Finite Group Databasebeta

← C11×#24747 #14601940

Subgroups — C11×#24747 #14601940

Order 2816.

968 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×#464C212yesmaximal, complemented
2C2×C11×#460C211yesmaximal, characteristic
3C2×C11×#441C211yesmaximal, characteristic, complemented
4C11×#2548C211yesmaximal, characteristic
5C11×#2351C211yesmaximal, characteristic, complemented
6C11×#2065C212yesmaximal, complemented
7C11×#2042C212yesmaximal, complemented
8C11×#1961C211yesmaximal, characteristic
9C11×#1940C211yesmaximal, characteristic, complemented
10C11×#1880C212yesmaximal, complemented
11C11×#1805C211yesmaximal, characteristic, complemented
12C22×C11×Q16C2211yescharacteristic
13C22×C11×SD16C2212yes—
14C2×C11×#127C2211yescharacteristic
15C2×C11×#124C2212yes—
16C2×C4×Q8×C11C2211yescharacteristic
17C2×C4×Q8×C11C2212yes—
18C2×C4×Q8×C11C2211yescharacteristic
19C11×#464—28no—
20C11×#460—24no—
21C11×#441—24no—
22C2×C11×#106C2211yescharacteristic
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C11×C4⋊C8C2212yes—
25C2×C11×#103C2211yescharacteristic
26C2×C11×#103C2211yescharacteristic
27C2×C11×#103C2212yes—
28C2×C11×#102C2212yes—
29C2×C11×#102C2212yes—
30C2×C11×#102C2212yes—
31C2×C11×#97C2211yescharacteristic
32C11×#394—21no—
33C11×#394—21no—
34C11×#390—22no—
35C11×#390C2212yes—
36C11×#389—22no—
37C11×#389C2212yes—
38C11×#382—21no—
39C11×#382C2211yescharacteristic
40C4×C11×C4⋊C4—21no—
41C4×C11×C4⋊C4C2211yescharacteristic
42C11×#340C2212yes—
43C11×#336C2212yes—
44C22×Q8×C11C2311yescharacteristic
45C22×Q8×C11C2311yescharacteristic
46C22×D4×C11—21no—
47C22×D4×C11—21no—
48C22×D4×C11C2312yes—
49C2×C11×Q16—22no—
50C2×C11×Q16—22no—
51C2×C11×Q16D414yescomplemented
52C2×C11×SD16—24no—
53C2×C11×SD16—24no—
54C2×C11×SD16—24no—
55C22×C8×C11C2311yescharacteristic
56C22×C8×C11C2312yes—
57C22×C8×C11C2311yescharacteristic
58C11×#127—22no—
59C11×#127—22no—
60C11×#124—24no—
61C11×#124—42no—
62C4×Q8×C11—22no—
63C4×Q8×C11—24no—
64C4×Q8×C11—22no—
65C4×Q8×C11—22no—
66C4×Q8×C11—42no—
67C4×Q8×C11D414yes—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—22no—
70C2×C11×C4⋊C4—22no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4D412yes—
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2312yes—
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C22⋊C4—22no—
77C2×C11×C22⋊C4—22no—
78C2×C11×C22⋊C4—22no—
79C2×C11×C22⋊C4—22no—
80C2×C42×C11—21no—
81C2×C42×C11—22no—
82C2×C42×C11—21no—
83C2×C42×C11C2312yes—
84C2×C42×C11C2311yescharacteristic
85C11×#106—22no—
86C11×C4⋊C8—24no—
87C11×C4⋊C8—22no—
88C11×#103—22no—
89C11×#103—24no—
90C11×#103—22no—
91C11×#102—24no—
92C11×#102—24no—
93C11×#102—42no—
94C11×#97—22no—
95C11×#95—21no—
96C11×#95—22no—
97C11×#95—21no—
98C11×#95D411yescharacteristic
99C11×#95D411yescharacteristic
100#24747C1111yesmaximal, characteristic, direct product factor, Sylow
101C24×C11—22no—
102C2×Q8×C11—21no—
103C2×Q8×C11—21no—
104C2×Q8×C11—21no—
105C2×Q8×C11—21no—
