Finite Group Databasebeta

← C11×#9509 #14586702

Subgroups — C11×#9509 #14586702

Order 2816.

524 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 524 conjugacy classes of subgroups — too many to draw. Only its 126 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×#2973C211yesmaximal, characteristic
2C11×#2487C211yesmaximal, characteristic
3C11×#1821C212yesmaximal, complemented
4C11×#1465C211yesmaximal, characteristic
5C11×#1305C212yesmaximal, complemented
6C2×C4×D4×C11C2211yescharacteristic
7C22×C11×C4⋊C4C2211yescharacteristic
8C11×#435—24no—
9C11×#432—21no—
10C11×#407C2212yes—
11C11×#407C2212yes—
12C2×C11×C22⋊C8—21no—
13C11×#400—21no—
14C11×#399—21no—
15C11×#389—21no—
16C11×#386C412yes—
17C11×#385C412yes—
18C11×#380—21no—
19C11×#380C2211yescharacteristic
20C11×#343—24no—
21C11×#324—21no—
22C11×#323—21no—
23C22×D4×C11C2×C411yescharacteristic
24C23×C4×C11C2×C412yes—
25C23×C4×C11D411yescharacteristic
26C23×C4×C11C2311yescharacteristic
27C2×C11×M16—22no—
28C2×C11×M16D414yes—
29C22×C8×C11—22no—
30C4×D4×C11—22no—
31C4×D4×C11—22no—
32C2×C11×C4⋊C4—22no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4—22no—
37C2×C11×C4⋊C4—22no—
38C2×C11×C4⋊C4D411yescharacteristic
39C2×C11×C22⋊C4—22no—
40C2×C11×C22⋊C4C2×C411yescharacteristic
41C2×C11×C22⋊C4C2×C412yes—
42C2×C11×C22⋊C4D411yescharacteristic
43C2×C42×C11D411yescharacteristic
44C11×C4⋊C8—22no—
45C11×C22⋊C8—22no—
46C11×C22⋊C8—22no—
47C11×C22⋊C8—22no—
48C11×C22⋊C8—22no—
49C11×C22⋊C8—22no—
50C11×#97—22no—
51C11×#95—22no—
52C11×#95—22no—
53C11×#95—21no—
54#9509C1111yesmaximal, characteristic, direct product factor, Sylow
55C24×C11C22⋊C411yescharacteristic
56C24×C11C22×C411yescharacteristic
57C2×D4×C11—22no—
58C2×D4×C11—22no—
59C2×D4×C11—41no—
60C22×C4×C11—21no—
61C22×C4×C11—21no—
62C22×C4×C11—22no—
63C22×C4×C11—22no—
64C22×C4×C11—24no—
65C22×C4×C11—42no—
66C22×C4×C11—42no—
67C22×C4×C11—82no—
68C22×C4×C11C22⋊C411yescharacteristic
69C22×C4×C11C22⋊C411yescharacteristic
70C22×C4×C11C22⋊C411yescharacteristic
71C22×C4×C11C2×D412yes—
72C22×C4×C11C2×D411yescharacteristic
73C22×C4×C11C2×D411yescharacteristic
74C22×C4×C11#4112yes—
75C11×M16—44no—
76C11×M16—44no—
77C2×C8×C11—24no—
78C2×C8×C11—42no—
79C2×C8×C11—82no—
80C11×C4⋊C4—22no—
81C11×C4⋊C4—42no—
82C11×C4⋊C4—41no—
83C11×C4⋊C4—42no—
84C11×C4⋊C4—41no—
85C11×C4⋊C4—82no—
86C11×C22⋊C4—22no—
87C11×C22⋊C4—22no—
88C11×C22⋊C4—42no—
89C11×C22⋊C4—82no—
90C42×C11—21no—
91C42×C11—21no—
92#2973C2×C1111yescharacteristic
93#2487C2×C1111yescharacteristic
94#1821C2×C1112yescomplemented
95#1465C2×C1111yescharacteristic
96#1305C2×C1112yescomplemented
97C23×C11—21no—
98C23×C11—21no—
99C23×C11—21no—
100C23×C11—21no—
101C23×C11—41no—
102C23×C11—41no—
103C23×C11—41no—
104C23×C11—41no—
105C23×C11#10112yes—
106C23×C11C2×C22⋊C411yescharacteristic
107C23×C11C4×D412yes—
108D4×C11—44no—
109C2×C4×C11—22no—
110C2×C4×C11—24no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—41no—
117C2×C4×C11—42no—
118C2×C4×C11—42no—
119C2×C4×C11—41no—
120C2×C4×C11—41no—
121C2×C4×C11—42no—
122C2×C4×C11—42no—
123C2×C4×C11—42no—
124C2×C4×C11—42no—
125C2×C4×C11—42no—
126C2×C4×C11—42no—
127C2×C4×C11—81no—
128C2×C4×C11—84no—
129C2×C4×C11#12011yescharacteristic
130C2×C4×C11#12112yes—
131C2×C4×C11#12311yescharacteristic
132C8×C11—44no—
133C8×C11—82no—
134C2×C4×D4C22×C1111yescharacteristic
135C22×C4⋊C4C22×C1111yescharacteristic
136#435—24no—
137#432—21no—
138#407C22×C1112yes—
139#407C22×C1112yes—
140C2×C22⋊C8—21no—
141#400—21no—
142#399—21no—
143#389—21no—
144#386C4×C1112yes—
145#385C4×C1112yes—
146#380—21no—
147#380C22×C1111yescharacteristic
148#343—24no—
149#324—21no—
150#323—21no—
151C22×C11—21no—
