Finite Group Databasebeta

← C11×#24498 #14601691

Subgroups — C11×#24498 #14601691

Order 2816.

924 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#485C211yesmaximal, characteristic
2C2×C11×#419C211yesmaximal, characteristic
3C11×#2434C211yesmaximal, characteristic
4C11×#2346C211yesmaximal, characteristic
5C11×#2068C212yesmaximal, complemented
6C11×#2043C212yesmaximal, complemented
7C11×#1981C212yesmaximal, complemented
8C11×#1927C212yesmaximal, complemented
9C11×#1894C211yesmaximal, characteristic
10C11×#1851C211yesmaximal, characteristic
11C11×#1787C211yesmaximal, characteristic
12C23×Q8×C11C2211yescharacteristic
13C22×C11×M16C2211yescharacteristic
14C2×C11×C4⋊Q8C2212yes—
15C2×C11×C22⋊Q8C2211yescharacteristic
16C2×C11×#117C2211yescharacteristic
17C11×#485—24no—
18C2×C11×#107C2211yescharacteristic
19C2×C11×#106C2211yescharacteristic
20C2×C11×C4⋊C8C2212yes—
21C11×#419—24no—
22C2×C11×#103C2212yes—
23C2×C11×#103C2212yes—
24C2×C11×#103C2212yes—
25C2×C11×#103C2211yescharacteristic
26C2×C11×#103C2211yescharacteristic
27C2×C11×#103C2212yes—
28C2×C11×#103C2212yes—
29C2×C11×C22⋊C8C2211yescharacteristic
30C11×#395—21no—
31C11×#395—21no—
32C11×#391C2212yes—
33C11×#389C2212yes—
34C11×#388—22no—
35C11×#385—22no—
36C11×#382—21no—
37C11×#380C2211yescharacteristic
38C4×C11×C4⋊C4C2212yes—
39C4×C11×C22⋊C4C2211yescharacteristic
40C11×#376—21no—
41C11×#340C2212yes—
42C11×#336C2212yes—
43C22×Q8×C11—21no—
44C22×Q8×C11—24no—
45C22×Q8×C11—22no—
46C22×Q8×C11—22no—
47C22×Q8×C11—42no—
48C22×Q8×C11C2311yescharacteristic
49C22×Q8×C11C2312yes—
50C23×C4×C11—21no—
51C23×C4×C11C2311yescharacteristic
52C2×C11×M16—22no—
53C2×C11×M16—42no—
54C22×C8×C11C2311yescharacteristic
55C22×C8×C11C2312yes—
56C22×C8×C11C2311yescharacteristic
57C11×C4⋊Q8—24no—
58C11×C4⋊Q8—42no—
59C11×C22⋊Q8—22no—
60C11×C22⋊Q8—22no—
61C11×#117—22no—
62C11×#117D414yes—
63C2×C11×C4⋊C4—22no—
64C2×C11×C4⋊C4—22no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—22no—
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2312yes—
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C22⋊C4—21no—
72C2×C11×C22⋊C4—21no—
73C2×C11×C22⋊C4—21no—
74C2×C11×C22⋊C4D412yes—
75C2×C42×C11—21no—
76C2×C42×C11—22no—
77C2×C42×C11C2312yes—
78C11×#107—22no—
79C11×#106—22no—
80C11×C4⋊C8—42no—
81C11×#103—24no—
82C11×#103—24no—
83C11×#103—24no—
84C11×#103—22no—
85C11×#103—22no—
86C11×#103—42no—
87C11×#103—42no—
88C11×C22⋊C8—22no—
89C11×#95—21no—
90C11×#95—22no—
91C11×#95—22no—
92C11×#95—22no—
93C11×#95—22no—
94C11×#95D411yescharacteristic
95C11×#95D411yescharacteristic
96#24498C1111yesmaximal, characteristic, direct product factor, Sylow
97C24×C11C2×D411yescharacteristic
98C2×Q8×C11—22no—
