Finite Group Databasebeta

← C11×#22996 #14600189

Subgroups — C11×#22996 #14600189

Order 2816.

1030 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×#461C211yesmaximal, characteristic
2C2×C4×C11×SD16C212yesmaximal
3C11×#2365C211yesmaximal, characteristic, complemented
4D4×C11×C4⋊C4C211yesmaximal, characteristic
5C11×#1956C211yesmaximal, characteristic, complemented
6C11×#1948C211yesmaximal, characteristic, complemented
7C11×#1933C212yesmaximal, complemented
8C11×#1877C212yesmaximal
9C11×#1865C212yesmaximal, complemented
10C8×C11×C4⋊C4C211yesmaximal, characteristic, complemented
11C4×C11×#102C211yesmaximal, characteristic
12C22×C11×SD16C2212yes—
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×C4×Q8×C11C2212yes—
15C2×C4×D4×C11C2212yes—
16C2×C4×D4×C11C2211yescharacteristic
17C22×C11×C4⋊C4—21no—
18C11×#461C418yescomplemented
19C4×C11×SD16—28no—
20C2×C11×#106C2212yes—
21C2×C11×C4⋊C8C2211yescharacteristic
22C2×C11×#103C2212yes—
23C2×C11×#103C2212yes—
24C2×C11×#103C2212yes—
25C2×C11×#102C2211yescharacteristic
26C2×C11×#102C2211yescharacteristic
27C2×C4×C8×C11C2212yes—
28C2×C4×C8×C11C2211yescharacteristic
29C11×#391C2212yes—
30C11×#389—21no—
31C11×#389C2212yes—
32C11×#387—22no—
33C11×#385—22no—
34C11×#384C2211yescharacteristic
35C11×#380—21no—
36C4×C11×C4⋊C4—21no—
37C4×C11×C4⋊C4C2211yescharacteristic
38C4×C11×C4⋊C4C2211yescharacteristic
39C11×#340C2212yes—
40C11×#340C2211yescharacteristic
41C11×#340C2211yescharacteristic
42C11×#336C2212yes—
43C22×Q8×C11C2312yes—
44C22×D4×C11C2311yescharacteristic
45C23×C4×C11—21no—
46C23×C4×C11—22no—
47C2×C11×SD16—24no—
48C2×C11×SD16—24no—
49C2×C11×SD16C2×C418yes—
50C22×C8×C11C2311yescharacteristic
51C22×C8×C11C2312yes—
52C22×C8×C11C2311yescharacteristic
53C11×C4⋊Q8—22no—
54C11×C4⋊Q8C2×C414yescomplemented
55C4×Q8×C11—24no—
56C4×Q8×C11—42no—
57C4×D4×C11—24no—
58C4×D4×C11—22no—
59C4×D4×C11—42no—
60C4×D4×C11C2×C414yes—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—22no—
65C2×C11×C4⋊C4—22no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4—44no—
68C2×C11×C4⋊C4D411yescharacteristic
69C2×C11×C4⋊C4D411yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2312yes—
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C22⋊C4—21no—
75C2×C11×C22⋊C4—22no—
76C2×C42×C11—21no—
77C2×C42×C11—22no—
78C2×C42×C11C2312yes—
79C2×C42×C11C2311yescharacteristic
80C11×#106—24no—
81C11×C4⋊C8C2×C414yescomplemented
82C11×#103—24no—
83C11×#103—42no—
84C11×#103C2×C418yescomplemented
85C11×#102—22no—
86C11×#102D414yes—
87C4×C8×C11—24no—
88C4×C8×C11—22no—
89C11×#95—22no—
90C11×#95—21no—
91C11×#95—22no—
92C11×#95—22no—
93C11×#95D412yes—
94#22996C1111yesmaximal, characteristic, direct product factor, Sylow
95C24×C11—21no—
96C2×Q8×C11—22no—
97C2×Q8×C11—22no—
98C2×Q8×C11—22no—
99C2×Q8×C11—22no—
100C2×Q8×C11—22no—
101C2×Q8×C11C22×C414yes—
102C2×D4×C11—21no—
103C2×D4×C11—21no—
104C2×D4×C11—21no—
105C2×D4×C11C22×C412yes—
106C2×D4×C11C2×D412yes—
107C2×D4×C11#4112yes—
108C22×C4×C11—22no—
109C22×C4×C11—21no—
110C22×C4×C11—21no—
111C22×C4×C11—24no—
112C22×C4×C11—21no—
113C22×C4×C11—22no—
114C22×C4×C11—44no—
