Finite Group Databasebeta

← C11×#36676 #14613869

Subgroups — C11×#36676 #14613869

Order 2816.

2006 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2842C211yesmaximal, characteristic, complemented
2C11×#2834C211yesmaximal, characteristic, complemented
3C11×#2827C216yesmaximal, complemented
4C11×#2826C213yesmaximal, complemented
5C11×#2825C212yesmaximal, complemented
6C11×#2812C213yesmaximal, complemented
7C11×#2401C212yesmaximal, complemented
8C11×#2397C211yesmaximal, characteristic, complemented
9C11×#2395C213yesmaximal, complemented
10C11×#2392C216yesmaximal, complemented
11C4×C11×#120C213yesmaximal, complemented
12C24×C4×C11C2211yescharacteristic
13C2×C11×#120C2213yes—
14C2×C4×D4×C11C2216yes—
15C2×C4×D4×C11C2213yes—
16C2×C4×D4×C11C2213yescomplemented
17C2×C11×#117C2213yescomplemented
18C11×#401C2212yescomplemented
19C11×#400C2213yescomplemented
20C11×#400C2216yescomplemented
21C11×#399C2213yes—
22C11×#399C2211yescharacteristic
23C11×#399C2213yescomplemented
24C11×#398C2216yescomplemented
25C11×#398C2213yescomplemented
26C11×#397C2213yes—
27C11×#397C2216yes—
28C11×#397C2216yescomplemented
29C11×#397C2216yescomplemented
30C11×#396C2216yes—
31C11×#396C2212yes—
32C11×#396C2216yescomplemented
33C11×#394C2216yes—
34C11×#394C2216yes—
35C11×#394C2216yes—
36C11×#394C2216yescomplemented
37C11×#392C2216yes—
38C11×#392C2213yes—
39C11×#392C2211yescharacteristic, complemented
40C11×#386C2216yes—
41C11×#386C2213yes—
42C11×#385C2213yes—
43C11×#385C2216yes—
44C11×#379C2213yes—
45C4×C11×C4⋊C4C2216yescomplemented
46C4×C11×C22⋊C4C2216yes—
47C4×C11×C22⋊C4C2213yes—
48C4×C11×C22⋊C4C2213yescomplemented
49C11×#376C2211yescharacteristic, complemented
50C25×C11C2311yescharacteristic
51C22×D4×C11C2316yes—
52C22×D4×C11C2313yes—
53C22×D4×C11C2313yes—
54C23×C4×C11—46no—
55C23×C4×C11C2313yes—
56C23×C4×C11C2312yes—
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2312yes—
60C11×#120—212no—
61C4×D4×C11—412no—
62C4×D4×C11—46no—
63C4×D4×C11—46no—
64C11×#117—46no—
65C2×C11×C4⋊C4C2313yes—
66C2×C11×C4⋊C4C2313yes—
67C2×C11×C4⋊C4C2316yes—
68C2×C11×C4⋊C4C2313yes—
69C2×C11×C4⋊C4C2313yes—
70C2×C11×C4⋊C4C2316yes—
71C2×C11×C4⋊C4C2316yes—
72C2×C11×C22⋊C4C2316yes—
73C2×C11×C22⋊C4C2313yes—
74C2×C11×C22⋊C4C2316yes—
75C2×C11×C22⋊C4C2316yes—
76C2×C11×C22⋊C4C2313yes—
77C2×C11×C22⋊C4C2316yes—
78C2×C11×C22⋊C4C2313yes—
79C2×C11×C22⋊C4C2316yes—
80C2×C11×C22⋊C4C2313yes—
81C2×C11×C22⋊C4C2316yes—
82C2×C11×C22⋊C4C2316yes—
83C2×C42×C11C2313yes—
84C2×C42×C11C2316yes—
85C11×#95C2313yes—
86C11×#95C2311yescharacteristic
87C11×#95C2316yes—
88C11×#95C2316yes—
89C11×#95C2316yes—
90C11×#95C2313yes—
91C11×#95C2313yes—
92C11×#95C2316yes—
93C11×#95C2316yes—
94#36676C1111yesmaximal, characteristic, direct product factor, Sylow
95C24×C11—43no—
96C24×C11—43no—
97C24×C11#4114yes—
98C24×C11C2413yes—
99C24×C11C2412yes—
100C24×C11C2411yescharacteristic
