Finite Group Databasebeta

← C11×#24830 #14602023

Subgroups — C11×#24830 #14602023

Order 2816.

900 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#474C211yesmaximal, characteristic, complemented
2C2×C11×#442C211yesmaximal, characteristic
3C11×#2563C211yesmaximal, characteristic, complemented
4C11×#2349C211yesmaximal, characteristic, complemented
5C11×#2085C212yesmaximal, complemented
6C11×#2067C212yesmaximal, complemented
7C11×#1993C211yesmaximal, characteristic, complemented
8C11×#1940C211yesmaximal, characteristic, complemented
9C11×#1879C212yesmaximal
10C11×#1804C212yesmaximal, complemented
11C11×#1804C211yesmaximal, characteristic, complemented
12C22×C11×D8C2211yescharacteristic
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×C4×D4×C11C2211yescharacteristic
15C2×C4×D4×C11C2212yes—
16C2×C4×D4×C11C2211yescharacteristic
17C11×#474—24no—
18C11×#442—24no—
19C2×C11×#107C2212yes—
20C2×C11×#106C2211yescharacteristic
21C2×C11×C4⋊C8C2211yescharacteristic
22C2×C11×C4⋊C8C2212yes—
23C2×C11×#102C2212yes—
24C2×C11×#102C2211yescharacteristic
25C2×C11×#102C2211yescharacteristic
26C2×C11×#102C2212yes—
27C2×C11×#97C2211yescharacteristic
28C11×#393—21no—
29C11×#393—21no—
30C11×#390C2212yes—
31C11×#389C2212yes—
32C11×#385—22no—
33C11×#382C2211yescharacteristic
34C11×#382C2212yes—
35C11×#380—22no—
36C11×#380—21no—
37C4×C11×C4⋊C4C2211yescharacteristic
38C2×C11×#95—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—
48C23×C4×C11—22no—
49C2×C11×D8—22no—
50C2×C11×D8—22no—
51C2×C11×D8Q814yescomplemented
52C22×C8×C11C2312yes—
53C22×C8×C11C2311yescharacteristic
54C22×C8×C11C2311yescharacteristic
55C11×C4⋊Q8—22no—
56C11×C4⋊Q8—22no—
57C4×D4×C11—24no—
58C4×D4×C11—22no—
59C4×D4×C11—22no—
60C4×D4×C11—22no—
61C4×D4×C11—42no—
62C4×D4×C11D414yes—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—22no—
65C2×C11×C4⋊C4D412yes—
66C2×C11×C4⋊C4C2312yes—
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2312yes—
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C22⋊C4—21no—
71C2×C11×C22⋊C4—22no—
72C2×C11×C22⋊C4—21no—
73C2×C11×C22⋊C4—22no—
74C2×C11×C22⋊C4—22no—
75C2×C42×C11C2312yes—
76C2×C42×C11C2311yescharacteristic
77C11×#107—24no—
78C11×#106—22no—
79C11×C4⋊C8—22no—
80C11×C4⋊C8—42no—
81C11×#102—22no—
82C11×#102—24no—
83C11×#102—22no—
84C11×#102—42no—
85C11×#97—22no—
86C11×#95—21no—
87C11×#95—22no—
88C11×#95—22no—
89C11×#95—22no—
90C11×#95—21no—
91C11×#95D411yescharacteristic
92C11×#95D411yescharacteristic
93#24830C1111yesmaximal, characteristic, direct product factor, Sylow
94C24×C11—21no—
95C24×C11—21no—
96C2×Q8×C11—42no—
97C2×Q8×C11—82no—
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×C11C2×D412yes—
107C2×D4×C11C2×Q812yes—
108C2×D4×C11C2×Q812yes—
109C2×D4×C11#4112yes—
110C22×C4×C11—21no—
111C22×C4×C11—24no—
