Finite Group Databasebeta

← C11×#24312 #14601505

Subgroups — C11×#24312 #14601505

Order 2816.

1170 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3501C211yesmaximal, characteristic, complemented
2C11×#3077C212yesmaximal, complemented
3C4×C11×#127C211yesmaximal, characteristic
4C11×#2060C212yesmaximal, complemented
5C11×#2027C212yesmaximal, complemented
6C11×#1994C212yesmaximal, complemented
7C11×#1887C212yesmaximal
8C11×#1856C212yesmaximal, complemented
9C11×#1800C211yesmaximal, characteristic, complemented
10C11×#554—22no—
11C11×#554—24no—
12D4×Q8×C11—22no—
13C11×#544C2212yes—
14C11×#543—22no—
15C11×#533C2212yes—
16C2×C11×#127C2211yescharacteristic
17C2×C11×C22⋊Q8—22no—
18C11×#518C2212yes—
19C2×C4×D4×C11—22no—
20C2×C4×D4×C11C2211yescharacteristic
21C2×C4×D4×C11C2211yescharacteristic
22C11×#478—24no—
23C11×#476—22no—
24C11×#474—22no—
25C11×#428C2214yes—
26C11×#423C2212yes—
27C11×#418C2214yes—
28C2×C11×#100C2212yes—
29C11×#390—22no—
30C11×#390C2211yescharacteristic
31C11×#390C2211yescharacteristic
32C11×#384C2211yescharacteristic
33C43×C11C2211yescharacteristic
34C11×#343C2212yes—
35C11×#339C2214yes—
36C11×#339C2214yes—
37C22×Q8×C11—22no—
38C22×D4×C11—22no—
39C22×D4×C11C2311yescharacteristic
40C22×D4×C11C2311yescharacteristic
41C23×C4×C11—21no—
42C23×C4×C11D412yes—
43C2×C11×M16C2314yes—
44C11×C4⋊Q8—24no—
45C11×C4⋊Q8D412yescomplemented
46C11×C4⋊Q8D412yescomplemented
47C11×#127—22no—
48C11×#127Q814yescomplemented
49C11×#125—24no—
50C11×#125D414yescomplemented
51C11×C22⋊Q8—24no—
52C11×C22⋊Q8—24no—
53C11×C22⋊Q8—28no—
54C11×C22⋊Q8—28no—
55C11×C22⋊Q8—22no—
56C11×C22⋊Q8—24no—
57C11×C22⋊Q8—22no—
58C4×Q8×C11—22no—
59C4×Q8×C11—22no—
60C4×D4×C11—24no—
61C4×D4×C11—24no—
62C4×D4×C11—22no—
63C4×D4×C11—22no—
64C4×D4×C11—22no—
65C4×D4×C11—22no—
66C4×D4×C11—48no—
67C11×#117C2314yes—
68C2×C11×C4⋊C4—22no—
69C2×C11×C4⋊C4—24no—
70C2×C11×C4⋊C4—22no—
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C22⋊C4—24no—
74C2×C11×C22⋊C4—22no—
75C2×C11×C22⋊C4—22no—
76C2×C11×C22⋊C4—21no—
77C2×C11×C22⋊C4D412yes—
78C2×C42×C11—21no—
79C2×C42×C11—21no—
80C2×C42×C11C2311yescharacteristic
81C2×C42×C11C2311yescharacteristic
82C2×C42×C11C2311yescharacteristic
83C11×#107—24no—
84C11×#106—24no—
85C11×C4⋊C8—22no—
86C11×C4⋊C8—22no—
87C11×#102—24no—
88C11×#102—24no—
89C11×#100—24no—
90#24312C1111yesmaximal, characteristic, direct product factor, Sylow
91C24×C11—21no—
92C24×C11C2×D412yes—
93C2×Q8×C11—24no—
94C2×Q8×C11—22no—
95C2×Q8×C11—22no—
96C2×Q8×C11—84no—
97C2×D4×C11—28no—
98C2×D4×C11—22no—
99C2×D4×C11—22no—
100C2×D4×C11—21no—
101C2×D4×C11—22no—
102C2×D4×C11—22no—
103C2×D4×C11—44no—
104C2×D4×C11—44no—
105C2×D4×C11C2×Q812yes—
