Finite Group Databasebeta

← C11×#24692 #14601885

Subgroups — C11×#24692 #14601885

Order 2816.

884 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#476C211yesmaximal, characteristic, complemented
2C2×C11×#442C211yesmaximal, characteristic
3C11×#2542C211yesmaximal, characteristic, complemented
4C11×#2357C211yesmaximal, characteristic, complemented
5C11×#2071C212yesmaximal, complemented
6C11×#2054C212yesmaximal
7C11×#1993C211yesmaximal, characteristic, complemented
8C11×#1948C212yesmaximal, complemented
9C11×#1940C211yesmaximal, characteristic, complemented
10C11×#1926C212yesmaximal, complemented
11C11×#1804C211yesmaximal, characteristic, complemented
12C22×C11×D8C2211yescharacteristic
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×C11×C22⋊Q8—22no—
15C2×C4×D4×C11C2211yescharacteristic
16C2×C4×D4×C11C2211yescharacteristic
17C11×#476—24no—
18C11×#442—24no—
19C2×C11×#106C2211yescharacteristic
20C2×C11×#106C2212yes—
21C2×C11×C4⋊C8C2212yes—
22C2×C11×C4⋊C8C2211yescharacteristic
23C2×C11×#102C2211yescharacteristic
24C2×C11×#102C2211yescharacteristic
25C2×C11×#102C2212yes—
26C2×C11×#102C2212yes—
27C2×C11×#97C2211yescharacteristic
28C11×#399—21no—
29C11×#399—21no—
30C11×#390C2212yes—
31C11×#390C2212yes—
32C11×#388—22no—
33C11×#384C2212yes—
34C11×#382C2211yescharacteristic
35C11×#381—21no—
36C4×C11×C4⋊C4C2212yes—
37C4×C11×C4⋊C4C2211yescharacteristic
38C4×C11×C22⋊C4—21no—
39C11×#340C2212yes—
40C11×#340C2212yes—
41C11×#340C2212yes—
42C11×#336C2212yes—
43C22×Q8×C11—21no—
44C22×D4×C11C2311yescharacteristic
45C22×D4×C11C2311yescharacteristic
46C23×C4×C11—21no—
47C23×C4×C11—21no—
48C2×C11×D8—22no—
49C2×C11×D8—22no—
50C2×C11×D8—22no—
51C22×C8×C11C2311yescharacteristic
52C22×C8×C11C2312yes—
53C22×C8×C11C2311yescharacteristic
54C11×C4⋊Q8—22no—
55C11×C4⋊Q8—22no—
56C11×C22⋊Q8—48no—
57C4×D4×C11—22no—
58C4×D4×C11—22no—
59C4×D4×C11—22no—
60C4×D4×C11D414yes—
61C2×C11×C4⋊C4—22no—
62C2×C11×C4⋊C4—22no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4D412yes—
65C2×C11×C4⋊C4C2312yes—
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C4⋊C4C2312yes—
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C22⋊C4—21no—
70C2×C11×C22⋊C4—22no—
71C2×C11×C22⋊C4—21no—
72C2×C11×C22⋊C4—22no—
73C2×C11×C22⋊C4—22no—
74C2×C11×C22⋊C4—22no—
75C2×C42×C11—22no—
76C2×C42×C11C2312yes—
77C2×C42×C11C2311yescharacteristic
78C11×#106—22no—
79C11×#106—24no—
80C11×C4⋊C8—24no—
81C11×C4⋊C8—22no—
82C11×#102—22no—
83C11×#102—24no—
84C11×#102—24no—
85C11×#102—22no—
86C11×#97—22no—
87C11×#95—21no—
88C11×#95—22no—
89C11×#95—21no—
90C11×#95D411yescharacteristic
91C11×#95D411yescharacteristic
92#24692C1111yesmaximal, characteristic, direct product factor, Sylow
93C24×C11—21no—
94C24×C11—21no—
95C2×Q8×C11—44no—
96C2×Q8×C11—42no—
97C2×D4×C11—21no—
98C2×D4×C11—21no—
99C2×D4×C11—21no—
100C2×D4×C11—21no—
101C2×D4×C11—21no—
102C2×D4×C11—21no—