99C2×Q8×C11—28no—
100C2×Q8×C11—22no—
101C2×Q8×C11—21no—
102C2×Q8×C11—22no—
103C2×Q8×C11—22no—
104C2×Q8×C11—21no—
105C2×Q8×C11—22no—
106C2×Q8×C11—22no—
107C2×Q8×C11—22no—
108C2×Q8×C11—44no—
109C2×Q8×C11—48no—
110C2×Q8×C11—44no—
111C2×Q8×C11—42no—
112C2×Q8×C11#4114yes—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—21no—
116C22×C4×C11—21no—
117C22×C4×C11—22no—
118C22×C4×C11—21no—
119C22×C4×C11—22no—
120C22×C4×C11—21no—
121C22×C4×C11—44no—
122C22×C4×C11—42no—
123C22×C4×C11C2×D412yes—
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D412yes—
126C22×C4×C11C2×D412yes—
127C22×C4×C11#4112yes—
128C22×C4×C11C2411yescharacteristic
129C11×M16—44no—
130C2×C8×C11—21no—
131C2×C8×C11—21no—
132C2×C8×C11—22no—
133C2×C8×C11—22no—
134C2×C8×C11—22no—
135C2×C8×C11—22no—
136C2×C8×C11—22no—
137C11×C4⋊C4—21no—
138C11×C4⋊C4—21no—
139C11×C4⋊C4—21no—
140C11×C4⋊C4—22no—
141C11×C4⋊C4—21no—
142C11×C4⋊C4—22no—
143C11×C4⋊C4—44no—
144C11×C4⋊C4—44no—
145C11×C4⋊C4—42no—
146C11×C4⋊C4—82no—
147C11×C4⋊C4C2×D412yes—
148C11×C4⋊C4C2×D412yes—
149C11×C22⋊C4—24no—
150C11×C22⋊C4—24no—
151C11×C22⋊C4—42no—
152C11×C22⋊C4—81no—
153C42×C11—24no—
154C42×C11—22no—
155C42×C11—22no—
156C42×C11—44no—
157C2×#485C2×C1111yescharacteristic
158C2×#419C2×C1111yescharacteristic
159#2434C2×C1111yescharacteristic
160#2346C2×C1111yescharacteristic
161#2068C2×C1112yescomplemented
162#2043C2×C1112yescomplemented
163#1981C2×C1112yescomplemented
164#1927C2×C1112yescomplemented
165#1894C2×C1111yescharacteristic
166#1851C2×C1111yescharacteristic
167#1787C2×C1111yescharacteristic
168C23×C11—22no—
169C23×C11—22no—
170C23×C11—21no—
171C23×C11—21no—
172C23×C11#12112yes—
173C23×C11C22×D411yescharacteristic
174Q8×C11—24no—
175Q8×C11—24no—
176Q8×C11—48no—
177Q8×C11—42no—
178Q8×C11—42no—
179Q8×C11—41no—
180Q8×C11—41no—
181Q8×C11—42no—
182C2×C4×C11—22no—
183C2×C4×C11—22no—
184C2×C4×C11—22no—
185C2×C4×C11—22no—
186C2×C4×C11—22no—
187C2×C4×C11—24no—
188C2×C4×C11—22no—
189C2×C4×C11—22no—
190C2×C4×C11—22no—
191C2×C4×C11—24no—
192C2×C4×C11—22no—
193C2×C4×C11—22no—
194C2×C4×C11—48no—
195C2×C4×C11—42no—
196C2×C4×C11—42no—
197C2×C4×C11—42no—
198C2×C4×C11—41no—
199C2×C4×C11—41no—
200C2×C4×C11—41no—
201C2×C4×C11—41no—
202C2×C4×C11—42no—
203C2×C4×C11—42no—
204C2×C4×C11—42no—
205C2×C4×C11—42no—
206C2×C4×C11—41no—
207C2×C4×C11—41no—
208C2×C4×C11#12112yes—
209C2×C4×C11#13714yes—
210C2×C4×C11C22×D411yescharacteristic
211C2×C4×C11C2×#4112yes—
212C2×C4×C11C2×#4111yescharacteristic
213C2×C4×C11H(5,𝔽2)12yes—
214C8×C11—41no—
215C8×C11—41no—
216C8×C11—42no—
217C23×Q8C22×C1111yescharacteristic
218C22×M16C22×C1111yescharacteristic
219C2×C4⋊Q8C22×C1112yes—
220C2×C22⋊Q8C22×C1111yescharacteristic