106C2×Q8×C11—21no—
107C2×Q8×C11—21no—
108C2×Q8×C11—21no—
109C2×Q8×C11—21no—
110C2×Q8×C11C2×D412yes—
111C2×Q8×C11C2×D412yes—
112C2×Q8×C11C2×D412yes—
113C2×Q8×C11#4112yes—
114C2×D4×C11—22no—
115C2×D4×C11—22no—
116C2×D4×C11—22no—
117C2×D4×C11—22no—
118C2×D4×C11—22no—
119C2×D4×C11—22no—
120C2×D4×C11—44no—
121C2×D4×C11—42no—
122C2×D4×C11—42no—
123C2×D4×C11—82no—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—22no—
128C22×C4×C11—21no—
129C22×C4×C11C2×D412yes—
130C22×C4×C11C2×D412yes—
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2411yescharacteristic
134C11×Q16—28no—
135C11×SD16—48no—
136C2×C8×C11—21no—
137C2×C8×C11—21no—
138C2×C8×C11—22no—
139C2×C8×C11—22no—
140C2×C8×C11—21no—
141C2×C8×C11—22no—
142C2×C8×C11—21no—
143C2×C8×C11—21no—
144C2×C8×C11C2×D412yes—
145C11×C4⋊C4—24no—
146C11×C4⋊C4—21no—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—22no—
151C11×C4⋊C4—42no—
152C11×C4⋊C4—44no—
153C11×C4⋊C4—44no—
154C11×C4⋊C4—42no—
155C11×C4⋊C4C2×D412yes—
156C11×C22⋊C4—44no—
157C11×C22⋊C4—44no—
158C11×C22⋊C4—82no—
159C11×C22⋊C4—82no—
160C42×C11—24no—
161C42×C11—22no—
162C42×C11—22no—
163C42×C11—44no—
164C42×C11—42no—
165C42×C11C2×D412yes—
166C42×C11#4112yes—
167C2×#464C2×C1112yescomplemented
168C2×#460C2×C1111yescharacteristic
169C2×#441C2×C1111yescharacteristic, complemented
170#2548C2×C1111yescharacteristic
171#2351C2×C1111yescharacteristic, complemented
172#2065C2×C1112yescomplemented
173#2042C2×C1112yescomplemented
174#1961C2×C1111yescharacteristic
175#1940C2×C1111yescharacteristic, complemented
176#1880C2×C1112yescomplemented
177#1805C2×C1111yescharacteristic, complemented
178C23×C11—42no—
179C23×C11—42no—
180C23×C11—42no—
181C23×C11—42no—
182C23×C11—42no—
183C23×C11—42no—
184C23×C11—42no—
185C23×C11C22×D411yescharacteristic
186Q8×C11—22no—
187Q8×C11—22no—
188Q8×C11—22no—
189Q8×C11—22no—
190Q8×C11—22no—
191Q8×C11—41no—
192Q8×C11—41no—
193Q8×C11#12114yes—
194D4×C11—42no—
195D4×C11—42no—
196D4×C11—42no—
197D4×C11—42no—
198D4×C11—84no—
199D4×C11—84no—
200C2×C4×C11—22no—
201C2×C4×C11—22no—
202C2×C4×C11—22no—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
205C2×C4×C11—22no—
206C2×C4×C11—22no—
207C2×C4×C11—22no—
208C2×C4×C11—22no—
209C2×C4×C11—22no—
210C2×C4×C11—22no—
211C2×C4×C11—22no—
212C2×C4×C11—22no—
213C2×C4×C11—41no—
214C2×C4×C11—41no—
215C2×C4×C11—42no—
216C2×C4×C11—41no—
217C2×C4×C11—42no—
218C2×C4×C11—42no—
219C2×C4×C11—42no—
220C2×C4×C11—42no—
221C2×C4×C11#12112yes—
222C2×C4×C11#12112yes—
223C2×C4×C11C22×D411yescharacteristic
224C2×C4×C11C22×D411yescharacteristic
225C2×C4×C11C2×#4111yescharacteristic
226C2×C4×C11C2×#4111yescharacteristic
227C2×C4×C11H(5,𝔽2)11yescharacteristic
228C2×C4×C112−1+411yescharacteristic
229C8×C11—22no—
230C8×C11—42no—
231C8×C11—41no—
232C22×Q16C22×C1111yescharacteristic
233C22×SD16C22×C1112yes—
234C2×#127C22×C1111yescharacteristic
235C2×#124C22×C1112yes—
236C2×C4×Q8C22×C1111yescharacteristic
237C2×C4×Q8C22×C1112yes—
