Finite Group Databasebeta

← C11×#24807 #14602000

Subgroups — C11×#24807 #14602000

Order 2816.

844 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×#473C211yesmaximal, characteristic, complemented
2C11×#3056C212yesmaximal
3C2×C11×#470C211yesmaximal, characteristic, complemented
4C11×#2930C211yesmaximal, characteristic
5C2×C11×#430C211yesmaximal, characteristic, complemented
6C11×#2064C212yesmaximal, complemented
7C11×#2052C212yesmaximal, complemented
8C11×#1979C211yesmaximal, characteristic, complemented
9C11×#1951C211yesmaximal, characteristic, complemented
10C11×#1901C212yesmaximal, complemented
11C11×#1815C211yesmaximal, characteristic, complemented
12C2×C11×#137C2212yes—
13C22×C11×Q16C2211yescharacteristic
14C2×C11×#131C2211yescharacteristic
15C22×C11×M16C2212yes—
16C22×C11×M16C2211yescharacteristic
17C11×#525C2211yescharacteristic
18C2×C11×C22⋊Q8C2212yes—
19C11×#473—24no—
20C11×#470—22no—
21C11×#470—22no—
22C11×#470—22no—
23C11×#468—22no—
24C11×#467—22no—
25C11×#465—22no—
26C11×#436—22no—
27C11×#435—22no—
28C11×#430—24no—
29C2×C11×#108C2211yescharacteristic
30C2×C11×#108C2212yes—
31C2×C11×#108C2211yescharacteristic
32C11×#428C2212yes—
33C2×C11×#106C2211yescharacteristic
34C11×#424C2211yescharacteristic
35C11×#419C2212yes—
36C11×#417C2212yes—
37C2×C11×#103C2212yes—
38C2×C11×#101C2212yes—
39C2×C11×#101C2212yes—
40C11×#408C2211yescharacteristic
41C11×#407C2211yescharacteristic
42C11×#405C2211yescharacteristic
43C11×#343C2212yes—
44C11×#343C2212yes—
45C2×C11×#41C2311yescharacteristic
46C22×Q8×C11C2312yes—
47C23×C4×C11C2311yescharacteristic
48C11×#137—24no—
49C11×#137—42no—
50C2×C11×Q16—22no—
51C2×C11×Q16—21no—
52C2×C11×Q16—21no—
53C2×C11×Q16—22no—
54C2×C11×Q16—22no—
55C2×C11×SD16—22no—
56C11×#131—22no—
57C11×#131—22no—
58C2×C11×M16—22no—
59C2×C11×M16—22no—
60C2×C11×M16—21no—
61C2×C11×M16—22no—
62C2×C11×M16—24no—
63C2×C11×M16—42no—
64C2×C11×M16D412yes—
65C2×C11×M16D412yes—
66C2×C11×M16C2311yescharacteristic
67C2×C11×M16C2311yescharacteristic
68C2×C11×M16C2312yes—
69C2×C11×M16C2312yes—
70C22×C8×C11—22no—
71C22×C8×C11—21no—
72C22×C8×C11C2311yescharacteristic
73C22×C8×C11C2311yescharacteristic
74C11×#123—21no—
75C11×C22⋊Q8—22no—
76C11×C22⋊Q8—22no—
77C11×C22⋊Q8—22no—
78C11×C22⋊Q8—22no—
79C11×C22⋊Q8D412yes—
80C11×#121D412yes—
81C11×#120—21no—
82C4×D4×C11—22no—
83C11×#117C2311yescharacteristic
84C2×C11×C4⋊C4—22no—
85C2×C11×C4⋊C4C2312yes—
86C2×C11×C22⋊C4—22no—
87C11×#108—24no—
88C11×#108—22no—
89C11×#108D414yescomplemented
90C11×#107—22no—
91C11×#106—21no—
92C11×#106—21no—
93C11×#106—22no—
94C11×C4⋊C8—22no—
95C11×#103—22no—
96C11×#103—24no—
97C11×#103—22no—
98C11×#103—22no—
99C11×#102—22no—
100C11×#101—24no—
101C11×#101—42no—
102C11×C22⋊C8—22no—
103C11×C22⋊C8—22no—
104C11×#97—21no—
105C4×C8×C11—21no—
106#24807C1111yesmaximal, characteristic, direct product factor, Sylow
107C24×C11#4111yescharacteristic
108C11×#41—21no—
