Finite Group Databasebeta

← C11×#24733 #14601926

Subgroups — C11×#24733 #14601926

Order 2816.

982 conjugacy classes of subgroups.

The subgroup lattice has 530 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×C4×C11×Q16C211yesmaximal, characteristic, complemented
4C11×#2548C211yesmaximal, characteristic
5Q8×C11×C4⋊C4C211yesmaximal, characteristic, complemented
6C11×#2067C212yesmaximal, complemented
7C11×#2042C212yesmaximal, complemented
8C11×#1957C211yesmaximal, characteristic
9C11×#1939C211yesmaximal, characteristic, complemented
10C11×#1880C212yesmaximal, complemented
11C11×#1803C211yesmaximal, 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—
21C4×C11×Q16—24no—
22C2×C11×#107C2211yescharacteristic
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×C4×C8×C11C2211yescharacteristic
32C11×#394—22no—
33C11×#390—21no—
34C11×#390—21no—
35C11×#390C2212yes—
36C11×#389—22no—
37C11×#389C2212yes—
38C11×#384—21no—
39C11×#384C2211yescharacteristic
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—21no—
70C2×C11×C4⋊C4—22no—
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—22no—
80C2×C11×C22⋊C4—22no—
81C2×C11×C22⋊C4—22no—
82C2×C11×C22⋊C4—22no—
83C2×C42×C11—21no—
84C2×C42×C11—22no—
85C2×C42×C11—21no—
86C2×C42×C11C2312yes—
87C2×C42×C11C2311yescharacteristic
88C11×#107—22no—
89C11×C4⋊C8—24no—
90C11×C4⋊C8—22no—
91C11×#103—22no—
92C11×#103—24no—
93C11×#103—22no—
94C11×#102—24no—
95C11×#102—24no—
96C11×#102—42no—
97C4×C8×C11—22no—
98C11×#95—22no—
99C11×#95D412yes—
100#24733C1111yesmaximal, 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—42no—
121C2×D4×C11—42no—
122C2×D4×C11—42no—
123C2×D4×C11—42no—
124C2×D4×C11—81no—
125C2×D4×C11—81no—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—22no—
130C22×C4×C11—21no—
131C22×C4×C11C2×D412yes—
132C22×C4×C11C2×D412yes—
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2411yescharacteristic
136C11×Q16—28no—
137C11×SD16—48no—
138C2×C8×C11—21no—
139C2×C8×C11—21no—
140C2×C8×C11—22no—
141C2×C8×C11—22no—
142C2×C8×C11—21no—
143C2×C8×C11—22no—
144C2×C8×C11—21no—
145C2×C8×C11—21no—
146C2×C8×C11C2×D412yes—
147C11×C4⋊C4—24no—
148C11×C4⋊C4—22no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—44no—
156C11×C4⋊C4—42no—
157C11×C4⋊C4—42no—
158C11×C4⋊C4—81no—
159C11×C4⋊C4—82no—
160C11×C4⋊C4C2×D412yes—
161C11×C22⋊C4—44no—
162C11×C22⋊C4—44no—
163C11×C22⋊C4—82no—
164C11×C22⋊C4—82no—
165C42×C11—24no—
166C42×C11—22no—
167C42×C11—22no—
168C42×C11—44no—
169C42×C11—42no—
170C42×C11C2×D412yes—
171C42×C11#4112yes—
172C2×#464C2×C1112yescomplemented
173C2×#460C2×C1111yescharacteristic
174C2×C4×Q16C2×C1111yescharacteristic, complemented
175#2548C2×C1111yescharacteristic
