Finite Group Databasebeta

← C11×#23095 #14600288

Subgroups — C11×#23095 #14600288

Order 2816.

966 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×#460C211yesmaximal, characteristic
2C11×#2366C211yesmaximal, characteristic
3C11×#2355C211yesmaximal, characteristic, complemented
4C11×#1968C212yesmaximal, complemented
5C11×#1957C211yesmaximal, characteristic
6C11×#1948C211yesmaximal, characteristic, complemented
7C11×#1926C212yesmaximal, complemented
8C11×#1877C212yesmaximal, complemented
9C8×C11×C4⋊C4C211yesmaximal, characteristic, complemented
10C4×C11×#103C211yesmaximal, characteristic, complemented
11C4×C11×#102C212yesmaximal, complemented
12C22×C11×SD16C2212yes—
13C2×C11×#127C2211yescharacteristic
14C2×C4×Q8×C11C2211yescharacteristic
15C2×C4×D4×C11—21no—
16C2×C4×D4×C11C2212yes—
17C11×#460C418yescomplemented
18C2×C11×#106C2212yes—
19C2×C11×C4⋊C8C2211yescharacteristic
20C2×C11×#103C2211yescharacteristic
21C2×C11×#103C2211yescharacteristic
22C2×C11×#102C2212yes—
23C2×C11×#102C2212yes—
24C2×C11×#102C2212yes—
25C2×C4×C8×C11C2211yescharacteristic
26C2×C4×C8×C11C2212yes—
27C11×#391C2212yes—
28C11×#390—21no—
29C11×#390C2212yes—
30C11×#387—22no—
31C11×#386—22no—
32C11×#384C2211yescharacteristic
33C11×#382—21no—
34C4×C11×C4⋊C4—21no—
35C4×C11×C4⋊C4C2212yes—
36C4×C11×C4⋊C4C2211yescharacteristic
37C4×C11×C4⋊C4C2211yescharacteristic
38C11×#340C2212yes—
39C11×#340C2211yescharacteristic
40C11×#340C2211yescharacteristic
41C11×#336C2212yes—
42C22×Q8×C11C2311yescharacteristic
43C22×D4×C11—21no—
44C22×D4×C11—21no—
45C22×D4×C11C2312yes—
46C23×C4×C11—22no—
47C2×C11×SD16—42no—
48C2×C11×SD16—42no—
49C2×C11×SD16C2×C418yescomplemented
50C22×C8×C11C2311yescharacteristic
51C22×C8×C11C2312yes—
52C22×C8×C11C2311yescharacteristic
53C11×#127—22no—
54C11×#127C2×C414yes—
55C4×Q8×C11—22no—
56C4×Q8×C11C2×C414yescomplemented
57C4×D4×C11—24no—
58C4×D4×C11—42no—
59C4×D4×C11—44no—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4D411yescharacteristic
64C2×C11×C4⋊C4D411yescharacteristic
65C2×C11×C4⋊C4C2312yes—
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C22⋊C4—22no—
70C2×C11×C22⋊C4—22no—
71C2×C11×C22⋊C4—22no—
72C2×C42×C11—21no—
73C2×C42×C11—21no—
74C2×C42×C11—22no—
75C2×C42×C11C2312yes—
76C2×C42×C11C2311yescharacteristic
77C11×#106—42no—
78C11×C4⋊C8C2×C414yescomplemented
79C11×#103—22no—
80C11×#103—22no—
81C11×#102—24no—
82C11×#102—42no—
83C11×#102C2×C418yescomplemented
84C4×C8×C11—22no—
85C4×C8×C11—42no—
86C11×#95—22no—
87C11×#95—22no—
88C11×#95—21no—
89C11×#95—22no—
90C11×#95D412yes—
91#23095C1111yesmaximal, characteristic, direct product factor, Sylow
92C24×C11—22no—
93C2×Q8×C11—21no—
94C2×Q8×C11—21no—
95C2×Q8×C11—21no—
96C2×Q8×C11—21no—
97C2×Q8×C11—21no—
98C2×Q8×C11C22×C412yes—
99C2×D4×C11—24no—
100C2×D4×C11—24no—
101C2×D4×C11—22no—
102C2×D4×C11—22no—
103C2×D4×C11—22no—
104C2×D4×C11—22no—
105C2×D4×C11—22no—
106C2×D4×C11—42no—
107C2×D4×C11—42no—
