Finite Group Databasebeta

← C11×#60032 #14637225

Subgroups — C11×#60032 #14637225

Order 2816.

2212 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2736C211yesmaximal, characteristic, complemented
2C11×#2668C213yesmaximal, complemented
3C11×#2578C216yesmaximal, complemented
4C11×#2564C213yesmaximal, complemented
5C11×#2535C213yesmaximal, complemented
6C11×#2517C213yesmaximal, complemented
7C11×#2463C213yesmaximal, complemented
8C11×#2364C216yesmaximal, complemented
9C4×C11×#120C213yesmaximal, complemented
10C24×C4×C11C2211yescharacteristic
11C2×C11×C22⋊Q8C2213yescomplemented
12C2×C11×#121C2216yes—
13C2×C11×#120C2213yes—
14C2×C4×D4×C11C2216yes—
15C2×C4×D4×C11C2213yes—
16C2×C4×D4×C11C2213yescomplemented
17C11×#400C2213yescomplemented
18C11×#399C2213yes—
19C11×#397C2216yes—
20C11×#397C2213yes—
21C11×#397C2213yescomplemented
22C11×#395C2211yescharacteristic, complemented
23C11×#394C2216yes—
24C11×#393C2213yes—
25C11×#392C2213yes—
26C11×#392C2211yescharacteristic, complemented
27C11×#388C2216yes—
28C11×#388C2216yescomplemented
29C11×#387C2216yescomplemented
30C11×#387C2216yescomplemented
31C11×#387C2216yescomplemented
32C11×#386C2216yes—
33C11×#386C2216yes—
34C11×#386C2216yes—
35C11×#386C2213yes—
36C11×#386C2216yescomplemented
37C11×#385C2213yes—
38C11×#385C2216yes—
39C11×#383C2212yescomplemented
40C11×#382C2213yescomplemented
41C11×#380C2216yescomplemented
42C11×#379C2213yes—
43C4×C11×C22⋊C4C2216yes—
44C4×C11×C22⋊C4C2213yes—
45C4×C11×C22⋊C4C2216yescomplemented
46C2×C11×#95C2213yescomplemented
47C25×C11C2311yescharacteristic
48C22×Q8×C11C2311yescharacteristic
49C22×D4×C11C2316yes—
50C22×D4×C11C2313yes—
51C22×D4×C11C2313yes—
52C23×C4×C11—46no—
53C23×C4×C11C2313yes—
54C23×C4×C11C2316yes—
55C23×C4×C11C2313yes—
56C23×C4×C11C2313yes—
57C11×C22⋊Q8—46no—
58C11×#121—224no—
59C11×#120—212no—
60C4×D4×C11—46no—
61C4×D4×C11—46no—
62C4×D4×C11—412no—
63C2×C11×C4⋊C4C2316yes—
64C2×C11×C4⋊C4C2316yes—
65C2×C11×C4⋊C4C2313yes—
66C2×C11×C4⋊C4C2313yes—
67C2×C11×C4⋊C4C2313yes—
68C2×C11×C22⋊C4C2316yes—
69C2×C11×C22⋊C4C2316yes—
70C2×C11×C22⋊C4C2313yes—
71C2×C11×C22⋊C4C2316yes—
72C2×C11×C22⋊C4C2316yes—
73C2×C11×C22⋊C4C2313yes—
74C2×C11×C22⋊C4C2316yes—
75C2×C11×C22⋊C4C2313yes—
76C2×C11×C22⋊C4C2313yes—
77C2×C11×C22⋊C4C2316yes—
78C2×C42×C11C2313yes—
79C2×C42×C11C2316yes—
80C2×C42×C11C2312yes—
81C11×#95C2316yes—
82C11×#95C2313yes—
83C11×#95C2313yes—
84C11×#95C2316yes—
85C11×#95C2316yes—
86C11×#95C2316yes—
87C11×#95C2316yes—
88C11×#95C2311yescharacteristic
89C11×#95C2313yes—
90C11×#95C2316yes—
91#60032C1111yesmaximal, characteristic, direct product factor, Sylow
92C24×C11—26no—
93C24×C11—43no—
94C24×C11—41no—
95C24×C11C2413yes—
96C24×C11C2413yes—
97C2×Q8×C11—43no—
