Finite Group Databasebeta

← C11×#20973 #14598166

Subgroups — C11×#20973 #14598166

Order 2816.

2238 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C11×M16C211yesmaximal, characteristic, complemented
2C22×C11×#121C211yesmaximal, characteristic
3C2×C11×#418C212yesmaximal, complemented
4C11×#2280C211yesmaximal, characteristic, complemented
5C11×#1895C214yesmaximal, complemented
6C11×#1893C214yesmaximal, complemented
7C11×#1736C212yesmaximal, complemented
8C23×D4×C11—21no—
9C23×D4×C11C2211yescharacteristic
10C24×C4×C11C2211yescharacteristic
11C22×C11×M16—24no—
12C22×C11×M16—28no—
13C22×C11×M16C2212yes—
14C22×C11×M16C2212yescomplemented
15C23×C8×C11C2212yescomplemented
16C2×C11×#121—24no—
17C2×C11×#121—21no—
18C2×C11×#121—21no—
19C2×C11×#121C418yescomplemented
20C2×C11×#121C2212yes—
21C2×C11×#121C2212yes—
22C2×C11×#117C2212yes—
23C22×C11×C4⋊C4C2211yescharacteristic
24C22×C11×C22⋊C4—21no—
25C11×#418—28no—
26C2×C11×#102C2218yescomplemented
27C11×#381—21no—
28C11×#380C2212yescomplemented
29C11×#380C2212yescomplemented
30C11×#379—21no—
31C4×C11×C22⋊C4—21no—
32C4×C11×C22⋊C4—21no—
33C11×#340C2218yescomplemented
34C25×C11—21no—
35C25×C11D411yescharacteristic
36C22×D4×C11—28no—
37C22×D4×C11—22no—
38C22×D4×C11—22no—
39C22×D4×C11—24no—
40C22×D4×C11—21no—
41C22×D4×C11—22no—
42C22×D4×C11—24no—
43C22×D4×C11—48no—
44C22×D4×C11C2×C414yes—
45C22×D4×C11C2312yes—
46C23×C4×C11—24no—
47C23×C4×C11—24no—
48C23×C4×C11—21no—
49C23×C4×C11C2×C414yes—
50C23×C4×C11D411yescharacteristic
51C23×C4×C11D411yescharacteristic
52C23×C4×C11D411yescharacteristic
53C23×C4×C11D414yes—
54C23×C4×C11C2311yescharacteristic
55C23×C4×C11C2311yescharacteristic
56C23×C4×C11C2311yescharacteristic
57C2×C11×M16—232no—
58C2×C11×M16—24no—
59C2×C11×M16—24no—
60C2×C11×M16—24no—
61C2×C11×M16—28no—
62C2×C11×M16D418yescomplemented
63C22×C8×C11—24no—
64C22×C8×C11—28no—
65C22×C8×C11C2314yes—
66C11×#121—28no—
67C11×#121—28no—
68C11×#121—24no—
69C11×#121—24no—
70C11×#121C2×C418yes—
71C11×#121C2×C418yes—
72C11×#117—24no—
73C11×#117—24no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—22no—
76C2×C11×C4⋊C4C2×C414yes—
77C2×C11×C4⋊C4C2314yes—
78C2×C11×C4⋊C4C2312yes—
79C2×C11×C22⋊C4—28no—
80C2×C11×C22⋊C4—22no—
81C2×C11×C22⋊C4—22no—
82C2×C11×C22⋊C4—22no—
83C2×C11×C22⋊C4—22no—
84C2×C11×C22⋊C4—22no—
85C2×C42×C11—22no—
86C11×#102—216no—
87C11×#95—22no—
88C11×#95—22no—
89#20973C1111yesmaximal, characteristic, direct product factor, Sylow
90C24×C11—24no—
91C24×C11—24no—
92C24×C11—24no—
93C24×C11—22no—
94C24×C11—42no—
95C24×C11—44no—
96C24×C11—44no—
97C24×C11—44no—
98C24×C11C22⋊C414yes—
99C24×C11C2×D411yescharacteristic
100C24×C11C2×D411yescharacteristic
101C24×C11C2×D411yescharacteristic
102C2×D4×C11—28no—
103C2×D4×C11—28no—
104C2×D4×C11—24no—
105C2×D4×C11—216no—
106C2×D4×C11—24no—
107C2×D4×C11—22no—
108C2×D4×C11—24no—
109C2×D4×C11—432no—
110C2×D4×C11—48no—
111C2×D4×C11—48no—
112C2×D4×C11—44no—
113C2×D4×C11—44no—
114C2×D4×C11—44no—
115C2×D4×C11C22×C414yes—
116C22×C4×C11—24no—
117C22×C4×C11—216no—
118C22×C4×C11—28no—
119C22×C4×C11—24no—
120C22×C4×C11—24no—
121C22×C4×C11—28no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—24no—