238C2×C4×Q8C22×C1111yescharacteristic
239#464—28no—
240#460—24no—
241#441—24no—
242C2×#106C22×C1111yescharacteristic
243C2×C4⋊C8C22×C1111yescharacteristic
244C2×C4⋊C8C22×C1112yes—
245C2×#103C22×C1112yes—
246C2×#103C22×C1111yescharacteristic
247C2×#103C22×C1111yescharacteristic
248C2×#102C22×C1112yes—
249C2×#102C22×C1112yes—
250C2×#102C22×C1112yes—
251C2×#97C22×C1111yescharacteristic
252#394—21no—
253#394—21no—
254#390—22no—
255#390C22×C1112yes—
256#389—22no—
257#389C22×C1112yes—
258#382—21no—
259#382C22×C1111yescharacteristic
260C4×C4⋊C4—21no—
261C4×C4⋊C4C22×C1111yescharacteristic
262#340C22×C1112yes—
263#336C22×C1112yes—
264C22×C11—82no—
265C22×C11—82no—
266C22×C11—82no—
267C22×C11—82no—
268C22×C11—82no—
269C22×C11—82no—
270C22×C11—82no—
271C22×C11C2×#12111yescharacteristic
272C22×C11D4211yescharacteristic
273C22×C11#54811yescharacteristic
274C22×C11#57512yes—
275C22×C11#57712yes—
276C4×C11—24no—
277C4×C11—22no—
278C4×C11—22no—
279C4×C11—42no—
280C4×C11—42no—
281C4×C11—42no—
282C4×C11—42no—
283C4×C11—82no—
284C4×C11—81no—
285C4×C11C2×#12111yescharacteristic
286C4×C11#53711yescharacteristic
287C4×C11#54711yescharacteristic
288C4×C11#55311yescharacteristic
289C22×Q8C23×C1111yescharacteristic
290C22×Q8C23×C1111yescharacteristic
291C22×D4—21no—
292C22×D4—21no—
293C22×D4C23×C1112yes—
294C2×Q16—22no—
295C2×Q16—22no—
296C2×Q16D4×C1114yescomplemented
297C2×SD16—24no—
298C2×SD16—24no—
299C2×SD16—24no—
300C22×C8C23×C1112yes—
301C22×C8C23×C1111yescharacteristic
302C22×C8C23×C1111yescharacteristic
303#127—22no—
304#127—22no—
305#124—24no—
306#124—42no—
307C4×Q8—22no—
308C4×Q8—24no—
309C4×Q8—22no—
310C4×Q8—22no—
311C4×Q8—42no—
312C4×Q8D4×C1114yes—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4D4×C1112yes—
318C2×C4⋊C4C23×C1111yescharacteristic
319C2×C4⋊C4C23×C1112yes—
320C2×C4⋊C4C23×C1111yescharacteristic
321C2×C22⋊C4—22no—
322C2×C22⋊C4—22no—
323C2×C22⋊C4—22no—
324C2×C22⋊C4—22no—
325C2×C42—21no—
326C2×C42—22no—
327C2×C42—21no—
328C2×C42C23×C1112yes—
329C2×C42C23×C1111yescharacteristic
330#106—22no—
331C4⋊C8—24no—
332C4⋊C8—22no—
333#103—22no—
334#103—24no—
335#103—22no—
336#102—24no—
337#102—24no—
338#102—42no—
339#97—22no—
340#95—21no—
341#95—22no—
342#95—21no—
343#95D4×C1111yescharacteristic
344#95D4×C1111yescharacteristic
345C2×C11—162no—
346C2×C11#241611yescharacteristic
347C2×C11#304011yescharacteristic
348C2×C11#304311yescharacteristic
349C2×C11#327112yes—
350C2×C11#337112yes—
351C24—22no—
352C2×Q8—21no—
353C2×Q8—21no—
354C2×Q8—21no—
355C2×Q8—21no—
356C2×Q8—21no—
357C2×Q8—21no—
358C2×Q8—21no—
359C2×Q8—21no—
360C2×Q8C2×D4×C1112yes—
361C2×Q8C2×D4×C1112yes—
362C2×Q8C2×D4×C1112yes—
363C2×Q8C11×#4112yes—
364C2×D4—22no—
365C2×D4—22no—
366C2×D4—22no—
367C2×D4—22no—
368C2×D4—22no—
369C2×D4—22no—
370C2×D4—44no—
371C2×D4—42no—
372C2×D4—42no—
373C2×D4—82no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—22no—
378C22×C4—21no—
379C22×C4C2×D4×C1112yes—
380C22×C4C2×D4×C1112yes—
