Finite Group Databasebeta

← C11×#22773 #14599966

Subgroups — C11×#22773 #14599966

Order 2816.

842 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C11×SD16C211yesmaximal, characteristic
2C11×#2357C211yesmaximal, characteristic
3C11×#2351C211yesmaximal, characteristic, complemented
4C11×#1934C212yesmaximal
5C11×#1919C212yesmaximal, complemented
6C11×#1880C212yesmaximal
7C11×#1835C211yesmaximal, characteristic, complemented
8C11×#1805C211yesmaximal, characteristic, complemented
9C11×#1804C211yesmaximal, characteristic
10C8×C11×C4⋊C4C211yesmaximal, characteristic, complemented
11C4×C11×#103C212yesmaximal, complemented
12C22×C11×SD16C2211yescharacteristic
13C2×C4×Q8×C11C2212yes—
14C2×C4×Q8×C11C2211yescharacteristic
15C2×C4×D4×C11C2211yescharacteristic
16C4×C11×SD16C418yescomplemented
17C2×C11×#106C2211yescharacteristic
18C2×C11×C4⋊C8C2211yescharacteristic
19C2×C11×#103C2212yes—
20C2×C11×#103C2211yescharacteristic
21C2×C11×#102C2212yes—
22C2×C11×#102C2211yescharacteristic
23C2×C4×C8×C11C2212yes—
24C2×C4×C8×C11C2211yescharacteristic
25C11×#390C2212yes—
26C11×#389—22no—
27C11×#389C2212yes—
28C11×#388—22no—
29C11×#382—21no—
30C11×#382C2211yescharacteristic
31C11×#382C2211yescharacteristic
32C11×#381—21no—
33C4×C11×C4⋊C4—21no—
34C4×C11×C4⋊C4C2212yes—
35C4×C11×C4⋊C4C2211yescharacteristic
36C4×C11×C22⋊C4—21no—
37C11×#340C2212yes—
38C11×#340C2212yes—
39C11×#340C2212yes—
40C11×#340C2212yes—
41C11×#336C2212yes—
42C22×Q8×C11C2311yescharacteristic
43C22×D4×C11C2311yescharacteristic
44C23×C4×C11—21no—
45C2×C11×SD16—22no—
46C2×C11×SD16—22no—
47C2×C11×SD16C2×C414yes—
48C22×C8×C11C2312yes—
49C22×C8×C11C2311yescharacteristic
50C22×C8×C11C2311yescharacteristic
51C4×Q8×C11—22no—
52C4×Q8×C11—24no—
53C4×Q8×C11—42no—
54C4×Q8×C11C2×C414yes—
55C4×D4×C11—22no—
56C4×D4×C11C2×C414yes—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4—22no—
59C2×C11×C4⋊C4—22no—
60C2×C11×C4⋊C4D412yes—
61C2×C11×C4⋊C4C2312yes—
62C2×C11×C4⋊C4C2312yes—
63C2×C11×C4⋊C4C2311yescharacteristic
64C2×C11×C4⋊C4C2311yescharacteristic
65C2×C11×C22⋊C4—21no—
66C2×C11×C22⋊C4—22no—
67C2×C11×C22⋊C4—22no—
68C2×C42×C11—21no—
69C2×C42×C11—22no—
70C2×C42×C11—22no—
71C2×C42×C11C2312yes—
72C2×C42×C11C2311yescharacteristic
73C11×#106C2×C414yes—
74C11×C4⋊C8—22no—
75C11×#103—24no—
76C11×#103C2×C414yes—
77C11×#102—42no—
78C11×#102C2×C414yes—
79C4×C8×C11—42no—
80C4×C8×C11C2×C414yes—
81C11×#95—21no—
82C11×#95—21no—
83C11×#95—22no—
84C11×#95—22no—
85C11×#95—21no—
86C11×#95—21no—
87C11×#95D411yescharacteristic
88C11×#95D411yescharacteristic
89#22773C1111yesmaximal, characteristic, direct product factor, Sylow
90C24×C11—21no—
91C2×Q8×C11—21no—
92C2×Q8×C11—21no—
93C2×Q8×C11—21no—
94C2×Q8×C11C22×C412yes—
95C2×Q8×C11#4112yes—
96C2×Q8×C11#4112yes—
