Finite Group Databasebeta

← C11×#18292 #14595485

Subgroups — C11×#18292 #14595485

Order 2816.

1282 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#537C211yesmaximal, characteristic, complemented
2C11×#3186C212yesmaximal, complemented
3C11×#2618C211yesmaximal, characteristic, complemented
4C11×#1610C214yesmaximal, complemented
5C11×#1598C214yesmaximal, complemented
6C11×#1519C212yesmaximal, complemented
7C2×C11×#324C211yesmaximal, characteristic, complemented
8C22×C11×#41—21no—
9C11×#537—24no—
10C11×#537—22no—
11C11×#537C2214yes—
12C2×C11×#123—21no—
13C2×C11×C22⋊Q8—22no—
14C2×C11×#121—22no—
15C2×C11×#121—21no—
16C2×C11×#121C2212yes—
17C2×C11×#121C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C11×#480—22no—
20C11×#480C2214yescomplemented
21C11×#466—24no—
22C11×#447—22no—
23C11×#447C2214yescomplemented
24C2×C11×C22⋊C8C2212yes—
25C11×#398C2212yescomplemented
26C11×#396—22no—
27C11×#394C2212yescomplemented
28C11×#386—21no—
29C11×#380C2211yescharacteristic
30C11×#327C2218yescomplemented
31C11×#324C2214yescomplemented
32C2×C11×#41—24no—
33C2×C11×#41—24no—
34C2×C11×#41—44no—
35C2×C11×#41—44no—
36C22×Q8×C11—21no—
37C22×D4×C11—21no—
38C22×D4×C11—22no—
39C22×D4×C11—21no—
40C22×D4×C11—21no—
41C22×D4×C11D412yes—
42C22×D4×C11C2311yescharacteristic
43C23×C4×C11—22no—
44C23×C4×C11D411yescharacteristic
45C23×C4×C11D411yescharacteristic
46C23×C4×C11C2311yescharacteristic
47C2×C11×D8—24no—
48C22×C8×C11—22no—
49C11×#123—44no—
50C11×C22⋊Q8—28no—
51C11×C22⋊Q8—28no—
52C11×#121—24no—
53C11×#121—28no—
54C11×#121—28no—
55C11×#121—24no—
56C11×#121—22no—
57C11×#121—22no—
58C11×#121—22no—
59C11×#121—22no—
60C11×#121D414yes—
61C11×#121C2314yes—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4—22no—
64C2×C11×C4⋊C4—22no—
65C2×C11×C4⋊C4—22no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4D412yes—
68C2×C11×C4⋊C4D412yes—
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2312yes—
71C2×C11×C22⋊C4—22no—
72C2×C11×C22⋊C4—22no—
73C2×C11×C22⋊C4—21no—
74C2×C11×C22⋊C4—21no—
75C2×C11×C22⋊C4—22no—
76C2×C11×C22⋊C4—22no—
77C11×#107—24no—
78C11×#102—24no—
79C11×#102—24no—
80C11×C22⋊C8—22no—
81C11×C22⋊C8C2314yes—
82C11×#95—22no—
83C11×#95C2312yes—
84#18292C1111yesmaximal, characteristic, direct product factor, Sylow
85C24×C11—22no—
86C24×C11—21no—
87C24×C11C2×D411yescharacteristic
88C11×#41—48no—
89C11×#41—416no—
90C11×#41—48no—
91C2×Q8×C11—24no—
92C2×Q8×C11—44no—
93C2×D4×C11—24no—
94C2×D4×C11—24no—
95C2×D4×C11—24no—
96C2×D4×C11—24no—
97C2×D4×C11—22no—
98C2×D4×C11—22no—
99C2×D4×C11—44no—
100C2×D4×C11—44no—
101C2×D4×C11—44no—
102C2×D4×C11—41no—
103C2×D4×C11—41no—
104C2×D4×C11—42no—
105C2×D4×C11—42no—
