Finite Group Databasebeta

← C11×#23944 #14601137

Subgroups — C11×#23944 #14601137

Order 2816.

1206 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×#541C211yesmaximal, characteristic, complemented
2C2×C11×#452C212yesmaximal
3C11×#2311C211yesmaximal, characteristic
4C11×#2026C211yesmaximal, characteristic, complemented
5C11×#2025C211yesmaximal, characteristic, complemented
6C11×#2016C211yesmaximal, characteristic, complemented
7C11×#2013C211yesmaximal, characteristic, complemented
8C11×#1880C212yesmaximal, complemented
9C11×#1878C212yesmaximal, complemented
10C11×#1872C212yesmaximal, complemented
11C11×#1818C211yesmaximal, characteristic, complemented
12C22×C11×#41C2211yescharacteristic
13C22×C11×Q16C2212yes—
14C22×C11×SD16C2212yes—
15C11×#541—28no—
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C11×#126—22no—
18C2×C11×#125—22no—
19C2×C11×#125C2211yescharacteristic
20C2×C11×C22⋊Q8C2212yes—
21C2×C4×Q8×C11C2212yes—
22C2×C11×#117C2211yescharacteristic
23C22×C11×C4⋊C4C2211yescharacteristic
24C11×#452—28no—
25C2×C11×#103C2212yes—
26C2×C11×#103C2212yes—
27C2×C11×#103C2212yes—
28C2×C11×#102C2212yes—
29C2×C11×C22⋊C8C2212yes—
30C11×#391C2211yescharacteristic
31C11×#391C2211yescharacteristic
32C11×#390C2211yescharacteristic
33C11×#390C2211yescharacteristic
34C11×#386—22no—
35C11×#380—22no—
36C11×#340C2212yes—
37C11×#340C2212yes—
38C11×#336C2212yes—
39C11×#336C2211yescharacteristic
40C11×#336C2211yescharacteristic
41C2×C11×#41—22no—
42C2×C11×#41—22no—
43C2×C11×#41—24no—
44C2×C11×#41—42no—
45C22×Q8×C11C2312yes—
46C22×Q8×C11C2311yescharacteristic
47C22×D4×C11—21no—
48C22×D4×C11C2311yescharacteristic
49C23×C4×C11—21no—
50C23×C4×C11—21no—
51C23×C4×C11C2311yescharacteristic
52C2×C11×Q16—24no—
53C2×C11×Q16—24no—
54C2×C11×Q16—42no—
55C2×C11×SD16—24no—
56C2×C11×SD16—24no—
57C2×C11×SD16—42no—
58C22×C8×C11C2312yes—
59C22×C8×C11C2312yes—
60C11×C4⋊Q8—24no—
61C11×#126—216no—
62C11×#125—216no—
63C11×#125—24no—
64C11×C22⋊Q8—24no—
65C11×C22⋊Q8D418yes—
66C4×Q8×C11—24no—
67C4×Q8×C11—24no—
68C11×#117—24no—
69C2×C11×C4⋊C4—22no—
70C2×C11×C4⋊C4—22no—
71C2×C11×C4⋊C4—22no—
72C2×C11×C4⋊C4—22no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—42no—
75C2×C11×C4⋊C4D412yes—
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2312yes—
79C2×C11×C22⋊C4—22no—
80C2×C11×C22⋊C4—22no—
81C2×C11×C22⋊C4—22no—
82C2×C11×C22⋊C4D412yes—
83C2×C42×C11—22no—
84C2×C42×C11C2311yescharacteristic
85C2×C42×C11C2311yescharacteristic
86C11×#103—24no—
87C11×#103—42no—
88C11×#103—42no—
89C11×#102—24no—
90C11×C22⋊C8—24no—
91C11×#95—22no—
92C11×#95—22no—
93#23944C1111yesmaximal, characteristic, direct product factor, Sylow
94C24×C11—21no—
95C24×C11C2×D411yescharacteristic
96C11×#41—48no—
97C11×#41—48no—
98C2×Q8×C11—22no—
99C2×Q8×C11—21no—
100C2×Q8×C11—22no—
101C2×Q8×C11—22no—
