Finite Group Databasebeta

← C11×#13610 #14590803

Subgroups — C11×#13610 #14590803

Order 2816.

336 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 86 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×#3222C211yesmaximal, characteristic
2C11×#2128C211yesmaximal, characteristic
3C11×#2127C211yesmaximal, characteristic
4C11×#1412C212yesmaximal, complemented
5C11×#1409C212yesmaximal, complemented
6C11×#541C411yescharacteristic, complemented
7C11×#535C2211yescharacteristic
8C11×#497C411yescharacteristic, complemented
9C11×#492C2211yescharacteristic
10C11×#490C2211yescharacteristic
11C11×#488C411yescharacteristic, complemented
12C11×#464—21no—
13C11×#460—21no—
14C11×#452—21no—
15C11×#450—21no—
16C11×#433C411yescharacteristic, complemented
17C11×#410—21no—
18C2×C11×#99—21no—
19C11×#354—21no—
20C11×#353—21no—
21C11×#353C2212yes—
22C11×#353C2212yes—
23C2×C11×#41D411yescharacteristic
24C22×D4×C11D411yescharacteristic
25C2×C11×Q16—21no—
26C2×C11×SD16—21no—
27C2×C11×SD16—21no—
28C2×C11×SD16—21no—
29C11×C4⋊Q8C2×C411yescharacteristic, complemented
30C11×#127D411yescharacteristic
31C11×#127C2311yescharacteristic
32C11×#126—41no—
33C11×#125—41no—
34C11×#125C2×C411yescharacteristic, complemented
35C11×#124C2×C411yescharacteristic
36C11×#124D411yescharacteristic
37C11×C22⋊Q8—21no—
38C11×#121—41no—
39C11×#120—41no—
40C4×Q8×C11—21no—
41C11×#117—41no—
42C11×#117C2×C411yescharacteristic
43C2×C11×C22⋊C4—41no—
44C11×C4⋊C8—21no—
45C11×#103—21no—
46C11×#102—21no—
47C11×#102—21no—
48C11×#102—21no—
49C11×#99—22no—
50C11×#99—22no—
51C11×#99—41no—
52C11×#99—41no—
53C11×C22⋊C8—21no—
54C11×#97C2×C411yescharacteristic, complemented
55C4×C8×C11C2×C411yescharacteristic, complemented
56#13610C1111yesmaximal, characteristic, direct product factor, Sylow
57C24×C11—21no—
58C11×#41—81no—
59C2×Q8×C11—21no—
60C2×Q8×C11C22⋊C411yescharacteristic
61C2×D4×C11—21no—
62C2×D4×C11—21no—
63C2×D4×C11—41no—
64C2×D4×C11—41no—
65C2×D4×C11—81no—
66C2×D4×C11C22⋊C411yescharacteristic
67C2×D4×C11C2×D411yescharacteristic
68C2×D4×C11C2×D411yescharacteristic
69C22×C4×C11—21no—
70C22×C4×C11—81no—
71C22×C4×C11C22⋊C411yescharacteristic
72C11×Q16—81no—
73C11×SD16—81no—
74C11×SD16—81no—
75C11×SD16—81no—
76C2×C8×C11—21no—
77C2×C8×C11—21no—
78C11×C4⋊C4—21no—
79C11×C4⋊C4—21no—
80C11×C4⋊C4—41no—
81C11×C4⋊C4—41no—
82C11×C4⋊C4—41no—
83C11×C4⋊C4—41no—
84C11×C4⋊C4—81no—
85C11×C22⋊C4—21no—
86C11×C22⋊C4—41no—
87C11×C22⋊C4—41no—
88C11×C22⋊C4—41no—
89C11×C22⋊C4—42no—
90C11×C22⋊C4—42no—
91C11×C22⋊C4—81no—
92C42×C11—41no—
93C42×C11—81no—
94C42×C11C22⋊C411yescharacteristic
95C42×C11C22×C411yescharacteristic
96#3222C2×C1111yescharacteristic
97#2128C2×C1111yescharacteristic
98#2127C2×C1111yescharacteristic
99#1412C2×C1112yescomplemented
100#1409C2×C1112yescomplemented
101C23×C11—21no—
102C23×C11—21no—
103C23×C11—21no—
104C23×C11—41no—
105C23×C11—41no—
106C23×C11—161no—
107C23×C11#9911yescharacteristic
108Q8×C11—41no—
109Q8×C11—41no—
110Q8×C11—41no—
111D4×C11—41no—
112D4×C11—41no—
113D4×C11—41no—
114D4×C11—81no—
115D4×C11—81no—
116D4×C11—161no—
117D4×C11—161no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—41no—
122C2×C4×C11—41no—
123C2×C4×C11—41no—
124C2×C4×C11—41no—
125C2×C4×C11—41no—
126C2×C4×C11—82no—
127C2×C4×C11—82no—
128C2×C4×C11—162no—
129C2×C4×C11#9911yescharacteristic
130C2×C4×C11C2×C22⋊C411yescharacteristic
131C8×C11—41no—
132C8×C11—41no—
133#541C4×C1111yescharacteristic, complemented
134#535C22×C1111yescharacteristic
135#497C4×C1111yescharacteristic, complemented
136#492C22×C1111yescharacteristic
137#490C22×C1111yescharacteristic
138#488C4×C1111yescharacteristic, complemented
139#464—21no—
140#460—21no—
141#452—21no—
142#450—21no—
143#433C4×C1111yescharacteristic, complemented
144#410—21no—
145C2×#99—21no—
146#354—21no—
147#353—21no—
148#353C22×C1112yes—
149#353C22×C1112yes—
150C22×C11—21no—