109C11×#41—21no—
110C11×#41—21no—
111C11×#41—21no—
112C2×Q8×C11—22no—
113C2×Q8×C11—22no—
114C2×Q8×C11—22no—
115C2×Q8×C11—22no—
116C2×Q8×C11—22no—
117C2×Q8×C11—22no—
118C2×Q8×C11C2×D411yescharacteristic
119C2×D4×C11—21no—
120C2×D4×C11—22no—
121C2×D4×C11C2×D411yescharacteristic
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11C2×D412yes—
130C22×C4×C11C2×D412yes—
131C22×C4×C11#4111yescharacteristic
132C22×C4×C11C2411yescharacteristic
133C11×Q16—44no—
134C11×Q16—42no—
135C11×Q16—42no—
136C11×SD16—44no—
137C11×M16—24no—
138C11×M16—24no—
139C11×M16—21no—
140C11×M16—22no—
141C11×M16—21no—
142C11×M16—22no—
143C11×M16—21no—
144C11×M16—22no—
145C11×M16—21no—
146C11×M16—44no—
147C11×M16—42no—
148C11×M16C2×D414yes—
149C2×C8×C11—22no—
150C2×C8×C11—21no—
151C2×C8×C11—21no—
152C2×C8×C11—21no—
153C2×C8×C11—22no—
154C2×C8×C11—21no—
155C2×C8×C11—44no—
156C2×C8×C11—42no—
157C2×C8×C11C2×D412yes—
158C2×C8×C11C2×D411yescharacteristic
159C2×C8×C11C2×D411yescharacteristic
160C2×C8×C11C2×D412yes—
161C2×C8×C11#4112yes—
162C11×C4⋊C4—22no—
163C11×C4⋊C4—22no—
164C11×C4⋊C4—22no—
165C11×C4⋊C4—42no—
166C11×C4⋊C4—42no—
167C11×C4⋊C4C2×D412yes—
168C11×C22⋊C4—22no—
169C11×C22⋊C4—21no—
170C11×C22⋊C4—22no—
171C11×C22⋊C4—42no—
172C11×C22⋊C4—42no—
173C42×C11—21no—
174C2×#473C2×C1111yescharacteristic, complemented
175#3056C2×C1112yes—
176C2×#470C2×C1111yescharacteristic, complemented
177#2930C2×C1111yescharacteristic
178C2×#430C2×C1111yescharacteristic, complemented
179#2064C2×C1112yescomplemented
180#2052C2×C1112yescomplemented
181#1979C2×C1111yescharacteristic, complemented
182#1951C2×C1111yescharacteristic, complemented
183#1901C2×C1112yescomplemented
184#1815C2×C1111yescharacteristic, complemented
185C23×C11—21no—
186C23×C11—21no—
187C23×C11—21no—
188C23×C11—42no—
189C23×C11#12112yes—
190C23×C11C2×#4111yescharacteristic
191Q8×C11—21no—
192Q8×C11—21no—
193Q8×C11—42no—
194Q8×C11—42no—
195Q8×C11—42no—
196Q8×C11—42no—
197D4×C11—21no—
198D4×C11—21no—
199D4×C11—41no—
200D4×C11—41no—
201D4×C11—82no—
202C2×C4×C11—21no—
203C2×C4×C11—21no—
204C2×C4×C11—22no—
205C2×C4×C11—22no—
206C2×C4×C11—22no—
207C2×C4×C11—22no—
208C2×C4×C11—22no—
209C2×C4×C11—21no—
210C2×C4×C11—41no—
211C2×C4×C11—41no—
212C2×C4×C11—42no—
213C2×C4×C11—42no—
214C2×C4×C11—42no—
215C2×C4×C11—42no—
216C2×C4×C11—82no—
217C2×C4×C11#12112yes—
218C2×C4×C11C22×D411yescharacteristic
219C2×C4×C11C22×D411yescharacteristic
220C2×C4×C11C22×D411yescharacteristic
221C2×C4×C11C2×#4111yescharacteristic
222C2×C4×C11H(5,𝔽2)11yescharacteristic
223C2×C4×C112−1+411yescharacteristic
224C8×C11—22no—
225C8×C11—24no—
226C8×C11—41no—
227C8×C11—41no—
228C8×C11—42no—
229C8×C11#12112yes—
230C8×C11#12112yes—
231C2×#137C22×C1112yes—
232C22×Q16C22×C1111yescharacteristic
233C2×#131C22×C1111yescharacteristic
234C22×M16C22×C1112yes—
235C22×M16C22×C1111yescharacteristic
236#525C22×C1111yescharacteristic
237C2×C22⋊Q8C22×C1112yes—
