Finite Group Databasebeta

← C11×#23647 #14600840

Subgroups — C11×#23647 #14600840

Order 2816.

914 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#428C211yesmaximal, characteristic, complemented
2C11×#2896C211yesmaximal, characteristic
3C2×C11×#417C211yesmaximal, characteristic
4C11×#2879C211yesmaximal, characteristic
5C11×#2079C214yesmaximal, complemented
6C11×#2078C214yesmaximal, complemented
7C11×#1742C211yesmaximal, characteristic, complemented
8C2×C11×#343C211yesmaximal, characteristic, complemented
9C11×#1738C211yesmaximal, characteristic, complemented
10C22×C11×#41C2211yescharacteristic
11C22×C11×M16C2211yescharacteristic
12C22×C11×M16C2211yescharacteristic
13C22×C11×M16C2211yescharacteristic
14C22×C11×M16C2211yescharacteristic
15C2×C11×#117C2211yescharacteristic
16C22×C11×C4⋊C4C2211yescharacteristic
17C11×#428—22no—
18C11×#428—22no—
19C2×C11×#107C2212yescomplemented
20C2×C11×#106C2212yescomplemented
21C11×#419—21no—
22C11×#418—21no—
23C11×#417—22no—
24C11×#417C2214yes—
25C11×#417C2212yes—
26C11×#417C2212yes—
27C11×#416—22no—
28C2×C11×#103—21no—
29C2×C11×#102—21no—
30C11×#408—22no—
31C11×#408C2214yes—
32C11×#407—22no—
33C11×#343C2214yescomplemented
34C11×#343C2212yescomplemented
35C11×#343C2212yescomplemented
36C11×#341C2214yescomplemented
37C2×C11×#41—21no—
38C2×C11×#41—21no—
39C2×C11×#41—22no—
40C2×C11×#41—22no—
41C2×C11×#41—22no—
42C2×C11×#41—22no—
43C2×C11×#41D412yes—
44C2×C11×#41C2312yes—
45C22×Q8×C11D411yescharacteristic
46C22×D4×C11—21no—
47C22×D4×C11D411yescharacteristic
48C23×C4×C11—21no—
49C23×C4×C11—21no—
50C23×C4×C11C2311yescharacteristic
51C2×C11×M16—22no—
52C2×C11×M16—22no—
53C2×C11×M16—21no—
54C2×C11×M16—21no—
55C2×C11×M16—21no—
56C2×C11×M16—22no—
57C2×C11×M16—22no—
58C2×C11×M16—22no—
59C2×C11×M16—22no—
60C2×C11×M16—22no—
61C2×C11×M16—22no—
62C2×C11×M16D412yes—
63C2×C11×M16D412yes—
64C2×C11×M16C2312yes—
65C2×C11×M16C2312yes—
66C2×C11×M16C2312yes—
67C22×C8×C11—21no—
68C22×C8×C11—21no—
69C22×C8×C11—21no—
70C22×C8×C11C2312yes—
71C11×#117—21no—
72C11×#117—21no—
73C11×#117—21no—
74C11×#117—21no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4C2312yes—
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C22⋊C4—21no—
84C2×C42×C11—21no—
85C11×#107—24no—
86C11×#106—24no—
87C11×#103—24no—
88C11×#103—22no—
89C11×#103—22no—
90C11×#102—24no—
91C11×#102—22no—
92C11×#102—22no—
93C11×C22⋊C8—28no—
94#23647C1111yesmaximal, characteristic, direct product factor, Sylow
95C24×C11—21no—
96C24×C11#4111yescharacteristic
97C11×#41—24no—
98C11×#41—24no—
99C11×#41—22no—
100C11×#41—22no—
101C11×#41—22no—
102C11×#41—22no—
103C11×#41—42no—
104C11×#41—42no—
105C11×#41—42no—
106C11×#41—42no—
107C2×Q8×C11—21no—
108C2×Q8×C11—22no—
109C2×Q8×C11—22no—
110C2×Q8×C11C2×D412yes—
111C2×D4×C11—22no—
112C2×D4×C11—22no—
113C2×D4×C11—21no—
114C2×D4×C11—22no—
115C2×D4×C11—22no—
116C2×D4×C11—42no—
117C2×D4×C11—42no—
118C2×D4×C11C2×D412yes—
119C22×C4×C11—21no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—22no—
125C22×C4×C11—42no—
126C22×C4×C11—42no—
127C22×C4×C11—41no—
128C22×C4×C11—41no—
