Finite Group Databasebeta

← C11×#3376 #13066214

Subgroups — C11×#3376 #13066214

Order 1408.

346 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#556C211yesmaximal, characteristic, complemented
2C11×#554C211yesmaximal, characteristic, complemented
3C11×#491C211yesmaximal, characteristic, complemented
4C11×#489C211yesmaximal, characteristic, complemented
5C11×#488C211yesmaximal, characteristic, complemented
6C11×#479C211yesmaximal, characteristic, complemented
7C11×#478C211yesmaximal, characteristic, complemented
8C11×#475C211yesmaximal, characteristic, complemented
9C11×#463C211yesmaximal, characteristic
10C11×#463C211yesmaximal, characteristic
11C11×#461C211yesmaximal, characteristic, complemented
12C11×#446C211yesmaximal, characteristic, complemented
13C11×#442C211yesmaximal, characteristic
14C11×#440C211yesmaximal, characteristic, complemented
15C4×C11×SD16C211yesmaximal, characteristic, complemented
16C2×C11×SD16C2211yescharacteristic
17C2×C11×SD16C2211yescharacteristic
18C2×C11×D8C2211yescharacteristic
19C11×C4⋊Q8C2211yescharacteristic
20C11×C4⋊Q8C2211yescharacteristic
21C11×#126—21no—
22C11×#126—21no—
23C11×#125C2211yescharacteristic
24C11×#125C2211yescharacteristic
25C11×#124C2211yescharacteristic
26C11×#124C2211yescharacteristic
27C11×C22⋊Q8—21no—
28C11×C22⋊Q8—21no—
29C11×C22⋊Q8—21no—
30C11×C22⋊Q8—21no—
31C4×Q8×C11C2211yescharacteristic
32C4×Q8×C11C2211yescharacteristic
33C4×Q8×C11C2211yescharacteristic
34C4×D4×C11C2211yescharacteristic
35C4×D4×C11C2211yescharacteristic
36C4×D4×C11C2211yescharacteristic
37C4×D4×C11C2211yescharacteristic
38C11×#117—21no—
39C2×C11×C4⋊C4—21no—
40C11×#107C2211yescharacteristic
41C11×#106C2211yescharacteristic
42C11×#106C2211yescharacteristic
43C11×C4⋊C8C2211yescharacteristic
44C11×C4⋊C8C2211yescharacteristic
45C11×C4⋊C8C2211yescharacteristic
46C11×#103C2211yescharacteristic
47C11×#103C2211yescharacteristic
48C11×#103C2211yescharacteristic
49C11×#103C2211yescharacteristic
50C11×#103C2211yescharacteristic
51C11×#103C2211yescharacteristic
52C11×#102C2211yescharacteristic
53C11×#102C2211yescharacteristic
54C11×#102C2211yescharacteristic
55C11×#102C2211yescharacteristic
56C11×#97C2211yescharacteristic
57C11×#97C2211yescharacteristic
58C4×C8×C11C2211yescharacteristic
59C2×Q8×C11—21no—
60C2×Q8×C11D411yescharacteristic
61C2×Q8×C11C2311yescharacteristic
62C2×Q8×C11C2311yescharacteristic
63C2×D4×C11C2311yescharacteristic
64C2×D4×C11C2311yescharacteristic
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11—21no—
69C11×SD16—22no—
70C11×SD16—22no—
71C11×D8—22no—
72C2×C8×C11C2311yescharacteristic
73C2×C8×C11C2311yescharacteristic
74C2×C8×C11C2311yescharacteristic
75C2×C8×C11C2311yescharacteristic
76C11×C4⋊C4—21no—
77C11×C4⋊C4—21no—
78C11×C4⋊C4—21no—
79C11×C4⋊C4—21no—
80C11×C4⋊C4—21no—
81C11×C4⋊C4—21no—
82C11×C4⋊C4—21no—
83C11×C4⋊C4—21no—
84C11×C4⋊C4—21no—
85C11×C4⋊C4D411yescharacteristic
86C11×C4⋊C4D411yescharacteristic
87C11×C4⋊C4D411yescharacteristic
88C11×C4⋊C4C2311yescharacteristic
89C11×C4⋊C4C2311yescharacteristic
90C11×C4⋊C4C2311yescharacteristic
91C11×C4⋊C4C2311yescharacteristic
92C11×C22⋊C4—21no—
93C11×C22⋊C4—21no—
94C11×C22⋊C4—21no—
95C11×C22⋊C4—21no—
96C11×C22⋊C4—21no—
97C11×C22⋊C4—21no—
98C11×C22⋊C4—21no—
99C11×C22⋊C4—21no—
