Finite Group Databasebeta

← C11×#24748 #14601941

Subgroups — C11×#24748 #14601941

Order 2816.

976 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#461C212yesmaximal
2C2×C11×#461C211yesmaximal, characteristic
3C2×C11×#440C211yesmaximal, characteristic
4C11×#2546C211yesmaximal, characteristic, complemented
5C11×#2349C211yesmaximal, characteristic
6C11×#2068C212yesmaximal, complemented
7C11×#2043C212yesmaximal, complemented
8C11×#1960C211yesmaximal, characteristic, complemented
9C11×#1940C211yesmaximal, characteristic, complemented
10C11×#1877C212yesmaximal
11C11×#1805C211yesmaximal, 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
19C11×#461—28no—
20C11×#461—24no—
21C11×#440—24no—
22C2×C11×#107C2211yescharacteristic
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C11×C4⋊C8C2212yes—
25C2×C11×#103C2211yescharacteristic
26C2×C11×#103C2212yes—
27C2×C11×#103C2212yes—
28C2×C11×#103C2212yes—
29C2×C11×#103C2212yes—
30C2×C11×#102C2211yescharacteristic
31C2×C11×#97C2211yescharacteristic
32C11×#398—21no—
33C11×#398—21no—
34C11×#391C2212yes—
35C11×#389—22no—
36C11×#389C2212yes—
37C11×#385—22no—
38C11×#382C2211yescharacteristic
39C11×#380—21no—
40C4×C11×C4⋊C4C2211yescharacteristic
41C2×C11×#95—21no—
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—21no—
70C2×C11×C4⋊C4—22no—
71C2×C11×C4⋊C4—22no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—22no—
74C2×C11×C4⋊C4D412yes—
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2312yes—
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C22⋊C4—21no—
79C2×C11×C22⋊C4—22no—
80C2×C42×C11—21no—
81C2×C42×C11C2312yes—
82C2×C42×C11C2311yescharacteristic
83C11×#107—22no—
84C11×C4⋊C8—24no—
85C11×C4⋊C8—22no—
86C11×#103—24no—
87C11×#103—24no—
88C11×#103—22no—
89C11×#103—24no—
90C11×#103—42no—
91C11×#102—22no—
92C11×#97—22no—
93C11×#95—21no—
94C11×#95—22no—
95C11×#95—21no—
96C11×#95—22no—
97C11×#95—22no—
98C11×#95D411yescharacteristic
99C11×#95D411yescharacteristic
100#24748C1111yesmaximal, characteristic, direct product factor, Sylow
101C24×C11—21no—
102C2×Q8×C11—21no—
103C2×Q8×C11—21no—
104C2×Q8×C11—22no—
105C2×Q8×C11—22no—
106C2×Q8×C11—21no—
107C2×Q8×C11—21no—
108C2×Q8×C11—22no—
109C2×Q8×C11—22no—
110C2×Q8×C11—22no—
111C2×Q8×C11—21no—
112C2×Q8×C11—22no—
113C2×Q8×C11C2×D412yes—
114C2×D4×C11—21no—
115C2×D4×C11—21no—
116C2×D4×C11—21no—
117C2×D4×C11C2×D412yes—
118C2×D4×C11C2×D412yes—
119C2×D4×C11#4112yes—
120C22×C4×C11—21no—
121C22×C4×C11—21no—
122C22×C4×C11—24no—
123C22×C4×C11—21no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—44no—
127C22×C4×C11—44no—
128C22×C4×C11—82no—
129C22×C4×C11—82no—
130C22×C4×C11C2×D412yes—
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D412yes—
134C22×C4×C11C2411yescharacteristic
135C11×SD16—28no—
136C11×SD16—48no—
137C2×C8×C11—21no—
138C2×C8×C11—21no—
139C2×C8×C11—22no—
140C2×C8×C11—22no—
141C2×C8×C11—21no—
142C2×C8×C11—22no—
143C2×C8×C11—21no—
144C2×C8×C11—21no—
145C2×C8×C11C2×D412yes—
146C11×C4⋊C4—24no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—44no—
153C11×C4⋊C4—44no—
154C11×C4⋊C4—42no—
155C11×C4⋊C4—42no—
156C11×C4⋊C4—42no—
157C11×C4⋊C4—82no—
158C11×C4⋊C4C2×D412yes—
159C11×C22⋊C4—24no—
160C11×C22⋊C4—44no—
161C42×C11—22no—
162C42×C11—22no—
163C42×C11—42no—
164C42×C11C2×D412yes—
165C42×C11#4112yes—
166C2×#461C2×C1112yes—
167C2×#461C2×C1111yescharacteristic
168C2×#440C2×C1111yescharacteristic
169#2546C2×C1111yescharacteristic, complemented
170#2349C2×C1111yescharacteristic
