Finite Group Databasebeta

← C11×#24814 #14602007

Subgroups — C11×#24814 #14602007

Order 2816.

838 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×#477C211yesmaximal, characteristic, complemented
2C2×C4×C11×SD16C211yesmaximal, characteristic
3C11×#2563C211yesmaximal, characteristic
4Q8×C11×C4⋊C4C211yesmaximal, characteristic, complemented
5C11×#2085C212yesmaximal, complemented
6C11×#2067C212yesmaximal
7C11×#1990C211yesmaximal, characteristic, complemented
8C11×#1939C211yesmaximal, characteristic, complemented
9C11×#1880C212yesmaximal
10C11×#1805C212yesmaximal, complemented
11C11×#1802C211yesmaximal, characteristic
12C22×C11×SD16C2211yescharacteristic
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×C4×Q8×C11C2212yes—
15C2×C4×Q8×C11C2211yescharacteristic
16C2×C4×D4×C11C2211yescharacteristic
17C11×#477—24no—
18C4×C11×SD16—24no—
19C2×C11×#107C2212yes—
20C2×C11×#106C2211yescharacteristic
21C2×C11×C4⋊C8C2211yescharacteristic
22C2×C11×C4⋊C8C2212yes—
23C2×C11×#103C2212yes—
24C2×C11×#103C2211yescharacteristic
25C2×C11×#102C2211yescharacteristic
26C2×C11×#102C2212yes—
27C2×C4×C8×C11C2211yescharacteristic
28C11×#393—22no—
29C11×#390C2212yes—
30C11×#389—22no—
31C11×#389C2212yes—
32C11×#384—21no—
33C11×#384C2211yescharacteristic
34C11×#382C2212yes—
35C11×#380—21no—
36C11×#380—21no—
37C4×C11×C4⋊C4—21no—
38C4×C11×C4⋊C4C2211yescharacteristic
39C11×#340C2212yes—
40C11×#340C2212yes—
41C11×#340C2212yes—
42C11×#336C2212yes—
43C22×Q8×C11—21no—
44C22×Q8×C11C2311yescharacteristic
45C22×D4×C11C2311yescharacteristic
46C23×C4×C11—21no—
47C2×C11×SD16—22no—
48C2×C11×SD16—22no—
49C2×C11×SD16Q814yescomplemented
50C22×C8×C11C2312yes—
51C22×C8×C11C2311yescharacteristic
52C22×C8×C11C2311yescharacteristic
53C11×C4⋊Q8—22no—
54C11×C4⋊Q8—22no—
55C4×Q8×C11—22no—
56C4×Q8×C11—24no—
57C4×Q8×C11—42no—
58C4×Q8×C11D414yes—
59C4×D4×C11—22no—
60C4×D4×C11—22no—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4—22no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—22no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4D411yescharacteristic
68C2×C11×C4⋊C4D411yescharacteristic
69C2×C11×C4⋊C4C2312yes—
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2312yes—
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C22⋊C4—21no—
74C2×C11×C22⋊C4—22no—
75C2×C11×C22⋊C4—22no—
76C2×C42×C11—21no—
77C2×C42×C11—22no—
78C2×C42×C11C2312yes—
79C2×C42×C11C2311yescharacteristic
80C11×#107—24no—
81C11×#106—22no—
82C11×C4⋊C8—22no—
83C11×C4⋊C8—42no—
84C11×#103—22no—
85C11×#103—24no—
86C11×#102—22no—
87C11×#102—42no—
88C4×C8×C11—22no—
89C11×#95—22no—
90C11×#95—22no—
91C11×#95—22no—
92C11×#95D412yes—
93#24814C1111yesmaximal, characteristic, direct product factor, Sylow
94C24×C11—21no—
95C2×Q8×C11—21no—
96C2×Q8×C11—21no—
97C2×Q8×C11—21no—
98C2×Q8×C11—42no—
99C2×Q8×C11—81no—
100C2×Q8×C11—81no—
101C2×Q8×C11C2×D412yes—
102C2×Q8×C11C2×Q812yes—
103C2×Q8×C11#4112yes—
104C2×D4×C11—21no—
