Finite Group Databasebeta

← C11×#13147 #14590340

Subgroups — C11×#13147 #14590340

Order 2816.

394 conjugacy classes of subgroups.

The subgroup lattice has 326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#357C211yesmaximal, characteristic
2C2×C11×#357C211yesmaximal, characteristic
3C2×C4×C11×C16C211yesmaximal, characteristic, complemented
4C11×#1970C211yesmaximal, characteristic
5C11×#1942C211yesmaximal, characteristic, complemented
6C11×#1380C211yesmaximal, characteristic, complemented
7C11×#1380C211yesmaximal, characteristic, complemented
8C22×C11×D8C2211yescharacteristic
9C22×C11×C16C2211yescharacteristic
10C22×C11×C16C2211yescharacteristic
11C2×C11×#107C2211yescharacteristic
12C2×C11×#107C2211yescharacteristic
13C2×C11×#107C2211yescharacteristic
14C2×C11×#102—21no—
15C2×C4×C8×C11C2211yescharacteristic
16C11×#390—21no—
17C11×#389—21no—
18C11×#357—22no—
19C11×#357C414yescomplemented
20C4×C11×C16—22no—
21C11×#340—21no—
22C22×D4×C11—21no—
23C2×C11×D8—21no—
24C2×C11×D8—21no—
25C2×C11×D8—21no—
26C2×C11×D8—21no—
27C2×C11×D8—21no—
28C2×C11×D8C2×C412yes—
29C22×C8×C11D411yescharacteristic
30C22×C8×C11C2311yescharacteristic
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4—41no—
35C2×C11×C22⋊C4—41no—
36C2×C11×C22⋊C4—41no—
37C2×C42×C11D411yescharacteristic
38C2×C11×C16—21no—
39C2×C11×C16—21no—
40C2×C11×C16—21no—
41C2×C11×C16—21no—
42C2×C11×C16C2×C412yes—
43C2×C11×C16D412yes—
44C11×#107—21no—
45C11×#107—21no—
46C11×#107—21no—
47C11×#107—21no—
48C11×#107—21no—
49C11×#107C2×C412yes—
50C11×#102—42no—
51C4×C8×C11—21no—
52C4×C8×C11—21no—
53C11×#95—41no—
54#13147C1111yesmaximal, characteristic, direct product factor, Sylow
55C24×C11—41no—
56C2×D4×C11—22no—
57C2×D4×C11—41no—
58C2×D4×C11—41no—
59C2×D4×C11—41no—
60C2×D4×C11—41no—
61C2×D4×C11—41no—
62C22×C4×C11—41no—
63C22×C4×C11—41no—
64C22×C4×C11—41no—
65C22×C4×C11D811yescharacteristic
66C22×C4×C11D811yescharacteristic
67C22×C4×C11C2×D411yescharacteristic
68C11×D8—22no—
69C11×D8—22no—
70C11×D8—41no—
71C11×D8—41no—
72C2×C8×C11—21no—
73C2×C8×C11—21no—
74C2×C8×C11SD1612yes—
75C2×C8×C11C22×C411yescharacteristic
76C2×C8×C11C2×D411yescharacteristic
77C2×C8×C11#4111yescharacteristic
78C2×C8×C11#4111yescharacteristic
79C2×C8×C11#4111yescharacteristic
80C2×C8×C11#4111yescharacteristic
81C11×C4⋊C4—22no—
82C11×C4⋊C4—41no—
83C11×C4⋊C4—41no—
84C11×C4⋊C4—41no—
85C11×C4⋊C4—41no—
86C11×C4⋊C4—41no—
87C11×C4⋊C4—82no—
88C11×C22⋊C4—82no—
89C11×C22⋊C4—82no—
90C42×C11—21no—
91C42×C11—21no—
92C11×C16—22no—
93C11×C16—22no—
94C2×#357C2×C1111yescharacteristic
95C2×#357C2×C1111yescharacteristic
96C2×C4×C16C2×C1111yescharacteristic, complemented
97#1970C2×C1111yescharacteristic
98#1942C2×C1111yescharacteristic, complemented
99#1380C2×C1111yescharacteristic, complemented
100#1380C2×C1111yescharacteristic, complemented
101C23×C11—42no—
102C23×C11—81no—
103C23×C11—81no—
