Finite Group Databasebeta

← C11×#20972 #14598165

Subgroups — C11×#20972 #14598165

Order 2816.

1894 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C11×M16C211yesmaximal, characteristic
2C22×C11×C22⋊Q8C211yesmaximal, characteristic
3C2×C11×#419C212yesmaximal, complemented
4C11×#2280C211yesmaximal, characteristic
5C11×#1894C214yesmaximal, complemented
6C11×#1892C214yesmaximal, complemented
7C11×#1736C212yesmaximal, complemented
8C23×Q8×C11C2211yescharacteristic
9C24×C4×C11C2211yescharacteristic
10C22×C11×M16—24no—
11C22×C11×M16—28no—
12C22×C11×M16C2212yes—
13C22×C11×M16C2212yes—
14C23×C8×C11C2212yes—
15C2×C11×C22⋊Q8—24no—
16C2×C11×C22⋊Q8—21no—
17C2×C11×C22⋊Q8—21no—
18C2×C11×C22⋊Q8C418yescomplemented
19C2×C11×C22⋊Q8C2212yes—
20C2×C11×C22⋊Q8C2212yes—
21C2×C11×#117C2212yes—
22C22×C11×C4⋊C4—21no—
23C22×C11×C4⋊C4C2211yescharacteristic
24C22×C11×C22⋊C4—21no—
25C11×#419—28no—
26C2×C11×#103C2218yescomplemented
27C11×#381—21no—
28C11×#380C2212yes—
29C11×#380C2212yes—
30C11×#379—21no—
31C4×C11×C22⋊C4—21no—
32C4×C11×C22⋊C4—21no—
33C11×#340C2218yescomplemented
34C25×C11D411yescharacteristic
35C22×Q8×C11—22no—
36C22×Q8×C11—21no—
37C22×Q8×C11—24no—
38C22×Q8×C11—24no—
39C22×Q8×C11C2×C414yes—
40C22×Q8×C11C2312yes—
41C23×C4×C11—24no—
42C23×C4×C11—24no—
43C23×C4×C11—21no—
44C23×C4×C11—21no—
45C23×C4×C11C2×C414yes—
46C23×C4×C11D411yescharacteristic
47C23×C4×C11D411yescharacteristic
48C23×C4×C11D411yescharacteristic
49C23×C4×C11D414yes—
50C23×C4×C11C2311yescharacteristic
51C23×C4×C11C2311yescharacteristic
52C23×C4×C11C2311yescharacteristic
53C2×C11×M16—232no—
54C2×C11×M16—24no—
55C2×C11×M16—24no—
56C2×C11×M16—24no—
57C2×C11×M16—28no—
58C2×C11×M16D418yes—
59C22×C8×C11—24no—
60C22×C8×C11—28no—
61C22×C8×C11C2314yes—
62C11×C22⋊Q8—28no—
63C11×C22⋊Q8—28no—
64C11×C22⋊Q8—24no—
65C11×C22⋊Q8—24no—
66C11×C22⋊Q8C2×C418yes—
67C11×C22⋊Q8C2×C418yes—
68C11×#117—24no—
69C11×#117—24no—
70C2×C11×C4⋊C4—28no—
71C2×C11×C4⋊C4—22no—
72C2×C11×C4⋊C4—22no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—22no—
75C2×C11×C4⋊C4C2×C414yes—
76C2×C11×C4⋊C4C2314yes—
77C2×C11×C4⋊C4C2312yes—
78C2×C11×C22⋊C4—28no—
79C2×C11×C22⋊C4—22no—
80C2×C11×C22⋊C4—22no—
81C2×C11×C22⋊C4—22no—
82C2×C11×C22⋊C4—22no—
83C2×C11×C22⋊C4—22no—
84C2×C42×C11—22no—
85C11×#103—216no—
86C11×#95—22no—
87C11×#95—22no—
88#20972C1111yesmaximal, characteristic, direct product factor, Sylow
89C24×C11—24no—
90C24×C11—24no—
91C24×C11—42no—
92C24×C11C22⋊C414yes—
93C24×C11C2×D411yescharacteristic
94C24×C11C2×D411yescharacteristic
95C24×C11C2×D411yescharacteristic
96C2×Q8×C11—24no—
97C2×Q8×C11—22no—
98C2×Q8×C11—216no—
99C2×Q8×C11—24no—
100C2×Q8×C11—24no—
101C2×Q8×C11—44no—
102C2×Q8×C11—44no—
103C2×Q8×C11—44no—
104C2×Q8×C11C22×C414yes—
105C22×C4×C11—24no—
106C22×C4×C11—216no—
107C22×C4×C11—28no—
108C22×C4×C11—24no—
109C22×C4×C11—24no—
110C22×C4×C11—28no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—24no—