171#2068C2×C1112yescomplemented
172#2043C2×C1112yescomplemented
173#1960C2×C1111yescharacteristic, complemented
174#1940C2×C1111yescharacteristic, complemented
175#1877C2×C1112yes—
176#1805C2×C1111yescharacteristic, complemented
177C23×C11—22no—
178C23×C11—22no—
179C23×C11—22no—
180C23×C11—42no—
181C23×C11—42no—
182C23×C11C22×D411yescharacteristic
183Q8×C11—22no—
184Q8×C11—22no—
185Q8×C11—41no—
186Q8×C11—41no—
187Q8×C11—42no—
188Q8×C11—42no—
189Q8×C11—42no—
190Q8×C11—42no—
191D4×C11—22no—
192D4×C11—22no—
193D4×C11—22no—
194D4×C11#12114yes—
195C2×C4×C11—22no—
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—42no—
207C2×C4×C11—41no—
208C2×C4×C11—42no—
209C2×C4×C11—42no—
210C2×C4×C11—42no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11—42no—
214C2×C4×C11—42no—
215C2×C4×C11—84no—
216C2×C4×C11—88no—
217C2×C4×C11#12112yes—
218C2×C4×C11#12112yes—
219C2×C4×C11#13714yes—
220C2×C4×C11C22×D411yescharacteristic
221C2×C4×C11C22×D411yescharacteristic
222C2×C4×C11C2×#4111yescharacteristic
223C2×C4×C11C2×#4111yescharacteristic
224C2×C4×C11H(5,𝔽2)11yescharacteristic
225C2×C4×C112−1+411yescharacteristic
226C8×C11—22no—
227C8×C11—42no—
228C8×C11—41no—
229C22×SD16C22×C1112yes—
230C22×SD16C22×C1111yescharacteristic
231C2×C4⋊Q8C22×C1111yescharacteristic
232C2×C4⋊Q8C22×C1112yes—
233C2×C4×Q8C22×C1111yescharacteristic
234C2×C4×D4C22×C1112yes—
235C2×C4×D4C22×C1111yescharacteristic
236#461—28no—
237#461—24no—
238#440—24no—
239C2×#107C22×C1111yescharacteristic
240C2×C4⋊C8C22×C1111yescharacteristic
241C2×C4⋊C8C22×C1112yes—
242C2×#103C22×C1112yes—
243C2×#103C22×C1112yes—
244C2×#103C22×C1112yes—
245C2×#103C22×C1111yescharacteristic
246C2×#103C22×C1112yes—
247C2×#102C22×C1111yescharacteristic
248C2×#97C22×C1111yescharacteristic
249#398—21no—
250#398—21no—
251#391C22×C1112yes—
252#389—22no—
253#389C22×C1112yes—
254#385—22no—
255#382C22×C1111yescharacteristic
256#380—21no—
257C4×C4⋊C4C22×C1111yescharacteristic
258C2×#95—21no—
259#340C22×C1112yes—
260#336C22×C1112yes—
261C22×C11—24no—
262C22×C11—44no—
263C22×C11—44no—
264C22×C11—42no—
265C22×C11—42no—
266C22×C11C2×#12111yescharacteristic
267C22×C11D4211yescharacteristic
268C22×C11#54811yescharacteristic
269C22×C11C2×#13712yes—
270C22×C11#57712yes—
271C4×C11—24no—
272C4×C11—22no—
273C4×C11—22no—
274C4×C11—42no—
275C4×C11—42no—
276C4×C11—42no—
277C4×C11—82no—
278C4×C11—82no—
279C4×C11—81no—
280C4×C11C2×#12111yescharacteristic
281C4×C11#53711yescharacteristic
282C4×C11#54711yescharacteristic
283C4×C11#55311yescharacteristic
284C22×Q8C23×C1112yes—
285C22×Q8C23×C1111yescharacteristic
286C22×D4C23×C1111yescharacteristic
287C23×C4—21no—
288C23×C4—22no—
289C2×SD16—22no—
290C2×SD16—22no—
291C2×SD16—24no—
292C2×SD16—24no—
293C2×SD16—24no—
294C2×SD16D4×C1114yes—
295C22×C8C23×C1112yes—
296C22×C8C23×C1111yescharacteristic
297C22×C8C23×C1111yescharacteristic
298C4⋊Q8—24no—
299C4⋊Q8—22no—
300C4⋊Q8—22no—
301C4⋊Q8—42no—
302C4×Q8—22no—
303C4×Q8—22no—
304C4×D4—24no—
305C4×D4—22no—
306C4×D4—42no—
307C4×D4D4×C1114yes—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4D4×C1112yes—
315C2×C4⋊C4C23×C1112yes—
316C2×C4⋊C4C23×C1111yescharacteristic
317C2×C4⋊C4C23×C1111yescharacteristic
318C2×C22⋊C4—21no—
319C2×C22⋊C4—22no—
320C2×C42—21no—
321C2×C42C23×C1112yes—
322C2×C42C23×C1111yescharacteristic
323#107—22no—
324C4⋊C8—24no—
325C4⋊C8—22no—
326#103—24no—
327#103—24no—
328#103—22no—
329#103—24no—
330#103—42no—
331#102—22no—
332#97—22no—
333#95—21no—
334#95—22no—
335#95—21no—
