Finite Group Databasebeta

← C11×#60622 #14637815

Subgroups — C11×#60622 #14637815

Order 2816.

2178 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3503C211yesmaximal, characteristic, complemented
2C11×#3498C211yesmaximal, characteristic
3C11×#3141C213yesmaximal, complemented
4C11×#3138C213yesmaximal, complemented
5C11×#3136C2112yesmaximal, complemented
6C11×#3131C213yesmaximal, complemented
7C2×C11×#486C213yesmaximal, complemented
8C11×#2897C214yesmaximal, complemented
9C4×C11×#131C211yesmaximal, characteristic, complemented
10C2×C11×H(5,𝔽2)C2212yes—
11C2×C11×#131C2212yes—
12Q82×C11—21no—
13C11×#557—21no—
14C11×#554—23no—
15C11×#550—21no—
16C11×#550—21no—
17D4×Q8×C11—23no—
18D42×C11—23no—
19D42×C11—23no—
20C11×#544C2216yescomplemented
21C11×#535C2216yes—
22C11×#533C2213yescomplemented
23C11×#532C2213yes—
24C2×C11×C4⋊Q8C2213yescomplemented
25C2×C11×#127C2213yes—
26C11×#520C2212yes—
27C4×C11×#41C2211yescharacteristic
28C11×#490C22112yescomplemented
29C11×#489C22112yescomplemented
30C11×#488C22112yescomplemented
31C11×#487C2211yescharacteristic, complemented
32C11×#487C2213yescomplemented
33C11×#486C2213yescomplemented
34C11×#486C22112yescomplemented
35C11×#486C2216yescomplemented
36C11×#486C2213yescomplemented
37C11×#418C22112yescomplemented
38C11×#417C22112yescomplemented
39C11×#416C22112yescomplemented
40C2×C11×#102C22112yescomplemented
41C11×#405C2216yescomplemented
42C4×C11×M16C2213yescomplemented
43C2×C4×C8×C11C2213yescomplemented
44C11×H(5,𝔽2)—216no—
45C2×C11×#41—22no—
46C2×C11×#41C2316yes—
47C2×C11×#41C2311yescharacteristic
48C22×Q8×C11—23no—
49C22×D4×C11—26no—
50C22×D4×C11—23no—
51C22×D4×C11—23no—
52C22×D4×C11C2316yes—
53C11×#131—28no—
54C2×C11×M16C2316yes—
55C22×C8×C11C2316yes—
56C11×C4⋊Q8—26no—
57C11×C4⋊Q8—23no—
58C11×C4⋊Q8—23no—
59C11×C4⋊Q8C2311yescharacteristic
60C11×C4⋊Q8C2316yes—
61C11×C4⋊Q8C2313yes—
62C11×C4⋊Q8C2311yescharacteristic
63C11×#127—23no—
64C11×#127—23no—
65C11×#127C2316yes—
66C11×#127C2313yes—
67C11×#125—26no—
68C11×#125C2316yes—
69C11×#124C2316yes—
70C11×C22⋊Q8—23no—
71C11×C22⋊Q8—23no—
72C11×C22⋊Q8—212no—
73C11×#121—23no—
74C11×#121—23no—
75C11×#121—26no—
76C11×#121—26no—
77C11×#120—212no—
78C4×Q8×C11—22no—
79C4×Q8×C11—23no—
80C4×Q8×C11—23no—
81C4×Q8×C11D411yescharacteristic
82C4×Q8×C11D411yescharacteristic
83C4×D4×C11—26no—
84C4×D4×C11—23no—
85C4×D4×C11—23no—
86C4×D4×C11D413yes—
87C4×D4×C11D413yes—
88C11×#117C2316yes—
89C11×#117C2313yes—
90C2×C11×C4⋊C4—23no—
91C2×C11×C4⋊C4C2316yes—
92C2×C42×C11C2313yes—
93C11×#103C23112yes—
94C11×#103C2314yes—
95C11×#102C23124yes—
96C11×#102C23112yes—
97C11×#102C23112yes—
98C11×#97C2316yes—
99C4×C8×C11C2311yescharacteristic
100C4×C8×C11C2313yes—
101C4×C8×C11C2316yes—
102#60622C1111yesmaximal, characteristic, direct product factor, Sylow
103C24×C11—26no—
104C11×#41—224no—
105C11×#41—48no—
106C11×#41#4118yes—