102C2×Q8×C11—22no—
103C2×Q8×C11—22no—
104C2×Q8×C11—22no—
105C2×Q8×C11—22no—
106C2×Q8×C11C2×D414yes—
107C2×Q8×C11#4112yes—
108C2×D4×C11—24no—
109C2×D4×C11—22no—
110C2×D4×C11—21no—
111C2×D4×C11—22no—
112C2×D4×C11—42no—
113C2×D4×C11—42no—
114C2×D4×C11#4112yes—
115C22×C4×C11—21no—
116C22×C4×C11—21no—
117C22×C4×C11—22no—
118C22×C4×C11—24no—
119C22×C4×C11—21no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—42no—
125C22×C4×C11—42no—
126C22×C4×C11—42no—
127C22×C4×C11—82no—
128C22×C4×C11C2×D412yes—
129C22×C4×C11C2×D412yes—
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×D414yes—
132C22×C4×C11C2411yescharacteristic
133C11×Q16—48no—
134C11×SD16—48no—
135C2×C8×C11—22no—
136C2×C8×C11—22no—
137C2×C8×C11—22no—
138C2×C8×C11—22no—
139C2×C8×C11—22no—
140C2×C8×C11—22no—
141C11×C4⋊C4—28no—
142C11×C4⋊C4—28no—
143C11×C4⋊C4—28no—
144C11×C4⋊C4—28no—
145C11×C4⋊C4—24no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—22no—
149C11×C4⋊C4—42no—
150C11×C4⋊C4C2×D414yes—
151C11×C22⋊C4—28no—
152C11×C22⋊C4—24no—
153C11×C22⋊C4—82no—
154C11×C22⋊C4—82no—
155C42×C11—28no—
156C42×C11—22no—
157C42×C11—22no—
158C2×#541C2×C1111yescharacteristic, complemented
159C2×#452C2×C1112yes—
160#2311C2×C1111yescharacteristic
161#2026C2×C1111yescharacteristic, complemented
162#2025C2×C1111yescharacteristic, complemented
163#2016C2×C1111yescharacteristic, complemented
164#2013C2×C1111yescharacteristic, complemented
165#1880C2×C1112yescomplemented
166#1878C2×C1112yescomplemented
167#1872C2×C1112yescomplemented
168#1818C2×C1111yescharacteristic, complemented
169C23×C11—21no—
170C23×C11—21no—
171C23×C11—22no—
172C23×C11—22no—
173C23×C11—22no—
174C23×C11—41no—
175C23×C11—41no—
176C23×C11—42no—
177C23×C11—42no—
178C23×C11#12012yes—
179C23×C11C22×D411yescharacteristic
180Q8×C11—24no—
181Q8×C11—24no—
182Q8×C11—24no—
183Q8×C11—42no—
184Q8×C11—42no—
185Q8×C11—42no—
186D4×C11—24no—
187D4×C11—48no—
188D4×C11—42no—
189C2×C4×C11—21no—
190C2×C4×C11—21no—
191C2×C4×C11—24no—
192C2×C4×C11—24no—
193C2×C4×C11—22no—
194C2×C4×C11—22no—
195C2×C4×C11—24no—
196C2×C4×C11—24no—
197C2×C4×C11—22no—
198C2×C4×C11—22no—
199C2×C4×C11—22no—
200C2×C4×C11—22no—
201C2×C4×C11—22no—
202C2×C4×C11—48no—
203C2×C4×C11—41no—
204C2×C4×C11—42no—
205C2×C4×C11—41no—
206C2×C4×C11—42no—
207C2×C4×C11—42no—
208C2×C4×C11—42no—
209C2×C4×C11—41no—
210C2×C4×C11—41no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11—84no—
214C2×C4×C11#12012yes—
215C2×C4×C11C22×D412yes—
216C2×C4×C11C2×#4111yescharacteristic
217C2×C4×C11C2×#4111yescharacteristic
218C2×C4×C11H(5,𝔽2)12yes—
219C8×C11—42no—
220C8×C11—42no—
221C22×#41C22×C1111yescharacteristic
222C22×Q16C22×C1112yes—
223C22×SD16C22×C1112yes—
224#541—28no—
225C2×C4⋊Q8C22×C1111yescharacteristic
226C2×#126—22no—
227C2×#125—22no—
228C2×#125C22×C1111yescharacteristic
