Finite Group Databasebeta

← C11×#24730 #14601923

Subgroups — C11×#24730 #14601923

Order 2816.

1018 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#461C212yesmaximal
2C2×C11×#461C211yesmaximal, characteristic
3C2×C4×C11×SD16C211yesmaximal, characteristic
4C11×#2546C211yesmaximal, characteristic, complemented
5D4×C11×C4⋊C4C211yesmaximal, characteristic
6C11×#2066C212yesmaximal, complemented
7C11×#2043C212yesmaximal, complemented
8C11×#1956C211yesmaximal, characteristic, complemented
9C11×#1939C211yesmaximal, characteristic, complemented
10C11×#1877C212yesmaximal
11C11×#1803C211yesmaximal, characteristic, complemented
12C22×C11×SD16C2212yes—
13C22×C11×SD16C2211yescharacteristic
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C11×C4⋊Q8C2212yes—
16C2×C4×Q8×C11C2211yescharacteristic
17C2×C4×D4×C11C2212yes—
18C2×C4×D4×C11C2211yescharacteristic
19C22×C11×C4⋊C4—21no—
20C11×#461—28no—
21C11×#461—24no—
22C4×C11×SD16—24no—
23C2×C11×#106C2211yescharacteristic
24C2×C11×C4⋊C8C2211yescharacteristic
25C2×C11×C4⋊C8C2212yes—
26C2×C11×#103C2211yescharacteristic
27C2×C11×#103C2212yes—
28C2×C11×#103C2212yes—
29C2×C11×#103C2212yes—
30C2×C11×#103C2212yes—
31C2×C11×#102C2211yescharacteristic
32C2×C4×C8×C11C2211yescharacteristic
33C11×#398—22no—
34C11×#391C2212yes—
35C11×#389—21no—
36C11×#389—21no—
37C11×#389C2212yes—
38C11×#385—22no—
39C11×#384C2211yescharacteristic
40C11×#380—21no—
41C4×C11×C4⋊C4C2211yescharacteristic
42C11×#340C2212yes—
43C11×#336C2212yes—
44C22×Q8×C11C2312yes—
45C22×Q8×C11C2311yescharacteristic
46C22×D4×C11C2311yescharacteristic
47C23×C4×C11—21no—
48C23×C4×C11—22no—
49C2×C11×SD16—22no—
50C2×C11×SD16—22no—
51C2×C11×SD16—24no—
52C2×C11×SD16—24no—
53C2×C11×SD16—24no—
54C2×C11×SD16D414yes—
55C22×C8×C11C2311yescharacteristic
56C22×C8×C11C2312yes—
57C22×C8×C11C2311yescharacteristic
58C11×C4⋊Q8—24no—
59C11×C4⋊Q8—22no—
60C11×C4⋊Q8—22no—
61C11×C4⋊Q8—42no—
62C4×Q8×C11—22no—
63C4×Q8×C11—22no—
64C4×D4×C11—24no—
65C4×D4×C11—22no—
66C4×D4×C11—42no—
67C4×D4×C11D414yes—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—22no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—22no—
73C2×C11×C4⋊C4—22no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—44no—
77C2×C11×C4⋊C4D411yescharacteristic
78C2×C11×C4⋊C4D411yescharacteristic
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C4⋊C4C2312yes—
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C22⋊C4—21no—
83C2×C11×C22⋊C4—22no—
84C2×C42×C11—21no—
85C2×C42×C11C2312yes—
86C2×C42×C11C2311yescharacteristic
87C11×#106—22no—
88C11×C4⋊C8—24no—
89C11×C4⋊C8—22no—
90C11×#103—24no—
91C11×#103—24no—
92C11×#103—22no—
93C11×#103—24no—
94C11×#103—42no—
95C11×#102—22no—
96C4×C8×C11—22no—
97C11×#95—22no—
98C11×#95—22no—
99C11×#95—22no—
100C11×#95D412yes—
101#24730C1111yesmaximal, characteristic, direct product factor, Sylow
102C24×C11—21no—
103C2×Q8×C11—21no—
104C2×Q8×C11—21no—
105C2×Q8×C11—22no—
106C2×Q8×C11—22no—
107C2×Q8×C11—21no—
108C2×Q8×C11—21no—
109C2×Q8×C11—22no—
110C2×Q8×C11—22no—
111C2×Q8×C11—22no—
112C2×Q8×C11—21no—
113C2×Q8×C11—22no—
114C2×Q8×C11C2×D412yes—
115C2×D4×C11—21no—
