Finite Group Databasebeta

← C11×#14051 #14591244

Subgroups — C11×#14051 #14591244

Order 2816.

1326 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#389C211yesmaximal, characteristic
2C2×C11×#382C211yesmaximal, characteristic
3C2×C4×C11×C4⋊C4C211yesmaximal, characteristic
4C11×#1442C214yesmaximal
5C11×C4⋊#95C211yesmaximal, characteristic
6C11×C4⋊#95C211yesmaximal, characteristic
7C11×C4⋊#95C211yesmaximal, characteristic
8C11×#1434C214yesmaximal
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×C42×C11C2211yescharacteristic
16C22×C42×C11C2212yes—
17C22×C42×C11C2211yescharacteristic
18C22×C42×C11C2211yescharacteristic
19C11×#389—24no—
20C11×#382C418yescomplemented
21C4×C11×C4⋊C4—24no—
22C2×C11×#95C2212yes—
23C2×C11×#95C2212yes—
24C2×C11×#95C2212yes—
25C2×C11×#95C2214yes—
26C2×C11×#95C2212yes—
27C2×C11×#95C2214yes—
28C2×C11×#95C2214yes—
29C2×C11×#95C2214yes—
30C23×C4×C11C2312yes—
31C23×C4×C11C2312yes—
32C23×C4×C11C2312yes—
33C23×C4×C11C2312yes—
34C23×C4×C11C2311yescharacteristic
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⋊C4C2×C414yes—
51C2×C11×C4⋊C4C2×C414yes—
52C2×C11×C4⋊C4Q814yes—
53C2×C42×C11—22no—
54C2×C42×C11—22no—
55C2×C42×C11—22no—
56C2×C42×C11—22no—
57C2×C42×C11—24no—
58C2×C42×C11—28no—
59C2×C42×C11—22no—
60C2×C42×C11—22no—
61C2×C42×C11—22no—
62C2×C42×C11C2×C414yes—
63C2×C42×C11D414yes—
64C11×#95—24no—
65C11×#95—24no—
66C11×#95—24no—
67C11×#95—24no—
68C11×#95—28no—
69C11×#95—44no—
70C11×#95—44no—
71C11×#95C2×C4116yes—
72#14051C1111yesmaximal, characteristic, direct product factor, Sylow
73C24×C11C2411yescharacteristic
74C22×C4×C11—21no—
75C22×C4×C11—21no—
76C22×C4×C11—22no—
77C22×C4×C11—22no—
78C22×C4×C11—22no—
79C22×C4×C11—22no—
80C22×C4×C11—24no—
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—24no—
88C22×C4×C11—21no—
89C22×C4×C11—21no—
90C22×C4×C11—22no—
91C22×C4×C11—22no—
92C22×C4×C11—22no—
93C22×C4×C11—24no—
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—22no—
102C22×C4×C11—24no—
103C22×C4×C11—22no—
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×Q812yes—
119C22×C4×C11#4114yes—
120C22×C4×C11#4114yes—
121C22×C4×C11#4112yes—
122C22×C4×C11#4112yes—
123C22×C4×C11#4112yes—
124C22×C4×C11#4112yes—
125C11×C4⋊C4—28no—
126C11×C4⋊C4—28no—
127C11×C4⋊C4—28no—
128C11×C4⋊C4—48no—
129C11×C4⋊C4—44no—
130C42×C11—28no—
131C42×C11—28no—
132C42×C11—48no—
133C42×C11—44no—
134C2×#389C2×C1111yescharacteristic
135C2×#382C2×C1111yescharacteristic
136C2×C4×C4⋊C4C2×C1111yescharacteristic
137#1442C2×C1114yes—
138C4⋊#95C2×C1111yescharacteristic
