Finite Group Databasebeta

← C11×#33669 #14610862

Subgroups — C11×#33669 #14610862

Order 2816.

650 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3169C211yesmaximal, characteristic, complemented
2C2×C4×C11×D8C211yesmaximal, characteristic, complemented
3C11×#2233C212yesmaximal, complemented
4C11×#2226C212yesmaximal, complemented
5C11×#2206C212yesmaximal, complemented
6C11×#2184C212yesmaximal, complemented
7C11×#2177C214yesmaximal, complemented
8C11×#2163C211yesmaximal, characteristic, complemented
9C22×C11×D8C2211yescharacteristic
10C11×#532—21no—
11C2×C4×D4×C11—21no—
12C2×C11×D16C2214yes—
13C11×#500C2211yescharacteristic, complemented
14C11×#493C2211yescharacteristic, complemented
15C11×#486—21no—
16C11×#466—21no—
17C11×#466C2212yes—
18C4×C11×D8—21no—
19C4×C11×D8—21no—
20C4×C11×D8—21no—
21C4×C11×D8C2212yes—
22C4×C11×D8C2212yes—
23C4×C11×D8C2212yescomplemented
24C2×C11×#107C2211yescharacteristic
25C2×C11×#102—21no—
26C2×C4×C8×C11C2211yescharacteristic
27C11×#367C2214yescomplemented
28C11×C4⋊C16C2212yescomplemented
29C11×#357C2214yes—
30C11×#357C2214yescomplemented
31C11×C22⋊C16C2212yes—
32C11×#346C2212yescomplemented
33C2×C11×#41—41no—
34C22×D4×C11—21no—
35C23×C4×C11—41no—
36C2×C11×D8—24no—
37C2×C11×D8—21no—
38C2×C11×D8—21no—
39C2×C11×D8C2312yes—
40C2×C11×D8C2312yes—
41C22×C8×C11D411yescharacteristic
42C22×C8×C11C2311yescharacteristic
43C11×C4⋊Q8—21no—
44C11×#127—21no—
45C11×#124—41no—
46C11×#121—22no—
47C11×#121—41no—
48C4×D4×C11—22no—
49C4×D4×C11—22no—
50C4×D4×C11—22no—
51C4×D4×C11—41no—
52C4×D4×C11—41no—
53C4×D4×C11—41no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C22⋊C4—41no—
56C2×C42×C11D411yescharacteristic
57C11×D16—28no—
58C2×C11×C16C2314yes—
59C11×#107—21no—
60C11×#107—21no—
61C11×#107C2312yes—
62C11×#107C2312yes—
63C11×#102—22no—
64C11×#102—22no—
65C11×#102—22no—
66C11×#102—22no—
67C4×C8×C11D411yescharacteristic
68C4×C8×C11D411yescharacteristic
69C4×C8×C11C2311yescharacteristic
70C4×C8×C11C2311yescharacteristic
71#33669C1111yesmaximal, characteristic, direct product factor, Sylow
72C24×C11—41no—
73C11×#41—84no—
74C2×Q8×C11—41no—
75C2×D4×C11—24no—
76C2×D4×C11—22no—
77C2×D4×C11—22no—
78C2×D4×C11—42no—
79C2×D4×C11—42no—
80C2×D4×C11—41no—
81C2×D4×C11—41no—
82C2×D4×C11—41no—
83C22×C4×C11—41no—
84C22×C4×C11—42no—
85C22×C4×C11—42no—
86C22×C4×C11—42no—
87C22×C4×C11—84no—
88C22×C4×C11D811yescharacteristic
89C22×C4×C11D811yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C11×D8—24no—
92C11×D8—22no—
93C11×D8—24no—
94C11×D8—42no—
95C11×D8#4114yescomplemented
96C2×C8×C11—22no—
97C2×C8×C11—41no—
98C2×C8×C11C2×D411yescharacteristic
99C2×C8×C11C2×D411yescharacteristic
100C2×C8×C11C2×D411yescharacteristic
101C2×C8×C11C2411yescharacteristic
102C11×C4⋊C4—22no—
103C11×C4⋊C4—22no—
104C11×C4⋊C4—41no—
105C11×C4⋊C4—41no—
106C11×C22⋊C4—42no—
107C11×C22⋊C4—42no—
108C11×C22⋊C4—42no—
109C11×C22⋊C4—42no—
110C42×C11D811yescharacteristic
111C42×C11D811yescharacteristic
112C42×C11C2×D411yescharacteristic
113C42×C11C2×D411yescharacteristic
114C11×C16—24no—
115#3169C2×C1111yescharacteristic, complemented
116C2×C4×D8C2×C1111yescharacteristic, complemented
