Finite Group Databasebeta

← C11×#23003 #14600196

Subgroups — C11×#23003 #14600196

Order 2816.

1054 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#460C211yesmaximal, characteristic
2C2×C11×#440C212yesmaximal, complemented
3C11×#2366C211yesmaximal, characteristic
4Q8×C11×C4⋊C4C211yesmaximal, characteristic, complemented
5C11×#1957C211yesmaximal, characteristic
6C11×#1947C211yesmaximal, characteristic, complemented
7C11×#1936C212yesmaximal, complemented
8C11×#1880C212yesmaximal, complemented
9C11×#1862C212yesmaximal, complemented
10C11×#1770C211yesmaximal, characteristic, complemented
11C4×C11×#103C211yesmaximal, characteristic, complemented
12C22×C11×SD16C2212yes—
13C2×C11×#127C2211yescharacteristic
14C2×C4×Q8×C11C2212yes—
15C2×C4×Q8×C11C2211yescharacteristic
16C2×C4×D4×C11—21no—
17C2×C4×D4×C11C2212yes—
18C11×#460C418yescomplemented
19C11×#440—28no—
20C2×C11×#107C2212yes—
21C2×C11×C4⋊C8C2211yescharacteristic
22C2×C11×#103C2211yescharacteristic
23C2×C11×#103C2211yescharacteristic
24C2×C11×#102C2212yes—
25C2×C11×#102C2212yes—
26C2×C11×#102C2212yes—
27C2×C11×#97C2212yes—
28C2×C4×C8×C11C2211yescharacteristic
29C11×#390—21no—
30C11×#390C2212yes—
31C11×#389—22no—
32C11×#389C2212yes—
33C11×#386—22no—
34C11×#384—21no—
35C11×#384C2211yescharacteristic
36C4×C11×C4⋊C4—21no—
37C4×C11×C4⋊C4C2211yescharacteristic
38C4×C11×C4⋊C4C2211yescharacteristic
39C11×#340C2212yes—
40C11×#340C2211yescharacteristic
41C11×#340C2211yescharacteristic
42C11×#336C2212yes—
43C22×Q8×C11C2311yescharacteristic
44C22×D4×C11—21no—
45C22×D4×C11—21no—
46C22×D4×C11C2312yes—
47C23×C4×C11—22no—
48C2×C11×SD16—24no—
49C2×C11×SD16—24no—
50C2×C11×SD16C2×C418yescomplemented
51C22×C8×C11C2311yescharacteristic
52C22×C8×C11C2312yes—
53C22×C8×C11C2311yescharacteristic
54C11×#127—22no—
55C11×#127C2×C414yes—
56C4×Q8×C11—22no—
57C4×Q8×C11—24no—
58C4×Q8×C11—42no—
59C4×Q8×C11C2×C414yescomplemented
60C4×D4×C11—24no—
61C4×D4×C11—42no—
62C4×D4×C11—44no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—22no—
66C2×C11×C4⋊C4—22no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4D411yescharacteristic
69C2×C11×C4⋊C4D411yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2312yes—
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C22⋊C4—22no—
75C2×C11×C22⋊C4—22no—
76C2×C11×C22⋊C4—22no—
77C2×C42×C11—21no—
78C2×C42×C11—21no—
79C2×C42×C11—22no—
80C2×C42×C11C2312yes—
81C2×C42×C11C2311yescharacteristic
82C11×#107—24no—
83C11×C4⋊C8C2×C414yescomplemented
84C11×#103—22no—
85C11×#103D414yescomplemented
86C11×#102—24no—
87C11×#102—42no—
88C11×#102C2×C418yescomplemented
89C11×#97—24no—
90C4×C8×C11—22no—
91C11×#95—22no—
92C11×#95—21no—
93C11×#95D412yes—
94#23003C1111yesmaximal, characteristic, direct product factor, Sylow
95C24×C11—22no—
96C2×Q8×C11—21no—
97C2×Q8×C11—21no—
98C2×Q8×C11—21no—
99C2×Q8×C11C22×C412yes—
100C2×Q8×C11C2×D412yes—
101C2×Q8×C11#4112yes—
102C2×D4×C11—24no—
103C2×D4×C11—24no—
104C2×D4×C11—22no—
105C2×D4×C11—22no—
106C2×D4×C11—22no—
107C2×D4×C11—22no—
108C2×D4×C11—22no—
109C2×D4×C11—42no—
110C2×D4×C11—42no—
111C2×D4×C11—81no—
112C2×D4×C11—81no—
113C2×D4×C11C22×C414yes—
114C22×C4×C11—21no—
115C22×C4×C11—21no—
116C22×C4×C11—21no—
117C22×C4×C11—21no—
118C22×C4×C11—22no—
119C22×C4×C11—44no—