112C22×C4×C11—21no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—44no—
116C22×C4×C11—44no—
117C22×C4×C11—44no—
118C22×C4×C11—42no—
119C22×C4×C11—82no—
120C22×C4×C11—82no—
121C22×C4×C11C2×D412yes—
122C22×C4×C11C2×D412yes—
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2411yescharacteristic
126C11×D8—28no—
127C2×C8×C11—21no—
128C2×C8×C11—21no—
129C2×C8×C11—22no—
130C2×C8×C11—21no—
131C2×C8×C11—22no—
132C2×C8×C11—21no—
133C2×C8×C11—22no—
134C2×C8×C11—21no—
135C2×C8×C11C2×Q812yes—
136C11×C4⋊C4—21no—
137C11×C4⋊C4—21no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4—21no—
140C11×C4⋊C4—22no—
141C11×C4⋊C4—22no—
142C11×C4⋊C4—22no—
143C11×C4⋊C4—42no—
144C11×C4⋊C4—42no—
145C11×C4⋊C4—82no—
146C11×C4⋊C4C2×D412yes—
147C11×C22⋊C4—24no—
148C11×C22⋊C4—44no—
149C11×C22⋊C4—42no—
150C11×C22⋊C4—82no—
151C11×C22⋊C4—82no—
152C42×C11—22no—
153C42×C11—22no—
154C42×C11C2×D412yes—
155C42×C11#4112yes—
156C2×#474C2×C1111yescharacteristic, complemented
157C2×#442C2×C1111yescharacteristic
158#2563C2×C1111yescharacteristic, complemented
159#2349C2×C1111yescharacteristic, complemented
160#2085C2×C1112yescomplemented
161#2067C2×C1112yescomplemented
162#1993C2×C1111yescharacteristic, complemented
163#1940C2×C1111yescharacteristic, complemented
164#1879C2×C1112yes—
165#1804C2×C1111yescharacteristic, complemented
166#1804C2×C1112yescomplemented
167C23×C11—22no—
168C23×C11—22no—
169C23×C11—22no—
170C23×C11—22no—
171C23×C11—42no—
172C23×C11—42no—
173C23×C11—41no—
174C23×C11—41no—
175C23×C11—42no—
176C23×C11—42no—
177C23×C11C22×D411yescharacteristic
178Q8×C11—84no—
179D4×C11—22no—
180D4×C11—22no—
181D4×C11—22no—
182D4×C11—22no—
183D4×C11—22no—
184D4×C11—41no—
185D4×C11—41no—
186D4×C11C22⋊Q814yes—
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—22no—
195C2×C4×C11—22no—
196C2×C4×C11—42no—
197C2×C4×C11—41no—
198C2×C4×C11—42no—
199C2×C4×C11—42no—
200C2×C4×C11—42no—
201C2×C4×C11—42no—
202C2×C4×C11—42no—
203C2×C4×C11—42no—
204C2×C4×C11—42no—
205C2×C4×C11—84no—
206C2×C4×C11—84no—
207C2×C4×C11—88no—
208C2×C4×C11#12112yes—
209C2×C4×C11#12112yes—
210C2×C4×C11C22×D411yescharacteristic
211C2×C4×C11C22×Q811yescharacteristic
212C2×C4×C11C2×#4111yescharacteristic
213C2×C4×C11C2×#4111yescharacteristic
214C2×C4×C11H(5,𝔽2)11yescharacteristic
215C2×C4×C112−1+411yescharacteristic
216C8×C11—22no—
217C8×C11—41no—
218C8×C11—42no—
219C22×D8C22×C1111yescharacteristic
220C2×C4⋊Q8C22×C1111yescharacteristic
221C2×C4×D4C22×C1111yescharacteristic
222C2×C4×D4C22×C1112yes—
223C2×C4×D4C22×C1111yescharacteristic
224#474—24no—
225#442—24no—
226C2×#107C22×C1112yes—
227C2×#106C22×C1111yescharacteristic
228C2×C4⋊C8C22×C1111yescharacteristic
229C2×C4⋊C8C22×C1112yes—
230C2×#102C22×C1111yescharacteristic
231C2×#102C22×C1112yes—
232C2×#102C22×C1111yescharacteristic
