Finite Group Databasebeta

← C11×#14284 #14591477

Subgroups — C11×#14284 #14591477

Order 2816.

1210 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#391C211yesmaximal, characteristic
2C11×#1446C212yesmaximal
3C11×#1443C212yesmaximal
4C11×#1442C212yesmaximal
5C11×#1441C212yesmaximal
6C11×#1436C212yesmaximal
7C11×#1434C211yesmaximal, characteristic
8C11×#1434C212yesmaximal
9C4×C11×#95C211yesmaximal, characteristic
10C23×Q8×C11C2211yescharacteristic
11C22×C11×C4⋊C4C2212yes—
12C22×C11×C4⋊C4C2211yescharacteristic
13C22×C42×C11C2211yescharacteristic
14C22×C42×C11C2211yescharacteristic
15C22×C42×C11C2211yescharacteristic
16C11×#391C418yescomplemented
17C2×C11×#95C2212yes—
18C2×C11×#95C2212yes—
19C2×C11×#95C2212yes—
20C2×C11×#95C2212yes—
21C2×C11×#95C2212yes—
22C2×C11×#95C2212yes—
23C2×C11×#95C2212yes—
24C2×C11×#95C2211yescharacteristic
25C2×C11×#95C2212yes—
26C2×C11×#95C2211yescharacteristic
27C2×C11×#95C2212yes—
28C2×C11×#95C2212yes—
29C2×C11×#95C2212yes—
30C2×C11×#95C2212yes—
31C2×C11×#95C2212yes—
32C22×Q8×C11—24no—
33C22×Q8×C11—41no—
34C22×Q8×C11—41no—
35C22×Q8×C11—42no—
36C22×Q8×C11C2×C414yes—
37C23×C4×C11C2312yes—
38C23×C4×C11C2312yes—
39C23×C4×C11C2311yescharacteristic
40C23×C4×C11C2312yes—
41C23×C4×C11C2312yes—
42C23×C4×C11C2312yes—
43C23×C4×C11C2312yes—
44C23×C4×C11C2311yescharacteristic
45C23×C4×C11C2311yescharacteristic
46C2×C11×C4⋊C4—24no—
47C2×C11×C4⋊C4—42no—
48C2×C11×C4⋊C4—42no—
49C2×C11×C4⋊C4—42no—
50C2×C11×C4⋊C4C2×C414yes—
51C2×C42×C11—22no—
52C2×C42×C11—41no—
53C2×C42×C11—41no—
54C2×C42×C11—41no—
55C2×C42×C11—41no—
56C2×C42×C11—41no—
57C2×C42×C11—41no—
58C2×C42×C11C2×C414yes—
59C2×C42×C11Q814yescomplemented
60C11×#95—24no—
61C11×#95—24no—
62C11×#95—24no—
63C11×#95—24no—
64C11×#95—24no—
65C11×#95—42no—
66C11×#95—42no—
67C11×#95—42no—
68C11×#95—42no—
69C11×#95—42no—
70C11×#95—41no—
71C11×#95—41no—
72C11×#95—42no—
73C11×#95C2×C418yes—
74C11×#95C2×C418yes—
75#14284C1111yesmaximal, characteristic, direct product factor, Sylow
76C24×C11C2411yescharacteristic
77C2×Q8×C11—28no—
78C2×Q8×C11—44no—
79C2×Q8×C11—44no—
80C2×Q8×C11—48no—
81C2×Q8×C11—48no—
82C22×C4×C11—21no—
83C22×C4×C11—21no—
84C22×C4×C11—21no—
85C22×C4×C11—21no—
86C22×C4×C11—21no—
87C22×C4×C11—22no—
88C22×C4×C11—21no—
89C22×C4×C11—22no—
90C22×C4×C11—22no—
91C22×C4×C11—22no—
92C22×C4×C11—22no—
93C22×C4×C11—22no—
94C22×C4×C11—22no—
95C22×C4×C11—22no—
96C22×C4×C11—22no—
97C22×C4×C11—22no—
98C22×C4×C11—22no—
99C22×C4×C11—21no—
100C22×C4×C11—21no—
101C22×C4×C11—22no—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—22no—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11C22×C412yes—
132C22×C4×C11C22×C414yes—
