Finite Group Databasebeta

← C11×#18286 #14595479

Subgroups — C11×#18286 #14595479

Order 2816.

1142 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×#543C211yesmaximal, characteristic, complemented
2C11×#3187C212yesmaximal, complemented
3C11×#2617C211yesmaximal, characteristic
4C11×#1608C214yesmaximal, complemented
5C11×#1596C214yesmaximal, complemented
6C11×#1520C212yesmaximal, complemented
7C2×C11×#323C211yesmaximal, characteristic, complemented
8C11×#543—24no—
9C11×#543—22no—
10C11×#543C2214yes—
11C2×C11×C22⋊Q8—22no—
12C2×C11×C22⋊Q8—21no—
13C2×C11×C22⋊Q8—22no—
14C2×C11×C22⋊Q8C2212yes—
15C2×C11×#121C2211yescharacteristic
16C2×C11×#120—21no—
17C22×C11×C22⋊C4—21no—
18C22×C11×C22⋊C4C2211yescharacteristic
19C11×#483C2214yescomplemented
20C11×#481—22no—
21C11×#465—24no—
22C11×#450C2214yescomplemented
23C11×#448—22no—
24C2×C11×C22⋊C8C2212yes—
25C11×#397C2212yes—
26C11×#394—22no—
27C11×#392C2212yes—
28C11×#386—21no—
29C11×#380C2211yescharacteristic
30C11×#328C2218yescomplemented
31C11×#323C2214yes—
32C25×C11D411yescharacteristic
33C22×Q8×C11—21no—
34C22×Q8×C11D412yescomplemented
35C22×D4×C11—21no—
36C22×D4×C11—22no—
37C22×D4×C11C2311yescharacteristic
38C23×C4×C11—21no—
39C23×C4×C11—21no—
40C23×C4×C11D411yescharacteristic
41C23×C4×C11C2311yescharacteristic
42C2×C11×SD16—24no—
43C22×C8×C11—22no—
44C11×C22⋊Q8—28no—
45C11×C22⋊Q8—28no—
46C11×C22⋊Q8—24no—
47C11×C22⋊Q8—28no—
48C11×C22⋊Q8—24no—
49C11×C22⋊Q8—22no—
50C11×C22⋊Q8—22no—
51C11×C22⋊Q8—28no—
52C11×C22⋊Q8D414yescomplemented
53C11×C22⋊Q8C2314yes—
54C11×#121—22no—
55C11×#121—22no—
56C11×#120—44no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4—22no—
59C2×C11×C4⋊C4—22no—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4D412yescomplemented
62C2×C11×C4⋊C4C2311yescharacteristic
63C2×C11×C22⋊C4—22no—
64C2×C11×C22⋊C4—24no—
65C2×C11×C22⋊C4—22no—
66C2×C11×C22⋊C4—24no—
67C2×C11×C22⋊C4—22no—
68C2×C11×C22⋊C4—22no—
69C2×C11×C22⋊C4—21no—
70C2×C11×C22⋊C4—22no—
71C2×C11×C22⋊C4—21no—
72C2×C11×C22⋊C4—22no—
73C2×C11×C22⋊C4D412yes—
74C2×C11×C22⋊C4C2312yes—
75C11×#106—24no—
76C11×#103—24no—
77C11×#102—24no—
78C11×C22⋊C8—22no—
79C11×C22⋊C8C2314yes—
80C11×#95—22no—
81C11×#95C2312yes—
82#18286C1111yesmaximal, characteristic, direct product factor, Sylow
83C24×C11—21no—
84C24×C11—21no—
85C24×C11—22no—
86C24×C11—21no—
87C24×C11—81no—
88C24×C11—81no—
89C24×C11SD1614yescomplemented
90C24×C11C2×D412yes—
91C24×C11C2×D411yescharacteristic
92C2×Q8×C11—24no—
93C2×Q8×C11—22no—
94C2×Q8×C11—82no—
95C2×Q8×C11—82no—
96C2×Q8×C11C2×D414yes—
97C2×D4×C11—22no—
98C2×D4×C11—41no—
99C2×D4×C11—41no—
100C2×D4×C11—44no—
101C2×D4×C11—42no—
102C2×D4×C11—42no—
103C2×D4×C11—81no—
104C2×D4×C11—82no—
105C2×D4×C11—82no—
106C22×C4×C11—22no—
