Finite Group Databasebeta

← C11×#24301 #14601494

Subgroups — C11×#24301 #14601494

Order 2816.

1294 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×C4⋊Q8C211yesmaximal, characteristic
2C2×C11×#475C212yesmaximal, complemented
3C4×C11×C22⋊Q8C211yesmaximal, characteristic
4C11×#2058C212yesmaximal, complemented
5C11×#2024C212yesmaximal, complemented
6C11×#1988C212yesmaximal, complemented
7C11×#1872C212yesmaximal
8C11×#1853C212yesmaximal
9C11×#1797C211yesmaximal, characteristic
10C23×Q8×C11—21no—
11C2×C11×C4⋊Q8—28no—
12C2×C11×C4⋊Q8—21no—
13C2×C11×C4⋊Q8—21no—
14C2×C11×C4⋊Q8C2212yes—
15C2×C11×C4⋊Q8C2212yes—
16C2×C11×C22⋊Q8C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C22×C11×C4⋊C4—21no—
19C22×C11×C4⋊C4C2212yes—
20C22×C42×C11C2211yescharacteristic
21C11×#475—28no—
22C2×C11×#106C2214yes—
23C2×C11×C4⋊C8C2212yes—
24C2×C11×#103C2214yes—
25C2×C11×C22⋊C8C2212yes—
26C11×#391C2211yescharacteristic
27C11×#389C2211yescharacteristic
28C11×#387—21no—
29C11×#385—21no—
30C11×#380C2211yescharacteristic
31C4×C11×C4⋊C4—21no—
32C4×C11×C4⋊C4C2211yescharacteristic
33C4×C11×C22⋊C4—21no—
34C11×#340C2214yes—
35C11×#340C2214yes—
36C11×#336C2212yes—
37C22×Q8×C11—28no—
38C22×Q8×C11—22no—
39C22×Q8×C11—22no—
40C22×Q8×C11—44no—
41C22×Q8×C11—44no—
42C22×Q8×C11C2311yescharacteristic
43C23×C4×C11—22no—
44C23×C4×C11D411yescharacteristic
45C23×C4×C11D411yescharacteristic
46C23×C4×C11C2311yescharacteristic
47C22×C8×C11C2314yes—
48C11×C4⋊Q8—28no—
49C11×C4⋊Q8—28no—
50C11×C4⋊Q8—28no—
51C11×C4⋊Q8—24no—
52C11×C4⋊Q8D418yes—
53C11×C22⋊Q8—22no—
54C11×C22⋊Q8Q814yescomplemented
55C4×Q8×C11—24no—
56C2×C11×C4⋊C4—28no—
57C2×C11×C4⋊C4—22no—
58C2×C11×C4⋊C4—22no—
59C2×C11×C4⋊C4—22no—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4—28no—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4C2311yescharacteristic
65C2×C11×C4⋊C4C2311yescharacteristic
66C2×C11×C4⋊C4C2314yes—
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C22⋊C4—21no—
69C2×C11×C22⋊C4—21no—
70C2×C42×C11—24no—
71C2×C42×C11—21no—
72C2×C42×C11—21no—
73C2×C42×C11D411yescharacteristic
74C2×C42×C11D411yescharacteristic
75C2×C42×C11C2311yescharacteristic
76C2×C42×C11C2311yescharacteristic
77C11×#106—28no—
78C11×C4⋊C8—24no—
79C11×#103—28no—
80C11×C22⋊C8—24no—
81C11×#95—21no—
82C11×#95—21no—
83C11×#95—21no—
84C11×#95—21no—
85C11×#95—21no—
86#24301C1111yesmaximal, characteristic, direct product factor, Sylow
87C24×C11C2×D411yescharacteristic
88C2×Q8×C11—28no—
89C2×Q8×C11—28no—
90C2×Q8×C11—21no—
91C2×Q8×C11—22no—
92C2×Q8×C11—22no—
93C2×Q8×C11—44no—
94C2×Q8×C11—432no—
95C2×Q8×C11—44no—
96C2×Q8×C11—44no—
97C2×Q8×C11—44no—
98C2×Q8×C11C2×Q812yescomplemented
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—22no—
106C22×C4×C11—28no—
107C22×C4×C11—21no—
108C22×C4×C11—21no—
109C22×C4×C11—24no—