117#2233C2×C1112yescomplemented
118#2226C2×C1112yescomplemented
119#2206C2×C1112yescomplemented
120#2184C2×C1112yescomplemented
121#2177C2×C1114yescomplemented
122#2163C2×C1111yescharacteristic, complemented
123C23×C11—44no—
124C23×C11—42no—
125C23×C11—42no—
126C23×C11—82no—
127C23×C11—82no—
128C23×C11C2×D811yescharacteristic
129Q8×C11—82no—
130D4×C11—24no—
131D4×C11—44no—
132D4×C11—42no—
133D4×C11—42no—
134D4×C11—42no—
135D4×C11—82no—
136D4×C11—84no—
137D4×C11—82no—
138C2×C4×C11—22no—
139C2×C4×C11—21no—
140C2×C4×C11—21no—
141C2×C4×C11—22no—
142C2×C4×C11—42no—
143C2×C4×C11—42no—
144C2×C4×C11—84no—
145C2×C4×C11—84no—
146C2×C4×C11—82no—
147C2×C4×C11—84no—
148C2×C4×C11C2×D811yescharacteristic
149C2×C4×C11C2×D811yescharacteristic
150C2×C4×C11C2×D811yescharacteristic
151C2×C4×C11C2×D811yescharacteristic
152C2×C4×C11C2×D811yescharacteristic
153C2×C4×C11C22×D411yescharacteristic
154C8×C11—21no—
155C8×C11—21no—
156C8×C11—21no—
157C8×C11C2×#4112yes—
158C22×D8C22×C1111yescharacteristic
159#532—21no—
160C2×C4×D4—21no—
161C2×D16C22×C1114yes—
162#500C22×C1111yescharacteristic, complemented
163#493C22×C1111yescharacteristic, complemented
164#486—21no—
165#466—21no—
166#466C22×C1112yes—
167C4×D8—21no—
168C4×D8—21no—
169C4×D8—21no—
170C4×D8C22×C1112yes—
171C4×D8C22×C1112yes—
172C4×D8C22×C1112yescomplemented
173C2×#107C22×C1111yescharacteristic
174C2×#102—21no—
175C2×C4×C8C22×C1111yescharacteristic
176#367C22×C1114yescomplemented
177C4⋊C16C22×C1112yescomplemented
178#357C22×C1114yes—
179#357C22×C1114yescomplemented
180C22⋊C16C22×C1112yes—
181#346C22×C1112yescomplemented
182C22×C11—21no—
183C22×C11—21no—
184C22×C11—44no—
185C22×C11—88no—
186C22×C11—82no—
187C22×C11—82no—
188C22×C11—82no—
189C22×C11—82no—
190C22×C11—82no—
191C22×C11#50912yes—
192C22×C11C22×D811yescharacteristic
193C4×C11—21no—
194C4×C11—21no—
195C4×C11—21no—
196C4×C11—21no—
197C4×C11—82no—
198C4×C11—82no—
199C4×C11#50912yes—
200C4×C11#52511yescharacteristic
201C4×C11#57511yescharacteristic
202C2×#41—41no—
203C22×D4—21no—
204C23×C4—41no—
205C2×D8—24no—
206C2×D8—21no—
207C2×D8—21no—
208C2×D8C23×C1112yes—
209C2×D8C23×C1112yes—
210C22×C8D4×C1111yescharacteristic
211C22×C8C23×C1111yescharacteristic
212C4⋊Q8—21no—
213#127—21no—
214#124—41no—
215#121—22no—
216#121—41no—
217C4×D4—22no—
218C4×D4—22no—
219C4×D4—22no—
220C4×D4—41no—
221C4×D4—41no—
222C4×D4—41no—
223C2×C4⋊C4—21no—
224C2×C22⋊C4—41no—
225C2×C42D4×C1111yescharacteristic
226D16—28no—
227C2×C16C23×C1114yes—
228#107—21no—
229#107—21no—
230#107C23×C1112yes—
231#107C23×C1112yes—
232#102—22no—
233#102—22no—
234#102—22no—
235#102—22no—
236C4×C8D4×C1111yescharacteristic
237C4×C8D4×C1111yescharacteristic
238C4×C8C23×C1111yescharacteristic
239C4×C8C23×C1111yescharacteristic
240C2×C11—22no—
241C2×C11—84no—
242C2×C11—162no—
243C2×C11#310011yescharacteristic
244C2×C11C2×#50911yescharacteristic
245C2×C11C2×#50911yescharacteristic
246C24—41no—
247#41—84no—
248C2×Q8—41no—
249C2×D4—24no—
250C2×D4—22no—
251C2×D4—22no—
252C2×D4—42no—
253C2×D4—42no—
254C2×D4—41no—
255C2×D4—41no—
256C2×D4—41no—
257C22×C4—41no—
258C22×C4—42no—
259C22×C4—42no—
260C22×C4—42no—
