Finite Group Databasebeta

← C11×#23027 #14600220

Subgroups — C11×#23027 #14600220

Order 2816.

1050 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#466C211yesmaximal, characteristic
2C2×C4×C11×D8C211yesmaximal, characteristic, complemented
3C2×C11×#427C211yesmaximal, characteristic, complemented
4C11×#2363C212yesmaximal, complemented
5C11×#1970C211yesmaximal, characteristic, complemented
6C11×#1942C211yesmaximal, characteristic, complemented
7C11×#1926C212yesmaximal, complemented
8C11×#1875C212yesmaximal, complemented
9C11×#1864C212yesmaximal, complemented
10C4×C11×#107C211yesmaximal, characteristic, complemented
11C8×C11×C22⋊C4C211yesmaximal, characteristic, complemented
12C22×C11×D8C2211yescharacteristic
13C23×C8×C11C2211yescharacteristic
14C2×C11×#121C2212yes—
15C2×C4×D4×C11C2212yes—
16C2×C11×#117C2212yes—
17C11×#466C418yescomplemented
18C4×C11×D8—24no—
19C11×#427—24no—
20C2×C11×#107C2211yescharacteristic
21C2×C11×#107C2211yescharacteristic
22C2×C11×#107C2211yescharacteristic
23C2×C11×#106C2212yes—
24C2×C11×#102C2212yes—
25C2×C11×#102C2212yes—
26C2×C11×#102C2212yes—
27C2×C11×C22⋊C8C2211yescharacteristic
28C2×C4×C8×C11C2211yescharacteristic
29C2×C4×C8×C11C2211yescharacteristic
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⋊C4D411yescharacteristic
72C2×C11×C22⋊C4D411yescharacteristic
73C2×C42×C11—22no—
74C2×C42×C11—22no—
75C2×C42×C11C2311yescharacteristic
76C2×C42×C11C2311yescharacteristic
77C11×#107—22no—
78C11×#107C2×C414yescomplemented
79C11×#107D414yescomplemented
80C11×#106—24no—
81C11×#102—24no—
82C11×#102—42no—
83C11×#102C2×C418yescomplemented
84C11×C22⋊C8—22no—
85C4×C8×C11—22no—
86C4×C8×C11—22no—
87C11×#95—22no—
88C11×#95—22no—
89C11×#95D411yescharacteristic
90C11×#95D411yescharacteristic
91#23027C1111yesmaximal, characteristic, direct product factor, Sylow
92C24×C11—22no—
93C24×C11C2×D411yescharacteristic
94C2×D4×C11—28no—
95C2×D4×C11—22no—
96C2×D4×C11—22no—
97C2×D4×C11—22no—
98C2×D4×C11—22no—
99C2×D4×C11—22no—
100C2×D4×C11—82no—
101C2×D4×C11—82no—
102C2×D4×C11C22×C414yes—
103C22×C4×C11—21no—
104C22×C4×C11—21no—
105C22×C4×C11—21no—
106C22×C4×C11—21no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—44no—
111C22×C4×C11—44no—
112C22×C4×C11—82no—
113C22×C4×C11C22×C412yes—
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11#4112yes—
120C22×C4×C11C2411yescharacteristic
121C11×D8—28no—
122C2×C8×C11—28no—
123C2×C8×C11—21no—
124C2×C8×C11—21no—
125C2×C8×C11—21no—
126C2×C8×C11—21no—
127C2×C8×C11—21no—
128C2×C8×C11—21no—
129C2×C8×C11—21no—
130C2×C8×C11—21no—
131C2×C8×C11C22×C412yes—
132C2×C8×C11C22×C412yes—
133C2×C8×C11C2×D412yes—
134C2×C8×C11#4112yes—
135C11×C4⋊C4—22no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4—82no—
140C11×C4⋊C4C22×C414yes—
141C11×C4⋊C4C2×D414yes—
142C11×C22⋊C4—28no—
143C11×C22⋊C4—22no—
144C11×C22⋊C4—22no—
145C11×C22⋊C4—44no—
146C11×C22⋊C4—44no—
147C11×C22⋊C4—44no—
148C11×C22⋊C4—82no—
149C42×C11—21no—
150C42×C11—21no—
151C42×C11—21no—
152C42×C11—21no—
153C42×C11—44no—