101C2×D4×C11—212no—
102C2×D4×C11—26no—
103C2×D4×C11—43no—
104C2×D4×C11—43no—
105C2×D4×C11—46no—
106C2×D4×C11—46no—
107C2×D4×C11—46no—
108C2×D4×C11—43no—
109C22×C4×C11—26no—
110C22×C4×C11—212no—
111C22×C4×C11—212no—
112C22×C4×C11—26no—
113C22×C4×C11—43no—
114C22×C4×C11—46no—
115C22×C4×C11—416no—
116C22×C4×C11C2413yes—
117C22×C4×C11C2416yes—
118C22×C4×C11C2413yes—
119C22×C4×C11C2412yes—
120C22×C4×C11C2411yescharacteristic
121C22×C4×C11C2416yes—
122C22×C4×C11C2413yes—
123C22×C4×C11C2411yescharacteristic
124C11×C4⋊C4—46no—
125C11×C4⋊C4—46no—
126C11×C4⋊C4—43no—
127C11×C4⋊C4—43no—
128C11×C4⋊C4—43no—
129C11×C4⋊C4—43no—
130C11×C4⋊C4—46no—
131C11×C22⋊C4—212no—
132C11×C22⋊C4—26no—
133C11×C22⋊C4—43no—
134C11×C22⋊C4—46no—
135C11×C22⋊C4—46no—
136C11×C22⋊C4—46no—
137C11×C22⋊C4—46no—
138C11×C22⋊C4—46no—
139C11×C22⋊C4—46no—
140C11×C22⋊C4—43no—
141C11×C22⋊C4—43no—
142C42×C11—212no—
143C42×C11—26no—
144#2842C2×C1111yescharacteristic, complemented
145#2834C2×C1111yescharacteristic, complemented
146#2827C2×C1116yescomplemented
147#2826C2×C1113yescomplemented
148#2825C2×C1112yescomplemented
149#2812C2×C1113yescomplemented
150#2401C2×C1112yescomplemented
151#2397C2×C1111yescharacteristic, complemented
152#2395C2×C1113yescomplemented
153#2392C2×C1116yescomplemented
154C4×#120C2×C1113yescomplemented
155C23×C11—26no—
156C23×C11—23no—
157C23×C11—23no—
158C23×C11—26no—
159C23×C11—23no—
160C23×C11—23no—
161C23×C11—26no—
162C23×C11—26no—
163C23×C11—23no—
164C23×C11—412no—
165C23×C11—44no—
166C23×C11—412no—
167C23×C11C2×#4114yes—
168C23×C11C2×#4112yes—
169C23×C11C2511yescharacteristic
170D4×C11—412no—
171D4×C11—424no—
172D4×C11—412no—
173C2×C4×C11—23no—
174C2×C4×C11—26no—
175C2×C4×C11—26no—
176C2×C4×C11—23no—
177C2×C4×C11—23no—
178C2×C4×C11—26no—
179C2×C4×C11—26no—
180C2×C4×C11—23no—
181C2×C4×C11—26no—
182C2×C4×C11—23no—
183C2×C4×C11—26no—
184C2×C4×C11—26no—
185C2×C4×C11—26no—
186C2×C4×C11—26no—
187C2×C4×C11—23no—
188C2×C4×C11—44no—
189C2×C4×C11—48no—
190C2×C4×C11—412no—
191C2×C4×C11—48no—
192C2×C4×C11—44no—
193C2×C4×C11H(5,𝔽2)16yes—
194C24×C4C22×C1111yescharacteristic
195C2×#120C22×C1113yes—
196C2×C4×D4C22×C1116yes—
197C2×C4×D4C22×C1113yes—
198C2×C4×D4C22×C1113yescomplemented
199C2×#117C22×C1113yescomplemented
200#401C22×C1112yescomplemented
201#400C22×C1116yescomplemented
202#400C22×C1113yescomplemented
203#399C22×C1113yes—
204#399C22×C1111yescharacteristic
205#399C22×C1113yescomplemented
206#398C22×C1113yescomplemented
207#398C22×C1116yescomplemented
208#397C22×C1116yes—
209#397C22×C1113yes—
210#397C22×C1116yescomplemented
211#397C22×C1116yescomplemented
212#396C22×C1112yes—
213#396C22×C1116yes—
214#396C22×C1116yescomplemented
215#394C22×C1116yes—
216#394C22×C1116yes—
217#394C22×C1116yes—
218#394C22×C1116yescomplemented
219#392C22×C1116yes—
220#392C22×C1113yes—
221#392C22×C1111yescharacteristic, complemented
