Finite Group Databasebeta

← C11×#11786 #14588979

Subgroups — C11×#11786 #14588979

Order 2816.

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

normal subgroups only

This group has 462 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×#99C211yesmaximal, characteristic
3C11×#1466C211yesmaximal, characteristic
4C11×#1352C214yesmaximal, complemented
5C2×C4×D4×C11C2211yescharacteristic
6C22×C11×C4⋊C4C411yescharacteristic, complemented
7C11×#432—21no—
8C2×C11×#99—21no—
9C11×#400C412yescomplemented
10C11×#399C2212yes—
11C11×#389—21no—
12C11×#386—21no—
13C11×#385—21no—
14C11×#380—21no—
15C11×#380C411yescharacteristic, complemented
16C4×C11×C22⋊C4—21no—
17C11×#342C2212yes—
18C11×#323—21no—
19C11×#323C2212yes—
20C22×D4×C11D411yescharacteristic
21C23×C4×C11—21no—
22C23×C4×C11C2×C411yescharacteristic
23C23×C4×C11D411yescharacteristic
24C4×D4×C11—41no—
25C4×D4×C11—41no—
26C2×C11×C4⋊C4—21no—
27C2×C11×C4⋊C4—21no—
28C2×C11×C4⋊C4—22no—
29C2×C11×C4⋊C4—41no—
30C2×C11×C4⋊C4—41no—
31C2×C11×C4⋊C4C2×C412yes—
32C2×C11×C4⋊C4C2×C411yescharacteristic
33C2×C11×C22⋊C4—22no—
34C2×C11×C22⋊C4—21no—
35C2×C11×C22⋊C4—22no—
36C2×C11×C22⋊C4D411yescharacteristic
37C2×C11×C22⋊C4C2311yescharacteristic
38C2×C42×C11—41no—
39C2×C42×C11D411yescharacteristic
40C11×C4⋊C8—41no—
41C11×#99—24no—
42C11×C22⋊C8—22no—
43C11×#97—41no—
44C11×#95—22no—
45C11×#95—22no—
46C11×#95—41no—
47C11×#95C2×C412yes—
48#11786C1111yesmaximal, characteristic, direct product factor, Sylow
49C24×C11C22⋊C411yescharacteristic
50C24×C11C2×D411yescharacteristic
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—42no—
64C22×C4×C11—82no—
65C22×C4×C11C22⋊C411yescharacteristic
66C22×C4×C11C22⋊C411yescharacteristic
67C22×C4×C11C22⋊C411yescharacteristic
68C22×C4×C11C22×C411yescharacteristic
69C22×C4×C11C2×D411yescharacteristic
70C2×C8×C11—42no—
71C11×C4⋊C4—41no—
72C11×C4⋊C4—42no—
73C11×C4⋊C4—42no—
74C11×C4⋊C4—41no—
75C11×C4⋊C4—41no—
76C11×C4⋊C4—82no—
77C11×C22⋊C4—24no—
78C11×C22⋊C4—41no—
79C11×C22⋊C4—41no—
80C11×C22⋊C4—42no—
81C11×C22⋊C4—42no—
82C11×C22⋊C4—82no—
83C42×C11—21no—
84C42×C11—21no—
85C42×C11—82no—
86#2487C2×C1111yescharacteristic
87C4×#99C2×C1111yescharacteristic
88#1466C2×C1111yescharacteristic
89#1352C2×C1114yescomplemented
90C23×C11—21no—
91C23×C11—21no—
92C23×C11—21no—
93C23×C11—21no—
94C23×C11—41no—
95C23×C11—41no—
96C23×C11—41no—
97C23×C11—41no—
98C23×C11#10412yes—
99C23×C11C2×C22⋊C411yescharacteristic
100C23×C11#13712yes—
101D4×C11—44no—
102C2×C4×C11—22no—
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—42no—
110C2×C4×C11—42no—
111C2×C4×C11—42no—
112C2×C4×C11—41no—
113C2×C4×C11—41no—
114C2×C4×C11—41no—
115C2×C4×C11—44no—
116C2×C4×C11—42no—
117C2×C4×C11—42no—
118C2×C4×C11—42no—
119C2×C4×C11—42no—
120C2×C4×C11—42no—
121C2×C4×C11—42no—
122C2×C4×C11—81no—
123C2×C4×C11—82no—
124C2×C4×C11—82no—
125C2×C4×C11—84no—
126C2×C4×C11#9911yescharacteristic
127C2×C4×C11#9911yescharacteristic
128C8×C11—82no—
129C2×C4×D4C22×C1111yescharacteristic
130C22×C4⋊C4C4×C1111yescharacteristic, complemented
131#432—21no—
132C2×#99—21no—
133#400C4×C1112yescomplemented
134#399C22×C1112yes—
135#389—21no—
136#386—21no—
137#385—21no—
138#380—21no—
139#380C4×C1111yescharacteristic, complemented
140C4×C22⋊C4—21no—
141#342C22×C1112yes—
142#323—21no—
143#323C22×C1112yes—
144C22×C11—21no—
145C22×C11—21no—
146C22×C11—22no—
147C22×C11—22no—
148C22×C11—42no—
149C22×C11—42no—
150C22×C11—42no—
151C22×C11—41no—
152C22×C11—41no—
153C22×C11—41no—
154C22×C11—41no—
