Finite Group Databasebeta

← C11×#60621 #14637814

Subgroups — C11×#60621 #14637814

Order 2816.

2078 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#544C211yesmaximal, characteristic, complemented
2C11×#3449C211yesmaximal, characteristic
3C11×#3142C214yesmaximal, complemented
4C11×#3141C214yesmaximal, complemented
5C11×#3137C218yesmaximal, complemented
6C11×#3136C218yesmaximal, complemented
7C11×#2896C212yesmaximal, complemented
8C2×C11×#417C212yesmaximal, complemented
9C11×#2873C211yesmaximal, characteristic, complemented
10C22×C11×#41C2212yes—
11C22×C11×M16C2212yes—
12C11×#544—24no—
13C11×#544C2218yescomplemented
14C11×#537—21no—
15C11×#537—21no—
16C11×#536C2214yes—
17C11×#535C2214yes—
18C11×#534—22no—
19C11×#532C2214yes—
20C2×C11×C4⋊Q8—21no—
21C2×C11×C4⋊Q8C2212yescomplemented
22C2×C11×#125—21no—
23C2×C11×#125C2212yescomplemented
24C11×#525—24no—
25C2×C11×C22⋊Q8—22no—
26C2×C11×#117C2211yescharacteristic
27C2×C11×#117C2211yescharacteristic
28C22×C11×C4⋊C4C2211yescharacteristic
29C11×#491C2218yescomplemented
30C11×#490C2218yescomplemented
31C11×#489C22116yescomplemented
32C11×#488C22116yescomplemented
33C11×#487C2218yescomplemented
34C11×#486C2218yescomplemented
35C11×#419C2214yescomplemented
36C11×#418C2214yescomplemented
37C11×#417C2218yes—
38C11×#417C2218yescomplemented
39C11×#417C2214yescomplemented
40C11×#417C2214yescomplemented
41C11×#416C2218yes—
42C2×C11×#103C2214yescomplemented
43C2×C11×#102C2214yescomplemented
44C11×#405C2218yescomplemented
45C4×C11×M16C2214yescomplemented
46C2×C11×#41—22no—
47C2×C11×#41—22no—
48C2×C11×#41—28no—
49C2×C11×#41—28no—
50C2×C11×#41C2314yes—
51C2×C11×#41C2314yes—
52C22×Q8×C11—22no—
53C22×Q8×C11C2312yes—
54C22×D4×C11—22no—
55C22×D4×C11C2312yes—
56C23×C4×C11—21no—
57C23×C4×C11—22no—
58C23×C4×C11C2311yescharacteristic
59C2×C11×M16—28no—
60C2×C11×M16C2314yes—
61C2×C11×M16C2314yes—
62C22×C8×C11C2314yes—
63C11×C4⋊Q8—28no—
64C11×C4⋊Q8—24no—
65C11×C4⋊Q8C2314yes—
66C11×C4⋊Q8C2318yes—
67C11×#127C2314yes—
68C11×#125—28no—
69C11×#125—24no—
70C11×#125C2318yes—
71C11×#124C2318yes—
72C11×#123—28no—
73C11×C22⋊Q8—24no—
74C11×C22⋊Q8—24no—
75C11×C22⋊Q8—216no—
76C11×#121—24no—
77C11×#121—24no—
78C11×#121—24no—
79C11×#121—24no—
80C11×#120—28no—
81C4×D4×C11—24no—
82C4×D4×C11—24no—
83C11×#117—22no—
84C11×#117D414yes—
85C11×#117C2314yes—
86C11×#117C2314yes—
87C2×C11×C4⋊C4—21no—
88C2×C11×C4⋊C4—22no—
89C2×C11×C4⋊C4—22no—
90C2×C11×C4⋊C4—22no—
91C2×C11×C4⋊C4—22no—
92C2×C11×C4⋊C4D411yescharacteristic
93C2×C11×C4⋊C4D411yescharacteristic
94C2×C11×C4⋊C4C2312yes—
95C2×C11×C4⋊C4C2314yes—
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C22⋊C4—21no—
99C2×C11×C22⋊C4D412yes—
100C2×C42×C11—21no—
101C2×C42×C11C2312yes—
102C11×#103C2318yes—
103C11×#103C23116yes—
104C11×#103C2318yes—
105C11×#102C2318yes—
106C11×#102C23116yes—
107C11×#102C2318yes—
108C11×#97C2318yes—
109C4×C8×C11C2318yes—
110#60621C1111yesmaximal, characteristic, direct product factor, Sylow
111C24×C11—22no—
112C24×C11C2×D411yescharacteristic
113C11×#41—28no—
114C11×#41—28no—
115C11×#41—28no—
116C11×#41—28no—
117C11×#41—48no—
118C11×#41—48no—
119C2×Q8×C11—22no—
120C2×Q8×C11—28no—
121C2×Q8×C11—24no—