116C22×C4×C11—24no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—24no—
120C22×C4×C11—44no—
121C22×C4×C11—44no—
122C22×C4×C11C22⋊C414yes—
123C22×C4×C11C22⋊C414yes—
124C22×C4×C11C22⋊C414yes—
125C22×C4×C11C22×C412yes—
126C22×C4×C11C22×C412yes—
127C22×C4×C11C22×C412yes—
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2×D412yes—
131C22×C4×C11C2×D412yes—
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D412yes—
134C22×C4×C11C2×D414yes—
135C22×C4×C11#4114yes—
136C22×C4×C11C2411yescharacteristic
137C11×M16—216no—
138C11×M16—216no—
139C2×C8×C11—216no—
140C2×C8×C11—24no—
141C2×C8×C11—24no—
142C2×C8×C11C2×D418yes—
143C11×C4⋊C4—28no—
144C11×C4⋊C4—28no—
145C11×C4⋊C4—24no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—24no—
148C11×C4⋊C4—24no—
149C11×C4⋊C4C22×C414yes—
150C11×C22⋊C4—28no—
151C11×C22⋊C4—28no—
152C11×C22⋊C4—44no—
153C11×C22⋊C4—44no—
154C11×C22⋊C4—44no—
155C42×C11—44no—
156C23×M16C2×C1111yescharacteristic
157C22×C22⋊Q8C2×C1111yescharacteristic
158C2×#419C2×C1112yescomplemented
159#2280C2×C1111yescharacteristic
160#1894C2×C1114yescomplemented
161#1892C2×C1114yescomplemented
162#1736C2×C1112yescomplemented
163C23×C11—22no—
164C23×C11—22no—
165C23×C11—22no—
166C23×C11—22no—
167C23×C11—22no—
168C23×C11—22no—
169C23×C11—22no—
170C23×C11—28no—
171C23×C11—28no—
172C23×C11—44no—
173C23×C11—416no—
174C23×C11C2×C22⋊C412yes—
175C23×C11C2×C22⋊C412yes—
176C23×C11C2×C22⋊C412yes—
177C23×C11#12114yes—
178C23×C11#13714yes—
179C23×C11C22×D411yescharacteristic
180Q8×C11—28no—
181Q8×C11—42no—
182Q8×C11—42no—
183Q8×C11—48no—
184C2×C4×C11—22no—
185C2×C4×C11—22no—
186C2×C4×C11—28no—
187C2×C4×C11—24no—
188C2×C4×C11—24no—
189C2×C4×C11—22no—
190C2×C4×C11—22no—
191C2×C4×C11—22no—
192C2×C4×C11—22no—
193C2×C4×C11—28no—
194C2×C4×C11—28no—
195C2×C4×C11—24no—
196C2×C4×C11—24no—
197C2×C4×C11—48no—
198C2×C4×C11—44no—
199C2×C4×C11—44no—
200C2×C4×C11—48no—
201C2×C4×C11—44no—
202C2×C4×C11—44no—
203C2×C4×C11—44no—
204C2×C4×C11C2×C22⋊C412yes—
205C2×C4×C11C2×C22⋊C412yes—
206C2×C4×C11C2×C22⋊C412yes—
207C2×C4×C11C4×D418yes—
208C2×C4×C11#12014yes—
209C2×C4×C11#12114yes—
210C2×C4×C11#12314yes—
211C2×C4×C11C23×C411yescharacteristic
212C2×C4×C11C22×D412yes—
213C2×C4×C11C22×D411yescharacteristic
214C2×C4×C11C2×#4112yes—
215C8×C11—28no—
216C23×Q8C22×C1111yescharacteristic
217C24×C4C22×C1111yescharacteristic
218C22×M16—24no—
219C22×M16—28no—
220C22×M16C22×C1112yes—
221C22×M16C22×C1112yes—
222C23×C8C22×C1112yes—
223C2×C22⋊Q8—24no—
224C2×C22⋊Q8—21no—
225C2×C22⋊Q8—21no—
226C2×C22⋊Q8C4×C1118yescomplemented
227C2×C22⋊Q8C22×C1112yes—
228C2×C22⋊Q8C22×C1112yes—
229C2×#117C22×C1112yes—
230C22×C4⋊C4—21no—
231C22×C4⋊C4C22×C1111yescharacteristic
232C22×C22⋊C4—21no—
233#419—28no—
234C2×#103C22×C1118yescomplemented
235#381—21no—
236#380C22×C1112yes—
237#380C22×C1112yes—
238#379—21no—
239C4×C22⋊C4—21no—
240C4×C22⋊C4—21no—