106C2×D4×C11—81no—
107C2×D4×C11—82no—
108C2×D4×C11—82no—
109C2×D4×C11C2×D414yes—
110C22×C4×C11—21no—
111C22×C4×C11—21no—
112C22×C4×C11—22no—
113C22×C4×C11—28no—
114C22×C4×C11—21no—
115C22×C4×C11—22no—
116C22×C4×C11—21no—
117C22×C4×C11—21no—
118C22×C4×C11—22no—
119C22×C4×C11—48no—
120C22×C4×C11—81no—
121C22×C4×C11—81no—
122C22×C4×C11D814yescomplemented
123C22×C4×C11C2×D412yes—
124C22×C4×C11C2×D412yes—
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D412yes—
127C22×C4×C11C2×D412yes—
128C22×C4×C11C2411yescharacteristic
129C11×D8—84no—
130C2×C8×C11—24no—
131C2×C8×C11—82no—
132C11×C4⋊C4—24no—
133C11×C4⋊C4—24no—
134C11×C4⋊C4—22no—
135C11×C4⋊C4—24no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—44no—
138C11×C4⋊C4—81no—
139C11×C4⋊C4C2×D414yes—
140C11×C22⋊C4—28no—
141C11×C22⋊C4—24no—
142C11×C22⋊C4—24no—
143C11×C22⋊C4—42no—
144C11×C22⋊C4—42no—
145C11×C22⋊C4—44no—
146C11×C22⋊C4—82no—
147C2×#537C2×C1111yescharacteristic, complemented
148#3186C2×C1112yescomplemented
149#2618C2×C1111yescharacteristic, complemented
150#1610C2×C1114yescomplemented
151#1598C2×C1114yescomplemented
152#1519C2×C1112yescomplemented
153C2×#324C2×C1111yescharacteristic, complemented
154C23×C11—24no—
155C23×C11—41no—
156C23×C11—41no—
157C23×C11—44no—
158C23×C11—44no—
159C23×C11—42no—
160C23×C11—42no—
161C23×C11—44no—
162C23×C11—41no—
163C23×C11—41no—
164C23×C11—41no—
165C23×C11#12011yescharacteristic
166C23×C11#12011yescharacteristic
167C23×C11C2×D812yes—
168C23×C11AGL(1,ℤ/8)12yes—
169C23×C11C22×D411yescharacteristic
170Q8×C11—48no—
171D4×C11—44no—
172D4×C11—48no—
173D4×C11—44no—
174D4×C11—44no—
175D4×C11—44no—
176D4×C11—48no—
177D4×C11—82no—
178D4×C11—84no—
179D4×C11—82no—
180D4×C11—82no—
181C2×C4×C11—22no—
182C2×C4×C11—22no—
183C2×C4×C11—24no—
184C2×C4×C11—24no—
185C2×C4×C11—22no—
186C2×C4×C11—24no—
187C2×C4×C11—41no—
188C2×C4×C11—42no—
189C2×C4×C11—42no—
190C2×C4×C11—41no—
191C2×C4×C11—416no—
192C2×C4×C11—42no—
193C2×C4×C11—44no—
194C2×C4×C11—42no—
195C2×C4×C11—42no—
196C2×C4×C11—42no—
197C2×C4×C11—41no—
198C2×C4×C11—42no—
199C2×C4×C11—41no—
200C2×C4×C11—41no—
201C2×C4×C11—81no—
202C2×C4×C11#12012yes—
203C2×C4×C11C2×D814yes—
204C2×C4×C11C22×D412yes—
205C8×C11—44no—
206C22×#41—21no—
207#537—24no—
208#537—22no—
209#537C22×C1114yes—
210C2×#123—21no—
211C2×C22⋊Q8—22no—
212C2×#121—22no—
213C2×#121—21no—
214C2×#121C22×C1112yes—
215C2×#121C22×C1111yescharacteristic
216C22×C4⋊C4C22×C1111yescharacteristic
217#480—22no—
218#480C22×C1114yescomplemented
219#466—24no—
220#447—22no—
221#447C22×C1114yescomplemented
222C2×C22⋊C8C22×C1112yes—
223#398C22×C1112yescomplemented
224#396—22no—
225#394C22×C1112yescomplemented
226#386—21no—
