Finite Group Databasebeta

← C11×#60626 #14637819

Subgroups — C11×#60626 #14637819

Order 2816.

2134 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3504C211yesmaximal, characteristic, complemented
2C11×#3498C211yesmaximal, characteristic
3C11×#3142C213yesmaximal, complemented
4C11×#3138C213yesmaximal, complemented
5C11×#3136C2112yesmaximal, complemented
6C11×#3135C213yesmaximal, complemented
7C2×C11×#490C213yesmaximal, complemented
8C11×#2897C214yesmaximal, complemented
9C11×#2875C211yesmaximal, characteristic, complemented
10C2×C11×H(5,𝔽2)C2212yes—
11C2×C11×#131C2212yes—
12C11×#557—22no—
13C11×#554—26no—
14C11×#550—22no—
15D42×C11—26no—
16C11×#544C2216yescomplemented
17C11×#535C2216yes—
18C11×#533C2213yescomplemented
19C11×#532C2213yes—
20C2×C11×#127C2213yes—
21C2×C11×#125C2213yescomplemented
22C11×#520C2212yes—
23C4×C11×#41C2211yescharacteristic
24C11×#491C2211yescharacteristic, complemented
25C11×#491C2213yescomplemented
26C11×#490C2213yescomplemented
27C11×#490C22112yescomplemented
28C11×#490C2216yescomplemented
29C11×#490C2213yescomplemented
30C11×#489C22112yescomplemented
31C11×#488C22112yescomplemented
32C11×#486C22112yescomplemented
33C11×#418C22112yescomplemented
34C11×#417C22112yescomplemented
35C11×#416C22112yescomplemented
36C2×C11×#102C22112yescomplemented
37C11×#405C2216yescomplemented
38C4×C11×M16C2213yescomplemented
39C2×C11×#97C2213yescomplemented
40C11×H(5,𝔽2)—216no—
41C2×C11×#41—22no—
42C2×C11×#41C2316yes—
43C2×C11×#41C2311yescharacteristic
44C22×D4×C11—26no—
45C22×D4×C11—26no—
46C22×D4×C11C2316yes—
47C11×#131—28no—
48C2×C11×M16C2316yes—
49C22×C8×C11C2316yes—
50C11×C4⋊Q8—26no—
51C11×C4⋊Q8C2311yescharacteristic
52C11×C4⋊Q8C2316yes—
53C11×#127—26no—
54C11×#127C2313yes—
55C11×#127C2316yes—
56C11×#125—26no—
57C11×#125—26no—
58C11×#125C2313yes—
59C11×#125C2311yescharacteristic
60C11×#125C2316yes—
61C11×#124C2316yes—
62C11×C22⋊Q8—26no—
63C11×C22⋊Q8—212no—
64C11×#121—26no—
65C11×#121—212no—
66C11×#120—212no—
67C4×Q8×C11—22no—
68C4×Q8×C11—26no—
69C4×Q8×C11D412yes—
70C4×D4×C11—26no—
71C4×D4×C11—26no—
72C4×D4×C11D416yes—
73C11×#117C2316yes—
74C11×#117C2313yes—
75C2×C11×C4⋊C4—26no—
76C2×C11×C4⋊C4C2316yes—
77C2×C42×C11C2313yes—
78C11×#103C2314yes—
79C11×#103C23112yes—
80C11×#102C23112yes—
81C11×#102C23112yes—
82C11×#102C23124yes—
83C11×#97C2316yes—
84C11×#97C2311yescharacteristic
85C11×#97C2313yes—
86C4×C8×C11C2316yes—
87#60626C1111yesmaximal, characteristic, direct product factor, Sylow
88C24×C11—26no—
89C11×#41—224no—
90C11×#41—48no—
91C11×#41#4118yes—
92C2×Q8×C11—26no—
93C2×Q8×C11C2×D411yescharacteristic
94C2×Q8×C11C2412yes—
95C2×D4×C11—26no—
96C2×D4×C11—26no—
97C2×D4×C11—26no—
98C2×D4×C11—212no—
99C2×D4×C11—224no—
100C2×D4×C11—424no—
101C2×D4×C11—812no—
102C2×D4×C11C2×D413yes—
103C2×D4×C11C2416yes—
104C22×C4×C11—26no—
105C22×C4×C11—26no—
106C22×C4×C11C2×D416yes—
107C22×C4×C11C2413yes—
108C11×M16—212no—
109C2×C8×C11—212no—
110C2×C8×C11C2416yes—
111C2×C8×C11C2412yes—
112C11×C4⋊C4—26no—
113C11×C4⋊C4—212no—
114C11×C4⋊C4—26no—
115C11×C4⋊C4—22no—
116C11×C4⋊C4—22no—
117C11×C4⋊C4—26no—
118C11×C4⋊C4C2×D416yes—
119C11×C4⋊C4C2416yes—
120C11×C4⋊C4C2412yes—
121C11×C22⋊C4—26no—
122C11×C22⋊C4—212no—
123C11×C22⋊C4C2×D416yes—
