Finite Group Databasebeta

← C11×#14600 #14591793

Subgroups — C11×#14600 #14591793

Order 2816.

1182 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#398C211yesmaximal, characteristic
2C11×#1445C211yesmaximal, characteristic
3C11×#1441C212yesmaximal
4C11×#1441C212yesmaximal
5C11×#1436C212yesmaximal
6C11×#1436C212yesmaximal
7C11×#1436C211yesmaximal, characteristic
8C11×#1436C212yesmaximal
9C11×C4⋊#95C212yesmaximal
10C22×C11×C4⋊C4C2212yes—
11C22×C11×C4⋊C4C2212yes—
12C22×C11×C4⋊C4C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C11×C4⋊C4C2212yes—
15C22×C42×C11C2212yes—
16C22×C42×C11C2211yescharacteristic
17C11×#398C418yescomplemented
18C2×C11×#95C2212yes—
19C2×C11×#95C2212yes—
20C2×C11×#95C2212yes—
21C2×C11×#95C2212yes—
22C2×C11×#95C2211yescharacteristic
23C2×C11×#95C2212yes—
24C2×C11×#95C2211yescharacteristic
25C2×C11×#95C2212yes—
26C2×C11×#95C2212yes—
27C2×C11×#95C2212yes—
28C2×C11×#95C2212yes—
29C2×C11×#95C2211yescharacteristic
30C2×C11×#95C2212yes—
31C2×C11×#95C2211yescharacteristic
32C23×C4×C11C2312yes—
33C23×C4×C11C2311yescharacteristic
34C23×C4×C11C2311yescharacteristic
35C23×C4×C11C2311yescharacteristic
36C23×C4×C11C2312yes—
37C23×C4×C11C2312yes—
38C23×C4×C11C2312yes—
39C23×C4×C11C2312yes—
40C23×C4×C11C2312yes—
41C2×C11×C4⋊C4—24no—
42C2×C11×C4⋊C4—42no—
43C2×C11×C4⋊C4—42no—
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⋊C4C2×C414yes—
53C2×C11×C4⋊C4C2×C414yes—
54C2×C11×C4⋊C4C2×C418yes—
55C2×C11×C4⋊C4Q818yes—
56C2×C42×C11—24no—
57C2×C42×C11—42no—
58C2×C42×C11—42no—
59C2×C42×C11—42no—
60C2×C42×C11—41no—
61C11×#95—24no—
62C11×#95—24no—
63C11×#95—24no—
64C11×#95—24no—
65C11×#95—41no—
66C11×#95—42no—
67C11×#95—42no—
68C11×#95—42no—
69C11×#95—42no—
70C11×#95—41no—
71C11×#95—42no—
72C11×#95—41no—
73C11×#95C2×C418yes—
74C11×#95C2×C414yes—
75#14600C1111yesmaximal, characteristic, direct product factor, Sylow
76C24×C11C2411yescharacteristic
77C22×C4×C11—22no—
78C22×C4×C11—22no—
79C22×C4×C11—22no—
80C22×C4×C11—22no—
81C22×C4×C11—22no—
82C22×C4×C11—22no—
83C22×C4×C11—22no—
84C22×C4×C11—22no—
85C22×C4×C11—22no—
86C22×C4×C11—22no—
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—22no—
95C22×C4×C11—22no—
96C22×C4×C11—22no—
97C22×C4×C11—21no—
98C22×C4×C11—22no—
99C22×C4×C11—21no—
100C22×C4×C11—22no—
101C22×C4×C11—21no—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—21no—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—21no—
111C22×C4×C11—21no—
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×C11C22×C412yes—
125C22×C4×C11C22×C414yes—
126C22×C4×C11C22×C412yes—
127C22×C4×C11C22×C412yes—
128C22×C4×C11C22×C414yes—
129C22×C4×C11C2×Q814yes—
130C22×C4×C11C2×Q814yes—
131C22×C4×C11C2×Q814yes—
132C22×C4×C11#4114yes—
133C22×C4×C11#4114yes—
134C11×C4⋊C4—48no—
135C11×C4⋊C4—44no—
136C11×C4⋊C4—44no—
137C11×C4⋊C4—48no—
138C11×C4⋊C4—48no—
139C42×C11—48no—
140C42×C11—44no—
141C2×#398C2×C1111yescharacteristic
142#1445C2×C1111yescharacteristic
143#1441C2×C1112yes—
144#1441C2×C1112yes—
145#1436C2×C1112yes—
146#1436C2×C1111yescharacteristic
147#1436C2×C1112yes—
148#1436C2×C1112yes—
149C4⋊#95C2×C1112yes—
150C23×C11C23×C411yescharacteristic