103C2×D4×C11—21no—
104C2×D4×C11—21no—
105C2×D4×C11—21no—
106C2×D4×C11—21no—
107C2×D4×C11C2×D412yes—
108C2×D4×C11#4112yes—
109C22×C4×C11—21no—
110C22×C4×C11—24no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—21no—
114C22×C4×C11—44no—
115C22×C4×C11—42no—
116C22×C4×C11—82no—
117C22×C4×C11C2×D412yes—
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2×D412yes—
121C22×C4×C11C2411yescharacteristic
122C11×D8—28no—
123C2×C8×C11—21no—
124C2×C8×C11—21no—
125C2×C8×C11—22no—
126C2×C8×C11—21no—
127C2×C8×C11—22no—
128C2×C8×C11—22no—
129C2×C8×C11—21no—
130C2×C8×C11—21no—
131C2×C8×C11#4112yes—
132C11×C4⋊C4—24no—
133C11×C4⋊C4—21no—
134C11×C4⋊C4—21no—
135C11×C4⋊C4—22no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—21no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4—22no—
140C11×C4⋊C4—44no—
141C11×C4⋊C4—42no—
142C11×C4⋊C4—44no—
143C11×C4⋊C4C2×D412yes—
144C11×C22⋊C4—24no—
145C11×C22⋊C4—44no—
146C11×C22⋊C4—42no—
147C11×C22⋊C4—44no—
148C11×C22⋊C4—44no—
149C11×C22⋊C4—82no—
150C42×C11—22no—
151C42×C11—22no—
152C42×C11—82no—
153C42×C11C2×D412yes—
154C42×C11#4112yes—
155C2×#476C2×C1111yescharacteristic, complemented
156C2×#442C2×C1111yescharacteristic
157#2542C2×C1111yescharacteristic, complemented
158#2357C2×C1111yescharacteristic, complemented
159#2071C2×C1112yescomplemented
160#2054C2×C1112yes—
161#1993C2×C1111yescharacteristic, complemented
162#1948C2×C1112yescomplemented
163#1940C2×C1111yescharacteristic, complemented
164#1926C2×C1112yescomplemented
165#1804C2×C1111yescharacteristic, complemented
166C23×C11—22no—
167C23×C11—22no—
168C23×C11—41no—
169C23×C11—41no—
170C23×C11—41no—
171C23×C11—41no—
172C23×C11—42no—
173C23×C11—42no—
174C23×C11—42no—
175C23×C11—42no—
176C23×C11C22×D411yescharacteristic
177Q8×C11—84no—
178D4×C11—22no—
179D4×C11—22no—
180D4×C11—22no—
181D4×C11—22no—
182D4×C11—41no—
183D4×C11—41no—
184D4×C11—41no—
185D4×C11—41no—
186C2×C4×C11—22no—
187C2×C4×C11—22no—
188C2×C4×C11—22no—
189C2×C4×C11—22no—
190C2×C4×C11—22no—
191C2×C4×C11—22no—
192C2×C4×C11—22no—
193C2×C4×C11—22no—
194C2×C4×C11—42no—
195C2×C4×C11—41no—
196C2×C4×C11—42no—
197C2×C4×C11—42no—
198C2×C4×C11—42no—
199C2×C4×C11—42no—
200C2×C4×C11—42no—
201C2×C4×C11—42no—
202C2×C4×C11—42no—
203C2×C4×C11—84no—
204C2×C4×C11—84no—
205C2×C4×C11#12112yes—
206C2×C4×C11#12112yes—
207C2×C4×C11AGL(1,ℤ/8)14yes—
208C2×C4×C11C22×D411yescharacteristic
209C2×C4×C11C2×#4111yescharacteristic
210C2×C4×C11C2×#4111yescharacteristic
211C2×C4×C11C2×#4111yescharacteristic
212C2×C4×C112−1+411yescharacteristic
213C2×C4×C112−1+411yescharacteristic
214C8×C11—22no—
215C8×C11—42no—
216C8×C11—41no—
217C22×D8C22×C1111yescharacteristic
218C2×C4⋊Q8C22×C1111yescharacteristic
219C2×C22⋊Q8—22no—
220C2×C4×D4C22×C1111yescharacteristic
221C2×C4×D4C22×C1111yescharacteristic
222#476—24no—
223#442—24no—
224C2×#106C22×C1111yescharacteristic
225C2×#106C22×C1112yes—