100C42×C11—21no—
101C42×C11—21no—
102C42×C11C2311yescharacteristic
103C42×C11C2311yescharacteristic
104C42×C11C2311yescharacteristic
105#3376C1111yesmaximal, characteristic, direct product factor, Sylow
106C23×C11—21no—
107C23×C11—21no—
108Q8×C11—21no—
109Q8×C11—21no—
110Q8×C11—21no—
111Q8×C11—21no—
112Q8×C11—41no—
113Q8×C11—81no—
114D4×C11—21no—
115D4×C11—21no—
116D4×C11—21no—
117D4×C11#4112yes—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—42no—
125C2×C4×C11—42no—
126C2×C4×C11—81no—
127C2×C4×C11—81no—
128C2×C4×C11C2×D411yescharacteristic
129C2×C4×C11C2×D411yescharacteristic
130C2×C4×C11C2×D411yescharacteristic
131C2×C4×C11C2×D411yescharacteristic
132C2×C4×C11C2×D411yescharacteristic
133C2×C4×C11C2×D411yescharacteristic
134C2×C4×C11C2411yescharacteristic
135C8×C11—21no—
136C8×C11—21no—
137C8×C11—21no—
138C8×C11—21no—
139#556C2×C1111yescharacteristic, complemented
140#554C2×C1111yescharacteristic, complemented
141#491C2×C1111yescharacteristic, complemented
142#489C2×C1111yescharacteristic, complemented
143#488C2×C1111yescharacteristic, complemented
144#479C2×C1111yescharacteristic, complemented
145#478C2×C1111yescharacteristic, complemented
146#475C2×C1111yescharacteristic, complemented
147#463C2×C1111yescharacteristic
148#463C2×C1111yescharacteristic
149#461C2×C1111yescharacteristic, complemented
150#446C2×C1111yescharacteristic, complemented
151#442C2×C1111yescharacteristic
152#440C2×C1111yescharacteristic, complemented
153C4×SD16C2×C1111yescharacteristic, complemented
154C22×C11—22no—
155C22×C11—41no—
156C22×C11—41no—
157C22×C11—41no—
158C22×C11—41no—
159C22×C11—41no—
160C22×C11C22×D411yescharacteristic
161C4×C11—21no—
162C4×C11—21no—
163C4×C11—21no—
164C4×C11—21no—
165C4×C11—21no—
166C4×C11—21no—
167C4×C11—41no—
168C4×C11—41no—
169C4×C11—41no—
170C4×C11—41no—
171C4×C11—41no—
172C4×C11—41no—
173C4×C11C2×#4111yescharacteristic
174C4×C112−1+411yescharacteristic
175C2×SD16C22×C1111yescharacteristic
176C2×SD16C22×C1111yescharacteristic
177C2×D8C22×C1111yescharacteristic
178C4⋊Q8C22×C1111yescharacteristic
179C4⋊Q8C22×C1111yescharacteristic
180#126—21no—
181#126—21no—
182#125C22×C1111yescharacteristic
183#125C22×C1111yescharacteristic
184#124C22×C1111yescharacteristic
185#124C22×C1111yescharacteristic
186C22⋊Q8—21no—
187C22⋊Q8—21no—
188C22⋊Q8—21no—
189C22⋊Q8—21no—
190C4×Q8C22×C1111yescharacteristic
191C4×Q8C22×C1111yescharacteristic
192C4×Q8C22×C1111yescharacteristic
193C4×D4C22×C1111yescharacteristic
194C4×D4C22×C1111yescharacteristic
195C4×D4C22×C1111yescharacteristic
196C4×D4C22×C1111yescharacteristic
197#117—21no—
198C2×C4⋊C4—21no—
199#107C22×C1111yescharacteristic
200#106C22×C1111yescharacteristic
201#106C22×C1111yescharacteristic
202C4⋊C8C22×C1111yescharacteristic
203C4⋊C8C22×C1111yescharacteristic
204C4⋊C8C22×C1111yescharacteristic
205#103C22×C1111yescharacteristic
206#103C22×C1111yescharacteristic
207#103C22×C1111yescharacteristic
208#103C22×C1111yescharacteristic
209#103C22×C1111yescharacteristic
210#103C22×C1111yescharacteristic
211#102C22×C1111yescharacteristic
212#102C22×C1111yescharacteristic
213#102C22×C1111yescharacteristic
214#102C22×C1111yescharacteristic
215#97C22×C1111yescharacteristic
216#97C22×C1111yescharacteristic
217C4×C8C22×C1111yescharacteristic
218C2×C11—42no—