120C22×C4×C11—44no—
121C22×C4×C11—82no—
122C22×C4×C11C2×D412yes—
123C22×C4×C11C2×D412yes—
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2411yescharacteristic
127C11×SD16—216no—
128C2×C8×C11—22no—
129C2×C8×C11—21no—
130C2×C8×C11—22no—
131C2×C8×C11—21no—
132C2×C8×C11—21no—
133C2×C8×C11—21no—
134C2×C8×C11—21no—
135C2×C8×C11C22×C414yes—
136C2×C8×C11C2×D412yes—
137C11×C4⋊C4—24no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4—22no—
140C11×C4⋊C4—21no—
141C11×C4⋊C4—21no—
142C11×C4⋊C4—22no—
143C11×C4⋊C4—21no—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—21no—
146C11×C4⋊C4—44no—
147C11×C4⋊C4—42no—
148C11×C4⋊C4—81no—
149C11×C4⋊C4—82no—
150C11×C4⋊C4C22×C412yes—
151C11×C4⋊C4C2×D412yes—
152C11×C22⋊C4—44no—
153C11×C22⋊C4—44no—
154C11×C22⋊C4—82no—
155C42×C11—24no—
156C42×C11—22no—
157C42×C11—22no—
158C42×C11—44no—
159C42×C11—42no—
160C42×C11C22×C412yes—
161C42×C11#4112yes—
162C2×#460C2×C1111yescharacteristic
163C2×#440C2×C1112yescomplemented
164#2366C2×C1111yescharacteristic
165Q8×C4⋊C4C2×C1111yescharacteristic, complemented
166#1957C2×C1111yescharacteristic
167#1947C2×C1111yescharacteristic, complemented
168#1936C2×C1112yescomplemented
169#1880C2×C1112yescomplemented
170#1862C2×C1112yescomplemented
171#1770C2×C1111yescharacteristic, complemented
172C4×#103C2×C1111yescharacteristic, complemented
173C23×C11—24no—
174C23×C11—42no—
175C23×C11—42no—
176C23×C11—42no—
177C23×C11—42no—
178C23×C11—42no—
179C23×C11—42no—
180C23×C11C22×D411yescharacteristic
181Q8×C11—22no—
182Q8×C11—22no—
183Q8×C11—22no—
184Q8×C11C4×D414yescomplemented
185D4×C11—24no—
186D4×C11—24no—
187D4×C11—42no—
188D4×C11—42no—
189D4×C11—48no—
190D4×C11—84no—
191C2×C4×C11—22no—
192C2×C4×C11—22no—
193C2×C4×C11—22no—
194C2×C4×C11—21no—
195C2×C4×C11—21no—
196C2×C4×C11—22no—
197C2×C4×C11—22no—
198C2×C4×C11—22no—
199C2×C4×C11—22no—
200C2×C4×C11—22no—
201C2×C4×C11—22no—
202C2×C4×C11—22no—
203C2×C4×C11—22no—
204C2×C4×C11—41no—
205C2×C4×C11—41no—
206C2×C4×C11—41no—
207C2×C4×C11—41no—
208C2×C4×C11—42no—
209C2×C4×C11—41no—
210C2×C4×C11—41no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11—41no—
214C2×C4×C11—88no—
215C2×C4×C11C4×D412yes—
216C2×C4×C11C4×D412yes—
217C2×C4×C11AGL(1,ℤ/8)12yes—
218C2×C4×C11#13712yes—
219C2×C4×C11C23×C411yescharacteristic
220C2×C4×C11C22×D411yescharacteristic
221C2×C4×C11C2×#4111yescharacteristic
222C2×C4×C11C2×#4111yescharacteristic
223C2×C4×C11H(5,𝔽2)11yescharacteristic
224C2×C4×C112−1+411yescharacteristic
225C8×C11—24no—
226C8×C11—22no—
227C8×C11—41no—
228C22×SD16C22×C1112yes—
229C2×#127C22×C1111yescharacteristic
230C2×C4×Q8C22×C1112yes—
231C2×C4×Q8C22×C1111yescharacteristic
232C2×C4×D4—21no—
233C2×C4×D4C22×C1112yes—
234#460C4×C1118yescomplemented
235#440—28no—
236C2×#107C22×C1112yes—
237C2×C4⋊C8C22×C1111yescharacteristic
238C2×#103C22×C1111yescharacteristic
239C2×#103C22×C1111yescharacteristic
240C2×#102C22×C1112yes—
241C2×#102C22×C1112yes—
242C2×#102C22×C1112yes—
243C2×#97C22×C1112yes—
244C2×C4×C8C22×C1111yescharacteristic
245#390—21no—
246#390C22×C1112yes—
247#389—22no—
248#389C22×C1112yes—
249#386—22no—
250#384—21no—
251#384C22×C1111yescharacteristic
252C4×C4⋊C4—21no—
253C4×C4⋊C4C22×C1111yescharacteristic
254C4×C4⋊C4C22×C1111yescharacteristic