107C22×C4×C11—21no—
108C22×C4×C11—22no—
109C22×C4×C11—24no—
110C22×C4×C11—24no—
111C22×C4×C11—21no—
112C22×C4×C11—21no—
113C22×C4×C11—22no—
114C22×C4×C11—81no—
115C22×C4×C11—81no—
116C22×C4×C11—82no—
117C22×C4×C11—82no—
118C22×C4×C11C2×D412yes—
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2×D412yes—
121C22×C4×C11C2×D412yes—
122C22×C4×C11C2411yescharacteristic
123C11×SD16—84no—
124C2×C8×C11—24no—
125C2×C8×C11—82no—
126C11×C4⋊C4—24no—
127C11×C4⋊C4—28no—
128C11×C4⋊C4—24no—
129C11×C4⋊C4—22no—
130C11×C4⋊C4—24no—
131C11×C4⋊C4—22no—
132C11×C4⋊C4—81no—
133C11×C4⋊C4C2×D414yes—
134C11×C22⋊C4—28no—
135C11×C22⋊C4—24no—
136C11×C22⋊C4—24no—
137C11×C22⋊C4—24no—
138C11×C22⋊C4—24no—
139C11×C22⋊C4—44no—
140C11×C22⋊C4—42no—
141C11×C22⋊C4—42no—
142C11×C22⋊C4—82no—
143C2×#543C2×C1111yescharacteristic, complemented
144#3187C2×C1112yescomplemented
145#2617C2×C1111yescharacteristic
146#1608C2×C1114yescomplemented
147#1596C2×C1114yescomplemented
148#1520C2×C1112yescomplemented
149C2×#323C2×C1111yescharacteristic, complemented
150C23×C11—22no—
151C23×C11—24no—
152C23×C11—22no—
153C23×C11—24no—
154C23×C11—41no—
155C23×C11—41no—
156C23×C11—42no—
157C23×C11—42no—
158C23×C11—42no—
159C23×C11—42no—
160C23×C11—42no—
161C23×C11—42no—
162C23×C11—41no—
163C23×C11—41no—
164C23×C11—41no—
165C23×C11—81no—
166C23×C11—81no—
167C23×C11—84no—
168C23×C11—84no—
169C23×C11#12011yescharacteristic
170C23×C11#12011yescharacteristic
171C23×C11C2×SD1614yes—
172C23×C11C2×SD1612yes—
173C23×C11#13712yes—
174C23×C11C22×D411yescharacteristic
175Q8×C11—44no—
176Q8×C11—82no—
177Q8×C11—84no—
178D4×C11—44no—
179D4×C11—88no—
180D4×C11—82no—
181D4×C11—82no—
182C2×C4×C11—24no—
183C2×C4×C11—22no—
184C2×C4×C11—24no—
185C2×C4×C11—41no—
186C2×C4×C11—42no—
187C2×C4×C11—42no—
188C2×C4×C11—41no—
189C2×C4×C11—42no—
190C2×C4×C11—44no—
191C2×C4×C11—44no—
192C2×C4×C11—42no—
193C2×C4×C11—42no—
194C2×C4×C11—42no—
195C2×C4×C11—41no—
196C2×C4×C11—42no—
197C2×C4×C11—41no—
198C2×C4×C11—41no—
199C2×C4×C11—81no—
200C2×C4×C11—84no—
201C2×C4×C11—84no—
202C2×C4×C11#12012yes—
203C2×C4×C11C22×D412yes—
204C8×C11—44no—
205#543—24no—
206#543—22no—
207#543C22×C1114yes—
208C2×C22⋊Q8—22no—
209C2×C22⋊Q8—21no—
210C2×C22⋊Q8—22no—
211C2×C22⋊Q8C22×C1112yes—
212C2×#121C22×C1111yescharacteristic
213C2×#120—21no—
214C22×C22⋊C4—21no—
215C22×C22⋊C4C22×C1111yescharacteristic
216#483C22×C1114yescomplemented
217#481—22no—
218#465—24no—
219#450C22×C1114yescomplemented
220#448—22no—
221C2×C22⋊C8C22×C1112yes—
222#397C22×C1112yes—
223#394—22no—
224#392C22×C1112yes—
225#386—21no—
226#380C22×C1111yescharacteristic
227#328C22×C1118yescomplemented
228#323C22×C1114yes—
229C22×C11—21no—
230C22×C11—21no—
231C22×C11—21no—
232C22×C11—21no—
