Finite Group Databasebeta

← C11×#32921 #14610114

Subgroups — C11×#32921 #14610114

Order 2816.

1402 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C11×2−1+4C211yesmaximal, characteristic, complemented
2C11×#3038C212yesmaximal, complemented
3C2×C11×#454C212yesmaximal, complemented
4C11×#2548C211yesmaximal, characteristic, complemented
5C11×#1888C212yesmaximal, complemented
6C11×#1883C214yesmaximal, complemented
7C11×#1806C212yesmaximal, complemented
8C11×#1801C211yesmaximal, characteristic, complemented
9C2×C11×2−1+4C2211yescharacteristic
10C2×C11×AGL(1,ℤ/8)C2214yes—
11C2×C11×#127C2211yescharacteristic
12C2×C11×#124C2212yes—
13C11×#520—22no—
14C11×#520—22no—
15C11×#520C2212yes—
16C11×#519—22no—
17C11×#519C2211yescharacteristic
18C4×C11×#41—22no—
19C4×C11×#41—22no—
20C4×C11×#41C2212yes—
21C2×C4×Q8×C11—22no—
22C2×C4×Q8×C11C2211yescharacteristic
23C11×#460—22no—
24C11×#460—22no—
25C11×#459—22no—
26C11×#459—22no—
27C11×#454—28no—
28C11×#423C2212yes—
29C2×C11×#104C2214yes—
30C11×#418C2214yes—
31C2×C11×#101C2212yes—
32C11×#394—22no—
33C11×#390—22no—
34C11×#390C2212yes—
35C4×C11×C4⋊C4C2211yescharacteristic
36C11×#343C2212yes—
37C11×#339C2214yes—
38C11×2−1+4—24no—
39C11×2−1+4—22no—
40C11×2−1+4D414yescomplemented
41C2×C11×#41—22no—
42C2×C11×#41—22no—
43C2×C11×#41C2312yes—
44C22×Q8×C11—22no—
45C22×Q8×C11C2311yescharacteristic
46C22×D4×C11—21no—
47C22×D4×C11—21no—
48C22×D4×C11C2312yes—
49C11×AGL(1,ℤ/8)—28no—
50C11×AGL(1,ℤ/8)—28no—
51C2×C11×SD16—24no—
52C2×C11×D8—24no—
53C2×C11×M16C2314yes—
54C11×#127—22no—
55C11×#127—22no—
56C11×#124—24no—
57C11×#124—24no—
58C4×Q8×C11—22no—
59C4×Q8×C11—24no—
60C4×Q8×C11—22no—
61C4×Q8×C11—22no—
62C4×Q8×C11—22no—
63C4×Q8×C11—22no—
64C4×Q8×C11—22no—
65C4×Q8×C11—22no—
66C4×Q8×C11D412yes—
67C4×Q8×C11D412yes—
68C4×D4×C11—22no—
69C4×D4×C11—24no—
70C4×D4×C11—22no—
71C4×D4×C11—22no—
72C4×D4×C11—22no—
73C4×D4×C11—24no—
74C4×D4×C11—22no—
75C4×D4×C11D412yes—
76C4×D4×C11D412yes—
77C11×#117—24no—
78C11×#117—24no—
79C11×#117—22no—
80C11×#117—22no—
81C11×#117—22no—
82C11×#117C2312yes—
83C2×C11×C4⋊C4—24no—
84C2×C11×C4⋊C4—22no—
85C2×C11×C4⋊C4—21no—
86C2×C11×C4⋊C4D412yes—
87C2×C11×C4⋊C4C2311yescharacteristic
88C2×C11×C22⋊C4—24no—
89C2×C11×C22⋊C4—24no—
90C2×C42×C11—24no—
91C2×C42×C11—22no—
92C2×C42×C11D412yes—
93C2×C42×C11C2312yes—
94C2×C42×C11C2311yescharacteristic
95C11×C4⋊C8—22no—
96C11×C4⋊C8—22no—
97C11×#104—28no—
98C11×#102—24no—
99C11×#102—24no—
100C11×#101—24no—
101C11×#95—21no—
102#32921C1111yesmaximal, characteristic, direct product factor, Sylow
103C24×C11—22no—
104C11×#41—28no—
105C11×#41—28no—
106C11×#41—28no—
107C11×#41—28no—
108C11×#41—22no—
109C11×#41—22no—
110C11×#41C2×D414yes—
111C11×#41#4114yes—
112C2×Q8×C11—22no—
113C2×Q8×C11—28no—
114C2×Q8×C11—28no—
115C2×Q8×C11—22no—
116C2×Q8×C11—22no—
