Finite Group Databasebeta

← C11×#24338 #14601531

Subgroups — C11×#24338 #14601531

Order 2816.

1296 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×Q8×C11C211yesmaximal, characteristic, complemented
2C2×C11×#476C211yesmaximal, characteristic, complemented
3C2×C11×#442C211yesmaximal, characteristic
4C11×#2580C211yesmaximal, characteristic, complemented
5C11×#2058C212yesmaximal, complemented
6C11×#2023C212yesmaximal, complemented
7C11×#1993C211yesmaximal, characteristic, complemented
8C11×#1985C211yesmaximal, characteristic, complemented
9C11×#1879C212yesmaximal
10C11×#1864C212yesmaximal, complemented
11C11×#1804C211yesmaximal, characteristic, complemented
12C23×Q8×C11—21no—
13C22×C11×D8C2211yescharacteristic
14D4×Q8×C11—24no—
15D4×Q8×C11—24no—
16C2×C11×C4⋊Q8C2212yes—
17C2×C11×C4⋊Q8C2211yescharacteristic
18C2×C11×C22⋊Q8—22no—
19C2×C11×C22⋊Q8—21no—
20C2×C4×Q8×C11C2211yescharacteristic
21C2×C4×D4×C11C2212yes—
22C2×C4×D4×C11C2211yescharacteristic
23C2×C4×D4×C11C2211yescharacteristic
24C11×#476—24no—
25C11×#442—24no—
26C2×C11×#106C2211yescharacteristic
27C2×C11×#106C2212yes—
28C2×C11×C4⋊C8C2211yescharacteristic
29C2×C11×#102C2212yes—
30C2×C11×#102C2212yes—
31C2×C11×#102C2211yescharacteristic
32C2×C11×#102C2211yescharacteristic
33C2×C11×#97C2211yescharacteristic
34C11×#399—21no—
35C11×#393—21no—
36C11×#390C2212yes—
37C11×#389C2212yes—
38C11×#385—22no—
39C11×#382C2211yescharacteristic
40C11×#340C2212yes—
41C11×#340C2212yes—
42C11×#340C2212yes—
43C11×#336C2212yes—
44C11×#336C2212yes—
45C22×Q8×C11—28no—
46C22×Q8×C11—21no—
47C22×Q8×C11—22no—
48C22×Q8×C11—48no—
49C22×Q8×C11D411yescharacteristic
50C22×D4×C11C2311yescharacteristic
51C22×D4×C11C2311yescharacteristic
52C23×C4×C11—22no—
53C23×C4×C11—21no—
54C23×C4×C11—21no—
55C2×C11×D8—22no—
56C2×C11×D8—22no—
57C2×C11×D8Q814yescomplemented
58C22×C8×C11C2311yescharacteristic
59C22×C8×C11C2312yes—
60C22×C8×C11C2311yescharacteristic
61C11×C4⋊Q8—24no—
62C11×C4⋊Q8—24no—
63C11×C4⋊Q8—22no—
64C11×C4⋊Q8D414yes—
65C11×C22⋊Q8—28no—
66C11×C22⋊Q8—216no—
67C4×Q8×C11—22no—
68C4×Q8×C11—22no—
69C4×D4×C11—24no—
70C4×D4×C11—24no—
71C4×D4×C11—22no—
72C4×D4×C11—22no—
73C4×D4×C11—22no—
74C4×D4×C11D414yes—
75C2×C11×C4⋊C4—22no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—22no—
78C2×C11×C4⋊C4D412yes—
79C2×C11×C4⋊C4D411yescharacteristic
80C2×C11×C4⋊C4C2312yes—
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C4⋊C4C2312yes—
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C22⋊C4—22no—
85C2×C11×C22⋊C4—21no—