105C2×D4×C11—21no—
106C2×D4×C11—21no—
107C2×D4×C11—21no—
108C2×D4×C11—21no—
109C2×D4×C11C2×Q812yes—
110C22×C4×C11—21no—
111C22×C4×C11—21no—
112C22×C4×C11—21no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—42no—
116C22×C4×C11—42no—
117C22×C4×C11—42no—
118C22×C4×C11C2×D412yes—
119C22×C4×C11C2×D412yes—
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2411yescharacteristic
123C11×SD16—28no—
124C2×C8×C11—21no—
125C2×C8×C11—21no—
126C2×C8×C11—22no—
127C2×C8×C11—21no—
128C2×C8×C11—22no—
129C2×C8×C11—21no—
130C2×C8×C11—22no—
131C2×C8×C11—21no—
132C2×C8×C11C2×Q812yes—
133C11×C4⋊C4—24no—
134C11×C4⋊C4—22no—
135C11×C4⋊C4—22no—
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—44no—
144C11×C4⋊C4—42no—
145C11×C4⋊C4—42no—
146C11×C4⋊C4—81no—
147C11×C4⋊C4—82no—
148C11×C4⋊C4C2×D412yes—
149C11×C22⋊C4—42no—
150C11×C22⋊C4—82no—
151C11×C22⋊C4—82no—
152C42×C11—24no—
153C42×C11—22no—
154C42×C11—22no—
155C42×C11—44no—
156C42×C11C2×D412yes—
157C42×C11#4112yes—
158C2×#477C2×C1111yescharacteristic, complemented
159C2×C4×SD16C2×C1111yescharacteristic
160#2563C2×C1111yescharacteristic
161Q8×C4⋊C4C2×C1111yescharacteristic, complemented
162#2085C2×C1112yescomplemented
163#2067C2×C1112yes—
164#1990C2×C1111yescharacteristic, complemented
165#1939C2×C1111yescharacteristic, complemented
166#1880C2×C1112yes—
167#1805C2×C1112yescomplemented
168#1802C2×C1111yescharacteristic
169C23×C11—22no—
170C23×C11—41no—
171C23×C11—41no—
172C23×C11—41no—
173C23×C11—41no—
174C23×C11—41no—
175C23×C11—41no—
176C23×C11C22×D411yescharacteristic
177Q8×C11—22no—
178Q8×C11—22no—
179Q8×C11—22no—
180Q8×C11—84no—
181Q8×C11C22⋊Q814yes—
182D4×C11—22no—
183D4×C11—22no—
184D4×C11—41no—
185D4×C11—41no—
186C2×C4×C11—22no—
187C2×C4×C11—22no—
188C2×C4×C11—22no—
189C2×C4×C11—21no—
190C2×C4×C11—21no—
191C2×C4×C11—22no—
192C2×C4×C11—22no—
193C2×C4×C11—22no—
194C2×C4×C11—22no—
195C2×C4×C11—22no—
196C2×C4×C11—22no—
197C2×C4×C11—22no—
198C2×C4×C11—41no—
199C2×C4×C11—41no—
200C2×C4×C11—41no—
201C2×C4×C11—42no—
202C2×C4×C11—42no—
203C2×C4×C11—42no—
204C2×C4×C11—41no—
205C2×C4×C11—41no—
206C2×C4×C11—42no—
207C2×C4×C11—42no—
208C2×C4×C11—42no—
209C2×C4×C11—84no—
210C2×C4×C11#12112yes—
211C2×C4×C11#12112yes—
212C2×C4×C11#13512yes—
213C2×C4×C11#13712yes—
214C2×C4×C11C22×D411yescharacteristic
215C2×C4×C11C22×Q811yescharacteristic
216C2×C4×C11C2×#4111yescharacteristic
217C2×C4×C11C2×#4111yescharacteristic
218C2×C4×C11H(5,𝔽2)11yescharacteristic
219C2×C4×C112−1+411yescharacteristic
220C8×C11—22no—
221C8×C11—41no—
222C8×C11—42no—
223C22×SD16C22×C1111yescharacteristic
224C2×C4⋊Q8C22×C1111yescharacteristic
225C2×C4×Q8C22×C1112yes—
226C2×C4×Q8C22×C1111yescharacteristic
227C2×C4×D4C22×C1111yescharacteristic
228#477—24no—
229C4×SD16—24no—
230C2×#107C22×C1112yes—
231C2×#106C22×C1111yescharacteristic
232C2×C4⋊C8C22×C1111yescharacteristic
233C2×C4⋊C8C22×C1112yes—
234C2×#103C22×C1112yes—
235C2×#103C22×C1111yescharacteristic