154C42×C11—82no—
155C2×#466C2×C1111yescharacteristic
156C2×C4×D8C2×C1111yescharacteristic, complemented
157C2×#427C2×C1111yescharacteristic, complemented
158#2363C2×C1112yescomplemented
159#1970C2×C1111yescharacteristic, complemented
160#1942C2×C1111yescharacteristic, complemented
161#1926C2×C1112yescomplemented
162#1875C2×C1112yescomplemented
163#1864C2×C1112yescomplemented
164C4×#107C2×C1111yescharacteristic, complemented
165C8×C22⋊C4C2×C1111yescharacteristic, complemented
166C23×C11—21no—
167C23×C11—21no—
168C23×C11—21no—
169C23×C11—21no—
170C23×C11—21no—
171C23×C11—21no—
172C23×C11—24no—
173C23×C11—42no—
174C23×C11—42no—
175C23×C11—42no—
176C23×C11—42no—
177C23×C11—42no—
178C23×C11—42no—
179C23×C11C4×D412yes—
180C23×C11C22×D411yescharacteristic
181D4×C11—24no—
182D4×C11—24no—
183D4×C11—42no—
184D4×C11—42no—
185D4×C11—88no—
186C2×C4×C11—21no—
187C2×C4×C11—21no—
188C2×C4×C11—21no—
189C2×C4×C11—21no—
190C2×C4×C11—21no—
191C2×C4×C11—21no—
192C2×C4×C11—22no—
193C2×C4×C11—22no—
194C2×C4×C11—22no—
195C2×C4×C11—22no—
196C2×C4×C11—24no—
197C2×C4×C11—21no—
198C2×C4×C11—24no—
199C2×C4×C11—21no—
200C2×C4×C11—21no—
201C2×C4×C11—21no—
202C2×C4×C11—21no—
203C2×C4×C11—21no—
204C2×C4×C11—42no—
205C2×C4×C11—42no—
206C2×C4×C11—42no—
207C2×C4×C11—42no—
208C2×C4×C11—42no—
209C2×C4×C11—42no—
210C2×C4×C11—42no—
211C2×C4×C11—88no—
212C2×C4×C11C4×D412yes—
213C2×C4×C11#13512yes—
214C2×C4×C11#13512yes—
215C2×C4×C11C23×C411yescharacteristic
216C2×C4×C11C22×D411yescharacteristic
217C2×C4×C11C2×#4111yescharacteristic
218C2×C4×C11C2×#4111yescharacteristic
219C2×C4×C11H(5,𝔽2)11yescharacteristic
220C2×C4×C112−1+411yescharacteristic
221C8×C11—22no—
222C8×C11—41no—
223C8×C11—41no—
224C8×C11C4×D414yes—
225C22×D8C22×C1111yescharacteristic
226C23×C8C22×C1111yescharacteristic
227C2×#121C22×C1112yes—
228C2×C4×D4C22×C1112yes—
229C2×#117C22×C1112yes—
230#466C4×C1118yescomplemented
231C4×D8—24no—
232#427—24no—
233C2×#107C22×C1111yescharacteristic
234C2×#107C22×C1111yescharacteristic
235C2×#107C22×C1111yescharacteristic
236C2×#106C22×C1112yes—
237C2×#102C22×C1112yes—
238C2×#102C22×C1112yes—
239C2×#102C22×C1112yes—
240C2×C22⋊C8C22×C1111yescharacteristic
241C2×C4×C8C22×C1111yescharacteristic
242C2×C4×C8C22×C1111yescharacteristic
243#390—22no—
244#390C22×C1112yes—
245#389C22×C1112yes—
246#388—22no—
247#386—22no—
248C4×C4⋊C4C22×C1112yes—
249C4×C22⋊C4—22no—
250C4×C22⋊C4C22×C1111yescharacteristic
251#340C22×C1112yes—
252#340C22×C1112yes—
253#336C22×C1111yescharacteristic
254#336C22×C1111yescharacteristic
255C22×C11—22no—
256C22×C11—22no—
257C22×C11—22no—
258C22×C11—41no—
259C22×C11—41no—
260C22×C11—41no—
261C22×C11—41no—
262C22×C11—44no—
263C22×C11—44no—
264C22×C11—44no—
265C22×C11—82no—
266C22×C11—82no—
267C22×C11—82no—
268C22×C11—82no—
269C22×C11C2×C4×D411yescharacteristic
270C22×C11D4211yescharacteristic
271C22×C11#54711yescharacteristic
272C22×C11C2×#13511yescharacteristic
273C22×C11C2×#13511yescharacteristic
274C22×C11#57611yescharacteristic
275C22×C11#57611yescharacteristic