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4—22no—
88C2×C11×C22⋊C4—22no—
89C2×C42×C11C2312yes—
90C2×C42×C11C2311yescharacteristic
91C11×#106—22no—
92C11×#106—24no—
93C11×C4⋊C8—22no—
94C11×#102—22no—
95C11×#102—24no—
96C11×#102—22no—
97C11×#102—24no—
98C11×#97—22no—
99C11×#95—21no—
100C11×#95—21no—
101C11×#95—22no—
102#24338C1111yesmaximal, characteristic, direct product factor, Sylow
103C24×C11—21no—
104C24×C11—21no—
105C2×Q8×C11—28no—
106C2×Q8×C11—22no—
107C2×Q8×C11—24no—
108C2×Q8×C11—24no—
109C2×Q8×C11—44no—
110C2×Q8×C11—44no—
111C2×Q8×C11—432no—
112C2×Q8×C11—44no—
113C2×D4×C11—21no—
114C2×D4×C11—21no—
115C2×D4×C11—21no—
116C2×D4×C11—21no—
117C2×D4×C11—21no—
118C2×D4×C11—21no—
119C2×D4×C11—21no—
120C2×D4×C11—21no—
121C2×D4×C11C2×D412yes—
122C2×D4×C11C2×Q812yes—
123C2×D4×C11C2×Q812yescomplemented
124C2×D4×C11#4112yes—
125C22×C4×C11—28no—
126C22×C4×C11—22no—
127C22×C4×C11—21no—
128C22×C4×C11—24no—
129C22×C4×C11—22no—
130C22×C4×C11—21no—
131C22×C4×C11—44no—
132C22×C4×C11—44no—
133C22×C4×C11—44no—
134C22×C4×C11—42no—
135C22×C4×C11—82no—
136C22×C4×C11C2×D412yes—
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D412yes—
140C22×C4×C11C2411yescharacteristic
141C11×D8—28no—
142C2×C8×C11—21no—
143C2×C8×C11—21no—
144C2×C8×C11—22no—
145C2×C8×C11—21no—
146C2×C8×C11—22no—
147C2×C8×C11—21no—
148C2×C8×C11—22no—
149C2×C8×C11—21no—
150C2×C8×C11C2×Q812yescomplemented
151C11×C4⋊C4—28no—
152C11×C4⋊C4—24no—
153C11×C4⋊C4—24no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—22no—
160C11×C4⋊C4—22no—
161C11×C4⋊C4—82no—
162C11×C4⋊C4C2×D414yes—
163C11×C4⋊C4C2×D412yes—
164C11×C22⋊C4—28no—
165C11×C22⋊C4—24no—
166C11×C22⋊C4—42no—
167C11×C22⋊C4—44no—
168C11×C22⋊C4—82no—
169C42×C11—22no—
170C42×C11—22no—
171C42×C11C2×D412yes—
172C42×C11C2×D412yes—
173C2×D4×Q8C2×C1111yescharacteristic, complemented
174C2×#476C2×C1111yescharacteristic, complemented
175C2×#442C2×C1111yescharacteristic
176#2580C2×C1111yescharacteristic, complemented
177#2058C2×C1112yescomplemented
178#2023C2×C1112yescomplemented
179#1993C2×C1111yescharacteristic, complemented
180#1985C2×C1111yescharacteristic, complemented
181#1879C2×C1112yes—
182#1864C2×C1112yescomplemented
183#1804C2×C1111yescharacteristic, complemented
184C23×C11—22no—
185C23×C11—22no—
186C23×C11—22no—
187C23×C11—22no—
188C23×C11—42no—
189C23×C11—42no—
190C23×C11—41no—
191C23×C11—41no—
192C23×C11—42no—
193C23×C11—42no—
194C23×C11C22×D411yescharacteristic
195Q8×C11—28no—
196Q8×C11—48no—
197Q8×C11—416no—
198D4×C11—22no—
199D4×C11—22no—
200D4×C11—22no—