108C2×D4×C11—81no—
109C2×D4×C11—81no—
110C2×D4×C11C22×C414yes—
111C22×C4×C11—21no—
112C22×C4×C11—21no—
113C22×C4×C11—21no—
114C22×C4×C11—22no—
115C22×C4×C11—21no—
116C22×C4×C11—44no—
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—48no—
125C2×C8×C11—21no—
126C2×C8×C11—21no—
127C2×C8×C11—21no—
128C2×C8×C11—21no—
129C2×C8×C11—22no—
130C2×C8×C11—22no—
131C2×C8×C11—21no—
132C2×C8×C11C22×C414yes—
133C2×C8×C11#4112yes—
134C11×C4⋊C4—24no—
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—21no—
142C11×C4⋊C4—42no—
143C11×C4⋊C4—81no—
144C11×C4⋊C4SD1614yescomplemented
145C11×C4⋊C4C22×C412yes—
146C11×C4⋊C4#4112yes—
147C11×C22⋊C4—44no—
148C11×C22⋊C4—44no—
149C11×C22⋊C4—82no—
150C42×C11—24no—
151C42×C11—22no—
152C42×C11—22no—
153C42×C11—42no—
154C42×C11—82no—
155C42×C11C22×C412yes—
156C42×C11#4112yes—
157C2×#460C2×C1111yescharacteristic
158#2366C2×C1111yescharacteristic
159#2355C2×C1111yescharacteristic, complemented
160#1968C2×C1112yescomplemented
161#1957C2×C1111yescharacteristic
162#1948C2×C1111yescharacteristic, complemented
163#1926C2×C1112yescomplemented
164#1877C2×C1112yescomplemented
165C8×C4⋊C4C2×C1111yescharacteristic, complemented
166C4×#103C2×C1111yescharacteristic, complemented
167C4×#102C2×C1112yescomplemented
168C23×C11—24no—
169C23×C11—42no—
170C23×C11—42no—
171C23×C11—42no—
172C23×C11—42no—
173C23×C11—42no—
174C23×C11—42no—
175C23×C11C22×D411yescharacteristic
176Q8×C11—22no—
177Q8×C11—22no—
178Q8×C11—41no—
179Q8×C11—41no—
180D4×C11—24no—
181D4×C11—24no—
182D4×C11—42no—
183D4×C11—42no—
184D4×C11—48no—
185D4×C11—84no—
186C2×C4×C11—22no—
187C2×C4×C11—22no—
188C2×C4×C11—21no—
189C2×C4×C11—21no—
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—41no—
197C2×C4×C11—41no—
198C2×C4×C11—41no—
199C2×C4×C11—41no—
200C2×C4×C11—41no—
201C2×C4×C11—41no—
202C2×C4×C11—41no—
203C2×C4×C11—42no—
204C2×C4×C11—41no—
205C2×C4×C11—42no—
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×C11C2×#4111yescharacteristic
216C2×C4×C11C2×#4111yescharacteristic
217C2×C4×C11C2×#4111yescharacteristic
218C2×C4×C11H(5,𝔽2)11yescharacteristic
219C2×C4×C11H(5,𝔽2)11yescharacteristic
220C8×C11—24no—
221C8×C11—22no—
222C8×C11—41no—
223C22×SD16C22×C1112yes—
224C2×#127C22×C1111yescharacteristic
225C2×C4×Q8C22×C1111yescharacteristic
226C2×C4×D4—21no—
227C2×C4×D4C22×C1112yes—
228#460C4×C1118yescomplemented
229C2×#106C22×C1112yes—
230C2×C4⋊C8C22×C1111yescharacteristic
231C2×#103C22×C1111yescharacteristic
232C2×#103C22×C1111yescharacteristic
233C2×#102C22×C1112yes—
234C2×#102C22×C1112yes—
235C2×#102C22×C1112yes—
236C2×C4×C8C22×C1111yescharacteristic
237C2×C4×C8C22×C1112yes—
238#391C22×C1112yes—
239#390—21no—
240#390C22×C1112yes—
241#387—22no—
242#386—22no—
243#384C22×C1111yescharacteristic
244#382—21no—
245C4×C4⋊C4—21no—
246C4×C4⋊C4C22×C1112yes—
247C4×C4⋊C4C22×C1111yescharacteristic
248C4×C4⋊C4C22×C1111yescharacteristic
249#340C22×C1112yes—
