Finite Group Databasebeta

← C11×#14599 #14591792

Subgroups — C11×#14599 #14591792

Order 2816.

1246 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#395C211yesmaximal, characteristic
2C11×#1446C212yesmaximal
3C11×#1445C211yesmaximal, characteristic
4C11×#1442C212yesmaximal
5C11×#1436C212yesmaximal
6C11×#1436C211yesmaximal, characteristic
7C11×#1436C212yesmaximal
8C11×C4⋊#95C212yesmaximal
9C11×#1434C212yesmaximal
10C23×Q8×C11C2211yescharacteristic
11C22×C11×C4⋊C4C2212yes—
12C22×C11×C4⋊C4C2212yes—
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C42×C11C2212yes—
15C22×C42×C11C2211yescharacteristic
16C11×#395C418yescomplemented
17C2×C11×#95C2212yes—
18C2×C11×#95C2212yes—
19C2×C11×#95C2211yescharacteristic
20C2×C11×#95C2212yes—
21C2×C11×#95C2212yes—
22C2×C11×#95C2211yescharacteristic
23C2×C11×#95C2212yes—
24C2×C11×#95C2212yes—
25C2×C11×#95C2212yes—
26C2×C11×#95C2212yes—
27C2×C11×#95C2212yes—
28C2×C11×#95C2211yescharacteristic
29C2×C11×#95C2212yes—
30C2×C11×#95C2211yescharacteristic
31C2×C11×#95C2212yes—
32C22×Q8×C11—41no—
33C22×Q8×C11—42no—
34C22×Q8×C11—41no—
35C22×Q8×C11—42no—
36C22×Q8×C11C2×C414yes—
37C23×C4×C11C2312yes—
38C23×C4×C11C2311yescharacteristic
39C23×C4×C11C2311yescharacteristic
40C23×C4×C11C2312yes—
41C23×C4×C11C2311yescharacteristic
42C23×C4×C11C2312yes—
43C23×C4×C11C2312yes—
44C23×C4×C11C2312yes—
45C23×C4×C11C2312yes—
46C2×C11×C4⋊C4—24no—
47C2×C11×C4⋊C4—24no—
48C2×C11×C4⋊C4—42no—
49C2×C11×C4⋊C4—42no—
50C2×C11×C4⋊C4—41no—
51C2×C11×C4⋊C4—41no—
52C2×C11×C4⋊C4—42no—
53C2×C11×C4⋊C4C2×C414yes—
54C2×C11×C4⋊C4C2×C418yes—
55C2×C42×C11—24no—
56C2×C42×C11—24no—
57C2×C42×C11—42no—
58C2×C42×C11—42no—
59C2×C42×C11—41no—
60C11×#95—24no—
61C11×#95—24no—
62C11×#95—41no—
63C11×#95—41no—
64C11×#95—42no—
65C11×#95—42no—
66C11×#95—42no—
67C11×#95—42no—
68C11×#95—42no—
69C11×#95—42no—
70C11×#95—42no—
71C11×#95—41no—
72C11×#95C2×C418yes—
73C11×#95C2×C414yes—
74C11×#95Q818yescomplemented
75#14599C1111yesmaximal, characteristic, direct product factor, Sylow
76C24×C11C2411yescharacteristic
77C2×Q8×C11—48no—
78C2×Q8×C11—44no—
79C2×Q8×C11—48no—
80C2×Q8×C11—44no—
81C2×Q8×C11—44no—
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—22no—
98C22×C4×C11—22no—
99C22×C4×C11—22no—
100C22×C4×C11—22no—
101C22×C4×C11—21no—
102C22×C4×C11—21no—
103C22×C4×C11—21no—
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—21no—
113C22×C4×C11—22no—
114C22×C4×C11—21no—
115C22×C4×C11—22no—
116C22×C4×C11—21no—
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×C11C22×C412yes—
130C22×C4×C11C22×C414yes—
131C22×C4×C11C22×C412yes—
132C22×C4×C11C22×C412yes—
133C22×C4×C11C22×C414yes—
134C22×C4×C11C2×Q814yes—
135C22×C4×C11C2×Q814yes—
136C22×C4×C11C2×Q814yes—
137C22×C4×C11#4114yes—
138C22×C4×C11#4114yes—
139C11×C4⋊C4—48no—
140C11×C4⋊C4—44no—
141C11×C4⋊C4—48no—
142C42×C11—48no—
143C42×C11—44no—
144C2×#395C2×C1111yescharacteristic
145#1446C2×C1112yes—
146#1445C2×C1111yescharacteristic
147#1442C2×C1112yes—
148#1436C2×C1112yes—
149#1436C2×C1112yes—
150#1436C2×C1111yescharacteristic
151C4⋊#95C2×C1112yes—
152#1434C2×C1112yes—
153C23×C11C23×C411yescharacteristic
154C23×C11C22×Q812yes—
155C23×C11C2×#4112yes—
156C23×C11C2×#4112yes—