152C22×C11—21no—
153C22×C11—22no—
154C22×C11—22no—
155C22×C11—22no—
156C22×C11—22no—
157C22×C11—42no—
158C22×C11—42no—
159C22×C11—42no—
160C22×C11—41no—
161C22×C11—41no—
162C22×C11—81no—
163C22×C11#38611yescharacteristic
164C22×C11C2×#10111yescharacteristic
165C22×C11#41311yescharacteristic
166C4×C11—21no—
167C4×C11—22no—
168C4×C11—41no—
169C4×C11—41no—
170C4×C11—41no—
171C4×C11—82no—
172C4×C11—82no—
173C4×C11#45812yes—
174C22×D4C2×C4×C1111yescharacteristic
175C23×C4C2×C4×C1112yes—
176C23×C4D4×C1111yescharacteristic
177C23×C4C23×C1111yescharacteristic
178C2×M16—22no—
179C2×M16D4×C1114yes—
180C22×C8—22no—
181C4×D4—22no—
182C4×D4—22no—
183C2×C4⋊C4—22no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—21no—
186C2×C4⋊C4—21no—
187C2×C4⋊C4—22no—
188C2×C4⋊C4—22no—
189C2×C4⋊C4D4×C1111yescharacteristic
190C2×C22⋊C4—22no—
191C2×C22⋊C4C2×C4×C1111yescharacteristic
192C2×C22⋊C4C2×C4×C1112yes—
193C2×C22⋊C4D4×C1111yescharacteristic
194C2×C42D4×C1111yescharacteristic
195C4⋊C8—22no—
196C22⋊C8—22no—
197C22⋊C8—22no—
198C22⋊C8—22no—
199C22⋊C8—22no—
200C22⋊C8—22no—
201#97—22no—
202#95—22no—
203#95—22no—
204#95—21no—
205C2×C11—21no—
206C2×C11—21no—
207C2×C11—42no—
208C2×C11—42no—
209C2×C11#189011yescharacteristic
210C2×C11#190111yescharacteristic
211C2×C11#191411yescharacteristic
212C24C11×C22⋊C411yescharacteristic
213C24C22×C4×C1111yescharacteristic
214C2×D4—22no—
215C2×D4—22no—
216C2×D4—41no—
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—22no—
220C22×C4—22no—
221C22×C4—24no—
222C22×C4—42no—
223C22×C4—42no—
224C22×C4—82no—
225C22×C4C11×C22⋊C411yescharacteristic
226C22×C4C11×C22⋊C411yescharacteristic
227C22×C4C11×C22⋊C411yescharacteristic
228C22×C4C2×D4×C1112yes—
229C22×C4C2×D4×C1111yescharacteristic
230C22×C4C2×D4×C1111yescharacteristic
231C22×C4C11×#4112yes—
232M16—44no—
233M16—44no—
234C2×C8—24no—
235C2×C8—42no—
236C2×C8—82no—
237C4⋊C4—22no—
238C4⋊C4—42no—
239C4⋊C4—41no—
240C4⋊C4—42no—
241C4⋊C4—41no—
242C4⋊C4—82no—
243C22⋊C4—22no—
244C22⋊C4—22no—
245C22⋊C4—42no—
246C22⋊C4—82no—
247C42—21no—
248C42—21no—
249C11#950911yescharacteristic, direct product factor, Sylow
250C23—21no—
251C23—21no—
252C23—21no—
253C23—21no—
254C23—41no—
255C23—41no—
256C23—41no—
257C23—41no—
258C23C11×#10112yes—
259C23C2×C11×C22⋊C411yescharacteristic
260C23C4×D4×C1112yes—
261D4—44no—
262C2×C4—22no—
263C2×C4—24no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—41no—
270C2×C4—42no—
271C2×C4—42no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—42no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—81no—
281C2×C4—84no—
282C2×C4C11×#12011yescharacteristic
283C2×C4C11×#12112yes—
284C2×C4C11×#12311yescharacteristic
285C8—44no—
286C8—82no—
287C22—21no—
288C22—21no—
289C22—22no—
290C22—22no—
291C22—22no—
292C22—22no—
293C22—42no—
294C22—42no—
295C22—42no—
296C22—41no—
297C22—41no—
298C22—81no—
299C22C11×#38611yescharacteristic
300C22C2×C11×#10111yescharacteristic
301C22C11×#41311yescharacteristic
302C4—22no—
303C4—21no—
304C4—41no—
305C4—41no—
306C4—41no—
307C4—82no—
308C4—82no—
309C4C11×#45812yes—
310C2—21no—
311C2—21no—
312C2—42no—
313C2—42no—
314C2C11×#189011yescharacteristic
315C2C11×#190111yescharacteristic
316C2C11×#191411yescharacteristic
subgroupG/H
center, socleC22×C11#386
commutatorC24C22×C4×C11
Frattini, cosocleC23×C4C23×C11
prime radicalC22×D4×C11C2×C4
LCSG ▷ C24 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
3. C11×#1821C2semidirect
5. C11×#1305C2semidirect
54. #9509C11direct (N × H)
94. #1821C2×C11semidirect
96. #1305C2×C11semidirect
249. C11#9509direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#29732
C11×#24872
C11×#18212
C11×#14652
C11×#13052
#950911