117C2×Q8×C11C2×D412yes—
118C2×Q8×C11C2×D412yes—
119C2×Q8×C11#4112yes—
120C2×D4×C11—22no—
121C2×D4×C11—22no—
122C2×D4×C11—24no—
123C2×D4×C11—22no—
124C2×D4×C11—22no—
125C2×D4×C11—24no—
126C2×D4×C11—44no—
127C2×D4×C11—41no—
128C2×D4×C11—42no—
129C2×D4×C11—41no—
130C2×D4×C11—82no—
131C2×D4×C11C2×D412yes—
132C22×C4×C11—24no—
133C22×C4×C11—22no—
134C22×C4×C11—24no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D412yes—
140C22×C4×C11C2×D412yes—
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2411yescharacteristic
143C11×SD16—48no—
144C11×D8—48no—
145C11×M16—24no—
146C11×M16—24no—
147C2×C8×C11—24no—
148C11×C4⋊C4—24no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—22no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—24no—
153C11×C4⋊C4—22no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—42no—
156C11×C4⋊C4C2×D412yes—
157C11×C4⋊C4C2×D412yes—
158C11×C22⋊C4—24no—
159C11×C22⋊C4—22no—
160C11×C22⋊C4—22no—
161C11×C22⋊C4—22no—
162C11×C22⋊C4—48no—
163C11×C22⋊C4—84no—
164C42×C11—24no—
165C42×C11—24no—
166C42×C11—22no—
167C42×C11—22no—
168C42×C11—22no—
169C42×C11—22no—
170C42×C11—22no—
171C42×C11—22no—
172C42×C11—22no—
173C42×C11C2×D412yes—
174C42×C11C2×D412yes—
175C4×2−1+4C2×C1111yescharacteristic, complemented
176#3038C2×C1112yescomplemented
177C2×#454C2×C1112yescomplemented
178#2548C2×C1111yescharacteristic, complemented
179#1888C2×C1112yescomplemented
180#1883C2×C1114yescomplemented
181#1806C2×C1112yescomplemented
182#1801C2×C1111yescharacteristic, complemented
183C23×C11—22no—
184C23×C11—44no—
185C23×C11—44no—
186C23×C11—42no—
187C23×C11—42no—
188C23×C11—42no—
189C23×C11C22×D411yescharacteristic
190Q8×C11—28no—
191Q8×C11—24no—
192Q8×C11—22no—
193Q8×C11—24no—
194Q8×C11#12114yes—
195D4×C11—28no—
196D4×C11—24no—
197D4×C11—24no—
198D4×C11—22no—
199D4×C11—44no—
200D4×C11—44no—
201D4×C11—82no—
202D4×C11—84no—
203D4×C11—82no—
204D4×C11#12114yes—
205C2×C4×C11—216no—
206C2×C4×C11—22no—
207C2×C4×C11—22no—
208C2×C4×C11—22no—
209C2×C4×C11—24no—
210C2×C4×C11—24no—
211C2×C4×C11—22no—
212C2×C4×C11—22no—
213C2×C4×C11—22no—
214C2×C4×C11—22no—
215C2×C4×C11—41no—
216C2×C4×C11—44no—
217C2×C4×C11—42no—
218C2×C4×C11—42no—
219C2×C4×C11—42no—
220C2×C4×C11—42no—
221C2×C4×C11—82no—
222C2×C4×C11—84no—
223C2×C4×C11#12011yescharacteristic
224C2×C4×C11#12012yes—
225C2×C4×C11#12011yescharacteristic
226C2×C4×C11#12114yes—
227C2×C4×C11C22×D411yescharacteristic
228C2×C4×C11C22×D412yes—
229C2×C4×C11C2×#4112yes—
230C2×C4×C11C2×#4111yescharacteristic
231C8×C11—44no—
232C2×2−1+4C22×C1111yescharacteristic
233C2×AGL(1,ℤ/8)C22×C1114yes—
234C2×#127C22×C1111yescharacteristic
235C2×#124C22×C1112yes—
236#520—22no—
237#520—22no—
238#520C22×C1112yes—
239#519—22no—
240#519C22×C1111yescharacteristic
241C4×#41—22no—
242C4×#41—22no—
243C4×#41C22×C1112yes—
244C2×C4×Q8—22no—