157C23×C11H(5,𝔽2)11yescharacteristic
158C23×C11H(5,𝔽2)11yescharacteristic
159C23×C11H(5,𝔽2)12yes—
160C23×C11H(5,𝔽2)12yes—
161C23×C112−1+412yes—
162Q8×C11—416no—
163C2×C4×C11—24no—
164C2×C4×C11—24no—
165C2×C4×C11—24no—
166C2×C4×C11—24no—
167C2×C4×C11—24no—
168C2×C4×C11—24no—
169C2×C4×C11—22no—
170C2×C4×C11—22no—
171C2×C4×C11—24no—
172C2×C4×C11—22no—
173C2×C4×C11—24no—
174C2×C4×C11—22no—
175C2×C4×C11—24no—
176C2×C4×C11—24no—
177C2×C4×C11—24no—
178C2×C4×C11—22no—
179C2×C4×C11—24no—
180C2×C4×C11—24no—
181C2×C4×C11—24no—
182C2×C4×C11—24no—
183C2×C4×C11—24no—
184C2×C4×C11—24no—
185C2×C4×C11—24no—
186C2×C4×C11—24no—
187C2×C4×C11—24no—
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—42no—
200C2×C4×C11—41no—
201C2×C4×C11—42no—
202C2×C4×C11—42no—
203C2×C4×C11—42no—
204C2×C4×C11—42no—
205C2×C4×C11—42no—
206C2×C4×C11—41no—
207C2×C4×C11—42no—
208C2×C4×C11—41no—
209C2×C4×C11—42no—
210C2×C4×C11—42no—
211C2×C4×C11—41no—
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×C11C4×Q818yes—
220C23×Q8C22×C1111yescharacteristic
221C22×C4⋊C4C22×C1112yes—
222C22×C4⋊C4C22×C1112yes—
223C22×C4⋊C4C22×C1111yescharacteristic
224C22×C42C22×C1112yes—
225C22×C42C22×C1111yescharacteristic
226#395C4×C1118yescomplemented
227C2×#95C22×C1112yes—
228C2×#95C22×C1112yes—
229C2×#95C22×C1111yescharacteristic
230C2×#95C22×C1112yes—
231C2×#95C22×C1112yes—
232C2×#95C22×C1111yescharacteristic
233C2×#95C22×C1112yes—
234C2×#95C22×C1112yes—
235C2×#95C22×C1112yes—
236C2×#95C22×C1112yes—
237C2×#95C22×C1112yes—
238C2×#95C22×C1111yescharacteristic
239C2×#95C22×C1112yes—
240C2×#95C22×C1111yescharacteristic
241C2×#95C22×C1112yes—
242C22×C11C2×C4×Q812yes—
243C22×C11C4×#4111yescharacteristic
244C22×C11#51812yes—
245C22×C11#51811yescharacteristic
246C22×C11#51911yescharacteristic
247C22×C11#53912yes—
248C22×C11#54212yes—
249C22×C11#54212yes—
250C22×C11#54212yes—
251C22×C11#54412yes—
252C22×C11#54412yes—
253C22×C11#55112yes—
254C22×C11#55112yes—
255C22×C11#55412yes—
256C22×C11#55412yes—
257C22×C11#55412yes—
258C22×C11#55511yescharacteristic
259C22×C11Q8211yescharacteristic
260C22×C11#56012yes—
261C22×C11#56011yescharacteristic
262C22×C11H(3,𝔽4)11yescharacteristic
263C4×C11—28no—
264C4×C11—42no—
265C4×C11—42no—
266C4×C11—44no—
267C4×C11—42no—
268C4×C11—44no—
269C4×C11—44no—
270C4×C11—44no—
271C4×C11—82no—
272C22×Q8—41no—
273C22×Q8—42no—
274C22×Q8—41no—
275C22×Q8—42no—
276C22×Q8C2×C4×C1114yes—
277C23×C4C23×C1112yes—
278C23×C4C23×C1111yescharacteristic
279C23×C4C23×C1112yes—
280C23×C4C23×C1111yescharacteristic
281C23×C4C23×C1111yescharacteristic
282C23×C4C23×C1112yes—
283C23×C4C23×C1112yes—
284C23×C4C23×C1112yes—
285C23×C4C23×C1112yes—
286C2×C4⋊C4—24no—
287C2×C4⋊C4—24no—
288C2×C4⋊C4—42no—
289C2×C4⋊C4—42no—
290C2×C4⋊C4—41no—
291C2×C4⋊C4—41no—
292C2×C4⋊C4—42no—
293C2×C4⋊C4C2×C4×C1114yes—
294C2×C4⋊C4C2×C4×C1118yes—
295C2×C42—24no—
296C2×C42—24no—
297C2×C42—42no—
298C2×C42—42no—
299C2×C42—41no—
300#95—24no—
301#95—24no—
302#95—41no—
303#95—41no—
304#95—42no—
305#95—42no—
306#95—42no—
307#95—42no—
308#95—42no—
309#95—42no—
310#95—42no—
311#95—41no—
312#95C2×C4×C1118yes—
313#95C2×C4×C1114yes—
314#95Q8×C1118yescomplemented
315C2×C11#233112yes—
316C2×C11#233211yescharacteristic