241#340C22×C1118yescomplemented
242C22×C11—22no—
243C22×C11—22no—
244C22×C11—22no—
245C22×C11—22no—
246C22×C11—28no—
247C22×C11—28no—
248C22×C11—22no—
249C22×C11—22no—
250C22×C11—22no—
251C22×C11—416no—
252C22×C11—44no—
253C22×C11#38614yes—
254C22×C11#41914yescomplemented
255C22×C11C22×C22⋊C411yescharacteristic
256C22×C11C2×#12112yes—
257C22×C11C2×#13712yes—
258C22×C11#57512yes—
259C4×C11—22no—
260C4×C11—22no—
261C4×C11—44no—
262C4×C11—44no—
263C4×C11—84no—
264C4×C11#38614yes—
265C4×C11C2×C4×D412yes—
266C4×C11C2×#12011yescharacteristic
267C4×C11C2×#12311yescharacteristic
268C25D4×C1111yescharacteristic
269C22×Q8—22no—
270C22×Q8—21no—
271C22×Q8—24no—
272C22×Q8—24no—
273C22×Q8C2×C4×C1114yes—
274C22×Q8C23×C1112yes—
275C23×C4—24no—
276C23×C4—24no—
277C23×C4—21no—
278C23×C4—21no—
279C23×C4C2×C4×C1114yes—
280C23×C4D4×C1111yescharacteristic
281C23×C4D4×C1111yescharacteristic
282C23×C4D4×C1111yescharacteristic
283C23×C4D4×C1114yes—
284C23×C4C23×C1111yescharacteristic
285C23×C4C23×C1111yescharacteristic
286C23×C4C23×C1111yescharacteristic
287C2×M16—232no—
288C2×M16—24no—
289C2×M16—24no—
290C2×M16—24no—
291C2×M16—28no—
292C2×M16D4×C1118yes—
293C22×C8—24no—
294C22×C8—28no—
295C22×C8C23×C1114yes—
296C22⋊Q8—28no—
297C22⋊Q8—28no—
298C22⋊Q8—24no—
299C22⋊Q8—24no—
300C22⋊Q8C2×C4×C1118yes—
301C22⋊Q8C2×C4×C1118yes—
302#117—24no—
303#117—24no—
304C2×C4⋊C4—28no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4C2×C4×C1114yes—
310C2×C4⋊C4C23×C1114yes—
311C2×C4⋊C4C23×C1112yes—
312C2×C22⋊C4—28no—
313C2×C22⋊C4—22no—
314C2×C22⋊C4—22no—
315C2×C22⋊C4—22no—
316C2×C22⋊C4—22no—
317C2×C22⋊C4—22no—
318C2×C42—22no—
319#103—216no—
320#95—22no—
321#95—22no—
322C2×C11—24no—
323C2×C11—24no—
324C2×C11—42no—
325C2×C11C2×#38611yescharacteristic
326C2×C11C2×#41911yescharacteristic
327C2×C11#289611yescharacteristic
328C2×C11#305614yes—
329C24—24no—
330C24—24no—
331C24—42no—
332C24C11×C22⋊C414yes—
333C24C2×D4×C1111yescharacteristic
334C24C2×D4×C1111yescharacteristic
335C24C2×D4×C1111yescharacteristic
336C2×Q8—24no—
337C2×Q8—22no—
338C2×Q8—216no—
339C2×Q8—24no—
340C2×Q8—24no—
341C2×Q8—44no—
342C2×Q8—44no—
343C2×Q8—44no—
344C2×Q8C22×C4×C1114yes—
345C22×C4—24no—
346C22×C4—216no—
347C22×C4—28no—
348C22×C4—24no—
349C22×C4—24no—
350C22×C4—28no—
351C22×C4—22no—
352C22×C4—22no—
353C22×C4—22no—
354C22×C4—22no—
355C22×C4—24no—
356C22×C4—24no—
357C22×C4—22no—
358C22×C4—22no—
359C22×C4—24no—
360C22×C4—44no—
361C22×C4—44no—
362C22×C4C11×C22⋊C414yes—
363C22×C4C11×C22⋊C414yes—
364C22×C4C11×C22⋊C414yes—
365C22×C4C22×C4×C1112yes—
366C22×C4C22×C4×C1112yes—
367C22×C4C22×C4×C1112yes—
368C22×C4C2×D4×C1111yescharacteristic
369C22×C4C2×D4×C1111yescharacteristic
370C22×C4C2×D4×C1112yes—
371C22×C4C2×D4×C1112yes—
372C22×C4C2×D4×C1111yescharacteristic
373C22×C4C2×D4×C1112yes—
374C22×C4C2×D4×C1114yes—
375C22×C4C11×#4114yes—
376C22×C4C24×C1111yescharacteristic
