Finite Group Databasebeta

← C11×#14639 #14591832

Subgroups — C11×#14639 #14591832

Order 2816.

1074 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×#400C211yesmaximal, characteristic
2C11×#1444C212yesmaximal
3C11×#1444C212yesmaximal
4C11×#1443C212yesmaximal
5C11×#1442C212yesmaximal
6C11×#1441C211yesmaximal, characteristic
7C11×#1441C212yesmaximal
8C11×C4⋊#95C211yesmaximal, characteristic
9C11×#1434C212yesmaximal
10C22×C11×C4⋊C4C2211yescharacteristic
11C22×C11×C4⋊C4C2211yescharacteristic
12C22×C11×C4⋊C4C2212yes—
13C22×C11×C4⋊C4C2212yes—
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C11×C4⋊C4C2211yescharacteristic
16C22×C42×C11C2211yescharacteristic
17C11×#400C418yescomplemented
18C2×C11×#95C2212yes—
19C2×C11×#95C2212yes—
20C2×C11×#95C2212yes—
21C2×C11×#95C2212yes—
22C2×C11×#95C2212yes—
23C2×C11×#95C2212yes—
24C2×C11×#95C2212yes—
25C2×C11×#95C2212yes—
26C2×C11×#95C2211yescharacteristic
27C2×C11×#95C2212yes—
28C2×C11×#95C2212yes—
29C2×C11×#95C2212yes—
30C2×C11×#95C2211yescharacteristic
31C2×C11×#95C2212yes—
32C23×C4×C11C2312yes—
33C23×C4×C11C2312yes—
34C23×C4×C11C2312yes—
35C23×C4×C11C2312yes—
36C23×C4×C11C2311yescharacteristic
37C23×C4×C11C2312yes—
38C23×C4×C11C2311yescharacteristic
39C23×C4×C11C2312yes—
40C23×C4×C11C2311yescharacteristic
41C2×C11×C4⋊C4—22no—
42C2×C11×C4⋊C4—41no—
43C2×C11×C4⋊C4—41no—
44C2×C11×C4⋊C4—41no—
45C2×C11×C4⋊C4—41no—
46C2×C11×C4⋊C4—41no—
47C2×C11×C4⋊C4—41no—
48C2×C11×C4⋊C4—42no—
49C2×C11×C4⋊C4—42no—
50C2×C11×C4⋊C4—42no—
51C2×C11×C4⋊C4—42no—
52C2×C11×C4⋊C4—42no—
53C2×C11×C4⋊C4—42no—
54C2×C11×C4⋊C4—41no—
55C2×C11×C4⋊C4—42no—
56C2×C11×C4⋊C4C2×C414yes—
57C2×C11×C4⋊C4C2×C414yes—
58C2×C42×C11—41no—
59C2×C42×C11—41no—
60C2×C42×C11Q814yes—
61C11×#95—24no—
62C11×#95—42no—
63C11×#95—42no—
64C11×#95—42no—
65C11×#95—42no—
66C11×#95—42no—
67C11×#95—42no—
68C11×#95—42no—
69C11×#95—41no—
70C11×#95—42no—
71C11×#95—42no—
72C11×#95C2×C414yes—
73C11×#95C2×C418yes—
74C11×#95C2×C418yes—
75#14639C1111yesmaximal, characteristic, direct product factor, Sylow
76C24×C11C2411yescharacteristic
77C22×C4×C11—21no—
78C22×C4×C11—21no—
79C22×C4×C11—21no—
80C22×C4×C11—21no—
81C22×C4×C11—22no—
82C22×C4×C11—22no—
83C22×C4×C11—22no—
84C22×C4×C11—22no—
85C22×C4×C11—22no—
86C22×C4×C11—21no—
87C22×C4×C11—22no—
88C22×C4×C11—22no—
89C22×C4×C11—22no—
90C22×C4×C11—22no—
91C22×C4×C11—22no—
92C22×C4×C11—22no—
93C22×C4×C11—22no—
94C22×C4×C11—21no—
95C22×C4×C11—21no—
96C22×C4×C11—21no—
97C22×C4×C11—22no—
98C22×C4×C11—22no—
99C22×C4×C11—22no—
100C22×C4×C11—22no—
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×C11C22×C414yes—
129C22×C4×C11C22×C412yes—
130C22×C4×C11C22×C414yes—
131C22×C4×C11C22×C412yes—
132C22×C4×C11C22×C412yes—
133C22×C4×C11C2×Q814yes—
134C22×C4×C11C2×Q812yes—
135C22×C4×C11#4112yes—
136C11×C4⋊C4—44no—
137C11×C4⋊C4—44no—
138C11×C4⋊C4—44no—
139C11×C4⋊C4—44no—
140C11×C4⋊C4—48no—
141C11×C4⋊C4—48no—
142C42×C11—44no—
143C2×#400C2×C1111yescharacteristic
144#1444C2×C1112yes—
145#1444C2×C1112yes—
146#1443C2×C1112yes—
147#1442C2×C1112yes—
148#1441C2×C1111yescharacteristic
149#1441C2×C1112yes—
150C4⋊#95C2×C1111yescharacteristic
151#1434C2×C1112yes—
152C23×C11C23×C411yescharacteristic
153C23×C11C22×Q811yescharacteristic
154C23×C11C2×#4111yescharacteristic
155C23×C11H(5,𝔽2)11yescharacteristic