110C22×C4×C11—21no—
111C22×C4×C11—21no—
112C22×C4×C11—44no—
113C22×C4×C11—44no—
114C22×C4×C11SD1614yes—
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2×Q812yes—
121C22×C4×C11#4112yes—
122C22×C4×C11C2411yescharacteristic
123C2×C8×C11—24no—
124C2×C8×C11—24no—
125C2×C8×C11—24no—
126C11×C4⋊C4—28no—
127C11×C4⋊C4—28no—
128C11×C4⋊C4—28no—
129C11×C4⋊C4—24no—
130C11×C4⋊C4—24no—
131C11×C4⋊C4—21no—
132C11×C4⋊C4—22no—
133C11×C4⋊C4—22no—
134C11×C4⋊C4—42no—
135C11×C4⋊C4—42no—
136C11×C4⋊C4C2×D418yes—
137C11×C4⋊C4C2×Q812yescomplemented
138C11×C22⋊C4—24no—
139C11×C22⋊C4—42no—
140C42×C11—22no—
141C42×C11—22no—
142C42×C11—22no—
143C42×C11—42no—
144C42×C11—42no—
145C42×C11C2×D414yes—
146C22×C4⋊Q8C2×C1111yescharacteristic
147C2×#475C2×C1112yescomplemented
148C4×C22⋊Q8C2×C1111yescharacteristic
149#2058C2×C1112yescomplemented
150#2024C2×C1112yescomplemented
151#1988C2×C1112yescomplemented
152#1872C2×C1112yes—
153#1853C2×C1112yes—
154#1797C2×C1111yescharacteristic
155C23×C11—21no—
156C23×C11—21no—
157C23×C11—21no—
158C23×C11—21no—
159C23×C11C22⋊Q812yes—
160C23×C11C2×SD1612yes—
161C23×C11#13712yes—
162C23×C11C22×D411yescharacteristic
163Q8×C11—24no—
164Q8×C11—416no—
165Q8×C11—42no—
166Q8×C11—416no—
167C2×C4×C11—28no—
168C2×C4×C11—21no—
169C2×C4×C11—21no—
170C2×C4×C11—21no—
171C2×C4×C11—21no—
172C2×C4×C11—21no—
173C2×C4×C11—21no—
174C2×C4×C11—21no—
175C2×C4×C11—21no—
176C2×C4×C11—24no—
177C2×C4×C11—24no—
178C2×C4×C11—28no—
179C2×C4×C11—28no—
180C2×C4×C11—22no—
181C2×C4×C11—22no—
182C2×C4×C11—416no—
183C2×C4×C11—41no—
184C2×C4×C11—41no—
185C2×C4×C11—44no—
186C2×C4×C11—41no—
187C2×C4×C11—44no—
188C2×C4×C11—41no—
189C2×C4×C11—41no—
190C2×C4×C11—41no—
191C2×C4×C11—41no—
192C2×C4×C11—41no—
193C2×C4×C11—41no—
194C2×C4×C11—41no—
195C2×C4×C11#12012yes—
196C2×C4×C11#12012yes—
197C2×C4×C11C22⋊Q812yes—
198C2×C4×C11C2×SD1612yes—
199C2×C4×C11C2×SD1612yes—
200C2×C4×C11AGL(1,ℤ/8)12yes—
201C2×C4×C11#13712yes—
202C2×C4×C11C22×D412yes—
203C2×C4×C11C22×Q811yescharacteristic
204C2×C4×C11C2×#4111yescharacteristic
205C2×C4×C112−1+412yes—
206C8×C11—44no—
207C23×Q8—21no—
208C2×C4⋊Q8—28no—
209C2×C4⋊Q8—21no—
210C2×C4⋊Q8—21no—
211C2×C4⋊Q8C22×C1112yes—
212C2×C4⋊Q8C22×C1112yes—
213C2×C22⋊Q8C22×C1111yescharacteristic
214C2×C4×Q8C22×C1111yescharacteristic
215C22×C4⋊C4—21no—
216C22×C4⋊C4C22×C1112yes—
217C22×C42C22×C1111yescharacteristic
218#475—28no—
219C2×#106C22×C1114yes—
220C2×C4⋊C8C22×C1112yes—
221C2×#103C22×C1114yes—
222C2×C22⋊C8C22×C1112yes—
223#391C22×C1111yescharacteristic
224#389C22×C1111yescharacteristic
225#387—21no—
226#385—21no—
227#380C22×C1111yescharacteristic
228C4×C4⋊C4—21no—
229C4×C4⋊C4C22×C1111yescharacteristic
230C4×C22⋊C4—21no—
231#340C22×C1114yes—
232#340C22×C1114yes—
233#336C22×C1112yes—
234C22×C11—22no—
235C22×C11—22no—
236C22×C11—22no—
237C22×C11—22no—
