Finite Group Databasebeta

← C11×#14574 #14591767

Subgroups — C11×#14574 #14591767

Order 2816.

1358 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#395C211yesmaximal, characteristic
2C2×C11×#391C212yesmaximal
3C2×C11×#387C212yesmaximal
4C11×#1445C211yesmaximal, characteristic
5C11×#1443C212yesmaximal
6C11×#1442C212yesmaximal
7C11×#1436C212yesmaximal
8C11×#1436C211yesmaximal, characteristic
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
17C11×#391—28no—
18C11×#387—28no—
19C2×C11×#95C2212yes—
20C2×C11×#95C2212yes—
21C2×C11×#95C2212yes—
22C2×C11×#95C2212yes—
23C2×C11×#95C2212yes—
24C2×C11×#95C2212yes—
25C2×C11×#95C2212yes—
26C2×C11×#95C2212yes—
27C2×C11×#95C2212yes—
28C2×C11×#95C2211yescharacteristic
29C2×C11×#95C2211yescharacteristic
30C2×C11×#95C2211yescharacteristic
31C2×C11×#95C2212yes—
32C2×C11×#95C2211yescharacteristic
33C2×C11×#95C2212yes—
34C22×Q8×C11—24no—
35C22×Q8×C11—24no—
36C22×Q8×C11—41no—
37C22×Q8×C11—41no—
38C22×Q8×C11C2×C414yes—
39C23×C4×C11C2312yes—
40C23×C4×C11C2311yescharacteristic
41C23×C4×C11C2312yes—
42C23×C4×C11C2311yescharacteristic
43C23×C4×C11C2311yescharacteristic
44C23×C4×C11C2312yes—
45C23×C4×C11C2312yes—
46C23×C4×C11C2312yes—
47C23×C4×C11C2312yes—
48C2×C11×C4⋊C4—24no—
49C2×C11×C4⋊C4—24no—
50C2×C11×C4⋊C4—24no—
51C2×C11×C4⋊C4—24no—
52C2×C11×C4⋊C4—41no—
53C2×C11×C4⋊C4—41no—
54C2×C11×C4⋊C4—42no—
55C2×C11×C4⋊C4C2×C418yes—
56C2×C11×C4⋊C4C2×C414yes—
57C2×C42×C11—24no—
58C2×C42×C11—24no—
59C2×C42×C11—24no—
60C2×C42×C11—42no—
61C2×C42×C11—41no—
62C11×#95—24no—
63C11×#95—24no—
64C11×#95—24no—
65C11×#95—24no—
66C11×#95—24no—
67C11×#95—24no—
68C11×#95—24no—
69C11×#95—24no—
70C11×#95—24no—
71C11×#95—41no—
72C11×#95—41no—
73C11×#95—41no—
74C11×#95C2×C414yes—
75C11×#95C2×C418yes—
76C11×#95D418yes—
77#14574C1111yesmaximal, characteristic, direct product factor, Sylow
78C24×C11C2411yescharacteristic
79C2×Q8×C11—216no—
80C2×Q8×C11—44no—
81C2×Q8×C11—44no—
82C2×Q8×C11—48no—
83C2×Q8×C11—44no—
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—22no—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—21no—
106C22×C4×C11—21no—
107C22×C4×C11—21no—
108C22×C4×C11—21no—
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×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11C22×C414yes—
132C22×C4×C11C22×C412yes—
133C22×C4×C11C22×C412yes—
134C22×C4×C11C22×C412yes—
135C22×C4×C11C22×C414yes—
136C22×C4×C11C2×D414yes—
137C22×C4×C11C2×D414yes—
138C22×C4×C11C2×D414yes—
139C22×C4×C11#4114yes—
140C22×C4×C11#4114yes—
141C11×C4⋊C4—216no—
142C11×C4⋊C4—44no—
143C11×C4⋊C4—48no—
144C42×C11—48no—
145C42×C11—44no—
146C2×#395C2×C1111yescharacteristic
147C2×#391C2×C1112yes—
148C2×#387C2×C1112yes—
149#1445C2×C1111yescharacteristic
150#1443C2×C1112yes—
151#1442C2×C1112yes—
152#1436C2×C1112yes—
153#1436C2×C1111yescharacteristic
154#1434C2×C1112yes—
155C23×C11C23×C411yescharacteristic
156C23×C11C22×D412yes—
157C23×C11C2×#4112yes—
158C23×C11C2×#4112yes—
159C23×C11H(5,𝔽2)11yescharacteristic
