Finite Group Databasebeta

← C11×#23931 #14601124

Subgroups — C11×#23931 #14601124

Order 2816.

1552 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#532C211yesmaximal, characteristic
2C2×C11×#448C212yesmaximal, complemented
3C2×C11×#391C211yesmaximal, characteristic, complemented
4C11×#2024C212yesmaximal, complemented
5C11×#2014C212yesmaximal, complemented
6C11×#1877C214yesmaximal, complemented
7C11×#1874C212yesmaximal, complemented
8C11×#1817C211yesmaximal, characteristic, complemented
9C22×C11×#41—21no—
10C23×Q8×C11C2211yescharacteristic
11C22×C11×SD16C2214yes—
12C11×#532—28no—
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×C11×#127C2211yescharacteristic
15C2×C11×#124—21no—
16C2×C11×#121—21no—
17C2×C11×#121C2212yes—
18C2×C4×D4×C11—21no—
19C2×C4×D4×C11C2212yes—
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×C42×C11C2211yescharacteristic
22C11×#448—28no—
23C2×C11×#103C2214yes—
24C2×C11×#102C2214yes—
25C2×C11×C22⋊C8C2212yes—
26C11×#391—21no—
27C11×#391—21no—
28C11×#391C2212yes—
29C11×#391C2212yes—
30C2×C11×#95—21no—
31C2×C11×#95—21no—
32C11×#340C2214yes—
33C11×#336C2212yes—
34C11×#336C2212yes—
35C2×C11×#41—28no—
36C2×C11×#41—44no—
37C2×C11×#41—44no—
38C22×Q8×C11—24no—
39C22×Q8×C11—21no—
40C22×Q8×C11—21no—
41C22×Q8×C11—24no—
42C22×Q8×C11—42no—
43C22×Q8×C11C2312yes—
44C22×D4×C11—22no—
45C22×D4×C11—21no—
46C22×D4×C11—21no—
47C22×D4×C11C2312yes—
48C23×C4×C11—21no—
49C23×C4×C11—22no—
50C23×C4×C11—21no—
51C23×C4×C11D411yescharacteristic
52C23×C4×C11D411yescharacteristic
53C23×C4×C11C2311yescharacteristic
54C2×C11×SD16—28no—
55C2×C11×SD16—28no—
56C2×C11×SD16—44no—
57C22×C8×C11C2314yes—
58C11×C4⋊Q8—24no—
59C11×#127—24no—
60C11×#124—28no—
61C11×#121—28no—
62C11×#121—24no—
63C11×#121D418yes—
64C4×D4×C11—28no—
65C4×D4×C11—24no—
66C4×D4×C11—24no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—42no—
70C2×C11×C4⋊C4C2312yes—
71C2×C11×C4⋊C4C2312yes—
72C2×C11×C22⋊C4—22no—
73C2×C11×C22⋊C4—22no—
74C2×C42×C11—24no—
75C2×C42×C11D411yescharacteristic
76C2×C42×C11D411yescharacteristic
77C2×C42×C11C2311yescharacteristic
78C2×C42×C11C2311yescharacteristic
79C11×#103—28no—
80C11×#102—44no—
81C11×C22⋊C8—24no—
82C11×#95—22no—
83C11×#95—22no—
84C11×#95—22no—
85C11×#95—22no—
86#23931C1111yesmaximal, characteristic, direct product factor, Sylow
87C24×C11—22no—
88C24×C11C2×D411yescharacteristic
89C11×#41—432no—
90C2×Q8×C11—24no—
91C2×Q8×C11—24no—
92C2×Q8×C11—22no—
93C2×Q8×C11—24no—
94C2×Q8×C11—24no—
95C2×Q8×C11—416no—
96C2×Q8×C11—42no—
97C2×Q8×C11—42no—
98C2×Q8×C11—42no—
99C2×Q8×C11—42no—
100C2×Q8×C11#4114yescomplemented
101C2×D4×C11—24no—
102C2×D4×C11—24no—
103C2×D4×C11—28no—
104C2×D4×C11—22no—
105C2×D4×C11—24no—
106C2×D4×C11—24no—
107C2×D4×C11—42no—
108C2×D4×C11—42no—
109C2×D4×C11—44no—
110C2×D4×C11—44no—
111C2×D4×C11—42no—
112C2×D4×C11—42no—
