Finite Group Databasebeta

← C11×#23031 #14600224

Subgroups — C11×#23031 #14600224

Order 2816.

1038 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#466C211yesmaximal, characteristic
2C2×C11×#442C211yesmaximal, characteristic, complemented
3C2×C11×#427C211yesmaximal, characteristic, complemented
4C11×#2363C212yesmaximal, complemented
5C11×#1972C211yesmaximal, characteristic, complemented
6C11×#1943C211yesmaximal, characteristic, complemented
7C11×#1925C212yesmaximal, complemented
8C11×#1875C212yesmaximal, complemented
9C11×#1862C212yesmaximal, complemented
10C11×#1776C211yesmaximal, characteristic, complemented
11C11×#1752C211yesmaximal, characteristic, complemented
12C22×C11×D8C2211yescharacteristic
13C23×C8×C11C2211yescharacteristic
14C2×C11×#121C2212yes—
15C2×C4×D4×C11C2212yes—
16C2×C11×#117C2212yes—
17C11×#466C418yescomplemented
18C11×#442—24no—
19C11×#427—24no—
20C2×C11×#107C2212yes—
21C2×C11×#107C2211yescharacteristic
22C2×C11×#106C2211yescharacteristic
23C2×C11×#106C2211yescharacteristic
24C2×C11×#102C2212yes—
25C2×C11×#102C2212yes—
26C2×C11×#102C2212yes—
27C2×C11×C22⋊C8C2211yescharacteristic
28C2×C11×#97C2211yescharacteristic
29C2×C11×#97C2211yescharacteristic
30C11×#390—22no—
31C11×#390C2212yes—
32C11×#389C2212yes—
33C11×#388—22no—
34C11×#386—22no—
35C4×C11×C4⋊C4C2212yes—
36C4×C11×C22⋊C4—22no—
37C4×C11×C22⋊C4C2211yescharacteristic
38C11×#340C2212yes—
39C11×#340C2212yes—
40C11×#336C2211yescharacteristic
41C11×#336C2211yescharacteristic
42C22×D4×C11—22no—
43C22×D4×C11C2312yes—
44C23×C4×C11—22no—
45C23×C4×C11C2311yescharacteristic
46C2×C11×D8—22no—
47C2×C11×D8—22no—
48C2×C11×D8C2×C414yes—
49C22×C8×C11—22no—
50C22×C8×C11—22no—
51C22×C8×C11C2×C414yescomplemented
52C22×C8×C11C2311yescharacteristic
53C22×C8×C11C2311yescharacteristic
54C22×C8×C11C2311yescharacteristic
55C22×C8×C11C2311yescharacteristic
56C11×#121—24no—
57C11×#121C2×C418yescomplemented
58C4×D4×C11—24no—
59C4×D4×C11—42no—
60C11×#117—24no—
61C11×#117—42no—
62C2×C11×C4⋊C4—22no—
63C2×C11×C4⋊C4C2312yes—
64C2×C11×C4⋊C4C2312yes—
65C2×C11×C4⋊C4C2312yes—
66C2×C11×C22⋊C4—22no—
67C2×C11×C22⋊C4—22no—
68C2×C11×C22⋊C4—22no—
69C2×C11×C22⋊C4—22no—
70C2×C11×C22⋊C4—22no—
71C2×C11×C22⋊C4D412yes—
72C2×C42×C11—22no—
73C2×C42×C11—22no—
74C2×C42×C11C2311yescharacteristic
75C2×C42×C11C2311yescharacteristic
76C11×#107—24no—
77C11×#107C2×C414yescomplemented
78C11×#106—22no—
79C11×#106D414yescomplemented
80C11×#102—24no—
81C11×#102—42no—
82C11×#102C2×C418yescomplemented
83C11×C22⋊C8—22no—
84C11×#97—22no—
85C11×#97—22no—
86C11×#95—22no—
87C11×#95—22no—
88C11×#95D412yes—
89#23031C1111yesmaximal, characteristic, direct product factor, Sylow
90C24×C11—22no—
91C24×C11C2×D411yescharacteristic
92C2×D4×C11—28no—
93C2×D4×C11—22no—
94C2×D4×C11—22no—
95C2×D4×C11—22no—
96C2×D4×C11—22no—
97C2×D4×C11—22no—
98C2×D4×C11—82no—
99C2×D4×C11—82no—
100C2×D4×C11C22×C414yes—
101C22×C4×C11—21no—
102C22×C4×C11—21no—
103C22×C4×C11—21no—
104C22×C4×C11—21no—