116C2×D4×C11—21no—
117C2×D4×C11—21no—
118C2×D4×C11C2×D412yes—
119C2×D4×C11C2×D412yes—
120C2×D4×C11#4112yes—
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—24no—
124C22×C4×C11—21no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—44no—
128C22×C4×C11—42no—
129C22×C4×C11—42no—
130C22×C4×C11—44no—
131C22×C4×C11—82no—
132C22×C4×C11C2×D412yes—
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D412yes—
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2411yescharacteristic
137C11×SD16—28no—
138C11×SD16—48no—
139C2×C8×C11—21no—
140C2×C8×C11—21no—
141C2×C8×C11—22no—
142C2×C8×C11—22no—
143C2×C8×C11—21no—
144C2×C8×C11—22no—
145C2×C8×C11—21no—
146C2×C8×C11—21no—
147C2×C8×C11C2×D412yes—
148C11×C4⋊C4—22no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—22no—
154C11×C4⋊C4—44no—
155C11×C4⋊C4—44no—
156C11×C4⋊C4—42no—
157C11×C4⋊C4—42no—
158C11×C4⋊C4—42no—
159C11×C4⋊C4—44no—
160C11×C4⋊C4—42no—
161C11×C4⋊C4—81no—
162C11×C4⋊C4SD1614yescomplemented
163C11×C4⋊C4C2×D412yes—
164C11×C22⋊C4—24no—
165C11×C22⋊C4—44no—
166C42×C11—22no—
167C42×C11—22no—
168C42×C11—42no—
169C42×C11C2×D412yes—
170C42×C11#4112yes—
171C2×#461C2×C1112yes—
172C2×#461C2×C1111yescharacteristic
173C2×C4×SD16C2×C1111yescharacteristic
174#2546C2×C1111yescharacteristic, complemented
175D4×C4⋊C4C2×C1111yescharacteristic
176#2066C2×C1112yescomplemented
177#2043C2×C1112yescomplemented
178#1956C2×C1111yescharacteristic, complemented
179#1939C2×C1111yescharacteristic, complemented
180#1877C2×C1112yes—
181#1803C2×C1111yescharacteristic, complemented
182C23×C11—22no—
183C23×C11—22no—
184C23×C11—22no—
185C23×C11—41no—
186C23×C11—41no—
187C23×C11—41no—
188C23×C11—41no—
189C23×C11C22×D411yescharacteristic
190Q8×C11—22no—
191Q8×C11—22no—
192Q8×C11—41no—
193Q8×C11—41no—
194Q8×C11—42no—
195Q8×C11—42no—
196Q8×C11—42no—
197Q8×C11—42no—
198D4×C11—22no—
199D4×C11—22no—
200D4×C11—22no—
201D4×C11#12114yes—
202C2×C4×C11—22no—
203C2×C4×C11—21no—
204C2×C4×C11—22no—
205C2×C4×C11—21no—
206C2×C4×C11—22no—
207C2×C4×C11—22no—
208C2×C4×C11—22no—
209C2×C4×C11—22no—
210C2×C4×C11—22no—
211C2×C4×C11—41no—
212C2×C4×C11—41no—
213C2×C4×C11—41no—
214C2×C4×C11—41no—
215C2×C4×C11—48no—
216C2×C4×C11—41no—
217C2×C4×C11—42no—
218C2×C4×C11—42no—
219C2×C4×C11—42no—
220C2×C4×C11—42no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11—41no—
224C2×C4×C11—41no—
225C2×C4×C11—88no—
226C2×C4×C11#12112yes—
227C2×C4×C11#12112yes—
228C2×C4×C11C2×SD1614yes—
229C2×C4×C11C2×SD1612yes—
230C2×C4×C11#13712yes—
231C2×C4×C11C22×D411yescharacteristic
232C2×C4×C11C22×D411yescharacteristic
233C2×C4×C11C2×#4111yescharacteristic
234C2×C4×C11C2×#4111yescharacteristic
235C2×C4×C11H(5,𝔽2)11yescharacteristic
236C2×C4×C112−1+411yescharacteristic
237C8×C11—22no—
238C8×C11—42no—
239C8×C11—41no—
240C22×SD16C22×C1112yes—
241C22×SD16C22×C1111yescharacteristic
242C2×C4⋊Q8C22×C1111yescharacteristic
243C2×C4⋊Q8C22×C1112yes—
244C2×C4×Q8C22×C1111yescharacteristic
245C2×C4×D4C22×C1112yes—
246C2×C4×D4C22×C1111yescharacteristic
247C22×C4⋊C4—21no—
248#461—28no—
249#461—24no—
250C4×SD16—24no—
251C2×#106C22×C1111yescharacteristic
252C2×C4⋊C8C22×C1111yescharacteristic