381C22×C4C2×D4×C1111yescharacteristic
382C22×C4C2×D4×C1111yescharacteristic
383C22×C4C24×C1111yescharacteristic
384Q16—28no—
385SD16—48no—
386C2×C8—21no—
387C2×C8—21no—
388C2×C8—21no—
389C2×C8—22no—
390C2×C8—22no—
391C2×C8—22no—
392C2×C8—21no—
393C2×C8—21no—
394C2×C8C2×D4×C1112yes—
395C4⋊C4—24no—
396C4⋊C4—21no—
397C4⋊C4—22no—
398C4⋊C4—21no—
399C4⋊C4—21no—
400C4⋊C4—22no—
401C4⋊C4—42no—
402C4⋊C4—44no—
403C4⋊C4—44no—
404C4⋊C4—42no—
405C4⋊C4C2×D4×C1112yes—
406C22⋊C4—44no—
407C22⋊C4—44no—
408C22⋊C4—82no—
409C22⋊C4—82no—
410C42—24no—
411C42—22no—
412C42—22no—
413C42—44no—
414C42—42no—
415C42C2×D4×C1112yes—
416C42C11×#4112yes—
417C11#2474711yescharacteristic, direct product factor, Sylow
418C23—42no—
419C23—42no—
420C23—42no—
421C23—42no—
422C23—42no—
423C23—42no—
424C23—42no—
425C23C22×D4×C1111yescharacteristic
426Q8—22no—
427Q8—22no—
428Q8—22no—
429Q8—22no—
430Q8—22no—
431Q8—41no—
432Q8—41no—
433Q8C11×#12114yes—
434D4—42no—
435D4—42no—
436D4—42no—
437D4—42no—
438D4—84no—
439D4—84no—
440C2×C4—22no—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—42no—
456C2×C4—41no—
457C2×C4—42no—
458C2×C4—42no—
459C2×C4—42no—
460C2×C4—42no—
461C2×C4C11×#12112yes—
462C2×C4C11×#12112yes—
463C2×C4C22×D4×C1111yescharacteristic
464C2×C4C22×D4×C1111yescharacteristic
465C2×C4C2×C11×#4111yescharacteristic
466C2×C4C2×C11×#4111yescharacteristic
467C2×C4C11×H(5,𝔽2)11yescharacteristic
468C2×C4C11×2−1+411yescharacteristic
469C8—22no—
470C8—42no—
471C8—41no—
472C22—82no—
473C22—82no—
474C22—82no—
475C22—82no—
476C22—82no—
477C22—82no—
478C22—82no—
479C22C2×C11×#12111yescharacteristic
480C22D42×C1111yescharacteristic
481C22C11×#54811yescharacteristic
482C22C11×#57512yes—
483C22C11×#57712yes—
484C4—24no—
485C4—22no—
486C4—22no—
487C4—42no—
488C4—42no—
489C4—42no—
490C4—42no—
491C4—82no—
492C4—81no—
493C4C2×C11×#12111yescharacteristic
494C4C11×#53711yescharacteristic
495C4C11×#54711yescharacteristic
496C4C11×#55311yescharacteristic
497C2—162no—
498C2C11×#241611yescharacteristic
499C2C11×#304011yescharacteristic
500C2C11×#304311yescharacteristic
501C2C11×#327112yes—
502C2C11×#337112yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#127C22
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
1. C2×C11×#464C2semidirect
3. C2×C11×#441C2semidirect
5. C11×#2351C2semidirect
6. C11×#2065C2semidirect
7. C11×#2042C2semidirect
9. C11×#1940C2semidirect
10. C11×#1880C2semidirect
11. C11×#1805C2semidirect
51. C2×C11×Q16D4semidirect
100. #24747C11direct (N × H)
167. C2×#464C2×C11semidirect
169. C2×#441C2×C11semidirect
171. #2351C2×C11semidirect
172. #2065C2×C11semidirect
173. #2042C2×C11semidirect
175. #1940C2×C11semidirect
176. #1880C2×C11semidirect
177. #1805C2×C11semidirect
296. C2×Q16D4×C11semidirect
417. C11#24747direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4642
C2×C11×#4602
C2×C11×#4412
C11×#25482
C11×#23512
C11×#20652
C11×#20422
C11×#19612
C11×#19402
C11×#18802
C11×#18052
#2474711