Finite Group Databasebeta

← C11×#24729 #14601922

Subgroups — C11×#24729 #14601922

Order 2816.

946 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#464C212yesmaximal
2C2×C11×#462C211yesmaximal, characteristic, complemented
3C2×C4×C11×SD16C211yesmaximal, characteristic
4C11×#2547C211yesmaximal, characteristic
5Q8×C11×C4⋊C4C211yesmaximal, characteristic, complemented
6C11×#2066C212yesmaximal, complemented
7C11×#2042C212yesmaximal
8C11×#1956C211yesmaximal, characteristic, complemented
9C11×#1939C211yesmaximal, characteristic, complemented
10C11×#1878C212yesmaximal, complemented
11C11×#1802C211yesmaximal, characteristic
12C22×C11×Q16C2212yes—
13C22×C11×SD16C2211yescharacteristic
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C11×#124C2212yes—
16C2×C4×Q8×C11C2212yes—
17C2×C4×Q8×C11C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C11×#464—28no—
20C11×#462—24no—
21C4×C11×SD16—24no—
22C2×C11×#106C2211yescharacteristic
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C11×C4⋊C8C2212yes—
25C2×C11×#103C2211yescharacteristic
26C2×C11×#103C2212yes—
27C2×C11×#103C2212yes—
28C2×C11×#103C2212yes—
29C2×C11×#102C2211yescharacteristic
30C2×C11×#102C2212yes—
31C2×C4×C8×C11C2211yescharacteristic
32C11×#397—22no—
33C11×#391C2212yes—
34C11×#389—22no—
35C11×#389C2212yes—
36C11×#384—21no—
37C11×#384C2211yescharacteristic
38C11×#380—21no—
39C11×#380—21no—
40C4×C11×C4⋊C4—21no—
41C4×C11×C4⋊C4C2211yescharacteristic
42C11×#340C2212yes—
43C11×#336C2212yes—
44C22×Q8×C11C2312yes—
45C22×Q8×C11C2311yescharacteristic
46C22×D4×C11C2311yescharacteristic
47C23×C4×C11—21no—
48C2×C11×Q16—24no—
49C2×C11×Q16—24no—
50C2×C11×Q16—24no—
51C2×C11×SD16—22no—
52C2×C11×SD16—22no—
53C2×C11×SD16D414yes—
54C22×C8×C11C2311yescharacteristic
55C22×C8×C11C2312yes—
56C22×C8×C11C2311yescharacteristic
57C11×C4⋊Q8—22no—
58C11×C4⋊Q8—22no—
59C11×#124—24no—
60C11×#124—42no—
61C4×Q8×C11—22no—
62C4×Q8×C11—24no—
63C4×Q8×C11—42no—
64C4×Q8×C11D414yes—
65C4×D4×C11—22no—
66C4×D4×C11—22no—
67C2×C11×C4⋊C4—21no—
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—21no—
74C2×C11×C4⋊C4D411yescharacteristic
75C2×C11×C4⋊C4D411yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C4⋊C4C2312yes—
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C22⋊C4—21no—
80C2×C11×C22⋊C4—22no—
81C2×C11×C22⋊C4—22no—
82C2×C42×C11—21no—
83C2×C42×C11—22no—
84C2×C42×C11C2312yes—
85C2×C42×C11C2311yescharacteristic
86C11×#106—22no—
87C11×C4⋊C8—24no—
88C11×C4⋊C8—22no—
89C11×#103—22no—
90C11×#103—24no—
91C11×#103—24no—
92C11×#103—42no—
93C11×#102—24no—
94C11×#102—22no—
95C4×C8×C11—22no—
96C11×#95—22no—
97C11×#95—22no—
98C11×#95—22no—
99C11×#95D412yes—
100#24729C1111yesmaximal, characteristic, direct product factor, Sylow
101C24×C11—21no—
102C2×Q8×C11—21no—
103C2×Q8×C11—21no—
104C2×Q8×C11—21no—
105C2×Q8×C11—22no—
106C2×Q8×C11—22no—
107C2×Q8×C11—22no—
108C2×Q8×C11—22no—
109C2×Q8×C11—22no—
110C2×Q8×C11—22no—
111C2×Q8×C11C2×D412yes—