233C22×C11—21no—
234C22×C11—21no—
235C22×C11—24no—
236C22×C11—42no—
237C22×C11—42no—
238C22×C11—44no—
239C22×C11—48no—
240C22×C11—42no—
241C22×C11—42no—
242C22×C11—82no—
243C22×C11—84no—
244C22×C11—82no—
245C22×C11—82no—
246C22×C11—81no—
247C22×C11—81no—
248C22×C11—81no—
249C22×C11#44812yes—
250C22×C11#44812yes—
251C22×C11C2×#12011yescharacteristic
252C22×C11C22×SD1611yescharacteristic
253C22×C11C2×#13711yescharacteristic
254C4×C11—22no—
255C4×C11—22no—
256C4×C11—42no—
257C4×C11—44no—
258C4×C11—44no—
259C4×C11—82no—
260C4×C11—81no—
261C25D4×C1111yescharacteristic
262C22×Q8—21no—
263C22×Q8D4×C1112yescomplemented
264C22×D4—21no—
265C22×D4—22no—
266C22×D4C23×C1111yescharacteristic
267C23×C4—21no—
268C23×C4—21no—
269C23×C4D4×C1111yescharacteristic
270C23×C4C23×C1111yescharacteristic
271C2×SD16—24no—
272C22×C8—22no—
273C22⋊Q8—28no—
274C22⋊Q8—28no—
275C22⋊Q8—24no—
276C22⋊Q8—28no—
277C22⋊Q8—24no—
278C22⋊Q8—22no—
279C22⋊Q8—22no—
280C22⋊Q8—28no—
281C22⋊Q8D4×C1114yescomplemented
282C22⋊Q8C23×C1114yes—
283#121—22no—
284#121—22no—
285#120—44no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4D4×C1112yescomplemented
291C2×C4⋊C4C23×C1111yescharacteristic
292C2×C22⋊C4—22no—
293C2×C22⋊C4—24no—
294C2×C22⋊C4—22no—
295C2×C22⋊C4—24no—
296C2×C22⋊C4—22no—
297C2×C22⋊C4—22no—
298C2×C22⋊C4—21no—
299C2×C22⋊C4—22no—
300C2×C22⋊C4—21no—
301C2×C22⋊C4—22no—
302C2×C22⋊C4D4×C1112yes—
303C2×C22⋊C4C23×C1112yes—
304#106—24no—
305#103—24no—
306#102—24no—
307C22⋊C8—22no—
308C22⋊C8C23×C1114yes—
309#95—22no—
310#95C23×C1112yes—
311C2×C11—21no—
312C2×C11—22no—
313C2×C11—21no—
314C2×C11—22no—
315C2×C11—44no—
316C2×C11—161no—
317C2×C11C2×#44811yescharacteristic
318C2×C11#301911yescharacteristic
319C2×C11#302611yescharacteristic
320C24—21no—
321C24—21no—
322C24—22no—
323C24—21no—
324C24—81no—
325C24—81no—
326C24C11×SD1614yescomplemented
327C24C2×D4×C1112yes—
328C24C2×D4×C1111yescharacteristic
329C2×Q8—24no—
330C2×Q8—22no—
331C2×Q8—82no—
332C2×Q8—82no—
333C2×Q8C2×D4×C1114yes—
334C2×D4—22no—
335C2×D4—41no—
336C2×D4—41no—
337C2×D4—44no—
338C2×D4—42no—
339C2×D4—42no—
340C2×D4—81no—
341C2×D4—82no—
342C2×D4—82no—
343C22×C4—22no—
344C22×C4—21no—
345C22×C4—22no—
346C22×C4—24no—
347C22×C4—24no—
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—22no—
351C22×C4—81no—
352C22×C4—81no—
353C22×C4—82no—
354C22×C4—82no—
355C22×C4C2×D4×C1112yes—
356C22×C4C2×D4×C1111yescharacteristic
357C22×C4C2×D4×C1112yes—
358C22×C4C2×D4×C1112yes—
359C22×C4C24×C1111yescharacteristic
360SD16—84no—
361C2×C8—24no—
362C2×C8—82no—
363C4⋊C4—24no—
364C4⋊C4—28no—
365C4⋊C4—24no—
366C4⋊C4—22no—
367C4⋊C4—24no—
368C4⋊C4—22no—
369C4⋊C4—81no—
370C4⋊C4C2×D4×C1114yes—
371C22⋊C4—28no—
372C22⋊C4—24no—
373C22⋊C4—24no—