245C2×C4×Q8C22×C1111yescharacteristic
246#460—22no—
247#460—22no—
248#459—22no—
249#459—22no—
250#454—28no—
251#423C22×C1112yes—
252C2×#104C22×C1114yes—
253#418C22×C1114yes—
254C2×#101C22×C1112yes—
255#394—22no—
256#390—22no—
257#390C22×C1112yes—
258C4×C4⋊C4C22×C1111yescharacteristic
259#343C22×C1112yes—
260#339C22×C1114yes—
261C22×C11—21no—
262C22×C11—21no—
263C22×C11—24no—
264C22×C11—42no—
265C22×C11—42no—
266C22×C11—84no—
267C22×C11—84no—
268C22×C11—82no—
269C22×C11—82no—
270C22×C11—82no—
271C22×C11C2×#12011yescharacteristic
272C22×C11C2×#12111yescharacteristic
273C22×C11#52511yescharacteristic
274C4×C11—24no—
275C4×C11—24no—
276C4×C11—21no—
277C4×C11—22no—
278C4×C11—42no—
279C4×C11—42no—
280C4×C11—42no—
281C4×C11—82no—
282C4×C11#45412yescomplemented
283C4×C11C2×#12112yes—
284C4×C11#52512yes—
2852−1+4—24no—
2862−1+4—22no—
2872−1+4D4×C1114yescomplemented
288C2×#41—22no—
289C2×#41—22no—
290C2×#41C23×C1112yes—
291C22×Q8—22no—
292C22×Q8C23×C1111yescharacteristic
293C22×D4—21no—
294C22×D4—21no—
295C22×D4C23×C1112yes—
296AGL(1,ℤ/8)—28no—
297AGL(1,ℤ/8)—28no—
298C2×SD16—24no—
299C2×D8—24no—
300C2×M16C23×C1114yes—
301#127—22no—
302#127—22no—
303#124—24no—
304#124—24no—
305C4×Q8—22no—
306C4×Q8—24no—
307C4×Q8—22no—
308C4×Q8—22no—
309C4×Q8—22no—
310C4×Q8—22no—
311C4×Q8—22no—
312C4×Q8—22no—
313C4×Q8D4×C1112yes—
314C4×Q8D4×C1112yes—
315C4×D4—22no—
316C4×D4—24no—
317C4×D4—22no—
318C4×D4—22no—
319C4×D4—22no—
320C4×D4—24no—
321C4×D4—22no—
322C4×D4D4×C1112yes—
323C4×D4D4×C1112yes—
324#117—24no—
325#117—24no—
326#117—22no—
327#117—22no—
328#117—22no—
329#117C23×C1112yes—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4D4×C1112yes—
334C2×C4⋊C4C23×C1111yescharacteristic
335C2×C22⋊C4—24no—
336C2×C22⋊C4—24no—
337C2×C42—24no—
338C2×C42—22no—
339C2×C42D4×C1112yes—
340C2×C42C23×C1112yes—
341C2×C42C23×C1111yescharacteristic
342C4⋊C8—22no—
343C4⋊C8—22no—
344#104—28no—
345#102—24no—
346#102—24no—
347#101—24no—
348#95—21no—
349C2×C11—21no—
350C2×C11—21no—
351C2×C11—44no—
352C2×C11—162no—
353C2×C11#284711yescharacteristic
354C2×C11C2×#45411yescharacteristic
355C2×C11#302111yescharacteristic
356C24—22no—
357#41—28no—
358#41—28no—
359#41—28no—
360#41—28no—
361#41—22no—
362#41—22no—
363#41C2×D4×C1114yes—
364#41C11×#4114yes—
365C2×Q8—22no—
366C2×Q8—28no—
367C2×Q8—28no—
368C2×Q8—22no—
369C2×Q8—22no—
370C2×Q8C2×D4×C1112yes—
371C2×Q8C2×D4×C1112yes—
372C2×Q8C11×#4112yes—
373C2×D4—22no—
374C2×D4—22no—
375C2×D4—24no—
376C2×D4—22no—
377C2×D4—22no—
378C2×D4—24no—
379C2×D4—44no—
380C2×D4—41no—
381C2×D4—42no—
382C2×D4—41no—
383C2×D4—82no—
384C2×D4C2×D4×C1112yes—
385C22×C4—24no—
386C22×C4—22no—
387C22×C4—24no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4C2×D4×C1111yescharacteristic
392C22×C4C2×D4×C1112yes—
393C22×C4C2×D4×C1112yes—
394C22×C4C2×D4×C1111yescharacteristic
