Finite Group Databasebeta

← C11×#25035 #14602228

Subgroups — C11×#25035 #14602228

Order 2816.

810 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×#467C211yesmaximal, characteristic
2C2×C4×C11×Q16C211yesmaximal, characteristic, complemented
3C11×#2423C212yesmaximal
4C11×#2072C212yesmaximal, complemented
5C11×#2036C212yesmaximal
6C11×#1969C211yesmaximal, characteristic, complemented
7C11×#1942C211yesmaximal, characteristic, complemented
8C11×#1863C212yesmaximal, complemented
9C11×#1845C211yesmaximal, characteristic, complemented
10C11×#1808C211yesmaximal, characteristic
11C8×C11×C22⋊C4C211yesmaximal, characteristic
12C22×C11×Q16C2211yescharacteristic
13C23×C8×C11C2211yescharacteristic
14C2×C11×C22⋊Q8C2212yes—
15C2×C4×Q8×C11C2212yes—
16C11×#467—24no—
17C4×C11×Q16—24no—
18C2×C11×#107C2211yescharacteristic
19C2×C11×#107C2211yescharacteristic
20C2×C11×#107C2211yescharacteristic
21C2×C11×#107C2212yes—
22C2×C11×#103C2212yes—
23C2×C11×#103C2212yes—
24C2×C11×#103C2212yes—
25C2×C11×C22⋊C8C2211yescharacteristic
26C2×C4×C8×C11C2211yescharacteristic
27C2×C4×C8×C11C2211yescharacteristic
28C11×#399—22no—
29C11×#398—22no—
30C11×#391C2212yes—
31C11×#389C2212yes—
32C11×#388—22no—
33C11×#387—22no—
34C11×#384C2212yes—
35C11×#380C2212yes—
36C4×C11×C22⋊C4C2211yescharacteristic
37C11×#340C2212yes—
38C11×#340C2212yes—
39C11×#336C2211yescharacteristic
40C11×#336C2211yescharacteristic
41C22×Q8×C11C2312yes—
42C23×C4×C11C2311yescharacteristic
43C2×C11×Q16—22no—
44C2×C11×Q16—22no—
45C2×C11×Q16D414yes—
46C22×C8×C11—22no—
47C22×C8×C11—22no—
48C22×C8×C11—22no—
49C22×C8×C11C2311yescharacteristic
50C22×C8×C11C2311yescharacteristic
51C22×C8×C11C2311yescharacteristic
52C22×C8×C11C2311yescharacteristic
53C11×C22⋊Q8—24no—
54C11×C22⋊Q8—42no—
55C4×Q8×C11—24no—
56C4×Q8×C11—42no—
57C2×C11×C4⋊C4—22no—
58C2×C11×C4⋊C4—22no—
59C2×C11×C4⋊C4—22no—
60C2×C11×C4⋊C4—22no—
61C2×C11×C4⋊C4—22no—
62C2×C11×C4⋊C4C2312yes—
63C2×C11×C4⋊C4C2312yes—
64C2×C11×C4⋊C4C2312yes—
65C2×C11×C22⋊C4—22no—
66C2×C11×C22⋊C4—22no—
67C2×C11×C22⋊C4D411yescharacteristic
68C2×C11×C22⋊C4D411yescharacteristic
69C2×C42×C11—22no—
70C2×C42×C11C2311yescharacteristic
71C2×C42×C11C2311yescharacteristic
72C11×#107—22no—
73C11×#107—22no—
74C11×#107—22no—
75C11×#107—42no—
76C11×#103—24no—
77C11×#103—24no—
78C11×#103—24no—
79C11×C22⋊C8—22no—
80C4×C8×C11—22no—
81C4×C8×C11—22no—
82C11×#95—22no—
83C11×#95—22no—
84C11×#95—22no—
85C11×#95—22no—
86C11×#95D411yescharacteristic
87C11×#95D411yescharacteristic
88#25035C1111yesmaximal, characteristic, direct product factor, Sylow
89C24×C11C2×D411yescharacteristic
90C2×Q8×C11—22no—
91C2×Q8×C11—22no—
92C2×Q8×C11—22no—
93C2×Q8×C11—22no—
94C2×Q8×C11—22no—
95C2×Q8×C11C2×D414yes—
96C22×C4×C11—22no—
97C22×C4×C11—21no—
98C22×C4×C11—21no—
99C22×C4×C11—21no—
100C22×C4×C11—21no—