156C23×C11H(5,𝔽2)11yescharacteristic
157C23×C11H(5,𝔽2)11yescharacteristic
158C23×C11H(5,𝔽2)12yes—
159C23×C11H(5,𝔽2)12yes—
160C23×C112−1+411yescharacteristic
161C23×C112−1+412yes—
162C23×C112−1+412yes—
163C2×C4×C11—22no—
164C2×C4×C11—22no—
165C2×C4×C11—22no—
166C2×C4×C11—22no—
167C2×C4×C11—22no—
168C2×C4×C11—22no—
169C2×C4×C11—22no—
170C2×C4×C11—22no—
171C2×C4×C11—24no—
172C2×C4×C11—24no—
173C2×C4×C11—24no—
174C2×C4×C11—24no—
175C2×C4×C11—24no—
176C2×C4×C11—24no—
177C2×C4×C11—24no—
178C2×C4×C11—24no—
179C2×C4×C11—24no—
180C2×C4×C11—24no—
181C2×C4×C11—24no—
182C2×C4×C11—41no—
183C2×C4×C11—42no—
184C2×C4×C11—42no—
185C2×C4×C11—41no—
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—42no—
193C2×C4×C11—42no—
194C2×C4×C11—41no—
195C2×C4×C11—41no—
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×C11C4×Q814yes—
222C22×C4⋊C4C22×C1111yescharacteristic
223C22×C4⋊C4C22×C1111yescharacteristic
224C22×C4⋊C4C22×C1112yes—
225C22×C4⋊C4C22×C1112yes—
226C22×C4⋊C4C22×C1111yescharacteristic
227C22×C4⋊C4C22×C1111yescharacteristic
228C22×C42C22×C1111yescharacteristic
229#400C4×C1118yescomplemented
230C2×#95C22×C1112yes—
231C2×#95C22×C1112yes—
232C2×#95C22×C1112yes—
233C2×#95C22×C1112yes—
234C2×#95C22×C1112yes—
235C2×#95C22×C1112yes—
236C2×#95C22×C1112yes—
237C2×#95C22×C1112yes—
238C2×#95C22×C1111yescharacteristic
239C2×#95C22×C1112yes—
240C2×#95C22×C1112yes—
241C2×#95C22×C1112yes—
242C2×#95C22×C1111yescharacteristic
243C2×#95C22×C1112yes—
244C22×C11C2×C4×Q811yescharacteristic
245C22×C11#51811yescharacteristic
246C22×C11#52011yescharacteristic
247C22×C11#52012yes—
248C22×C11#52012yes—
249C22×C11#53811yescharacteristic
250C22×C11#53911yescharacteristic
251C22×C11#54012yes—
252C22×C11#54112yes—
253C22×C11#54311yescharacteristic
254C22×C11#54411yescharacteristic
255C22×C11#54412yes—
256C22×C11#54412yes—
257C22×C11#56012yes—
258C22×C11#56011yescharacteristic
259C22×C11H(3,𝔽4)11yescharacteristic
260C22×C11#56212yes—
261C22×C11#56212yes—
262C22×C11#56312yes—
263C22×C11#56311yescharacteristic
264C22×C11#56311yescharacteristic
265C22×C11#56312yes—
266C22×C11#56312yes—
267C4×C11—24no—
268C4×C11—44no—
269C4×C11—42no—
270C4×C11—42no—
271C4×C11—44no—
272C4×C11—44no—
273C4×C11—82no—
274C4×C11—82no—
275C4×C11—82no—
276C23×C4C23×C1112yes—
277C23×C4C23×C1112yes—
278C23×C4C23×C1112yes—
279C23×C4C23×C1111yescharacteristic
280C23×C4C23×C1111yescharacteristic
281C23×C4C23×C1112yes—
282C23×C4C23×C1112yes—
283C23×C4C23×C1112yes—
284C23×C4C23×C1111yescharacteristic
285C2×C4⋊C4—22no—
286C2×C4⋊C4—41no—
287C2×C4⋊C4—41no—
288C2×C4⋊C4—41no—
289C2×C4⋊C4—41no—
290C2×C4⋊C4—41no—
291C2×C4⋊C4—41no—
292C2×C4⋊C4—42no—
293C2×C4⋊C4—42no—
294C2×C4⋊C4—42no—
295C2×C4⋊C4—42no—
296C2×C4⋊C4—42no—
297C2×C4⋊C4—42no—
298C2×C4⋊C4—41no—
299C2×C4⋊C4—42no—
300C2×C4⋊C4C2×C4×C1114yes—
301C2×C4⋊C4C2×C4×C1114yes—
302C2×C42—41no—
303C2×C42—41no—
304C2×C42Q8×C1114yes—
305#95—24no—
306#95—42no—
307#95—42no—
308#95—42no—
309#95—42no—
310#95—42no—
311#95—42no—
312#95—42no—
313#95—41no—
314#95—42no—
315#95—42no—
316#95C2×C4×C1114yes—
317#95C2×C4×C1118yes—
318#95C2×C4×C1118yes—
319C2×C11#232911yescharacteristic
320C2×C11#233012yes—
321C2×C11#237611yescharacteristic
322C2×C11#237911yescharacteristic
323C2×C11#238312yes—
324C2×C11#282811yescharacteristic