253C2×C4⋊C8C22×C1112yes—
254C2×#103C22×C1112yes—
255C2×#103C22×C1112yes—
256C2×#103C22×C1112yes—
257C2×#103C22×C1111yescharacteristic
258C2×#103C22×C1112yes—
259C2×#102C22×C1111yescharacteristic
260C2×C4×C8C22×C1111yescharacteristic
261#398—22no—
262#391C22×C1112yes—
263#389—21no—
264#389—21no—
265#389C22×C1112yes—
266#385—22no—
267#384C22×C1111yescharacteristic
268#380—21no—
269C4×C4⋊C4C22×C1111yescharacteristic
270#340C22×C1112yes—
271#336C22×C1112yes—
272C22×C11—24no—
273C22×C11—42no—
274C22×C11—42no—
275C22×C11—42no—
276C22×C11—42no—
277C22×C11—42no—
278C22×C11—42no—
279C22×C11C2×#12111yescharacteristic
280C22×C11D4211yescharacteristic
281C22×C11#54811yescharacteristic
282C22×C11C22×SD1611yescharacteristic
283C22×C11C2×#13711yescharacteristic
284C22×C11#57711yescharacteristic
285C22×C11#57811yescharacteristic
286C4×C11—24no—
287C4×C11—22no—
288C4×C11—42no—
289C4×C11—42no—
290C4×C11—42no—
291C4×C11—82no—
292C4×C11—82no—
293C4×C11—81no—
294C4×C11#46114yescomplemented
295C4×C11C2×#12111yescharacteristic
296C4×C11#53711yescharacteristic
297C4×C11#54711yescharacteristic
298C4×C11#55311yescharacteristic
299C22×Q8C23×C1112yes—
300C22×Q8C23×C1111yescharacteristic
301C22×D4C23×C1111yescharacteristic
302C23×C4—21no—
303C23×C4—22no—
304C2×SD16—22no—
305C2×SD16—22no—
306C2×SD16—24no—
307C2×SD16—24no—
308C2×SD16—24no—
309C2×SD16D4×C1114yes—
310C22×C8C23×C1112yes—
311C22×C8C23×C1111yescharacteristic
312C22×C8C23×C1111yescharacteristic
313C4⋊Q8—24no—
314C4⋊Q8—22no—
315C4⋊Q8—22no—
316C4⋊Q8—42no—
317C4×Q8—22no—
318C4×Q8—22no—
319C4×D4—24no—
320C4×D4—22no—
321C4×D4—42no—
322C4×D4D4×C1114yes—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—44no—
332C2×C4⋊C4D4×C1111yescharacteristic
333C2×C4⋊C4D4×C1111yescharacteristic
334C2×C4⋊C4C23×C1112yes—
335C2×C4⋊C4C23×C1111yescharacteristic
336C2×C4⋊C4C23×C1111yescharacteristic
337C2×C22⋊C4—21no—
338C2×C22⋊C4—22no—
339C2×C42—21no—
340C2×C42C23×C1112yes—
341C2×C42C23×C1111yescharacteristic
342#106—22no—
343C4⋊C8—24no—
344C4⋊C8—22no—
345#103—24no—
346#103—24no—
347#103—22no—
348#103—24no—
349#103—42no—
350#102—22no—
351C4×C8—22no—
352#95—22no—
353#95—22no—
354#95—22no—
355#95D4×C1112yes—
356C2×C11—44no—
357C2×C11#241611yescharacteristic
358C2×C11C2×#46111yescharacteristic
359C2×C11#304611yescharacteristic
360C2×C11#327611yescharacteristic
361C2×C11D4×SD1611yescharacteristic
362C2×C11#335911yescharacteristic
363C2×C11#337211yescharacteristic
364C24—21no—
365C2×Q8—21no—
366C2×Q8—21no—
367C2×Q8—22no—
368C2×Q8—22no—
369C2×Q8—21no—
370C2×Q8—21no—
371C2×Q8—22no—
372C2×Q8—22no—
373C2×Q8—22no—
374C2×Q8—21no—
375C2×Q8—22no—
376C2×Q8C2×D4×C1112yes—
377C2×D4—21no—
378C2×D4—21no—
379C2×D4—21no—
380C2×D4C2×D4×C1112yes—
381C2×D4C2×D4×C1112yes—
382C2×D4C11×#4112yes—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—24no—
386C22×C4—21no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—44no—
390C22×C4—42no—
391C22×C4—42no—
392C22×C4—44no—
393C22×C4—82no—
394C22×C4C2×D4×C1112yes—
395C22×C4C2×D4×C1111yescharacteristic
396C22×C4C2×D4×C1112yes—
397C22×C4C2×D4×C1111yescharacteristic
398C22×C4C24×C1111yescharacteristic