105C22×C4×C11—22no—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—44no—
109C22×C4×C11—44no—
110C22×C4×C11—82no—
111C22×C4×C11C22×C412yes—
112C22×C4×C11C2×D412yes—
113C22×C4×C11C2×D412yes—
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11#4112yes—
116C22×C4×C11C2411yescharacteristic
117C11×D8—28no—
118C2×C8×C11—28no—
119C2×C8×C11—21no—
120C2×C8×C11—21no—
121C2×C8×C11—21no—
122C2×C8×C11—21no—
123C2×C8×C11—21no—
124C2×C8×C11—21no—
125C2×C8×C11—21no—
126C2×C8×C11—21no—
127C2×C8×C11C22×C412yes—
128C2×C8×C11C22×C412yes—
129C2×C8×C11C2×D412yes—
130C2×C8×C11#4112yes—
131C11×C4⋊C4—22no—
132C11×C4⋊C4—22no—
133C11×C4⋊C4—22no—
134C11×C4⋊C4—22no—
135C11×C4⋊C4—82no—
136C11×C4⋊C4C22×C414yes—
137C11×C4⋊C4C2×D414yes—
138C11×C22⋊C4—28no—
139C11×C22⋊C4—42no—
140C11×C22⋊C4—44no—
141C11×C22⋊C4—44no—
142C11×C22⋊C4—44no—
143C11×C22⋊C4—82no—
144C42×C11—21no—
145C42×C11—21no—
146C42×C11—21no—
147C42×C11—21no—
148C42×C11—44no—
149C42×C11—82no—
150C2×#466C2×C1111yescharacteristic
151C2×#442C2×C1111yescharacteristic, complemented
152C2×#427C2×C1111yescharacteristic, complemented
153#2363C2×C1112yescomplemented
154#1972C2×C1111yescharacteristic, complemented
155#1943C2×C1111yescharacteristic, complemented
156#1925C2×C1112yescomplemented
157#1875C2×C1112yescomplemented
158#1862C2×C1112yescomplemented
159#1776C2×C1111yescharacteristic, complemented
160#1752C2×C1111yescharacteristic, complemented
161C23×C11—21no—
162C23×C11—21no—
163C23×C11—22no—
164C23×C11—22no—
165C23×C11—24no—
166C23×C11—42no—
167C23×C11—42no—
168C23×C11—42no—
169C23×C11—42no—
170C23×C11—42no—
171C23×C11—42no—
172C23×C11C4×D412yes—
173C23×C11C22×D411yescharacteristic
174D4×C11—24no—
175D4×C11—24no—
176D4×C11—42no—
177D4×C11—42no—
178D4×C11—88no—
179C2×C4×C11—21no—
180C2×C4×C11—21no—
181C2×C4×C11—22no—
182C2×C4×C11—22no—
183C2×C4×C11—22no—
184C2×C4×C11—22no—
185C2×C4×C11—24no—
186C2×C4×C11—22no—
187C2×C4×C11—24no—
188C2×C4×C11—22no—
189C2×C4×C11—22no—
190C2×C4×C11—22no—
191C2×C4×C11—22no—
192C2×C4×C11—22no—
193C2×C4×C11—42no—
194C2×C4×C11—42no—
195C2×C4×C11—42no—
196C2×C4×C11—42no—
197C2×C4×C11—42no—
198C2×C4×C11—42no—
199C2×C4×C11—42no—
200C2×C4×C11—88no—
201C2×C4×C11C4×D412yes—
202C2×C4×C11C23×C411yescharacteristic
203C2×C4×C11C22×D411yescharacteristic
204C2×C4×C11C2×#4111yescharacteristic
205C2×C4×C11C2×#4111yescharacteristic
206C2×C4×C11H(5,𝔽2)11yescharacteristic
207C2×C4×C112−1+411yescharacteristic
208C8×C11—22no—
209C8×C11—41no—
210C8×C11—41no—
211C8×C11C4×D414yes—
212C22×D8C22×C1111yescharacteristic
213C23×C8C22×C1111yescharacteristic
214C2×#121C22×C1112yes—
215C2×C4×D4C22×C1112yes—
216C2×#117C22×C1112yes—
217#466C4×C1118yescomplemented
218#442—24no—
219#427—24no—
220C2×#107C22×C1112yes—
221C2×#107C22×C1111yescharacteristic
222C2×#106C22×C1111yescharacteristic
223C2×#106C22×C1111yescharacteristic
224C2×#102C22×C1112yes—
225C2×#102C22×C1112yes—
226C2×#102C22×C1112yes—
227C2×C22⋊C8C22×C1111yescharacteristic
228C2×#97C22×C1111yescharacteristic
229C2×#97C22×C1111yescharacteristic
230#390—22no—