221C2×#117C22×C1111yescharacteristic
222#485—24no—
223C2×#107C22×C1111yescharacteristic
224C2×#106C22×C1111yescharacteristic
225C2×C4⋊C8C22×C1112yes—
226#419—24no—
227C2×#103C22×C1111yescharacteristic
228C2×#103C22×C1111yescharacteristic
229C2×#103C22×C1112yes—
230C2×#103C22×C1112yes—
231C2×#103C22×C1112yes—
232C2×#103C22×C1112yes—
233C2×#103C22×C1112yes—
234C2×C22⋊C8C22×C1111yescharacteristic
235#395—21no—
236#395—21no—
237#391C22×C1112yes—
238#389C22×C1112yes—
239#388—22no—
240#385—22no—
241#382—21no—
242#380C22×C1111yescharacteristic
243C4×C4⋊C4C22×C1112yes—
244C4×C22⋊C4C22×C1111yescharacteristic
245#376—21no—
246#340C22×C1112yes—
247#336C22×C1112yes—
248C22×C11—22no—
249C22×C11—22no—
250C22×C11—22no—
251C22×C11—42no—
252C22×C11—42no—
253C22×C11C2×#12111yescharacteristic
254C22×C11#54612yes—
255C22×C11C2×#13712yes—
256C22×C11#57711yescharacteristic
257C22×C11#57811yescharacteristic
258C4×C11—22no—
259C4×C11—24no—
260C4×C11—42no—
261C4×C11—44no—
262C4×C11—42no—
263C4×C11—42no—
264C4×C11—82no—
265C4×C11—81no—
266C4×C11—81no—
267C4×C11#52511yescharacteristic
268C4×C11#53511yescharacteristic
269C4×C11#55112yes—
270C22×Q8—21no—
271C22×Q8—24no—
272C22×Q8—22no—
273C22×Q8—22no—
274C22×Q8—42no—
275C22×Q8C23×C1111yescharacteristic
276C22×Q8C23×C1112yes—
277C23×C4—21no—
278C23×C4C23×C1111yescharacteristic
279C2×M16—22no—
280C2×M16—42no—
281C22×C8C23×C1112yes—
282C22×C8C23×C1111yescharacteristic
283C22×C8C23×C1111yescharacteristic
284C4⋊Q8—24no—
285C4⋊Q8—42no—
286C22⋊Q8—22no—
287C22⋊Q8—22no—
288#117—22no—
289#117D4×C1114yes—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4C23×C1111yescharacteristic
295C2×C4⋊C4C23×C1112yes—
296C2×C4⋊C4C23×C1111yescharacteristic
297C2×C4⋊C4C23×C1111yescharacteristic
298C2×C22⋊C4—21no—
299C2×C22⋊C4—21no—
300C2×C22⋊C4—21no—
301C2×C22⋊C4D4×C1112yes—
302C2×C42—21no—
303C2×C42—22no—
304C2×C42C23×C1112yes—
305#107—22no—
306#106—22no—
307C4⋊C8—42no—
308#103—24no—
309#103—24no—
310#103—24no—
311#103—22no—
312#103—22no—
313#103—42no—
314#103—42no—
315C22⋊C8—22no—
316#95—21no—
317#95—22no—
318#95—22no—
319#95—22no—
320#95—22no—
321#95D4×C1111yescharacteristic
322#95D4×C1111yescharacteristic
323C2×C11—42no—
324C2×C11#241111yescharacteristic
325C2×C11#303911yescharacteristic
326C2×C11#304611yescharacteristic
327C2×C11#331212yes—
328C2×C11#332912yes—
329C24C2×D4×C1111yescharacteristic
330C2×Q8—22no—
331C2×Q8—28no—
332C2×Q8—22no—
333C2×Q8—21no—
334C2×Q8—22no—
335C2×Q8—22no—
336C2×Q8—21no—
337C2×Q8—22no—
338C2×Q8—22no—
339C2×Q8—22no—
340C2×Q8—44no—
341C2×Q8—48no—
342C2×Q8—44no—
343C2×Q8—42no—
344C2×Q8C11×#4114yes—
345C22×C4—22no—
346C22×C4—22no—
347C22×C4—21no—
348C22×C4—21no—