122C2×Q8×C11—24no—
123C2×Q8×C11—84no—
124C2×Q8×C11C2414yes—
125C2×D4×C11—24no—
126C2×D4×C11—24no—
127C2×D4×C11—22no—
128C2×D4×C11—24no—
129C2×D4×C11—24no—
130C2×D4×C11—24no—
131C2×D4×C11—24no—
132C2×D4×C11—48no—
133C2×D4×C11C2414yes—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—24no—
139C22×C4×C11—24no—
140C22×C4×C11—24no—
141C22×C4×C11—48no—
142C22×C4×C11—82no—
143C22×C4×C11C2×D412yes—
144C22×C4×C11C2×D412yes—
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D412yes—
147C22×C4×C11#4118yes—
148C22×C4×C11C2411yescharacteristic
149C22×C4×C11C2412yes—
150C11×M16—28no—
151C11×M16—28no—
152C2×C8×C11—28no—
153C2×C8×C11C2418yes—
154C11×C4⋊C4—24no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—28no—
157C11×C4⋊C4—28no—
158C11×C4⋊C4—28no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—24no—
162C11×C4⋊C4—24no—
163C11×C4⋊C4C2×D414yes—
164C11×C4⋊C4C2×D414yes—
165C11×C4⋊C4C2414yes—
166C11×C4⋊C4C2412yes—
167C11×C4⋊C4C2412yes—
168C11×C22⋊C4—24no—
169C11×C22⋊C4—28no—
170C11×C22⋊C4—28no—
171C11×C22⋊C4C2×D418yes—
172C42×C11—24no—
173C42×C11C2×D414yes—
174C42×C11C2414yes—
175C2×#544C2×C1111yescharacteristic, complemented
176#3449C2×C1111yescharacteristic
177#3142C2×C1114yescomplemented
178#3141C2×C1114yescomplemented
179#3137C2×C1118yescomplemented
180#3136C2×C1118yescomplemented
181#2896C2×C1112yescomplemented
182C2×#417C2×C1112yescomplemented
183#2873C2×C1111yescharacteristic, complemented
184C23×C11—24no—
185C23×C11—41no—
186C23×C11—41no—
187C23×C11—44no—
188C23×C11—82no—
189C23×C11—82no—
190C23×C11#12414yes—
191C23×C11C22×D412yes—
192C23×C11C22×D411yescharacteristic
193Q8×C11—24no—
194Q8×C11—24no—
195Q8×C11—44no—
196Q8×C11—88no—
197D4×C11—24no—
198D4×C11—24no—
199D4×C11—48no—
200D4×C11—48no—
201D4×C11—44no—
202D4×C11—84no—
203D4×C11—84no—
204C2×C4×C11—22no—
205C2×C4×C11—22no—
206C2×C4×C11—24no—
207C2×C4×C11—24no—
208C2×C4×C11—42no—
209C2×C4×C11—42no—
210C2×C4×C11—42no—
211C2×C4×C11—44no—
212C2×C4×C11—42no—
213C2×C4×C11—44no—
214C2×C4×C11—48no—
215C2×C4×C11—48no—
216C2×C4×C11—84no—
217C2×C4×C11#12418yes—
218C2×C4×C11#12414yes—
219C2×C4×C11C22×D414yes—
220C2×C4×C11C22×D414yes—
221C2×C4×C11C22×D412yes—
222C2×C4×C11C22×D411yescharacteristic
223C2×C4×C11C2×#4114yes—
224C2×C4×C11C2×#4114yes—
225C2×C4×C11C2×#4114yes—
226C2×C4×C11C2511yescharacteristic
227C8×C11—28no—
228C22×#41C22×C1112yes—
229C22×M16C22×C1112yes—
230#544—24no—
231#544C22×C1118yescomplemented
232#537—21no—
233#537—21no—
234#536C22×C1114yes—
235#535C22×C1114yes—
236#534—22no—
237#532C22×C1114yes—
238C2×C4⋊Q8—21no—
239C2×C4⋊Q8C22×C1112yescomplemented
240C2×#125—21no—
241C2×#125C22×C1112yescomplemented
242#525—24no—
243C2×C22⋊Q8—22no—
244C2×#117C22×C1111yescharacteristic
245C2×#117C22×C1111yescharacteristic
246C22×C4⋊C4C22×C1111yescharacteristic
247#491C22×C1118yescomplemented
248#490C22×C1118yescomplemented
249#489C22×C11116yescomplemented
250#488C22×C11116yescomplemented
251#487C22×C1118yescomplemented
252#486C22×C1118yescomplemented
253#419C22×C1114yescomplemented
254#418C22×C1114yescomplemented
255#417C22×C1118yes—
256#417C22×C1114yescomplemented
257#417C22×C1118yescomplemented
