Finite Group Databasebeta

← C11×#13611 #14590804

Subgroups — C11×#13611 #14590804

Order 2816.

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

normal subgroups only

This group has 316 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×#3221C211yesmaximal, characteristic
2C11×#2135C211yesmaximal, characteristic, complemented
3C11×#2133C211yesmaximal, characteristic, complemented
4C11×#1413C212yesmaximal, complemented
5C11×#1410C212yesmaximal, complemented
6C11×#540C411yescharacteristic
7C11×#536C2211yescharacteristic
8C11×#496C411yescharacteristic
9C11×#492C2211yescharacteristic
10C11×#491C2211yescharacteristic
11C11×#488C411yescharacteristic
12C11×#463—21no—
13C11×#461—21no—
14C11×#449—21no—
15C11×#448—21no—
16C11×#433C411yescharacteristic
17C11×#413—21no—
18C2×C11×#101—21no—
19C11×#356—21no—
20C11×#356C2212yes—
21C11×#356C2212yes—
22C11×#355—21no—
23C2×C11×#41D411yescharacteristic
24C22×Q8×C11D411yescharacteristic
25C2×C11×SD16—21no—
26C2×C11×SD16—21no—
27C2×C11×SD16—21no—
28C2×C11×D8—21no—
29C2×C11×M16—41no—
30C2×C11×M16—41no—
31C11×C4⋊Q8D411yescharacteristic
32C11×C4⋊Q8C2311yescharacteristic
33C11×#127C2×C411yescharacteristic
34C11×#125C2×C411yescharacteristic
35C11×#124C2×C411yescharacteristic
36C11×#124D411yescharacteristic
37C11×#123—41no—
38C11×#123—41no—
39C11×C22⋊Q8—41no—
40C11×#121—21no—
41C11×#121—41no—
42C4×D4×C11—21no—
43C11×#117C2×C411yescharacteristic
44C11×C4⋊C8—21no—
45C11×#103—21no—
46C11×#103—21no—
47C11×#103—21no—
48C11×#102—21no—
49C11×#101—22no—
50C11×#101—22no—
51C11×#101—41no—
52C11×#100—41no—
53C11×C22⋊C8—21no—
54C11×#97C2×C411yescharacteristic
55C4×C8×C11C2×C411yescharacteristic
56#13611C1111yesmaximal, characteristic, direct product factor, Sylow
57C11×#41—81no—
58C2×Q8×C11—21no—
59C2×Q8×C11—81no—
60C2×Q8×C11C22⋊C411yescharacteristic
61C2×Q8×C11C2×D411yescharacteristic
62C2×Q8×C11C2×D411yescharacteristic
63C2×D4×C11—21no—
64C2×D4×C11—21no—
65C2×D4×C11—41no—
66C2×D4×C11—41no—
67C2×D4×C11C22⋊C411yescharacteristic
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11—41no—
71C22×C4×C11C22⋊C411yescharacteristic
72C11×SD16—81no—
73C11×SD16—81no—
74C11×SD16—81no—
75C11×D8—81no—
76C11×M16—42no—
77C11×M16—42no—
78C11×M16—81no—
79C11×M16—81no—
80C2×C8×C11—21no—
81C2×C8×C11—21no—
82C2×C8×C11—81no—
83C2×C8×C11—81no—
84C11×C4⋊C4—21no—
85C11×C4⋊C4—21no—
86C11×C4⋊C4—41no—
87C11×C4⋊C4—41no—
88C11×C4⋊C4—41no—
89C11×C22⋊C4—21no—
90C11×C22⋊C4—41no—
91C11×C22⋊C4—41no—
92C11×C22⋊C4—41no—
93C11×C22⋊C4—41no—
94C42×C11C22⋊C411yescharacteristic
95C42×C11C22×C411yescharacteristic
96#3221C2×C1111yescharacteristic
97#2135C2×C1111yescharacteristic, complemented
98#2133C2×C1111yescharacteristic, complemented
99#1413C2×C1112yescomplemented
100#1410C2×C1112yescomplemented
101C23×C11—21no—
102C23×C11—41no—
103C23×C11#9911yescharacteristic
104Q8×C11—41no—
105Q8×C11—41no—
106Q8×C11—41no—
107Q8×C11—81no—
108D4×C11—41no—
109D4×C11—41no—
110D4×C11—41no—
111D4×C11—81no—
112D4×C11—161no—
113D4×C11—161no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—41no—
120C2×C4×C11—41no—
121C2×C4×C11—41no—
122C2×C4×C11—41no—
123C2×C4×C11—41no—
124C2×C4×C11—41no—
125C2×C4×C11—161no—
126C2×C4×C11#9911yescharacteristic
127C2×C4×C11C2×C22⋊C411yescharacteristic
128C8×C11—41no—
129C8×C11—41no—
130C8×C11—82no—
131C8×C11—82no—
132#540C4×C1111yescharacteristic
133#536C22×C1111yescharacteristic
134#496C4×C1111yescharacteristic
135#492C22×C1111yescharacteristic