231#390C22×C1112yes—
232#389C22×C1112yes—
233#388—22no—
234#386—22no—
235C4×C4⋊C4C22×C1112yes—
236C4×C22⋊C4—22no—
237C4×C22⋊C4C22×C1111yescharacteristic
238#340C22×C1112yes—
239#340C22×C1112yes—
240#336C22×C1111yescharacteristic
241#336C22×C1111yescharacteristic
242C22×C11—22no—
243C22×C11—22no—
244C22×C11—22no—
245C22×C11—42no—
246C22×C11—42no—
247C22×C11—44no—
248C22×C11—44no—
249C22×C11—44no—
250C22×C11—82no—
251C22×C11—82no—
252C22×C11—82no—
253C22×C11—82no—
254C22×C11C2×C4×D411yescharacteristic
255C22×C11D4211yescharacteristic
256C22×C11#54711yescharacteristic
257C22×C11#57512yes—
258C22×C11#57612yes—
259C4×C11—22no—
260C4×C11—42no—
261C4×C11—44no—
262C4×C11—42no—
263C4×C11—44no—
264C4×C11—82no—
265C4×C11C2×C4×D411yescharacteristic
266C4×C11#52011yescharacteristic
267C4×C11#54811yescharacteristic
268C4×C11#55311yescharacteristic
269C22×D4—22no—
270C22×D4C23×C1112yes—
271C23×C4—22no—
272C23×C4C23×C1111yescharacteristic
273C2×D8—22no—
274C2×D8—22no—
275C2×D8C2×C4×C1114yes—
276C22×C8—22no—
277C22×C8—22no—
278C22×C8C2×C4×C1114yescomplemented
279C22×C8C23×C1111yescharacteristic
280C22×C8C23×C1111yescharacteristic
281C22×C8C23×C1111yescharacteristic
282C22×C8C23×C1111yescharacteristic
283#121—24no—
284#121C2×C4×C1118yescomplemented
285C4×D4—24no—
286C4×D4—42no—
287#117—24no—
288#117—42no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4C23×C1112yes—
291C2×C4⋊C4C23×C1112yes—
292C2×C4⋊C4C23×C1112yes—
293C2×C22⋊C4—22no—
294C2×C22⋊C4—22no—
295C2×C22⋊C4—22no—
296C2×C22⋊C4—22no—
297C2×C22⋊C4—22no—
298C2×C22⋊C4D4×C1112yes—
299C2×C42—22no—
300C2×C42—22no—
301C2×C42C23×C1111yescharacteristic
302C2×C42C23×C1111yescharacteristic
303#107—24no—
304#107C2×C4×C1114yescomplemented
305#106—22no—
306#106D4×C1114yescomplemented
307#102—24no—
308#102—42no—
309#102C2×C4×C1118yescomplemented
310C22⋊C8—22no—
311#97—22no—
312#97—22no—
313#95—22no—
314#95—22no—
315#95D4×C1112yes—
316C2×C11—42no—
317C2×C11—84no—
318C2×C11#236111yescharacteristic
319C2×C11#294311yescharacteristic
320C2×C11#294811yescharacteristic
321C2×C11#326812yes—
322C2×C11#334712yes—
323C24—22no—
324C24C2×D4×C1111yescharacteristic
325C2×D4—28no—
326C2×D4—22no—
327C2×D4—22no—
328C2×D4—22no—
329C2×D4—22no—
330C2×D4—22no—
331C2×D4—82no—
332C2×D4—82no—
333C2×D4C22×C4×C1114yes—
334C22×C4—21no—
335C22×C4—21no—
336C22×C4—21no—
337C22×C4—21no—
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—44no—
342C22×C4—44no—
343C22×C4—82no—
344C22×C4C22×C4×C1112yes—
345C22×C4C2×D4×C1112yes—
346C22×C4C2×D4×C1112yes—
347C22×C4C2×D4×C1111yescharacteristic
348C22×C4C11×#4112yes—
349C22×C4C24×C1111yescharacteristic
350D8—28no—
351C2×C8—21no—
352C2×C8—21no—
353C2×C8—28no—
354C2×C8—21no—
355C2×C8—21no—
356C2×C8—21no—
357C2×C8—21no—
358C2×C8—21no—
359C2×C8—21no—
360C2×C8C22×C4×C1112yes—
361C2×C8C22×C4×C1112yes—
362C2×C8C2×D4×C1112yes—
363C2×C8C11×#4112yes—
364C4⋊C4—22no—
365C4⋊C4—22no—
366C4⋊C4—22no—
367C4⋊C4—22no—
368C4⋊C4—82no—
369C4⋊C4C22×C4×C1114yes—
370C4⋊C4C2×D4×C1114yes—
371C22⋊C4—28no—