258#417C22×C1114yescomplemented
259#416C22×C1118yes—
260C2×#103C22×C1114yescomplemented
261C2×#102C22×C1114yescomplemented
262#405C22×C1118yescomplemented
263C4×M16C22×C1114yescomplemented
264C22×C11—21no—
265C22×C11—22no—
266C22×C11—21no—
267C22×C11—22no—
268C22×C11—44no—
269C22×C11—44no—
270C22×C11—44no—
271C22×C11—44no—
272C22×C11—88no—
273C22×C11C2×#12414yes—
274C22×C11C2×#12412yes—
275C22×C11C23×D411yescharacteristic
276C4×C11—24no—
277C4×C11—24no—
278C4×C11—44no—
279C4×C11—42no—
280C4×C11—42no—
281C4×C11—44no—
282C4×C11C2×#12412yes—
283C4×C11C2×#12414yes—
284C4×C11C22×#4112yes—
285C2×#41—22no—
286C2×#41—22no—
287C2×#41—28no—
288C2×#41—28no—
289C2×#41C23×C1114yes—
290C2×#41C23×C1114yes—
291C22×Q8—22no—
292C22×Q8C23×C1112yes—
293C22×D4—22no—
294C22×D4C23×C1112yes—
295C23×C4—21no—
296C23×C4—22no—
297C23×C4C23×C1111yescharacteristic
298C2×M16—28no—
299C2×M16C23×C1114yes—
300C2×M16C23×C1114yes—
301C22×C8C23×C1114yes—
302C4⋊Q8—28no—
303C4⋊Q8—24no—
304C4⋊Q8C23×C1114yes—
305C4⋊Q8C23×C1118yes—
306#127C23×C1114yes—
307#125—28no—
308#125—24no—
309#125C23×C1118yes—
310#124C23×C1118yes—
311#123—28no—
312C22⋊Q8—24no—
313C22⋊Q8—24no—
314C22⋊Q8—216no—
315#121—24no—
316#121—24no—
317#121—24no—
318#121—24no—
319#120—28no—
320C4×D4—24no—
321C4×D4—24no—
322#117—22no—
323#117D4×C1114yes—
324#117C23×C1114yes—
325#117C23×C1114yes—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4D4×C1111yescharacteristic
332C2×C4⋊C4D4×C1111yescharacteristic
333C2×C4⋊C4C23×C1112yes—
334C2×C4⋊C4C23×C1114yes—
335C2×C4⋊C4C23×C1111yescharacteristic
336C2×C4⋊C4C23×C1111yescharacteristic
337C2×C22⋊C4—21no—
338C2×C22⋊C4D4×C1112yes—
339C2×C42—21no—
340C2×C42C23×C1112yes—
341#103C23×C11116yes—
342#103C23×C1118yes—
343#103C23×C1118yes—
344#102C23×C11116yes—
345#102C23×C1118yes—
346#102C23×C1118yes—
347#97C23×C1118yes—
348C4×C8C23×C1118yes—
349C2×C11—24no—
350C2×C11—22no—
351C2×C11—84no—
352C2×C11C22×#12411yescharacteristic
353C2×C11#358511yescharacteristic
354C2×C11#358611yescharacteristic
355C24—22no—
356C24C2×D4×C1111yescharacteristic
357#41—28no—
358#41—28no—
359#41—28no—
360#41—28no—
361#41—48no—
362#41—48no—
363C2×Q8—22no—
364C2×Q8—28no—
365C2×Q8—24no—
366C2×Q8—24no—
367C2×Q8—84no—
368C2×Q8C24×C1114yes—
369C2×D4—24no—
370C2×D4—24no—
371C2×D4—22no—
372C2×D4—24no—
373C2×D4—24no—
374C2×D4—24no—
375C2×D4—24no—
376C2×D4—48no—
377C2×D4C24×C1114yes—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—24no—
383C22×C4—24no—
384C22×C4—24no—
385C22×C4—48no—
386C22×C4—82no—
387C22×C4C2×D4×C1112yes—
388C22×C4C2×D4×C1112yes—
389C22×C4C2×D4×C1111yescharacteristic
390C22×C4C2×D4×C1112yes—
391C22×C4C11×#4118yes—
392C22×C4C24×C1111yescharacteristic
393C22×C4C24×C1112yes—
394M16—28no—
395M16—28no—
396C2×C8—28no—
397C2×C8C24×C1118yes—
398C4⋊C4—24no—
399C4⋊C4—22no—
400C4⋊C4—28no—
401C4⋊C4—28no—
402C4⋊C4—28no—
403C4⋊C4—21no—
404C4⋊C4—21no—
405C4⋊C4—24no—
406C4⋊C4—24no—
407C4⋊C4C2×D4×C1114yes—
408C4⋊C4C2×D4×C1114yes—
409C4⋊C4C24×C1114yes—
410C4⋊C4C24×C1112yes—
411C4⋊C4C24×C1112yes—
412C22⋊C4—24no—
413C22⋊C4—28no—
414C22⋊C4—28no—
415C22⋊C4C2×D4×C1118yes—
416C42—24no—
417C42C2×D4×C1114yes—
418C42C24×C1114yes—