226C2×C4⋊C8C22×C1112yes—
227C2×C4⋊C8C22×C1111yescharacteristic
228C2×#102C22×C1112yes—
229C2×#102C22×C1112yes—
230C2×#102C22×C1111yescharacteristic
231C2×#102C22×C1111yescharacteristic
232C2×#97C22×C1111yescharacteristic
233#399—21no—
234#399—21no—
235#390C22×C1112yes—
236#390C22×C1112yes—
237#388—22no—
238#384C22×C1112yes—
239#382C22×C1111yescharacteristic
240#381—21no—
241C4×C4⋊C4C22×C1112yes—
242C4×C4⋊C4C22×C1111yescharacteristic
243C4×C22⋊C4—21no—
244#340C22×C1112yes—
245#340C22×C1112yes—
246#340C22×C1112yes—
247#336C22×C1112yes—
248C22×C11—44no—
249C22×C11—42no—
250C22×C11—42no—
251C22×C11—42no—
252C22×C11—42no—
253C22×C11—82no—
254C22×C11—82no—
255C22×C11—82no—
256C22×C11—81no—
257C22×C11—81no—
258C22×C11C2×#12111yescharacteristic
259C22×C11#54711yescharacteristic
260C22×C11#54811yescharacteristic
261C22×C11C2×AGL(1,ℤ/8)12yes—
262C22×C11#57712yes—
263C4×C11—24no—
264C4×C11—22no—
265C4×C11—22no—
266C4×C11—42no—
267C4×C11—42no—
268C4×C11—82no—
269C4×C11—81no—
270C4×C11—82no—
271C4×C11#52511yescharacteristic
272C4×C11#53611yescharacteristic
273C4×C11#55211yescharacteristic
274C4×C11#55611yescharacteristic
275C22×Q8—21no—
276C22×D4C23×C1111yescharacteristic
277C22×D4C23×C1111yescharacteristic
278C23×C4—21no—
279C23×C4—21no—
280C2×D8—22no—
281C2×D8—22no—
282C2×D8—22no—
283C22×C8C23×C1111yescharacteristic
284C22×C8C23×C1112yes—
285C22×C8C23×C1111yescharacteristic
286C4⋊Q8—22no—
287C4⋊Q8—22no—
288C22⋊Q8—48no—
289C4×D4—22no—
290C4×D4—22no—
291C4×D4—22no—
292C4×D4D4×C1114yes—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4D4×C1112yes—
297C2×C4⋊C4C23×C1111yescharacteristic
298C2×C4⋊C4C23×C1112yes—
299C2×C4⋊C4C23×C1112yes—
300C2×C4⋊C4C23×C1111yescharacteristic
301C2×C22⋊C4—21no—
302C2×C22⋊C4—21no—
303C2×C22⋊C4—22no—
304C2×C22⋊C4—22no—
305C2×C22⋊C4—22no—
306C2×C22⋊C4—22no—
307C2×C42—22no—
308C2×C42C23×C1112yes—
309C2×C42C23×C1111yescharacteristic
310#106—22no—
311#106—24no—
312C4⋊C8—24no—
313C4⋊C8—22no—
314#102—22no—
315#102—24no—
316#102—24no—
317#102—22no—
318#97—22no—
319#95—21no—
320#95—22no—
321#95—21no—
322#95D4×C1111yescharacteristic
323#95D4×C1111yescharacteristic
324C2×C11—82no—
325C2×C11—82no—
326C2×C11#241511yescharacteristic
327C2×C11#303811yescharacteristic
328C2×C11#304211yescharacteristic
329C2×C11#334512yes—
330C2×C11#337312yes—
331C24—21no—
332C24—21no—
333C2×Q8—44no—
334C2×Q8—42no—
335C2×D4—21no—
336C2×D4—21no—
337C2×D4—21no—
338C2×D4—21no—
339C2×D4—21no—
340C2×D4—21no—
341C2×D4—21no—
342C2×D4—21no—
343C2×D4—21no—
344C2×D4—21no—
345C2×D4C2×D4×C1112yes—
346C2×D4C11×#4112yes—
347C22×C4—21no—
348C22×C4—24no—
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—21no—
352C22×C4—44no—
353C22×C4—42no—
354C22×C4—82no—
355C22×C4C2×D4×C1112yes—
356C22×C4C2×D4×C1111yescharacteristic
357C22×C4C2×D4×C1111yescharacteristic
358C22×C4C2×D4×C1112yes—
359C22×C4C24×C1111yescharacteristic
360D8—28no—