124C42×C11—26no—
125C42×C11C2×D416yes—
126C42×C11C2413yes—
127C42×C11C2411yescharacteristic
128#3504C2×C1111yescharacteristic, complemented
129#3498C2×C1111yescharacteristic
130#3142C2×C1113yescomplemented
131#3138C2×C1113yescomplemented
132#3136C2×C11112yescomplemented
133#3135C2×C1113yescomplemented
134C2×#490C2×C1113yescomplemented
135#2897C2×C1114yescomplemented
136#2875C2×C1111yescharacteristic, complemented
137C23×C11—26no—
138C23×C11—412no—
139C23×C11—812no—
140C23×C11C22×D413yes—
141Q8×C11—24no—
142Q8×C11—86no—
143Q8×C11#12414yes—
144D4×C11—212no—
145D4×C11—412no—
146D4×C11—412no—
147D4×C11—412no—
148D4×C11—812no—
149D4×C11#124112yes—
150C2×C4×C11—22no—
151C2×C4×C11—26no—
152C2×C4×C11—22no—
153C2×C4×C11—46no—
154C2×C4×C11—412no—
155C2×C4×C11—86no—
156C2×C4×C11C22×D412yes—
157C2×C4×C11C22×D416yes—
158C2×C4×C11C22×D413yes—
159C2×C4×C11C2×#41112yes—
160C2×C4×C11C2511yescharacteristic
161C8×C11—22no—
162C8×C11—26no—
163C2×H(5,𝔽2)C22×C1112yes—
164C2×#131C22×C1112yes—
165#557—22no—
166#554—26no—
167#550—22no—
168D42—26no—
169#544C22×C1116yescomplemented
170#535C22×C1116yes—
171#533C22×C1113yescomplemented
172#532C22×C1113yes—
173C2×#127C22×C1113yes—
174C2×#125C22×C1113yescomplemented
175#520C22×C1112yes—
176C4×#41C22×C1111yescharacteristic
177#491C22×C1111yescharacteristic, complemented
178#491C22×C1113yescomplemented
179#490C22×C1113yescomplemented
180#490C22×C11112yescomplemented
181#490C22×C1116yescomplemented
182#490C22×C1113yescomplemented
183#489C22×C11112yescomplemented
184#488C22×C11112yescomplemented
185#486C22×C11112yescomplemented
186#418C22×C11112yescomplemented
187#417C22×C11112yescomplemented
188#416C22×C11112yescomplemented
189C2×#102C22×C11112yescomplemented
190#405C22×C1116yescomplemented
191C4×M16C22×C1113yescomplemented
192C2×#97C22×C1113yescomplemented
193C22×C11—26no—
194C22×C11—412no—
195C22×C11—46no—
196C22×C11—1612no—
197C22×C11C2×#12416yes—
198C22×C11C23×D411yescharacteristic
199C4×C11—22no—
200C4×C11—26no—
201C4×C11—46no—
202C4×C11—42no—
203C4×C11—42no—
204C4×C11C2×#12416yes—
205C4×C11C22×#4112yes—
206H(5,𝔽2)—216no—
207C2×#41—22no—
208C2×#41C23×C1116yes—
209C2×#41C23×C1111yescharacteristic
210C22×D4—26no—
211C22×D4—26no—
212C22×D4C23×C1116yes—
213#131—28no—
214C2×M16C23×C1116yes—
215C22×C8C23×C1116yes—
216C4⋊Q8—26no—
217C4⋊Q8C23×C1111yescharacteristic
218C4⋊Q8C23×C1116yes—
219#127—26no—
220#127C23×C1113yes—
221#127C23×C1116yes—
222#125—26no—
223#125—26no—
224#125C23×C1113yes—
225#125C23×C1116yes—
226#125C23×C1111yescharacteristic
227#124C23×C1116yes—
228C22⋊Q8—26no—
229C22⋊Q8—212no—
230#121—26no—
231#121—212no—
232#120—212no—
233C4×Q8—22no—
234C4×Q8—26no—
235C4×Q8D4×C1112yes—
236C4×D4—26no—
237C4×D4—26no—
238C4×D4D4×C1116yes—
239#117C23×C1116yes—
240#117C23×C1113yes—
241C2×C4⋊C4—26no—
242C2×C4⋊C4C23×C1116yes—
243C2×C42C23×C1113yes—
244#103C23×C1114yes—
245#103C23×C11112yes—
246#102C23×C11112yes—
247#102C23×C11124yes—
248#102C23×C11112yes—
249#97C23×C1111yescharacteristic
250#97C23×C1113yes—
251#97C23×C1116yes—
252C4×C8C23×C1116yes—
253C2×C11—26no—
254C2×C11—86no—
255C2×C11C22×#12411yescharacteristic
256C2×C11#358512yes—
257C24—26no—
258#41—224no—
259#41—48no—
260#41C11×#4118yes—
261C2×Q8—26no—