101C22×C4×C11—21no—
102C22×C4×C11—21no—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—22no—
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2411yescharacteristic
112C11×Q16—28no—
113C2×C8×C11—21no—
114C2×C8×C11—21no—
115C2×C8×C11—21no—
116C2×C8×C11—21no—
117C2×C8×C11—21no—
118C2×C8×C11—21no—
119C2×C8×C11—21no—
120C2×C8×C11—21no—
121C2×C8×C11—44no—
122C2×C8×C11C2×D412yes—
123C2×C8×C11#4112yes—
124C2×C8×C11#4112yes—
125C2×C8×C11#4112yes—
126C11×C4⋊C4—22no—
127C11×C4⋊C4—22no—
128C11×C4⋊C4—22no—
129C11×C4⋊C4—22no—
130C11×C4⋊C4—22no—
131C11×C4⋊C4—22no—
132C11×C4⋊C4—44no—
133C11×C4⋊C4—44no—
134C11×C4⋊C4—44no—
135C11×C4⋊C4—82no—
136C11×C4⋊C4—82no—
137C11×C22⋊C4—22no—
138C11×C22⋊C4—44no—
139C11×C22⋊C4—82no—
140C11×C22⋊C4Q1614yescomplemented
141C42×C11—21no—
142C42×C11—21no—
143C42×C11—21no—
144C42×C11—21no—
145C42×C11—44no—
146C2×#467C2×C1111yescharacteristic
147C2×C4×Q16C2×C1111yescharacteristic, complemented
148#2423C2×C1112yes—
149#2072C2×C1112yescomplemented
150#2036C2×C1112yes—
151#1969C2×C1111yescharacteristic, complemented
152#1942C2×C1111yescharacteristic, complemented
153#1863C2×C1112yescomplemented
154#1845C2×C1111yescharacteristic, complemented
155#1808C2×C1111yescharacteristic
156C8×C22⋊C4C2×C1111yescharacteristic
157C23×C11—21no—
158C23×C11—21no—
159C23×C11—21no—
160C23×C11—21no—
161C23×C11—21no—
162C23×C11—21no—
163C23×C11C2×Q1612yes—
164C23×C11C22×D411yescharacteristic
165Q8×C11—24no—
166Q8×C11—24no—
167Q8×C11—42no—
168Q8×C11—42no—
169C2×C4×C11—21no—
170C2×C4×C11—21no—
171C2×C4×C11—21no—
172C2×C4×C11—21no—
173C2×C4×C11—21no—
174C2×C4×C11—21no—
175C2×C4×C11—21no—
176C2×C4×C11—21no—
177C2×C4×C11—24no—
178C2×C4×C11—21no—
179C2×C4×C11—21no—
180C2×C4×C11—21no—
181C2×C4×C11—21no—
182C2×C4×C11—42no—
183C2×C4×C11—42no—
184C2×C4×C11—41no—
185C2×C4×C11—41no—
186C2×C4×C11—41no—
187C2×C4×C11—41no—
188C2×C4×C11—42no—
189C2×C4×C11—42no—
190C2×C4×C11—42no—
191C2×C4×C11—42no—
192C2×C4×C11—42no—
193C2×C4×C11—42no—
194C2×C4×C11—42no—
195C2×C4×C11—42no—
196C2×C4×C11—42no—
197C2×C4×C11C2×Q1612yes—
198C2×C4×C11C2×Q1612yes—
199C2×C4×C11#13512yes—
200C2×C4×C11C22×D411yescharacteristic
201C2×C4×C11C2×#4111yescharacteristic
202C2×C4×C11C2×#4111yescharacteristic
203C2×C4×C11C2×#4111yescharacteristic
204C2×C4×C11H(5,𝔽2)11yescharacteristic
205C2×C4×C112−1+411yescharacteristic
206C8×C11—22no—
207C8×C11—41no—
208C8×C11—41no—
209C8×C11#12314yes—
210C22×Q16C22×C1111yescharacteristic
211C23×C8C22×C1111yescharacteristic
212C2×C22⋊Q8C22×C1112yes—
213C2×C4×Q8C22×C1112yes—
214#467—24no—
215C4×Q16—24no—
216C2×#107C22×C1111yescharacteristic
217C2×#107C22×C1111yescharacteristic
218C2×#107C22×C1111yescharacteristic
219C2×#107C22×C1112yes—
220C2×#103C22×C1112yes—
221C2×#103C22×C1112yes—
222C2×#103C22×C1112yes—
223C2×C22⋊C8C22×C1111yescharacteristic