374C22⋊C4—24no—
375C22⋊C4—24no—
376C22⋊C4—44no—
377C22⋊C4—42no—
378C22⋊C4—42no—
379C22⋊C4—82no—
380C11#1828611yescharacteristic, direct product factor, Sylow
381C23—22no—
382C23—24no—
383C23—22no—
384C23—24no—
385C23—41no—
386C23—41no—
387C23—42no—
388C23—42no—
389C23—42no—
390C23—42no—
391C23—42no—
392C23—42no—
393C23—41no—
394C23—41no—
395C23—41no—
396C23—81no—
397C23—81no—
398C23—84no—
399C23—84no—
400C23C11×#12011yescharacteristic
401C23C11×#12011yescharacteristic
402C23C2×C11×SD1614yes—
403C23C2×C11×SD1612yes—
404C23C11×#13712yes—
405C23C22×D4×C1111yescharacteristic
406Q8—44no—
407Q8—82no—
408Q8—84no—
409D4—44no—
410D4—88no—
411D4—82no—
412D4—82no—
413C2×C4—24no—
414C2×C4—22no—
415C2×C4—24no—
416C2×C4—41no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4—41no—
420C2×C4—42no—
421C2×C4—44no—
422C2×C4—44no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—41no—
427C2×C4—42no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—81no—
431C2×C4—84no—
432C2×C4—84no—
433C2×C4C11×#12012yes—
434C2×C4C22×D4×C1112yes—
435C8—44no—
436C22—21no—
437C22—21no—
438C22—21no—
439C22—21no—
440C22—21no—
441C22—21no—
442C22—24no—
443C22—42no—
444C22—42no—
445C22—44no—
446C22—48no—
447C22—42no—
448C22—42no—
449C22—82no—
450C22—84no—
451C22—82no—
452C22—82no—
453C22—81no—
454C22—81no—
455C22—81no—
456C22C11×#44812yes—
457C22C11×#44812yes—
458C22C2×C11×#12011yescharacteristic
459C22C22×C11×SD1611yescharacteristic
460C22C2×C11×#13711yescharacteristic
461C4—22no—
462C4—22no—
463C4—42no—
464C4—44no—
465C4—44no—
466C4—82no—
467C4—81no—
468C2—21no—
469C2—22no—
470C2—21no—
471C2—22no—
472C2—44no—
473C2—161no—
474C2C2×C11×#44811yescharacteristic
475C2C11×#301911yescharacteristic
476C2C11×#302611yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#2617C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×C11×#543C2semidirect
2. C11×#3187C2semidirect
4. C11×#1608C2semidirect
5. C11×#1596C2semidirect
6. C11×#1520C2semidirect
7. C2×C11×#323C2semidirect
19. C11×#483C22semidirect
22. C11×#450C22semidirect
30. C11×#328C22semidirect
34. C22×Q8×C11D4semidirect
52. C11×C22⋊Q8D4semidirect
61. C2×C11×C4⋊C4D4semidirect
82. #18286C11direct (N × H)
89. C24×C11SD16semidirect
143. C2×#543C2×C11semidirect
144. #3187C2×C11semidirect
146. #1608C2×C11semidirect
147. #1596C2×C11semidirect
148. #1520C2×C11semidirect
149. C2×#323C2×C11semidirect
216. #483C22×C11semidirect
219. #450C22×C11semidirect
227. #328C22×C11semidirect
263. C22×Q8D4×C11semidirect
281. C22⋊Q8D4×C11semidirect
290. C2×C4⋊C4D4×C11semidirect
326. C24C11×SD16semidirect
380. C11#18286direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5432
C11×#31872
C11×#26172
C11×#16082
C11×#15962
C11×#15202
C2×C11×#3232
#1828611