113C2×D4×C11C2×D414yes—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—28no—
119C22×C4×C11—24no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—41no—
126C22×C4×C11—44no—
127C22×C4×C11—42no—
128C22×C4×C11—42no—
129C22×C4×C11—44no—
130C22×C4×C11—42no—
131C22×C4×C11—42no—
132C22×C4×C11—42no—
133C22×C4×C11SD1614yescomplemented
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D414yes—
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2411yescharacteristic
141C11×SD16—416no—
142C2×C8×C11—24no—
143C2×C8×C11—24no—
144C2×C8×C11—24no—
145C11×C4⋊C4—24no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—24no—
148C11×C4⋊C4—42no—
149C11×C4⋊C4C2×D414yes—
150C11×C22⋊C4—28no—
151C11×C22⋊C4—28no—
152C42×C11—22no—
153C42×C11—22no—
154C42×C11—22no—
155C42×C11—22no—
156C2×#532C2×C1111yescharacteristic
157C2×#448C2×C1112yescomplemented
158C2×#391C2×C1111yescharacteristic, complemented
159#2024C2×C1112yescomplemented
160#2014C2×C1112yescomplemented
161#1877C2×C1114yescomplemented
162#1874C2×C1112yescomplemented
163#1817C2×C1111yescharacteristic, complemented
164C23×C11—21no—
165C23×C11—21no—
166C23×C11—21no—
167C23×C11—21no—
168C23×C11—24no—
169C23×C11—42no—
170C23×C11—42no—
171C23×C11—42no—
172C23×C11—42no—
173C23×C11—42no—
174C23×C11—42no—
175C23×C11#12012yes—
176C23×C11C2×SD1612yes—
177C23×C11AGL(1,ℤ/8)12yes—
178C23×C11C22×D411yescharacteristic
179Q8×C11—28no—
180Q8×C11—48no—
181Q8×C11—48no—
182Q8×C11—44no—
183D4×C11—28no—
184D4×C11—48no—
185D4×C11—48no—
186D4×C11—416no—
187D4×C11—44no—
188C2×C4×C11—21no—
189C2×C4×C11—21no—
190C2×C4×C11—21no—
191C2×C4×C11—21no—
192C2×C4×C11—21no—
193C2×C4×C11—21no—
194C2×C4×C11—21no—
195C2×C4×C11—21no—
196C2×C4×C11—28no—
197C2×C4×C11—28no—
198C2×C4×C11—21no—
199C2×C4×C11—24no—
200C2×C4×C11—24no—
201C2×C4×C11—21no—
202C2×C4×C11—21no—
203C2×C4×C11—44no—
204C2×C4×C11—416no—
205C2×C4×C11—48no—
206C2×C4×C11—42no—
207C2×C4×C11—42no—
208C2×C4×C11—42no—
209C2×C4×C11—42no—
210C2×C4×C11—42no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11—84no—
214C2×C4×C11#12012yes—
215C2×C4×C11C2×SD1612yes—
216C2×C4×C11C2×SD1612yes—
217C2×C4×C11#13712yes—
218C2×C4×C11C22×D412yes—
219C2×C4×C11C2×#4112yes—
220C2×C4×C11H(5,𝔽2)12yes—
221C8×C11—44no—
222C22×#41—21no—
223C23×Q8C22×C1111yescharacteristic
224C22×SD16C22×C1114yes—
225#532—28no—
226C2×C4⋊Q8C22×C1111yescharacteristic
227C2×#127C22×C1111yescharacteristic
228C2×#124—21no—
229C2×#121—21no—
230C2×#121C22×C1112yes—
231C2×C4×D4—21no—
232C2×C4×D4C22×C1112yes—
233C22×C4⋊C4C22×C1111yescharacteristic
234C22×C42C22×C1111yescharacteristic
235#448—28no—
236C2×#103C22×C1114yes—
237C2×#102C22×C1114yes—
238C2×C22⋊C8C22×C1112yes—
239#391—21no—
240#391—21no—
241#391C22×C1112yes—
242#391C22×C1112yes—
243C2×#95—21no—
244C2×#95—21no—
245#340C22×C1114yes—
246#336C22×C1112yes—
247#336C22×C1112yes—
248C22×C11—22no—
249C22×C11—22no—
250C22×C11—22no—
251C22×C11—22no—
