Finite Group Databasebeta

← C11×#36607 #14613800

Subgroups — C11×#36607 #14613800

Order 2816.

2524 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2847C213yesmaximal, complemented
2C11×#2569C213yesmaximal, complemented
3C11×#2543C213yesmaximal, complemented
4C11×#2510C216yesmaximal, complemented
5C11×#2444C216yesmaximal, complemented
6C11×#2364C213yesmaximal, complemented
7C11×#2353C213yesmaximal, complemented
8C4×C11×#120C213yesmaximal, complemented
9C22×C11×#95C211yesmaximal, characteristic, complemented
10C24×C4×C11C2213yes—
11C2×C11×#121C2213yes—
12C2×C11×#121C2216yes—
13C2×C11×#120C2213yes—
14C2×C4×D4×C11C2213yes—
15C2×C4×D4×C11C2216yes—
16C11×#401C2212yescomplemented
17C11×#400C2216yescomplemented
18C11×#398C2213yescomplemented
19C11×#397C2216yescomplemented
20C11×#397C2213yescomplemented
21C11×#394C2213yescomplemented
22C11×#392C2211yescharacteristic, complemented
23C11×#388C2216yescomplemented
24C11×#388C2216yescomplemented
25C11×#387C2216yescomplemented
26C11×#387C2216yescomplemented
27C11×#386C2213yes—
28C11×#386C2216yes—
29C11×#386C2216yes—
30C11×#386C2216yes—
31C11×#386C2216yes—
32C11×#386C2216yescomplemented
33C11×#385C2216yes—
34C11×#385C2213yes—
35C11×#383C2213yescomplemented
36C11×#381C2213yescomplemented
37C11×#380C2216yes—
38C11×#380C2213yes—
39C11×#379C2211yescharacteristic
40C4×C11×C22⋊C4C2216yes—
41C4×C11×C22⋊C4C2213yes—
42C4×C11×C22⋊C4C2213yescomplemented
43C11×#376C2211yescharacteristic, complemented
44C2×C11×#95C2216yes—
45C2×C11×#95C2213yes—
46C2×C11×#95C2213yes—
47C25×C11C2311yescharacteristic
48C22×D4×C11C2313yes—
49C22×D4×C11C2316yes—
50C22×D4×C11C2313yes—
51C23×C4×C11—212no—
52C23×C4×C11—412no—
53C23×C4×C11C2316yes—
54C23×C4×C11C2316yes—
55C23×C4×C11C2313yes—
56C23×C4×C11C2313yes—
57C23×C4×C11C2313yes—
58C11×#121—212no—
59C11×#121—412no—
60C11×#120—212no—
61C4×D4×C11—212no—
62C4×D4×C11—412no—
63C2×C11×C4⋊C4C2313yes—
64C2×C11×C4⋊C4C2313yes—
65C2×C11×C4⋊C4C2316yes—
66C2×C11×C4⋊C4C2316yes—
67C2×C11×C22⋊C4C2313yes—
68C2×C11×C22⋊C4C2313yes—
69C2×C11×C22⋊C4C2316yes—
70C2×C11×C22⋊C4C2313yes—
71C2×C11×C22⋊C4C2316yes—
72C2×C11×C22⋊C4C2313yes—
73C2×C11×C22⋊C4C2316yes—
74C2×C11×C22⋊C4C2316yes—
75C2×C11×C22⋊C4C2316yes—
76C2×C42×C11C2313yes—
77C2×C42×C11C2316yes—
78C11×#95C2311yescharacteristic
79C11×#95C2313yes—
80C11×#95C2316yes—
81C11×#95C2311yescharacteristic
82C11×#95C2313yes—
83C11×#95C2312yes—
84C11×#95C2313yes—
85C11×#95C2316yes—
86C11×#95C2316yes—
87C11×#95C2316yes—
88C11×#95C2313yes—
89C11×#95C2316yes—
90C11×#95C2316yes—
91#36607C1111yesmaximal, characteristic, direct product factor, Sylow
92C24×C11—26no—
93C24×C11—26no—
94C24×C11#4114yes—
95C24×C11C2413yes—
96C24×C11C2413yes—
