11—42no—
111C2×C4×C11—41no—
112C2×C4×C11—41no—
113C2×C4×C11—41no—
114C2×C4×C11—42no—
115C2×C4×C11—42no—
116C2×C4×C11—42no—
117C2×C4×C11—42no—
118C2×C4×C11—42no—
119C2×C4×C11—42no—
120C2×C4×C11—81no—
121C2×C4×C11—84no—
122C2×C4×C11#9911yescharacteristic
123C2×C4×C11#9911yescharacteristic
124C2×C4×C11#13712yes—
125C8×C11—44no—
126C8×C11—82no—
127C2×C4×D4C22×C1111yescharacteristic
128C22×C4⋊C4C4×C1111yescharacteristic
129C2×#100—21no—
130#407—21no—
131C4×M16—21no—
132#400C22×C1112yes—
133#399C4×C1112yes—
134#389—21no—
135#386—21no—
136#385—21no—
137#380—21no—
138#380C4×C1111yescharacteristic
139#343C22×C1112yes—
140#324C22×C1112yes—
141#323—21no—
142C22×C11—21no—
143C22×C11—21no—
144C22×C11—22no—
145C22×C11—42no—
146C22×C11—42no—
147C22×C11—42no—
148C22×C11—41no—
149C22×C11—41no—
150C22×C11—41no—
151C22×C11—41no—
152C22×C11—41no—
153C22×C11—81no—
154C22×C11C2×#9911yescharacteristic
155C22×C11#41911yescharacteristic
156C22×C11C2×#10411yescharacteristic
157C4×C11—21no—
158C4×C11—22no—
159C4×C11—41no—
160C4×C11—41no—
161C4×C11—41no—
162C4×C11—82no—
163C4×C11—82no—
164C4×C11#35212yes—
165C22×D4D4×C1111yescharacteristic
166C23×C4—21no—
167C23×C4C2×C4×C1111yescharacteristic
168C23×C4D4×C1111yescharacteristic
169C2×M16—22no—
170C2×M16—41no—
171C4×D4—41no—
172C4×D4—41no—
173C2×C4⋊C4—21no—
174C2×C4⋊C4—21no—
175C2×C4⋊C4—22no—
176C2×C4⋊C4—41no—
177C2×C4⋊C4—41no—
178C2×C4⋊C4C2×C4×C1112yes—
179C2×C4⋊C4C23×C1111yescharacteristic
180C2×C22⋊C4—21no—
181C2×C22⋊C4—22no—
182C2×C22⋊C4C2×C4×C1111yescharacteristic
183C2×C22⋊C4D4×C1111yescharacteristic
184C2×C42D4×C1111yescharacteristic
185#100—24no—
186C22⋊C8—22no—
187C22⋊C8—41no—
188#97—41no—
189C4×C8—41no—
190#95—22no—
191#95—22no—
192#95C2×C4×C1112yes—
193C2×C11—21no—
194C2×C11—21no—
195C2×C11—42no—
196C2×C11—81no—
197C2×C11#150811yescharacteristic
198C2×C11C2×#35211yescharacteristic
199C2×C11#213411yescharacteristic
200C24C11×C22⋊C411yescharacteristic
201C24C11×C22⋊C411yescharacteristic
202C2×D4—22no—
203C2×D4—22no—
204C2×D4—41no—
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—21no—
209C22×C4—22no—
210C22×C4—22no—
211C22×C4—42no—
212C22×C4—42no—
213C22×C4—42no—
214C22×C4—82no—
215C22×C4C11×C22⋊C411yescharacteristic
216C22×C4C11×C22⋊C411yescharacteristic
217C22×C4C22×C4×C1111yescharacteristic
218C22×C4C2×D4×C1111yescharacteristic
219C22×C4C2×D4×C1111yescharacteristic
220M16—24no—
221M16—42no—
222M16—82no—
223C2×C8—42no—
224C2×C8—42no—
225C4⋊C4—41no—
226C4⋊C4—42no—
227C4⋊C4—42no—
228C4⋊C4—41no—
229C4⋊C4—41no—
230C4⋊C4—82no—
231C22⋊C4—41no—
232C22⋊C4—41no—
233C22⋊C4—42no—
234C22⋊C4—82no—
235C42—21no—
236C42—21no—
237C11#1179011yescharacteristic, direct product factor, Sylow
238C23—21no—
239C23—21no—
240C23—21no—
241C23—21no—
242C23—21no—
243C23—41no—
244C23—41no—
245C23—41no—
246C23—41no—
247C23C11×#10412yes—
248C23C2×C11×C22⋊C411yescharacteristic
249D4—44no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—22no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—42no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—42no—
265C2×C4—42no—
266C2×C4—42no—
267C2×C4—42no—
268C2×C4—81no—
269C2×C4—84no—
270C2×C4C11×#9911yescharacteristic
271C2×C4C11×#9911yescharacteristic
272C2×C4C11×#13712yes—
273C8—44no—
274C8—82no—
275C22—21no—
276C22—21no—
277C22—22no—
278C22—42no—
279C22—42no—
280C22—42no—
281C22—41no—
282C22—41no—
283C22—41no—
284C22—41no—
285C22—41no—
286C22—81no—
287C22C2×C11×#9911yescharacteristic
288C22C11×#41911yescharacteristic
289C22C2×C11×#10411yescharacteristic
290C4—22no—
291C4—21no—
292C4—41no—
293C4—41no—
294C4—41no—
295C4—82no—
296C4—82no—
297C4C11×#35212yes—
298C2—21no—
299C2—21no—
300C2—42no—
301C2—81no—
302C2C11×#150811yescharacteristic
303C2C2×C11×#35211yescharacteristic
304C2C11×#213411yescharacteristic
subgroupG/H
center, socleC22×C11C2×#99
commutatorC22×C4C22×C4×C11
Frattini, cosocleC2×C4⋊C4C23×C11
prime radicalC22×D4×C11D4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C22×C4×C11 ◁ C2×C4×D4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
4. C11×#1353C2semidirect
48. #11790C11direct (N × H)
89. #1353C2×C11semidirect
237. C11#11790direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#24872
C4×C11×#1002
C11×#14652
C11×#13532
#1179011