139C4⋊#95C2×C1111yescharacteristic
140C4⋊#95C2×C1111yescharacteristic
141#1434C2×C1114yes—
142C4×#95C2×C1111yescharacteristic
143C23×C11C23×C411yescharacteristic
144C23×C11C22×D411yescharacteristic
145C23×C11C22×Q811yescharacteristic
146C23×C11C2×#4111yescharacteristic
147C23×C11C2×#4111yescharacteristic
148C23×C11C2×#4111yescharacteristic
149C23×C11C2×#4111yescharacteristic
150C23×C11C2×#4112yes—
151C23×C11C2×#4112yes—
152C23×C11H(5,𝔽2)12yes—
153C23×C112−1+412yes—
154C2×C4×C11—22no—
155C2×C4×C11—22no—
156C2×C4×C11—24no—
157C2×C4×C11—24no—
158C2×C4×C11—24no—
159C2×C4×C11—24no—
160C2×C4×C11—24no—
161C2×C4×C11—24no—
162C2×C4×C11—28no—
163C2×C4×C11—28no—
164C2×C4×C11—24no—
165C2×C4×C11—24no—
166C2×C4×C11—22no—
167C2×C4×C11—24no—
168C2×C4×C11—22no—
169C2×C4×C11—22no—
170C2×C4×C11—24no—
171C2×C4×C11—24no—
172C2×C4×C11—28no—
173C2×C4×C11—42no—
174C2×C4×C11—42no—
175C2×C4×C11—42no—
176C2×C4×C11—44no—
177C2×C4×C11—42no—
178C2×C4×C11—42no—
179C2×C4×C11—42no—
180C2×C4×C11—42no—
181C2×C4×C11—44no—
182C2×C4×C11—42no—
183C2×C4×C11—42no—
184C2×C4×C11—42no—
185C2×C4×C11—42no—
186C2×C4×C11—42no—
187C2×C4×C11—44no—
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—44no—
196C2×C4×C11—44no—
197C2×C4×C11#11714yes—
198C2×C4×C11C4×D414yes—
199C2×C4×C11C4×Q814yes—
200C2×C4×C11C22⋊Q814yes—
201C2×C4×C11#12314yes—
202C2×C4×C11#12414yes—
203C2×C4×C11#12514yes—
204C2×C4×C11#12614yes—
205C22×C4⋊C4C22×C1111yescharacteristic
206C22×C4⋊C4C22×C1111yescharacteristic
207C22×C4⋊C4C22×C1111yescharacteristic
208C22×C4⋊C4C22×C1111yescharacteristic
209C22×C4⋊C4C22×C1112yes—
210C22×C42C22×C1111yescharacteristic
211C22×C42C22×C1112yes—
212C22×C42C22×C1111yescharacteristic
213C22×C42C22×C1111yescharacteristic
214#389—24no—
215#382C4×C1118yescomplemented
216C4×C4⋊C4—24no—
217C2×#95C22×C1112yes—
218C2×#95C22×C1112yes—
219C2×#95C22×C1112yes—
220C2×#95C22×C1114yes—
221C2×#95C22×C1112yes—
222C2×#95C22×C1114yes—
223C2×#95C22×C1114yes—
224C2×#95C22×C1114yes—
225C22×C11C2×#11711yescharacteristic
226C22×C11C2×C4×D411yescharacteristic
227C22×C11C2×C4×Q811yescharacteristic
228C22×C11C4×#4112yes—
229C22×C11#52012yes—
230C22×C11C2×C22⋊Q811yescharacteristic
231C22×C11C2×#12311yescharacteristic
232C22×C11C2×#12411yescharacteristic
233C22×C11C2×#12511yescharacteristic
234C22×C11C2×#12611yescharacteristic
235C22×C11#52912yes—
236C22×C11#53211yescharacteristic
237C22×C11#53511yescharacteristic
238C22×C11#53611yescharacteristic
239C22×C11#54212yes—
240C22×C11#55212yes—
241C22×C11#55212yes—
242C22×C11#55212yes—
243C22×C11#55312yes—