129C22×C4×C11—82no—
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11#4111yescharacteristic
135C22×C4×C11#4112yes—
136C22×C4×C11#4112yes—
137C22×C4×C11#4112yes—
138C22×C4×C11#4112yes—
139C22×C4×C11C2411yescharacteristic
140C11×M16—24no—
141C11×M16—24no—
142C11×M16—22no—
143C11×M16—22no—
144C11×M16—22no—
145C11×M16—22no—
146C11×M16—22no—
147C11×M16—22no—
148C11×M16—42no—
149C11×M16—42no—
150C11×M16—42no—
151C2×C8×C11—22no—
152C2×C8×C11—22no—
153C2×C8×C11—22no—
154C2×C8×C11—22no—
155C2×C8×C11—22no—
156C2×C8×C11—42no—
157C2×C8×C11—42no—
158C2×C8×C11—42no—
159C2×C8×C11C2×D414yes—
160C11×C4⋊C4—22no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—22no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—41no—
167C11×C4⋊C4—41no—
168C11×C22⋊C4—41no—
169C11×C22⋊C4—41no—
170C42×C11—41no—
171C42×C11—41no—
172C2×#428C2×C1111yescharacteristic, complemented
173#2896C2×C1111yescharacteristic
174C2×#417C2×C1111yescharacteristic
175#2879C2×C1111yescharacteristic
176#2079C2×C1114yescomplemented
177#2078C2×C1114yescomplemented
178#1742C2×C1111yescharacteristic, complemented
179C2×#343C2×C1111yescharacteristic, complemented
180#1738C2×C1111yescharacteristic, complemented
181C23×C11—22no—
182C23×C11—41no—
183C23×C11—41no—
184C23×C11—42no—
185C23×C11—81no—
186C23×C11—81no—
187C23×C11#12111yescharacteristic
188C23×C11#12111yescharacteristic
189C23×C11#12612yes—
190C23×C11#12612yes—
191C23×C11C2×#4111yescharacteristic
192Q8×C11—22no—
193Q8×C11—22no—
194Q8×C11—42no—
195D4×C11—22no—
196D4×C11—22no—
197D4×C11—42no—
198D4×C11—42no—
199D4×C11—44no—
200D4×C11—42no—
201C2×C4×C11—22no—
202C2×C4×C11—42no—
203C2×C4×C11—42no—
204C2×C4×C11—42no—
205C2×C4×C11—44no—
206C2×C4×C11—41no—
207C2×C4×C11—41no—
208C2×C4×C11—42no—
209C2×C4×C11—82no—
210C2×C4×C11—82no—
211C2×C4×C11—81no—
212C2×C4×C11—81no—
213C2×C4×C11—82no—
214C2×C4×C11#12111yescharacteristic
215C2×C4×C11#12111yescharacteristic
216C2×C4×C11#12312yes—
217C2×C4×C11#12312yes—
218C2×C4×C11#12312yes—
219C2×C4×C11#12312yes—
220C2×C4×C11#12312yes—
221C2×C4×C11#12312yes—
222C2×C4×C11#12412yes—
223C2×C4×C11#12412yes—
224C2×C4×C11#12612yes—
225C2×C4×C11#12612yes—
226C2×C4×C11C22×D411yescharacteristic
227C2×C4×C11C22×D411yescharacteristic
228C2×C4×C11C2×#4111yescharacteristic
229C2×C4×C11C2×#4111yescharacteristic
230C2×C4×C11C2×#4111yescharacteristic
231C2×C4×C11C2×#4111yescharacteristic
232C8×C11—24no—
233C8×C11—42no—
234C8×C11—42no—
235C8×C11—42no—
236C22×#41C22×C1111yescharacteristic
237C22×M16C22×C1111yescharacteristic
238C22×M16C22×C1111yescharacteristic
239C22×M16C22×C1111yescharacteristic
240C22×M16C22×C1111yescharacteristic
241C2×#117C22×C1111yescharacteristic
242C22×C4⋊C4C22×C1111yescharacteristic
243#428—22no—
244#428—22no—
245C2×#107C22×C1112yescomplemented
246C2×#106C22×C1112yescomplemented
247#419—21no—
248#418—21no—
249#417—22no—
250#417C22×C1112yes—
251#417C22×C1114yes—
252#417C22×C1112yes—
253#416—22no—
254C2×#103—21no—
255C2×#102—21no—
256#408—22no—
257#408C22×C1114yes—
258#407—22no—
259#343C22×C1112yescomplemented
260#343C22×C1114yescomplemented