229C2×C22⋊Q8C22×C1112yes—
230C2×C4×Q8C22×C1112yes—
231C2×#117C22×C1111yescharacteristic
232C22×C4⋊C4C22×C1111yescharacteristic
233#452—28no—
234C2×#103C22×C1112yes—
235C2×#103C22×C1112yes—
236C2×#103C22×C1112yes—
237C2×#102C22×C1112yes—
238C2×C22⋊C8C22×C1112yes—
239#391C22×C1111yescharacteristic
240#391C22×C1111yescharacteristic
241#390C22×C1111yescharacteristic
242#390C22×C1111yescharacteristic
243#386—22no—
244#380—22no—
245#340C22×C1112yes—
246#340C22×C1112yes—
247#336C22×C1112yes—
248#336C22×C1111yescharacteristic
249#336C22×C1111yescharacteristic
250C22×C11—22no—
251C22×C11—24no—
252C22×C11—42no—
253C22×C11—41no—
254C22×C11—41no—
255C22×C11—44no—
256C22×C11—42no—
257C22×C11—81no—
258C22×C11—81no—
259C22×C11—82no—
260C22×C11C2×#12011yescharacteristic
261C22×C11#52511yescharacteristic
262C22×C11#53511yescharacteristic
263C22×C11#57712yes—
264C22×C11#57812yes—
265C4×C11—22no—
266C4×C11—42no—
267C4×C11—44no—
268C4×C11—42no—
269C4×C11—42no—
270C4×C11—44no—
271C4×C11—81no—
272C4×C11—81no—
273C4×C11#54612yes—
274C4×C11#54612yes—
275C2×#41—22no—
276C2×#41—22no—
277C2×#41—24no—
278C2×#41—42no—
279C22×Q8C23×C1112yes—
280C22×Q8C23×C1111yescharacteristic
281C22×D4—21no—
282C22×D4C23×C1111yescharacteristic
283C23×C4—21no—
284C23×C4—21no—
285C23×C4C23×C1111yescharacteristic
286C2×Q16—24no—
287C2×Q16—24no—
288C2×Q16—42no—
289C2×SD16—24no—
290C2×SD16—24no—
291C2×SD16—42no—
292C22×C8C23×C1112yes—
293C22×C8C23×C1112yes—
294C4⋊Q8—24no—
295#126—216no—
296#125—216no—
297#125—24no—
298C22⋊Q8—24no—
299C22⋊Q8D4×C1118yes—
300C4×Q8—24no—
301C4×Q8—24no—
302#117—24no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—42no—
309C2×C4⋊C4D4×C1112yes—
310C2×C4⋊C4C23×C1111yescharacteristic
311C2×C4⋊C4C23×C1111yescharacteristic
312C2×C4⋊C4C23×C1112yes—
313C2×C22⋊C4—22no—
314C2×C22⋊C4—22no—
315C2×C22⋊C4—22no—
316C2×C22⋊C4D4×C1112yes—
317C2×C42—22no—
318C2×C42C23×C1111yescharacteristic
319C2×C42C23×C1111yescharacteristic
320#103—24no—
321#103—42no—
322#103—42no—
323#102—24no—
324C22⋊C8—24no—
325#95—22no—
326#95—22no—
327C2×C11—42no—
328C2×C11—82no—
329C2×C11#240411yescharacteristic
330C2×C11#301312yes—
331C2×C11#312012yes—
332C2×C11#322211yescharacteristic
333C2×C11#322311yescharacteristic
334C24—21no—
335C24C2×D4×C1111yescharacteristic
336#41—48no—
337#41—48no—
338C2×Q8—22no—
339C2×Q8—21no—
340C2×Q8—22no—
341C2×Q8—22no—
342C2×Q8—22no—
343C2×Q8—22no—
344C2×Q8—22no—
345C2×Q8—22no—
346C2×Q8C2×D4×C1114yes—
347C2×Q8C11×#4112yes—
348C2×D4—24no—
349C2×D4—22no—
350C2×D4—21no—
351C2×D4—22no—
352C2×D4—42no—
353C2×D4—42no—
354C2×D4C11×#4112yes—
355C22×C4—21no—
356C22×C4—21no—
357C22×C4—22no—
358C22×C4—24no—
359C22×C4—21no—
360C22×C4—22no—
361C22×C4—22no—
362C22×C4—21no—
363C22×C4—21no—
364C22×C4—42no—
365C22×C4—42no—
366C22×C4—42no—
367C22×C4—82no—