250#340C22×C1111yescharacteristic
251#340C22×C1111yescharacteristic
252#336C22×C1112yes—
253C22×C11—44no—
254C22×C11—44no—
255C22×C11—44no—
256C22×C11—82no—
257C22×C11—82no—
258C22×C11—82no—
259C22×C11—82no—
260C22×C11C2×C4×D411yescharacteristic
261C22×C11#54611yescharacteristic
262C22×C11#55011yescharacteristic
263C22×C11C22×SD1611yescharacteristic
264C22×C11C2×#13511yescharacteristic
265C22×C11#57611yescharacteristic
266C22×C11#57711yescharacteristic
267C4×C11—22no—
268C4×C11—24no—
269C4×C11—42no—
270C4×C11—42no—
271C4×C11—42no—
272C4×C11—42no—
273C4×C11—81no—
274C4×C11—82no—
275C4×C11C4×SD1614yes—
276C4×C11C4×#4111yescharacteristic
277C4×C11#51811yescharacteristic
278C4×C11#55311yescharacteristic
279C4×C11#55511yescharacteristic
280C22×Q8C23×C1111yescharacteristic
281C22×D4—21no—
282C22×D4—21no—
283C22×D4C23×C1112yes—
284C23×C4—22no—
285C2×SD16—42no—
286C2×SD16—42no—
287C2×SD16C2×C4×C1118yescomplemented
288C22×C8C23×C1111yescharacteristic
289C22×C8C23×C1112yes—
290C22×C8C23×C1111yescharacteristic
291#127—22no—
292#127C2×C4×C1114yes—
293C4×Q8—22no—
294C4×Q8C2×C4×C1114yescomplemented
295C4×D4—24no—
296C4×D4—42no—
297C4×D4—44no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4D4×C1111yescharacteristic
302C2×C4⋊C4D4×C1111yescharacteristic
303C2×C4⋊C4C23×C1112yes—
304C2×C4⋊C4C23×C1111yescharacteristic
305C2×C4⋊C4C23×C1111yescharacteristic
306C2×C4⋊C4C23×C1111yescharacteristic
307C2×C22⋊C4—22no—
308C2×C22⋊C4—22no—
309C2×C22⋊C4—22no—
310C2×C42—21no—
311C2×C42—21no—
312C2×C42—22no—
313C2×C42C23×C1112yes—
314C2×C42C23×C1111yescharacteristic
315#106—42no—
316C4⋊C8C2×C4×C1114yescomplemented
317#103—22no—
318#103—22no—
319#102—24no—
320#102—42no—
321#102C2×C4×C1118yescomplemented
322C4×C8—22no—
323C4×C8—42no—
324#95—22no—
325#95—22no—
326#95—21no—
327#95—22no—
328#95D4×C1112yes—
329C2×C11—84no—
330C2×C11#236311yescharacteristic
331C2×C11C2×C4×SD1611yescharacteristic
332C2×C11#294611yescharacteristic
333C2×C11#329511yescharacteristic
334C2×C11#330411yescharacteristic
335C2×C11#339211yescharacteristic
336C2×C11#339611yescharacteristic
337C24—22no—
338C2×Q8—21no—
339C2×Q8—21no—
340C2×Q8—21no—
341C2×Q8—21no—
342C2×Q8—21no—
343C2×Q8C22×C4×C1112yes—
344C2×D4—24no—
345C2×D4—24no—
346C2×D4—22no—
347C2×D4—22no—
348C2×D4—22no—
349C2×D4—22no—
350C2×D4—22no—
351C2×D4—42no—
352C2×D4—42no—
353C2×D4—81no—
354C2×D4—81no—
355C2×D4C22×C4×C1114yes—
356C22×C4—21no—
357C22×C4—21no—
358C22×C4—21no—
359C22×C4—22no—
360C22×C4—21no—
361C22×C4—44no—
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—48no—
370C2×C8—21no—
371C2×C8—21no—
372C2×C8—22no—
373C2×C8—22no—
374C2×C8—21no—
375C2×C8—21no—
376C2×C8—21no—
377C2×C8C22×C4×C1114yes—
378C2×C8C11×#4112yes—
379C4⋊C4—24no—
380C4⋊C4—22no—
381C4⋊C4—21no—
382C4⋊C4—21no—
383C4⋊C4—22no—
384C4⋊C4—21no—
385C4⋊C4—22no—
386C4⋊C4—21no—
387C4⋊C4—42no—
388C4⋊C4—81no—
389C4⋊C4C11×SD1614yescomplemented
390C4⋊C4C22×C4×C1112yes—