98C2×D4×C11—212no—
99C2×D4×C11—212no—
100C2×D4×C11—212no—
101C2×D4×C11—43no—
102C2×D4×C11—43no—
103C2×D4×C11—46no—
104C2×D4×C11—43no—
105C2×D4×C11#41112yes—
106C22×C4×C11—212no—
107C22×C4×C11—26no—
108C22×C4×C11—212no—
109C22×C4×C11—26no—
110C22×C4×C11—43no—
111C22×C4×C11—46no—
112C22×C4×C11—46no—
113C22×C4×C11—46no—
114C22×C4×C11—46no—
115C22×C4×C11—416no—
116C22×C4×C11C2416yes—
117C22×C4×C11C2416yes—
118C22×C4×C11C2413yes—
119C22×C4×C11C2411yescharacteristic
120C22×C4×C11C2413yes—
121C22×C4×C11C2413yes—
122C22×C4×C11C2413yes—
123C11×C4⋊C4—212no—
124C11×C4⋊C4—212no—
125C11×C4⋊C4—43no—
126C11×C4⋊C4—43no—
127C11×C4⋊C4—43no—
128C11×C22⋊C4—26no—
129C11×C22⋊C4—212no—
130C11×C22⋊C4—212no—
131C11×C22⋊C4—212no—
132C11×C22⋊C4—212no—
133C11×C22⋊C4—43no—
134C11×C22⋊C4—43no—
135C11×C22⋊C4—43no—
136C11×C22⋊C4—46no—
137C11×C22⋊C4—46no—
138C42×C11—26no—
139C42×C11—42no—
140C42×C11—46no—
141#2736C2×C1111yescharacteristic, complemented
142#2668C2×C1113yescomplemented
143#2578C2×C1116yescomplemented
144#2564C2×C1113yescomplemented
145#2535C2×C1113yescomplemented
146#2517C2×C1113yescomplemented
147#2463C2×C1113yescomplemented
148#2364C2×C1116yescomplemented
149C4×#120C2×C1113yescomplemented
150C23×C11—26no—
151C23×C11—26no—
152C23×C11—26no—
153C23×C11—23no—
154C23×C11—26no—
155C23×C11—23no—
156C23×C11—23no—
157C23×C11—23no—
158C23×C11—412no—
159C23×C11—412no—
160C23×C11—44no—
161C23×C11C2×#4116yes—
162C23×C11C2×#4116yes—
163C23×C11C2511yescharacteristic
164Q8×C11—82no—
165D4×C11—412no—
166D4×C11—412no—
167D4×C11—424no—
168C2×C4×C11—23no—
169C2×C4×C11—26no—
170C2×C4×C11—23no—
171C2×C4×C11—26no—
172C2×C4×C11—26no—
173C2×C4×C11—26no—
174C2×C4×C11—26no—
175C2×C4×C11—23no—
176C2×C4×C11—26no—
177C2×C4×C11—26no—
178C2×C4×C11—26no—
179C2×C4×C11—23no—
180C2×C4×C11—23no—
181C2×C4×C11—26no—
182C2×C4×C11—412no—
183C2×C4×C11—412no—
184C2×C4×C11—812no—
185C2×C4×C11—86no—
186C2×C4×C11C2×#4116yes—
187C2×C4×C11H(5,𝔽2)16yes—
188C24×C4C22×C1111yescharacteristic
189C2×C22⋊Q8C22×C1113yescomplemented
190C2×#121C22×C1116yes—
191C2×#120C22×C1113yes—
192C2×C4×D4C22×C1113yes—
193C2×C4×D4C22×C1116yes—
194C2×C4×D4C22×C1113yescomplemented
195#400C22×C1113yescomplemented
196#399C22×C1113yes—
197#397C22×C1116yes—
198#397C22×C1113yes—
199#397C22×C1113yescomplemented
200#395C22×C1111yescharacteristic, complemented
201#394C22×C1116yes—
202#393C22×C1113yes—
203#392C22×C1113yes—
204#392C22×C1111yescharacteristic, complemented
205#388C22×C1116yes—
206#388C22×C1116yescomplemented
207#387C22×C1116yescomplemented
208#387C22×C1116yescomplemented
209#387C22×C1116yescomplemented
210#386C22×C1116yes—
211#386C22×C1116yes—
212#386C22×C1116yes—
213#386C22×C1113yes—
214#386C22×C1116yescomplemented
