Finite Group Databasebeta

← C11×#61698 #14638891

Subgroups — C11×#61698 #14638891

Order 2816.

1802 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3501C211yesmaximal, characteristic
2C2×C11×#554C211yesmaximal, characteristic
3C11×#3338C218yesmaximal, complemented
4C11×#3299C218yesmaximal, complemented
5C11×#3230C212yesmaximal, complemented
6C11×#3189C214yesmaximal, complemented
7C11×#3104C212yesmaximal, complemented
8C2×C11×#484C214yesmaximal, complemented
9C11×#2972C211yesmaximal, characteristic
10C11×#554—24no—
11C11×#554—24no—
12C11×#554C2218yes—
13C11×#554C2214yes—
14D4×Q8×C11C2214yes—
15C11×#544—21no—
16C11×#543—22no—
17C11×#533C2212yes—
18C2×C11×C4⋊Q8C2211yescharacteristic
19C2×C11×#125—21no—
20C2×C11×C22⋊Q8—22no—
21C2×C11×C22⋊Q8C2212yes—
22C2×C11×C22⋊Q8C2214yes—
23C11×#518—21no—
24C2×C4×Q8×C11C2211yescharacteristic
25C2×C4×D4×C11—21no—
26C2×C4×D4×C11C2211yescharacteristic
27C22×C11×C4⋊C4C2212yes—
28C11×#500C2214yescomplemented
29C11×#487C2214yescomplemented
30C11×#484C2218yes—
31C11×#484C2214yes—
32C11×#484C2218yescomplemented
33C11×#484C22116yescomplemented
34C11×#477C2218yescomplemented
35C11×#477C2214yescomplemented
36C11×#467C22116yescomplemented
37C11×#462C2214yescomplemented
38C11×#451C2214yes—
39C11×#451C2218yescomplemented
40C4×C11×Q16C2218yescomplemented
41C8×D4×C11C2218yes—
42C11×#431C2212yes—
43C2×C11×#107C2218yescomplemented
44C2×C11×#103C2218yescomplemented
45C2×C11×C22⋊C8C2214yes—
46C22×Q8×C11—21no—
47C22×Q8×C11C2311yescharacteristic
48C22×Q8×C11C2314yes—
49C22×D4×C11D411yescharacteristic
50C23×C4×C11—22no—
51C23×C4×C11C2312yes—
52C2×C11×Q16C2318yes—
53C22×C8×C11C2318yes—
54C11×C4⋊Q8—24no—
55C11×C4⋊Q8—22no—
56C11×C4⋊Q8C2312yes—
57C11×C4⋊Q8C2312yes—
58C11×C4⋊Q8C2314yes—
59C11×#125—28no—
60C11×#125—24no—
61C11×#125—22no—
62C11×C22⋊Q8—24no—
63C11×C22⋊Q8—24no—
64C11×C22⋊Q8—24no—
65C11×C22⋊Q8—22no—
66C11×C22⋊Q8—216no—
67C11×C22⋊Q8—28no—
68C11×C22⋊Q8—28no—
69C11×C22⋊Q8C2314yes—
70C11×C22⋊Q8C2318yes—
71C11×C22⋊Q8C2318yes—
72C4×Q8×C11—22no—
73C4×Q8×C11—22no—
74C4×Q8×C11C2314yes—
75C4×Q8×C11C2314yes—
76C4×D4×C11—28no—
77C4×D4×C11—24no—
78C4×D4×C11—24no—
79C4×D4×C11D414yes—
80C4×D4×C11C2314yes—
81C11×#117—22no—
82C2×C11×C4⋊C4—22no—
83C2×C11×C4⋊C4—24no—
84C2×C11×C4⋊C4—21no—
85C2×C11×C4⋊C4—21no—
86C2×C11×C4⋊C4—22no—
87C2×C11×C4⋊C4—24no—
88C2×C11×C4⋊C4D411yescharacteristic
89C2×C11×C4⋊C4C2311yescharacteristic
90C2×C11×C4⋊C4C2312yes—
91C2×C11×C4⋊C4C2318yes—
92C2×C11×C4⋊C4C2314yes—
93C2×C11×C22⋊C4—22no—
94C2×C11×C22⋊C4—24no—
95C2×C11×C22⋊C4D412yes—
96C2×C42×C11—21no—
97C2×C42×C11C2311yescharacteristic
98C11×#107C23116yes—
99C11×#107C2318yes—
100C11×C4⋊C8C2314yes—
101C11×#103C2318yes—
102C11×#103C23116yes—
103C11×#103C2318yes—
104C11×C22⋊C8C2314yes—
105C11×C22⋊C8C2318yes—
106C4×C8×C11C2314yes—
107#61698C1111yesmaximal, characteristic, direct product factor, Sylow