112C2×Q8×C11C2×D412yes—
113C2×Q8×C11#4112yes—
114C2×D4×C11—21no—
115C2×D4×C11—21no—
116C2×D4×C11—21no—
117C2×D4×C11—21no—
118C2×D4×C11—21no—
119C2×D4×C11C2×D412yes—
120C22×C4×C11—21no—
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—42no—
126C22×C4×C11—42no—
127C22×C4×C11—42no—
128C22×C4×C11C2×D412yes—
129C22×C4×C11C2×D412yes—
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2411yescharacteristic
133C11×Q16—48no—
134C11×SD16—28no—
135C2×C8×C11—21no—
136C2×C8×C11—21no—
137C2×C8×C11—22no—
138C2×C8×C11—22no—
139C2×C8×C11—21no—
140C2×C8×C11—22no—
141C2×C8×C11—21no—
142C2×C8×C11—21no—
143C2×C8×C11C2×D412yes—
144C11×C4⋊C4—24no—
145C11×C4⋊C4—22no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—22no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—44no—
153C11×C4⋊C4—42no—
154C11×C4⋊C4—42no—
155C11×C4⋊C4—42no—
156C11×C4⋊C4—81no—
157C11×C4⋊C4—82no—
158C11×C4⋊C4C2×D412yes—
159C11×C22⋊C4—44no—
160C11×C22⋊C4—44no—
161C11×C22⋊C4—42no—
162C42×C11—24no—
163C42×C11—22no—
164C42×C11—22no—
165C42×C11—44no—
166C42×C11C2×D412yes—
167C42×C11#4112yes—
168C2×#464C2×C1112yes—
169C2×#462C2×C1111yescharacteristic, complemented
170C2×C4×SD16C2×C1111yescharacteristic
171#2547C2×C1111yescharacteristic
172Q8×C4⋊C4C2×C1111yescharacteristic, complemented
173#2066C2×C1112yescomplemented
174#2042C2×C1112yes—
175#1956C2×C1111yescharacteristic, complemented
176#1939C2×C1111yescharacteristic, complemented
177#1878C2×C1112yescomplemented
178#1802C2×C1111yescharacteristic
179C23×C11—22no—
180C23×C11—41no—
181C23×C11—41no—
182C23×C11—41no—
183C23×C11—41no—
184C23×C11—41no—
185C23×C11—41no—
186C23×C11C22×D411yescharacteristic
187Q8×C11—22no—
188Q8×C11—22no—
189Q8×C11—22no—
190Q8×C11—42no—
191Q8×C11—42no—
192Q8×C11—42no—
193Q8×C11—42no—
194Q8×C11#12114yes—
195D4×C11—22no—
196D4×C11—22no—
197D4×C11—41no—
198D4×C11—41no—
199C2×C4×C11—22no—
200C2×C4×C11—22no—
201C2×C4×C11—22no—
202C2×C4×C11—21no—
203C2×C4×C11—21no—
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—41no—
212C2×C4×C11—41no—
213C2×C4×C11—41no—
214C2×C4×C11—42no—
215C2×C4×C11—42no—
216C2×C4×C11—42no—
217C2×C4×C11—42no—
218C2×C4×C11—42no—
219C2×C4×C11—41no—
220C2×C4×C11—41no—
221C2×C4×C11—42no—
222C2×C4×C11—84no—
223C2×C4×C11#12112yes—
224C2×C4×C11#12112yes—
225C2×C4×C11#13512yes—
226C2×C4×C11#13712yes—
227C2×C4×C11C22×D411yescharacteristic
228C2×C4×C11C22×D411yescharacteristic
229C2×C4×C11C2×#4111yescharacteristic
230C2×C4×C11C2×#4111yescharacteristic
231C2×C4×C11H(5,𝔽2)11yescharacteristic
232C2×C4×C112−1+411yescharacteristic
233C8×C11—22no—
234C8×C11—42no—
235C8×C11—41no—
236C22×Q16C22×C1112yes—
237C22×SD16C22×C1111yescharacteristic
238C2×C4⋊Q8C22×C1111yescharacteristic
239C2×#124C22×C1112yes—
240C2×C4×Q8C22×C1112yes—
241C2×C4×Q8C22×C1111yescharacteristic
242C2×C4×D4C22×C1111yescharacteristic
243#464—28no—
244#462—24no—
245C4×SD16—24no—
246C2×#106C22×C1111yescharacteristic
247C2×C4⋊C8C22×C1111yescharacteristic