151C23×C11C22×Q812yes—
152C23×C11C2×#4112yes—
153C23×C11C2×#4112yes—
154C23×C11H(5,𝔽2)12yes—
155C23×C11H(5,𝔽2)11yescharacteristic
156C23×C11H(5,𝔽2)11yescharacteristic
157C23×C11H(5,𝔽2)12yes—
158C23×C112−1+412yes—
159C2×C4×C11—24no—
160C2×C4×C11—24no—
161C2×C4×C11—24no—
162C2×C4×C11—24no—
163C2×C4×C11—24no—
164C2×C4×C11—24no—
165C2×C4×C11—22no—
166C2×C4×C11—24no—
167C2×C4×C11—22no—
168C2×C4×C11—22no—
169C2×C4×C11—24no—
170C2×C4×C11—22no—
171C2×C4×C11—24no—
172C2×C4×C11—22no—
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—24no—
183C2×C4×C11—24no—
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—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—41no—
200C2×C4×C11—42no—
201C2×C4×C11—41no—
202C2×C4×C11—42no—
203C2×C4×C11—42no—
204C2×C4×C11—42no—
205C2×C4×C11—42no—
206C2×C4×C11—41no—
207C2×C4×C11—41no—
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×C11C4×Q818yes—
216C22×C4⋊C4C22×C1112yes—
217C22×C4⋊C4C22×C1112yes—
218C22×C4⋊C4C22×C1111yescharacteristic
219C22×C4⋊C4C22×C1111yescharacteristic
220C22×C4⋊C4C22×C1112yes—
221C22×C42C22×C1112yes—
222C22×C42C22×C1111yescharacteristic
223#398C4×C1118yescomplemented
224C2×#95C22×C1112yes—
225C2×#95C22×C1112yes—
226C2×#95C22×C1112yes—
227C2×#95C22×C1112yes—
228C2×#95C22×C1111yescharacteristic
229C2×#95C22×C1112yes—
230C2×#95C22×C1111yescharacteristic
231C2×#95C22×C1112yes—
232C2×#95C22×C1112yes—
233C2×#95C22×C1112yes—
234C2×#95C22×C1112yes—
235C2×#95C22×C1111yescharacteristic
236C2×#95C22×C1112yes—
237C2×#95C22×C1111yescharacteristic
238C22×C11C2×C4×Q812yes—
239C22×C11C4×#4111yescharacteristic
240C22×C11#51811yescharacteristic
241C22×C11#51811yescharacteristic
242C22×C11#52012yes—
243C22×C11#53812yes—
244C22×C11#53812yes—
245C22×C11#53912yes—
246C22×C11#54012yes—
247C22×C11#54312yes—
248C22×C11#54412yes—
249C22×C11#55212yes—
250C22×C11#55312yes—
251C22×C11#55412yes—
252C22×C11#55412yes—
253C22×C11#55511yescharacteristic
254C22×C11#55712yes—
255C22×C11Q8211yescharacteristic
256C22×C11#56011yescharacteristic
257C22×C11#56212yes—
258C22×C11#56311yescharacteristic
259C4×C11—28no—
260C4×C11—42no—
261C4×C11—44no—
262C4×C11—42no—
263C4×C11—42no—
264C4×C11—44no—
265C4×C11—44no—
266C4×C11—44no—
267C4×C11—82no—
268C23×C4C23×C1112yes—
269C23×C4C23×C1111yescharacteristic
270C23×C4C23×C1112yes—
271C23×C4C23×C1111yescharacteristic
272C23×C4C23×C1111yescharacteristic
273C23×C4C23×C1112yes—
274C23×C4C23×C1112yes—
275C23×C4C23×C1112yes—
276C23×C4C23×C1112yes—
277C2×C4⋊C4—24no—
278C2×C4⋊C4—42no—
279C2×C4⋊C4—42no—
280C2×C4⋊C4—41no—
281C2×C4⋊C4—41no—
282C2×C4⋊C4—41no—
283C2×C4⋊C4—41no—
284C2×C4⋊C4—42no—
285C2×C4⋊C4—42no—
286C2×C4⋊C4—42no—
287C2×C4⋊C4—42no—
288C2×C4⋊C4C2×C4×C1114yes—
289C2×C4⋊C4C2×C4×C1114yes—
290C2×C4⋊C4C2×C4×C1118yes—
291C2×C4⋊C4Q8×C1118yes—
292C2×C42—24no—
293C2×C42—42no—
294C2×C42—42no—
295C2×C42—42no—
296C2×C42—41no—
297#95—24no—
298#95—24no—
299#95—24no—
300#95—24no—
301#95—41no—
302#95—42no—
303#95—42no—
304#95—42no—
305#95—42no—
306#95—41no—
307#95—42no—
308#95—41no—
309#95C2×C4×C1118yes—
310#95C2×C4×C1114yes—
311C2×C11#232912yes—
312C2×C11#233311yescharacteristic
313C2×C11#236911yescharacteristic