155C22×C11—81no—
156C22×C11C2×#9911yescharacteristic
157C22×C11#41911yescharacteristic
158C22×C11C2×#10411yescharacteristic
159C4×C11—21no—
160C4×C11—41no—
161C4×C11—41no—
162C4×C11—41no—
163C4×C11—41no—
164C4×C11—82no—
165C4×C11—84no—
166C4×C11—82no—
167C4×C11#35212yes—
168C22×D4D4×C1111yescharacteristic
169C23×C4—21no—
170C23×C4C2×C4×C1111yescharacteristic
171C23×C4D4×C1111yescharacteristic
172C4×D4—41no—
173C4×D4—41no—
174C2×C4⋊C4—21no—
175C2×C4⋊C4—21no—
176C2×C4⋊C4—22no—
177C2×C4⋊C4—41no—
178C2×C4⋊C4—41no—
179C2×C4⋊C4C2×C4×C1112yes—
180C2×C4⋊C4C2×C4×C1111yescharacteristic
181C2×C22⋊C4—22no—
182C2×C22⋊C4—21no—
183C2×C22⋊C4—22no—
184C2×C22⋊C4D4×C1111yescharacteristic
185C2×C22⋊C4C23×C1111yescharacteristic
186C2×C42—41no—
187C2×C42D4×C1111yescharacteristic
188C4⋊C8—41no—
189#99—24no—
190C22⋊C8—22no—
191#97—41no—
192#95—22no—
193#95—22no—
194#95—41no—
195#95C2×C4×C1112yes—
196C2×C11—21no—
197C2×C11—21no—
198C2×C11—42no—
199C2×C11—42no—
200C2×C11#150811yescharacteristic
201C2×C11C2×#35211yescharacteristic
202C2×C11#212811yescharacteristic
203C24C11×C22⋊C411yescharacteristic
204C24C2×D4×C1111yescharacteristic
205C2×D4—22no—
206C2×D4—22no—
207C2×D4—41no—
208C22×C4—21no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—22no—
213C22×C4—22no—
214C22×C4—42no—
215C22×C4—42no—
216C22×C4—42no—
217C22×C4—42no—
218C22×C4—82no—
219C22×C4C11×C22⋊C411yescharacteristic
220C22×C4C11×C22⋊C411yescharacteristic
221C22×C4C11×C22⋊C411yescharacteristic
222C22×C4C22×C4×C1111yescharacteristic
223C22×C4C2×D4×C1111yescharacteristic
224C2×C8—42no—
225C4⋊C4—41no—
226C4⋊C4—42no—
227C4⋊C4—42no—
228C4⋊C4—41no—
229C4⋊C4—41no—
230C4⋊C4—82no—
231C22⋊C4—24no—
232C22⋊C4—41no—
233C22⋊C4—41no—
234C22⋊C4—42no—
235C22⋊C4—42no—
236C22⋊C4—82no—
237C42—21no—
238C42—21no—
239C42—82no—
240C11#1178611yescharacteristic, direct product factor, Sylow
241C23—21no—
242C23—21no—
243C23—21no—
244C23—21no—
245C23—41no—
246C23—41no—
247C23—41no—
248C23—41no—
249C23C11×#10412yes—
250C23C2×C11×C22⋊C411yescharacteristic
251C23C11×#13712yes—
252D4—44no—
253C2×C4—22no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—42no—
261C2×C4—42no—
262C2×C4—42no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—44no—
267C2×C4—42no—
268C2×C4—42no—
269C2×C4—42no—
270C2×C4—42no—
271C2×C4—42no—
272C2×C4—42no—
273C2×C4—81no—
274C2×C4—82no—
275C2×C4—82no—
276C2×C4—84no—
277C2×C4C11×#9911yescharacteristic
278C2×C4C11×#9911yescharacteristic
279C8—82no—
280C22—21no—
281C22—21no—
282C22—22no—
283C22—22no—
284C22—42no—
285C22—42no—
286C22—42no—
287C22—41no—
288C22—41no—
289C22—41no—
290C22—41no—
291C22—81no—
292C22C2×C11×#9911yescharacteristic
293C22C11×#41911yescharacteristic
294C22C2×C11×#10411yescharacteristic
295C4—21no—
296C4—41no—
297C4—41no—
298C4—41no—
299C4—41no—
300C4—82no—
301C4—84no—
302C4—82no—
303C4C11×#35212yes—
304C2—21no—
305C2—21no—
306C2—42no—
307C2—42no—
308C2C11×#150811yescharacteristic
309C2C2×C11×#35211yescharacteristic
310C2C11×#212811yescharacteristic
subgroupG/H
center, socleC22×C11C2×#99
commutatorC22×C4C22×C4×C11
Frattini, cosocleC2×C22⋊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×#1352C2semidirect
6. C22×C11×C4⋊C4C4semidirect
9. C11×#400C4semidirect
15. C11×#380C4semidirect
48. #11786C11direct (N × H)
89. #1352C2×C11semidirect
130. C22×C4⋊C4C4×C11semidirect
133. #400C4×C11semidirect
139. #380C4×C11semidirect
240. C11#11786direct (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×#992
C11×#14662
C11×#13522
#1178611