97C2×D4×C11—26no—
98C2×D4×C11—26no—
99C2×D4×C11—212no—
100C2×D4×C11—212no—
101C2×D4×C11—212no—
102C2×D4×C11—26no—
103C2×D4×C11—26no—
104C2×D4×C11—46no—
105C22×C4×C11—26no—
106C22×C4×C11—212no—
107C22×C4×C11—212no—
108C22×C4×C11—212no—
109C22×C4×C11—212no—
110C22×C4×C11—26no—
111C22×C4×C11—46no—
112C22×C4×C11—46no—
113C22×C4×C11—46no—
114C22×C4×C11—46no—
115C22×C4×C11—46no—
116C22×C4×C11—448no—
117C22×C4×C11#41112yes—
118C22×C4×C11C2416yes—
119C22×C4×C11C2411yescharacteristic
120C22×C4×C11C2413yes—
121C22×C4×C11C2416yes—
122C22×C4×C11C2413yes—
123C22×C4×C11C2413yes—
124C22×C4×C11C2413yes—
125C11×C4⋊C4—26no—
126C11×C4⋊C4—26no—
127C11×C4⋊C4—46no—
128C11×C4⋊C4—46no—
129C11×C22⋊C4—26no—
130C11×C22⋊C4—212no—
131C11×C22⋊C4—26no—
132C11×C22⋊C4—26no—
133C11×C22⋊C4—26no—
134C11×C22⋊C4—212no—
135C11×C22⋊C4—46no—
136C11×C22⋊C4—46no—
137C11×C22⋊C4—46no—
138C42×C11—26no—
139C42×C11—46no—
140#2847C2×C1113yescomplemented
141#2569C2×C1113yescomplemented
142#2543C2×C1113yescomplemented
143#2510C2×C1116yescomplemented
144#2444C2×C1116yescomplemented
145#2364C2×C1113yescomplemented
146#2353C2×C1113yescomplemented
147C4×#120C2×C1113yescomplemented
148C22×#95C2×C1111yescharacteristic, complemented
149C23×C11—224no—
150C23×C11—28no—
151C23×C11—224no—
152C23×C11—26no—
153C23×C11—26no—
154C23×C11—23no—
155C23×C11—26no—
156C23×C11—23no—
157C23×C11—26no—
158C23×C11—23no—
159C23×C11C2×#4116yes—
160C23×C11C2×#4116yes—
161C23×C11H(5,𝔽2)16yes—
162C23×C11C2511yescharacteristic
163D4×C11—412no—
164D4×C11—424no—
165D4×C11—86no—
166C2×C4×C11—26no—
167C2×C4×C11—26no—
168C2×C4×C11—23no—
169C2×C4×C11—23no—
170C2×C4×C11—23no—
171C2×C4×C11—26no—
172C2×C4×C11—23no—
173C2×C4×C11—26no—
174C2×C4×C11—26no—
175C2×C4×C11—26no—
176C2×C4×C11—26no—
177C2×C4×C11—23no—
178C2×C4×C11—26no—
179C2×C4×C11—26no—
180C2×C4×C11—412no—
181C2×C4×C11—424no—
182C2×C4×C11—424no—
183C2×C4×C11—412no—
184C2×C4×C11—86no—
185C2×C4×C11C2×#4116yes—
186C2×C4×C11C2×#4116yes—
187C24×C4C22×C1113yes—
188C2×#121C22×C1113yes—
189C2×#121C22×C1116yes—
190C2×#120C22×C1113yes—
191C2×C4×D4C22×C1113yes—
192C2×C4×D4C22×C1116yes—
193#401C22×C1112yescomplemented
194#400C22×C1116yescomplemented
195#398C22×C1113yescomplemented
196#397C22×C1116yescomplemented
197#397C22×C1113yescomplemented
198#394C22×C1113yescomplemented
199#392C22×C1111yescharacteristic, complemented
200#388C22×C1116yescomplemented
201#388C22×C1116yescomplemented
202#387C22×C1116yescomplemented
203#387C22×C1116yescomplemented
204#386C22×C1116yes—
205#386C22×C1116yes—
206#386C22×C1116yes—
207#386C22×C1113yes—
208#386C22×C1116yes—
209#386C22×C1116yescomplemented
210#385C22×C1116yes—
211#385C22×C1113yes—
212#383C22×C1113yescomplemented