106C2×D4×C11C2×Q812yescomplemented
107C2×D4×C11#4112yes—
108C22×C4×C11—21no—
109C22×C4×C11—21no—
110C22×C4×C11—24no—
111C22×C4×C11—24no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—21no—
115C22×C4×C11—44no—
116C22×C4×C11—44no—
117C22×C4×C11—41no—
118C22×C4×C11—41no—
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2×D412yes—
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2411yescharacteristic
123C11×M16—24no—
124C11×M16—24no—
125C2×C8×C11—24no—
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—22no—
133C11×C4⋊C4—22no—
134C11×C4⋊C4—44no—
135C11×C4⋊C4C2×D414yes—
136C11×C4⋊C4C2×D414yes—
137C11×C22⋊C4—28no—
138C11×C22⋊C4—24no—
139C11×C22⋊C4—24no—
140C11×C22⋊C4—44no—
141C11×C22⋊C4—44no—
142C11×C22⋊C4—42no—
143C42×C11—24no—
144C42×C11—24no—
145C42×C11—21no—
146C42×C11—22no—
147C42×C11—42no—
148C42×C11C2×D412yes—
149C42×C11C2×D412yes—
150C42×C11C2×Q812yescomplemented
151#3501C2×C1111yescharacteristic, complemented
152#3077C2×C1112yescomplemented
153C4×#127C2×C1111yescharacteristic
154#2060C2×C1112yescomplemented
155#2027C2×C1112yescomplemented
156#1994C2×C1112yescomplemented
157#1887C2×C1112yes—
158#1856C2×C1112yescomplemented
159#1800C2×C1111yescharacteristic, complemented
160C23×C11—22no—
161C23×C11—22no—
162C23×C11—22no—
163C23×C11—42no—
164C23×C11—42no—
165C23×C11—42no—
166C23×C11—42no—
167C23×C11—41no—
168C23×C11—41no—
169C23×C11C22⋊Q814yes—
170C23×C11C22×D411yescharacteristic
171Q8×C11—44no—
172Q8×C11—82no—
173Q8×C11—84no—
174D4×C11—24no—
175D4×C11—24no—
176D4×C11—24no—
177D4×C11—416no—
178D4×C11—42no—
179C2×C4×C11—22no—
180C2×C4×C11—22no—
181C2×C4×C11—22no—
182C2×C4×C11—22no—
183C2×C4×C11—22no—
184C2×C4×C11—24no—
185C2×C4×C11—24no—
186C2×C4×C11—22no—
187C2×C4×C11—41no—
188C2×C4×C11—41no—
189C2×C4×C11—41no—
190C2×C4×C11—44no—
191C2×C4×C11—42no—
192C2×C4×C11—42no—
193C2×C4×C11—41no—
194C2×C4×C11—82no—
195C2×C4×C11—82no—
196C2×C4×C11—84no—
197C2×C4×C11—84no—
198C2×C4×C11—82no—
199C2×C4×C11#12012yes—
200C2×C4×C11#12011yescharacteristic
201C2×C4×C11#12011yescharacteristic
202C2×C4×C11C22×D412yes—
203C2×C4×C11C22×Q811yescharacteristic
204C2×C4×C11C2×#4111yescharacteristic
205C2×C4×C112−1+412yes—
206C8×C11—44no—
207#554—22no—
208#554—24no—
209D4×Q8—22no—
210#544C22×C1112yes—
211#543—22no—
212#533C22×C1112yes—
213C2×#127C22×C1111yescharacteristic
214C2×C22⋊Q8—22no—
215#518C22×C1112yes—
216C2×C4×D4—22no—
217C2×C4×D4C22×C1111yescharacteristic
218C2×C4×D4C22×C1111yescharacteristic
219#478—24no—
220#476—22no—
221#474—22no—
222#428C22×C1114yes—
223#423C22×C1112yes—
224#418C22×C1114yes—
225C2×#100C22×C1112yes—
226#390—22no—
227#390C22×C1111yescharacteristic
228#390C22×C1111yescharacteristic
229#384C22×C1111yescharacteristic