419C11#6062111yescharacteristic, direct product factor, Sylow
420C23—24no—
421C23—41no—
422C23—41no—
423C23—44no—
424C23—82no—
425C23—82no—
426C23C11×#12414yes—
427C23C22×D4×C1112yes—
428C23C22×D4×C1111yescharacteristic
429Q8—24no—
430Q8—24no—
431Q8—44no—
432Q8—88no—
433D4—24no—
434D4—24no—
435D4—48no—
436D4—48no—
437D4—44no—
438D4—84no—
439D4—84no—
440C2×C4—22no—
441C2×C4—22no—
442C2×C4—24no—
443C2×C4—24no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—42no—
447C2×C4—44no—
448C2×C4—42no—
449C2×C4—44no—
450C2×C4—48no—
451C2×C4—48no—
452C2×C4—84no—
453C2×C4C11×#12418yes—
454C2×C4C11×#12414yes—
455C2×C4C22×D4×C1114yes—
456C2×C4C22×D4×C1114yes—
457C2×C4C22×D4×C1112yes—
458C2×C4C22×D4×C1111yescharacteristic
459C2×C4C2×C11×#4114yes—
460C2×C4C2×C11×#4114yes—
461C2×C4C2×C11×#4114yes—
462C2×C4C25×C1111yescharacteristic
463C8—28no—
464C22—21no—
465C22—22no—
466C22—21no—
467C22—22no—
468C22—44no—
469C22—44no—
470C22—44no—
471C22—44no—
472C22—88no—
473C22C2×C11×#12414yes—
474C22C2×C11×#12412yes—
475C22C23×D4×C1111yescharacteristic
476C4—24no—
477C4—24no—
478C4—44no—
479C4—44no—
480C4—42no—
481C4—42no—
482C4C2×C11×#12412yes—
483C4C2×C11×#12414yes—
484C4C22×C11×#4112yes—
485C2—24no—
486C2—22no—
487C2—84no—
488C2C22×C11×#12411yescharacteristic
489C2C11×#358511yescharacteristic
490C2C11×#358611yescharacteristic
subgroupG/H
center, socleC22×C11C23×D4
commutator, Frattini, cosocleC2×C4C25×C11
prime radicalC11×#3449C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C11×#117 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#544C2semidirect
3. C11×#3142C2semidirect
4. C11×#3141C2semidirect
5. C11×#3137C2semidirect
6. C11×#3136C2semidirect
7. C11×#2896C2semidirect
8. C2×C11×#417C2semidirect
9. C11×#2873C2semidirect
13. C11×#544C22semidirect
21. C2×C11×C4⋊Q8C22semidirect
23. C2×C11×#125C22semidirect
29. C11×#491C22semidirect
30. C11×#490C22semidirect
31. C11×#489C22semidirect
32. C11×#488C22semidirect
33. C11×#487C22semidirect
34. C11×#486C22semidirect
35. C11×#419C22semidirect
36. C11×#418C22semidirect
38. C11×#417C22semidirect
39. C11×#417C22semidirect
40. C11×#417C22semidirect
42. C2×C11×#103C22semidirect
43. C2×C11×#102C22semidirect
44. C11×#405C22semidirect
45. C4×C11×M16C22semidirect
110. #60621C11direct (N × H)
175. C2×#544C2×C11semidirect
177. #3142C2×C11semidirect
178. #3141C2×C11semidirect
179. #3137C2×C11semidirect
180. #3136C2×C11semidirect
181. #2896C2×C11semidirect
182. C2×#417C2×C11semidirect
183. #2873C2×C11semidirect
231. #544C22×C11semidirect
239. C2×C4⋊Q8C22×C11semidirect
241. C2×#125C22×C11semidirect
247. #491C22×C11semidirect
248. #490C22×C11semidirect
249. #489C22×C11semidirect
250. #488C22×C11semidirect
251. #487C22×C11semidirect
252. #486C22×C11semidirect
253. #419C22×C11semidirect
254. #418C22×C11semidirect
256. #417C22×C11semidirect
257. #417C22×C11semidirect
258. #417C22×C11semidirect
260. C2×#103C22×C11semidirect
261. C2×#102C22×C11semidirect
262. #405C22×C11semidirect
263. C4×M16C22×C11semidirect
419. C11#60621direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5442
C11×#34492
C11×#31422
C11×#31412
C11×#31372
C11×#31362
C11×#28962
C2×C11×#4172
C11×#28732
#6062111