133C22×C4×C11C22×C414yes—
134C22×C4×C11C22×C412yes—
135C22×C4×C11C22×C412yes—
136C22×C4×C11C2×Q814yes—
137C22×C4×C11C2×Q812yes—
138C22×C4×C11#4114yes—
139C22×C4×C11#4114yes—
140C22×C4×C11#4112yes—
141C11×C4⋊C4—44no—
142C11×C4⋊C4—48no—
143C42×C11—44no—
144C42×C11—44no—
145C42×C11—44no—
146C2×#391C2×C1111yescharacteristic
147#1446C2×C1112yes—
148#1443C2×C1112yes—
149#1442C2×C1112yes—
150#1441C2×C1112yes—
151#1436C2×C1112yes—
152#1434C2×C1111yescharacteristic
153#1434C2×C1112yes—
154C4×#95C2×C1111yescharacteristic
155C23×C11C23×C411yescharacteristic
156C23×C11C22×Q811yescharacteristic
157C23×C11C2×#4112yes—
158C23×C11C2×#4111yescharacteristic
159C23×C11C2×#4112yes—
160C23×C11H(5,𝔽2)11yescharacteristic
161C23×C11H(5,𝔽2)12yes—
162C23×C11H(5,𝔽2)11yescharacteristic
163C23×C11H(5,𝔽2)11yescharacteristic
164C23×C112−1+412yes—
165C23×C112−1+411yescharacteristic
166Q8×C11—416no—
167C2×C4×C11—22no—
168C2×C4×C11—22no—
169C2×C4×C11—22no—
170C2×C4×C11—22no—
171C2×C4×C11—22no—
172C2×C4×C11—24no—
173C2×C4×C11—24no—
174C2×C4×C11—22no—
175C2×C4×C11—22no—
176C2×C4×C11—22no—
177C2×C4×C11—24no—
178C2×C4×C11—22no—
179C2×C4×C11—24no—
180C2×C4×C11—22no—
181C2×C4×C11—24no—
182C2×C4×C11—24no—
183C2×C4×C11—24no—
184C2×C4×C11—22no—
185C2×C4×C11—24no—
186C2×C4×C11—24no—
187C2×C4×C11—24no—
188C2×C4×C11—24no—
189C2×C4×C11—24no—
190C2×C4×C11—24no—
191C2×C4×C11—24no—
192C2×C4×C11—42no—
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—42no—
201C2×C4×C11—42no—
202C2×C4×C11—42no—
203C2×C4×C11—42no—
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—42no—
212C2×C4×C11—42no—
213C2×C4×C11—42no—
214C2×C4×C11—42no—
215C2×C4×C11—42no—
216C2×C4×C11—42no—
217C2×C4×C11—42no—
218C2×C4×C11—42no—
219C2×C4×C11—42no—
220C2×C4×C11—42no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11—42no—
224C2×C4×C11#11714yes—
225C2×C4×C11C4×Q814yes—
226C23×Q8C22×C1111yescharacteristic
227C22×C4⋊C4C22×C1112yes—
228C22×C4⋊C4C22×C1111yescharacteristic
229C22×C42C22×C1111yescharacteristic
230C22×C42C22×C1111yescharacteristic
231C22×C42C22×C1111yescharacteristic
232#391C4×C1118yescomplemented
233C2×#95C22×C1112yes—
234C2×#95C22×C1112yes—
235C2×#95C22×C1112yes—
236C2×#95C22×C1112yes—
237C2×#95C22×C1112yes—
238C2×#95C22×C1112yes—
239C2×#95C22×C1112yes—
240C2×#95C22×C1111yescharacteristic
241C2×#95C22×C1112yes—
242C2×#95C22×C1111yescharacteristic
243C2×#95C22×C1112yes—
244C2×#95C22×C1112yes—
245C2×#95C22×C1112yes—
246C2×#95C22×C1112yes—
247C2×#95C22×C1112yes—
248C22×C11C2×#11711yescharacteristic
249C22×C11C2×C4×Q811yescharacteristic
250C22×C11C4×#4111yescharacteristic
251C22×C11#51811yescharacteristic
252C22×C11#51811yescharacteristic