213#381C22×C1113yescomplemented
214#380C22×C1113yes—
215#380C22×C1116yes—
216#379C22×C1111yescharacteristic
217C4×C22⋊C4C22×C1113yes—
218C4×C22⋊C4C22×C1116yes—
219C4×C22⋊C4C22×C1113yescomplemented
220#376C22×C1111yescharacteristic, complemented
221C2×#95C22×C1113yes—
222C2×#95C22×C1113yes—
223C2×#95C22×C1116yes—
224C22×C11—232no—
225C22×C11—26no—
226C22×C11—212no—
227C22×C11—26no—
228C22×C11—212no—
229C22×C11—43no—
230C22×C11—43no—
231C22×C11—46no—
232C22×C11—43no—
233C22×C11—46no—
234C22×C11#553112yes—
235C22×C11C22×#4113yes—
236C22×C11C22×#4111yescharacteristic
237C22×C11C2×H(5,𝔽2)13yes—
238C4×C11—26no—
239C4×C11—26no—
240C4×C11—41no—
241C4×C11—43no—
242C4×C11—46no—
243C4×C11—46no—
244C4×C11—43no—
245C25C23×C1111yescharacteristic
246C22×D4C23×C1113yes—
247C22×D4C23×C1116yes—
248C22×D4C23×C1113yes—
249C23×C4—212no—
250C23×C4—412no—
251C23×C4C23×C1116yes—
252C23×C4C23×C1116yes—
253C23×C4C23×C1113yes—
254C23×C4C23×C1113yes—
255C23×C4C23×C1113yes—
256#121—212no—
257#121—412no—
258#120—212no—
259C4×D4—212no—
260C4×D4—412no—
261C2×C4⋊C4C23×C1113yes—
262C2×C4⋊C4C23×C1113yes—
263C2×C4⋊C4C23×C1116yes—
264C2×C4⋊C4C23×C1116yes—
265C2×C22⋊C4C23×C1113yes—
266C2×C22⋊C4C23×C1113yes—
267C2×C22⋊C4C23×C1113yes—
268C2×C22⋊C4C23×C1113yes—
269C2×C22⋊C4C23×C1116yes—
270C2×C22⋊C4C23×C1116yes—
271C2×C22⋊C4C23×C1116yes—
272C2×C22⋊C4C23×C1116yes—
273C2×C22⋊C4C23×C1116yes—
274C2×C42C23×C1113yes—
275C2×C42C23×C1116yes—
276#95C23×C1111yescharacteristic
277#95C23×C1113yes—
278#95C23×C1116yes—
279#95C23×C1111yescharacteristic
280#95C23×C1113yes—
281#95C23×C1112yes—
282#95C23×C1113yes—
283#95C23×C1116yes—
284#95C23×C1116yes—
285#95C23×C1116yes—
286#95C23×C1113yes—
287#95C23×C1116yes—
288#95C23×C1116yes—
289C2×C11—212no—
290C2×C11—83no—
291C2×C11#344411yescharacteristic
292C2×C11C2×#55313yes—
293C2×C11#349013yes—
294C24—26no—
295C24—26no—
296C24C11×#4114yes—
297C24C24×C1113yes—
298C24C24×C1113yes—
299C2×D4—26no—
300C2×D4—26no—
301C2×D4—212no—
302C2×D4—212no—
303C2×D4—212no—
304C2×D4—26no—
305C2×D4—26no—
306C2×D4—46no—
307C22×C4—26no—
308C22×C4—212no—
309C22×C4—212no—
310C22×C4—212no—
311C22×C4—212no—
312C22×C4—26no—
313C22×C4—46no—
314C22×C4—46no—
315C22×C4—46no—
316C22×C4—46no—
317C22×C4—46no—
318C22×C4—448no—
319C22×C4C11×#41112yes—
320C22×C4C24×C1116yes—
321C22×C4C24×C1111yescharacteristic
322C22×C4C24×C1113yes—
323C22×C4C24×C1116yes—
324C22×C4C24×C1113yes—
325C22×C4C24×C1113yes—
326C22×C4C24×C1113yes—
327C4⋊C4—26no—
328C4⋊C4—26no—
329C4⋊C4—46no—
330C4⋊C4—46no—
331C22⋊C4—26no—
332C22⋊C4—26no—
333C22⋊C4—212no—
334C22⋊C4—26no—
335C22⋊C4—26no—
336C22⋊C4—212no—
337C22⋊C4—46no—
338C22⋊C4—46no—
339C22⋊C4—46no—
340C42—26no—
341C42—46no—
