Finite Group Databasebeta

← C11×#24318 #14601511

Subgroups — C11×#24318 #14601511

Order 2816.

1014 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3501C211yesmaximal, characteristic
2C11×#3078C212yesmaximal, complemented
3C11×#2326C211yesmaximal, characteristic
4C11×#2060C212yesmaximal, complemented
5C11×#2028C212yesmaximal, complemented
6C11×#1995C212yesmaximal, complemented
7C11×#1885C212yesmaximal
8C11×#1856C212yesmaximal
9C11×#1800C211yesmaximal, characteristic
10C11×#554—22no—
11C11×#554—24no—
12D4×Q8×C11—22no—
13C11×#544C2212yes—
14C11×#543—22no—
15C11×#533C2212yes—
16C2×C11×#124C2211yescharacteristic
17C2×C11×C22⋊Q8—22no—
18C11×#518C2212yes—
19C2×C4×Q8×C11C2211yescharacteristic
20C2×C4×D4×C11C2211yescharacteristic
21C11×#479—24no—
22C11×#477—22no—
23C11×#475—22no—
24C11×#428C2214yes—
25C11×#423C2212yes—
26C11×#419C2214yes—
27C2×C11×#100C2212yes—
28C11×#391C2211yescharacteristic
29C11×#390C2211yescharacteristic
30C11×#388—22no—
31C11×#385—22no—
32C11×#384C2211yescharacteristic
33C11×#376C2211yescharacteristic
34C11×#343C2212yes—
35C11×#339C2214yes—
36C11×#339C2214yes—
37C22×Q8×C11—22no—
38C22×Q8×C11C2311yescharacteristic
39C22×D4×C11C2311yescharacteristic
40C23×C4×C11D412yes—
41C2×C11×M16C2314yes—
42C11×C4⋊Q8—24no—
43C11×C4⋊Q8D412yes—
44C11×C4⋊Q8D412yes—
45C11×#125—24no—
46C11×#125D414yes—
47C11×#124—22no—
48C11×#124Q814yescomplemented
49C11×C22⋊Q8—24no—
50C11×C22⋊Q8—24no—
51C11×C22⋊Q8—28no—
52C11×C22⋊Q8—28no—
53C11×C22⋊Q8—22no—
54C11×C22⋊Q8—24no—
55C11×C22⋊Q8—22no—
56C4×Q8×C11—22no—
57C4×Q8×C11—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—
64C11×#117C2314yes—
65C2×C11×C4⋊C4—22no—
66C2×C11×C4⋊C4—24no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4—22no—
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C22⋊C4—24no—
72C2×C11×C22⋊C4—22no—
73C2×C11×C22⋊C4—22no—
74C2×C11×C22⋊C4D412yes—
75C2×C42×C11—21no—
76C2×C42×C11C2311yescharacteristic
77C2×C42×C11C2311yescharacteristic
78C2×C42×C11C2311yescharacteristic
79C11×#107—24no—
80C11×#106—24no—
81C11×C4⋊C8—22no—
82C11×C4⋊C8—22no—
83C11×#103—24no—
84C11×#103—24no—
85C11×#100—24no—
86C11×#95—21no—
87C11×#95—21no—
88C11×#95—22no—
89#24318C1111yesmaximal, characteristic, direct product factor, Sylow
90C24×C11C2×D412yes—
91C2×Q8×C11—24no—
92C2×Q8×C11—22no—
93C2×Q8×C11—22no—
94C2×Q8×C11—21no—
95C2×Q8×C11—22no—
96C2×Q8×C11—22no—
97C2×Q8×C11—84no—
98C2×Q8×C11C2×Q812yescomplemented
99C2×D4×C11—22no—
100C2×D4×C11—22no—
101C2×D4×C11C2×Q812yes—
102C2×D4×C11#4112yes—
103C22×C4×C11—21no—
104C22×C4×C11—21no—
105C22×C4×C11—24no—
106C22×C4×C11—24no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—21no—
110C22×C4×C11—21no—
111C22×C4×C11—82no—
112C22×C4×C11C2×D412yes—
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2411yescharacteristic
116C11×M16—24no—
117C11×M16—24no—
118C2×C8×C11—24no—
119C11×C4⋊C4—24no—
120C11×C4⋊C4—28no—
121C11×C4⋊C4—24no—
122C11×C4⋊C4—22no—
123C11×C4⋊C4—24no—
124C11×C4⋊C4—22no—
125C11×C4⋊C4—22no—
126C11×C4⋊C4—22no—
127C11×C4⋊C4—41no—
128C11×C4⋊C4—41no—
129C11×C4⋊C4—82no—
130C11×C4⋊C4C2×D414yes—
131C11×C4⋊C4C2×D414yes—
132C11×C22⋊C4—28no—
133C11×C22⋊C4—28no—
134C11×C22⋊C4—24no—
135C11×C22⋊C4—24no—
136C11×C22⋊C4—82no—
137C42×C11—24no—
138C42×C11—21no—
139C42×C11—22no—