325C2×C11#283311yescharacteristic
326C2×C11#283612yes—
327C2×C11#284112yes—
328C2×C11#284311yescharacteristic
329C2×C11#284411yescharacteristic
330C24C24×C1111yescharacteristic
331C22×C4—21no—
332C22×C4—21no—
333C22×C4—21no—
334C22×C4—21no—
335C22×C4—22no—
336C22×C4—22no—
337C22×C4—22no—
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—21no—
342C22×C4—22no—
343C22×C4—22no—
344C22×C4—22no—
345C22×C4—22no—
346C22×C4—22no—
347C22×C4—22no—
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—21no—
351C22×C4—22no—
352C22×C4—22no—
353C22×C4—22no—
354C22×C4—22no—
355C22×C4—22no—
356C22×C4—22no—
357C22×C4—22no—
358C22×C4—22no—
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×C4C22×C4×C1114yes—
383C22×C4C22×C4×C1114yes—
384C22×C4C22×C4×C1112yes—
385C22×C4C22×C4×C1112yes—
386C22×C4C22×C4×C1112yes—
387C22×C4C2×Q8×C1114yes—
388C22×C4C2×Q8×C1112yes—
389C22×C4C11×#4112yes—
390C4⋊C4—44no—
391C4⋊C4—44no—
392C4⋊C4—44no—
393C4⋊C4—48no—
394C4⋊C4—44no—
395C4⋊C4—48no—
396C42—44no—
397C11#1463911yescharacteristic, direct product factor, Sylow
398C23C23×C4×C1111yescharacteristic
399C23C22×Q8×C1111yescharacteristic
400C23C2×C11×#4111yescharacteristic
401C23C11×H(5,𝔽2)11yescharacteristic
402C23C11×H(5,𝔽2)11yescharacteristic
403C23C11×H(5,𝔽2)11yescharacteristic
404C23C11×H(5,𝔽2)12yes—
405C23C11×H(5,𝔽2)12yes—
406C23C11×2−1+411yescharacteristic
407C23C11×2−1+412yes—
408C23C11×2−1+412yes—
409C2×C4—22no—
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—22no—
415C2×C4—22no—
416C2×C4—24no—
417C2×C4—22no—
418C2×C4—24no—
419C2×C4—24no—
420C2×C4—24no—
421C2×C4—24no—
422C2×C4—24no—
423C2×C4—24no—
424C2×C4—24no—
425C2×C4—24no—
426C2×C4—24no—
427C2×C4—24no—
428C2×C4—42no—
429C2×C4—41no—
430C2×C4—42no—
431C2×C4—41no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—42no—
444C2×C4—41no—
445C2×C4—41no—
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×C4C4×Q8×C1114yes—
468C22C2×C4×Q8×C1111yescharacteristic
469C22C11×#51811yescharacteristic
470C22C11×#52012yes—
471C22C11×#52011yescharacteristic
472C22C11×#52012yes—
473C22C11×#53811yescharacteristic
474C22C11×#53911yescharacteristic
475C22C11×#54012yes—
476C22C11×#54112yes—
477C22C11×#54311yescharacteristic
478C22C11×#54411yescharacteristic
479C22C11×#54412yes—
480C22C11×#54412yes—
481C22C11×#56012yes—
482C22C11×#56011yescharacteristic
483C22C11×H(3,𝔽4)11yescharacteristic
484C22C11×#56212yes—
485C22C11×#56212yes—
486C22C11×#56311yescharacteristic
487C22C11×#56312yes—
488C22C11×#56312yes—
489C22C11×#56312yes—
490C22C11×#56311yescharacteristic
491C4—24no—
492C4—44no—
493C4—44no—
494C4—44no—
495C4—42no—
496C4—42no—
497C4—82no—
498C4—82no—
499C4—82no—
500C2C11×#232911yescharacteristic
501C2C11×#233012yes—
502C2C11×#237611yescharacteristic
503C2C11×#237911yescharacteristic
504C2C11×#238312yes—
505C2C11×#282811yescharacteristic
506C2C11×#283311yescharacteristic
507C2C11×#283612yes—
508C2C11×#284112yes—
509C2C11×#284311yescharacteristic
510C2C11×#284411yescharacteristic
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
17. C11×#400C4semidirect
75. #14639C11direct (N × H)
229. #400C4×C11semidirect
397. C11#14639direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4002
C11×#14442
C11×#14432
C11×#14422
C11×#14412
C11×C4⋊#952
C11×#14342
#1463911