238#473—24no—
239#470—22no—
240#470—22no—
241#470—22no—
242#468—22no—
243#467—22no—
244#465—22no—
245#436—22no—
246#435—22no—
247#430—24no—
248C2×#108C22×C1112yes—
249C2×#108C22×C1111yescharacteristic
250C2×#108C22×C1111yescharacteristic
251#428C22×C1112yes—
252C2×#106C22×C1111yescharacteristic
253#424C22×C1111yescharacteristic
254#419C22×C1112yes—
255#417C22×C1112yes—
256C2×#103C22×C1112yes—
257C2×#101C22×C1112yes—
258C2×#101C22×C1112yes—
259#408C22×C1111yescharacteristic
260#407C22×C1111yescharacteristic
261#405C22×C1111yescharacteristic
262#343C22×C1112yes—
263#343C22×C1112yes—
264C22×C11—22no—
265C22×C11—22no—
266C22×C11—22no—
267C22×C11—22no—
268C22×C11—41no—
269C22×C11—42no—
270C22×C11—81no—
271C22×C11—81no—
272C22×C11C2×#12111yescharacteristic
273C22×C11#54811yescharacteristic
274C22×C11#55311yescharacteristic
275C4×C11—22no—
276C4×C11—41no—
277C4×C11—42no—
278C4×C11—82no—
279C4×C11—82no—
280C4×C11C2×#12111yescharacteristic
281C4×C11#53711yescharacteristic
282C4×C11D4211yescharacteristic
283C4×C11#54711yescharacteristic
284C2×#41C23×C1111yescharacteristic
285C22×Q8C23×C1112yes—
286C23×C4C23×C1111yescharacteristic
287#137—24no—
288#137—42no—
289C2×Q16—22no—
290C2×Q16—21no—
291C2×Q16—21no—
292C2×Q16—22no—
293C2×Q16—22no—
294C2×SD16—22no—
295#131—22no—
296#131—22no—
297C2×M16—22no—
298C2×M16—22no—
299C2×M16—21no—
300C2×M16—22no—
301C2×M16—24no—
302C2×M16—42no—
303C2×M16D4×C1112yes—
304C2×M16D4×C1112yes—
305C2×M16C23×C1112yes—
306C2×M16C23×C1111yescharacteristic
307C2×M16C23×C1111yescharacteristic
308C2×M16C23×C1112yes—
309C22×C8—22no—
310C22×C8—21no—
311C22×C8C23×C1111yescharacteristic
312C22×C8C23×C1111yescharacteristic
313#123—21no—
314C22⋊Q8—22no—
315C22⋊Q8—22no—
316C22⋊Q8—22no—
317C22⋊Q8—22no—
318C22⋊Q8D4×C1112yes—
319#121D4×C1112yes—
320#120—21no—
321C4×D4—22no—
322#117C23×C1111yescharacteristic
323C2×C4⋊C4—22no—
324C2×C4⋊C4C23×C1112yes—
325C2×C22⋊C4—22no—
326#108—24no—
327#108—22no—
328#108D4×C1114yescomplemented
329#107—22no—
330#106—21no—
331#106—21no—
332#106—22no—
333C4⋊C8—22no—
334#103—22no—
335#103—24no—
336#103—22no—
337#103—22no—
338#102—22no—
339#101—24no—
340#101—42no—
341C22⋊C8—22no—
342C22⋊C8—22no—
343#97—21no—
344C4×C8—21no—
345C2×C11—21no—
346C2×C11—21no—
347C2×C11—42no—
348C2×C11—81no—
349C2×C11#241611yescharacteristic
350C2×C11#306912yes—
351C24C11×#4111yescharacteristic
352#41—21no—
353#41—21no—
354#41—21no—
355#41—21no—
356C2×Q8—22no—
357C2×Q8—22no—
358C2×Q8—22no—
359C2×Q8—22no—
360C2×Q8—22no—
361C2×Q8—22no—
362C2×Q8C2×D4×C1111yescharacteristic
363C2×D4—21no—
364C2×D4—22no—
365C2×D4C2×D4×C1111yescharacteristic
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4C2×D4×C1112yes—
374C22×C4C2×D4×C1112yes—
375C22×C4C11×#4111yescharacteristic
376C22×C4C24×C1111yescharacteristic
377Q16—44no—
378Q16—42no—
379Q16—42no—
380SD16—44no—
381M16—22no—
382M16—24no—
383M16—24no—
384M16—21no—
385M16—22no—
386M16—21no—