227#380C22×C1111yescharacteristic
228#327C22×C1118yescomplemented
229#324C22×C1114yescomplemented
230C22×C11—21no—
231C22×C11—21no—
232C22×C11—21no—
233C22×C11—21no—
234C22×C11—21no—
235C22×C11—21no—
236C22×C11—42no—
237C22×C11—42no—
238C22×C11—44no—
239C22×C11—44no—
240C22×C11—44no—
241C22×C11—88no—
242C22×C11—82no—
243C22×C11—82no—
244C22×C11—81no—
245C22×C11—81no—
246C22×C11—81no—
247C22×C11#44712yes—
248C22×C11#44712yes—
249C22×C11C2×#12011yescharacteristic
250C22×C11C22×D811yescharacteristic
251C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
252C4×C11—24no—
253C4×C11—22no—
254C4×C11—22no—
255C4×C11—44no—
256C4×C11—42no—
257C4×C11—82no—
258C4×C11—81no—
259C2×#41—24no—
260C2×#41—24no—
261C2×#41—44no—
262C2×#41—44no—
263C22×Q8—21no—
264C22×D4—21no—
265C22×D4—22no—
266C22×D4—21no—
267C22×D4—21no—
268C22×D4D4×C1112yes—
269C22×D4C23×C1111yescharacteristic
270C23×C4—22no—
271C23×C4D4×C1111yescharacteristic
272C23×C4D4×C1111yescharacteristic
273C23×C4C23×C1111yescharacteristic
274C2×D8—24no—
275C22×C8—22no—
276#123—44no—
277C22⋊Q8—28no—
278C22⋊Q8—28no—
279#121—24no—
280#121—28no—
281#121—28no—
282#121—24no—
283#121—22no—
284#121—22no—
285#121—22no—
286#121—22no—
287#121D4×C1114yes—
288#121C23×C1114yes—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4D4×C1112yes—
295C2×C4⋊C4D4×C1112yes—
296C2×C4⋊C4C23×C1111yescharacteristic
297C2×C4⋊C4C23×C1112yes—
298C2×C22⋊C4—22no—
299C2×C22⋊C4—22no—
300C2×C22⋊C4—21no—
301C2×C22⋊C4—21no—
302C2×C22⋊C4—22no—
303C2×C22⋊C4—22no—
304#107—24no—
305#102—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—84no—
316C2×C11—161no—
317C2×C11C2×#44711yescharacteristic
318C2×C11#302011yescharacteristic
319C2×C11#302611yescharacteristic
320C24—22no—
321C24—21no—
322C24C2×D4×C1111yescharacteristic
323#41—48no—
324#41—416no—
325#41—48no—
326C2×Q8—24no—
327C2×Q8—44no—
328C2×D4—24no—
329C2×D4—24no—
330C2×D4—24no—
331C2×D4—24no—
332C2×D4—22no—
333C2×D4—22no—
334C2×D4—44no—
335C2×D4—44no—
336C2×D4—44no—
337C2×D4—41no—
338C2×D4—41no—
339C2×D4—42no—
340C2×D4—42no—
341C2×D4—81no—
342C2×D4—82no—
343C2×D4—82no—
344C2×D4C2×D4×C1114yes—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—22no—
348C22×C4—28no—
349C22×C4—21no—
350C22×C4—22no—
351C22×C4—21no—
352C22×C4—21no—
353C22×C4—22no—
354C22×C4—48no—
355C22×C4—81no—
356C22×C4—81no—
357C22×C4C11×D814yescomplemented
358C22×C4C2×D4×C1112yes—
359C22×C4C2×D4×C1112yes—
360C22×C4C2×D4×C1111yescharacteristic
361C22×C4C2×D4×C1112yes—
362C22×C4C2×D4×C1112yes—
363C22×C4C24×C1111yescharacteristic
364D8—84no—
365C2×C8—24no—
366C2×C8—82no—
367C4⋊C4—24no—
368C4⋊C4—24no—
369C4⋊C4—22no—
370C4⋊C4—24no—
371C4⋊C4—22no—
372C4⋊C4—44no—
373C4⋊C4—81no—