136#491C22×C1111yescharacteristic
137#488C4×C1111yescharacteristic
138#463—21no—
139#461—21no—
140#449—21no—
141#448—21no—
142#433C4×C1111yescharacteristic
143#413—21no—
144C2×#101—21no—
145#356—21no—
146#356C22×C1112yes—
147#356C22×C1112yes—
148#355—21no—
149C22×C11—21no—
150C22×C11—41no—
151C22×C11—41no—
152C22×C11—81no—
153C22×C11—81no—
154C22×C11—81no—
155C22×C11—81no—
156C22×C11C2×#9911yescharacteristic
157C4×C11—21no—
158C4×C11—21no—
159C4×C11—41no—
160C4×C11—41no—
161C4×C11—41no—
162C4×C11—41no—
163C4×C11—41no—
164C4×C11—81no—
165C2×#41D4×C1111yescharacteristic
166C22×Q8D4×C1111yescharacteristic
167C2×SD16—21no—
168C2×SD16—21no—
169C2×SD16—21no—
170C2×D8—21no—
171C2×M16—41no—
172C2×M16—41no—
173C4⋊Q8D4×C1111yescharacteristic
174C4⋊Q8C23×C1111yescharacteristic
175#127C2×C4×C1111yescharacteristic
176#125C2×C4×C1111yescharacteristic
177#124C2×C4×C1111yescharacteristic
178#124D4×C1111yescharacteristic
179#123—41no—
180#123—41no—
181C22⋊Q8—41no—
182#121—21no—
183#121—41no—
184C4×D4—21no—
185#117C2×C4×C1111yescharacteristic
186C4⋊C8—21no—
187#103—21no—
188#103—21no—
189#103—21no—
190#102—21no—
191#101—22no—
192#101—22no—
193#101—41no—
194#100—41no—
195C22⋊C8—21no—
196#97C2×C4×C1111yescharacteristic
197C4×C8C2×C4×C1111yescharacteristic
198C2×C11—21no—
199C2×C11—41no—
200C2×C11—81no—
201C2×C11—161no—
202C2×C11#212711yescharacteristic
203#41—81no—
204C2×Q8—21no—
205C2×Q8—81no—
206C2×Q8C11×C22⋊C411yescharacteristic
207C2×Q8C2×D4×C1111yescharacteristic
208C2×Q8C2×D4×C1111yescharacteristic
209C2×D4—21no—
210C2×D4—21no—
211C2×D4—41no—
212C2×D4—41no—
213C2×D4C11×C22⋊C411yescharacteristic
214C22×C4—21no—
215C22×C4—21no—
216C22×C4—41no—
217C22×C4C11×C22⋊C411yescharacteristic
218SD16—81no—
219SD16—81no—
220SD16—81no—
221D8—81no—
222M16—42no—
223M16—42no—
224M16—81no—
225M16—81no—
226C2×C8—21no—
227C2×C8—21no—
228C2×C8—81no—
229C2×C8—81no—
230C4⋊C4—21no—
231C4⋊C4—21no—
232C4⋊C4—41no—
233C4⋊C4—41no—
234C4⋊C4—41no—
235C22⋊C4—21no—
236C22⋊C4—41no—
237C22⋊C4—41no—
238C22⋊C4—41no—
239C22⋊C4—41no—
240C42C11×C22⋊C411yescharacteristic
241C42C22×C4×C1111yescharacteristic
242C11#1361111yescharacteristic, direct product factor, Sylow
243C23—21no—
244C23—41no—
245C23C11×#9911yescharacteristic
246Q8—41no—
247Q8—41no—
248Q8—41no—
249Q8—81no—
250D4—41no—
251D4—41no—
252D4—41no—
253D4—81no—
254D4—161no—
255D4—161no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—161no—
268C2×C4C11×#9911yescharacteristic
269C2×C4C2×C11×C22⋊C411yescharacteristic
270C8—41no—
271C8—41no—
272C8—82no—
273C8—82no—
274C22—21no—
275C22—41no—
276C22—41no—
277C22—81no—
278C22—81no—
279C22—81no—
280C22—81no—
281C22C2×C11×#9911yescharacteristic
282C4—21no—
283C4—21no—
284C4—41no—
285C4—41no—
286C4—41no—
287C4—41no—
288C4—41no—
289C4—81no—
290C2—21no—
291C2—41no—
292C2—81no—
293C2—161no—
294C2C11×#212711yescharacteristic
subgroupG/H
center, socleC2×C11#2127
commutatorC42C22×C4×C11
Frattini, cosocleC4⋊Q8C23×C11
prime radicalC11×#3221C2
LCSG ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C11 ◁ C22×C11 ◁ C22×C4×C11 ◁ C11×#536 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#2135C2semidirect
3. C11×#2133C2semidirect
4. C11×#1413C2semidirect
5. C11×#1410C2semidirect
56. #13611C11direct (N × H)
97. #2135C2×C11semidirect
98. #2133C2×C11semidirect
99. #1413C2×C11semidirect
100. #1410C2×C11semidirect
242. C11#13611direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32212
C11×#21352
C11×#21332
C11×#14132
C11×#14102
#1361111