224C2×C4×C8C22×C1111yescharacteristic
225C2×C4×C8C22×C1111yescharacteristic
226#399—22no—
227#398—22no—
228#391C22×C1112yes—
229#389C22×C1112yes—
230#388—22no—
231#387—22no—
232#384C22×C1112yes—
233#380C22×C1112yes—
234C4×C22⋊C4C22×C1111yescharacteristic
235#340C22×C1112yes—
236#340C22×C1112yes—
237#336C22×C1111yescharacteristic
238#336C22×C1111yescharacteristic
239C22×C11—22no—
240C22×C11—22no—
241C22×C11—22no—
242C22×C11—41no—
243C22×C11—41no—
244C22×C11—41no—
245C22×C11—41no—
246C22×C11#53211yescharacteristic
247C22×C11D4211yescharacteristic
248C22×C11#54711yescharacteristic
249C22×C11C22×Q1611yescharacteristic
250C22×C11C2×#13511yescharacteristic
251C22×C11#57611yescharacteristic
252C22×C11#57811yescharacteristic
253C4×C11—22no—
254C4×C11—22no—
255C4×C11—22no—
256C4×C11—41no—
257C4×C11—44no—
258C4×C11—41no—
259C4×C11—82no—
260C4×C11—82no—
261C4×C11—82no—
262C4×C11C2×#12311yescharacteristic
263C4×C11#54211yescharacteristic
264C4×C11#54711yescharacteristic
265C4×C11#55311yescharacteristic
266C22×Q8C23×C1112yes—
267C23×C4C23×C1111yescharacteristic
268C2×Q16—22no—
269C2×Q16—22no—
270C2×Q16D4×C1114yes—
271C22×C8—22no—
272C22×C8—22no—
273C22×C8—22no—
274C22×C8C23×C1111yescharacteristic
275C22×C8C23×C1111yescharacteristic
276C22×C8C23×C1111yescharacteristic
277C22×C8C23×C1111yescharacteristic
278C22⋊Q8—24no—
279C22⋊Q8—42no—
280C4×Q8—24no—
281C4×Q8—42no—
282C2×C4⋊C4—22no—
283C2×C4⋊C4—22no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—22no—
286C2×C4⋊C4—22no—
287C2×C4⋊C4C23×C1112yes—
288C2×C4⋊C4C23×C1112yes—
289C2×C4⋊C4C23×C1112yes—
290C2×C22⋊C4—22no—
291C2×C22⋊C4—22no—
292C2×C22⋊C4D4×C1111yescharacteristic
293C2×C22⋊C4D4×C1111yescharacteristic
294C2×C42—22no—
295C2×C42C23×C1111yescharacteristic
296C2×C42C23×C1111yescharacteristic
297#107—22no—
298#107—22no—
299#107—22no—
300#107—42no—
301#103—24no—
302#103—24no—
303#103—24no—
304C22⋊C8—22no—
305C4×C8—22no—
306C4×C8—22no—
307#95—22no—
308#95—22no—
309#95—22no—
310#95—22no—
311#95D4×C1111yescharacteristic
312#95D4×C1111yescharacteristic
313C2×C11—42no—
314C2×C11#242211yescharacteristic
315C2×C11#317011yescharacteristic
316C2×C11#317511yescharacteristic
317C2×C11D4×Q1611yescharacteristic
318C2×C11#328711yescharacteristic
319C2×C11#333611yescharacteristic
320C2×C11#333811yescharacteristic
321C24C2×D4×C1111yescharacteristic
322C2×Q8—22no—
323C2×Q8—22no—
324C2×Q8—22no—
325C2×Q8—22no—
326C2×Q8—22no—
327C2×Q8C2×D4×C1114yes—
328C22×C4—22no—
329C22×C4—21no—
330C22×C4—21no—
331C22×C4—21no—
332C22×C4—21no—
333C22×C4—21no—
334C22×C4—21no—
335C22×C4—22no—
336C22×C4—22no—
337C22×C4—22no—
338C22×C4C2×D4×C1111yescharacteristic
339C22×C4C2×D4×C1111yescharacteristic
340C22×C4C2×D4×C1111yescharacteristic
341C22×C4C2×D4×C1111yescharacteristic
342C22×C4C2×D4×C1111yescharacteristic