261#343C22×C1112yescomplemented
262#341C22×C1114yescomplemented
263C22×C11—21no—
264C22×C11—21no—
265C22×C11—21no—
266C22×C11—21no—
267C22×C11—21no—
268C22×C11—21no—
269C22×C11—42no—
270C22×C11—42no—
271C22×C11—42no—
272C22×C11—42no—
273C22×C11—42no—
274C22×C11—84no—
275C22×C11#39712yes—
276C22×C11#39712yes—
277C22×C11C2×#12111yescharacteristic
278C22×C11C2×#12611yescharacteristic
279C22×C11C2×#12611yescharacteristic
280C4×C11—42no—
281C4×C11—81no—
282C4×C11—82no—
283C4×C11—81no—
284C4×C11#39712yes—
285C4×C11#39712yes—
286C4×C11C2×#12311yescharacteristic
287C4×C11C2×#12311yescharacteristic
288C4×C11C2×#12311yescharacteristic
289C4×C11C2×#12411yescharacteristic
290C2×#41—21no—
291C2×#41—21no—
292C2×#41—22no—
293C2×#41—22no—
294C2×#41—22no—
295C2×#41—22no—
296C2×#41D4×C1112yes—
297C2×#41C23×C1112yes—
298C22×Q8D4×C1111yescharacteristic
299C22×D4—21no—
300C22×D4D4×C1111yescharacteristic
301C23×C4—21no—
302C23×C4—21no—
303C23×C4C23×C1111yescharacteristic
304C2×M16—22no—
305C2×M16—22no—
306C2×M16—21no—
307C2×M16—21no—
308C2×M16—21no—
309C2×M16—22no—
310C2×M16—22no—
311C2×M16—22no—
312C2×M16—22no—
313C2×M16—22no—
314C2×M16—22no—
315C2×M16D4×C1112yes—
316C2×M16D4×C1112yes—
317C2×M16C23×C1112yes—
318C2×M16C23×C1112yes—
319C2×M16C23×C1112yes—
320C22×C8—21no—
321C22×C8—21no—
322C22×C8—21no—
323C22×C8C23×C1112yes—
324#117—21no—
325#117—21no—
326#117—21no—
327#117—21no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4C23×C1112yes—
334C2×C4⋊C4C23×C1111yescharacteristic
335C2×C4⋊C4C23×C1111yescharacteristic
336C2×C22⋊C4—21no—
337C2×C42—21no—
338#107—24no—
339#106—24no—
340#103—24no—
341#103—22no—
342#103—22no—
343#102—24no—
344#102—22no—
345#102—22no—
346C22⋊C8—28no—
347C2×C11—22no—
348C2×C11—21no—
349C2×C11—21no—
350C2×C11—22no—
351C2×C11—82no—
352C2×C11C2×#39711yescharacteristic
353C2×C11#306811yescharacteristic
354C2×C11#306911yescharacteristic
355C24—21no—
356C24C11×#4111yescharacteristic
357#41—24no—
358#41—24no—
359#41—22no—
360#41—22no—
361#41—22no—
362#41—22no—
363#41—42no—
364#41—42no—
365#41—42no—
366#41—42no—
367C2×Q8—21no—
368C2×Q8—22no—
369C2×Q8—22no—
370C2×Q8C2×D4×C1112yes—
371C2×D4—22no—
372C2×D4—22no—
373C2×D4—21no—
374C2×D4—22no—
375C2×D4—22no—
376C2×D4—42no—
377C2×D4—42no—
378C2×D4C2×D4×C1112yes—
379C22×C4—21no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—22no—
385C22×C4—42no—
386C22×C4—42no—
387C22×C4—41no—
388C22×C4—41no—
389C22×C4—82no—
390C22×C4C2×D4×C1111yescharacteristic
391C22×C4C2×D4×C1111yescharacteristic
392C22×C4C2×D4×C1111yescharacteristic
393C22×C4C2×D4×C1111yescharacteristic
394C22×C4C11×#4111yescharacteristic
395C22×C4C11×#4112yes—
396C22×C4C11×#4112yes—
397C22×C4C11×#4112yes—
398C22×C4C11×#4112yes—
399C22×C4C24×C1111yescharacteristic
400M16—24no—
401M16—24no—
402M16—22no—
403M16—22no—
404M16—22no—
405M16—22no—
406M16—22no—
407M16—22no—
408M16—42no—
409M16—42no—
410M16—42no—
411C2×C8—22no—
412C2×C8—22no—
413C2×C8—22no—
414C2×C8—22no—
415C2×C8—22no—
416C2×C8—42no—
417C2×C8—42no—
418C2×C8—42no—
419C2×C8C2×D4×C1114yes—
420C4⋊C4—22no—
421C4⋊C4—21no—