201D4×C11—22no—
202D4×C11—22no—
203D4×C11—41no—
204D4×C11—41no—
205D4×C11C22⋊Q814yes—
206C2×C4×C11—22no—
207C2×C4×C11—22no—
208C2×C4×C11—22no—
209C2×C4×C11—22no—
210C2×C4×C11—22no—
211C2×C4×C11—24no—
212C2×C4×C11—22no—
213C2×C4×C11—22no—
214C2×C4×C11—22no—
215C2×C4×C11—48no—
216C2×C4×C11—416no—
217C2×C4×C11—42no—
218C2×C4×C11—42no—
219C2×C4×C11—42no—
220C2×C4×C11—41no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11—42no—
224C2×C4×C11—42no—
225C2×C4×C11—84no—
226C2×C4×C11#12012yes—
227C2×C4×C11#12012yes—
228C2×C4×C11AGL(1,ℤ/8)14yes—
229C2×C4×C11C22×D411yescharacteristic
230C2×C4×C11C22×D411yescharacteristic
231C2×C4×C11C22×Q811yescharacteristic
232C2×C4×C11C2×#4111yescharacteristic
233C2×C4×C112−1+411yescharacteristic
234C2×C4×C112−1+411yescharacteristic
235C8×C11—22no—
236C8×C11—41no—
237C8×C11—42no—
238C23×Q8—21no—
239C22×D8C22×C1111yescharacteristic
240D4×Q8—24no—
241D4×Q8—24no—
242C2×C4⋊Q8C22×C1112yes—
243C2×C4⋊Q8C22×C1111yescharacteristic
244C2×C22⋊Q8—22no—
245C2×C22⋊Q8—21no—
246C2×C4×Q8C22×C1111yescharacteristic
247C2×C4×D4C22×C1111yescharacteristic
248C2×C4×D4C22×C1112yes—
249C2×C4×D4C22×C1111yescharacteristic
250#476—24no—
251#442—24no—
252C2×#106C22×C1111yescharacteristic
253C2×#106C22×C1112yes—
254C2×C4⋊C8C22×C1111yescharacteristic
255C2×#102C22×C1112yes—
256C2×#102C22×C1111yescharacteristic
257C2×#102C22×C1112yes—
258C2×#102C22×C1111yescharacteristic
259C2×#97C22×C1111yescharacteristic
260#399—21no—
261#393—21no—
262#390C22×C1112yes—
263#389C22×C1112yes—
264#385—22no—
265#382C22×C1111yescharacteristic
266#340C22×C1112yes—
267#340C22×C1112yes—
268#340C22×C1112yes—
269#336C22×C1112yes—
270#336C22×C1112yes—
271C22×C11—24no—
272C22×C11—44no—
273C22×C11—44no—
274C22×C11—42no—
275C22×C11—42no—
276C22×C11—44no—
277C22×C11—42no—
278C22×C11—82no—
279C22×C11—81no—
280C22×C11—81no—
281C22×C11C2×#12011yescharacteristic
282C22×C11#54811yescharacteristic
283C22×C11D4×Q811yescharacteristic
284C22×C11C2×AGL(1,ℤ/8)12yes—
285C22×C11#57712yes—
286C4×C11—22no—
287C4×C11—24no—
288C4×C11—22no—
289C4×C11—44no—
290C4×C11—42no—
291C4×C11—42no—
292C4×C11—82no—
293C4×C11—81no—
294C4×C11C2×C22⋊Q811yescharacteristic
295C4×C11#53611yescharacteristic
296C4×C11#54811yescharacteristic
297C4×C11D4×Q811yescharacteristic
298C22×Q8—28no—
299C22×Q8—21no—
300C22×Q8—22no—
301C22×Q8—48no—
302C22×Q8D4×C1111yescharacteristic
303C22×D4C23×C1111yescharacteristic
304C22×D4C23×C1111yescharacteristic
305C23×C4—22no—
306C23×C4—21no—
307C23×C4—21no—
308C2×D8—22no—
309C2×D8—22no—