368C22×C4C2×D4×C1112yes—
369C22×C4C2×D4×C1112yes—
370C22×C4C2×D4×C1111yescharacteristic
371C22×C4C2×D4×C1114yes—
372C22×C4C24×C1111yescharacteristic
373Q16—48no—
374SD16—48no—
375C2×C8—22no—
376C2×C8—22no—
377C2×C8—22no—
378C2×C8—22no—
379C2×C8—22no—
380C2×C8—22no—
381C4⋊C4—28no—
382C4⋊C4—28no—
383C4⋊C4—28no—
384C4⋊C4—28no—
385C4⋊C4—24no—
386C4⋊C4—22no—
387C4⋊C4—22no—
388C4⋊C4—22no—
389C4⋊C4—42no—
390C4⋊C4C2×D4×C1114yes—
391C22⋊C4—28no—
392C22⋊C4—24no—
393C22⋊C4—82no—
394C22⋊C4—82no—
395C42—28no—
396C42—22no—
397C42—22no—
398C11#2394411yescharacteristic, direct product factor, Sylow
399C23—21no—
400C23—21no—
401C23—22no—
402C23—22no—
403C23—22no—
404C23—41no—
405C23—41no—
406C23—42no—
407C23—42no—
408C23C11×#12012yes—
409C23C22×D4×C1111yescharacteristic
410Q8—24no—
411Q8—24no—
412Q8—24no—
413Q8—42no—
414Q8—42no—
415Q8—42no—
416D4—24no—
417D4—48no—
418D4—42no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—24no—
422C2×C4—24no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—24no—
426C2×C4—24no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—22no—
432C2×C4—48no—
433C2×C4—41no—
434C2×C4—42no—
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—84no—
444C2×C4C11×#12012yes—
445C2×C4C22×D4×C1112yes—
446C2×C4C2×C11×#4111yescharacteristic
447C2×C4C2×C11×#4111yescharacteristic
448C2×C4C11×H(5,𝔽2)12yes—
449C8—42no—
450C8—42no—
451C22—22no—
452C22—24no—
453C22—41no—
454C22—41no—
455C22—42no—
456C22—42no—
457C22—44no—
458C22—81no—
459C22—81no—
460C22—82no—
461C22C2×C11×#12011yescharacteristic
462C22C11×#52511yescharacteristic
463C22C11×#53511yescharacteristic
464C22C11×#57712yes—
465C22C11×#57812yes—
466C4—22no—
467C4—42no—
468C4—44no—
469C4—42no—
470C4—42no—
471C4—44no—
472C4—81no—
473C4—81no—
474C4C11×#54612yes—
475C4C11×#54612yes—
476C2—42no—
477C2—82no—
478C2C11×#240411yescharacteristic
479C2C11×#301312yes—
480C2C11×#312012yes—
481C2C11×#322211yescharacteristic
482C2C11×#322311yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×C11×#41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C11×#117 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#541C2semidirect
4. C11×#2026C2semidirect
5. C11×#2025C2semidirect
6. C11×#2016C2semidirect
7. C11×#2013C2semidirect
8. C11×#1880C2semidirect
9. C11×#1878C2semidirect
10. C11×#1872C2semidirect
11. C11×#1818C2semidirect
93. #23944C11direct (N × H)
158. C2×#541C2×C11semidirect
161. #2026C2×C11semidirect
162. #2025C2×C11semidirect
163. #2016C2×C11semidirect
164. #2013C2×C11semidirect
165. #1880C2×C11semidirect
166. #1878C2×C11semidirect
167. #1872C2×C11semidirect
168. #1818C2×C11semidirect
398. C11#23944direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5412
C2×C11×#4522
C11×#23112
C11×#20262
C11×#20252
C11×#20162
C11×#20132
C11×#18802
C11×#18782
C11×#18722
C11×#18182
#2394411