361C2×C8—21no—
362C2×C8—21no—
363C2×C8—21no—
364C2×C8—22no—
365C2×C8—22no—
366C2×C8—22no—
367C2×C8—21no—
368C2×C8—21no—
369C2×C8C11×#4112yes—
370C4⋊C4—24no—
371C4⋊C4—21no—
372C4⋊C4—21no—
373C4⋊C4—22no—
374C4⋊C4—22no—
375C4⋊C4—21no—
376C4⋊C4—22no—
377C4⋊C4—22no—
378C4⋊C4—44no—
379C4⋊C4—42no—
380C4⋊C4—44no—
381C4⋊C4C2×D4×C1112yes—
382C22⋊C4—24no—
383C22⋊C4—44no—
384C22⋊C4—42no—
385C22⋊C4—44no—
386C22⋊C4—44no—
387C22⋊C4—82no—
388C42—22no—
389C42—22no—
390C42—82no—
391C42C2×D4×C1112yes—
392C42C11×#4112yes—
393C11#2469211yescharacteristic, direct product factor, Sylow
394C23—22no—
395C23—22no—
396C23—41no—
397C23—41no—
398C23—41no—
399C23—41no—
400C23—42no—
401C23—42no—
402C23—42no—
403C23—42no—
404C23C22×D4×C1111yescharacteristic
405Q8—84no—
406D4—22no—
407D4—22no—
408D4—22no—
409D4—22no—
410D4—41no—
411D4—41no—
412D4—41no—
413D4—41no—
414C2×C4—22no—
415C2×C4—22no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—42no—
423C2×C4—41no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—84no—
432C2×C4—84no—
433C2×C4C11×#12112yes—
434C2×C4C11×#12112yes—
435C2×C4C11×AGL(1,ℤ/8)14yes—
436C2×C4C22×D4×C1111yescharacteristic
437C2×C4C2×C11×#4111yescharacteristic
438C2×C4C2×C11×#4111yescharacteristic
439C2×C4C2×C11×#4111yescharacteristic
440C2×C4C11×2−1+411yescharacteristic
441C2×C4C11×2−1+411yescharacteristic
442C8—22no—
443C8—42no—
444C8—41no—
445C22—42no—
446C22—42no—
447C22—42no—
448C22—42no—
449C22—44no—
450C22—81no—
451C22—81no—
452C22—82no—
453C22—82no—
454C22—82no—
455C22C2×C11×#12111yescharacteristic
456C22C11×#54711yescharacteristic
457C22C11×#54811yescharacteristic
458C22C2×C11×AGL(1,ℤ/8)12yes—
459C22C11×#57712yes—
460C4—22no—
461C4—22no—
462C4—24no—
463C4—42no—
464C4—42no—
465C4—81no—
466C4—82no—
467C4—82no—
468C4C11×#52511yescharacteristic
469C4C11×#53611yescharacteristic
470C4C11×#55211yescharacteristic
471C4C11×#55611yescharacteristic
472C2—82no—
473C2—82no—
474C2C11×#241511yescharacteristic
475C2C11×#303811yescharacteristic
476C2C11×#304211yescharacteristic
477C2C11×#334512yes—
478C2C11×#337312yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×C11×D8C22
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×#476C2semidirect
3. C11×#2542C2semidirect
4. C11×#2357C2semidirect
5. C11×#2071C2semidirect
7. C11×#1993C2semidirect
8. C11×#1948C2semidirect
9. C11×#1940C2semidirect
10. C11×#1926C2semidirect
11. C11×#1804C2semidirect
92. #24692C11direct (N × H)
155. C2×#476C2×C11semidirect
157. #2542C2×C11semidirect
158. #2357C2×C11semidirect
159. #2071C2×C11semidirect
161. #1993C2×C11semidirect
162. #1948C2×C11semidirect
163. #1940C2×C11semidirect
164. #1926C2×C11semidirect
165. #1804C2×C11semidirect
393. C11#24692direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4762
C2×C11×#4422
C11×#25422
C11×#23572
C11×#20712
C11×#20542
C11×#19932
C11×#19482
C11×#19402
C11×#19262
C11×#18042
#2469211