342C11#3660711yescharacteristic, direct product factor, Sylow
343C23—224no—
344C23—28no—
345C23—224no—
346C23—26no—
347C23—26no—
348C23—23no—
349C23—26no—
350C23—23no—
351C23—26no—
352C23—23no—
353C23C2×C11×#4116yes—
354C23C2×C11×#4116yes—
355C23C11×H(5,𝔽2)16yes—
356C23C25×C1111yescharacteristic
357D4—412no—
358D4—424no—
359D4—86no—
360C2×C4—26no—
361C2×C4—26no—
362C2×C4—23no—
363C2×C4—23no—
364C2×C4—23no—
365C2×C4—26no—
366C2×C4—23no—
367C2×C4—26no—
368C2×C4—26no—
369C2×C4—26no—
370C2×C4—26no—
371C2×C4—23no—
372C2×C4—26no—
373C2×C4—26no—
374C2×C4—412no—
375C2×C4—424no—
376C2×C4—424no—
377C2×C4—412no—
378C2×C4—86no—
379C2×C4C2×C11×#4116yes—
380C2×C4C2×C11×#4116yes—
381C22—232no—
382C22—26no—
383C22—212no—
384C22—26no—
385C22—212no—
386C22—43no—
387C22—43no—
388C22—46no—
389C22—43no—
390C22—46no—
391C22C11×#553112yes—
392C22C22×C11×#4113yes—
393C22C22×C11×#4111yescharacteristic
394C22C2×C11×H(5,𝔽2)13yes—
395C4—26no—
396C4—26no—
397C4—41no—
398C4—43no—
399C4—46no—
400C4—46no—
401C4—43no—
402C2—212no—
403C2—83no—
404C2C11×#344411yescharacteristic
405C2C2×C11×#55313yes—
406C2C11×#349013yes—
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×#2847C2semidirect
2. C11×#2569C2semidirect
3. C11×#2543C2semidirect
4. C11×#2510C2semidirect
5. C11×#2444C2semidirect
6. C11×#2364C2semidirect
7. C11×#2353C2semidirect
8. C4×C11×#120C2semidirect
9. C22×C11×#95C2semidirect
16. C11×#401C22semidirect
17. C11×#400C22semidirect
18. C11×#398C22semidirect
19. C11×#397C22semidirect
20. C11×#397C22semidirect
21. C11×#394C22semidirect
22. C11×#392C22semidirect
23. C11×#388C22semidirect
24. C11×#388C22semidirect
25. C11×#387C22semidirect
26. C11×#387C22semidirect
32. C11×#386C22semidirect
35. C11×#383C22semidirect
36. C11×#381C22semidirect
42. C4×C11×C22⋊C4C22semidirect
43. C11×#376C22semidirect
91. #36607C11direct (N × H)
140. #2847C2×C11semidirect
141. #2569C2×C11semidirect
142. #2543C2×C11semidirect
143. #2510C2×C11semidirect
144. #2444C2×C11semidirect
145. #2364C2×C11semidirect
146. #2353C2×C11semidirect
147. C4×#120C2×C11semidirect
148. C22×#95C2×C11semidirect
193. #401C22×C11semidirect
194. #400C22×C11semidirect
195. #398C22×C11semidirect
196. #397C22×C11semidirect
197. #397C22×C11semidirect
198. #394C22×C11semidirect
199. #392C22×C11semidirect
200. #388C22×C11semidirect
201. #388C22×C11semidirect
202. #387C22×C11semidirect
203. #387C22×C11semidirect
209. #386C22×C11semidirect
212. #383C22×C11semidirect
213. #381C22×C11semidirect
219. C4×C22⋊C4C22×C11semidirect
220. #376C22×C11semidirect
342. C11#36607direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#28472
C11×#25692
C11×#25432
C11×#25102
C11×#24442
C11×#23642
C11×#23532
C4×C11×#1202
C22×C11×#952
#3660711