127C22×C4×C11—22no—
128C22×C4×C11—24no—
129C22×C4×C11—44no—
130C22×C4×C11C22⋊C414yes—
131C22×C4×C11C22⋊C414yes—
132C22×C4×C11C22⋊C414yes—
133C22×C4×C11C22×C412yes—
134C22×C4×C11C22×C412yes—
135C22×C4×C11C22×C412yes—
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D412yes—
139C22×C4×C11C2×D412yes—
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D412yes—
142C22×C4×C11C2×D414yes—
143C22×C4×C11#4114yes—
144C22×C4×C11C2411yescharacteristic
145C11×M16—216no—
146C11×M16—216no—
147C2×C8×C11—216no—
148C2×C8×C11—24no—
149C2×C8×C11—24no—
150C2×C8×C11C2×D418yescomplemented
151C11×C4⋊C4—24no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4—24no—
154C11×C4⋊C4—24no—
155C11×C4⋊C4C22×C414yes—
156C11×C22⋊C4—28no—
157C11×C22⋊C4—28no—
158C11×C22⋊C4—44no—
159C11×C22⋊C4—44no—
160C11×C22⋊C4—44no—
161C42×C11—44no—
162C23×M16C2×C1111yescharacteristic, complemented
163C22×#121C2×C1111yescharacteristic
164C2×#418C2×C1112yescomplemented
165#2280C2×C1111yescharacteristic, complemented
166#1895C2×C1114yescomplemented
167#1893C2×C1114yescomplemented
168#1736C2×C1112yescomplemented
169C23×C11—22no—
170C23×C11—22no—
171C23×C11—22no—
172C23×C11—22no—
173C23×C11—22no—
174C23×C11—22no—
175C23×C11—22no—
176C23×C11—28no—
177C23×C11—28no—
178C23×C11—24no—
179C23×C11—44no—
180C23×C11—416no—
181C23×C11—48no—
182C23×C11—48no—
183C23×C11—44no—
184C23×C11—44no—
185C23×C11—44no—
186C23×C11—48no—
187C23×C11—816no—
188C23×C11C2×C22⋊C412yes—
189C23×C11C2×C22⋊C412yes—
190C23×C11C2×C22⋊C412yes—
191C23×C11#12114yes—
192C23×C11AGL(1,ℤ/8)14yes—
193C23×C11C22×D411yescharacteristic
194D4×C11—28no—
195D4×C11—416no—
196D4×C11—416no—
197D4×C11—42no—
198D4×C11—42no—
199D4×C11—48no—
200C2×C4×C11—22no—
201C2×C4×C11—22no—
202C2×C4×C11—28no—
203C2×C4×C11—24no—
204C2×C4×C11—24no—
205C2×C4×C11—22no—
206C2×C4×C11—22no—
207C2×C4×C11—22no—
208C2×C4×C11—22no—
209C2×C4×C11—28no—
210C2×C4×C11—28no—
211C2×C4×C11—24no—
212C2×C4×C11—48no—
213C2×C4×C11—44no—
214C2×C4×C11—44no—
215C2×C4×C11—44no—
216C2×C4×C11—44no—
217C2×C4×C11C2×C22⋊C412yes—
218C2×C4×C11C2×C22⋊C412yes—
219C2×C4×C11C2×C22⋊C412yes—
220C2×C4×C11C4×D418yes—
221C2×C4×C11#12014yes—
222C2×C4×C11#12114yes—
223C2×C4×C11#12314yes—
224C2×C4×C11C23×C411yescharacteristic
225C2×C4×C11C22×D412yes—
226C2×C4×C11C22×D411yescharacteristic
227C2×C4×C11C2×#4112yes—
228C8×C11—28no—
229C23×D4—21no—
230C23×D4C22×C1111yescharacteristic
231C24×C4C22×C1111yescharacteristic
232C22×M16—24no—
233C22×M16—28no—
234C22×M16C22×C1112yes—
235C22×M16C22×C1112yescomplemented
236C23×C8C22×C1112yescomplemented
237C2×#121—24no—
238C2×#121—21no—
239C2×#121—21no—
240C2×#121C4×C1118yescomplemented
241C2×#121C22×C1112yes—
242C2×#121C22×C1112yes—
243C2×#117C22×C1112yes—
244C22×C4⋊C4C22×C1111yescharacteristic
245C22×C22⋊C4—21no—
246#418—28no—
247C2×#102C22×C1118yescomplemented
248#381—21no—
249#380C22×C1112yescomplemented
250#380C22×C1112yescomplemented
251#379—21no—
252C4×C22⋊C4—21no—
253C4×C22⋊C4—21no—
254#340C22×C1118yescomplemented
255C22×C11—22no—
256C22×C11—22no—
257C22×C11—22no—
258C22×C11—22no—
259C22×C11—28no—
260C22×C11—28no—
261C22×C11—22no—
262C22×C11—22no—