104C23×C11—81no—
105C23×C11—81no—
106C23×C11—81no—
107C23×C11—81no—
108C23×C11C2×D811yescharacteristic
109D4×C11—42no—
110D4×C11—42no—
111D4×C11—81no—
112D4×C11—81no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—42no—
118C2×C4×C11—81no—
119C2×C4×C11—81no—
120C2×C4×C11—81no—
121C2×C4×C11—81no—
122C2×C4×C11—81no—
123C2×C4×C11—81no—
124C2×C4×C11—81no—
125C2×C4×C11—81no—
126C2×C4×C11D1612yes—
127C2×C4×C11SD3212yes—
128C2×C4×C11C4×D411yescharacteristic
129C2×C4×C11#12111yescharacteristic
130C2×C4×C11#12411yescharacteristic
131C2×C4×C11C2×SD1611yescharacteristic
132C2×C4×C11#13511yescharacteristic
133C2×C4×C11#13511yescharacteristic
134C8×C11—22no—
135C8×C11#11711yescharacteristic
136C8×C11C4×D411yescharacteristic
137C8×C11#12311yescharacteristic
138C8×C11#12611yescharacteristic
139C22×D8C22×C1111yescharacteristic
140C22×C16C22×C1111yescharacteristic
141C22×C16C22×C1111yescharacteristic
142C2×#107C22×C1111yescharacteristic
143C2×#107C22×C1111yescharacteristic
144C2×#107C22×C1111yescharacteristic
145C2×#102—21no—
146C2×C4×C8C22×C1111yescharacteristic
147#390—21no—
148#389—21no—
149#357—22no—
150#357C4×C1114yescomplemented
151C4×C16—22no—
152#340—21no—
153C22×C11—82no—
154C22×C11—82no—
155C22×C11—82no—
156C22×C11—161no—
157C22×C11—161no—
158C22×C11—161no—
159C22×C11—161no—
160C22×C11C4×D811yescharacteristic
161C22×C11#46611yescharacteristic
162C22×C11#48611yescharacteristic
163C22×C11C2×D1611yescharacteristic
164C22×C11C2×SD3211yescharacteristic
165C22×C11#50811yescharacteristic
166C22×C11#50811yescharacteristic
167C4×C11—22no—
168C4×C11—22no—
169C4×C11—82no—
170C4×C11—161no—
171C4×C11—161no—
172C4×C11#38811yescharacteristic
173C4×C11C4×SD1611yescharacteristic
174C4×C11#46511yescharacteristic
175C4×C11#48811yescharacteristic
176C22×D4—21no—
177C2×D8—21no—
178C2×D8—21no—
179C2×D8—21no—
180C2×D8—21no—
181C2×D8—21no—
182C2×D8C2×C4×C1112yes—
183C22×C8D4×C1111yescharacteristic
184C22×C8C23×C1111yescharacteristic
185C2×C4⋊C4—21no—
186C2×C4⋊C4—21no—
187C2×C4⋊C4—21no—
188C2×C4⋊C4—41no—
189C2×C22⋊C4—41no—
190C2×C22⋊C4—41no—
191C2×C42D4×C1111yescharacteristic
192C2×C16—21no—
193C2×C16—21no—
194C2×C16—21no—
195C2×C16—21no—
196C2×C16C2×C4×C1112yes—
197C2×C16D4×C1112yes—
198#107—21no—
199#107—21no—
200#107—21no—
201#107—21no—
202#107—21no—
203#107C2×C4×C1112yes—
204#102—42no—
205C4×C8—21no—
206C4×C8—21no—
207#95—41no—
208C2×C11—162no—
209C2×C11#193411yescharacteristic
210C2×C11C4×D1611yescharacteristic
211C2×C11C4×SD3211yescharacteristic
212C2×C11#221511yescharacteristic
213C2×C11#221711yescharacteristic
214C2×C11#224011yescharacteristic
215C2×C11#224211yescharacteristic
216C24—41no—
217C2×D4—22no—
218C2×D4—41no—
219C2×D4—41no—
220C2×D4—41no—
221C2×D4—41no—
222C2×D4—41no—
223C22×C4—41no—
224C22×C4—41no—
225C22×C4—41no—
226C22×C4C11×D811yescharacteristic
227C22×C4C11×D811yescharacteristic