372C22⋊C4—42no—
373C22⋊C4—44no—
374C22⋊C4—44no—
375C22⋊C4—44no—
376C22⋊C4—82no—
377C42—21no—
378C42—21no—
379C42—21no—
380C42—21no—
381C42—44no—
382C42—82no—
383C11#2303111yescharacteristic, direct product factor, Sylow
384C23—21no—
385C23—21no—
386C23—22no—
387C23—22no—
388C23—24no—
389C23—42no—
390C23—42no—
391C23—42no—
392C23—42no—
393C23—42no—
394C23—42no—
395C23C4×D4×C1112yes—
396C23C22×D4×C1111yescharacteristic
397D4—24no—
398D4—24no—
399D4—42no—
400D4—42no—
401D4—88no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—22no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—24no—
409C2×C4—22no—
410C2×C4—24no—
411C2×C4—22no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—22no—
415C2×C4—22no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—88no—
424C2×C4C4×D4×C1112yes—
425C2×C4C23×C4×C1111yescharacteristic
426C2×C4C22×D4×C1111yescharacteristic
427C2×C4C2×C11×#4111yescharacteristic
428C2×C4C2×C11×#4111yescharacteristic
429C2×C4C11×H(5,𝔽2)11yescharacteristic
430C2×C4C11×2−1+411yescharacteristic
431C8—22no—
432C8—41no—
433C8—41no—
434C8C4×D4×C1114yes—
435C22—22no—
436C22—22no—
437C22—22no—
438C22—42no—
439C22—42no—
440C22—44no—
441C22—44no—
442C22—44no—
443C22—82no—
444C22—82no—
445C22—82no—
446C22—82no—
447C22C2×C4×D4×C1111yescharacteristic
448C22D42×C1111yescharacteristic
449C22C11×#54711yescharacteristic
450C22C11×#57512yes—
451C22C11×#57612yes—
452C4—22no—
453C4—44no—
454C4—42no—
455C4—44no—
456C4—42no—
457C4—82no—
458C4C2×C4×D4×C1111yescharacteristic
459C4C11×#52011yescharacteristic
460C4C11×#54811yescharacteristic
461C4C11×#55311yescharacteristic
462C2—42no—
463C2—84no—
464C2C11×#236111yescharacteristic
465C2C11×#294311yescharacteristic
466C2C11×#294811yescharacteristic
467C2C11×#326812yes—
468C2C11×#334712yes—
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#466C2
LCSG ▷ C2×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×C11×#442C2semidirect
3. C2×C11×#427C2semidirect
4. C11×#2363C2semidirect
5. C11×#1972C2semidirect
6. C11×#1943C2semidirect
7. C11×#1925C2semidirect
8. C11×#1875C2semidirect
9. C11×#1862C2semidirect
10. C11×#1776C2semidirect
11. C11×#1752C2semidirect
17. C11×#466C4semidirect
51. C22×C8×C11C2×C4semidirect
57. C11×#121C2×C4semidirect
77. C11×#107C2×C4semidirect
79. C11×#106D4semidirect
82. C11×#102C2×C4semidirect
89. #23031C11direct (N × H)
151. C2×#442C2×C11semidirect
152. C2×#427C2×C11semidirect
153. #2363C2×C11semidirect
154. #1972C2×C11semidirect
155. #1943C2×C11semidirect
156. #1925C2×C11semidirect
157. #1875C2×C11semidirect
158. #1862C2×C11semidirect
159. #1776C2×C11semidirect
160. #1752C2×C11semidirect
217. #466C4×C11semidirect
278. C22×C8C2×C4×C11semidirect
284. #121C2×C4×C11semidirect
304. #107C2×C4×C11semidirect
306. #106D4×C11semidirect
309. #102C2×C4×C11semidirect
383. C11#23031direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4662
C2×C11×#4422
C2×C11×#4272
C11×#23632
C11×#19722
C11×#19432
C11×#19252
C11×#18752
C11×#18622
C11×#17762
C11×#17522
#2303111