160C23×C11H(5,𝔽2)11yescharacteristic
161C23×C112−1+412yes—
162C23×C112−1+412yes—
163C23×C112−1+412yes—
164Q8×C11—416no—
165C2×C4×C11—24no—
166C2×C4×C11—24no—
167C2×C4×C11—24no—
168C2×C4×C11—24no—
169C2×C4×C11—24no—
170C2×C4×C11—24no—
171C2×C4×C11—24no—
172C2×C4×C11—24no—
173C2×C4×C11—24no—
174C2×C4×C11—22no—
175C2×C4×C11—24no—
176C2×C4×C11—22no—
177C2×C4×C11—22no—
178C2×C4×C11—22no—
179C2×C4×C11—22no—
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—24no—
189C2×C4×C11—24no—
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—41no—
199C2×C4×C11—41no—
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—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×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×D418yes—
222C23×Q8C22×C1111yescharacteristic
223C22×C4⋊C4C22×C1112yes—
224C22×C4⋊C4C22×C1112yes—
225C22×C4⋊C4C22×C1111yescharacteristic
226C22×C42C22×C1112yes—
227C22×C42C22×C1111yescharacteristic
228#395C4×C1118yescomplemented
229#391—28no—
230#387—28no—
231C2×#95C22×C1112yes—
232C2×#95C22×C1112yes—
233C2×#95C22×C1112yes—
234C2×#95C22×C1112yes—
235C2×#95C22×C1112yes—
236C2×#95C22×C1112yes—
237C2×#95C22×C1112yes—
238C2×#95C22×C1112yes—
239C2×#95C22×C1112yes—
240C2×#95C22×C1111yescharacteristic
241C2×#95C22×C1111yescharacteristic
242C2×#95C22×C1111yescharacteristic
243C2×#95C22×C1112yes—
244C2×#95C22×C1111yescharacteristic
245C2×#95C22×C1112yes—
246C22×C11C2×C4×D412yes—
247C22×C11C4×#4111yescharacteristic
248C22×C11#51811yescharacteristic
249C22×C11#51911yescharacteristic
250C22×C11#51912yes—
251C22×C11#53612yes—
252C22×C11#53612yes—
253C22×C11#53912yes—
254C22×C11#54112yes—
255C22×C11#54112yes—
256C22×C11#54212yes—
257C22×C11D4211yescharacteristic
258C22×C11#54612yes—
259C22×C11#54712yes—
260C22×C11#54812yes—
261C22×C11#55111yescharacteristic
262C22×C11#55212yes—
263C22×C11#55612yes—
264C22×C11#56312yes—
265C22×C11#56311yescharacteristic
266C22×C11#56311yescharacteristic
267C4×C11—28no—
268C4×C11—42no—
269C4×C11—42no—
270C4×C11—42no—
271C4×C11—44no—
272C4×C11—44no—
273C4×C11—44no—
274C4×C11—44no—
275C4×C11—82no—
276C22×Q8—24no—
277C22×Q8—24no—
278C22×Q8—41no—
279C22×Q8—41no—
280C22×Q8C2×C4×C1114yes—
281C23×C4C23×C1112yes—
282C23×C4C23×C1111yescharacteristic
283C23×C4C23×C1111yescharacteristic
284C23×C4C23×C1112yes—
285C23×C4C23×C1111yescharacteristic
286C23×C4C23×C1112yes—
287C23×C4C23×C1112yes—
288C23×C4C23×C1112yes—
289C23×C4C23×C1112yes—
290C2×C4⋊C4—24no—
291C2×C4⋊C4—24no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—41no—
295C2×C4⋊C4—41no—
296C2×C4⋊C4—42no—
297C2×C4⋊C4C2×C4×C1118yes—
298C2×C4⋊C4C2×C4×C1114yes—
299C2×C42—24no—
300C2×C42—24no—
301C2×C42—24no—
302C2×C42—42no—
303C2×C42—41no—
304#95—24no—
305#95—24no—
306#95—24no—
307#95—24no—
308#95—24no—
309#95—24no—
310#95—24no—
311#95—24no—
312#95—24no—
313#95—41no—
314#95—41no—
315#95—41no—
316#95C2×C4×C1114yes—
317#95C2×C4×C1118yes—
318#95D4×C1118yes—
319C2×C11#232712yes—
320C2×C11#233211yescharacteristic
321C2×C11#235811yescharacteristic