317C2×C11#236812yes—
318C2×C11#236911yescharacteristic
319C2×C11#237511yescharacteristic
320C2×C11#273712yes—
321C2×C11#274212yes—
322C2×C11#276312yes—
323C2×C11#279212yes—
324C24C24×C1111yescharacteristic
325C2×Q8—48no—
326C2×Q8—44no—
327C2×Q8—48no—
328C2×Q8—44no—
329C2×Q8—44no—
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—22no—
342C22×C4—22no—
343C22×C4—22no—
344C22×C4—22no—
345C22×C4—22no—
346C22×C4—22no—
347C22×C4—22no—
348C22×C4—22no—
349C22×C4—21no—
350C22×C4—21no—
351C22×C4—21no—
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—21no—
361C22×C4—22no—
362C22×C4—21no—
363C22×C4—22no—
364C22×C4—21no—
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×C4C22×C4×C1112yes—
378C22×C4C22×C4×C1114yes—
379C22×C4C22×C4×C1112yes—
380C22×C4C22×C4×C1112yes—
381C22×C4C22×C4×C1114yes—
382C22×C4C2×Q8×C1114yes—
383C22×C4C2×Q8×C1114yes—
384C22×C4C2×Q8×C1114yes—
385C22×C4C11×#4114yes—
386C22×C4C11×#4114yes—
387C4⋊C4—48no—
388C4⋊C4—44no—
389C4⋊C4—48no—
390C42—48no—
391C42—44no—
392C11#1459911yescharacteristic, direct product factor, Sylow
393C23C23×C4×C1111yescharacteristic
394C23C22×Q8×C1112yes—
395C23C2×C11×#4112yes—
396C23C2×C11×#4112yes—
397C23C11×H(5,𝔽2)11yescharacteristic
398C23C11×H(5,𝔽2)11yescharacteristic
399C23C11×H(5,𝔽2)12yes—
400C23C11×H(5,𝔽2)12yes—
401C23C11×2−1+412yes—
402Q8—416no—
403C2×C4—24no—
404C2×C4—24no—
405C2×C4—24no—
406C2×C4—24no—
407C2×C4—24no—
408C2×C4—24no—
409C2×C4—22no—
410C2×C4—22no—
411C2×C4—24no—
412C2×C4—22no—
413C2×C4—24no—
414C2×C4—22no—
415C2×C4—24no—
416C2×C4—24no—
417C2×C4—24no—
418C2×C4—22no—
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—42no—
430C2×C4—42no—
431C2×C4—42no—
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—41no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—41no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—41no—
450C2×C4—42no—
451C2×C4—41no—
452C2×C4—42no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—42no—
459C2×C4C4×Q8×C1118yes—
460C22C2×C4×Q8×C1112yes—
461C22C4×C11×#4111yescharacteristic
462C22C11×#51812yes—
463C22C11×#51811yescharacteristic
464C22C11×#51911yescharacteristic
465C22C11×#53912yes—
466C22C11×#54212yes—
467C22C11×#54212yes—
468C22C11×#54212yes—
469C22C11×#54412yes—
470C22C11×#54412yes—
471C22C11×#55112yes—
472C22C11×#55112yes—
473C22C11×#55412yes—
474C22C11×#55412yes—
475C22C11×#55412yes—
476C22C11×#55511yescharacteristic
477C22Q82×C1111yescharacteristic
478C22C11×#56012yes—
479C22C11×#56011yescharacteristic
480C22C11×H(3,𝔽4)11yescharacteristic
481C4—28no—
482C4—44no—
483C4—44no—
484C4—44no—
485C4—42no—
486C4—44no—
487C4—42no—
488C4—42no—
489C4—82no—
490C2C11×#233112yes—
491C2C11×#233211yescharacteristic
492C2C11×#236812yes—
493C2C11×#236911yescharacteristic
494C2C11×#237511yescharacteristic
495C2C11×#273712yes—
496C2C11×#274212yes—
497C2C11×#276312yes—
498C2C11×#279212yes—
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×#395C4semidirect
74. C11×#95Q8semidirect
75. #14599C11direct (N × H)
226. #395C4×C11semidirect
314. #95Q8×C11semidirect
392. C11#14599direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#3952
C11×#14462
C11×#14452
C11×#14422
C11×#14362
C11×C4⋊#952
C11×#14342
#1459911