263C22×C11—22no—
264C22×C11—416no—
265C22×C11—44no—
266C22×C11—44no—
267C22×C11—44no—
268C22×C11—44no—
269C22×C11—816no—
270C22×C11—88no—
271C22×C11#38614yes—
272C22×C11#41814yescomplemented
273C22×C11C22×C22⋊C411yescharacteristic
274C22×C11C2×#12112yes—
275C22×C11C2×AGL(1,ℤ/8)12yes—
276C22×C11#57512yes—
277C4×C11—22no—
278C4×C11—22no—
279C4×C11—44no—
280C4×C11—84no—
281C4×C11#38614yes—
282C4×C11C2×C4×D412yes—
283C4×C11C2×#12011yescharacteristic
284C4×C11C2×#12311yescharacteristic
285C25—21no—
286C25D4×C1111yescharacteristic
287C22×D4—28no—
288C22×D4—22no—
289C22×D4—22no—
290C22×D4—24no—
291C22×D4—21no—
292C22×D4—22no—
293C22×D4—24no—
294C22×D4—48no—
295C22×D4C2×C4×C1114yes—
296C22×D4C23×C1112yes—
297C23×C4—24no—
298C23×C4—24no—
299C23×C4—21no—
300C23×C4C2×C4×C1114yes—
301C23×C4D4×C1111yescharacteristic
302C23×C4D4×C1111yescharacteristic
303C23×C4D4×C1111yescharacteristic
304C23×C4D4×C1114yes—
305C23×C4C23×C1111yescharacteristic
306C23×C4C23×C1111yescharacteristic
307C23×C4C23×C1111yescharacteristic
308C2×M16—232no—
309C2×M16—24no—
310C2×M16—24no—
311C2×M16—24no—
312C2×M16—28no—
313C2×M16D4×C1118yescomplemented
314C22×C8—24no—
315C22×C8—28no—
316C22×C8C23×C1114yes—
317#121—28no—
318#121—28no—
319#121—24no—
320#121—24no—
321#121C2×C4×C1118yes—
322#121C2×C4×C1118yes—
323#117—24no—
324#117—24no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4C2×C4×C1114yes—
328C2×C4⋊C4C23×C1114yes—
329C2×C4⋊C4C23×C1112yes—
330C2×C22⋊C4—28no—
331C2×C22⋊C4—22no—
332C2×C22⋊C4—22no—
333C2×C22⋊C4—22no—
334C2×C22⋊C4—22no—
335C2×C22⋊C4—22no—
336C2×C42—22no—
337#102—216no—
338#95—22no—
339#95—22no—
340C2×C11—24no—
341C2×C11—24no—
342C2×C11—42no—
343C2×C11—84no—
344C2×C11C2×#38611yescharacteristic
345C2×C11C2×#41811yescharacteristic
346C2×C11#289611yescharacteristic
347C2×C11#305514yes—
348C24—24no—
349C24—24no—
350C24—24no—
351C24—22no—
352C24—42no—
353C24—44no—
354C24—44no—
355C24—44no—
356C24C11×C22⋊C414yes—
357C24C2×D4×C1111yescharacteristic
358C24C2×D4×C1111yescharacteristic
359C24C2×D4×C1111yescharacteristic
360C2×D4—28no—
361C2×D4—28no—
362C2×D4—24no—
363C2×D4—216no—
364C2×D4—24no—
365C2×D4—22no—
366C2×D4—24no—
367C2×D4—432no—
368C2×D4—48no—
369C2×D4—48no—
370C2×D4—44no—
371C2×D4—44no—
372C2×D4—44no—
373C2×D4C22×C4×C1114yes—
374C22×C4—24no—
375C22×C4—216no—
376C22×C4—28no—
377C22×C4—24no—
378C22×C4—24no—
379C22×C4—28no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—24no—
385C22×C4—22no—
386C22×C4—24no—
387C22×C4—44no—
388C22×C4C11×C22⋊C414yes—
389C22×C4C11×C22⋊C414yes—
390C22×C4C11×C22⋊C414yes—
391C22×C4C22×C4×C1112yes—
392C22×C4C22×C4×C1112yes—
393C22×C4C22×C4×C1112yes—
394C22×C4C2×D4×C1111yescharacteristic
395C22×C4C2×D4×C1111yescharacteristic
396C22×C4C2×D4×C1112yes—
397C22×C4C2×D4×C1112yes—
398C22×C4C2×D4×C1111yescharacteristic
399C22×C4C2×D4×C1112yes—
400C22×C4C2×D4×C1114yes—
401C22×C4C11×#4114yes—
402C22×C4C24×C1111yescharacteristic
403M16—216no—
404M16—216no—
405C2×C8—216no—
406C2×C8—24no—
407C2×C8—24no—
408C2×C8C2×D4×C1118yescomplemented
409C4⋊C4—24no—
410C4⋊C4—22no—
411C4⋊C4—24no—
412C4⋊C4—24no—
413C4⋊C4C22×C4×C1114yes—
414C22⋊C4—28no—
415C22⋊C4—28no—
416C22⋊C4—44no—