97C2×D4×C11—21no—
98C2×D4×C11—21no—
99C2×D4×C11—21no—
100C2×D4×C11—21no—
101C2×D4×C11—21no—
102C2×D4×C11C22×C412yes—
103C22×C4×C11—21no—
104C22×C4×C11—21no—
105C22×C4×C11—21no—
106C22×C4×C11—24no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—82no—
110C22×C4×C11C2×D412yes—
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11C2×D412yes—
114C22×C4×C11C2411yescharacteristic
115C11×SD16—28no—
116C2×C8×C11—21no—
117C2×C8×C11—21no—
118C2×C8×C11—22no—
119C2×C8×C11—22no—
120C2×C8×C11—21no—
121C2×C8×C11—22no—
122C2×C8×C11—21no—
123C2×C8×C11C22×C412yes—
124C2×C8×C11C22×C412yes—
125C11×C4⋊C4—24no—
126C11×C4⋊C4—24no—
127C11×C4⋊C4—21no—
128C11×C4⋊C4—21no—
129C11×C4⋊C4—22no—
130C11×C4⋊C4—22no—
131C11×C4⋊C4—22no—
132C11×C4⋊C4—22no—
133C11×C4⋊C4—44no—
134C11×C4⋊C4—44no—
135C11×C4⋊C4C22×C412yes—
136C11×C4⋊C4C22×C412yes—
137C11×C22⋊C4—24no—
138C11×C22⋊C4—44no—
139C11×C22⋊C4—82no—
140C42×C11—24no—
141C42×C11—22no—
142C42×C11—22no—
143C42×C11—44no—
144C42×C11—82no—
145C42×C11C22×C412yes—
146C42×C11#4112yes—
147C2×C4×SD16C2×C1111yescharacteristic
148#2357C2×C1111yescharacteristic
149#2351C2×C1111yescharacteristic, complemented
150#1934C2×C1112yes—
151#1919C2×C1112yescomplemented
152#1880C2×C1112yes—
153#1835C2×C1111yescharacteristic, complemented
154#1805C2×C1111yescharacteristic, complemented
155#1804C2×C1111yescharacteristic
156C8×C4⋊C4C2×C1111yescharacteristic, complemented
157C4×#103C2×C1112yescomplemented
158C23×C11—22no—
159C23×C11—41no—
160C23×C11—41no—
161C23×C11—42no—
162C23×C11—42no—
163C23×C11C22×D411yescharacteristic
164Q8×C11—22no—
165Q8×C11—22no—
166Q8×C11—22no—
167Q8×C11#11714yes—
168D4×C11—22no—
169D4×C11—22no—
170D4×C11—41no—
171D4×C11—41no—
172C2×C4×C11—22no—
173C2×C4×C11—22no—
174C2×C4×C11—22no—
175C2×C4×C11—22no—
176C2×C4×C11—22no—
177C2×C4×C11—22no—
178C2×C4×C11—22no—
179C2×C4×C11—22no—
180C2×C4×C11—22no—
181C2×C4×C11—22no—
182C2×C4×C11—22no—
183C2×C4×C11—22no—
184C2×C4×C11—42no—
185C2×C4×C11—42no—
186C2×C4×C11—42no—
187C2×C4×C11—42no—
188C2×C4×C11—42no—
189C2×C4×C11—42no—
190C2×C4×C11—42no—
191C2×C4×C11—42no—
192C2×C4×C11—84no—
193C2×C4×C11C4×D412yes—
194C2×C4×C11C4×D412yes—
195C2×C4×C11#13514yes—
196C2×C4×C11C23×C411yescharacteristic
197C2×C4×C11C2×#4111yescharacteristic
198C2×C4×C11C2×#4111yescharacteristic
199C2×C4×C11C2×#4111yescharacteristic
200C2×C4×C11H(5,𝔽2)11yescharacteristic
201C2×C4×C112−1+411yescharacteristic
202C8×C11—22no—
203C8×C11—22no—
204C8×C11—42no—
205C22×SD16C22×C1111yescharacteristic
206C2×C4×Q8C22×C1112yes—
207C2×C4×Q8C22×C1111yescharacteristic
208C2×C4×D4C22×C1111yescharacteristic
209C4×SD16C4×C1118yescomplemented
210C2×#106C22×C1111yescharacteristic
211C2×C4⋊C8C22×C1111yescharacteristic
212C2×#103C22×C1112yes—
213C2×#103C22×C1111yescharacteristic