230C43C22×C1111yescharacteristic
231#343C22×C1112yes—
232#339C22×C1114yes—
233#339C22×C1114yes—
234C22×C11—21no—
235C22×C11—21no—
236C22×C11—24no—
237C22×C11—44no—
238C22×C11—44no—
239C22×C11—42no—
240C22×C11—42no—
241C22×C11—42no—
242C22×C11—82no—
243C22×C11—82no—
244C22×C11—81no—
245C22×C11—81no—
246C22×C11C2×#12011yescharacteristic
247C22×C11C2×C22⋊Q811yescharacteristic
248C22×C11#53611yescharacteristic
249C4×C11—24no—
250C4×C11—21no—
251C4×C11—22no—
252C4×C11—42no—
253C4×C11—42no—
254C4×C11—44no—
255C4×C11—44no—
256C4×C11—81no—
257C4×C11#45312yes—
258C4×C11#54812yes—
259C4×C11D4×Q812yes—
260C22×Q8—22no—
261C22×D4—22no—
262C22×D4C23×C1111yescharacteristic
263C22×D4C23×C1111yescharacteristic
264C23×C4—21no—
265C23×C4D4×C1112yes—
266C2×M16C23×C1114yes—
267C4⋊Q8—24no—
268C4⋊Q8D4×C1112yescomplemented
269C4⋊Q8D4×C1112yescomplemented
270#127—22no—
271#127Q8×C1114yescomplemented
272#125—24no—
273#125D4×C1114yescomplemented
274C22⋊Q8—24no—
275C22⋊Q8—24no—
276C22⋊Q8—28no—
277C22⋊Q8—28no—
278C22⋊Q8—22no—
279C22⋊Q8—24no—
280C22⋊Q8—22no—
281C4×Q8—22no—
282C4×Q8—22no—
283C4×D4—24no—
284C4×D4—24no—
285C4×D4—22no—
286C4×D4—22no—
287C4×D4—22no—
288C4×D4—22no—
289C4×D4—48no—
290#117C23×C1114yes—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4C23×C1111yescharacteristic
295C2×C4⋊C4C23×C1111yescharacteristic
296C2×C22⋊C4—24no—
297C2×C22⋊C4—22no—
298C2×C22⋊C4—22no—
299C2×C22⋊C4—21no—
300C2×C22⋊C4D4×C1112yes—
301C2×C42—21no—
302C2×C42—21no—
303C2×C42C23×C1111yescharacteristic
304C2×C42C23×C1111yescharacteristic
305C2×C42C23×C1111yescharacteristic
306#107—24no—
307#106—24no—
308C4⋊C8—22no—
309C4⋊C8—22no—
310#102—24no—
311#102—24no—
312#100—24no—
313C2×C11—21no—
314C2×C11—21no—
315C2×C11—44no—
316C2×C11—82no—
317C2×C11#240911yescharacteristic
318C2×C11C2×#45311yescharacteristic
319C2×C11#301811yescharacteristic
320C24—21no—
321C24C2×D4×C1112yes—
322C2×Q8—24no—
323C2×Q8—22no—
324C2×Q8—22no—
325C2×Q8—84no—
326C2×D4—28no—
327C2×D4—22no—
328C2×D4—22no—
329C2×D4—21no—
330C2×D4—22no—
331C2×D4—22no—
332C2×D4—44no—
333C2×D4—44no—
334C2×D4C2×Q8×C1112yes—
335C2×D4C2×Q8×C1112yescomplemented
336C2×D4C11×#4112yes—
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—24no—
340C22×C4—24no—
341C22×C4—22no—
342C22×C4—22no—
343C22×C4—21no—
344C22×C4—44no—
345C22×C4—44no—
346C22×C4—41no—
347C22×C4—41no—
348C22×C4C2×D4×C1111yescharacteristic
349C22×C4C2×D4×C1112yes—
350C22×C4C2×D4×C1111yescharacteristic
351C22×C4C24×C1111yescharacteristic
352M16—24no—
353M16—24no—
354C2×C8—24no—
355C4⋊C4—24no—
356C4⋊C4—28no—
357C4⋊C4—24no—
358C4⋊C4—22no—
359C4⋊C4—24no—
360C4⋊C4—22no—
361C4⋊C4—22no—
362C4⋊C4—22no—
363C4⋊C4—44no—
364C4⋊C4C2×D4×C1114yes—