140C42×C11—42no—
141C42×C11C2×D412yes—
142C42×C11C2×D412yes—
143C42×C11C2×Q812yescomplemented
144#3501C2×C1111yescharacteristic
145#3078C2×C1112yescomplemented
146#2326C2×C1111yescharacteristic
147#2060C2×C1112yescomplemented
148#2028C2×C1112yescomplemented
149#1995C2×C1112yescomplemented
150#1885C2×C1112yes—
151#1856C2×C1112yes—
152#1800C2×C1111yescharacteristic
153C23×C11—22no—
154C23×C11—22no—
155C23×C11—42no—
156C23×C11—42no—
157C23×C11C22⋊Q814yes—
158C23×C11C22×D411yescharacteristic
159Q8×C11—24no—
160Q8×C11—44no—
161Q8×C11—42no—
162Q8×C11—82no—
163Q8×C11—84no—
164D4×C11—24no—
165D4×C11—24no—
166C2×C4×C11—24no—
167C2×C4×C11—24no—
168C2×C4×C11—22no—
169C2×C4×C11—22no—
170C2×C4×C11—22no—
171C2×C4×C11—41no—
172C2×C4×C11—41no—
173C2×C4×C11—44no—
174C2×C4×C11—41no—
175C2×C4×C11—41no—
176C2×C4×C11—41no—
177C2×C4×C11—41no—
178C2×C4×C11—42no—
179C2×C4×C11—41no—
180C2×C4×C11—42no—
181C2×C4×C11—41no—
182C2×C4×C11—41no—
183C2×C4×C11—41no—
184C2×C4×C11—82no—
185C2×C4×C11—84no—
186C2×C4×C11—84no—
187C2×C4×C11#12012yes—
188C2×C4×C11#12011yescharacteristic
189C2×C4×C11#12011yescharacteristic
190C2×C4×C11C22×D412yes—
191C2×C4×C11C22×Q811yescharacteristic
192C2×C4×C11C2×#4111yescharacteristic
193C2×C4×C112−1+412yes—
194C8×C11—44no—
195#554—22no—
196#554—24no—
197D4×Q8—22no—
198#544C22×C1112yes—
199#543—22no—
200#533C22×C1112yes—
201C2×#124C22×C1111yescharacteristic
202C2×C22⋊Q8—22no—
203#518C22×C1112yes—
204C2×C4×Q8C22×C1111yescharacteristic
205C2×C4×D4C22×C1111yescharacteristic
206#479—24no—
207#477—22no—
208#475—22no—
209#428C22×C1114yes—
210#423C22×C1112yes—
211#419C22×C1114yes—
212C2×#100C22×C1112yes—
213#391C22×C1111yescharacteristic
214#390C22×C1111yescharacteristic
215#388—22no—
216#385—22no—
217#384C22×C1111yescharacteristic
218#376C22×C1111yescharacteristic
219#343C22×C1112yes—
220#339C22×C1114yes—
221#339C22×C1114yes—
222C22×C11—21no—
223C22×C11—21no—
224C22×C11—24no—
225C22×C11—44no—
226C22×C11—42no—
227C22×C11—42no—
228C22×C11—82no—
229C22×C11C2×#12011yescharacteristic
230C22×C11C2×C22⋊Q811yescharacteristic
231C22×C11#53611yescharacteristic
232C4×C11—21no—
233C4×C11—21no—
234C4×C11—22no—
235C4×C11—42no—
236C4×C11—42no—
237C4×C11—42no—
238C4×C11—44no—
239C4×C11—44no—
240C4×C11—81no—
241C4×C11—81no—
242C4×C11#54812yes—
243C4×C11D4×Q812yes—
244C22×Q8—22no—
245C22×Q8C23×C1111yescharacteristic
246C22×D4C23×C1111yescharacteristic
247C23×C4D4×C1112yes—
248C2×M16C23×C1114yes—
249C4⋊Q8—24no—
250C4⋊Q8D4×C1112yes—
251C4⋊Q8D4×C1112yes—
252#125—24no—
253#125D4×C1114yes—
254#124—22no—
255#124Q8×C1114yescomplemented
256C22⋊Q8—24no—
257C22⋊Q8—24no—
258C22⋊Q8—28no—
259C22⋊Q8—28no—
260C22⋊Q8—22no—
261C22⋊Q8—24no—
262C22⋊Q8—22no—
263C4×Q8—22no—
264C4×Q8—22no—
265C4×Q8—22no—
266C4×Q8—22no—
267C4×D4—24no—
268C4×D4—24no—
269C4×D4—22no—
270C4×D4—22no—
271#117C23×C1114yes—
272C2×C4⋊C4—22no—
273C2×C4⋊C4—24no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—22no—
276C2×C4⋊C4C23×C1111yescharacteristic
277C2×C4⋊C4C23×C1111yescharacteristic
278C2×C22⋊C4—24no—
279C2×C22⋊C4—22no—
280C2×C22⋊C4—22no—
281C2×C22⋊C4D4×C1112yes—
282C2×C42—21no—
283C2×C42C23×C1111yescharacteristic
284C2×C42C23×C1111yescharacteristic
285C2×C42C23×C1111yescharacteristic
286#107—24no—
287#106—24no—