228C22×C4C2×D4×C1111yescharacteristic
229D8—22no—
230D8—22no—
231D8—41no—
232D8—41no—
233C2×C8—21no—
234C2×C8—21no—
235C2×C8C11×SD1612yes—
236C2×C8C22×C4×C1111yescharacteristic
237C2×C8C2×D4×C1111yescharacteristic
238C2×C8C11×#4111yescharacteristic
239C2×C8C11×#4111yescharacteristic
240C2×C8C11×#4111yescharacteristic
241C2×C8C11×#4111yescharacteristic
242C4⋊C4—22no—
243C4⋊C4—41no—
244C4⋊C4—41no—
245C4⋊C4—41no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C4⋊C4—82no—
249C22⋊C4—82no—
250C22⋊C4—82no—
251C42—21no—
252C42—21no—
253C16—22no—
254C16—22no—
255C11#1314711yescharacteristic, direct product factor, Sylow
256C23—42no—
257C23—81no—
258C23—81no—
259C23—81no—
260C23—81no—
261C23—81no—
262C23—81no—
263C23C2×C11×D811yescharacteristic
264D4—42no—
265D4—42no—
266D4—81no—
267D4—81no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—42no—
273C2×C4—81no—
274C2×C4—81no—
275C2×C4—81no—
276C2×C4—81no—
277C2×C4—81no—
278C2×C4—81no—
279C2×C4—81no—
280C2×C4—81no—
281C2×C4C11×D1612yes—
282C2×C4C11×SD3212yes—
283C2×C4C4×D4×C1111yescharacteristic
284C2×C4C11×#12111yescharacteristic
285C2×C4C11×#12411yescharacteristic
286C2×C4C2×C11×SD1611yescharacteristic
287C2×C4C11×#13511yescharacteristic
288C2×C4C11×#13511yescharacteristic
289C8—22no—
290C8C11×#11711yescharacteristic
291C8C4×D4×C1111yescharacteristic
292C8C11×#12311yescharacteristic
293C8C11×#12611yescharacteristic
294C22—82no—
295C22—82no—
296C22—82no—
297C22—161no—
298C22—161no—
299C22—161no—
300C22—161no—
301C22C4×C11×D811yescharacteristic
302C22C11×#46611yescharacteristic
303C22C11×#48611yescharacteristic
304C22C2×C11×D1611yescharacteristic
305C22C2×C11×SD3211yescharacteristic
306C22C11×#50811yescharacteristic
307C22C11×#50811yescharacteristic
308C4—22no—
309C4—22no—
310C4—82no—
311C4—161no—
312C4—161no—
313C4C11×#38811yescharacteristic
314C4C4×C11×SD1611yescharacteristic
315C4C11×#46511yescharacteristic
316C4C11×#48811yescharacteristic
317C2—162no—
318C2C11×#193411yescharacteristic
319C2C4×C11×D1611yescharacteristic
320C2C4×C11×SD3211yescharacteristic
321C2C11×#221511yescharacteristic
322C2C11×#221711yescharacteristic
323C2C11×#224011yescharacteristic
324C2C11×#224211yescharacteristic
subgroupG/H
center, socleC23×C11C2×D8
commutatorC2×C8C22×C4×C11
Frattini, cosocleC22×C8C23×C11
prime radicalC22×C11×D8C22
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C42×C11 ◁ C2×C4×C8×C11 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C4×C11×C16C2semidirect
5. C11×#1942C2semidirect
6. C11×#1380C2semidirect
7. C11×#1380C2semidirect
19. C11×#357C4semidirect
54. #13147C11direct (N × H)
96. C2×C4×C16C2×C11semidirect
98. #1942C2×C11semidirect
99. #1380C2×C11semidirect
100. #1380C2×C11semidirect
150. #357C4×C11semidirect
255. C11#13147direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#3572
C2×C4×C11×C162
C11×#19702
C11×#19422
C11×#13802
#1314711