115C22×C4×C11—42no—
116C22×C4×C11—42no—
117C22×C4×C11—44no—
118C22×C4×C11—82no—
119C22×C4×C11C2×D412yes—
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2×D412yes—
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2411yescharacteristic
124C11×SD16—216no—
125C2×C8×C11—22no—
126C2×C8×C11—21no—
127C2×C8×C11—22no—
128C2×C8×C11—21no—
129C2×C8×C11—21no—
130C2×C8×C11—21no—
131C2×C8×C11—21no—
132C2×C8×C11C22×C414yes—
133C2×C8×C11C2×D412yes—
134C11×C4⋊C4—24no—
135C11×C4⋊C4—24no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—21no—
138C11×C4⋊C4—21no—
139C11×C4⋊C4—22no—
140C11×C4⋊C4—21no—
141C11×C4⋊C4—22no—
142C11×C4⋊C4—21no—
143C11×C4⋊C4—44no—
144C11×C4⋊C4—44no—
145C11×C4⋊C4—42no—
146C11×C4⋊C4—81no—
147C11×C4⋊C4SD1614yescomplemented
148C11×C4⋊C4C22×C412yes—
149C11×C4⋊C4C2×D412yes—
150C11×C22⋊C4—24no—
151C11×C22⋊C4—44no—
152C42×C11—22no—
153C42×C11—22no—
154C42×C11—44no—
155C42×C11—42no—
156C42×C11C22×C412yes—
157C42×C11#4112yes—
158C2×#461C2×C1111yescharacteristic
159C2×C4×SD16C2×C1112yes—
160#2365C2×C1111yescharacteristic, complemented
161D4×C4⋊C4C2×C1111yescharacteristic
162#1956C2×C1111yescharacteristic, complemented
163#1948C2×C1111yescharacteristic, complemented
164#1933C2×C1112yescomplemented
165#1877C2×C1112yes—
166#1865C2×C1112yescomplemented
167C8×C4⋊C4C2×C1111yescharacteristic, complemented
168C4×#102C2×C1111yescharacteristic
169C23×C11—22no—
170C23×C11—22no—
171C23×C11—22no—
172C23×C11—41no—
173C23×C11—41no—
174C23×C11—41no—
175C23×C11—41no—
176C23×C11C22×D411yescharacteristic
177Q8×C11—24no—
178Q8×C11—24no—
179Q8×C11—42no—
180Q8×C11—42no—
181D4×C11—22no—
182D4×C11—22no—
183D4×C11—22no—
184D4×C11C4×D414yes—
185C2×C4×C11—22no—
186C2×C4×C11—21no—
187C2×C4×C11—22no—
188C2×C4×C11—21no—
189C2×C4×C11—22no—
190C2×C4×C11—24no—
191C2×C4×C11—22no—
192C2×C4×C11—22no—
193C2×C4×C11—22no—
194C2×C4×C11—22no—
195C2×C4×C11—42no—
196C2×C4×C11—42no—
197C2×C4×C11—41no—
198C2×C4×C11—41no—
199C2×C4×C11—41no—
200C2×C4×C11—41no—
201C2×C4×C11—48no—
202C2×C4×C11—42no—
203C2×C4×C11—41no—
204C2×C4×C11—42no—
205C2×C4×C11—41no—
206C2×C4×C11—42no—
207C2×C4×C11—41no—
208C2×C4×C11—88no—
209C2×C4×C11C4×D412yes—
210C2×C4×C11C4×D412yes—
211C2×C4×C11C2×SD1614yes—
212C2×C4×C11C2×SD1612yes—
213C2×C4×C11#13512yes—
214C2×C4×C11C23×C411yescharacteristic
215C2×C4×C11C22×D411yescharacteristic
216C2×C4×C11C2×#4111yescharacteristic
217C2×C4×C11C2×#4111yescharacteristic
218C2×C4×C11H(5,𝔽2)11yescharacteristic
219C2×C4×C112−1+411yescharacteristic
220C8×C11—24no—
221C8×C11—22no—
222C8×C11—41no—
223C22×SD16C22×C1112yes—
224C2×C4⋊Q8C22×C1111yescharacteristic
225C2×C4×Q8C22×C1112yes—
226C2×C4×D4C22×C1112yes—
227C2×C4×D4C22×C1111yescharacteristic
228C22×C4⋊C4—21no—
229#461C4×C1118yescomplemented
230C4×SD16—28no—
231C2×#106C22×C1112yes—
232C2×C4⋊C8C22×C1111yescharacteristic
233C2×#103C22×C1112yes—
234C2×#103C22×C1112yes—
235C2×#103C22×C1112yes—
236C2×#102C22×C1111yescharacteristic
237C2×#102C22×C1111yescharacteristic
238C2×C4×C8C22×C1112yes—
239C2×C4×C8C22×C1111yescharacteristic
240#391C22×C1112yes—
241#389—21no—
242#389C22×C1112yes—
243#387—22no—
244#385—22no—