219C2×C11—81no—
220C2×C11#54811yescharacteristic
221C2×C11#57511yescharacteristic
222C2×C11#57711yescharacteristic
223C2×Q8—21no—
224C2×Q8D4×C1111yescharacteristic
225C2×Q8C23×C1111yescharacteristic
226C2×Q8C23×C1111yescharacteristic
227C2×D4C23×C1111yescharacteristic
228C2×D4C23×C1111yescharacteristic
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233SD16—22no—
234SD16—22no—
235D8—22no—
236C2×C8C23×C1111yescharacteristic
237C2×C8C23×C1111yescharacteristic
238C2×C8C23×C1111yescharacteristic
239C2×C8C23×C1111yescharacteristic
240C4⋊C4—21no—
241C4⋊C4—21no—
242C4⋊C4—21no—
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4D4×C1111yescharacteristic
250C4⋊C4D4×C1111yescharacteristic
251C4⋊C4D4×C1111yescharacteristic
252C4⋊C4C23×C1111yescharacteristic
253C4⋊C4C23×C1111yescharacteristic
254C4⋊C4C23×C1111yescharacteristic
255C4⋊C4C23×C1111yescharacteristic
256C22⋊C4—21no—
257C22⋊C4—21no—
258C22⋊C4—21no—
259C22⋊C4—21no—
260C22⋊C4—21no—
261C22⋊C4—21no—
262C22⋊C4—21no—
263C22⋊C4—21no—
264C42—21no—
265C42—21no—
266C42C23×C1111yescharacteristic
267C42C23×C1111yescharacteristic
268C42C23×C1111yescharacteristic
269C11#337611yescharacteristic, direct product factor, Sylow
270C23—21no—
271C23—21no—
272Q8—21no—
273Q8—21no—
274Q8—21no—
275Q8—21no—
276Q8—41no—
277Q8—81no—
278D4—21no—
279D4—21no—
280D4—21no—
281D4C11×#4112yes—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—81no—
291C2×C4—81no—
292C2×C4C2×D4×C1111yescharacteristic
293C2×C4C2×D4×C1111yescharacteristic
294C2×C4C2×D4×C1111yescharacteristic
295C2×C4C2×D4×C1111yescharacteristic
296C2×C4C2×D4×C1111yescharacteristic
297C2×C4C2×D4×C1111yescharacteristic
298C2×C4C24×C1111yescharacteristic
299C8—21no—
300C8—21no—
301C8—21no—
302C8—21no—
303C22—22no—
304C22—41no—
305C22—41no—
306C22—41no—
307C22—41no—
308C22—41no—
309C22C22×D4×C1111yescharacteristic
310C4—21no—
311C4—21no—
312C4—21no—
313C4—21no—
314C4—21no—
315C4—21no—
316C4—41no—
317C4—41no—
318C4—41no—
319C4—41no—
320C4—41no—
321C4—41no—
322C4C2×C11×#4111yescharacteristic
323C4C11×2−1+411yescharacteristic
324C2—42no—
325C2—81no—
326C2C11×#54811yescharacteristic
327C2C11×#57511yescharacteristic
328C2C11×#57711yescharacteristic
subgroupG/H
center, socleC22×C11C22×D4
commutator, Frattini, cosocleC2×C4C24×C11
prime radicalC2×C11×D8C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C4×Q8×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#556C2semidirect
2. C11×#554C2semidirect
3. C11×#491C2semidirect
4. C11×#489C2semidirect
5. C11×#488C2semidirect
6. C11×#479C2semidirect
7. C11×#478C2semidirect
8. C11×#475C2semidirect
11. C11×#461C2semidirect
12. C11×#446C2semidirect
14. C11×#440C2semidirect
15. C4×C11×SD16C2semidirect
105. #3376C11direct (N × H)
139. #556C2×C11semidirect
140. #554C2×C11semidirect
141. #491C2×C11semidirect
142. #489C2×C11semidirect
143. #488C2×C11semidirect
144. #479C2×C11semidirect
145. #478C2×C11semidirect
146. #475C2×C11semidirect
149. #461C2×C11semidirect
150. #446C2×C11semidirect
152. #440C2×C11semidirect
153. C4×SD16C2×C11semidirect
269. C11#3376direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#5562
C11×#5542
C11×#4912
C11×#4892
C11×#4882
C11×#4792
C11×#4782
C11×#4752
C11×#4632
C11×#4612
C11×#4462
C11×#4422
C11×#4402
C4×C11×SD162
#337611