244C22×C11#55412yes—
245C22×C11#55512yes—
246C22×C11#55512yes—
247C22×C11#55712yes—
248C4×C11—24no—
249C4×C11—44no—
250C4×C11—44no—
251C4×C11—44no—
252C4×C11—44no—
253C4×C11—42no—
254C4×C11—44no—
255C4×C11—82no—
256C4×C11#38718yes—
257C23×C4C23×C1112yes—
258C23×C4C23×C1112yes—
259C23×C4C23×C1112yes—
260C23×C4C23×C1112yes—
261C23×C4C23×C1111yescharacteristic
262C23×C4C23×C1112yes—
263C23×C4C23×C1112yes—
264C23×C4C23×C1111yescharacteristic
265C23×C4C23×C1111yescharacteristic
266C2×C4⋊C4—22no—
267C2×C4⋊C4—22no—
268C2×C4⋊C4—22no—
269C2×C4⋊C4—22no—
270C2×C4⋊C4—22no—
271C2×C4⋊C4—22no—
272C2×C4⋊C4—24no—
273C2×C4⋊C4—22no—
274C2×C4⋊C4—22no—
275C2×C4⋊C4—22no—
276C2×C4⋊C4—44no—
277C2×C4⋊C4C2×C4×C1114yes—
278C2×C4⋊C4C2×C4×C1114yes—
279C2×C4⋊C4Q8×C1114yes—
280C2×C42—22no—
281C2×C42—22no—
282C2×C42—22no—
283C2×C42—22no—
284C2×C42—24no—
285C2×C42—28no—
286C2×C42—22no—
287C2×C42—22no—
288C2×C42—22no—
289C2×C42C2×C4×C1114yes—
290C2×C42D4×C1114yes—
291#95—24no—
292#95—24no—
293#95—24no—
294#95—24no—
295#95—28no—
296#95—44no—
297#95—44no—
298#95C2×C4×C11116yes—
299C2×C11C2×#38711yescharacteristic
300C2×C11C4×#12411yescharacteristic
301C2×C11#232611yescharacteristic
302C2×C11#234612yes—
303C2×C11#237012yes—
304C2×C11#249512yes—
305C2×C11#250011yescharacteristic
306C2×C11#250311yescharacteristic
307C2×C11#250812yes—
308C2×C11#256311yescharacteristic
309C2×C11#256511yescharacteristic
310C24C24×C1111yescharacteristic
311C22×C4—21no—
312C22×C4—21no—
313C22×C4—22no—
314C22×C4—22no—
315C22×C4—22no—
316C22×C4—22no—
317C22×C4—24no—
318C22×C4—22no—
319C22×C4—22no—
320C22×C4—22no—
321C22×C4—22no—
322C22×C4—22no—
323C22×C4—22no—
324C22×C4—24no—
325C22×C4—21no—
326C22×C4—21no—
327C22×C4—22no—
328C22×C4—22no—
329C22×C4—22no—
330C22×C4—24no—
331C22×C4—22no—
332C22×C4—22no—
333C22×C4—22no—
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—24no—
337C22×C4—24no—
338C22×C4—22no—
339C22×C4—24no—
340C22×C4—22no—
341C22×C4—22no—
342C22×C4—22no—
343C22×C4—24no—
344C22×C4—22no—
345C22×C4—22no—
346C22×C4—24no—
347C22×C4C22×C4×C1114yes—
348C22×C4C22×C4×C1114yes—
349C22×C4C22×C4×C1114yes—
350C22×C4C22×C4×C1112yes—
351C22×C4C2×D4×C1112yes—
352C22×C4C2×D4×C1112yes—
353C22×C4C2×D4×C1112yes—
354C22×C4C2×Q8×C1114yes—
355C22×C4C2×Q8×C1112yes—
356C22×C4C11×#4114yes—
357C22×C4C11×#4114yes—
358C22×C4C11×#4112yes—
359C22×C4C11×#4112yes—
360C22×C4C11×#4112yes—
361C22×C4C11×#4112yes—
362C4⋊C4—28no—
363C4⋊C4—28no—
364C4⋊C4—28no—
365C4⋊C4—48no—
366C4⋊C4—44no—
367C42—28no—
368C42—28no—
369C42—48no—
370C42—44no—