107C2×Q8×C11—21no—
108C2×Q8×C11—23no—
109C2×Q8×C11—26no—
110C2×Q8×C11—86no—
111C2×Q8×C11C2×D411yescharacteristic
112C2×Q8×C11C2412yes—
113C2×D4×C11—26no—
114C2×D4×C11—23no—
115C2×D4×C11—23no—
116C2×D4×C11—26no—
117C2×D4×C11—26no—
118C2×D4×C11—26no—
119C2×D4×C11—224no—
120C2×D4×C11—424no—
121C2×D4×C11—86no—
122C2×D4×C11—86no—
123C2×D4×C11C2×D413yes—
124C2×D4×C11C2416yes—
125C22×C4×C11—26no—
126C22×C4×C11—26no—
127C22×C4×C11C2×D413yes—
128C22×C4×C11C2×D413yes—
129C22×C4×C11C2413yes—
130C11×M16—212no—
131C2×C8×C11—212no—
132C2×C8×C11C2412yes—
133C2×C8×C11C2416yes—
134C11×C4⋊C4—23no—
135C11×C4⋊C4—26no—
136C11×C4⋊C4—26no—
137C11×C4⋊C4—21no—
138C11×C4⋊C4—21no—
139C11×C4⋊C4—21no—
140C11×C4⋊C4—26no—
141C11×C4⋊C4—26no—
142C11×C4⋊C4C2×D413yes—
143C11×C4⋊C4C2×D413yes—
144C11×C4⋊C4C2416yes—
145C11×C4⋊C4C2412yes—
146C11×C22⋊C4—26no—
147C11×C22⋊C4—26no—
148C11×C22⋊C4—26no—
149C11×C22⋊C4C2×D416yes—
150C42×C11—26no—
151C42×C11C2×D413yes—
152C42×C11C2×D413yes—
153C42×C11C2411yescharacteristic
154C42×C11C2413yes—
155#3503C2×C1111yescharacteristic, complemented
156#3498C2×C1111yescharacteristic
157#3141C2×C1113yescomplemented
158#3138C2×C1113yescomplemented
159#3136C2×C11112yescomplemented
160#3131C2×C1113yescomplemented
161C2×#486C2×C1113yescomplemented
162#2897C2×C1114yescomplemented
163C4×#131C2×C1111yescharacteristic, complemented
164C23×C11—26no—
165C23×C11—412no—
166C23×C11—86no—
167C23×C11—86no—
168C23×C11C22×D413yes—
169Q8×C11—24no—
170Q8×C11—46no—
171Q8×C11—42no—
172Q8×C11—86no—
173Q8×C11#12414yes—
174D4×C11—212no—
175D4×C11—412no—
176D4×C11—412no—
177D4×C11—46no—
178D4×C11—46no—
179D4×C11—86no—
180D4×C11—86no—
181D4×C11#124112yes—
182C2×C4×C11—26no—
183C2×C4×C11—26no—
184C2×C4×C11—22no—
185C2×C4×C11—26no—
186C2×C4×C11—22no—
187C2×C4×C11—412no—
188C2×C4×C11—86no—
189C2×C4×C11C22×D413yes—
190C2×C4×C11C22×D413yes—
191C2×C4×C11C22×D413yes—
192C2×C4×C11C22×D411yescharacteristic
193C2×C4×C11C22×D411yescharacteristic
194C2×C4×C11C2×#41112yes—
195C2×C4×C11C2511yescharacteristic
196C8×C11—22no—
197C8×C11—26no—
198C2×H(5,𝔽2)C22×C1112yes—
199C2×#131C22×C1112yes—
200Q82—21no—
201#557—21no—
202#554—23no—
203#550—21no—
204#550—21no—
205D4×Q8—23no—
206D42—23no—
207D42—23no—
208#544C22×C1116yescomplemented
209#535C22×C1116yes—
210#533C22×C1113yescomplemented
211#532C22×C1113yes—
212C2×C4⋊Q8C22×C1113yescomplemented
213C2×#127C22×C1113yes—
214#520C22×C1112yes—
215C4×#41C22×C1111yescharacteristic
216#490C22×C11112yescomplemented
217#489C22×C11112yescomplemented
218#488C22×C11112yescomplemented
219#487C22×C1111yescharacteristic, complemented
220#487C22×C1113yescomplemented
221#486C22×C1113yescomplemented
222#486C22×C11112yescomplemented
223#486C22×C1116yescomplemented
224#486C22×C1113yescomplemented
225#418C22×C11112yescomplemented
226#417C22×C11112yescomplemented
227#416C22×C11112yescomplemented
