Finite Group Databasebeta

← C11×#14048 #14591241

Subgroups — C11×#14048 #14591241

Order 2816.

1414 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#389C211yesmaximal, characteristic
2C2×C11×#384C211yesmaximal, characteristic
3C2×C4×C11×C4⋊C4C211yesmaximal, characteristic
4C11×#1441C214yesmaximal
5C11×#1436C214yesmaximal
6C11×C4⋊#95C211yesmaximal, characteristic
7C11×C4⋊#95C211yesmaximal, characteristic
8C11×C4⋊#95C211yesmaximal, characteristic
9C4×C11×#95C211yesmaximal, characteristic
10C22×C11×C4⋊C4C2211yescharacteristic
11C22×C11×C4⋊C4C2211yescharacteristic
12C22×C11×C4⋊C4C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C11×C4⋊C4C2212yes—
15C22×C11×C4⋊C4C2214yes—
16C22×C42×C11C2211yescharacteristic
17C22×C42×C11C2211yescharacteristic
18C22×C42×C11C2211yescharacteristic
19C22×C42×C11C2212yes—
20C11×#389—24no—
21C11×#384C418yescomplemented
22C4×C11×C4⋊C4—24no—
23C2×C11×#95C2212yes—
24C2×C11×#95C2214yes—
25C2×C11×#95C2212yes—
26C2×C11×#95C2212yes—
27C2×C11×#95C2214yes—
28C2×C11×#95C2214yes—
29C2×C11×#95C2212yes—
30C23×C4×C11C2312yes—
31C23×C4×C11C2312yes—
32C23×C4×C11C2312yes—
33C23×C4×C11C2311yescharacteristic
34C23×C4×C11C2312yes—
35C23×C4×C11C2312yes—
36C23×C4×C11C2312yes—
37C23×C4×C11C2311yescharacteristic
38C23×C4×C11C2311yescharacteristic
39C2×C11×C4⋊C4—22no—
40C2×C11×C4⋊C4—22no—
41C2×C11×C4⋊C4—22no—
42C2×C11×C4⋊C4—22no—
43C2×C11×C4⋊C4—22no—
44C2×C11×C4⋊C4—22no—
45C2×C11×C4⋊C4—24no—
46C2×C11×C4⋊C4—22no—
47C2×C11×C4⋊C4—22no—
48C2×C11×C4⋊C4—22no—
49C2×C11×C4⋊C4—44no—
50C2×C11×C4⋊C4—44no—
51C2×C11×C4⋊C4—44no—
52C2×C11×C4⋊C4C2×C414yes—
53C2×C11×C4⋊C4C2×C414yes—
54C2×C11×C4⋊C4C2×C4116yes—
55C2×C11×C4⋊C4Q814yes—
56C2×C42×C11—22no—
57C2×C42×C11—22no—
58C2×C42×C11—22no—
59C2×C42×C11—22no—
60C2×C42×C11—24no—
61C2×C42×C11—22no—
62C2×C42×C11—22no—
63C2×C42×C11—22no—
64C2×C42×C11—44no—
65C2×C42×C11C2×C414yes—
66C2×C42×C11D414yes—
67C11×#95—24no—
68C11×#95—24no—
69C11×#95—24no—
70C11×#95—28no—
71C11×#95—44no—
72C11×#95—44no—
73C11×#95Q818yes—
74#14048C1111yesmaximal, characteristic, direct product factor, Sylow
75C24×C11C2411yescharacteristic
76C22×C4×C11—22no—
77C22×C4×C11—22no—
78C22×C4×C11—21no—
79C22×C4×C11—21no—
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—24no—
89C22×C4×C11—21no—
90C22×C4×C11—21no—
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—24no—
100C22×C4×C11—24no—
101C22×C4×C11—24no—
102C22×C4×C11—24no—
103C22×C4×C11—24no—
104C22×C4×C11—22no—
105C22×C4×C11—22no—
106C22×C4×C11—24no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—24no—
110C22×C4×C11C22×C414yes—
111C22×C4×C11C22×C414yes—
112C22×C4×C11C22×C414yes—
113C22×C4×C11C22×C412yes—
114C22×C4×C11C2×D412yes—
115C22×C4×C11C2×D412yes—
116C22×C4×C11C2×D412yes—