255#340C22×C1111yescharacteristic
256#340C22×C1112yes—
257#340C22×C1111yescharacteristic
258#336C22×C1112yes—
259C22×C11—44no—
260C22×C11—44no—
261C22×C11—44no—
262C22×C11—82no—
263C22×C11—82no—
264C22×C11—82no—
265C22×C11—82no—
266C22×C11C2×C4×D411yescharacteristic
267C22×C11D4211yescharacteristic
268C22×C11#54811yescharacteristic
269C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
270C22×C11C2×#13711yescharacteristic
271C22×C11#57611yescharacteristic
272C22×C11#57711yescharacteristic
273C4×C11—24no—
274C4×C11—22no—
275C4×C11—42no—
276C4×C11—42no—
277C4×C11—42no—
278C4×C11—42no—
279C4×C11—81no—
280C4×C11—82no—
281C4×C11#44014yescomplemented
282C4×C11C2×C4×D411yescharacteristic
283C4×C11#52011yescharacteristic
284C4×C11#54711yescharacteristic
285C4×C11#55311yescharacteristic
286C22×Q8C23×C1111yescharacteristic
287C22×D4—21no—
288C22×D4—21no—
289C22×D4C23×C1112yes—
290C23×C4—22no—
291C2×SD16—24no—
292C2×SD16—24no—
293C2×SD16C2×C4×C1118yescomplemented
294C22×C8C23×C1111yescharacteristic
295C22×C8C23×C1112yes—
296C22×C8C23×C1111yescharacteristic
297#127—22no—
298#127C2×C4×C1114yes—
299C4×Q8—22no—
300C4×Q8—24no—
301C4×Q8—42no—
302C4×Q8C2×C4×C1114yescomplemented
303C4×D4—24no—
304C4×D4—42no—
305C4×D4—44no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4D4×C1111yescharacteristic
312C2×C4⋊C4D4×C1111yescharacteristic
313C2×C4⋊C4C23×C1112yes—
314C2×C4⋊C4C23×C1111yescharacteristic
315C2×C4⋊C4C23×C1111yescharacteristic
316C2×C4⋊C4C23×C1111yescharacteristic
317C2×C22⋊C4—22no—
318C2×C22⋊C4—22no—
319C2×C22⋊C4—22no—
320C2×C42—21no—
321C2×C42—21no—
322C2×C42—22no—
323C2×C42C23×C1112yes—
324C2×C42C23×C1111yescharacteristic
325#107—24no—
326C4⋊C8C2×C4×C1114yescomplemented
327#103—22no—
328#103D4×C1114yescomplemented
329#102—24no—
330#102—42no—
331#102C2×C4×C1118yescomplemented
332#97—24no—
333C4×C8—22no—
334#95—22no—
335#95—21no—
336#95D4×C1112yes—
337C2×C11—84no—
338C2×C11#236111yescharacteristic
339C2×C11C2×#44011yescharacteristic
340C2×C11#294611yescharacteristic
341C2×C11#327411yescharacteristic
342C2×C11#327811yescharacteristic
343C2×C11#336811yescharacteristic
344C2×C11#337511yescharacteristic
345C24—22no—
346C2×Q8—21no—
347C2×Q8—21no—
348C2×Q8—21no—
349C2×Q8C22×C4×C1112yes—
350C2×Q8C2×D4×C1112yes—
351C2×Q8C11×#4112yes—
352C2×D4—24no—
353C2×D4—24no—
354C2×D4—22no—
355C2×D4—22no—
356C2×D4—22no—
357C2×D4—22no—
358C2×D4—22no—
359C2×D4—42no—
360C2×D4—42no—
361C2×D4—81no—
362C2×D4—81no—
363C2×D4C22×C4×C1114yes—
364C22×C4—21no—
365C22×C4—21no—
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—22no—
369C22×C4—44no—
370C22×C4—44no—
371C22×C4—82no—
372C22×C4C2×D4×C1112yes—
373C22×C4C2×D4×C1112yes—
374C22×C4C2×D4×C1111yescharacteristic
375C22×C4C2×D4×C1111yescharacteristic
376C22×C4C24×C1111yescharacteristic
377SD16—216no—
378C2×C8—22no—
379C2×C8—21no—
380C2×C8—22no—
381C2×C8—21no—
382C2×C8—21no—
383C2×C8—21no—
384C2×C8—21no—
385C2×C8C22×C4×C1114yes—
386C2×C8C2×D4×C1112yes—
387C4⋊C4—24no—
388C4⋊C4—22no—
389C4⋊C4—22no—
390C4⋊C4—21no—
391C4⋊C4—21no—
392C4⋊C4—22no—
393C4⋊C4—21no—
394C4⋊C4—22no—
395C4⋊C4—21no—
396C4⋊C4—44no—
397C4⋊C4—42no—
398C4⋊C4—81no—
399C4⋊C4—82no—
400C4⋊C4C22×C4×C1112yes—
401C4⋊C4C2×D4×C1112yes—
402C22⋊C4—44no—
403C22⋊C4—44no—
404C22⋊C4—82no—
405C42—24no—