236C2×#102C22×C1111yescharacteristic
237C2×#102C22×C1112yes—
238C2×C4×C8C22×C1111yescharacteristic
239#393—22no—
240#390C22×C1112yes—
241#389—22no—
242#389C22×C1112yes—
243#384—21no—
244#384C22×C1111yescharacteristic
245#382C22×C1112yes—
246#380—21no—
247#380—21no—
248C4×C4⋊C4—21no—
249C4×C4⋊C4C22×C1111yescharacteristic
250#340C22×C1112yes—
251#340C22×C1112yes—
252#340C22×C1112yes—
253#336C22×C1112yes—
254C22×C11—42no—
255C22×C11—42no—
256C22×C11—42no—
257C22×C11—81no—
258C22×C11—81no—
259C22×C11—81no—
260C22×C11—81no—
261C22×C11C2×#12111yescharacteristic
262C22×C11#54611yescharacteristic
263C22×C11D4×Q811yescharacteristic
264C22×C11C2×#13511yescharacteristic
265C22×C11C2×#13711yescharacteristic
266C22×C11#57611yescharacteristic
267C22×C11#57711yescharacteristic
268C4×C11—24no—
269C4×C11—22no—
270C4×C11—42no—
271C4×C11—42no—
272C4×C11—42no—
273C4×C11—81no—
274C4×C11—82no—
275C4×C11—82no—
276C4×C11#46414yes—
277C4×C11C2×C22⋊Q811yescharacteristic
278C4×C11#53711yescharacteristic
279C4×C11#55211yescharacteristic
280C4×C11#55411yescharacteristic
281C22×Q8—21no—
282C22×Q8C23×C1111yescharacteristic
283C22×D4C23×C1111yescharacteristic
284C23×C4—21no—
285C2×SD16—22no—
286C2×SD16—22no—
287C2×SD16Q8×C1114yescomplemented
288C22×C8C23×C1112yes—
289C22×C8C23×C1111yescharacteristic
290C22×C8C23×C1111yescharacteristic
291C4⋊Q8—22no—
292C4⋊Q8—22no—
293C4×Q8—22no—
294C4×Q8—24no—
295C4×Q8—42no—
296C4×Q8D4×C1114yes—
297C4×D4—22no—
298C4×D4—22no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4D4×C1111yescharacteristic
306C2×C4⋊C4D4×C1111yescharacteristic
307C2×C4⋊C4C23×C1111yescharacteristic
308C2×C4⋊C4C23×C1112yes—
309C2×C4⋊C4C23×C1112yes—
310C2×C4⋊C4C23×C1111yescharacteristic
311C2×C22⋊C4—21no—
312C2×C22⋊C4—22no—
313C2×C22⋊C4—22no—
314C2×C42—21no—
315C2×C42—22no—
316C2×C42C23×C1112yes—
317C2×C42C23×C1111yescharacteristic
318#107—24no—
319#106—22no—
320C4⋊C8—22no—
321C4⋊C8—42no—
322#103—22no—
323#103—24no—
324#102—22no—
325#102—42no—
326C4×C8—22no—
327#95—22no—
328#95—22no—
329#95—22no—
330#95D4×C1112yes—
331C2×C11—82no—
332C2×C11#241711yescharacteristic
333C2×C11C2×#46411yescharacteristic
334C2×C11#304511yescharacteristic
335C2×C11#330511yescharacteristic
336C2×C11#332911yescharacteristic
337C2×C11#338111yescharacteristic
338C2×C11#338511yescharacteristic
339C24—21no—
340C2×Q8—21no—
341C2×Q8—21no—
342C2×Q8—21no—
343C2×Q8—42no—
344C2×Q8—81no—
345C2×Q8—81no—
346C2×Q8C2×D4×C1112yes—
347C2×Q8C2×Q8×C1112yes—
348C2×Q8C11×#4112yes—
349C2×D4—21no—
350C2×D4—21no—
351C2×D4—21no—
352C2×D4—21no—
353C2×D4—21no—
354C2×D4C2×Q8×C1112yes—
355C22×C4—21no—
356C22×C4—21no—
357C22×C4—21no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—42no—
361C22×C4—42no—
362C22×C4—42no—
363C22×C4C2×D4×C1112yes—
364C22×C4C2×D4×C1112yes—
365C22×C4C2×D4×C1111yescharacteristic
366C22×C4C2×D4×C1111yescharacteristic
367C22×C4C24×C1111yescharacteristic
368SD16—28no—
369C2×C8—21no—
370C2×C8—21no—