422C4⋊C4—21no—
423C4⋊C4—21no—
424C4⋊C4—22no—
425C4⋊C4—21no—
426C4⋊C4—41no—
427C4⋊C4—41no—
428C22⋊C4—41no—
429C22⋊C4—41no—
430C42—41no—
431C42—41no—
432C11#2364711yescharacteristic, direct product factor, Sylow
433C23—22no—
434C23—41no—
435C23—41no—
436C23—42no—
437C23—81no—
438C23—81no—
439C23C11×#12111yescharacteristic
440C23C11×#12111yescharacteristic
441C23C11×#12612yes—
442C23C11×#12612yes—
443C23C2×C11×#4111yescharacteristic
444Q8—22no—
445Q8—22no—
446Q8—42no—
447D4—22no—
448D4—22no—
449D4—42no—
450D4—42no—
451D4—44no—
452D4—42no—
453C2×C4—22no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—44no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—42no—
461C2×C4—82no—
462C2×C4—82no—
463C2×C4—81no—
464C2×C4—81no—
465C2×C4—82no—
466C2×C4C11×#12111yescharacteristic
467C2×C4C11×#12111yescharacteristic
468C2×C4C11×#12312yes—
469C2×C4C11×#12312yes—
470C2×C4C11×#12312yes—
471C2×C4C11×#12312yes—
472C2×C4C11×#12312yes—
473C2×C4C11×#12312yes—
474C2×C4C11×#12412yes—
475C2×C4C11×#12412yes—
476C2×C4C11×#12612yes—
477C2×C4C11×#12612yes—
478C2×C4C22×D4×C1111yescharacteristic
479C2×C4C22×D4×C1111yescharacteristic
480C2×C4C2×C11×#4111yescharacteristic
481C2×C4C2×C11×#4111yescharacteristic
482C2×C4C2×C11×#4111yescharacteristic
483C2×C4C2×C11×#4111yescharacteristic
484C8—24no—
485C8—42no—
486C8—42no—
487C8—42no—
488C22—21no—
489C22—21no—
490C22—21no—
491C22—21no—
492C22—21no—
493C22—21no—
494C22—42no—
495C22—42no—
496C22—42no—
497C22—42no—
498C22—42no—
499C22—84no—
500C22C11×#39712yes—
501C22C11×#39712yes—
502C22C2×C11×#12111yescharacteristic
503C22C2×C11×#12611yescharacteristic
504C22C2×C11×#12611yescharacteristic
505C4—42no—
506C4—82no—
507C4—81no—
508C4—81no—
509C4C11×#39712yes—
510C4C11×#39712yes—
511C4C2×C11×#12311yescharacteristic
512C4C2×C11×#12311yescharacteristic
513C4C2×C11×#12311yescharacteristic
514C4C2×C11×#12411yescharacteristic
515C2—22no—
516C2—21no—
517C2—21no—
518C2—22no—
519C2—82no—
520C2C2×C11×#39711yescharacteristic
521C2C11×#306811yescharacteristic
522C2C11×#306911yescharacteristic
subgroupG/H
center, socleC22×C11C2×#121
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×C11×#41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#428C2semidirect
5. C11×#2079C2semidirect
6. C11×#2078C2semidirect
7. C11×#1742C2semidirect
8. C2×C11×#343C2semidirect
9. C11×#1738C2semidirect
19. C2×C11×#107C22semidirect
20. C2×C11×#106C22semidirect
33. C11×#343C22semidirect
34. C11×#343C22semidirect
35. C11×#343C22semidirect
36. C11×#341C22semidirect
94. #23647C11direct (N × H)
172. C2×#428C2×C11semidirect
176. #2079C2×C11semidirect
177. #2078C2×C11semidirect
178. #1742C2×C11semidirect
179. C2×#343C2×C11semidirect
180. #1738C2×C11semidirect
245. C2×#107C22×C11semidirect
246. C2×#106C22×C11semidirect
259. #343C22×C11semidirect
260. #343C22×C11semidirect
261. #343C22×C11semidirect
262. #341C22×C11semidirect
432. C11#23647direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4282
C11×#28962
C2×C11×#4172
C11×#28792
C11×#20792
C11×#20782
C11×#17422
C2×C11×#3432
C11×#17382
#2364711