117C22×C4×C11C2×Q814yes—
118C22×C4×C11C2×Q814yes—
119C22×C4×C11C2×Q814yes—
120C22×C4×C11C2×Q814yes—
121C22×C4×C11C2×Q812yes—
122C22×C4×C11#4114yes—
123C22×C4×C11#4112yes—
124C22×C4×C11#4112yes—
125C22×C4×C11#4112yes—
126C22×C4×C11#4112yes—
127C11×C4⋊C4—28no—
128C11×C4⋊C4—28no—
129C11×C4⋊C4—28no—
130C11×C4⋊C4—416no—
131C11×C4⋊C4—48no—
132C11×C4⋊C4—44no—
133C42×C11—28no—
134C42×C11—28no—
135C42×C11—48no—
136C42×C11—44no—
137C2×#389C2×C1111yescharacteristic
138C2×#384C2×C1111yescharacteristic
139C2×C4×C4⋊C4C2×C1111yescharacteristic
140#1441C2×C1114yes—
141#1436C2×C1114yes—
142C4⋊#95C2×C1111yescharacteristic
143C4⋊#95C2×C1111yescharacteristic
144C4⋊#95C2×C1111yescharacteristic
145C4×#95C2×C1111yescharacteristic
146C23×C11C23×C411yescharacteristic
147C23×C11C22×D411yescharacteristic
148C23×C11C22×Q811yescharacteristic
149C23×C11C22×Q812yes—
150C23×C11C2×#4111yescharacteristic
151C23×C11C2×#4111yescharacteristic
152C23×C11C2×#4111yescharacteristic
153C23×C11C2×#4111yescharacteristic
154C23×C11C2×#4112yes—
155C23×C11H(5,𝔽2)12yes—
156C23×C11H(5,𝔽2)12yes—
157C2×C4×C11—24no—
158C2×C4×C11—24no—
159C2×C4×C11—22no—
160C2×C4×C11—22no—
161C2×C4×C11—24no—
162C2×C4×C11—24no—
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—28no—
170C2×C4×C11—28no—
171C2×C4×C11—24no—
172C2×C4×C11—22no—
173C2×C4×C11—22no—
174C2×C4×C11—24no—
175C2×C4×C11—22no—
176C2×C4×C11—28no—
177C2×C4×C11—24no—
178C2×C4×C11—24no—
179C2×C4×C11—42no—
180C2×C4×C11—42no—
181C2×C4×C11—42no—
182C2×C4×C11—42no—
183C2×C4×C11—42no—
184C2×C4×C11—42no—
185C2×C4×C11—42no—
186C2×C4×C11—44no—
187C2×C4×C11—44no—
188C2×C4×C11—42no—
189C2×C4×C11—44no—
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—44no—
198C2×C4×C11—44no—
199C2×C4×C11#11714yes—
200C2×C4×C11C4×D414yes—
201C2×C4×C11C4×Q818yes—
202C2×C4×C11C4×Q814yes—
203C2×C4×C11C22⋊Q814yes—
204C2×C4×C11#12314yes—
205C2×C4×C11#12514yes—
206C2×C4×C11#12614yes—
207C2×C4×C11C4⋊Q814yes—
208C22×C4⋊C4C22×C1111yescharacteristic
209C22×C4⋊C4C22×C1111yescharacteristic
210C22×C4⋊C4C22×C1111yescharacteristic
211C22×C4⋊C4C22×C1111yescharacteristic
212C22×C4⋊C4C22×C1112yes—
213C22×C4⋊C4C22×C1114yes—
214C22×C42C22×C1111yescharacteristic
215C22×C42C22×C1111yescharacteristic
216C22×C42C22×C1111yescharacteristic
217C22×C42C22×C1112yes—
218#389—24no—
219#384C4×C1118yescomplemented
220C4×C4⋊C4—24no—
221C2×#95C22×C1112yes—
222C2×#95C22×C1114yes—
223C2×#95C22×C1112yes—
224C2×#95C22×C1112yes—
225C2×#95C22×C1114yes—
226C2×#95C22×C1114yes—
227C2×#95C22×C1112yes—
228C22×C11C2×#11711yescharacteristic
229C22×C11C2×C4×D411yescharacteristic
230C22×C11C2×C4×Q812yes—
231C22×C11C2×C4×Q811yescharacteristic
232C22×C11#51812yes—
233C22×C11C2×C22⋊Q811yescharacteristic
234C22×C11C2×#12311yescharacteristic