214C2×#102C22×C1112yes—
215C2×#102C22×C1111yescharacteristic
216C2×C4×C8C22×C1112yes—
217C2×C4×C8C22×C1111yescharacteristic
218#390C22×C1112yes—
219#389—22no—
220#389C22×C1112yes—
221#388—22no—
222#382—21no—
223#382C22×C1111yescharacteristic
224#382C22×C1111yescharacteristic
225#381—21no—
226C4×C4⋊C4—21no—
227C4×C4⋊C4C22×C1112yes—
228C4×C4⋊C4C22×C1111yescharacteristic
229C4×C22⋊C4—21no—
230#340C22×C1112yes—
231#340C22×C1112yes—
232#340C22×C1112yes—
233#340C22×C1112yes—
234#336C22×C1112yes—
235C22×C11—42no—
236C22×C11—42no—
237C22×C11—42no—
238C22×C11—82no—
239C22×C11—82no—
240C22×C11C2×C4×D411yescharacteristic
241C22×C11#54611yescharacteristic
242C22×C11#54811yescharacteristic
243C22×C11C2×#13512yes—
244C22×C11#57712yes—
245C4×C11—24no—
246C4×C11—22no—
247C4×C11—22no—
248C4×C11—24no—
249C4×C11—42no—
250C4×C11—42no—
251C4×C11—42no—
252C4×C11—82no—
253C4×C11—82no—
254C4×C11C2×#11711yescharacteristic
255C4×C11#52011yescharacteristic
256C4×C11#55211yescharacteristic
257C4×C11#55311yescharacteristic
258C22×Q8C23×C1111yescharacteristic
259C22×D4C23×C1111yescharacteristic
260C23×C4—21no—
261C2×SD16—22no—
262C2×SD16—22no—
263C2×SD16C2×C4×C1114yes—
264C22×C8C23×C1112yes—
265C22×C8C23×C1111yescharacteristic
266C22×C8C23×C1111yescharacteristic
267C4×Q8—22no—
268C4×Q8—24no—
269C4×Q8—42no—
270C4×Q8C2×C4×C1114yes—
271C4×D4—22no—
272C4×D4C2×C4×C1114yes—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—22no—
275C2×C4⋊C4—22no—
276C2×C4⋊C4D4×C1112yes—
277C2×C4⋊C4C23×C1112yes—
278C2×C4⋊C4C23×C1112yes—
279C2×C4⋊C4C23×C1111yescharacteristic
280C2×C4⋊C4C23×C1111yescharacteristic
281C2×C22⋊C4—21no—
282C2×C22⋊C4—22no—
283C2×C22⋊C4—22no—
284C2×C42—21no—
285C2×C42—22no—
286C2×C42—22no—
287C2×C42C23×C1112yes—
288C2×C42C23×C1111yescharacteristic
289#106C2×C4×C1114yes—
290C4⋊C8—22no—
291#103—24no—
292#103C2×C4×C1114yes—
293#102—42no—
294#102C2×C4×C1114yes—
295C4×C8—42no—
296C4×C8C2×C4×C1114yes—
297#95—21no—
298#95—21no—
299#95—22no—
300#95—22no—
301#95—21no—
302#95—21no—
303#95D4×C1111yescharacteristic
304#95D4×C1111yescharacteristic
305C2×C11—82no—
306C2×C11#235211yescharacteristic
307C2×C11C4×#13511yescharacteristic
308C2×C11#294911yescharacteristic
309C2×C11#330112yes—
310C2×C11#336512yes—
311C24—21no—
312C2×Q8—21no—
313C2×Q8—21no—
314C2×Q8—21no—
315C2×Q8C22×C4×C1112yes—
316C2×Q8C11×#4112yes—
317C2×Q8C11×#4112yes—
318C2×D4—21no—
319C2×D4—21no—
320C2×D4—21no—
321C2×D4—21no—
322C2×D4—21no—
323C2×D4C22×C4×C1112yes—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—21no—
327C22×C4—24no—
328C22×C4—22no—
329C22×C4—22no—
330C22×C4—82no—
331C22×C4C2×D4×C1112yes—
332C22×C4C2×D4×C1111yescharacteristic
333C22×C4C2×D4×C1111yescharacteristic
334C22×C4C2×D4×C1112yes—
335C22×C4C24×C1111yescharacteristic
336SD16—28no—