108C24×C11C2×D412yes—
109C2×Q8×C11—21no—
110C2×Q8×C11—22no—
111C2×Q8×C11—24no—
112C2×Q8×C11—24no—
113C2×Q8×C11—42no—
114C2×Q8×C11—48no—
115C2×Q8×C11—82no—
116C2×Q8×C11C2414yes—
117C2×Q8×C11C2412yes—
118C2×D4×C11Q1618yescomplemented
119C2×D4×C11C2×D414yes—
120C22×C4×C11—21no—
121C22×C4×C11—21no—
122C22×C4×C11—22no—
123C22×C4×C11—24no—
124C22×C4×C11—24no—
125C22×C4×C11—28no—
126C22×C4×C11—44no—
127C22×C4×C11—84no—
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2×D412yes—
130C22×C4×C11C2×D414yes—
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2411yescharacteristic
133C22×C4×C11C2414yes—
134C11×Q16—48no—
135C2×C8×C11—48no—
136C2×C8×C11C2418yes—
137C11×C4⋊C4—21no—
138C11×C4⋊C4—28no—
139C11×C4⋊C4—22no—
140C11×C4⋊C4—24no—
141C11×C4⋊C4—24no—
142C11×C4⋊C4—24no—
143C11×C4⋊C4—28no—
144C11×C4⋊C4—28no—
145C11×C4⋊C4—24no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—22no—
149C11×C4⋊C4—24no—
150C11×C4⋊C4C2×D414yes—
151C11×C4⋊C4C2412yes—
152C11×C4⋊C4C2414yes—
153C11×C4⋊C4C2414yes—
154C11×C22⋊C4—24no—
155C11×C22⋊C4—28no—
156C11×C22⋊C4—28no—
157C11×C22⋊C4C2×D418yes—
158C42×C11—24no—
159C42×C11—24no—
160C42×C11C2×D412yes—
161C42×C11C2412yes—
162#3501C2×C1111yescharacteristic
163C2×#554C2×C1111yescharacteristic
164#3338C2×C1118yescomplemented
165#3299C2×C1118yescomplemented
166#3230C2×C1112yescomplemented
167#3189C2×C1114yescomplemented
168#3104C2×C1112yescomplemented
169C2×#484C2×C1114yescomplemented
170#2972C2×C1111yescharacteristic
171C23×C11—42no—
172C23×C11—42no—
173C23×C11C2×Q1618yes—
174C23×C11C22×D414yes—
175C23×C11C22×D411yescharacteristic
176Q8×C11—24no—
177Q8×C11—28no—
178Q8×C11—42no—
179Q8×C11—82no—
180Q8×C11—84no—
181Q8×C11—84no—
182D4×C11C2×Q16116yes—
183C2×C4×C11—28no—
184C2×C4×C11—22no—
185C2×C4×C11—22no—
186C2×C4×C11—22no—
187C2×C4×C11—24no—
188C2×C4×C11—24no—
189C2×C4×C11—24no—
190C2×C4×C11—44no—
191C2×C4×C11—42no—
192C2×C4×C11—41no—
193C2×C4×C11—42no—
194C2×C4×C11—44no—
195C2×C4×C11—42no—
196C2×C4×C11—84no—
197C2×C4×C11—88no—
198C2×C4×C11—84no—
199C2×C4×C11C2×Q1614yes—
200C2×C4×C11C22×D411yescharacteristic
201C2×C4×C11C22×D412yes—
202C2×C4×C11C22×D414yes—
203C2×C4×C11C22×D412yes—
204C2×C4×C11C2511yescharacteristic
205C8×C11—28no—
206#554—24no—
207#554—24no—
208#554C22×C1114yes—
209#554C22×C1118yes—
210D4×Q8C22×C1114yes—
211#544—21no—
212#543—22no—
213#533C22×C1112yes—
214C2×C4⋊Q8C22×C1111yescharacteristic
215C2×#125—21no—
216C2×C22⋊Q8—22no—
217C2×C22⋊Q8C22×C1114yes—
218C2×C22⋊Q8C22×C1112yes—
219#518—21no—
220C2×C4×Q8C22×C1111yescharacteristic
221C2×C4×D4—21no—
222C2×C4×D4C22×C1111yescharacteristic
223C22×C4⋊C4C22×C1112yes—
224#500C22×C1114yescomplemented
225#487C22×C1114yescomplemented
226#484C22×C1114yes—
227#484C22×C1118yes—
228#484C22×C1118yescomplemented
229#484C22×C11116yescomplemented
230#477C22×C1114yescomplemented