310C2×D8Q8×C1114yescomplemented
311C22×C8C23×C1111yescharacteristic
312C22×C8C23×C1112yes—
313C22×C8C23×C1111yescharacteristic
314C4⋊Q8—24no—
315C4⋊Q8—24no—
316C4⋊Q8—22no—
317C4⋊Q8D4×C1114yes—
318C22⋊Q8—28no—
319C22⋊Q8—216no—
320C4×Q8—22no—
321C4×Q8—22no—
322C4×D4—24no—
323C4×D4—24no—
324C4×D4—22no—
325C4×D4—22no—
326C4×D4—22no—
327C4×D4D4×C1114yes—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4D4×C1112yes—
332C2×C4⋊C4D4×C1111yescharacteristic
333C2×C4⋊C4C23×C1111yescharacteristic
334C2×C4⋊C4C23×C1112yes—
335C2×C4⋊C4C23×C1112yes—
336C2×C4⋊C4C23×C1111yescharacteristic
337C2×C22⋊C4—22no—
338C2×C22⋊C4—21no—
339C2×C22⋊C4—21no—
340C2×C22⋊C4—22no—
341C2×C22⋊C4—22no—
342C2×C42C23×C1112yes—
343C2×C42C23×C1111yescharacteristic
344#106—22no—
345#106—24no—
346C4⋊C8—22no—
347#102—22no—
348#102—24no—
349#102—22no—
350#102—24no—
351#97—22no—
352#95—21no—
353#95—21no—
354#95—22no—
355C2×C11—44no—
356C2×C11—82no—
357C2×C11#240911yescharacteristic
358C2×C11#300311yescharacteristic
359C2×C11#301011yescharacteristic
360C2×C11#337312yes—
361C2×C11#338412yes—
362C24—21no—
363C24—21no—
364C2×Q8—28no—
365C2×Q8—22no—
366C2×Q8—24no—
367C2×Q8—24no—
368C2×Q8—44no—
369C2×Q8—44no—
370C2×Q8—432no—
371C2×Q8—44no—
372C2×D4—21no—
373C2×D4—21no—
374C2×D4—21no—
375C2×D4—21no—
376C2×D4—21no—
377C2×D4—21no—
378C2×D4—21no—
379C2×D4—21no—
380C2×D4C2×D4×C1112yes—
381C2×D4C2×Q8×C1112yes—
382C2×D4C2×Q8×C1112yescomplemented
383C2×D4C11×#4112yes—
384C22×C4—28no—
385C22×C4—22no—
386C22×C4—21no—
387C22×C4—24no—
388C22×C4—22no—
389C22×C4—21no—
390C22×C4—44no—
391C22×C4—44no—
392C22×C4—44no—
393C22×C4—42no—
394C22×C4—82no—
395C22×C4C2×D4×C1112yes—
396C22×C4C2×D4×C1111yescharacteristic
397C22×C4C2×D4×C1111yescharacteristic
398C22×C4C2×D4×C1112yes—
399C22×C4C24×C1111yescharacteristic
400D8—28no—
401C2×C8—21no—
402C2×C8—21no—
403C2×C8—21no—
404C2×C8—22no—
405C2×C8—22no—
406C2×C8—21no—
407C2×C8—21no—
408C2×C8—22no—
409C2×C8C2×Q8×C1112yescomplemented
410C4⋊C4—28no—
411C4⋊C4—24no—
412C4⋊C4—24no—
413C4⋊C4—22no—
414C4⋊C4—22no—
415C4⋊C4—21no—
416C4⋊C4—21no—
417C4⋊C4—21no—
418C4⋊C4—22no—
419C4⋊C4—22no—
420C4⋊C4—82no—
421C4⋊C4C2×D4×C1114yes—
422C4⋊C4C2×D4×C1112yes—
423C22⋊C4—28no—
424C22⋊C4—24no—
425C22⋊C4—42no—
426C22⋊C4—44no—
427C22⋊C4—82no—
428C42—22no—
429C42—22no—
430C42C2×D4×C1112yes—
431C42C2×D4×C1112yes—
432C11#2433811yescharacteristic, direct product factor, Sylow
433C23—22no—
434C23—22no—
435C23—22no—
436C23—22no—
437C23—42no—
438C23—42no—
439C23—41no—
440C23—41no—
441C23—42no—
442C23—42no—