337C2×C8—21no—
338C2×C8—21no—
339C2×C8—21no—
340C2×C8—21no—
341C2×C8—22no—
342C2×C8—22no—
343C2×C8—22no—
344C2×C8C22×C4×C1112yes—
345C2×C8C22×C4×C1112yes—
346C4⋊C4—24no—
347C4⋊C4—24no—
348C4⋊C4—21no—
349C4⋊C4—21no—
350C4⋊C4—22no—
351C4⋊C4—22no—
352C4⋊C4—22no—
353C4⋊C4—22no—
354C4⋊C4—44no—
355C4⋊C4—44no—
356C4⋊C4C22×C4×C1112yes—
357C4⋊C4C22×C4×C1112yes—
358C22⋊C4—24no—
359C22⋊C4—44no—
360C22⋊C4—82no—
361C42—24no—
362C42—22no—
363C42—22no—
364C42—44no—
365C42—82no—
366C42C22×C4×C1112yes—
367C42C11×#4112yes—
368C11#2277311yescharacteristic, direct product factor, Sylow
369C23—22no—
370C23—41no—
371C23—41no—
372C23—42no—
373C23—42no—
374C23C22×D4×C1111yescharacteristic
375Q8—22no—
376Q8—22no—
377Q8—22no—
378Q8C11×#11714yes—
379D4—22no—
380D4—22no—
381D4—41no—
382D4—41no—
383C2×C4—22no—
384C2×C4—22no—
385C2×C4—22no—
386C2×C4—22no—
387C2×C4—22no—
388C2×C4—22no—
389C2×C4—22no—
390C2×C4—22no—
391C2×C4—22no—
392C2×C4—22no—
393C2×C4—22no—
394C2×C4—22no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—42no—
401C2×C4—42no—
402C2×C4—42no—
403C2×C4—84no—
404C2×C4C4×D4×C1112yes—
405C2×C4C4×D4×C1112yes—
406C2×C4C11×#13514yes—
407C2×C4C23×C4×C1111yescharacteristic
408C2×C4C2×C11×#4111yescharacteristic
409C2×C4C2×C11×#4111yescharacteristic
410C2×C4C2×C11×#4111yescharacteristic
411C2×C4C11×H(5,𝔽2)11yescharacteristic
412C2×C4C11×2−1+411yescharacteristic
413C8—22no—
414C8—22no—
415C8—42no—
416C22—42no—
417C22—42no—
418C22—42no—
419C22—82no—
420C22—82no—
421C22C2×C4×D4×C1111yescharacteristic
422C22C11×#54611yescharacteristic
423C22C11×#54811yescharacteristic
424C22C2×C11×#13512yes—
425C22C11×#57712yes—
426C4—22no—
427C4—22no—
428C4—24no—
429C4—24no—
430C4—42no—
431C4—42no—
432C4—42no—
433C4—82no—
434C4—82no—
435C4C2×C11×#11711yescharacteristic
436C4C11×#52011yescharacteristic
437C4C11×#55211yescharacteristic
438C4C11×#55311yescharacteristic
439C2—82no—
440C2C11×#235211yescharacteristic
441C2C4×C11×#13511yescharacteristic
442C2C11×#294911yescharacteristic
443C2C11×#330112yes—
444C2C11×#336512yes—
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11C23
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×#2351C2semidirect
5. C11×#1919C2semidirect
7. C11×#1835C2semidirect
8. C11×#1805C2semidirect
10. C8×C11×C4⋊C4C2semidirect
11. C4×C11×#103C2semidirect
16. C4×C11×SD16C4semidirect
89. #22773C11direct (N × H)
149. #2351C2×C11semidirect
151. #1919C2×C11semidirect
153. #1835C2×C11semidirect
154. #1805C2×C11semidirect
156. C8×C4⋊C4C2×C11semidirect
157. C4×#103C2×C11semidirect
209. C4×SD16C4×C11semidirect
368. C11#22773direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×C11×SD162
C11×#23572
C11×#23512
C11×#19342
C11×#19192
C11×#18802
C11×#18352
C11×#18052
C11×#18042
C8×C11×C4⋊C42
C4×C11×#1032
#2277311