371C11#1405111yescharacteristic, direct product factor, Sylow
372C23C23×C4×C1111yescharacteristic
373C23C22×D4×C1111yescharacteristic
374C23C22×Q8×C1111yescharacteristic
375C23C2×C11×#4111yescharacteristic
376C23C2×C11×#4111yescharacteristic
377C23C2×C11×#4111yescharacteristic
378C23C2×C11×#4111yescharacteristic
379C23C2×C11×#4112yes—
380C23C2×C11×#4112yes—
381C23C11×H(5,𝔽2)12yes—
382C23C11×2−1+412yes—
383C2×C4—22no—
384C2×C4—22no—
385C2×C4—24no—
386C2×C4—24no—
387C2×C4—24no—
388C2×C4—24no—
389C2×C4—24no—
390C2×C4—28no—
391C2×C4—24no—
392C2×C4—28no—
393C2×C4—24no—
394C2×C4—24no—
395C2×C4—22no—
396C2×C4—24no—
397C2×C4—22no—
398C2×C4—22no—
399C2×C4—24no—
400C2×C4—24no—
401C2×C4—28no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—44no—
406C2×C4—42no—
407C2×C4—42no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—44no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—44no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—44no—
425C2×C4—44no—
426C2×C4C11×#11714yes—
427C2×C4C4×D4×C1114yes—
428C2×C4C4×Q8×C1114yes—
429C2×C4C11×C22⋊Q814yes—
430C2×C4C11×#12314yes—
431C2×C4C11×#12414yes—
432C2×C4C11×#12514yes—
433C2×C4C11×#12614yes—
434C22C2×C11×#11711yescharacteristic
435C22C2×C4×D4×C1111yescharacteristic
436C22C2×C4×Q8×C1111yescharacteristic
437C22C4×C11×#4112yes—
438C22C11×#52012yes—
439C22C2×C11×C22⋊Q811yescharacteristic
440C22C2×C11×#12311yescharacteristic
441C22C2×C11×#12411yescharacteristic
442C22C2×C11×#12511yescharacteristic
443C22C2×C11×#12611yescharacteristic
444C22C11×#52912yes—
445C22C11×#53211yescharacteristic
446C22C11×#53511yescharacteristic
447C22C11×#53611yescharacteristic
448C22C11×#54212yes—
449C22C11×#55212yes—
450C22C11×#55212yes—
451C22C11×#55212yes—
452C22C11×#55312yes—
453C22C11×#55412yes—
454C22C11×#55512yes—
455C22C11×#55512yes—
456C22C11×#55712yes—
457C4—24no—
458C4—44no—
459C4—42no—
460C4—44no—
461C4—44no—
462C4—44no—
463C4—44no—
464C4—82no—
465C4C11×#38718yes—
466C2C2×C11×#38711yescharacteristic
467C2C4×C11×#12411yescharacteristic
468C2C11×#232611yescharacteristic
469C2C11×#234612yes—
470C2C11×#237012yes—
471C2C11×#249512yes—
472C2C11×#250011yescharacteristic
473C2C11×#250311yescharacteristic
474C2C11×#250812yes—
475C2C11×#256311yescharacteristic
476C2C11×#256511yescharacteristic
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
20. C11×#382C4semidirect
72. #14051C11direct (N × H)
215. #382C4×C11semidirect
371. C11#14051direct (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×#3822
C2×C4×C11×C4⋊C42
C11×#14422
C11×C4⋊#952
C11×#14342
C4×C11×#952
#1405111