245#384C22×C1111yescharacteristic
246#380—21no—
247C4×C4⋊C4—21no—
248C4×C4⋊C4C22×C1111yescharacteristic
249C4×C4⋊C4C22×C1111yescharacteristic
250#340C22×C1111yescharacteristic
251#340C22×C1112yes—
252#340C22×C1111yescharacteristic
253#336C22×C1112yes—
254C22×C11—24no—
255C22×C11—42no—
256C22×C11—42no—
257C22×C11—42no—
258C22×C11—42no—
259C22×C11—42no—
260C22×C11—42no—
261C22×C11C2×C4×D411yescharacteristic
262C22×C11D4211yescharacteristic
263C22×C11#54811yescharacteristic
264C22×C11C22×SD1611yescharacteristic
265C22×C11C2×#13511yescharacteristic
266C22×C11#57711yescharacteristic
267C22×C11#57811yescharacteristic
268C4×C11—22no—
269C4×C11—24no—
270C4×C11—44no—
271C4×C11—42no—
272C4×C11—42no—
273C4×C11—42no—
274C4×C11—81no—
275C4×C11—82no—
276C4×C11C4×SD1614yescomplemented
277C4×C11C2×C4×D411yescharacteristic
278C4×C11#52011yescharacteristic
279C4×C11#54711yescharacteristic
280C4×C11#55311yescharacteristic
281C22×Q8C23×C1112yes—
282C22×D4C23×C1111yescharacteristic
283C23×C4—21no—
284C23×C4—22no—
285C2×SD16—24no—
286C2×SD16—24no—
287C2×SD16C2×C4×C1118yes—
288C22×C8C23×C1111yescharacteristic
289C22×C8C23×C1112yes—
290C22×C8C23×C1111yescharacteristic
291C4⋊Q8—22no—
292C4⋊Q8C2×C4×C1114yescomplemented
293C4×Q8—24no—
294C4×Q8—42no—
295C4×D4—24no—
296C4×D4—22no—
297C4×D4—42no—
298C4×D4C2×C4×C1114yes—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—44no—
306C2×C4⋊C4D4×C1111yescharacteristic
307C2×C4⋊C4D4×C1111yescharacteristic
308C2×C4⋊C4C23×C1112yes—
309C2×C4⋊C4C23×C1111yescharacteristic
310C2×C4⋊C4C23×C1111yescharacteristic
311C2×C4⋊C4C23×C1111yescharacteristic
312C2×C22⋊C4—21no—
313C2×C22⋊C4—22no—
314C2×C42—22no—
315C2×C42—21no—
316C2×C42C23×C1112yes—
317C2×C42C23×C1111yescharacteristic
318#106—24no—
319C4⋊C8C2×C4×C1114yescomplemented
320#103—24no—
321#103—42no—
322#103C2×C4×C1118yescomplemented
323#102—22no—
324#102D4×C1114yes—
325C4×C8—24no—
326C4×C8—22no—
327#95—22no—
328#95—21no—
329#95—22no—
330#95—22no—
331#95D4×C1112yes—
332C2×C11—44no—
333C2×C11#236111yescharacteristic
334C2×C11C2×C4×SD1611yescharacteristic
335C2×C11#294711yescharacteristic
336C2×C11D4×SD1611yescharacteristic
337C2×C11#328311yescharacteristic
338C2×C11#335911yescharacteristic
339C2×C11#336011yescharacteristic
340C24—21no—
341C2×Q8—22no—
342C2×Q8—22no—
343C2×Q8—22no—
344C2×Q8—22no—
345C2×Q8—22no—
346C2×Q8C22×C4×C1114yes—
347C2×D4—21no—
348C2×D4—21no—
349C2×D4—21no—
350C2×D4C22×C4×C1112yes—
351C2×D4C2×D4×C1112yes—
352C2×D4C11×#4112yes—
353C22×C4—22no—
354C22×C4—21no—
355C22×C4—21no—
356C22×C4—24no—
357C22×C4—21no—
358C22×C4—22no—
359C22×C4—44no—
360C22×C4—42no—
361C22×C4—42no—
362C22×C4—44no—
363C22×C4—82no—
364C22×C4C2×D4×C1112yes—
365C22×C4C2×D4×C1111yescharacteristic
366C22×C4C2×D4×C1112yes—
367C22×C4C2×D4×C1111yescharacteristic
368C22×C4C24×C1111yescharacteristic
369SD16—216no—
370C2×C8—22no—
371C2×C8—21no—
372C2×C8—22no—
373C2×C8—21no—
374C2×C8—21no—
375C2×C8—21no—
376C2×C8—21no—
377C2×C8C22×C4×C1114yes—
378C2×C8C2×D4×C1112yes—
379C4⋊C4—24no—
380C4⋊C4—24no—
381C4⋊C4—22no—
382C4⋊C4—21no—
383C4⋊C4—21no—
384C4⋊C4—22no—
385C4⋊C4—21no—
386C4⋊C4—22no—
387C4⋊C4—21no—