231#477C22×C1118yescomplemented
232#467C22×C11116yescomplemented
233#462C22×C1114yescomplemented
234#451C22×C1114yes—
235#451C22×C1118yescomplemented
236C4×Q16C22×C1118yescomplemented
237C8×D4C22×C1118yes—
238#431C22×C1112yes—
239C2×#107C22×C1118yescomplemented
240C2×#103C22×C1118yescomplemented
241C2×C22⋊C8C22×C1114yes—
242C22×C11—21no—
243C22×C11—24no—
244C22×C11—21no—
245C22×C11—24no—
246C22×C11—48no—
247C22×C11C22×Q1612yes—
248C22×C11C22×Q1618yes—
249C22×C11C23×D411yescharacteristic
250C4×C11—22no—
251C4×C11—21no—
252C4×C11—24no—
253C4×C11—42no—
254C4×C11—44no—
255C4×C11—44no—
256C4×C11—42no—
257C4×C11—44no—
258C4×C11C22×Q1614yes—
259C4×C11#58512yes—
260C22×Q8—21no—
261C22×Q8C23×C1111yescharacteristic
262C22×Q8C23×C1114yes—
263C22×D4D4×C1111yescharacteristic
264C23×C4—22no—
265C23×C4C23×C1112yes—
266C2×Q16C23×C1118yes—
267C22×C8C23×C1118yes—
268C4⋊Q8—24no—
269C4⋊Q8—22no—
270C4⋊Q8C23×C1112yes—
271C4⋊Q8C23×C1114yes—
272C4⋊Q8C23×C1112yes—
273#125—28no—
274#125—24no—
275#125—22no—
276C22⋊Q8—24no—
277C22⋊Q8—24no—
278C22⋊Q8—24no—
279C22⋊Q8—22no—
280C22⋊Q8—216no—
281C22⋊Q8—28no—
282C22⋊Q8—28no—
283C22⋊Q8C23×C1114yes—
284C22⋊Q8C23×C1118yes—
285C22⋊Q8C23×C1118yes—
286C4×Q8—22no—
287C4×Q8—22no—
288C4×Q8C23×C1114yes—
289C4×Q8C23×C1114yes—
290C4×D4—28no—
291C4×D4—24no—
292C4×D4—24no—
293C4×D4D4×C1114yes—
294C4×D4C23×C1114yes—
295#117—22no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4D4×C1111yescharacteristic
303C2×C4⋊C4C23×C1111yescharacteristic
304C2×C4⋊C4C23×C1112yes—
305C2×C4⋊C4C23×C1118yes—
306C2×C4⋊C4C23×C1114yes—
307C2×C22⋊C4—22no—
308C2×C22⋊C4—24no—
309C2×C22⋊C4D4×C1112yes—
310C2×C42—21no—
311C2×C42C23×C1111yescharacteristic
312#107C23×C1118yes—
313#107C23×C11116yes—
314C4⋊C8C23×C1114yes—
315#103C23×C1118yes—
316#103C23×C11116yes—
317#103C23×C1118yes—
318C22⋊C8C23×C1114yes—
319C22⋊C8C23×C1118yes—
320C4×C8C23×C1114yes—
321C2×C11—22no—
322C2×C11—28no—
323C2×C11#348511yescharacteristic
324C2×C11C23×Q1611yescharacteristic
325C2×C11#358511yescharacteristic
326C24C2×D4×C1112yes—
327C2×Q8—21no—
328C2×Q8—22no—
329C2×Q8—24no—
330C2×Q8—24no—
331C2×Q8—42no—
332C2×Q8—48no—
333C2×Q8—82no—
334C2×Q8C24×C1114yes—
335C2×Q8C24×C1112yes—
336C2×D4C11×Q1618yescomplemented
337C2×D4C2×D4×C1114yes—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—22no—
341C22×C4—24no—
342C22×C4—24no—
343C22×C4—28no—
344C22×C4—44no—
345C22×C4—84no—
346C22×C4C2×D4×C1111yescharacteristic
347C22×C4C2×D4×C1112yes—
348C22×C4C2×D4×C1114yes—
349C22×C4C2×D4×C1111yescharacteristic
350C22×C4C24×C1111yescharacteristic
351C22×C4C24×C1114yes—
352Q16—48no—
353C2×C8—48no—
354C2×C8C24×C1118yes—
355C4⋊C4—21no—
356C4⋊C4—28no—
357C4⋊C4—22no—
358C4⋊C4—24no—
359C4⋊C4—24no—
360C4⋊C4—24no—
361C4⋊C4—28no—
362C4⋊C4—28no—
363C4⋊C4—24no—
364C4⋊C4—22no—
365C4⋊C4—22no—
366C4⋊C4—22no—
367C4⋊C4—24no—