176Q8×C4⋊C4C2×C1111yescharacteristic, complemented
177#2067C2×C1112yescomplemented
178#2042C2×C1112yescomplemented
179#1957C2×C1111yescharacteristic
180#1939C2×C1111yescharacteristic, complemented
181#1880C2×C1112yescomplemented
182#1803C2×C1111yescharacteristic, complemented
183C23×C11—42no—
184C23×C11—42no—
185C23×C11—42no—
186C23×C11—42no—
187C23×C11—42no—
188C23×C11—42no—
189C23×C11—42no—
190C23×C11C22×D411yescharacteristic
191Q8×C11—22no—
192Q8×C11—22no—
193Q8×C11—22no—
194Q8×C11—22no—
195Q8×C11—22no—
196Q8×C11—41no—
197Q8×C11—41no—
198Q8×C11#12114yes—
199D4×C11—42no—
200D4×C11—42no—
201D4×C11—42no—
202D4×C11—42no—
203D4×C11—84no—
204D4×C11—84no—
205C2×C4×C11—22no—
206C2×C4×C11—22no—
207C2×C4×C11—22no—
208C2×C4×C11—21no—
209C2×C4×C11—21no—
210C2×C4×C11—22no—
211C2×C4×C11—22no—
212C2×C4×C11—22no—
213C2×C4×C11—22no—
214C2×C4×C11—22no—
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—22no—
218C2×C4×C11—41no—
219C2×C4×C11—41no—
220C2×C4×C11—41no—
221C2×C4×C11—41no—
222C2×C4×C11—41no—
223C2×C4×C11—42no—
224C2×C4×C11—42no—
225C2×C4×C11—41no—
226C2×C4×C11—42no—
227C2×C4×C11—41no—
228C2×C4×C11#12112yes—
229C2×C4×C11#12112yes—
230C2×C4×C11#13512yes—
231C2×C4×C11#13712yes—
232C2×C4×C11C22×D411yescharacteristic
233C2×C4×C11C22×D411yescharacteristic
234C2×C4×C11C2×#4111yescharacteristic
235C2×C4×C11C2×#4111yescharacteristic
236C2×C4×C11H(5,𝔽2)11yescharacteristic
237C2×C4×C112−1+411yescharacteristic
238C8×C11—22no—
239C8×C11—42no—
240C8×C11—41no—
241C22×Q16C22×C1111yescharacteristic
242C22×SD16C22×C1112yes—
243C2×#127C22×C1111yescharacteristic
244C2×#124C22×C1112yes—
245C2×C4×Q8C22×C1111yescharacteristic
246C2×C4×Q8C22×C1112yes—
247C2×C4×Q8C22×C1111yescharacteristic
248#464—28no—
249#460—24no—
250C4×Q16—24no—
251C2×#107C22×C1111yescharacteristic
252C2×C4⋊C8C22×C1111yescharacteristic
253C2×C4⋊C8C22×C1112yes—
254C2×#103C22×C1112yes—
255C2×#103C22×C1111yescharacteristic
256C2×#103C22×C1111yescharacteristic
257C2×#102C22×C1112yes—
258C2×#102C22×C1112yes—
259C2×#102C22×C1112yes—
260C2×C4×C8C22×C1111yescharacteristic
261#394—22no—
262#390—21no—
263#390—21no—
264#390C22×C1112yes—
265#389—22no—
266#389C22×C1112yes—
267#384—21no—
268#384C22×C1111yescharacteristic
269C4×C4⋊C4—21no—
270C4×C4⋊C4C22×C1111yescharacteristic
271#340C22×C1112yes—
272#336C22×C1112yes—
273C22×C11—82no—
274C22×C11—82no—
275C22×C11—82no—
276C22×C11—82no—
277C22×C11—82no—
278C22×C11—82no—
279C22×C11—82no—
280C22×C11C2×#12111yescharacteristic
281C22×C11D4211yescharacteristic
282C22×C11#54811yescharacteristic
283C22×C11C2×#13511yescharacteristic
284C22×C11C2×#13711yescharacteristic
285C22×C11#57611yescharacteristic