343C22×C4C24×C1111yescharacteristic
344Q16—28no—
345C2×C8—21no—
346C2×C8—21no—
347C2×C8—21no—
348C2×C8—21no—
349C2×C8—21no—
350C2×C8—21no—
351C2×C8—21no—
352C2×C8—21no—
353C2×C8—44no—
354C2×C8C2×D4×C1112yes—
355C2×C8C11×#4112yes—
356C2×C8C11×#4112yes—
357C2×C8C11×#4112yes—
358C4⋊C4—22no—
359C4⋊C4—22no—
360C4⋊C4—22no—
361C4⋊C4—22no—
362C4⋊C4—22no—
363C4⋊C4—22no—
364C4⋊C4—44no—
365C4⋊C4—44no—
366C4⋊C4—44no—
367C4⋊C4—82no—
368C4⋊C4—82no—
369C22⋊C4—22no—
370C22⋊C4—44no—
371C22⋊C4—82no—
372C22⋊C4C11×Q1614yescomplemented
373C42—21no—
374C42—21no—
375C42—21no—
376C42—21no—
377C42—44no—
378C11#2503511yescharacteristic, direct product factor, Sylow
379C23—21no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—21no—
385C23C2×C11×Q1612yes—
386C23C22×D4×C1111yescharacteristic
387Q8—24no—
388Q8—24no—
389Q8—42no—
390Q8—42no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—24no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4C2×C11×Q1612yes—
420C2×C4C2×C11×Q1612yes—
421C2×C4C11×#13512yes—
422C2×C4C22×D4×C1111yescharacteristic
423C2×C4C2×C11×#4111yescharacteristic
424C2×C4C2×C11×#4111yescharacteristic
425C2×C4C2×C11×#4111yescharacteristic
426C2×C4C11×H(5,𝔽2)11yescharacteristic
427C2×C4C11×2−1+411yescharacteristic
428C8—22no—
429C8—41no—
430C8—41no—
431C8C11×#12314yes—
432C22—22no—
433C22—22no—
434C22—22no—
435C22—41no—
436C22—41no—
437C22—41no—
438C22—41no—
439C22C11×#53211yescharacteristic
440C22D42×C1111yescharacteristic
441C22C11×#54711yescharacteristic
442C22C22×C11×Q1611yescharacteristic
443C22C2×C11×#13511yescharacteristic
444C22C11×#57611yescharacteristic
445C22C11×#57811yescharacteristic
446C4—22no—
447C4—22no—
448C4—22no—
449C4—41no—
450C4—44no—
451C4—41no—
452C4—82no—
453C4—82no—
454C4—82no—
455C4C2×C11×#12311yescharacteristic
456C4C11×#54211yescharacteristic
457C4C11×#54711yescharacteristic
458C4C11×#55311yescharacteristic
459C2—42no—
460C2C11×#242211yescharacteristic
461C2C11×#317011yescharacteristic
462C2C11×#317511yescharacteristic
463C2D4×C11×Q1611yescharacteristic
464C2C11×#328711yescharacteristic
465C2C11×#333611yescharacteristic
466C2C11×#333811yescharacteristic
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
2. C2×C4×C11×Q16C2semidirect
4. C11×#2072C2semidirect
6. C11×#1969C2semidirect
7. C11×#1942C2semidirect
8. C11×#1863C2semidirect
9. C11×#1845C2semidirect
88. #25035C11direct (N × H)
140. C11×C22⋊C4Q16semidirect
147. C2×C4×Q16C2×C11semidirect
149. #2072C2×C11semidirect
151. #1969C2×C11semidirect
152. #1942C2×C11semidirect
153. #1863C2×C11semidirect
154. #1845C2×C11semidirect
372. C22⋊C4C11×Q16semidirect
378. C11#25035direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4672
C2×C4×C11×Q162
C11×#24232
C11×#20722
C11×#20362
C11×#19692
C11×#19422
C11×#18632
C11×#18452
C11×#18082
C8×C11×C22⋊C42
#2503511