417C22⋊C4—44no—
418C22⋊C4—44no—
419C42—44no—
420C11#2097311yescharacteristic, direct product factor, Sylow
421C23—22no—
422C23—22no—
423C23—22no—
424C23—22no—
425C23—22no—
426C23—28no—
427C23—28no—
428C23—22no—
429C23—22no—
430C23—24no—
431C23—44no—
432C23—416no—
433C23—48no—
434C23—48no—
435C23—44no—
436C23—48no—
437C23—44no—
438C23—44no—
439C23—816no—
440C23C2×C11×C22⋊C412yes—
441C23C2×C11×C22⋊C412yes—
442C23C2×C11×C22⋊C412yes—
443C23C11×#12114yes—
444C23C11×AGL(1,ℤ/8)14yes—
445C23C22×D4×C1111yescharacteristic
446D4—28no—
447D4—416no—
448D4—416no—
449D4—42no—
450D4—48no—
451D4—42no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—28no—
455C2×C4—24no—
456C2×C4—24no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—28no—
460C2×C4—28no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—24no—
464C2×C4—48no—
465C2×C4—44no—
466C2×C4—44no—
467C2×C4—44no—
468C2×C4—44no—
469C2×C4C2×C11×C22⋊C412yes—
470C2×C4C2×C11×C22⋊C412yes—
471C2×C4C2×C11×C22⋊C412yes—
472C2×C4C4×D4×C1118yes—
473C2×C4C11×#12014yes—
474C2×C4C11×#12114yes—
475C2×C4C11×#12314yes—
476C2×C4C23×C4×C1111yescharacteristic
477C2×C4C22×D4×C1112yes—
478C2×C4C22×D4×C1111yescharacteristic
479C2×C4C2×C11×#4112yes—
480C8—28no—
481C22—22no—
482C22—22no—
483C22—22no—
484C22—22no—
485C22—28no—
486C22—28no—
487C22—22no—
488C22—22no—
489C22—22no—
490C22—416no—
491C22—44no—
492C22—44no—
493C22—44no—
494C22—44no—
495C22—816no—
496C22—88no—
497C22C11×#38614yes—
498C22C11×#41814yescomplemented
499C22C22×C11×C22⋊C411yescharacteristic
500C22C2×C11×#12112yes—
501C22C2×C11×AGL(1,ℤ/8)12yes—
502C22C11×#57512yes—
503C4—22no—
504C4—22no—
505C4—44no—
506C4—84no—
507C4C11×#38614yes—
508C4C2×C4×D4×C1112yes—
509C4C2×C11×#12011yescharacteristic
510C4C2×C11×#12311yescharacteristic
511C2—24no—
512C2—24no—
513C2—42no—
514C2—84no—
515C2C2×C11×#38611yescharacteristic
516C2C2×C11×#41811yescharacteristic
517C2C11×#289611yescharacteristic
518C2C11×#305514yes—
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC22×C11×#121C2
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
1. C23×C11×M16C2semidirect
3. C2×C11×#418C2semidirect
4. C11×#2280C2semidirect
5. C11×#1895C2semidirect
6. C11×#1893C2semidirect
7. C11×#1736C2semidirect
14. C22×C11×M16C22semidirect
15. C23×C8×C11C22semidirect
19. C2×C11×#121C4semidirect
26. C2×C11×#102C22semidirect
28. C11×#380C22semidirect
29. C11×#380C22semidirect
33. C11×#340C22semidirect
62. C2×C11×M16D4semidirect
89. #20973C11direct (N × H)
150. C2×C8×C11C2×D4semidirect
162. C23×M16C2×C11semidirect
164. C2×#418C2×C11semidirect
165. #2280C2×C11semidirect
166. #1895C2×C11semidirect
167. #1893C2×C11semidirect
168. #1736C2×C11semidirect
235. C22×M16C22×C11semidirect
236. C23×C8C22×C11semidirect
240. C2×#121C4×C11semidirect
247. C2×#102C22×C11semidirect
249. #380C22×C11semidirect
250. #380C22×C11semidirect
254. #340C22×C11semidirect
272. C22×C11#418semidirect
313. C2×M16D4×C11semidirect
408. C2×C8C2×D4×C11semidirect
420. C11#20973direct (N × H)
498. C22C11×#418semidirect

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×#1212
C2×C11×#4182
C11×#22802
C11×#18952
C11×#18932
C11×#17362
#2097311