286C22×C11#57711yescharacteristic
287C4×C11—24no—
288C4×C11—22no—
289C4×C11—42no—
290C4×C11—42no—
291C4×C11—42no—
292C4×C11—42no—
293C4×C11—82no—
294C4×C11—81no—
295C4×C11#46414yescomplemented
296C4×C11C2×#12111yescharacteristic
297C4×C11#53711yescharacteristic
298C4×C11#54711yescharacteristic
299C4×C11#55311yescharacteristic
300C22×Q8C23×C1111yescharacteristic
301C22×Q8C23×C1111yescharacteristic
302C22×D4—21no—
303C22×D4—21no—
304C22×D4C23×C1112yes—
305C2×Q16—22no—
306C2×Q16—22no—
307C2×Q16D4×C1114yescomplemented
308C2×SD16—24no—
309C2×SD16—24no—
310C2×SD16—24no—
311C22×C8C23×C1112yes—
312C22×C8C23×C1111yescharacteristic
313C22×C8C23×C1111yescharacteristic
314#127—22no—
315#127—22no—
316#124—24no—
317#124—42no—
318C4×Q8—22no—
319C4×Q8—24no—
320C4×Q8—22no—
321C4×Q8—22no—
322C4×Q8—42no—
323C4×Q8D4×C1114yes—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4D4×C1111yescharacteristic
331C2×C4⋊C4D4×C1111yescharacteristic
332C2×C4⋊C4C23×C1111yescharacteristic
333C2×C4⋊C4C23×C1112yes—
334C2×C4⋊C4C23×C1111yescharacteristic
335C2×C22⋊C4—22no—
336C2×C22⋊C4—22no—
337C2×C22⋊C4—22no—
338C2×C22⋊C4—22no—
339C2×C42—21no—
340C2×C42—22no—
341C2×C42—21no—
342C2×C42C23×C1112yes—
343C2×C42C23×C1111yescharacteristic
344#107—22no—
345C4⋊C8—24no—
346C4⋊C8—22no—
347#103—22no—
348#103—24no—
349#103—22no—
350#102—24no—
351#102—24no—
352#102—42no—
353C4×C8—22no—
354#95—22no—
355#95D4×C1112yes—
356C2×C11—162no—
357C2×C11#241611yescharacteristic
358C2×C11C2×#46411yescharacteristic
359C2×C11#304511yescharacteristic
360C2×C11#327811yescharacteristic
361C2×C11#328711yescharacteristic
362C2×C11#336511yescharacteristic
363C2×C11#337511yescharacteristic
364C24—22no—
365C2×Q8—21no—
366C2×Q8—21no—
367C2×Q8—21no—
368C2×Q8—21no—
369C2×Q8—21no—
370C2×Q8—21no—
371C2×Q8—21no—
372C2×Q8—21no—
373C2×Q8C2×D4×C1112yes—
374C2×Q8C2×D4×C1112yes—
375C2×Q8C2×D4×C1112yes—
376C2×Q8C11×#4112yes—
377C2×D4—22no—
378C2×D4—22no—
379C2×D4—22no—
380C2×D4—22no—
381C2×D4—22no—
382C2×D4—22no—
383C2×D4—42no—
384C2×D4—42no—
385C2×D4—42no—
386C2×D4—42no—
387C2×D4—81no—
388C2×D4—81no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—22no—
393C22×C4—21no—
394C22×C4C2×D4×C1112yes—
395C22×C4C2×D4×C1112yes—
396C22×C4C2×D4×C1111yescharacteristic
397C22×C4C2×D4×C1111yescharacteristic
398C22×C4C24×C1111yescharacteristic
399Q16—28no—
400SD16—48no—
401C2×C8—21no—
402C2×C8—21no—
403C2×C8—21no—
404C2×C8—22no—
405C2×C8—22no—
406C2×C8—22no—
407C2×C8—21no—
408C2×C8—21no—
409C2×C8C2×D4×C1112yes—
410C4⋊C4—24no—
411C4⋊C4—22no—
412C4⋊C4—22no—
413C4⋊C4—21no—
414C4⋊C4—22no—
415C4⋊C4—21no—
416C4⋊C4—21no—
417C4⋊C4—22no—
418C4⋊C4—44no—
419C4⋊C4—42no—
420C4⋊C4—42no—
421C4⋊C4—81no—