391C4⋊C4C11×#4112yes—
392C22⋊C4—44no—
393C22⋊C4—44no—
394C22⋊C4—82no—
395C42—24no—
396C42—22no—
397C42—22no—
398C42—42no—
399C42—82no—
400C42C22×C4×C1112yes—
401C42C11×#4112yes—
402C11#2309511yescharacteristic, direct product factor, Sylow
403C23—24no—
404C23—42no—
405C23—42no—
406C23—42no—
407C23—42no—
408C23—42no—
409C23—42no—
410C23C22×D4×C1111yescharacteristic
411Q8—22no—
412Q8—22no—
413Q8—41no—
414Q8—41no—
415D4—24no—
416D4—24no—
417D4—42no—
418D4—42no—
419D4—48no—
420D4—84no—
421C2×C4—22no—
422C2×C4—22no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—22no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—42no—
439C2×C4—41no—
440C2×C4—42no—
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×C4C2×C11×#4111yescharacteristic
451C2×C4C2×C11×#4111yescharacteristic
452C2×C4C2×C11×#4111yescharacteristic
453C2×C4C11×H(5,𝔽2)11yescharacteristic
454C2×C4C11×H(5,𝔽2)11yescharacteristic
455C8—24no—
456C8—22no—
457C8—41no—
458C22—44no—
459C22—44no—
460C22—44no—
461C22—82no—
462C22—82no—
463C22—82no—
464C22—82no—
465C22C2×C4×D4×C1111yescharacteristic
466C22C11×#54611yescharacteristic
467C22C11×#55011yescharacteristic
468C22C22×C11×SD1611yescharacteristic
469C22C2×C11×#13511yescharacteristic
470C22C11×#57611yescharacteristic
471C22C11×#57711yescharacteristic
472C4—22no—
473C4—24no—
474C4—42no—
475C4—42no—
476C4—42no—
477C4—42no—
478C4—81no—
479C4—82no—
480C4C4×C11×SD1614yes—
481C4C4×C11×#4111yescharacteristic
482C4C11×#51811yescharacteristic
483C4C11×#55311yescharacteristic
484C4C11×#55511yescharacteristic
485C2—84no—
486C2C11×#236311yescharacteristic
487C2C2×C4×C11×SD1611yescharacteristic
488C2C11×#294611yescharacteristic
489C2C11×#329511yescharacteristic
490C2C11×#330411yescharacteristic
491C2C11×#339211yescharacteristic
492C2C11×#339611yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#127C22
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×#2355C2semidirect
4. C11×#1968C2semidirect
6. C11×#1948C2semidirect
7. C11×#1926C2semidirect
8. C11×#1877C2semidirect
9. C8×C11×C4⋊C4C2semidirect
10. C4×C11×#103C2semidirect
11. C4×C11×#102C2semidirect
17. C11×#460C4semidirect
49. C2×C11×SD16C2×C4semidirect
56. C4×Q8×C11C2×C4semidirect
78. C11×C4⋊C8C2×C4semidirect
83. C11×#102C2×C4semidirect
91. #23095C11direct (N × H)
144. C11×C4⋊C4SD16semidirect
159. #2355C2×C11semidirect
160. #1968C2×C11semidirect
162. #1948C2×C11semidirect
163. #1926C2×C11semidirect
164. #1877C2×C11semidirect
165. C8×C4⋊C4C2×C11semidirect
166. C4×#103C2×C11semidirect
167. C4×#102C2×C11semidirect
228. #460C4×C11semidirect
287. C2×SD16C2×C4×C11semidirect
294. C4×Q8C2×C4×C11semidirect
316. C4⋊C8C2×C4×C11semidirect
321. #102C2×C4×C11semidirect
389. C4⋊C4C11×SD16semidirect
402. C11#23095direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4602
C11×#23662
C11×#23552
C11×#19682
C11×#19572
C11×#19482
C11×#19262
C11×#18772
C8×C11×C4⋊C42
C4×C11×#1032
C4×C11×#1022
#2309511