151C22×C11—41no—
152C22×C11—41no—
153C22×C11—41no—
154C22×C11—41no—
155C22×C11—81no—
156C22×C11—81no—
157C22×C11—81no—
158C22×C11—82no—
159C22×C11—161no—
160C22×C11C2×#9911yescharacteristic
161C4×C11—21no—
162C4×C11—21no—
163C4×C11—41no—
164C4×C11—41no—
165C4×C11—41no—
166C4×C11—81no—
167C4×C11—81no—
168C4×C11—162no—
169C4×C11—162no—
170C2×#41D4×C1111yescharacteristic
171C22×D4D4×C1111yescharacteristic
172C2×Q16—21no—
173C2×SD16—21no—
174C2×SD16—21no—
175C2×SD16—21no—
176C4⋊Q8C2×C4×C1111yescharacteristic, complemented
177#127D4×C1111yescharacteristic
178#127C23×C1111yescharacteristic
179#126—41no—
180#125—41no—
181#125C2×C4×C1111yescharacteristic, complemented
182#124C2×C4×C1111yescharacteristic
183#124D4×C1111yescharacteristic
184C22⋊Q8—21no—
185#121—41no—
186#120—41no—
187C4×Q8—21no—
188#117—41no—
189#117C2×C4×C1111yescharacteristic
190C2×C22⋊C4—41no—
191C4⋊C8—21no—
192#103—21no—
193#102—21no—
194#102—21no—
195#102—21no—
196#99—22no—
197#99—22no—
198#99—41no—
199#99—41no—
200C22⋊C8—21no—
201#97C2×C4×C1111yescharacteristic, complemented
202C4×C8C2×C4×C1111yescharacteristic, complemented
203C2×C11—21no—
204C2×C11—41no—
205C2×C11—81no—
206C2×C11—81no—
207C2×C11—81no—
208C2×C11#212711yescharacteristic
209C24—21no—
210#41—81no—
211C2×Q8—21no—
212C2×Q8C11×C22⋊C411yescharacteristic
213C2×D4—21no—
214C2×D4—21no—
215C2×D4—41no—
216C2×D4—41no—
217C2×D4—81no—
218C2×D4C11×C22⋊C411yescharacteristic
219C2×D4C2×D4×C1111yescharacteristic
220C2×D4C2×D4×C1111yescharacteristic
221C22×C4—21no—
222C22×C4—81no—
223C22×C4C11×C22⋊C411yescharacteristic
224Q16—81no—
225SD16—81no—
226SD16—81no—
227SD16—81no—
228C2×C8—21no—
229C2×C8—21no—
230C4⋊C4—21no—
231C4⋊C4—21no—
232C4⋊C4—41no—
233C4⋊C4—41no—
234C4⋊C4—41no—
235C4⋊C4—41no—
236C4⋊C4—81no—
237C22⋊C4—21no—
238C22⋊C4—41no—
239C22⋊C4—41no—
240C22⋊C4—41no—
241C22⋊C4—42no—
242C22⋊C4—42no—
243C22⋊C4—81no—
244C42—41no—
245C42—81no—
246C42C11×C22⋊C411yescharacteristic
247C42C22×C4×C1111yescharacteristic
248C11#1361011yescharacteristic, direct product factor, Sylow
249C23—21no—
250C23—21no—
251C23—21no—
252C23—41no—
253C23—41no—
254C23—161no—
255C23C11×#9911yescharacteristic
256Q8—41no—
257Q8—41no—
258Q8—41no—
259D4—41no—
260D4—41no—
261D4—41no—
262D4—81no—
263D4—81no—
264D4—161no—
265D4—161no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—82no—
275C2×C4—82no—
276C2×C4—162no—
277C2×C4C11×#9911yescharacteristic
278C2×C4C2×C11×C22⋊C411yescharacteristic
279C8—41no—
280C8—41no—
281C22—21no—
282C22—41no—
283C22—41no—
284C22—41no—
285C22—41no—
286C22—81no—
287C22—81no—
288C22—81no—
289C22—82no—
290C22—161no—
291C22C2×C11×#9911yescharacteristic
292C4—21no—
293C4—21no—
294C4—41no—
295C4—41no—
296C4—41no—
297C4—81no—
298C4—81no—
299C4—162no—
300C4—162no—
301C2—21no—
302C2—41no—
303C2—81no—
304C2—81no—
305C2—81no—
306C2C11×#212711yescharacteristic
subgroupG/H
center, socleC2×C11#2127
commutatorC42C22×C4×C11
Frattini, cosocle#127C23×C11
prime radicalC11×#535C22
LCSG ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C11 ◁ C22×C11 ◁ C22×C4×C11 ◁ C11×#535 ◁ G

Complements

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

NH ≅ G/Ntype
4. C11×#1412C2semidirect
5. C11×#1409C2semidirect
6. C11×#541C4semidirect
8. C11×#497C4semidirect
11. C11×#488C4semidirect
16. C11×#433C4semidirect
29. C11×C4⋊Q8C2×C4semidirect
34. C11×#125C2×C4semidirect
54. C11×#97C2×C4semidirect
55. C4×C8×C11C2×C4semidirect
56. #13610C11direct (N × H)
99. #1412C2×C11semidirect
100. #1409C2×C11semidirect
133. #541C4×C11semidirect
135. #497C4×C11semidirect
138. #488C4×C11semidirect
143. #433C4×C11semidirect
176. C4⋊Q8C2×C4×C11semidirect
181. #125C2×C4×C11semidirect
201. #97C2×C4×C11semidirect
202. C4×C8C2×C4×C11semidirect
248. C11#13610direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32222
C11×#21282
C11×#21272
C11×#14122
C11×#14092
#1361011