235C22×C11C2×#12511yescharacteristic
236C22×C11C2×#12611yescharacteristic
237C22×C11C2×C4⋊Q811yescharacteristic
238C22×C11#53211yescharacteristic
239C22×C11#53312yes—
240C22×C11#53511yescharacteristic
241C22×C11#53511yescharacteristic
242C22×C11#54012yes—
243C22×C11#55312yes—
244C22×C11#55312yes—
245C22×C11#55412yes—
246C22×C11#55412yes—
247C22×C11#55412yes—
248C22×C11#55412yes—
249C22×C11#55512yes—
250C22×C11Q8212yes—
251C4×C11—28no—
252C4×C11—24no—
253C4×C11—44no—
254C4×C11—44no—
255C4×C11—44no—
256C4×C11—44no—
257C4×C11—42no—
258C4×C11—82no—
259C4×C11#38718yes—
260C23×C4C23×C1112yes—
261C23×C4C23×C1112yes—
262C23×C4C23×C1112yes—
263C23×C4C23×C1111yescharacteristic
264C23×C4C23×C1112yes—
265C23×C4C23×C1112yes—
266C23×C4C23×C1112yes—
267C23×C4C23×C1111yescharacteristic
268C23×C4C23×C1111yescharacteristic
269C2×C4⋊C4—22no—
270C2×C4⋊C4—22no—
271C2×C4⋊C4—22no—
272C2×C4⋊C4—22no—
273C2×C4⋊C4—22no—
274C2×C4⋊C4—22no—
275C2×C4⋊C4—24no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—22no—
279C2×C4⋊C4—44no—
280C2×C4⋊C4—44no—
281C2×C4⋊C4—44no—
282C2×C4⋊C4C2×C4×C1114yes—
283C2×C4⋊C4C2×C4×C1114yes—
284C2×C4⋊C4C2×C4×C11116yes—
285C2×C4⋊C4Q8×C1114yes—
286C2×C42—22no—
287C2×C42—22no—
288C2×C42—22no—
289C2×C42—22no—
290C2×C42—24no—
291C2×C42—22no—
292C2×C42—22no—
293C2×C42—22no—
294C2×C42—44no—
295C2×C42C2×C4×C1114yes—
296C2×C42D4×C1114yes—
297#95—24no—
298#95—24no—
299#95—24no—
300#95—28no—
301#95—44no—
302#95—44no—
303#95Q8×C1118yes—
304C2×C11C2×#38711yescharacteristic
305C2×C11C4×C4⋊Q811yescharacteristic
306C2×C11#232811yescharacteristic
307C2×C11#234512yes—
308C2×C11#236912yes—
309C2×C11#249712yes—
310C2×C11#250011yescharacteristic
311C2×C11#250211yescharacteristic
312C2×C11#250712yes—
313C2×C11#256611yescharacteristic
314C2×C11#256711yescharacteristic
315C24C24×C1111yescharacteristic
316C22×C4—22no—
317C22×C4—22no—
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—22no—
321C22×C4—22no—
322C22×C4—22no—
323C22×C4—22no—
324C22×C4—22no—
325C22×C4—22no—
326C22×C4—22no—
327C22×C4—22no—
328C22×C4—24no—
329C22×C4—21no—
330C22×C4—21no—
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—24no—
340C22×C4—24no—
341C22×C4—24no—
342C22×C4—24no—
343C22×C4—24no—
344C22×C4—22no—
345C22×C4—22no—
346C22×C4—24no—
347C22×C4—22no—
348C22×C4—22no—
349C22×C4—24no—
350C22×C4C22×C4×C1114yes—
351C22×C4C22×C4×C1114yes—
352C22×C4C22×C4×C1114yes—
353C22×C4C22×C4×C1112yes—
354C22×C4C2×D4×C1112yes—
355C22×C4C2×D4×C1112yes—
356C22×C4C2×D4×C1112yes—
357C22×C4C2×Q8×C1114yes—
358C22×C4C2×Q8×C1114yes—
359C22×C4C2×Q8×C1114yes—
360C22×C4C2×Q8×C1114yes—
361C22×C4C2×Q8×C1112yes—
362C22×C4C11×#4114yes—
363C22×C4C11×#4112yes—
364C22×C4C11×#4112yes—
365C22×C4C11×#4112yes—
366C22×C4C11×#4112yes—