388C4⋊C4—44no—
389C4⋊C4—44no—
390C4⋊C4—42no—
391C4⋊C4—81no—
392C4⋊C4C11×SD1614yescomplemented
393C4⋊C4C22×C4×C1112yes—
394C4⋊C4C2×D4×C1112yes—
395C22⋊C4—24no—
396C22⋊C4—44no—
397C42—22no—
398C42—22no—
399C42—44no—
400C42—42no—
401C42C22×C4×C1112yes—
402C42C11×#4112yes—
403C11#2299611yescharacteristic, direct product factor, Sylow
404C23—22no—
405C23—22no—
406C23—22no—
407C23—41no—
408C23—41no—
409C23—41no—
410C23—41no—
411C23C22×D4×C1111yescharacteristic
412Q8—24no—
413Q8—24no—
414Q8—42no—
415Q8—42no—
416D4—22no—
417D4—22no—
418D4—22no—
419D4C4×D4×C1114yes—
420C2×C4—22no—
421C2×C4—21no—
422C2×C4—22no—
423C2×C4—21no—
424C2×C4—22no—
425C2×C4—24no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—48no—
437C2×C4—42no—
438C2×C4—41no—
439C2×C4—42no—
440C2×C4—41no—
441C2×C4—42no—
442C2×C4—41no—
443C2×C4—88no—
444C2×C4C4×D4×C1112yes—
445C2×C4C4×D4×C1112yes—
446C2×C4C2×C11×SD1614yes—
447C2×C4C2×C11×SD1612yes—
448C2×C4C11×#13512yes—
449C2×C4C23×C4×C1111yescharacteristic
450C2×C4C22×D4×C1111yescharacteristic
451C2×C4C2×C11×#4111yescharacteristic
452C2×C4C2×C11×#4111yescharacteristic
453C2×C4C11×H(5,𝔽2)11yescharacteristic
454C2×C4C11×2−1+411yescharacteristic
455C8—24no—
456C8—22no—
457C8—41no—
458C22—24no—
459C22—42no—
460C22—42no—
461C22—42no—
462C22—42no—
463C22—42no—
464C22—42no—
465C22C2×C4×D4×C1111yescharacteristic
466C22D42×C1111yescharacteristic
467C22C11×#54811yescharacteristic
468C22C22×C11×SD1611yescharacteristic
469C22C2×C11×#13511yescharacteristic
470C22C11×#57711yescharacteristic
471C22C11×#57811yescharacteristic
472C4—22no—
473C4—24no—
474C4—42no—
475C4—42no—
476C4—42no—
477C4—44no—
478C4—82no—
479C4—81no—
480C4C4×C11×SD1614yescomplemented
481C4C2×C4×D4×C1111yescharacteristic
482C4C11×#52011yescharacteristic
483C4C11×#54711yescharacteristic
484C4C11×#55311yescharacteristic
485C2—44no—
486C2C11×#236111yescharacteristic
487C2C2×C4×C11×SD1611yescharacteristic
488C2C11×#294711yescharacteristic
489C2D4×C11×SD1611yescharacteristic
490C2C11×#328311yescharacteristic
491C2C11×#335911yescharacteristic
492C2C11×#336011yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11C23
LCSG ▷ C2×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
3. C11×#2365C2semidirect
5. C11×#1956C2semidirect
6. C11×#1948C2semidirect
7. C11×#1933C2semidirect
9. C11×#1865C2semidirect
10. C8×C11×C4⋊C4C2semidirect
18. C11×#461C4semidirect
54. C11×C4⋊Q8C2×C4semidirect
81. C11×C4⋊C8C2×C4semidirect
84. C11×#103C2×C4semidirect
94. #22996C11direct (N × H)
147. C11×C4⋊C4SD16semidirect
160. #2365C2×C11semidirect
162. #1956C2×C11semidirect
163. #1948C2×C11semidirect
164. #1933C2×C11semidirect
166. #1865C2×C11semidirect
167. C8×C4⋊C4C2×C11semidirect
229. #461C4×C11semidirect
276. C4×C11C4×SD16semidirect
292. C4⋊Q8C2×C4×C11semidirect
319. C4⋊C8C2×C4×C11semidirect
322. #103C2×C4×C11semidirect
392. C4⋊C4C11×SD16semidirect
403. C11#22996direct (N × H)
480. C4C4×C11×SD16semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#4612
C2×C4×C11×SD162
C11×#23652
D4×C11×C4⋊C42
C11×#19562
C11×#19482
C11×#19332
C11×#18772
C11×#18652
C8×C11×C4⋊C42
C4×C11×#1022
#2299611