248C2×C4⋊C8C22×C1112yes—
249C2×#103C22×C1112yes—
250C2×#103C22×C1112yes—
251C2×#103C22×C1111yescharacteristic
252C2×#103C22×C1112yes—
253C2×#102C22×C1112yes—
254C2×#102C22×C1111yescharacteristic
255C2×C4×C8C22×C1111yescharacteristic
256#397—22no—
257#391C22×C1112yes—
258#389—22no—
259#389C22×C1112yes—
260#384—21no—
261#384C22×C1111yescharacteristic
262#380—21no—
263#380—21no—
264C4×C4⋊C4—21no—
265C4×C4⋊C4C22×C1111yescharacteristic
266#340C22×C1112yes—
267#336C22×C1112yes—
268C22×C11—42no—
269C22×C11—42no—
270C22×C11—42no—
271C22×C11—81no—
272C22×C11—81no—
273C22×C11—81no—
274C22×C11—81no—
275C22×C11C2×#12111yescharacteristic
276C22×C11D4211yescharacteristic
277C22×C11#54811yescharacteristic
278C22×C11C2×#13511yescharacteristic
279C22×C11C2×#13711yescharacteristic
280C22×C11#57711yescharacteristic
281C22×C11#57811yescharacteristic
282C4×C11—24no—
283C4×C11—22no—
284C4×C11—42no—
285C4×C11—42no—
286C4×C11—42no—
287C4×C11—82no—
288C4×C11—82no—
289C4×C11—81no—
290C4×C11#46414yescomplemented
291C4×C11C2×#12111yescharacteristic
292C4×C11#53711yescharacteristic
293C4×C11#54711yescharacteristic
294C4×C11#55311yescharacteristic
295C22×Q8C23×C1112yes—
296C22×Q8C23×C1111yescharacteristic
297C22×D4C23×C1111yescharacteristic
298C23×C4—21no—
299C2×Q16—24no—
300C2×Q16—24no—
301C2×Q16—24no—
302C2×SD16—22no—
303C2×SD16—22no—
304C2×SD16D4×C1114yes—
305C22×C8C23×C1112yes—
306C22×C8C23×C1111yescharacteristic
307C22×C8C23×C1111yescharacteristic
308C4⋊Q8—22no—
309C4⋊Q8—22no—
310#124—24no—
311#124—42no—
312C4×Q8—22no—
313C4×Q8—24no—
314C4×Q8—42no—
315C4×Q8D4×C1114yes—
316C4×D4—22no—
317C4×D4—22no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4D4×C1111yescharacteristic
326C2×C4⋊C4D4×C1111yescharacteristic
327C2×C4⋊C4C23×C1111yescharacteristic
328C2×C4⋊C4C23×C1112yes—
329C2×C4⋊C4C23×C1111yescharacteristic
330C2×C22⋊C4—21no—
331C2×C22⋊C4—22no—
332C2×C22⋊C4—22no—
333C2×C42—21no—
334C2×C42—22no—
335C2×C42C23×C1112yes—
336C2×C42C23×C1111yescharacteristic
337#106—22no—
338C4⋊C8—24no—
339C4⋊C8—22no—
340#103—22no—
341#103—24no—
342#103—24no—
343#103—42no—
344#102—24no—
345#102—22no—
346C4×C8—22no—
347#95—22no—
348#95—22no—
349#95—22no—
350#95D4×C1112yes—
351C2×C11—82no—
352C2×C11#241611yescharacteristic
353C2×C11C2×#46411yescharacteristic
354C2×C11#304611yescharacteristic
355C2×C11#327611yescharacteristic
356C2×C11#328411yescharacteristic
357C2×C11#336411yescharacteristic
358C2×C11#336911yescharacteristic
359C24—21no—
360C2×Q8—21no—
361C2×Q8—21no—
362C2×Q8—21no—
363C2×Q8—22no—
364C2×Q8—22no—
365C2×Q8—22no—
366C2×Q8—22no—
367C2×Q8—22no—
368C2×Q8—22no—
369C2×Q8C2×D4×C1112yes—
370C2×Q8C2×D4×C1112yes—
371C2×Q8C11×#4112yes—
372C2×D4—21no—
373C2×D4—21no—
374C2×D4—21no—
375C2×D4—21no—
376C2×D4—21no—
377C2×D4C2×D4×C1112yes—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—42no—
384C22×C4—42no—
385C22×C4—42no—
386C22×C4C2×D4×C1112yes—
387C22×C4C2×D4×C1112yes—
388C22×C4C2×D4×C1111yescharacteristic