368C4⋊C4C2×D4×C1114yes—
369C4⋊C4C24×C1112yes—
370C4⋊C4C24×C1114yes—
371C4⋊C4C24×C1114yes—
372C22⋊C4—24no—
373C22⋊C4—28no—
374C22⋊C4—28no—
375C22⋊C4C2×D4×C1118yes—
376C42—24no—
377C42—24no—
378C42C2×D4×C1112yes—
379C42C24×C1112yes—
380C11#6169811yescharacteristic, direct product factor, Sylow
381C23—42no—
382C23—42no—
383C23C2×C11×Q1618yes—
384C23C22×D4×C1114yes—
385C23C22×D4×C1111yescharacteristic
386Q8—24no—
387Q8—28no—
388Q8—42no—
389Q8—82no—
390Q8—84no—
391Q8—84no—
392D4C2×C11×Q16116yes—
393C2×C4—28no—
394C2×C4—22no—
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—24no—
398C2×C4—24no—
399C2×C4—24no—
400C2×C4—44no—
401C2×C4—42no—
402C2×C4—41no—
403C2×C4—42no—
404C2×C4—44no—
405C2×C4—42no—
406C2×C4—84no—
407C2×C4—88no—
408C2×C4—84no—
409C2×C4C2×C11×Q1614yes—
410C2×C4C22×D4×C1111yescharacteristic
411C2×C4C22×D4×C1112yes—
412C2×C4C22×D4×C1114yes—
413C2×C4C22×D4×C1112yes—
414C2×C4C25×C1111yescharacteristic
415C8—28no—
416C22—21no—
417C22—24no—
418C22—21no—
419C22—24no—
420C22—48no—
421C22C22×C11×Q1612yes—
422C22C22×C11×Q1618yes—
423C22C23×D4×C1111yescharacteristic
424C4—21no—
425C4—24no—
426C4—22no—
427C4—42no—
428C4—44no—
429C4—42no—
430C4—44no—
431C4—44no—
432C4C22×C11×Q1614yes—
433C4C11×#58512yes—
434C2—22no—
435C2—28no—
436C2C11×#348511yescharacteristic
437C2C23×C11×Q1611yescharacteristic
438C2C11×#358511yescharacteristic
subgroupG/H
center, socleC22×C11C23×D4
commutator, Frattini, cosocleC2×C4C25×C11
prime radicalC22×D4×C11D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C4×D4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
3. C11×#3338C2semidirect
4. C11×#3299C2semidirect
5. C11×#3230C2semidirect
6. C11×#3189C2semidirect
7. C11×#3104C2semidirect
8. C2×C11×#484C2semidirect
28. C11×#500C22semidirect
29. C11×#487C22semidirect
32. C11×#484C22semidirect
33. C11×#484C22semidirect
34. C11×#477C22semidirect
35. C11×#477C22semidirect
36. C11×#467C22semidirect
37. C11×#462C22semidirect
39. C11×#451C22semidirect
40. C4×C11×Q16C22semidirect
43. C2×C11×#107C22semidirect
44. C2×C11×#103C22semidirect
107. #61698C11direct (N × H)
118. C2×D4×C11Q16semidirect
164. #3338C2×C11semidirect
165. #3299C2×C11semidirect
166. #3230C2×C11semidirect
167. #3189C2×C11semidirect
168. #3104C2×C11semidirect
169. C2×#484C2×C11semidirect
224. #500C22×C11semidirect
225. #487C22×C11semidirect
228. #484C22×C11semidirect
229. #484C22×C11semidirect
230. #477C22×C11semidirect
231. #477C22×C11semidirect
232. #467C22×C11semidirect
233. #462C22×C11semidirect
235. #451C22×C11semidirect
236. C4×Q16C22×C11semidirect
239. C2×#107C22×C11semidirect
240. C2×#103C22×C11semidirect
336. C2×D4C11×Q16semidirect
380. C11#61698direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35012
C2×C11×#5542
C11×#33382
C11×#32992
C11×#32302
C11×#31892
C11×#31042
C2×C11×#4842
C11×#29722
#6169811