387M16—21no—
388M16—22no—
389M16—21no—
390M16—44no—
391M16—42no—
392M16C2×D4×C1114yes—
393C2×C8—22no—
394C2×C8—21no—
395C2×C8—21no—
396C2×C8—21no—
397C2×C8—21no—
398C2×C8—22no—
399C2×C8—44no—
400C2×C8—42no—
401C2×C8C2×D4×C1112yes—
402C2×C8C2×D4×C1111yescharacteristic
403C2×C8C2×D4×C1111yescharacteristic
404C2×C8C2×D4×C1112yes—
405C2×C8C11×#4112yes—
406C4⋊C4—22no—
407C4⋊C4—22no—
408C4⋊C4—22no—
409C4⋊C4—42no—
410C4⋊C4—42no—
411C4⋊C4C2×D4×C1112yes—
412C22⋊C4—22no—
413C22⋊C4—21no—
414C22⋊C4—22no—
415C22⋊C4—42no—
416C22⋊C4—42no—
417C42—21no—
418C11#2480711yescharacteristic, direct product factor, Sylow
419C23—21no—
420C23—21no—
421C23—21no—
422C23—42no—
423C23C11×#12112yes—
424C23C2×C11×#4111yescharacteristic
425Q8—21no—
426Q8—21no—
427Q8—42no—
428Q8—42no—
429Q8—42no—
430Q8—42no—
431D4—21no—
432D4—21no—
433D4—41no—
434D4—41no—
435D4—82no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—22no—
439C2×C4—22no—
440C2×C4—22no—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—21no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—42no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—82no—
451C2×C4C11×#12112yes—
452C2×C4C22×D4×C1111yescharacteristic
453C2×C4C22×D4×C1111yescharacteristic
454C2×C4C22×D4×C1111yescharacteristic
455C2×C4C2×C11×#4111yescharacteristic
456C2×C4C11×H(5,𝔽2)11yescharacteristic
457C2×C4C11×2−1+411yescharacteristic
458C8—22no—
459C8—24no—
460C8—41no—
461C8—41no—
462C8—42no—
463C8C11×#12112yes—
464C8C11×#12112yes—
465C22—22no—
466C22—22no—
467C22—22no—
468C22—22no—
469C22—41no—
470C22—42no—
471C22—81no—
472C22—81no—
473C22C2×C11×#12111yescharacteristic
474C22C11×#54811yescharacteristic
475C22C11×#55311yescharacteristic
476C4—22no—
477C4—41no—
478C4—42no—
479C4—82no—
480C4—82no—
481C4C2×C11×#12111yescharacteristic
482C4C11×#53711yescharacteristic
483C4D42×C1111yescharacteristic
484C4C11×#54711yescharacteristic
485C2—21no—
486C2—21no—
487C2—42no—
488C2—81no—
489C2C11×#241611yescharacteristic
490C2C11×#306912yes—
subgroupG/H
center, socleC22×C11C2×#121
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#525C22
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×#473C2semidirect
3. C2×C11×#470C2semidirect
5. C2×C11×#430C2semidirect
6. C11×#2064C2semidirect
7. C11×#2052C2semidirect
8. C11×#1979C2semidirect
9. C11×#1951C2semidirect
10. C11×#1901C2semidirect
11. C11×#1815C2semidirect
89. C11×#108D4semidirect
106. #24807C11direct (N × H)
174. C2×#473C2×C11semidirect
176. C2×#470C2×C11semidirect
178. C2×#430C2×C11semidirect
179. #2064C2×C11semidirect
180. #2052C2×C11semidirect
181. #1979C2×C11semidirect
182. #1951C2×C11semidirect
183. #1901C2×C11semidirect
184. #1815C2×C11semidirect
328. #108D4×C11semidirect
418. C11#24807direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4732
C11×#30562
C2×C11×#4702
C11×#29302
C2×C11×#4302
C11×#20642
C11×#20522
C11×#19792
C11×#19512
C11×#19012
C11×#18152
#2480711