395C22×C4C24×C1111yescharacteristic
396SD16—48no—
397D8—48no—
398M16—24no—
399M16—24no—
400C2×C8—24no—
401C4⋊C4—24no—
402C4⋊C4—22no—
403C4⋊C4—22no—
404C4⋊C4—22no—
405C4⋊C4—24no—
406C4⋊C4—22no—
407C4⋊C4—22no—
408C4⋊C4—42no—
409C4⋊C4C2×D4×C1112yes—
410C4⋊C4C2×D4×C1112yes—
411C22⋊C4—24no—
412C22⋊C4—22no—
413C22⋊C4—22no—
414C22⋊C4—22no—
415C22⋊C4—48no—
416C22⋊C4—84no—
417C42—24no—
418C42—24no—
419C42—22no—
420C42—22no—
421C42—22no—
422C42—22no—
423C42—22no—
424C42—22no—
425C42—22no—
426C42C2×D4×C1112yes—
427C42C2×D4×C1112yes—
428C11#3292111yescharacteristic, direct product factor, Sylow
429C23—22no—
430C23—44no—
431C23—44no—
432C23—42no—
433C23—42no—
434C23—42no—
435C23C22×D4×C1111yescharacteristic
436Q8—28no—
437Q8—24no—
438Q8—22no—
439Q8—24no—
440Q8C11×#12114yes—
441D4—28no—
442D4—24no—
443D4—24no—
444D4—22no—
445D4—44no—
446D4—44no—
447D4—82no—
448D4—84no—
449D4—82no—
450D4C11×#12114yes—
451C2×C4—216no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—24no—
456C2×C4—24no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—41no—
462C2×C4—44no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—82no—
468C2×C4—84no—
469C2×C4C11×#12011yescharacteristic
470C2×C4C11×#12012yes—
471C2×C4C11×#12011yescharacteristic
472C2×C4C11×#12114yes—
473C2×C4C22×D4×C1111yescharacteristic
474C2×C4C22×D4×C1112yes—
475C2×C4C2×C11×#4112yes—
476C2×C4C2×C11×#4111yescharacteristic
477C8—44no—
478C22—21no—
479C22—21no—
480C22—24no—
481C22—42no—
482C22—42no—
483C22—84no—
484C22—84no—
485C22—82no—
486C22—82no—
487C22—82no—
488C22C2×C11×#12011yescharacteristic
489C22C2×C11×#12111yescharacteristic
490C22C11×#52511yescharacteristic
491C4—21no—
492C4—22no—
493C4—24no—
494C4—24no—
495C4—42no—
496C4—42no—
497C4—42no—
498C4—82no—
499C4C11×#45412yescomplemented
500C4C2×C11×#12112yes—
501C4C11×#52512yes—
502C2—21no—
503C2—21no—
504C2—44no—
505C2—162no—
506C2C11×#284711yescharacteristic
507C2C2×C11×#45411yescharacteristic
508C2C11×#302111yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C4×C11×2−1+4C2semidirect
2. C11×#3038C2semidirect
3. C2×C11×#454C2semidirect
4. C11×#2548C2semidirect
5. C11×#1888C2semidirect
6. C11×#1883C2semidirect
7. C11×#1806C2semidirect
8. C11×#1801C2semidirect
40. C11×2−1+4D4semidirect
102. #32921C11direct (N × H)
175. C4×2−1+4C2×C11semidirect
176. #3038C2×C11semidirect
177. C2×#454C2×C11semidirect
178. #2548C2×C11semidirect
179. #1888C2×C11semidirect
180. #1883C2×C11semidirect
181. #1806C2×C11semidirect
182. #1801C2×C11semidirect
282. C4×C11#454semidirect
287. 2−1+4D4×C11semidirect
428. C11#32921direct (N × H)
499. C4C11×#454semidirect

Maximal subgroups

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

subgroupindex
C4×C11×2−1+42
C11×#30382
C2×C11×#4542
C11×#25482
C11×#18882
C11×#18832
C11×#18062
C11×#18012
#3292111