252C22×C11—22no—
253C22×C11—22no—
254C22×C11—44no—
255C22×C11—44no—
256C22×C11—44no—
257C22×C11—82no—
258C22×C11—82no—
259C22×C11—82no—
260C22×C11—82no—
261C22×C11#45014yes—
262C22×C11C2×#12011yescharacteristic
263C22×C11#52511yescharacteristic
264C22×C11#53511yescharacteristic
265C22×C11C22×SD1611yescharacteristic
266C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
267C22×C11C2×#13711yescharacteristic
268C22×C11#57511yescharacteristic
269C4×C11—22no—
270C4×C11—22no—
271C4×C11—22no—
272C4×C11—22no—
273C4×C11—44no—
274C4×C11—44no—
275C4×C11—41no—
276C4×C11—82no—
277C4×C11#54614yes—
278C2×#41—28no—
279C2×#41—44no—
280C2×#41—44no—
281C22×Q8—24no—
282C22×Q8—21no—
283C22×Q8—21no—
284C22×Q8—24no—
285C22×Q8—42no—
286C22×Q8C23×C1112yes—
287C22×D4—22no—
288C22×D4—21no—
289C22×D4—21no—
290C22×D4C23×C1112yes—
291C23×C4—21no—
292C23×C4—22no—
293C23×C4—21no—
294C23×C4D4×C1111yescharacteristic
295C23×C4D4×C1111yescharacteristic
296C23×C4C23×C1111yescharacteristic
297C2×SD16—28no—
298C2×SD16—28no—
299C2×SD16—44no—
300C22×C8C23×C1114yes—
301C4⋊Q8—24no—
302#127—24no—
303#124—28no—
304#121—28no—
305#121—24no—
306#121D4×C1118yes—
307C4×D4—28no—
308C4×D4—24no—
309C4×D4—24no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—42no—
313C2×C4⋊C4C23×C1112yes—
314C2×C4⋊C4C23×C1112yes—
315C2×C22⋊C4—22no—
316C2×C22⋊C4—22no—
317C2×C42—24no—
318C2×C42D4×C1111yescharacteristic
319C2×C42D4×C1111yescharacteristic
320C2×C42C23×C1111yescharacteristic
321C2×C42C23×C1111yescharacteristic
322#103—28no—
323#102—44no—
324C22⋊C8—24no—
325#95—22no—
326#95—22no—
327#95—22no—
328#95—22no—
329C2×C11—24no—
330C2×C11—84no—
331C2×C11#240411yescharacteristic
332C2×C11C2×#45011yescharacteristic
333C2×C11#300711yescharacteristic
334C2×C11#310311yescharacteristic
335C2×C11#311211yescharacteristic
336C2×C11#320611yescharacteristic
337C2×C11#321311yescharacteristic
338C24—22no—
339C24C2×D4×C1111yescharacteristic
340#41—432no—
341C2×Q8—24no—
342C2×Q8—24no—
343C2×Q8—22no—
344C2×Q8—24no—
345C2×Q8—24no—
346C2×Q8—416no—
347C2×Q8—42no—
348C2×Q8—42no—
349C2×Q8—42no—
350C2×Q8—42no—
351C2×Q8C11×#4114yescomplemented
352C2×D4—24no—
353C2×D4—24no—
354C2×D4—28no—
355C2×D4—22no—
356C2×D4—24no—
357C2×D4—24no—
358C2×D4—42no—
359C2×D4—42no—
360C2×D4—44no—
361C2×D4—44no—
362C2×D4—42no—
363C2×D4—42no—
364C2×D4C2×D4×C1114yes—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—28no—
370C22×C4—24no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—41no—
377C22×C4—44no—
378C22×C4—42no—
379C22×C4—42no—
380C22×C4—44no—
381C22×C4—42no—
382C22×C4—42no—
383C22×C4—42no—
384C22×C4C11×SD1614yescomplemented
385C22×C4C2×D4×C1111yescharacteristic
386C22×C4C2×D4×C1111yescharacteristic
387C22×C4C2×D4×C1114yes—
388C22×C4C2×D4×C1111yescharacteristic
389C22×C4C2×D4×C1111yescharacteristic
390C22×C4C2×D4×C1111yescharacteristic
391C22×C4C24×C1111yescharacteristic