215#385C22×C1116yes—
216#385C22×C1113yes—
217#383C22×C1112yescomplemented
218#382C22×C1113yescomplemented
219#380C22×C1116yescomplemented
220#379C22×C1113yes—
221C4×C22⋊C4C22×C1113yes—
222C4×C22⋊C4C22×C1116yes—
223C4×C22⋊C4C22×C1116yescomplemented
224C2×#95C22×C1113yescomplemented
225C22×C11—212no—
226C22×C11—212no—
227C22×C11—26no—
228C22×C11—26no—
229C22×C11—416no—
230C22×C11—43no—
231C22×C11—43no—
232C22×C11—46no—
233C22×C11—46no—
234C22×C11—43no—
235C22×C11—43no—
236C22×C11C22×#4113yes—
237C22×C11C2×H(5,𝔽2)13yes—
238C22×C11#58511yescharacteristic
239C4×C11—26no—
240C4×C11—26no—
241C4×C11—46no—
242C4×C11—43no—
243C4×C11—46no—
244C4×C11—41no—
245C4×C11—43no—
246C25C23×C1111yescharacteristic
247C22×Q8C23×C1111yescharacteristic
248C22×D4C23×C1116yes—
249C22×D4C23×C1113yes—
250C22×D4C23×C1113yes—
251C23×C4—46no—
252C23×C4C23×C1113yes—
253C23×C4C23×C1113yes—
254C23×C4C23×C1113yes—
255C23×C4C23×C1116yes—
256C22⋊Q8—46no—
257#121—224no—
258#120—212no—
259C4×D4—46no—
260C4×D4—46no—
261C4×D4—412no—
262C2×C4⋊C4C23×C1116yes—
263C2×C4⋊C4C23×C1116yes—
264C2×C4⋊C4C23×C1113yes—
265C2×C4⋊C4C23×C1113yes—
266C2×C4⋊C4C23×C1113yes—
267C2×C22⋊C4C23×C1116yes—
268C2×C22⋊C4C23×C1116yes—
269C2×C22⋊C4C23×C1113yes—
270C2×C22⋊C4C23×C1116yes—
271C2×C22⋊C4C23×C1116yes—
272C2×C22⋊C4C23×C1116yes—
273C2×C22⋊C4C23×C1113yes—
274C2×C22⋊C4C23×C1113yes—
275C2×C22⋊C4C23×C1116yes—
276C2×C22⋊C4C23×C1113yes—
277C2×C42C23×C1113yes—
278C2×C42C23×C1116yes—
279C2×C42C23×C1112yes—
280#95C23×C1116yes—
281#95C23×C1113yes—
282#95C23×C1113yes—
283#95C23×C1116yes—
284#95C23×C1116yes—
285#95C23×C1116yes—
286#95C23×C1116yes—
287#95C23×C1111yescharacteristic
288#95C23×C1113yes—
289#95C23×C1116yes—
290C2×C11—46no—
291C2×C11—46no—
292C2×C11#348113yes—
293C2×C11#350513yes—
294C2×C11#353211yescharacteristic
295C24—26no—
296C24—43no—
297C24—41no—
298C24C24×C1113yes—
299C24C24×C1113yes—
300C2×Q8—43no—
301C2×D4—212no—
302C2×D4—212no—
303C2×D4—212no—
304C2×D4—43no—
305C2×D4—43no—
306C2×D4—46no—
307C2×D4—43no—
308C2×D4C11×#41112yes—
309C22×C4—212no—
310C22×C4—26no—
311C22×C4—212no—
312C22×C4—26no—
313C22×C4—43no—
314C22×C4—46no—
315C22×C4—46no—
316C22×C4—46no—
317C22×C4—46no—
318C22×C4—416no—
319C22×C4C24×C1116yes—
320C22×C4C24×C1116yes—
321C22×C4C24×C1113yes—
322C22×C4C24×C1111yescharacteristic
323C22×C4C24×C1113yes—
324C22×C4C24×C1113yes—
325C22×C4C24×C1113yes—
326C4⋊C4—212no—
327C4⋊C4—212no—
328C4⋊C4—43no—
329C4⋊C4—43no—
330C4⋊C4—43no—
331C22⋊C4—26no—
332C22⋊C4—212no—
333C22⋊C4—212no—
334C22⋊C4—212no—
335C22⋊C4—212no—
336C22⋊C4—43no—
337C22⋊C4—43no—
338C22⋊C4—46no—
339C22⋊C4—46no—
340C22⋊C4—43no—
341C42—26no—
342C42—46no—
343C42—42no—
344C11#6003211yescharacteristic, direct product factor, Sylow