389C22×C4C2×D4×C1111yescharacteristic
390C22×C4C24×C1111yescharacteristic
391Q16—48no—
392SD16—28no—
393C2×C8—21no—
394C2×C8—21no—
395C2×C8—21no—
396C2×C8—22no—
397C2×C8—22no—
398C2×C8—22no—
399C2×C8—21no—
400C2×C8—21no—
401C2×C8C2×D4×C1112yes—
402C4⋊C4—24no—
403C4⋊C4—22no—
404C4⋊C4—22no—
405C4⋊C4—21no—
406C4⋊C4—22no—
407C4⋊C4—21no—
408C4⋊C4—21no—
409C4⋊C4—22no—
410C4⋊C4—44no—
411C4⋊C4—42no—
412C4⋊C4—42no—
413C4⋊C4—42no—
414C4⋊C4—81no—
415C4⋊C4—82no—
416C4⋊C4C2×D4×C1112yes—
417C22⋊C4—44no—
418C22⋊C4—44no—
419C22⋊C4—42no—
420C42—24no—
421C42—22no—
422C42—22no—
423C42—44no—
424C42C2×D4×C1112yes—
425C42C11×#4112yes—
426C11#2472911yescharacteristic, direct product factor, Sylow
427C23—22no—
428C23—41no—
429C23—41no—
430C23—41no—
431C23—41no—
432C23—41no—
433C23—41no—
434C23C22×D4×C1111yescharacteristic
435Q8—22no—
436Q8—22no—
437Q8—22no—
438Q8—42no—
439Q8—42no—
440Q8—42no—
441Q8—42no—
442Q8C11×#12114yes—
443D4—22no—
444D4—22no—
445D4—41no—
446D4—41no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—42no—
470C2×C4—84no—
471C2×C4C11×#12112yes—
472C2×C4C11×#12112yes—
473C2×C4C11×#13512yes—
474C2×C4C11×#13712yes—
475C2×C4C22×D4×C1111yescharacteristic
476C2×C4C22×D4×C1111yescharacteristic
477C2×C4C2×C11×#4111yescharacteristic
478C2×C4C2×C11×#4111yescharacteristic
479C2×C4C11×H(5,𝔽2)11yescharacteristic
480C2×C4C11×2−1+411yescharacteristic
481C8—22no—
482C8—42no—
483C8—41no—
484C22—42no—
485C22—42no—
486C22—42no—
487C22—81no—
488C22—81no—
489C22—81no—
490C22—81no—
491C22C2×C11×#12111yescharacteristic
492C22D42×C1111yescharacteristic
493C22C11×#54811yescharacteristic
494C22C2×C11×#13511yescharacteristic
495C22C2×C11×#13711yescharacteristic
496C22C11×#57711yescharacteristic
497C22C11×#57811yescharacteristic
498C4—24no—
499C4—22no—
500C4—42no—
501C4—42no—
502C4—42no—
503C4—82no—
504C4—82no—
505C4—81no—
506C4C11×#46414yescomplemented
507C4C2×C11×#12111yescharacteristic
508C4C11×#53711yescharacteristic
509C4C11×#54711yescharacteristic
510C4C11×#55311yescharacteristic
511C2—82no—
512C2C11×#241611yescharacteristic
513C2C2×C11×#46411yescharacteristic
514C2C11×#304611yescharacteristic
515C2C11×#327611yescharacteristic
516C2C11×#328411yescharacteristic
517C2C11×#336411yescharacteristic
518C2C11×#336911yescharacteristic
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
2. C2×C11×#462C2semidirect
5. Q8×C11×C4⋊C4C2semidirect
6. C11×#2066C2semidirect
8. C11×#1956C2semidirect
9. C11×#1939C2semidirect
10. C11×#1878C2semidirect
100. #24729C11direct (N × H)
169. C2×#462C2×C11semidirect
172. Q8×C4⋊C4C2×C11semidirect
173. #2066C2×C11semidirect
175. #1956C2×C11semidirect
176. #1939C2×C11semidirect
177. #1878C2×C11semidirect
290. C4×C11#464semidirect
426. C11#24729direct (N × H)
506. C4C11×#464semidirect

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×#4622
C2×C4×C11×SD162
C11×#25472
Q8×C11×C4⋊C42
C11×#20662
C11×#20422
C11×#19562
C11×#19392
C11×#18782
C11×#18022
#2472911