288C4⋊C8—22no—
289C4⋊C8—22no—
290#103—24no—
291#103—24no—
292#100—24no—
293#95—21no—
294#95—21no—
295#95—22no—
296C2×C11—21no—
297C2×C11—21no—
298C2×C11—44no—
299C2×C11#240911yescharacteristic
300C2×C11#301911yescharacteristic
301C2×C11#302211yescharacteristic
302C24C2×D4×C1112yes—
303C2×Q8—24no—
304C2×Q8—22no—
305C2×Q8—22no—
306C2×Q8—21no—
307C2×Q8—22no—
308C2×Q8—22no—
309C2×Q8—84no—
310C2×Q8C2×Q8×C1112yescomplemented
311C2×D4—22no—
312C2×D4—22no—
313C2×D4C2×Q8×C1112yes—
314C2×D4C11×#4112yes—
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—24no—
318C22×C4—24no—
319C22×C4—22no—
320C22×C4—22no—
321C22×C4—21no—
322C22×C4—21no—
323C22×C4—82no—
324C22×C4C2×D4×C1112yes—
325C22×C4C2×D4×C1111yescharacteristic
326C22×C4C2×D4×C1111yescharacteristic
327C22×C4C24×C1111yescharacteristic
328M16—24no—
329M16—24no—
330C2×C8—24no—
331C4⋊C4—24no—
332C4⋊C4—28no—
333C4⋊C4—24no—
334C4⋊C4—22no—
335C4⋊C4—24no—
336C4⋊C4—22no—
337C4⋊C4—22no—
338C4⋊C4—22no—
339C4⋊C4—41no—
340C4⋊C4—41no—
341C4⋊C4—82no—
342C4⋊C4C2×D4×C1114yes—
343C4⋊C4C2×D4×C1114yes—
344C22⋊C4—28no—
345C22⋊C4—28no—
346C22⋊C4—24no—
347C22⋊C4—24no—
348C22⋊C4—82no—
349C42—24no—
350C42—21no—
351C42—22no—
352C42—42no—
353C42C2×D4×C1112yes—
354C42C2×D4×C1112yes—
355C42C2×Q8×C1112yescomplemented
356C11#2431811yescharacteristic, direct product factor, Sylow
357C23—22no—
358C23—22no—
359C23—42no—
360C23—42no—
361C23C11×C22⋊Q814yes—
362C23C22×D4×C1111yescharacteristic
363Q8—24no—
364Q8—44no—
365Q8—42no—
366Q8—82no—
367Q8—84no—
368D4—24no—
369D4—24no—
370C2×C4—24no—
371C2×C4—24no—
372C2×C4—22no—
373C2×C4—22no—
374C2×C4—22no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—44no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—42no—
383C2×C4—41no—
384C2×C4—42no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—82no—
389C2×C4—84no—
390C2×C4—84no—
391C2×C4C11×#12012yes—
392C2×C4C11×#12011yescharacteristic
393C2×C4C11×#12011yescharacteristic
394C2×C4C22×D4×C1112yes—
395C2×C4C22×Q8×C1111yescharacteristic
396C2×C4C2×C11×#4111yescharacteristic
397C2×C4C11×2−1+412yes—
398C8—44no—
399C22—21no—
400C22—21no—
401C22—24no—
402C22—44no—
403C22—42no—
404C22—42no—
405C22—82no—
406C22C2×C11×#12011yescharacteristic
407C22C2×C11×C22⋊Q811yescharacteristic
408C22C11×#53611yescharacteristic
409C4—21no—
410C4—21no—
411C4—22no—
412C4—42no—
413C4—42no—
414C4—42no—
415C4—44no—
416C4—44no—
417C4—81no—
418C4—81no—
419C4C11×#54812yes—
420C4D4×Q8×C1112yes—
421C2—21no—
422C2—21no—
423C2—44no—
424C2C11×#240911yescharacteristic
425C2C11×#301911yescharacteristic
426C2C11×#302211yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11C23
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
2. C11×#3078C2semidirect
4. C11×#2060C2semidirect
5. C11×#2028C2semidirect
6. C11×#1995C2semidirect
48. C11×#124Q8semidirect
89. #24318C11direct (N × H)
98. C2×Q8×C11C2×Q8semidirect
143. C42×C11C2×Q8semidirect
145. #3078C2×C11semidirect
147. #2060C2×C11semidirect
148. #2028C2×C11semidirect
149. #1995C2×C11semidirect
255. #124Q8×C11semidirect
310. C2×Q8C2×Q8×C11semidirect
355. C42C2×Q8×C11semidirect
356. C11#24318direct (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×#30782
C11×#23262
C11×#20602
C11×#20282
C11×#19952
C11×#18852
C11×#18562
C11×#18002
#2431811