276C4×C11—22no—
277C4×C11—22no—
278C4×C11—22no—
279C4×C11—41no—
280C4×C11—44no—
281C4×C11—44no—
282C4×C11—41no—
283C4×C11—82no—
284C4×C11C2×C4×D411yescharacteristic
285C4×C11#52011yescharacteristic
286C4×C11#54811yescharacteristic
287C4×C11#55311yescharacteristic
288C22×D4—22no—
289C22×D4C23×C1112yes—
290C23×C4—22no—
291C23×C4C23×C1111yescharacteristic
292C2×D8—22no—
293C2×D8—22no—
294C2×D8C2×C4×C1114yes—
295C22×C8—22no—
296C22×C8—22no—
297C22×C8C2×C4×C1114yescomplemented
298C22×C8C23×C1111yescharacteristic
299C22×C8C23×C1111yescharacteristic
300C22×C8C23×C1111yescharacteristic
301C22×C8C23×C1111yescharacteristic
302#121—24no—
303#121C2×C4×C1118yescomplemented
304C4×D4—24no—
305C4×D4—42no—
306#117—24no—
307#117—42no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4C23×C1112yes—
310C2×C4⋊C4C23×C1112yes—
311C2×C4⋊C4C23×C1112yes—
312C2×C22⋊C4—22no—
313C2×C22⋊C4—22no—
314C2×C22⋊C4—22no—
315C2×C22⋊C4—22no—
316C2×C22⋊C4—22no—
317C2×C22⋊C4D4×C1111yescharacteristic
318C2×C22⋊C4D4×C1111yescharacteristic
319C2×C42—22no—
320C2×C42—22no—
321C2×C42C23×C1111yescharacteristic
322C2×C42C23×C1111yescharacteristic
323#107—22no—
324#107C2×C4×C1114yescomplemented
325#107D4×C1114yescomplemented
326#106—24no—
327#102—24no—
328#102—42no—
329#102C2×C4×C1118yescomplemented
330C22⋊C8—22no—
331C4×C8—22no—
332C4×C8—22no—
333#95—22no—
334#95—22no—
335#95D4×C1111yescharacteristic
336#95D4×C1111yescharacteristic
337C2×C11—42no—
338C2×C11—84no—
339C2×C11#236111yescharacteristic
340C2×C11C4×#13511yescharacteristic
341C2×C11#294811yescharacteristic
342C2×C11#328011yescharacteristic
343C2×C11#328711yescharacteristic
344C2×C11#333911yescharacteristic
345C2×C11#334111yescharacteristic
346C24—22no—
347C24C2×D4×C1111yescharacteristic
348C2×D4—28no—
349C2×D4—22no—
350C2×D4—22no—
351C2×D4—22no—
352C2×D4—22no—
353C2×D4—22no—
354C2×D4—82no—
355C2×D4—82no—
356C2×D4C22×C4×C1114yes—
357C22×C4—21no—
358C22×C4—21no—
359C22×C4—21no—
360C22×C4—21no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—44no—
365C22×C4—44no—
366C22×C4—82no—
367C22×C4C22×C4×C1112yes—
368C22×C4C2×D4×C1111yescharacteristic
369C22×C4C2×D4×C1111yescharacteristic
370C22×C4C2×D4×C1111yescharacteristic
371C22×C4C2×D4×C1111yescharacteristic
372C22×C4C2×D4×C1111yescharacteristic
373C22×C4C11×#4112yes—
374C22×C4C24×C1111yescharacteristic
375D8—28no—
376C2×C8—21no—
377C2×C8—21no—
378C2×C8—28no—
379C2×C8—21no—
380C2×C8—21no—
381C2×C8—21no—
382C2×C8—21no—
383C2×C8—21no—
384C2×C8—21no—
385C2×C8C22×C4×C1112yes—
386C2×C8C22×C4×C1112yes—
387C2×C8C2×D4×C1112yes—
388C2×C8C11×#4112yes—
389C4⋊C4—22no—
390C4⋊C4—22no—
391C4⋊C4—22no—
392C4⋊C4—22no—
393C4⋊C4—82no—
394C4⋊C4C22×C4×C1114yes—
395C4⋊C4C2×D4×C1114yes—
396C22⋊C4—28no—
397C22⋊C4—22no—
398C22⋊C4—22no—
399C22⋊C4—44no—
400C22⋊C4—44no—
401C22⋊C4—44no—
402C22⋊C4—82no—
403C42—21no—
404C42—21no—
405C42—21no—
406C42—21no—
407C42—44no—
408C42—82no—
409C11#2302711yescharacteristic, direct product factor, Sylow
410C23—21no—
411C23—21no—
412C23—21no—