261C22×C4—84no—
262C22×C4C11×D811yescharacteristic
263C22×C4C11×D811yescharacteristic
264C22×C4C2×D4×C1111yescharacteristic
265D8—24no—
266D8—22no—
267D8—24no—
268D8—42no—
269D8C11×#4114yescomplemented
270C2×C8—22no—
271C2×C8—41no—
272C2×C8C2×D4×C1111yescharacteristic
273C2×C8C2×D4×C1111yescharacteristic
274C2×C8C2×D4×C1111yescharacteristic
275C2×C8C24×C1111yescharacteristic
276C4⋊C4—22no—
277C4⋊C4—22no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C22⋊C4—42no—
281C22⋊C4—42no—
282C22⋊C4—42no—
283C22⋊C4—42no—
284C42C11×D811yescharacteristic
285C42C11×D811yescharacteristic
286C42C2×D4×C1111yescharacteristic
287C42C2×D4×C1111yescharacteristic
288C16—24no—
289C11#3366911yescharacteristic, direct product factor, Sylow
290C23—44no—
291C23—42no—
292C23—42no—
293C23—82no—
294C23—82no—
295C23C2×C11×D811yescharacteristic
296Q8—82no—
297D4—24no—
298D4—44no—
299D4—42no—
300D4—42no—
301D4—42no—
302D4—82no—
303D4—84no—
304D4—82no—
305C2×C4—22no—
306C2×C4—22no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—42no—
310C2×C4—42no—
311C2×C4—84no—
312C2×C4—84no—
313C2×C4—82no—
314C2×C4—84no—
315C2×C4C2×C11×D811yescharacteristic
316C2×C4C2×C11×D811yescharacteristic
317C2×C4C2×C11×D811yescharacteristic
318C2×C4C2×C11×D811yescharacteristic
319C2×C4C2×C11×D811yescharacteristic
320C2×C4C22×D4×C1111yescharacteristic
321C8—21no—
322C8—21no—
323C8—21no—
324C8C2×C11×#4112yes—
325C22—21no—
326C22—21no—
327C22—44no—
328C22—88no—
329C22—82no—
330C22—82no—
331C22—82no—
332C22—82no—
333C22—82no—
334C22C11×#50912yes—
335C22C22×C11×D811yescharacteristic
336C4—21no—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—82no—
341C4—82no—
342C4C11×#50912yes—
343C4C11×#52511yescharacteristic
344C4C11×#57511yescharacteristic
345C2—22no—
346C2—84no—
347C2—162no—
348C2C11×#310011yescharacteristic
349C2C2×C11×#50911yescharacteristic
350C2C2×C11×#50911yescharacteristic
subgroupG/H
center, socleC22×C11C22×D8
commutator, Frattini, cosocleC2×C8C24×C11
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ C2×C4×C8×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3169C2semidirect
2. C2×C4×C11×D8C2semidirect
3. C11×#2233C2semidirect
4. C11×#2226C2semidirect
5. C11×#2206C2semidirect
6. C11×#2184C2semidirect
7. C11×#2177C2semidirect
8. C11×#2163C2semidirect
13. C11×#500C22semidirect
14. C11×#493C22semidirect
23. C4×C11×D8C22semidirect
27. C11×#367C22semidirect
28. C11×C4⋊C16C22semidirect
30. C11×#357C22semidirect
32. C11×#346C22semidirect
71. #33669C11direct (N × H)
95. C11×D8#41semidirect
115. #3169C2×C11semidirect
116. C2×C4×D8C2×C11semidirect
117. #2233C2×C11semidirect
118. #2226C2×C11semidirect
119. #2206C2×C11semidirect
120. #2184C2×C11semidirect
121. #2177C2×C11semidirect
122. #2163C2×C11semidirect
162. #500C22×C11semidirect
163. #493C22×C11semidirect
172. C4×D8C22×C11semidirect
176. #367C22×C11semidirect
177. C4⋊C16C22×C11semidirect
179. #357C22×C11semidirect
181. #346C22×C11semidirect
269. D8C11×#41semidirect
289. C11#33669direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#31692
C2×C4×C11×D82
C11×#22332
C11×#22262
C11×#22062
C11×#21842
C11×#21772
C11×#21632
#3366911