371C2×C8—21no—
372C2×C8—22no—
373C2×C8—22no—
374C2×C8—21no—
375C2×C8—22no—
376C2×C8—21no—
377C2×C8C2×Q8×C1112yes—
378C4⋊C4—24no—
379C4⋊C4—22no—
380C4⋊C4—22no—
381C4⋊C4—21no—
382C4⋊C4—21no—
383C4⋊C4—22no—
384C4⋊C4—21no—
385C4⋊C4—22no—
386C4⋊C4—22no—
387C4⋊C4—22no—
388C4⋊C4—44no—
389C4⋊C4—42no—
390C4⋊C4—42no—
391C4⋊C4—81no—
392C4⋊C4—82no—
393C4⋊C4C2×D4×C1112yes—
394C22⋊C4—42no—
395C22⋊C4—82no—
396C22⋊C4—82no—
397C42—24no—
398C42—22no—
399C42—22no—
400C42—44no—
401C42C2×D4×C1112yes—
402C42C11×#4112yes—
403C11#2481411yescharacteristic, direct product factor, Sylow
404C23—22no—
405C23—41no—
406C23—41no—
407C23—41no—
408C23—41no—
409C23—41no—
410C23—41no—
411C23C22×D4×C1111yescharacteristic
412Q8—22no—
413Q8—22no—
414Q8—22no—
415Q8—84no—
416Q8C11×C22⋊Q814yes—
417D4—22no—
418D4—22no—
419D4—41no—
420D4—41no—
421C2×C4—22no—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—22no—
432C2×C4—22no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—42no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—42no—
444C2×C4—84no—
445C2×C4C11×#12112yes—
446C2×C4C11×#12112yes—
447C2×C4C11×#13512yes—
448C2×C4C11×#13712yes—
449C2×C4C22×D4×C1111yescharacteristic
450C2×C4C22×Q8×C1111yescharacteristic
451C2×C4C2×C11×#4111yescharacteristic
452C2×C4C2×C11×#4111yescharacteristic
453C2×C4C11×H(5,𝔽2)11yescharacteristic
454C2×C4C11×2−1+411yescharacteristic
455C8—22no—
456C8—41no—
457C8—42no—
458C22—42no—
459C22—42no—
460C22—42no—
461C22—81no—
462C22—81no—
463C22—81no—
464C22—81no—
465C22C2×C11×#12111yescharacteristic
466C22C11×#54611yescharacteristic
467C22D4×Q8×C1111yescharacteristic
468C22C2×C11×#13511yescharacteristic
469C22C2×C11×#13711yescharacteristic
470C22C11×#57611yescharacteristic
471C22C11×#57711yescharacteristic
472C4—24no—
473C4—22no—
474C4—42no—
475C4—42no—
476C4—42no—
477C4—81no—
478C4—82no—
479C4—82no—
480C4C11×#46414yes—
481C4C2×C11×C22⋊Q811yescharacteristic
482C4C11×#53711yescharacteristic
483C4C11×#55211yescharacteristic
484C4C11×#55411yescharacteristic
485C2—82no—
486C2C11×#241711yescharacteristic
487C2C2×C11×#46411yescharacteristic
488C2C11×#304511yescharacteristic
489C2C11×#330511yescharacteristic
490C2C11×#332911yescharacteristic
491C2C11×#338111yescharacteristic
492C2C11×#338511yescharacteristic
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
1. C2×C11×#477C2semidirect
4. Q8×C11×C4⋊C4C2semidirect
5. C11×#2085C2semidirect
7. C11×#1990C2semidirect
8. C11×#1939C2semidirect
10. C11×#1805C2semidirect
49. C2×C11×SD16Q8semidirect
93. #24814C11direct (N × H)
158. C2×#477C2×C11semidirect
161. Q8×C4⋊C4C2×C11semidirect
162. #2085C2×C11semidirect
164. #1990C2×C11semidirect
165. #1939C2×C11semidirect
167. #1805C2×C11semidirect
287. C2×SD16Q8×C11semidirect
403. C11#24814direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4772
C2×C4×C11×SD162
C11×#25632
Q8×C11×C4⋊C42
C11×#20852
C11×#20672
C11×#19902
C11×#19392
C11×#18802
C11×#18052
C11×#18022
#2481411