228C2×#102C22×C11112yescomplemented
229#405C22×C1116yescomplemented
230C4×M16C22×C1113yescomplemented
231C2×C4×C8C22×C1113yescomplemented
232C22×C11—23no—
233C22×C11—23no—
234C22×C11—46no—
235C22×C11—46no—
236C22×C11—46no—
237C22×C11—1612no—
238C22×C11C2×#12416yes—
239C22×C11C23×D411yescharacteristic
240C4×C11—23no—
241C4×C11—23no—
242C4×C11—42no—
243C4×C11—46no—
244C4×C11—42no—
245C4×C11C2×#12416yes—
246C4×C11#57612yes—
247C4×C11#57712yes—
248C4×C11C22×#4112yes—
249H(5,𝔽2)—216no—
250C2×#41—22no—
251C2×#41C23×C1116yes—
252C2×#41C23×C1111yescharacteristic
253C22×Q8—23no—
254C22×D4—26no—
255C22×D4—23no—
256C22×D4—23no—
257C22×D4C23×C1116yes—
258#131—28no—
259C2×M16C23×C1116yes—
260C22×C8C23×C1116yes—
261C4⋊Q8—26no—
262C4⋊Q8—23no—
263C4⋊Q8—23no—
264C4⋊Q8C23×C1111yescharacteristic
265C4⋊Q8C23×C1113yes—
266C4⋊Q8C23×C1116yes—
267C4⋊Q8C23×C1111yescharacteristic
268#127—23no—
269#127—23no—
270#127C23×C1113yes—
271#127C23×C1116yes—
272#125—26no—
273#125C23×C1116yes—
274#124C23×C1116yes—
275C22⋊Q8—23no—
276C22⋊Q8—23no—
277C22⋊Q8—212no—
278#121—23no—
279#121—23no—
280#121—26no—
281#121—26no—
282#120—212no—
283C4×Q8—22no—
284C4×Q8—23no—
285C4×Q8—23no—
286C4×Q8D4×C1111yescharacteristic
287C4×Q8D4×C1111yescharacteristic
288C4×D4—26no—
289C4×D4—23no—
290C4×D4—23no—
291C4×D4D4×C1113yes—
292C4×D4D4×C1113yes—
293#117C23×C1116yes—
294#117C23×C1113yes—
295C2×C4⋊C4—23no—
296C2×C4⋊C4C23×C1116yes—
297C2×C42C23×C1113yes—
298#103C23×C1114yes—
299#103C23×C11112yes—
300#102C23×C11112yes—
301#102C23×C11124yes—
302#102C23×C11112yes—
303#97C23×C1116yes—
304C4×C8C23×C1111yescharacteristic
305C4×C8C23×C1113yes—
306C4×C8C23×C1116yes—
307C2×C11—26no—
308C2×C11—86no—
309C2×C11C22×#12411yescharacteristic
310C2×C11C2×#57611yescharacteristic
311C2×C11C2×#57711yescharacteristic
312C24—26no—
313#41—224no—
314#41—48no—
315#41C11×#4118yes—
316C2×Q8—21no—
317C2×Q8—23no—
318C2×Q8—26no—
319C2×Q8—86no—
320C2×Q8C2×D4×C1111yescharacteristic
321C2×Q8C24×C1112yes—
322C2×D4—26no—
323C2×D4—23no—
324C2×D4—23no—
325C2×D4—26no—
326C2×D4—26no—
327C2×D4—26no—
328C2×D4—224no—
329C2×D4—424no—
330C2×D4—86no—
331C2×D4—86no—
332C2×D4C2×D4×C1113yes—
333C2×D4C24×C1116yes—
334C22×C4—26no—
335C22×C4—26no—
336C22×C4C2×D4×C1113yes—
337C22×C4C2×D4×C1113yes—
338C22×C4C24×C1113yes—
339M16—212no—
340C2×C8—212no—
341C2×C8C24×C1112yes—
342C2×C8C24×C1116yes—
343C4⋊C4—23no—
344C4⋊C4—26no—
345C4⋊C4—26no—
346C4⋊C4—21no—
347C4⋊C4—21no—
348C4⋊C4—21no—
349C4⋊C4—26no—
350C4⋊C4—26no—
351C4⋊C4C2×D4×C1113yes—
352C4⋊C4C2×D4×C1113yes—
353C4⋊C4C24×C1116yes—
354C4⋊C4C24×C1112yes—
355C22⋊C4—26no—
356C22⋊C4—26no—
357C22⋊C4—26no—
358C22⋊C4C2×D4×C1116yes—
359C42—26no—
360C42C2×D4×C1113yes—
361C42C2×D4×C1113yes—
362C42C24×C1111yescharacteristic
363C42C24×C1113yes—
364C11#6062211yescharacteristic, direct product factor, Sylow
365C23—26no—
366C23—412no—
367C23—86no—
368C23—86no—