413C23—21no—
414C23—21no—
415C23—21no—
416C23—24no—
417C23—42no—
418C23—42no—
419C23—42no—
420C23—42no—
421C23—42no—
422C23—42no—
423C23C4×D4×C1112yes—
424C23C22×D4×C1111yescharacteristic
425D4—24no—
426D4—24no—
427D4—42no—
428D4—42no—
429D4—88no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—21no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—22no—
440C2×C4—24no—
441C2×C4—21no—
442C2×C4—24no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4—42no—
452C2×C4—42no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—88no—
456C2×C4C4×D4×C1112yes—
457C2×C4C11×#13512yes—
458C2×C4C11×#13512yes—
459C2×C4C23×C4×C1111yescharacteristic
460C2×C4C22×D4×C1111yescharacteristic
461C2×C4C2×C11×#4111yescharacteristic
462C2×C4C2×C11×#4111yescharacteristic
463C2×C4C11×H(5,𝔽2)11yescharacteristic
464C2×C4C11×2−1+411yescharacteristic
465C8—22no—
466C8—41no—
467C8—41no—
468C8C4×D4×C1114yes—
469C22—22no—
470C22—22no—
471C22—22no—
472C22—41no—
473C22—41no—
474C22—41no—
475C22—41no—
476C22—44no—
477C22—44no—
478C22—44no—
479C22—82no—
480C22—82no—
481C22—82no—
482C22—82no—
483C22C2×C4×D4×C1111yescharacteristic
484C22D42×C1111yescharacteristic
485C22C11×#54711yescharacteristic
486C22C2×C11×#13511yescharacteristic
487C22C2×C11×#13511yescharacteristic
488C22C11×#57611yescharacteristic
489C22C11×#57611yescharacteristic
490C4—22no—
491C4—22no—
492C4—22no—
493C4—44no—
494C4—44no—
495C4—41no—
496C4—41no—
497C4—82no—
498C4C2×C4×D4×C1111yescharacteristic
499C4C11×#52011yescharacteristic
500C4C11×#54811yescharacteristic
501C4C11×#55311yescharacteristic
502C2—42no—
503C2—84no—
504C2C11×#236111yescharacteristic
505C2C4×C11×#13511yescharacteristic
506C2C11×#294811yescharacteristic
507C2C11×#328011yescharacteristic
508C2C11×#328711yescharacteristic
509C2C11×#333911yescharacteristic
510C2C11×#334111yescharacteristic
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×C4×C11×D8C2semidirect
3. C2×C11×#427C2semidirect
4. C11×#2363C2semidirect
5. C11×#1970C2semidirect
6. C11×#1942C2semidirect
7. C11×#1926C2semidirect
8. C11×#1875C2semidirect
9. C11×#1864C2semidirect
10. C4×C11×#107C2semidirect
11. C8×C11×C22⋊C4C2semidirect
17. C11×#466C4semidirect
51. C22×C8×C11C2×C4semidirect
57. C11×#121C2×C4semidirect
78. C11×#107C2×C4semidirect
79. C11×#107D4semidirect
83. C11×#102C2×C4semidirect
91. #23027C11direct (N × H)
156. C2×C4×D8C2×C11semidirect
157. C2×#427C2×C11semidirect
158. #2363C2×C11semidirect
159. #1970C2×C11semidirect
160. #1942C2×C11semidirect
161. #1926C2×C11semidirect
162. #1875C2×C11semidirect
163. #1864C2×C11semidirect
164. C4×#107C2×C11semidirect
165. C8×C22⋊C4C2×C11semidirect
230. #466C4×C11semidirect
297. C22×C8C2×C4×C11semidirect
303. #121C2×C4×C11semidirect
324. #107C2×C4×C11semidirect
325. #107D4×C11semidirect
329. #102C2×C4×C11semidirect
409. C11#23027direct (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×C4×C11×D82
C2×C11×#4272
C11×#23632
C11×#19702
C11×#19422
C11×#19262
C11×#18752
C11×#18642
C4×C11×#1072
C8×C11×C22⋊C42
#2302711