233C2×#102C22×C1112yes—
234C2×#97C22×C1111yescharacteristic
235#393—21no—
236#393—21no—
237#390C22×C1112yes—
238#389C22×C1112yes—
239#385—22no—
240#382C22×C1112yes—
241#382C22×C1111yescharacteristic
242#380—22no—
243#380—21no—
244C4×C4⋊C4C22×C1111yescharacteristic
245C2×#95—21no—
246#340C22×C1112yes—
247#340C22×C1112yes—
248#340C22×C1112yes—
249#336C22×C1112yes—
250C22×C11—24no—
251C22×C11—44no—
252C22×C11—42no—
253C22×C11—42no—
254C22×C11—44no—
255C22×C11—44no—
256C22×C11—42no—
257C22×C11—81no—
258C22×C11—81no—
259C22×C11—82no—
260C22×C11C2×#12111yescharacteristic
261C22×C11#54611yescharacteristic
262C22×C11D4×Q811yescharacteristic
263C22×C11#57512yes—
264C22×C11#57612yes—
265C4×C11—22no—
266C4×C11—22no—
267C4×C11—42no—
268C4×C11—42no—
269C4×C11—42no—
270C4×C11—81no—
271C4×C11—82no—
272C4×C11—82no—
273C4×C11C2×C22⋊Q811yescharacteristic
274C4×C11#53711yescharacteristic
275C4×C11#55211yescharacteristic
276C4×C11#55411yescharacteristic
277C22×Q8—21no—
278C22×D4C23×C1111yescharacteristic
279C22×D4C23×C1111yescharacteristic
280C23×C4—21no—
281C23×C4—21no—
282C23×C4—22no—
283C2×D8—22no—
284C2×D8—22no—
285C2×D8Q8×C1114yescomplemented
286C22×C8C23×C1112yes—
287C22×C8C23×C1111yescharacteristic
288C22×C8C23×C1111yescharacteristic
289C4⋊Q8—22no—
290C4⋊Q8—22no—
291C4×D4—24no—
292C4×D4—22no—
293C4×D4—22no—
294C4×D4—22no—
295C4×D4—42no—
296C4×D4D4×C1114yes—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4D4×C1112yes—
300C2×C4⋊C4C23×C1112yes—
301C2×C4⋊C4C23×C1111yescharacteristic
302C2×C4⋊C4C23×C1112yes—
303C2×C4⋊C4C23×C1111yescharacteristic
304C2×C22⋊C4—21no—
305C2×C22⋊C4—22no—
306C2×C22⋊C4—21no—
307C2×C22⋊C4—22no—
308C2×C22⋊C4—22no—
309C2×C42C23×C1112yes—
310C2×C42C23×C1111yescharacteristic
311#107—24no—
312#106—22no—
313C4⋊C8—22no—
314C4⋊C8—42no—
315#102—22no—
316#102—24no—
317#102—22no—
318#102—42no—
319#97—22no—
320#95—21no—
321#95—22no—
322#95—22no—
323#95—22no—
324#95—21no—
325#95D4×C1111yescharacteristic
326#95D4×C1111yescharacteristic
327C2×C11—44no—
328C2×C11—82no—
329C2×C11#241711yescharacteristic
330C2×C11#304011yescharacteristic
331C2×C11#304111yescharacteristic
332C2×C11#331912yes—
333C2×C11#338912yes—
334C24—21no—
335C24—21no—
336C2×Q8—42no—
337C2×Q8—82no—
338C2×D4—21no—
339C2×D4—21no—
340C2×D4—21no—
341C2×D4—21no—
342C2×D4—21no—
343C2×D4—21no—
344C2×D4—21no—
345C2×D4—21no—
346C2×D4C2×D4×C1112yes—
347C2×D4C2×Q8×C1112yes—
348C2×D4C2×Q8×C1112yes—
349C2×D4C11×#4112yes—
350C22×C4—21no—
351C22×C4—24no—
352C22×C4—21no—
353C22×C4—22no—
354C22×C4—22no—
355C22×C4—44no—
356C22×C4—44no—
357C22×C4—44no—
358C22×C4—42no—
359C22×C4—82no—
360C22×C4—82no—
361C22×C4C2×D4×C1112yes—
362C22×C4C2×D4×C1112yes—
363C22×C4C2×D4×C1111yescharacteristic
364C22×C4C2×D4×C1111yescharacteristic
365C22×C4C24×C1111yescharacteristic
366D8—28no—