222#386C22×C1116yes—
223#386C22×C1113yes—
224#385C22×C1113yes—
225#385C22×C1116yes—
226#379C22×C1113yes—
227C4×C4⋊C4C22×C1116yescomplemented
228C4×C22⋊C4C22×C1116yes—
229C4×C22⋊C4C22×C1113yes—
230C4×C22⋊C4C22×C1113yescomplemented
231#376C22×C1111yescharacteristic, complemented
232C22×C11—26no—
233C22×C11—212no—
234C22×C11—416no—
235C22×C11—42no—
236C22×C11—41no—
237C22×C11—46no—
238C22×C11—43no—
239C22×C11—43no—
240C22×C11—46no—
241C22×C11—43no—
242C22×C11—46no—
243C22×C11—43no—
244C22×C11C22×#4111yescharacteristic
245C22×C11C2×H(5,𝔽2)13yes—
246C22×C11#58513yes—
247C4×C11—43no—
248C4×C11—46no—
249C4×C11—43no—
250C4×C11—42no—
251C4×C11—41no—
252C4×C11—46no—
253C4×C11—43no—
254C4×C11#56014yes—
255C25C23×C1111yescharacteristic
256C22×D4C23×C1116yes—
257C22×D4C23×C1113yes—
258C22×D4C23×C1113yes—
259C23×C4—46no—
260C23×C4C23×C1113yes—
261C23×C4C23×C1112yes—
262C23×C4C23×C1111yescharacteristic
263C23×C4C23×C1111yescharacteristic
264C23×C4C23×C1112yes—
265#120—212no—
266C4×D4—412no—
267C4×D4—46no—
268C4×D4—46no—
269#117—46no—
270C2×C4⋊C4C23×C1113yes—
271C2×C4⋊C4C23×C1113yes—
272C2×C4⋊C4C23×C1116yes—
273C2×C4⋊C4C23×C1113yes—
274C2×C4⋊C4C23×C1113yes—
275C2×C4⋊C4C23×C1116yes—
276C2×C4⋊C4C23×C1116yes—
277C2×C22⋊C4C23×C1116yes—
278C2×C22⋊C4C23×C1113yes—
279C2×C22⋊C4C23×C1116yes—
280C2×C22⋊C4C23×C1113yes—
281C2×C22⋊C4C23×C1116yes—
282C2×C22⋊C4C23×C1113yes—
283C2×C22⋊C4C23×C1116yes—
284C2×C22⋊C4C23×C1116yes—
285C2×C22⋊C4C23×C1116yes—
286C2×C22⋊C4C23×C1113yes—
287C2×C22⋊C4C23×C1116yes—
288C2×C42C23×C1116yes—
289C2×C42C23×C1113yes—
290#95C23×C1113yes—
291#95C23×C1111yescharacteristic
292#95C23×C1116yes—
293#95C23×C1116yes—
294#95C23×C1116yes—
295#95C23×C1113yes—
296#95C23×C1113yes—
297#95C23×C1116yes—
298#95C23×C1116yes—
299C2×C11—42no—
300C2×C11—44no—
301C2×C11—83no—
302C2×C11#345913yes—
303C2×C11C2×#56011yescharacteristic
304C2×C11#352913yes—
305C24—43no—
306C24—43no—
307C24C11×#4114yes—
308C24C24×C1113yes—
309C24C24×C1111yescharacteristic
310C24C24×C1112yes—
311C2×D4—212no—
312C2×D4—26no—
313C2×D4—43no—
314C2×D4—43no—
315C2×D4—46no—
316C2×D4—46no—
317C2×D4—46no—
318C2×D4—43no—
319C22×C4—26no—
320C22×C4—212no—
321C22×C4—212no—
322C22×C4—26no—
323C22×C4—43no—
324C22×C4—46no—
325C22×C4—416no—
326C22×C4C24×C1113yes—
327C22×C4C24×C1116yes—
328C22×C4C24×C1113yes—
329C22×C4C24×C1112yes—
330C22×C4C24×C1111yescharacteristic
331C22×C4C24×C1116yes—
332C22×C4C24×C1113yes—
333C22×C4C24×C1111yescharacteristic
334C4⋊C4—43no—
335C4⋊C4—43no—
336C4⋊C4—43no—
337C4⋊C4—43no—
338C4⋊C4—46no—
339C4⋊C4—46no—
340C4⋊C4—46no—
341C22⋊C4—212no—
342C22⋊C4—26no—
343C22⋊C4—46no—
344C22⋊C4—46no—
345C22⋊C4—46no—
346C22⋊C4—46no—
347C22⋊C4—43no—
348C22⋊C4—43no—
349C22⋊C4—43no—
350C22⋊C4—46no—
351C22⋊C4—46no—
352C42—212no—
353C42—26no—
354C11#3667611yescharacteristic, direct product factor, Sylow
355C23—26no—
356C23—23no—
357C23—23no—