345C23—26no—
346C23—26no—
347C23—26no—
348C23—23no—
349C23—26no—
350C23—23no—
351C23—23no—
352C23—23no—
353C23—412no—
354C23—412no—
355C23—44no—
356C23C2×C11×#4116yes—
357C23C2×C11×#4116yes—
358C23C25×C1111yescharacteristic
359Q8—82no—
360D4—412no—
361D4—412no—
362D4—424no—
363C2×C4—23no—
364C2×C4—26no—
365C2×C4—23no—
366C2×C4—26no—
367C2×C4—26no—
368C2×C4—26no—
369C2×C4—26no—
370C2×C4—23no—
371C2×C4—26no—
372C2×C4—26no—
373C2×C4—26no—
374C2×C4—23no—
375C2×C4—23no—
376C2×C4—26no—
377C2×C4—412no—
378C2×C4—412no—
379C2×C4—812no—
380C2×C4—86no—
381C2×C4C2×C11×#4116yes—
382C2×C4C11×H(5,𝔽2)16yes—
383C22—212no—
384C22—212no—
385C22—26no—
386C22—26no—
387C22—416no—
388C22—43no—
389C22—43no—
390C22—46no—
391C22—46no—
392C22—43no—
393C22—43no—
394C22C22×C11×#4113yes—
395C22C2×C11×H(5,𝔽2)13yes—
396C22C11×#58511yescharacteristic
397C4—26no—
398C4—26no—
399C4—46no—
400C4—43no—
401C4—46no—
402C4—41no—
403C4—43no—
404C2—46no—
405C2—46no—
406C2C11×#348113yes—
407C2C11×#350513yes—
408C2C11×#353211yescharacteristic
subgroupG/H
center, socleC23×C11C25
commutator, Frattini, cosocleC23C25×C11
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#2736C2semidirect
2. C11×#2668C2semidirect
3. C11×#2578C2semidirect
4. C11×#2564C2semidirect
5. C11×#2535C2semidirect
6. C11×#2517C2semidirect
7. C11×#2463C2semidirect
8. C11×#2364C2semidirect
9. C4×C11×#120C2semidirect
11. C2×C11×C22⋊Q8C22semidirect
16. C2×C4×D4×C11C22semidirect
17. C11×#400C22semidirect
21. C11×#397C22semidirect
22. C11×#395C22semidirect
26. C11×#392C22semidirect
28. C11×#388C22semidirect
29. C11×#387C22semidirect
30. C11×#387C22semidirect
31. C11×#387C22semidirect
36. C11×#386C22semidirect
39. C11×#383C22semidirect
40. C11×#382C22semidirect
41. C11×#380C22semidirect
45. C4×C11×C22⋊C4C22semidirect
46. C2×C11×#95C22semidirect
91. #60032C11direct (N × H)
141. #2736C2×C11semidirect
142. #2668C2×C11semidirect
143. #2578C2×C11semidirect
144. #2564C2×C11semidirect
145. #2535C2×C11semidirect
146. #2517C2×C11semidirect
147. #2463C2×C11semidirect
148. #2364C2×C11semidirect
149. C4×#120C2×C11semidirect
189. C2×C22⋊Q8C22×C11semidirect
194. C2×C4×D4C22×C11semidirect
195. #400C22×C11semidirect
199. #397C22×C11semidirect
200. #395C22×C11semidirect
204. #392C22×C11semidirect
206. #388C22×C11semidirect
207. #387C22×C11semidirect
208. #387C22×C11semidirect
209. #387C22×C11semidirect
214. #386C22×C11semidirect
217. #383C22×C11semidirect
218. #382C22×C11semidirect
219. #380C22×C11semidirect
223. C4×C22⋊C4C22×C11semidirect
224. C2×#95C22×C11semidirect
344. C11#60032direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#27362
C11×#26682
C11×#25782
C11×#25642
C11×#25352
C11×#25172
C11×#24632
C11×#23642
C4×C11×#1202
#6003211