374C4⋊C4C2×D4×C1114yes—
375C22⋊C4—28no—
376C22⋊C4—24no—
377C22⋊C4—24no—
378C22⋊C4—42no—
379C22⋊C4—42no—
380C22⋊C4—44no—
381C22⋊C4—82no—
382C11#1829211yescharacteristic, direct product factor, Sylow
383C23—24no—
384C23—41no—
385C23—41no—
386C23—44no—
387C23—44no—
388C23—42no—
389C23—42no—
390C23—44no—
391C23—41no—
392C23—41no—
393C23—41no—
394C23C11×#12011yescharacteristic
395C23C11×#12011yescharacteristic
396C23C2×C11×D812yes—
397C23C11×AGL(1,ℤ/8)12yes—
398C23C22×D4×C1111yescharacteristic
399Q8—48no—
400D4—44no—
401D4—48no—
402D4—44no—
403D4—44no—
404D4—44no—
405D4—48no—
406D4—82no—
407D4—84no—
408D4—82no—
409D4—82no—
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—24no—
413C2×C4—24no—
414C2×C4—22no—
415C2×C4—24no—
416C2×C4—41no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4—41no—
420C2×C4—416no—
421C2×C4—42no—
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×C4C11×#12012yes—
432C2×C4C2×C11×D814yes—
433C2×C4C22×D4×C1112yes—
434C8—44no—
435C22—21no—
436C22—21no—
437C22—21no—
438C22—21no—
439C22—21no—
440C22—21no—
441C22—42no—
442C22—42no—
443C22—44no—
444C22—44no—
445C22—44no—
446C22—88no—
447C22—82no—
448C22—82no—
449C22—81no—
450C22—81no—
451C22—81no—
452C22C11×#44712yes—
453C22C11×#44712yes—
454C22C2×C11×#12011yescharacteristic
455C22C22×C11×D811yescharacteristic
456C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
457C4—24no—
458C4—22no—
459C4—22no—
460C4—44no—
461C4—42no—
462C4—82no—
463C4—81no—
464C2—21no—
465C2—22no—
466C2—21no—
467C2—22no—
468C2—84no—
469C2—161no—
470C2C2×C11×#44711yescharacteristic
471C2C11×#302011yescharacteristic
472C2C11×#302611yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
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×#537C2semidirect
2. C11×#3186C2semidirect
3. C11×#2618C2semidirect
4. C11×#1610C2semidirect
5. C11×#1598C2semidirect
6. C11×#1519C2semidirect
7. C2×C11×#324C2semidirect
20. C11×#480C22semidirect
23. C11×#447C22semidirect
25. C11×#398C22semidirect
27. C11×#394C22semidirect
30. C11×#327C22semidirect
31. C11×#324C22semidirect
84. #18292C11direct (N × H)
122. C22×C4×C11D8semidirect
147. C2×#537C2×C11semidirect
148. #3186C2×C11semidirect
149. #2618C2×C11semidirect
150. #1610C2×C11semidirect
151. #1598C2×C11semidirect
152. #1519C2×C11semidirect
153. C2×#324C2×C11semidirect
218. #480C22×C11semidirect
221. #447C22×C11semidirect
223. #398C22×C11semidirect
225. #394C22×C11semidirect
228. #327C22×C11semidirect
229. #324C22×C11semidirect
357. C22×C4C11×D8semidirect
382. C11#18292direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5372
C11×#31862
C11×#26182
C11×#16102
C11×#15982
C11×#15192
C2×C11×#3242
#1829211