358C23—26no—
359C23—23no—
360C23—23no—
361C23—26no—
362C23—26no—
363C23—23no—
364C23—412no—
365C23—44no—
366C23—412no—
367C23C2×C11×#4112yes—
368C23C2×C11×#4114yes—
369C23C25×C1111yescharacteristic
370D4—412no—
371D4—424no—
372D4—412no—
373C2×C4—23no—
374C2×C4—26no—
375C2×C4—26no—
376C2×C4—23no—
377C2×C4—23no—
378C2×C4—26no—
379C2×C4—26no—
380C2×C4—23no—
381C2×C4—26no—
382C2×C4—23no—
383C2×C4—26no—
384C2×C4—26no—
385C2×C4—26no—
386C2×C4—26no—
387C2×C4—23no—
388C2×C4—44no—
389C2×C4—48no—
390C2×C4—412no—
391C2×C4—48no—
392C2×C4—44no—
393C2×C4C11×H(5,𝔽2)16yes—
394C22—26no—
395C22—212no—
396C22—416no—
397C22—42no—
398C22—41no—
399C22—46no—
400C22—43no—
401C22—43no—
402C22—46no—
403C22—43no—
404C22—46no—
405C22—43no—
406C22C22×C11×#4111yescharacteristic
407C22C2×C11×H(5,𝔽2)13yes—
408C22C11×#58513yes—
409C4—43no—
410C4—46no—
411C4—42no—
412C4—41no—
413C4—43no—
414C4—43no—
415C4—46no—
416C4C11×#56014yes—
417C2—42no—
418C2—44no—
419C2—83no—
420C2C11×#345913yes—
421C2C2×C11×#56011yescharacteristic
422C2C11×#352913yes—
subgroupG/H
centerC22×C4×C11C24
commutator, Frattini, cosocleC23C25×C11
socleC23×C11C25
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#2842C2semidirect
2. C11×#2834C2semidirect
3. C11×#2827C2semidirect
4. C11×#2826C2semidirect
5. C11×#2825C2semidirect
6. C11×#2812C2semidirect
7. C11×#2401C2semidirect
8. C11×#2397C2semidirect
9. C11×#2395C2semidirect
10. C11×#2392C2semidirect
11. C4×C11×#120C2semidirect
16. C2×C4×D4×C11C22semidirect
17. C2×C11×#117C22semidirect
18. C11×#401C22semidirect
19. C11×#400C22semidirect
20. C11×#400C22semidirect
23. C11×#399C22semidirect
24. C11×#398C22semidirect
25. C11×#398C22semidirect
28. C11×#397C22semidirect
29. C11×#397C22semidirect
32. C11×#396C22semidirect
36. C11×#394C22semidirect
39. C11×#392C22semidirect
45. C4×C11×C4⋊C4C22semidirect
48. C4×C11×C22⋊C4C22semidirect
49. C11×#376C22semidirect
94. #36676C11direct (N × H)
144. #2842C2×C11semidirect
145. #2834C2×C11semidirect
146. #2827C2×C11semidirect
147. #2826C2×C11semidirect
148. #2825C2×C11semidirect
149. #2812C2×C11semidirect
150. #2401C2×C11semidirect
151. #2397C2×C11semidirect
152. #2395C2×C11semidirect
153. #2392C2×C11semidirect
154. C4×#120C2×C11semidirect
198. C2×C4×D4C22×C11semidirect
199. C2×#117C22×C11semidirect
200. #401C22×C11semidirect
201. #400C22×C11semidirect
202. #400C22×C11semidirect
205. #399C22×C11semidirect
206. #398C22×C11semidirect
207. #398C22×C11semidirect
210. #397C22×C11semidirect
211. #397C22×C11semidirect
214. #396C22×C11semidirect
218. #394C22×C11semidirect
221. #392C22×C11semidirect
227. C4×C4⋊C4C22×C11semidirect
230. C4×C22⋊C4C22×C11semidirect
231. #376C22×C11semidirect
354. C11#36676direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#28422
C11×#28342
C11×#28272
C11×#28262
C11×#28252
C11×#28122
C11×#24012
C11×#23972
C11×#23952
C11×#23922
C4×C11×#1202
#3667611