399SD16—28no—
400SD16—48no—
401C2×C8—21no—
402C2×C8—21no—
403C2×C8—21no—
404C2×C8—22no—
405C2×C8—22no—
406C2×C8—22no—
407C2×C8—21no—
408C2×C8—21no—
409C2×C8C2×D4×C1112yes—
410C4⋊C4—22no—
411C4⋊C4—21no—
412C4⋊C4—21no—
413C4⋊C4—22no—
414C4⋊C4—21no—
415C4⋊C4—22no—
416C4⋊C4—44no—
417C4⋊C4—44no—
418C4⋊C4—42no—
419C4⋊C4—42no—
420C4⋊C4—42no—
421C4⋊C4—44no—
422C4⋊C4—42no—
423C4⋊C4—81no—
424C4⋊C4C11×SD1614yescomplemented
425C4⋊C4C2×D4×C1112yes—
426C22⋊C4—24no—
427C22⋊C4—44no—
428C42—22no—
429C42—22no—
430C42—42no—
431C42C2×D4×C1112yes—
432C42C11×#4112yes—
433C11#2473011yescharacteristic, direct product factor, Sylow
434C23—22no—
435C23—22no—
436C23—22no—
437C23—41no—
438C23—41no—
439C23—41no—
440C23—41no—
441C23C22×D4×C1111yescharacteristic
442Q8—22no—
443Q8—22no—
444Q8—41no—
445Q8—41no—
446Q8—42no—
447Q8—42no—
448Q8—42no—
449Q8—42no—
450D4—22no—
451D4—22no—
452D4—22no—
453D4C11×#12114yes—
454C2×C4—22no—
455C2×C4—21no—
456C2×C4—22no—
457C2×C4—21no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—48no—
468C2×C4—41no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—88no—
478C2×C4C11×#12112yes—
479C2×C4C11×#12112yes—
480C2×C4C2×C11×SD1614yes—
481C2×C4C2×C11×SD1612yes—
482C2×C4C11×#13712yes—
483C2×C4C22×D4×C1111yescharacteristic
484C2×C4C22×D4×C1111yescharacteristic
485C2×C4C2×C11×#4111yescharacteristic
486C2×C4C2×C11×#4111yescharacteristic
487C2×C4C11×H(5,𝔽2)11yescharacteristic
488C2×C4C11×2−1+411yescharacteristic
489C8—22no—
490C8—42no—
491C8—41no—
492C22—24no—
493C22—42no—
494C22—42no—
495C22—42no—
496C22—42no—
497C22—42no—
498C22—42no—
499C22C2×C11×#12111yescharacteristic
500C22D42×C1111yescharacteristic
501C22C11×#54811yescharacteristic
502C22C22×C11×SD1611yescharacteristic
503C22C2×C11×#13711yescharacteristic
504C22C11×#57711yescharacteristic
505C22C11×#57811yescharacteristic
506C4—24no—
507C4—22no—
508C4—42no—
509C4—42no—
510C4—42no—
511C4—82no—
512C4—82no—
513C4—81no—
514C4C11×#46114yescomplemented
515C4C2×C11×#12111yescharacteristic
516C4C11×#53711yescharacteristic
517C4C11×#54711yescharacteristic
518C4C11×#55311yescharacteristic
519C2—44no—
520C2C11×#241611yescharacteristic
521C2C2×C11×#46111yescharacteristic
522C2C11×#304611yescharacteristic
523C2C11×#327611yescharacteristic
524C2D4×C11×SD1611yescharacteristic
525C2C11×#335911yescharacteristic
526C2C11×#337211yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C4×C11×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
4. C11×#2546C2semidirect
6. C11×#2066C2semidirect
7. C11×#2043C2semidirect
8. C11×#1956C2semidirect
9. C11×#1939C2semidirect
11. C11×#1803C2semidirect
101. #24730C11direct (N × H)
162. C11×C4⋊C4SD16semidirect
174. #2546C2×C11semidirect
176. #2066C2×C11semidirect
177. #2043C2×C11semidirect
178. #1956C2×C11semidirect
179. #1939C2×C11semidirect
181. #1803C2×C11semidirect
294. C4×C11#461semidirect
424. C4⋊C4C11×SD16semidirect
433. C11#24730direct (N × H)
514. C4C11×#461semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#4612
C2×C4×C11×SD162
C11×#25462
D4×C11×C4⋊C42
C11×#20662
C11×#20432
C11×#19562
C11×#19392
C11×#18772
C11×#18032
#2473011