349C22×C4—22no—
350C22×C4—21no—
351C22×C4—22no—
352C22×C4—21no—
353C22×C4—44no—
354C22×C4—42no—
355C22×C4C2×D4×C1112yes—
356C22×C4C2×D4×C1111yescharacteristic
357C22×C4C2×D4×C1112yes—
358C22×C4C2×D4×C1112yes—
359C22×C4C11×#4112yes—
360C22×C4C24×C1111yescharacteristic
361M16—44no—
362C2×C8—21no—
363C2×C8—21no—
364C2×C8—22no—
365C2×C8—22no—
366C2×C8—22no—
367C2×C8—22no—
368C2×C8—22no—
369C4⋊C4—21no—
370C4⋊C4—21no—
371C4⋊C4—21no—
372C4⋊C4—22no—
373C4⋊C4—21no—
374C4⋊C4—22no—
375C4⋊C4—44no—
376C4⋊C4—44no—
377C4⋊C4—42no—
378C4⋊C4—82no—
379C4⋊C4C2×D4×C1112yes—
380C4⋊C4C2×D4×C1112yes—
381C22⋊C4—24no—
382C22⋊C4—24no—
383C22⋊C4—42no—
384C22⋊C4—81no—
385C42—24no—
386C42—22no—
387C42—22no—
388C42—44no—
389C11#2449811yescharacteristic, direct product factor, Sylow
390C23—22no—
391C23—22no—
392C23—21no—
393C23—21no—
394C23C11×#12112yes—
395C23C22×D4×C1111yescharacteristic
396Q8—24no—
397Q8—24no—
398Q8—48no—
399Q8—42no—
400Q8—42no—
401Q8—41no—
402Q8—41no—
403Q8—42no—
404C2×C4—22no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—24no—
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—22no—
413C2×C4—24no—
414C2×C4—22no—
415C2×C4—22no—
416C2×C4—48no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4—42no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4C11×#12112yes—
431C2×C4C11×#13714yes—
432C2×C4C22×D4×C1111yescharacteristic
433C2×C4C2×C11×#4112yes—
434C2×C4C2×C11×#4111yescharacteristic
435C2×C4C11×H(5,𝔽2)12yes—
436C8—41no—
437C8—42no—
438C8—41no—
439C22—22no—
440C22—22no—
441C22—22no—
442C22—42no—
443C22—42no—
444C22C2×C11×#12111yescharacteristic
445C22C11×#54612yes—
446C22C2×C11×#13712yes—
447C22C11×#57711yescharacteristic
448C22C11×#57811yescharacteristic
449C4—22no—
450C4—24no—
451C4—44no—
452C4—42no—
453C4—42no—
454C4—42no—
455C4—81no—
456C4—81no—
457C4—82no—
458C4C11×#52511yescharacteristic
459C4C11×#53511yescharacteristic
460C4C11×#55112yes—
461C2—42no—
462C2C11×#241111yescharacteristic
463C2C11×#303911yescharacteristic
464C2C11×#304611yescharacteristic
465C2C11×#331212yes—
466C2C11×#332912yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC24×C11C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C4×C11×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
5. C11×#2068C2semidirect
6. C11×#2043C2semidirect
7. C11×#1981C2semidirect
8. C11×#1927C2semidirect
96. #24498C11direct (N × H)
161. #2068C2×C11semidirect
162. #2043C2×C11semidirect
163. #1981C2×C11semidirect
164. #1927C2×C11semidirect
389. C11#24498direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4852
C2×C11×#4192
C11×#24342
C11×#23462
C11×#20682
C11×#20432
C11×#19812
C11×#19272
C11×#18942
C11×#18512
C11×#17872
#2449811