253C22×C11#51911yescharacteristic
254C22×C11#52011yescharacteristic
255C22×C11#52912yes—
256C22×C11#53312yes—
257C22×C11#53812yes—
258C22×C11#53812yes—
259C22×C11#53811yescharacteristic
260C22×C11#53812yes—
261C22×C11#53911yescharacteristic
262C22×C11#53912yes—
263C22×C11#54112yes—
264C22×C11#54212yes—
265C22×C11#54212yes—
266C22×C11#54212yes—
267C22×C11#54212yes—
268C22×C11#54311yescharacteristic
269C22×C11#54411yescharacteristic
270C22×C11#54412yes—
271C4×C11—24no—
272C4×C11—24no—
273C4×C11—44no—
274C4×C11—42no—
275C4×C11—44no—
276C4×C11—44no—
277C4×C11—44no—
278C4×C11—82no—
279C4×C11—82no—
280C22×Q8—24no—
281C22×Q8—41no—
282C22×Q8—41no—
283C22×Q8—42no—
284C22×Q8C2×C4×C1114yes—
285C23×C4C23×C1112yes—
286C23×C4C23×C1112yes—
287C23×C4C23×C1112yes—
288C23×C4C23×C1112yes—
289C23×C4C23×C1111yescharacteristic
290C23×C4C23×C1112yes—
291C23×C4C23×C1112yes—
292C23×C4C23×C1111yescharacteristic
293C23×C4C23×C1111yescharacteristic
294C2×C4⋊C4—24no—
295C2×C4⋊C4—42no—
296C2×C4⋊C4—42no—
297C2×C4⋊C4—42no—
298C2×C4⋊C4C2×C4×C1114yes—
299C2×C42—22no—
300C2×C42—41no—
301C2×C42—41no—
302C2×C42—41no—
303C2×C42—41no—
304C2×C42—41no—
305C2×C42—41no—
306C2×C42C2×C4×C1114yes—
307C2×C42Q8×C1114yescomplemented
308#95—24no—
309#95—24no—
310#95—24no—
311#95—24no—
312#95—24no—
313#95—42no—
314#95—42no—
315#95—42no—
316#95—42no—
317#95—42no—
318#95—41no—
319#95—41no—
320#95—42no—
321#95C2×C4×C1118yes—
322#95C2×C4×C1118yes—
323C2×C11#229511yescharacteristic
324C2×C11#231211yescharacteristic
325C2×C11#232011yescharacteristic
326C2×C11#232911yescharacteristic
327C2×C11#233111yescharacteristic
328C2×C11#233211yescharacteristic
329C2×C11#233711yescharacteristic
330C2×C11#265012yes—
331C2×C11#265312yes—
332C2×C11#266512yes—
333C2×C11#266612yes—
334C24C24×C1111yescharacteristic
335C2×Q8—28no—
336C2×Q8—44no—
337C2×Q8—44no—
338C2×Q8—48no—
339C2×Q8—48no—
340C22×C4—21no—
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—21no—
344C22×C4—21no—
345C22×C4—22no—
346C22×C4—21no—
347C22×C4—22no—
348C22×C4—22no—
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—22no—
352C22×C4—22no—
353C22×C4—22no—
354C22×C4—22no—
355C22×C4—22no—
356C22×C4—22no—
357C22×C4—21no—
358C22×C4—21no—
359C22×C4—22no—
360C22×C4—22no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4C22×C4×C1112yes—
390C22×C4C22×C4×C1114yes—
391C22×C4C22×C4×C1114yes—
392C22×C4C22×C4×C1112yes—
393C22×C4C22×C4×C1112yes—
394C22×C4C2×Q8×C1114yes—
395C22×C4C2×Q8×C1112yes—
396C22×C4C11×#4114yes—
397C22×C4C11×#4114yes—
398C22×C4C11×#4112yes—
399C4⋊C4—44no—
400C4⋊C4—48no—
401C42—44no—
402C42—44no—
403C42—44no—
404C11#1428411yescharacteristic, direct product factor, Sylow