238C22×C11—22no—
239C22×C11—22no—
240C22×C11#47514yescomplemented
241C22×C11C2×#12011yescharacteristic
242C22×C11C2×C22⋊Q811yescharacteristic
243C22×C11#53611yescharacteristic
244C22×C11C22×SD1611yescharacteristic
245C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
246C22×C11C2×#13711yescharacteristic
247C22×C11C2×#13711yescharacteristic
248C4×C11—22no—
249C4×C11—22no—
250C4×C11—22no—
251C4×C11—22no—
252C4×C11—42no—
253C4×C11—42no—
254C4×C11—48no—
255C4×C11—81no—
256C4×C11—81no—
257C4×C11#45014yes—
258C4×C11#54812yes—
259C4×C11D4×Q812yes—
260C22×Q8—28no—
261C22×Q8—22no—
262C22×Q8—22no—
263C22×Q8—44no—
264C22×Q8—44no—
265C22×Q8C23×C1111yescharacteristic
266C23×C4—22no—
267C23×C4D4×C1111yescharacteristic
268C23×C4D4×C1111yescharacteristic
269C23×C4C23×C1111yescharacteristic
270C22×C8C23×C1114yes—
271C4⋊Q8—28no—
272C4⋊Q8—28no—
273C4⋊Q8—28no—
274C4⋊Q8—24no—
275C4⋊Q8D4×C1118yes—
276C22⋊Q8—22no—
277C22⋊Q8Q8×C1114yescomplemented
278C4×Q8—24no—
279C2×C4⋊C4—28no—
280C2×C4⋊C4—22no—
281C2×C4⋊C4—22no—
282C2×C4⋊C4—22no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—28no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4C23×C1111yescharacteristic
288C2×C4⋊C4C23×C1111yescharacteristic
289C2×C4⋊C4C23×C1114yes—
290C2×C4⋊C4C23×C1111yescharacteristic
291C2×C22⋊C4—21no—
292C2×C22⋊C4—21no—
293C2×C42—24no—
294C2×C42—21no—
295C2×C42—21no—
296C2×C42D4×C1111yescharacteristic
297C2×C42D4×C1111yescharacteristic
298C2×C42C23×C1111yescharacteristic
299C2×C42C23×C1111yescharacteristic
300#106—28no—
301C4⋊C8—24no—
302#103—28no—
303C22⋊C8—24no—
304#95—21no—
305#95—21no—
306#95—21no—
307#95—21no—
308#95—21no—
309C2×C11—24no—
310C2×C11#240911yescharacteristic
311C2×C11C2×#45011yescharacteristic
312C2×C11#300411yescharacteristic
313C2×C11C2×#47511yescharacteristic
314C2×C11#307911yescharacteristic
315C2×C11#322911yescharacteristic
316C2×C11#323911yescharacteristic
317C24C2×D4×C1111yescharacteristic
318C2×Q8—28no—
319C2×Q8—28no—
320C2×Q8—21no—
321C2×Q8—22no—
322C2×Q8—22no—
323C2×Q8—44no—
324C2×Q8—432no—
325C2×Q8—44no—
326C2×Q8—44no—
327C2×Q8—44no—
328C2×Q8C2×Q8×C1112yescomplemented
329C22×C4—22no—
330C22×C4—22no—
331C22×C4—22no—
332C22×C4—22no—
333C22×C4—22no—
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—28no—
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—24no—
340C22×C4—21no—
341C22×C4—21no—
342C22×C4—44no—
343C22×C4—44no—
344C22×C4C11×SD1614yes—
345C22×C4C2×D4×C1111yescharacteristic
346C22×C4C2×D4×C1111yescharacteristic
347C22×C4C2×D4×C1111yescharacteristic
348C22×C4C2×D4×C1111yescharacteristic
349C22×C4C2×D4×C1111yescharacteristic
350C22×C4C2×Q8×C1112yes—
351C22×C4C11×#4112yes—
352C22×C4C24×C1111yescharacteristic
353C2×C8—24no—
354C2×C8—24no—
355C2×C8—24no—
356C4⋊C4—28no—
357C4⋊C4—28no—
358C4⋊C4—28no—
359C4⋊C4—24no—