369C23C22×D4×C1113yes—
370Q8—24no—
371Q8—46no—
372Q8—42no—
373Q8—86no—
374Q8C11×#12414yes—
375D4—212no—
376D4—412no—
377D4—412no—
378D4—46no—
379D4—46no—
380D4—86no—
381D4—86no—
382D4C11×#124112yes—
383C2×C4—26no—
384C2×C4—26no—
385C2×C4—22no—
386C2×C4—26no—
387C2×C4—22no—
388C2×C4—412no—
389C2×C4—86no—
390C2×C4C22×D4×C1113yes—
391C2×C4C22×D4×C1113yes—
392C2×C4C22×D4×C1113yes—
393C2×C4C22×D4×C1111yescharacteristic
394C2×C4C22×D4×C1111yescharacteristic
395C2×C4C2×C11×#41112yes—
396C2×C4C25×C1111yescharacteristic
397C8—22no—
398C8—26no—
399C22—23no—
400C22—23no—
401C22—46no—
402C22—46no—
403C22—46no—
404C22—1612no—
405C22C2×C11×#12416yes—
406C22C23×D4×C1111yescharacteristic
407C4—23no—
408C4—23no—
409C4—42no—
410C4—46no—
411C4—42no—
412C4C2×C11×#12416yes—
413C4C11×#57612yes—
414C4C11×#57712yes—
415C4C22×C11×#4112yes—
416C2—26no—
417C2—86no—
418C2C22×C11×#12411yescharacteristic
419C2C2×C11×#57611yescharacteristic
420C2C2×C11×#57711yescharacteristic
subgroupG/H
center, socleC22×C11C23×D4
commutator, Frattini, cosocleC2×C4C25×C11
prime radicalC11×#3498C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C4×C11×#41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3503C2semidirect
3. C11×#3141C2semidirect
4. C11×#3138C2semidirect
5. C11×#3136C2semidirect
6. C11×#3131C2semidirect
7. C2×C11×#486C2semidirect
8. C11×#2897C2semidirect
9. C4×C11×#131C2semidirect
20. C11×#544C22semidirect
22. C11×#533C22semidirect
24. C2×C11×C4⋊Q8C22semidirect
28. C11×#490C22semidirect
29. C11×#489C22semidirect
30. C11×#488C22semidirect
31. C11×#487C22semidirect
32. C11×#487C22semidirect
33. C11×#486C22semidirect
34. C11×#486C22semidirect
35. C11×#486C22semidirect
36. C11×#486C22semidirect
37. C11×#418C22semidirect
38. C11×#417C22semidirect
39. C11×#416C22semidirect
40. C2×C11×#102C22semidirect
41. C11×#405C22semidirect
42. C4×C11×M16C22semidirect
43. C2×C4×C8×C11C22semidirect
102. #60622C11direct (N × H)
155. #3503C2×C11semidirect
157. #3141C2×C11semidirect
158. #3138C2×C11semidirect
159. #3136C2×C11semidirect
160. #3131C2×C11semidirect
161. C2×#486C2×C11semidirect
162. #2897C2×C11semidirect
163. C4×#131C2×C11semidirect
208. #544C22×C11semidirect
210. #533C22×C11semidirect
212. C2×C4⋊Q8C22×C11semidirect
216. #490C22×C11semidirect
217. #489C22×C11semidirect
218. #488C22×C11semidirect
219. #487C22×C11semidirect
220. #487C22×C11semidirect
221. #486C22×C11semidirect
222. #486C22×C11semidirect
223. #486C22×C11semidirect
224. #486C22×C11semidirect
225. #418C22×C11semidirect
226. #417C22×C11semidirect
227. #416C22×C11semidirect
228. C2×#102C22×C11semidirect
229. #405C22×C11semidirect
230. C4×M16C22×C11semidirect
231. C2×C4×C8C22×C11semidirect
364. C11#60622direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35032
C11×#34982
C11×#31412
C11×#31382
C11×#31362
C11×#31312
C2×C11×#4862
C11×#28972
C4×C11×#1312
#6062211