262C2×Q8C2×D4×C1111yescharacteristic
263C2×Q8C24×C1112yes—
264C2×D4—26no—
265C2×D4—26no—
266C2×D4—26no—
267C2×D4—212no—
268C2×D4—224no—
269C2×D4—424no—
270C2×D4—812no—
271C2×D4C2×D4×C1113yes—
272C2×D4C24×C1116yes—
273C22×C4—26no—
274C22×C4—26no—
275C22×C4C2×D4×C1116yes—
276C22×C4C24×C1113yes—
277M16—212no—
278C2×C8—212no—
279C2×C8C24×C1116yes—
280C2×C8C24×C1112yes—
281C4⋊C4—26no—
282C4⋊C4—212no—
283C4⋊C4—26no—
284C4⋊C4—22no—
285C4⋊C4—22no—
286C4⋊C4—26no—
287C4⋊C4C2×D4×C1116yes—
288C4⋊C4C24×C1116yes—
289C4⋊C4C24×C1112yes—
290C22⋊C4—26no—
291C22⋊C4—212no—
292C22⋊C4C2×D4×C1116yes—
293C42—26no—
294C42C2×D4×C1116yes—
295C42C24×C1113yes—
296C42C24×C1111yescharacteristic
297C11#6062611yescharacteristic, direct product factor, Sylow
298C23—26no—
299C23—412no—
300C23—812no—
301C23C22×D4×C1113yes—
302Q8—24no—
303Q8—86no—
304Q8C11×#12414yes—
305D4—212no—
306D4—412no—
307D4—412no—
308D4—412no—
309D4—812no—
310D4C11×#124112yes—
311C2×C4—22no—
312C2×C4—26no—
313C2×C4—22no—
314C2×C4—46no—
315C2×C4—412no—
316C2×C4—86no—
317C2×C4C22×D4×C1112yes—
318C2×C4C22×D4×C1116yes—
319C2×C4C22×D4×C1113yes—
320C2×C4C2×C11×#41112yes—
321C2×C4C25×C1111yescharacteristic
322C8—22no—
323C8—26no—
324C22—26no—
325C22—46no—
326C22—412no—
327C22—1612no—
328C22C2×C11×#12416yes—
329C22C23×D4×C1111yescharacteristic
330C4—22no—
331C4—26no—
332C4—42no—
333C4—46no—
334C4—42no—
335C4C2×C11×#12416yes—
336C4C22×C11×#4112yes—
337C2—26no—
338C2—86no—
339C2C22×C11×#12411yescharacteristic
340C2C11×#358512yes—
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×#3504C2semidirect
3. C11×#3142C2semidirect
4. C11×#3138C2semidirect
5. C11×#3136C2semidirect
6. C11×#3135C2semidirect
7. C2×C11×#490C2semidirect
8. C11×#2897C2semidirect
9. C11×#2875C2semidirect
16. C11×#544C22semidirect
18. C11×#533C22semidirect
21. C2×C11×#125C22semidirect
24. C11×#491C22semidirect
25. C11×#491C22semidirect
26. C11×#490C22semidirect
27. C11×#490C22semidirect
28. C11×#490C22semidirect
29. C11×#490C22semidirect
30. C11×#489C22semidirect
31. C11×#488C22semidirect
32. C11×#486C22semidirect
33. C11×#418C22semidirect
34. C11×#417C22semidirect
35. C11×#416C22semidirect
36. C2×C11×#102C22semidirect
37. C11×#405C22semidirect
38. C4×C11×M16C22semidirect
39. C2×C11×#97C22semidirect
87. #60626C11direct (N × H)
128. #3504C2×C11semidirect
130. #3142C2×C11semidirect
131. #3138C2×C11semidirect
132. #3136C2×C11semidirect
133. #3135C2×C11semidirect
134. C2×#490C2×C11semidirect
135. #2897C2×C11semidirect
136. #2875C2×C11semidirect
169. #544C22×C11semidirect
171. #533C22×C11semidirect
174. C2×#125C22×C11semidirect
177. #491C22×C11semidirect
178. #491C22×C11semidirect
179. #490C22×C11semidirect
180. #490C22×C11semidirect
181. #490C22×C11semidirect
182. #490C22×C11semidirect
183. #489C22×C11semidirect
184. #488C22×C11semidirect
185. #486C22×C11semidirect
186. #418C22×C11semidirect
187. #417C22×C11semidirect
188. #416C22×C11semidirect
189. C2×#102C22×C11semidirect
190. #405C22×C11semidirect
191. C4×M16C22×C11semidirect
192. C2×#97C22×C11semidirect
297. C11#60626direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35042
C11×#34982
C11×#31422
C11×#31382
C11×#31362
C11×#31352
C2×C11×#4902
C11×#28972
C11×#28752
#6062611