367C2×C8—21no—
368C2×C8—21no—
369C2×C8—21no—
370C2×C8—22no—
371C2×C8—22no—
372C2×C8—21no—
373C2×C8—22no—
374C2×C8—21no—
375C2×C8C2×Q8×C1112yes—
376C4⋊C4—21no—
377C4⋊C4—21no—
378C4⋊C4—22no—
379C4⋊C4—21no—
380C4⋊C4—22no—
381C4⋊C4—22no—
382C4⋊C4—22no—
383C4⋊C4—42no—
384C4⋊C4—42no—
385C4⋊C4—82no—
386C4⋊C4C2×D4×C1112yes—
387C22⋊C4—24no—
388C22⋊C4—44no—
389C22⋊C4—42no—
390C22⋊C4—82no—
391C22⋊C4—82no—
392C42—22no—
393C42—22no—
394C42C2×D4×C1112yes—
395C42C11×#4112yes—
396C11#2483011yescharacteristic, direct product factor, Sylow
397C23—22no—
398C23—22no—
399C23—22no—
400C23—22no—
401C23—42no—
402C23—42no—
403C23—41no—
404C23—41no—
405C23—42no—
406C23—42no—
407C23C22×D4×C1111yescharacteristic
408Q8—84no—
409D4—22no—
410D4—22no—
411D4—22no—
412D4—22no—
413D4—22no—
414D4—41no—
415D4—41no—
416D4C11×C22⋊Q814yes—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—22no—
426C2×C4—42no—
427C2×C4—41no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—84no—
436C2×C4—84no—
437C2×C4—88no—
438C2×C4C11×#12112yes—
439C2×C4C11×#12112yes—
440C2×C4C22×D4×C1111yescharacteristic
441C2×C4C22×Q8×C1111yescharacteristic
442C2×C4C2×C11×#4111yescharacteristic
443C2×C4C2×C11×#4111yescharacteristic
444C2×C4C11×H(5,𝔽2)11yescharacteristic
445C2×C4C11×2−1+411yescharacteristic
446C8—22no—
447C8—41no—
448C8—42no—
449C22—24no—
450C22—42no—
451C22—42no—
452C22—44no—
453C22—44no—
454C22—42no—
455C22—44no—
456C22—81no—
457C22—81no—
458C22—82no—
459C22C2×C11×#12111yescharacteristic
460C22C11×#54611yescharacteristic
461C22D4×Q8×C1111yescharacteristic
462C22C11×#57512yes—
463C22C11×#57612yes—
464C4—22no—
465C4—22no—
466C4—42no—
467C4—42no—
468C4—42no—
469C4—81no—
470C4—82no—
471C4—82no—
472C4C2×C11×C22⋊Q811yescharacteristic
473C4C11×#53711yescharacteristic
474C4C11×#55211yescharacteristic
475C4C11×#55411yescharacteristic
476C2—44no—
477C2—82no—
478C2C11×#241711yescharacteristic
479C2C11×#304011yescharacteristic
480C2C11×#304111yescharacteristic
481C2C11×#331912yes—
482C2C11×#338912yes—
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×#474C2semidirect
3. C11×#2563C2semidirect
4. C11×#2349C2semidirect
5. C11×#2085C2semidirect
6. C11×#2067C2semidirect
7. C11×#1993C2semidirect
8. C11×#1940C2semidirect
10. C11×#1804C2semidirect
11. C11×#1804C2semidirect
51. C2×C11×D8Q8semidirect
93. #24830C11direct (N × H)
156. C2×#474C2×C11semidirect
158. #2563C2×C11semidirect
159. #2349C2×C11semidirect
160. #2085C2×C11semidirect
161. #2067C2×C11semidirect
162. #1993C2×C11semidirect
163. #1940C2×C11semidirect
165. #1804C2×C11semidirect
166. #1804C2×C11semidirect
285. C2×D8Q8×C11semidirect
396. C11#24830direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4742
C2×C11×#4422
C11×#25632
C11×#23492
C11×#20852
C11×#20672
C11×#19932
C11×#19402
C11×#18792
C11×#18042
#2483011