377M16—216no—
378M16—216no—
379C2×C8—216no—
380C2×C8—24no—
381C2×C8—24no—
382C2×C8C2×D4×C1118yes—
383C4⋊C4—28no—
384C4⋊C4—28no—
385C4⋊C4—24no—
386C4⋊C4—22no—
387C4⋊C4—24no—
388C4⋊C4—24no—
389C4⋊C4C22×C4×C1114yes—
390C22⋊C4—28no—
391C22⋊C4—28no—
392C22⋊C4—44no—
393C22⋊C4—44no—
394C22⋊C4—44no—
395C42—44no—
396C11#2097211yescharacteristic, direct product factor, Sylow
397C23—22no—
398C23—22no—
399C23—22no—
400C23—22no—
401C23—22no—
402C23—28no—
403C23—28no—
404C23—22no—
405C23—22no—
406C23—44no—
407C23—416no—
408C23C2×C11×C22⋊C412yes—
409C23C2×C11×C22⋊C412yes—
410C23C2×C11×C22⋊C412yes—
411C23C11×#12114yes—
412C23C11×#13714yes—
413C23C22×D4×C1111yescharacteristic
414Q8—28no—
415Q8—42no—
416Q8—48no—
417Q8—42no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—28no—
421C2×C4—24no—
422C2×C4—24no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—28no—
426C2×C4—28no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—24no—
430C2×C4—24no—
431C2×C4—48no—
432C2×C4—44no—
433C2×C4—48no—
434C2×C4—44no—
435C2×C4—44no—
436C2×C4—44no—
437C2×C4—44no—
438C2×C4C2×C11×C22⋊C412yes—
439C2×C4C2×C11×C22⋊C412yes—
440C2×C4C2×C11×C22⋊C412yes—
441C2×C4C4×D4×C1118yes—
442C2×C4C11×#12014yes—
443C2×C4C11×#12114yes—
444C2×C4C11×#12314yes—
445C2×C4C23×C4×C1111yescharacteristic
446C2×C4C22×D4×C1112yes—
447C2×C4C22×D4×C1111yescharacteristic
448C2×C4C2×C11×#4112yes—
449C8—28no—
450C22—22no—
451C22—22no—
452C22—22no—
453C22—22no—
454C22—28no—
455C22—28no—
456C22—22no—
457C22—22no—
458C22—22no—
459C22—416no—
460C22—44no—
461C22C11×#38614yes—
462C22C11×#41914yescomplemented
463C22C22×C11×C22⋊C411yescharacteristic
464C22C2×C11×#12112yes—
465C22C2×C11×#13712yes—
466C22C11×#57512yes—
467C4—22no—
468C4—22no—
469C4—44no—
470C4—44no—
471C4—84no—
472C4C11×#38614yes—
473C4C2×C4×D4×C1112yes—
474C4C2×C11×#12011yescharacteristic
475C4C2×C11×#12311yescharacteristic
476C2—24no—
477C2—24no—
478C2—42no—
479C2C2×C11×#38611yescharacteristic
480C2C2×C11×#41911yescharacteristic
481C2C11×#289611yescharacteristic
482C2C11×#305614yes—
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC25×C11D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C24×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C11×#419C2semidirect
5. C11×#1894C2semidirect
6. C11×#1892C2semidirect
7. C11×#1736C2semidirect
18. C2×C11×C22⋊Q8C4semidirect
26. C2×C11×#103C22semidirect
33. C11×#340C22semidirect
88. #20972C11direct (N × H)
158. C2×#419C2×C11semidirect
160. #1894C2×C11semidirect
161. #1892C2×C11semidirect
162. #1736C2×C11semidirect
226. C2×C22⋊Q8C4×C11semidirect
234. C2×#103C22×C11semidirect
241. #340C22×C11semidirect
254. C22×C11#419semidirect
396. C11#20972direct (N × H)
462. C22C11×#419semidirect

Maximal subgroups

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

subgroupindex
C23×C11×M162
C22×C11×C22⋊Q82
C2×C11×#4192
C11×#22802
C11×#18942
C11×#18922
C11×#17362
#2097211