314C2×C11#237012yes—
315C2×C11#237611yescharacteristic
316C2×C11#278012yes—
317C2×C11#278112yes—
318C2×C11#279112yes—
319C2×C11#280612yes—
320C24C24×C1111yescharacteristic
321C22×C4—22no—
322C22×C4—22no—
323C22×C4—22no—
324C22×C4—22no—
325C22×C4—22no—
326C22×C4—22no—
327C22×C4—22no—
328C22×C4—22no—
329C22×C4—22no—
330C22×C4—22no—
331C22×C4—22no—
332C22×C4—22no—
333C22×C4—22no—
334C22×C4—22no—
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—21no—
344C22×C4—22no—
345C22×C4—21no—
346C22×C4—22no—
347C22×C4—22no—
348C22×C4—22no—
349C22×C4—21no—
350C22×C4—22no—
351C22×C4—22no—
352C22×C4—22no—
353C22×C4—22no—
354C22×C4—21no—
355C22×C4—21no—
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×C4C22×C4×C1112yes—
369C22×C4C22×C4×C1114yes—
370C22×C4C22×C4×C1112yes—
371C22×C4C22×C4×C1112yes—
372C22×C4C22×C4×C1114yes—
373C22×C4C2×Q8×C1114yes—
374C22×C4C2×Q8×C1114yes—
375C22×C4C2×Q8×C1114yes—
376C22×C4C11×#4114yes—
377C22×C4C11×#4114yes—
378C4⋊C4—48no—
379C4⋊C4—44no—
380C4⋊C4—44no—
381C4⋊C4—48no—
382C4⋊C4—48no—
383C42—48no—
384C42—44no—
385C11#1460011yescharacteristic, direct product factor, Sylow
386C23C23×C4×C1111yescharacteristic
387C23C22×Q8×C1112yes—
388C23C2×C11×#4112yes—
389C23C2×C11×#4112yes—
390C23C11×H(5,𝔽2)12yes—
391C23C11×H(5,𝔽2)11yescharacteristic
392C23C11×H(5,𝔽2)11yescharacteristic
393C23C11×H(5,𝔽2)12yes—
394C23C11×2−1+412yes—
395C2×C4—24no—
396C2×C4—24no—
397C2×C4—24no—
398C2×C4—24no—
399C2×C4—24no—
400C2×C4—24no—
401C2×C4—22no—
402C2×C4—24no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—24no—
406C2×C4—22no—
407C2×C4—24no—
408C2×C4—22no—
409C2×C4—24no—
410C2×C4—24no—
411C2×C4—24no—
412C2×C4—24no—
413C2×C4—24no—
414C2×C4—24no—
415C2×C4—24no—
416C2×C4—24no—
417C2×C4—24no—
418C2×C4—24no—
419C2×C4—24no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—41no—
437C2×C4—42no—
438C2×C4—41no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—42no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4C4×Q8×C1118yes—
452C22C2×C4×Q8×C1112yes—
453C22C4×C11×#4111yescharacteristic
454C22C11×#51811yescharacteristic
455C22C11×#51811yescharacteristic
456C22C11×#52012yes—
457C22C11×#53812yes—
458C22C11×#53812yes—
459C22C11×#53912yes—
460C22C11×#54012yes—
461C22C11×#54312yes—
462C22C11×#54412yes—
463C22C11×#55212yes—
464C22C11×#55312yes—
465C22C11×#55412yes—
466C22C11×#55412yes—
467C22C11×#55511yescharacteristic
468C22C11×#55712yes—
469C22Q82×C1111yescharacteristic
470C22C11×#56011yescharacteristic
471C22C11×#56212yes—
472C22C11×#56311yescharacteristic
473C4—28no—
474C4—44no—
475C4—44no—
476C4—44no—
477C4—42no—
478C4—44no—
479C4—42no—
480C4—42no—
481C4—82no—
482C2C11×#232912yes—
483C2C11×#233311yescharacteristic
484C2C11×#236911yescharacteristic
485C2C11×#237012yes—
486C2C11×#237611yescharacteristic
487C2C11×#278012yes—
488C2C11×#278112yes—
489C2C11×#279112yes—
490C2C11×#280612yes—
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×#398C4semidirect
75. #14600C11direct (N × H)
223. #398C4×C11semidirect
385. C11#14600direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#3982
C11×#14452
C11×#14412
C11×#14362
C11×C4⋊#952
#1460011