322C2×C11#236212yes—
323C2×C11#238111yescharacteristic
324C2×C11#267412yes—
325C2×C11#268912yes—
326C2×C11#269012yes—
327C2×C11#276212yes—
328C24C24×C1111yescharacteristic
329C2×Q8—216no—
330C2×Q8—44no—
331C2×Q8—44no—
332C2×Q8—48no—
333C2×Q8—44no—
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—22no—
350C22×C4—22no—
351C22×C4—22no—
352C22×C4—22no—
353C22×C4—22no—
354C22×C4—22no—
355C22×C4—21no—
356C22×C4—21no—
357C22×C4—21no—
358C22×C4—21no—
359C22×C4—22no—
360C22×C4—21no—
361C22×C4—21no—
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×C4C22×C4×C1114yes—
382C22×C4C22×C4×C1112yes—
383C22×C4C22×C4×C1112yes—
384C22×C4C22×C4×C1112yes—
385C22×C4C22×C4×C1114yes—
386C22×C4C2×D4×C1114yes—
387C22×C4C2×D4×C1114yes—
388C22×C4C2×D4×C1114yes—
389C22×C4C11×#4114yes—
390C22×C4C11×#4114yes—
391C4⋊C4—216no—
392C4⋊C4—44no—
393C4⋊C4—48no—
394C42—48no—
395C42—44no—
396C11#1457411yescharacteristic, direct product factor, Sylow
397C23C23×C4×C1111yescharacteristic
398C23C22×D4×C1112yes—
399C23C2×C11×#4112yes—
400C23C2×C11×#4112yes—
401C23C11×H(5,𝔽2)11yescharacteristic
402C23C11×H(5,𝔽2)11yescharacteristic
403C23C11×2−1+412yes—
404C23C11×2−1+412yes—
405C23C11×2−1+412yes—
406Q8—416no—
407C2×C4—24no—
408C2×C4—24no—
409C2×C4—24no—
410C2×C4—24no—
411C2×C4—24no—
412C2×C4—24no—
413C2×C4—24no—
414C2×C4—24no—
415C2×C4—24no—
416C2×C4—22no—
417C2×C4—24no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—24no—
423C2×C4—24no—
424C2×C4—24no—
425C2×C4—24no—
426C2×C4—24no—
427C2×C4—24no—
428C2×C4—24no—
429C2×C4—24no—
430C2×C4—24no—
431C2×C4—24no—
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—41no—
441C2×C4—41no—
442C2×C4—42no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—42no—
447C2×C4—42no—
448C2×C4—41no—
449C2×C4—41no—
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×C4C4×D4×C1118yes—
464C22C2×C4×D4×C1112yes—
465C22C4×C11×#4111yescharacteristic
466C22C11×#51811yescharacteristic
467C22C11×#51912yes—
468C22C11×#51911yescharacteristic
469C22C11×#53612yes—
470C22C11×#53612yes—
471C22C11×#53912yes—
472C22C11×#54112yes—
473C22C11×#54112yes—
474C22C11×#54212yes—
475C22D42×C1111yescharacteristic
476C22C11×#54612yes—
477C22C11×#54712yes—
478C22C11×#54812yes—
479C22C11×#55111yescharacteristic
480C22C11×#55212yes—
481C22C11×#55612yes—
482C22C11×#56312yes—
483C22C11×#56311yescharacteristic
484C22C11×#56311yescharacteristic
485C4—28no—
486C4—44no—
487C4—44no—
488C4—44no—
489C4—42no—
490C4—42no—
491C4—42no—
492C4—44no—
493C4—82no—
494C2C11×#232712yes—
495C2C11×#233211yescharacteristic
496C2C11×#235811yescharacteristic
497C2C11×#236212yes—
498C2C11×#238111yescharacteristic
499C2C11×#267412yes—
500C2C11×#268912yes—
501C2C11×#269012yes—
502C2C11×#276212yes—
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
77. #14574C11direct (N × H)
228. #395C4×C11semidirect
396. C11#14574direct (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
C2×C11×#3912
C2×C11×#3872
C11×#14452
C11×#14432
C11×#14422
C11×#14362
C11×#14342
#1457411