443C23C22×D4×C1111yescharacteristic
444Q8—28no—
445Q8—48no—
446Q8—416no—
447D4—22no—
448D4—22no—
449D4—22no—
450D4—22no—
451D4—22no—
452D4—41no—
453D4—41no—
454D4C11×C22⋊Q814yes—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—24no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—48no—
465C2×C4—416no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—41no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—84no—
475C2×C4C11×#12012yes—
476C2×C4C11×#12012yes—
477C2×C4C11×AGL(1,ℤ/8)14yes—
478C2×C4C22×D4×C1111yescharacteristic
479C2×C4C22×D4×C1111yescharacteristic
480C2×C4C22×Q8×C1111yescharacteristic
481C2×C4C2×C11×#4111yescharacteristic
482C2×C4C11×2−1+411yescharacteristic
483C2×C4C11×2−1+411yescharacteristic
484C8—22no—
485C8—41no—
486C8—42no—
487C22—24no—
488C22—42no—
489C22—42no—
490C22—44no—
491C22—44no—
492C22—42no—
493C22—44no—
494C22—81no—
495C22—81no—
496C22—82no—
497C22C2×C11×#12011yescharacteristic
498C22C11×#54811yescharacteristic
499C22D4×Q8×C1111yescharacteristic
500C22C2×C11×AGL(1,ℤ/8)12yes—
501C22C11×#57712yes—
502C4—22no—
503C4—24no—
504C4—22no—
505C4—44no—
506C4—42no—
507C4—42no—
508C4—81no—
509C4—82no—
510C4C2×C11×C22⋊Q811yescharacteristic
511C4C11×#53611yescharacteristic
512C4C11×#54811yescharacteristic
513C4D4×Q8×C1111yescharacteristic
514C2—44no—
515C2—82no—
516C2C11×#240911yescharacteristic
517C2C11×#300311yescharacteristic
518C2C11×#301011yescharacteristic
519C2C11×#337312yes—
520C2C11×#338412yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×C11×D8C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C4×Q8×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×D4×Q8×C11C2semidirect
2. C2×C11×#476C2semidirect
4. C11×#2580C2semidirect
5. C11×#2058C2semidirect
6. C11×#2023C2semidirect
7. C11×#1993C2semidirect
8. C11×#1985C2semidirect
10. C11×#1864C2semidirect
11. C11×#1804C2semidirect
57. C2×C11×D8Q8semidirect
102. #24338C11direct (N × H)
123. C2×D4×C11C2×Q8semidirect
150. C2×C8×C11C2×Q8semidirect
173. C2×D4×Q8C2×C11semidirect
174. C2×#476C2×C11semidirect
176. #2580C2×C11semidirect
177. #2058C2×C11semidirect
178. #2023C2×C11semidirect
179. #1993C2×C11semidirect
180. #1985C2×C11semidirect
182. #1864C2×C11semidirect
183. #1804C2×C11semidirect
310. C2×D8Q8×C11semidirect
382. C2×D4C2×Q8×C11semidirect
409. C2×C8C2×Q8×C11semidirect
432. C11#24338direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D4×Q8×C112
C2×C11×#4762
C2×C11×#4422
C11×#25802
C11×#20582
C11×#20232
C11×#19932
C11×#19852
C11×#18792
C11×#18642
C11×#18042
#2433811