392SD16—416no—
393C2×C8—24no—
394C2×C8—24no—
395C2×C8—24no—
396C4⋊C4—24no—
397C4⋊C4—22no—
398C4⋊C4—24no—
399C4⋊C4—42no—
400C4⋊C4C2×D4×C1114yes—
401C22⋊C4—28no—
402C22⋊C4—28no—
403C42—22no—
404C42—22no—
405C42—22no—
406C42—22no—
407C11#2393111yescharacteristic, direct product factor, Sylow
408C23—21no—
409C23—21no—
410C23—21no—
411C23—21no—
412C23—24no—
413C23—42no—
414C23—42no—
415C23—42no—
416C23—42no—
417C23—42no—
418C23—42no—
419C23C11×#12012yes—
420C23C2×C11×SD1612yes—
421C23C11×AGL(1,ℤ/8)12yes—
422C23C22×D4×C1111yescharacteristic
423Q8—28no—
424Q8—48no—
425Q8—48no—
426Q8—44no—
427D4—28no—
428D4—48no—
429D4—48no—
430D4—416no—
431D4—44no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—28no—
441C2×C4—28no—
442C2×C4—21no—
443C2×C4—24no—
444C2×C4—24no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—44no—
448C2×C4—416no—
449C2×C4—48no—
450C2×C4—42no—
451C2×C4—42no—
452C2×C4—42no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—84no—
458C2×C4C11×#12012yes—
459C2×C4C2×C11×SD1612yes—
460C2×C4C2×C11×SD1612yes—
461C2×C4C11×#13712yes—
462C2×C4C22×D4×C1112yes—
463C2×C4C2×C11×#4112yes—
464C2×C4C11×H(5,𝔽2)12yes—
465C8—44no—
466C22—22no—
467C22—22no—
468C22—22no—
469C22—22no—
470C22—22no—
471C22—22no—
472C22—44no—
473C22—44no—
474C22—44no—
475C22—82no—
476C22—82no—
477C22—82no—
478C22—82no—
479C22C11×#45014yes—
480C22C2×C11×#12011yescharacteristic
481C22C11×#52511yescharacteristic
482C22C11×#53511yescharacteristic
483C22C22×C11×SD1611yescharacteristic
484C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
485C22C2×C11×#13711yescharacteristic
486C22C11×#57511yescharacteristic
487C4—22no—
488C4—22no—
489C4—22no—
490C4—22no—
491C4—44no—
492C4—44no—
493C4—41no—
494C4—82no—
495C4C11×#54614yes—
496C2—24no—
497C2—84no—
498C2C11×#240411yescharacteristic
499C2C2×C11×#45011yescharacteristic
500C2C11×#300711yescharacteristic
501C2C11×#310311yescharacteristic
502C2C11×#311211yescharacteristic
503C2C11×#320611yescharacteristic
504C2C11×#321311yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#532C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C42×C11 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×C11×#448C2semidirect
3. C2×C11×#391C2semidirect
4. C11×#2024C2semidirect
5. C11×#2014C2semidirect
6. C11×#1877C2semidirect
7. C11×#1874C2semidirect
8. C11×#1817C2semidirect
86. #23931C11direct (N × H)
100. C2×Q8×C11#41semidirect
133. C22×C4×C11SD16semidirect
157. C2×#448C2×C11semidirect
158. C2×#391C2×C11semidirect
159. #2024C2×C11semidirect
160. #2014C2×C11semidirect
161. #1877C2×C11semidirect
162. #1874C2×C11semidirect
163. #1817C2×C11semidirect
351. C2×Q8C11×#41semidirect
384. C22×C4C11×SD16semidirect
407. C11#23931direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5322
C2×C11×#4482
C2×C11×#3912
C11×#20242
C11×#20142
C11×#18772
C11×#18742
C11×#18172
#2393111