405C23C23×C4×C1111yescharacteristic
406C23C22×Q8×C1111yescharacteristic
407C23C2×C11×#4112yes—
408C23C2×C11×#4111yescharacteristic
409C23C2×C11×#4112yes—
410C23C11×H(5,𝔽2)11yescharacteristic
411C23C11×H(5,𝔽2)12yes—
412C23C11×H(5,𝔽2)11yescharacteristic
413C23C11×H(5,𝔽2)11yescharacteristic
414C23C11×2−1+412yes—
415C23C11×2−1+411yescharacteristic
416Q8—416no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—24no—
423C2×C4—24no—
424C2×C4—22no—
425C2×C4—22no—
426C2×C4—22no—
427C2×C4—24no—
428C2×C4—22no—
429C2×C4—24no—
430C2×C4—22no—
431C2×C4—24no—
432C2×C4—24no—
433C2×C4—24no—
434C2×C4—22no—
435C2×C4—24no—
436C2×C4—24no—
437C2×C4—24no—
438C2×C4—24no—
439C2×C4—24no—
440C2×C4—24no—
441C2×C4—24no—
442C2×C4—42no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—42no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4—42no—
452C2×C4—42no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—42no—
459C2×C4—42no—
460C2×C4—42no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4C11×#11714yes—
475C2×C4C4×Q8×C1114yes—
476C22C2×C11×#11711yescharacteristic
477C22C2×C4×Q8×C1111yescharacteristic
478C22C4×C11×#4111yescharacteristic
479C22C11×#51811yescharacteristic
480C22C11×#51811yescharacteristic
481C22C11×#51911yescharacteristic
482C22C11×#52011yescharacteristic
483C22C11×#52912yes—
484C22C11×#53312yes—
485C22C11×#53812yes—
486C22C11×#53811yescharacteristic
487C22C11×#53812yes—
488C22C11×#53812yes—
489C22C11×#53911yescharacteristic
490C22C11×#53912yes—
491C22C11×#54112yes—
492C22C11×#54212yes—
493C22C11×#54212yes—
494C22C11×#54212yes—
495C22C11×#54212yes—
496C22C11×#54311yescharacteristic
497C22C11×#54412yes—
498C22C11×#54411yescharacteristic
499C4—24no—
500C4—24no—
501C4—44no—
502C4—44no—
503C4—44no—
504C4—42no—
505C4—44no—
506C4—82no—
507C4—82no—
508C2C11×#229511yescharacteristic
509C2C11×#231211yescharacteristic
510C2C11×#232011yescharacteristic
511C2C11×#232911yescharacteristic
512C2C11×#233111yescharacteristic
513C2C11×#233211yescharacteristic
514C2C11×#233711yescharacteristic
515C2C11×#265012yes—
516C2C11×#265312yes—
517C2C11×#266512yes—
518C2C11×#266612yes—
subgroupG/H
center, socle, prime radicalC24×C11C24
commutatorC23C23×C4×C11
Frattini, cosocleC24C24×C11
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C11 ◁ G

Complements

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

NH ≅ G/Ntype
16. C11×#391C4semidirect
59. C2×C42×C11Q8semidirect
75. #14284C11direct (N × H)
232. #391C4×C11semidirect
307. C2×C42Q8×C11semidirect
404. C11#14284direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#3912
C11×#14462
C11×#14432
C11×#14422
C11×#14412
C11×#14362
C11×#14342
C4×C11×#952
#1428411