360C4⋊C4—24no—
361C4⋊C4—21no—
362C4⋊C4—22no—
363C4⋊C4—22no—
364C4⋊C4—42no—
365C4⋊C4—42no—
366C4⋊C4C2×D4×C1118yes—
367C4⋊C4C2×Q8×C1112yescomplemented
368C22⋊C4—24no—
369C22⋊C4—42no—
370C42—22no—
371C42—22no—
372C42—22no—
373C42—42no—
374C42—42no—
375C42C2×D4×C1114yes—
376C11#2430111yescharacteristic, direct product factor, Sylow
377C23—21no—
378C23—21no—
379C23—21no—
380C23—21no—
381C23C11×C22⋊Q812yes—
382C23C2×C11×SD1612yes—
383C23C11×#13712yes—
384C23C22×D4×C1111yescharacteristic
385Q8—24no—
386Q8—416no—
387Q8—42no—
388Q8—416no—
389C2×C4—28no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—24no—
399C2×C4—24no—
400C2×C4—28no—
401C2×C4—28no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—416no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—44no—
408C2×C4—41no—
409C2×C4—44no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4C11×#12012yes—
418C2×C4C11×#12012yes—
419C2×C4C11×C22⋊Q812yes—
420C2×C4C2×C11×SD1612yes—
421C2×C4C2×C11×SD1612yes—
422C2×C4C11×AGL(1,ℤ/8)12yes—
423C2×C4C11×#13712yes—
424C2×C4C22×D4×C1112yes—
425C2×C4C22×Q8×C1111yescharacteristic
426C2×C4C2×C11×#4111yescharacteristic
427C2×C4C11×2−1+412yes—
428C8—44no—
429C22—22no—
430C22—22no—
431C22—22no—
432C22—22no—
433C22—22no—
434C22—22no—
435C22C11×#47514yescomplemented
436C22C2×C11×#12011yescharacteristic
437C22C2×C11×C22⋊Q811yescharacteristic
438C22C11×#53611yescharacteristic
439C22C22×C11×SD1611yescharacteristic
440C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
441C22C2×C11×#13711yescharacteristic
442C22C2×C11×#13711yescharacteristic
443C4—22no—
444C4—22no—
445C4—22no—
446C4—22no—
447C4—42no—
448C4—48no—
449C4—42no—
450C4—81no—
451C4—81no—
452C4C11×#45014yes—
453C4C11×#54812yes—
454C4D4×Q8×C1112yes—
455C2—24no—
456C2C11×#240911yescharacteristic
457C2C2×C11×#45011yescharacteristic
458C2C11×#300411yescharacteristic
459C2C2×C11×#47511yescharacteristic
460C2C11×#307911yescharacteristic
461C2C11×#322911yescharacteristic
462C2C11×#323911yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC24×C11C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#475C2semidirect
4. C11×#2058C2semidirect
5. C11×#2024C2semidirect
6. C11×#1988C2semidirect
54. C11×C22⋊Q8Q8semidirect
86. #24301C11direct (N × H)
98. C2×Q8×C11C2×Q8semidirect
137. C11×C4⋊C4C2×Q8semidirect
147. C2×#475C2×C11semidirect
149. #2058C2×C11semidirect
150. #2024C2×C11semidirect
151. #1988C2×C11semidirect
240. C22×C11#475semidirect
277. C22⋊Q8Q8×C11semidirect
328. C2×Q8C2×Q8×C11semidirect
367. C4⋊C4C2×Q8×C11semidirect
376. C11#24301direct (N × H)
435. C22C11×#475semidirect

Maximal subgroups

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

subgroupindex
C22×C11×C4⋊Q82
C2×C11×#4752
C4×C11×C22⋊Q82
C11×#20582
C11×#20242
C11×#19882
C11×#18722
C11×#18532
C11×#17972
#2430111