406C42—22no—
407C42—22no—
408C42—44no—
409C42—42no—
410C42C22×C4×C1112yes—
411C42C11×#4112yes—
412C11#2300311yescharacteristic, direct product factor, Sylow
413C23—24no—
414C23—42no—
415C23—42no—
416C23—42no—
417C23—42no—
418C23—42no—
419C23—42no—
420C23C22×D4×C1111yescharacteristic
421Q8—22no—
422Q8—22no—
423Q8—22no—
424Q8C4×D4×C1114yescomplemented
425D4—24no—
426D4—24no—
427D4—42no—
428D4—42no—
429D4—48no—
430D4—84no—
431C2×C4—22no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—21no—
435C2×C4—21no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—22no—
440C2×C4—22no—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—42no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—42no—
452C2×C4—42no—
453C2×C4—41no—
454C2×C4—88no—
455C2×C4C4×D4×C1112yes—
456C2×C4C4×D4×C1112yes—
457C2×C4C11×AGL(1,ℤ/8)12yes—
458C2×C4C11×#13712yes—
459C2×C4C23×C4×C1111yescharacteristic
460C2×C4C22×D4×C1111yescharacteristic
461C2×C4C2×C11×#4111yescharacteristic
462C2×C4C2×C11×#4111yescharacteristic
463C2×C4C11×H(5,𝔽2)11yescharacteristic
464C2×C4C11×2−1+411yescharacteristic
465C8—24no—
466C8—22no—
467C8—41no—
468C22—44no—
469C22—44no—
470C22—44no—
471C22—82no—
472C22—82no—
473C22—82no—
474C22—82no—
475C22C2×C4×D4×C1111yescharacteristic
476C22D42×C1111yescharacteristic
477C22C11×#54811yescharacteristic
478C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
479C22C2×C11×#13711yescharacteristic
480C22C11×#57611yescharacteristic
481C22C11×#57711yescharacteristic
482C4—22no—
483C4—24no—
484C4—42no—
485C4—42no—
486C4—42no—
487C4—42no—
488C4—82no—
489C4—81no—
490C4C11×#44014yescomplemented
491C4C2×C4×D4×C1111yescharacteristic
492C4C11×#52011yescharacteristic
493C4C11×#54711yescharacteristic
494C4C11×#55311yescharacteristic
495C2—84no—
496C2C11×#236111yescharacteristic
497C2C2×C11×#44011yescharacteristic
498C2C11×#294611yescharacteristic
499C2C11×#327411yescharacteristic
500C2C11×#327811yescharacteristic
501C2C11×#336811yescharacteristic
502C2C11×#337511yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#127C22
LCSG ▷ C2×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
2. C2×C11×#440C2semidirect
4. Q8×C11×C4⋊C4C2semidirect
6. C11×#1947C2semidirect
7. C11×#1936C2semidirect
8. C11×#1880C2semidirect
9. C11×#1862C2semidirect
10. C11×#1770C2semidirect
11. C4×C11×#103C2semidirect
18. C11×#460C4semidirect
50. C2×C11×SD16C2×C4semidirect
59. C4×Q8×C11C2×C4semidirect
83. C11×C4⋊C8C2×C4semidirect
85. C11×#103D4semidirect
88. C11×#102C2×C4semidirect
94. #23003C11direct (N × H)
163. C2×#440C2×C11semidirect
165. Q8×C4⋊C4C2×C11semidirect
167. #1947C2×C11semidirect
168. #1936C2×C11semidirect
169. #1880C2×C11semidirect
170. #1862C2×C11semidirect
171. #1770C2×C11semidirect
172. C4×#103C2×C11semidirect
184. Q8×C11C4×D4semidirect
234. #460C4×C11semidirect
281. C4×C11#440semidirect
293. C2×SD16C2×C4×C11semidirect
302. C4×Q8C2×C4×C11semidirect
326. C4⋊C8C2×C4×C11semidirect
328. #103D4×C11semidirect
331. #102C2×C4×C11semidirect
412. C11#23003direct (N × H)
424. Q8C4×D4×C11semidirect
490. C4C11×#440semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#4602
C2×C11×#4402
C11×#23662
Q8×C11×C4⋊C42
C11×#19572
C11×#19472
C11×#19362
C11×#18802
C11×#18622
C11×#17702
C4×C11×#1032
#2300311