336#95—22no—
337#95—22no—
338#95D4×C1111yescharacteristic
339#95D4×C1111yescharacteristic
340C2×C11—44no—
341C2×C11#241611yescharacteristic
342C2×C11#303911yescharacteristic
343C2×C11#304211yescharacteristic
344C2×C11#326612yes—
345C2×C11#337212yes—
346C24—21no—
347C2×Q8—21no—
348C2×Q8—21no—
349C2×Q8—22no—
350C2×Q8—22no—
351C2×Q8—21no—
352C2×Q8—21no—
353C2×Q8—22no—
354C2×Q8—22no—
355C2×Q8—22no—
356C2×Q8—21no—
357C2×Q8—22no—
358C2×Q8C2×D4×C1112yes—
359C2×D4—21no—
360C2×D4—21no—
361C2×D4—21no—
362C2×D4C2×D4×C1112yes—
363C2×D4C2×D4×C1112yes—
364C2×D4C11×#4112yes—
365C22×C4—21no—
366C22×C4—21no—
367C22×C4—24no—
368C22×C4—21no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—44no—
372C22×C4—44no—
373C22×C4—82no—
374C22×C4—82no—
375C22×C4C2×D4×C1112yes—
376C22×C4C2×D4×C1111yescharacteristic
377C22×C4C2×D4×C1111yescharacteristic
378C22×C4C2×D4×C1112yes—
379C22×C4C24×C1111yescharacteristic
380SD16—28no—
381SD16—48no—
382C2×C8—21no—
383C2×C8—21no—
384C2×C8—21no—
385C2×C8—22no—
386C2×C8—22no—
387C2×C8—22no—
388C2×C8—21no—
389C2×C8—21no—
390C2×C8C2×D4×C1112yes—
391C4⋊C4—24no—
392C4⋊C4—21no—
393C4⋊C4—21no—
394C4⋊C4—22no—
395C4⋊C4—21no—
396C4⋊C4—22no—
397C4⋊C4—44no—
398C4⋊C4—44no—
399C4⋊C4—42no—
400C4⋊C4—42no—
401C4⋊C4—42no—
402C4⋊C4—82no—
403C4⋊C4C2×D4×C1112yes—
404C22⋊C4—24no—
405C22⋊C4—44no—
406C42—22no—
407C42—22no—
408C42—42no—
409C42C2×D4×C1112yes—
410C42C11×#4112yes—
411C11#2474811yescharacteristic, direct product factor, Sylow
412C23—22no—
413C23—22no—
414C23—22no—
415C23—42no—
416C23—42no—
417C23C22×D4×C1111yescharacteristic
418Q8—22no—
419Q8—22no—
420Q8—41no—
421Q8—41no—
422Q8—42no—
423Q8—42no—
424Q8—42no—
425Q8—42no—
426D4—22no—
427D4—22no—
428D4—22no—
429D4C11×#12114yes—
430C2×C4—22no—
431C2×C4—22no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—42no—
442C2×C4—41no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—42no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—84no—
451C2×C4—88no—
452C2×C4C11×#12112yes—
453C2×C4C11×#12112yes—
454C2×C4C11×#13714yes—
455C2×C4C22×D4×C1111yescharacteristic
456C2×C4C22×D4×C1111yescharacteristic
457C2×C4C2×C11×#4111yescharacteristic
458C2×C4C2×C11×#4111yescharacteristic
459C2×C4C11×H(5,𝔽2)11yescharacteristic
460C2×C4C11×2−1+411yescharacteristic
461C8—22no—
462C8—42no—
463C8—41no—
464C22—24no—
465C22—44no—
466C22—42no—
467C22—42no—
468C22—44no—
469C22C2×C11×#12111yescharacteristic
470C22D42×C1111yescharacteristic
471C22C11×#54811yescharacteristic
472C22C2×C11×#13712yes—
473C22C11×#57712yes—
474C4—24no—
475C4—22no—
476C4—22no—
477C4—42no—
478C4—42no—
479C4—42no—
480C4—82no—
481C4—82no—
482C4—81no—
483C4C2×C11×#12111yescharacteristic
484C4C11×#53711yescharacteristic
485C4C11×#54711yescharacteristic
486C4C11×#55311yescharacteristic
487C2—44no—
488C2C11×#241611yescharacteristic
489C2C11×#303911yescharacteristic
490C2C11×#304211yescharacteristic
491C2C11×#326612yes—
492C2C11×#337212yes—
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×#2068C2semidirect
7. C11×#2043C2semidirect
8. C11×#1960C2semidirect
9. C11×#1940C2semidirect
11. C11×#1805C2semidirect
100. #24748C11direct (N × H)
169. #2546C2×C11semidirect
171. #2068C2×C11semidirect
172. #2043C2×C11semidirect
173. #1960C2×C11semidirect
174. #1940C2×C11semidirect
176. #1805C2×C11semidirect
411. C11#24748direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4612
C2×C11×#4402
C11×#25462
C11×#23492
C11×#20682
C11×#20432
C11×#19602
C11×#19402
C11×#18772
C11×#18052
#2474811