367C4⋊C4—28no—
368C4⋊C4—28no—
369C4⋊C4—28no—
370C4⋊C4—416no—
371C4⋊C4—48no—
372C4⋊C4—44no—
373C42—28no—
374C42—28no—
375C42—48no—
376C42—44no—
377C11#1404811yescharacteristic, direct product factor, Sylow
378C23C23×C4×C1111yescharacteristic
379C23C22×D4×C1111yescharacteristic
380C23C22×Q8×C1111yescharacteristic
381C23C22×Q8×C1112yes—
382C23C2×C11×#4111yescharacteristic
383C23C2×C11×#4111yescharacteristic
384C23C2×C11×#4111yescharacteristic
385C23C2×C11×#4111yescharacteristic
386C23C2×C11×#4112yes—
387C23C11×H(5,𝔽2)12yes—
388C23C11×H(5,𝔽2)12yes—
389C2×C4—24no—
390C2×C4—24no—
391C2×C4—22no—
392C2×C4—22no—
393C2×C4—24no—
394C2×C4—24no—
395C2×C4—24no—
396C2×C4—24no—
397C2×C4—24no—
398C2×C4—24no—
399C2×C4—24no—
400C2×C4—24no—
401C2×C4—28no—
402C2×C4—28no—
403C2×C4—24no—
404C2×C4—22no—
405C2×C4—22no—
406C2×C4—24no—
407C2×C4—22no—
408C2×C4—24no—
409C2×C4—24no—
410C2×C4—28no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4—44no—
420C2×C4—44no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—44no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—44no—
430C2×C4—44no—
431C2×C4C11×#11714yes—
432C2×C4C4×D4×C1114yes—
433C2×C4C4×Q8×C1118yes—
434C2×C4C4×Q8×C1114yes—
435C2×C4C11×C22⋊Q814yes—
436C2×C4C11×#12314yes—
437C2×C4C11×#12514yes—
438C2×C4C11×#12614yes—
439C2×C4C11×C4⋊Q814yes—
440C22C2×C11×#11711yescharacteristic
441C22C2×C4×D4×C1111yescharacteristic
442C22C2×C4×Q8×C1111yescharacteristic
443C22C2×C4×Q8×C1112yes—
444C22C11×#51812yes—
445C22C2×C11×C22⋊Q811yescharacteristic
446C22C2×C11×#12311yescharacteristic
447C22C2×C11×#12511yescharacteristic
448C22C2×C11×#12611yescharacteristic
449C22C2×C11×C4⋊Q811yescharacteristic
450C22C11×#53211yescharacteristic
451C22C11×#53312yes—
452C22C11×#53511yescharacteristic
453C22C11×#53511yescharacteristic
454C22C11×#54012yes—
455C22C11×#55312yes—
456C22C11×#55312yes—
457C22C11×#55412yes—
458C22C11×#55412yes—
459C22C11×#55412yes—
460C22C11×#55412yes—
461C22C11×#55512yes—
462C22Q82×C1112yes—
463C4—24no—
464C4—28no—
465C4—44no—
466C4—42no—
467C4—44no—
468C4—44no—
469C4—44no—
470C4—82no—
471C4C11×#38718yes—
472C2C2×C11×#38711yescharacteristic
473C2C4×C11×C4⋊Q811yescharacteristic
474C2C11×#232811yescharacteristic
475C2C11×#234512yes—
476C2C11×#236912yes—
477C2C11×#249712yes—
478C2C11×#250011yescharacteristic
479C2C11×#250211yescharacteristic
480C2C11×#250712yes—
481C2C11×#256611yescharacteristic
482C2C11×#256711yescharacteristic
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
21. C11×#384C4semidirect
74. #14048C11direct (N × H)
219. #384C4×C11semidirect
377. C11#14048direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#3892
C2×C11×#3842
C2×C4×C11×C4⋊C42
C11×#14412
C11×#14362
C11×C4⋊#952
C4×C11×#952
#1404811