365C4⋊C4C2×D4×C1114yes—
366C22⋊C4—28no—
367C22⋊C4—24no—
368C22⋊C4—24no—
369C22⋊C4—44no—
370C22⋊C4—44no—
371C22⋊C4—42no—
372C42—24no—
373C42—24no—
374C42—21no—
375C42—22no—
376C42—42no—
377C42C2×D4×C1112yes—
378C42C2×D4×C1112yes—
379C42C2×Q8×C1112yescomplemented
380C11#2431211yescharacteristic, direct product factor, Sylow
381C23—22no—
382C23—22no—
383C23—22no—
384C23—42no—
385C23—42no—
386C23—42no—
387C23—42no—
388C23—41no—
389C23—41no—
390C23C11×C22⋊Q814yes—
391C23C22×D4×C1111yescharacteristic
392Q8—44no—
393Q8—82no—
394Q8—84no—
395D4—24no—
396D4—24no—
397D4—24no—
398D4—416no—
399D4—42no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—24no—
406C2×C4—24no—
407C2×C4—22no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—44no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—41no—
415C2×C4—82no—
416C2×C4—82no—
417C2×C4—84no—
418C2×C4—84no—
419C2×C4—82no—
420C2×C4C11×#12012yes—
421C2×C4C11×#12011yescharacteristic
422C2×C4C11×#12011yescharacteristic
423C2×C4C22×D4×C1112yes—
424C2×C4C22×Q8×C1111yescharacteristic
425C2×C4C2×C11×#4111yescharacteristic
426C2×C4C11×2−1+412yes—
427C8—44no—
428C22—21no—
429C22—21no—
430C22—24no—
431C22—44no—
432C22—44no—
433C22—42no—
434C22—42no—
435C22—42no—
436C22—82no—
437C22—82no—
438C22—81no—
439C22—81no—
440C22C2×C11×#12011yescharacteristic
441C22C2×C11×C22⋊Q811yescharacteristic
442C22C11×#53611yescharacteristic
443C4—24no—
444C4—21no—
445C4—22no—
446C4—42no—
447C4—42no—
448C4—44no—
449C4—44no—
450C4—81no—
451C4C11×#45312yes—
452C4C11×#54812yes—
453C4D4×Q8×C1112yes—
454C2—21no—
455C2—21no—
456C2—44no—
457C2—82no—
458C2C11×#240911yescharacteristic
459C2C2×C11×#45311yescharacteristic
460C2C11×#301811yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#127C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3501C2semidirect
2. C11×#3077C2semidirect
4. C11×#2060C2semidirect
5. C11×#2027C2semidirect
6. C11×#1994C2semidirect
8. C11×#1856C2semidirect
9. C11×#1800C2semidirect
45. C11×C4⋊Q8D4semidirect
46. C11×C4⋊Q8D4semidirect
48. C11×#127Q8semidirect
50. C11×#125D4semidirect
90. #24312C11direct (N × H)
106. C2×D4×C11C2×Q8semidirect
150. C42×C11C2×Q8semidirect
151. #3501C2×C11semidirect
152. #3077C2×C11semidirect
154. #2060C2×C11semidirect
155. #2027C2×C11semidirect
156. #1994C2×C11semidirect
158. #1856C2×C11semidirect
159. #1800C2×C11semidirect
268. C4⋊Q8D4×C11semidirect
269. C4⋊Q8D4×C11semidirect
271. #127Q8×C11semidirect
273. #125D4×C11semidirect
335. C2×D4C2×Q8×C11semidirect
379. C42C2×Q8×C11semidirect
380. C11#24312direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35012
C11×#30772
C4×C11×#1272
C11×#20602
C11×#20272
C11×#19942
C11×#18872
C11×#18562
C11×#18002
#2431211