422C4⋊C4—82no—
423C4⋊C4C2×D4×C1112yes—
424C22⋊C4—44no—
425C22⋊C4—44no—
426C22⋊C4—82no—
427C22⋊C4—82no—
428C42—24no—
429C42—22no—
430C42—22no—
431C42—44no—
432C42—42no—
433C42C2×D4×C1112yes—
434C42C11×#4112yes—
435C11#2473311yescharacteristic, direct product factor, Sylow
436C23—42no—
437C23—42no—
438C23—42no—
439C23—42no—
440C23—42no—
441C23—42no—
442C23—42no—
443C23C22×D4×C1111yescharacteristic
444Q8—22no—
445Q8—22no—
446Q8—22no—
447Q8—22no—
448Q8—22no—
449Q8—41no—
450Q8—41no—
451Q8C11×#12114yes—
452D4—42no—
453D4—42no—
454D4—42no—
455D4—42no—
456D4—84no—
457D4—84no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—41no—
479C2×C4—42no—
480C2×C4—41no—
481C2×C4C11×#12112yes—
482C2×C4C11×#12112yes—
483C2×C4C11×#13512yes—
484C2×C4C11×#13712yes—
485C2×C4C22×D4×C1111yescharacteristic
486C2×C4C22×D4×C1111yescharacteristic
487C2×C4C2×C11×#4111yescharacteristic
488C2×C4C2×C11×#4111yescharacteristic
489C2×C4C11×H(5,𝔽2)11yescharacteristic
490C2×C4C11×2−1+411yescharacteristic
491C8—22no—
492C8—42no—
493C8—41no—
494C22—82no—
495C22—82no—
496C22—82no—
497C22—82no—
498C22—82no—
499C22—82no—
500C22—82no—
501C22C2×C11×#12111yescharacteristic
502C22D42×C1111yescharacteristic
503C22C11×#54811yescharacteristic
504C22C2×C11×#13511yescharacteristic
505C22C2×C11×#13711yescharacteristic
506C22C11×#57611yescharacteristic
507C22C11×#57711yescharacteristic
508C4—24no—
509C4—22no—
510C4—42no—
511C4—42no—
512C4—42no—
513C4—42no—
514C4—82no—
515C4—81no—
516C4C11×#46414yescomplemented
517C4C2×C11×#12111yescharacteristic
518C4C11×#53711yescharacteristic
519C4C11×#54711yescharacteristic
520C4C11×#55311yescharacteristic
521C2—162no—
522C2C11×#241611yescharacteristic
523C2C2×C11×#46411yescharacteristic
524C2C11×#304511yescharacteristic
525C2C11×#327811yescharacteristic
526C2C11×#328711yescharacteristic
527C2C11×#336511yescharacteristic
528C2C11×#337511yescharacteristic
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×C4×C11×Q16C2semidirect
5. Q8×C11×C4⋊C4C2semidirect
6. C11×#2067C2semidirect
7. C11×#2042C2semidirect
9. C11×#1939C2semidirect
10. C11×#1880C2semidirect
11. C11×#1803C2semidirect
51. C2×C11×Q16D4semidirect
100. #24733C11direct (N × H)
172. C2×#464C2×C11semidirect
174. C2×C4×Q16C2×C11semidirect
176. Q8×C4⋊C4C2×C11semidirect
177. #2067C2×C11semidirect
178. #2042C2×C11semidirect
180. #1939C2×C11semidirect
181. #1880C2×C11semidirect
182. #1803C2×C11semidirect
295. C4×C11#464semidirect
307. C2×Q16D4×C11semidirect
435. C11#24733direct (N × H)
516. 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×#4602
C2×C4×C11×Q162
C11×#25482
Q8×C11×C4⋊C42
C11×#20672
C11×#20422
C11×#19572
C11×#19392
C11×#18802
C11×#18032
#2473311