Finite Group Databasebeta

← C11×#24313 #14601506

Subgroups — C11×#24313 #14601506

Order 2816.

998 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3502C211yesmaximal, characteristic, complemented
2C11×#3077C212yesmaximal
3C4×C11×#124C211yesmaximal, characteristic
4C11×#2061C212yesmaximal, complemented
5C11×#2027C212yesmaximal
6C11×#1994C212yesmaximal, complemented
7C11×#1888C212yesmaximal
8C11×#1857C212yesmaximal, complemented
9C11×#1801C211yesmaximal, characteristic, complemented
10Q82×C11—22no—
11C11×#557—22no—
12C11×#557—24no—
13C11×#544—22no—
14C11×#544C2212yes—
15C11×#533—22no—
16C11×#533C2212yes—
17C2×C11×#124C2211yescharacteristic
18C11×#519C2212yes—
19C2×C4×Q8×C11C2211yescharacteristic
20C2×C4×D4×C11C2211yescharacteristic
21C11×#478—24no—
22C11×#476—22no—
23C11×#474—22no—
24C11×#428C2214yes—
25C11×#423C2212yes—
26C11×#418C2214yes—
27C2×C11×#101C2212yes—
28C11×#391C2211yescharacteristic
29C11×#390C2211yescharacteristic
30C11×#388—22no—
31C11×#382C2211yescharacteristic
32C4×C11×C22⋊C4—22no—
33C43×C11C2211yescharacteristic
34C11×#343C2212yes—
35C11×#339C2214yes—
36C11×#339C2214yes—
37C22×Q8×C11C2311yescharacteristic
38C22×D4×C11C2311yescharacteristic
39C23×C4×C11—21no—
40C2×C11×M16C2314yes—
41C11×C4⋊Q8—22no—
42C11×C4⋊Q8—22no—
43C11×C4⋊Q8—28no—
44C11×C4⋊Q8—24no—
45C11×C4⋊Q8D412yes—
46C11×C4⋊Q8D412yes—
47C11×#125—24no—
48C11×#125—28no—
49C11×#125—24no—
50C11×#125D414yes—
51C11×#124—22no—
52C11×#124Q814yescomplemented
53C11×C22⋊Q8—22no—
54C11×C22⋊Q8—24no—
55C11×C22⋊Q8—22no—
56C4×Q8×C11—24no—
57C4×Q8×C11—24no—
58C4×Q8×C11—24no—
59C4×Q8×C11—24no—
60C4×Q8×C11—22no—
61C4×Q8×C11—22no—
62C4×Q8×C11—22no—
63C4×Q8×C11—22no—
64C4×D4×C11—22no—
65C4×D4×C11—22no—
66C11×#117—24no—
67C11×#117C2314yes—
68C2×C11×C4⋊C4D412yes—
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C22⋊C4—22no—
72C2×C11×C22⋊C4—22no—
73C2×C11×C22⋊C4—21no—
74C2×C42×C11—21no—
75C2×C42×C11—21no—
76C2×C42×C11D412yes—
77C2×C42×C11C2311yescharacteristic
78C2×C42×C11C2311yescharacteristic
79C2×C42×C11C2311yescharacteristic
80C11×#107—24no—
81C11×#106—24no—
82C11×C4⋊C8—22no—
83C11×C4⋊C8—22no—
84C11×#102—24no—
85C11×#102—24no—
86C11×#101—24no—
87C11×#95—22no—
88C11×#95—22no—
89#24313C1111yesmaximal, characteristic, direct product factor, Sylow
90C24×C11—21no—
91C2×Q8×C11—24no—
92C2×Q8×C11—22no—
93C2×Q8×C11—22no—
94C2×Q8×C11—22no—
95C2×Q8×C11—22no—
96C2×Q8×C11C2×Q812yes—
97C2×Q8×C11#4112yes—
98C2×D4×C11—22no—
99C2×D4×C11—21no—
100C2×D4×C11—22no—
101C2×D4×C11C2×Q812yes—
102C22×C4×C11—21no—
103C22×C4×C11—21no—
104C22×C4×C11—21no—
105C22×C4×C11—44no—
106C22×C4×C11—41no—
107C22×C4×C11—41no—
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2×D412yes—
110C22×C4×C11C2×D412yes—
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2411yescharacteristic
113C11×M16—24no—
114C11×M16—24no—
115C2×C8×C11—24no—
116C11×C4⋊C4—24no—
117C11×C4⋊C4—24no—
118C11×C4⋊C4—24no—
119C11×C4⋊C4—28no—
120C11×C4⋊C4—24no—
121C11×C4⋊C4—24no—
122C11×C4⋊C4—22no—
123C11×C4⋊C4—22no—
124C11×C4⋊C4—24no—
125C11×C4⋊C4—22no—
126C11×C4⋊C4—22no—
127C11×C4⋊C4C2×D414yes—
128C11×C4⋊C4C2×D414yes—
129C11×C22⋊C4—24no—
130C11×C22⋊C4—28no—
131C11×C22⋊C4—44no—
132C11×C22⋊C4—42no—
133C42×C11—28no—
134C42×C11—22no—
135C42×C11—22no—
136C42×C11—24no—
137C42×C11—21no—
138C42×C11—22no—
139C42×C11—42no—
140C42×C11—42no—
141C42×C11C2×D412yes—
142C42×C11C2×D412yes—
143C42×C11C2×Q812yes—
144#3502C2×C1111yescharacteristic, complemented
145#3077C2×C1112yes—
146C4×#124C2×C1111yescharacteristic
147#2061C2×C1112yescomplemented
148#2027C2×C1112yes—
149#1994C2×C1112yescomplemented
150#1888C2×C1112yes—
151#1857C2×C1112yescomplemented
152#1801C2×C1111yescharacteristic, complemented
153C23×C11—22no—
154C23×C11—42no—
155C23×C11—42no—
156C23×C11—41no—
157C23×C11—41no—
158C23×C11C22×D411yescharacteristic
159Q8×C11—24no—
160Q8×C11—24no—
161Q8×C11—44no—
162Q8×C11—82no—
163Q8×C11—84no—
164D4×C11—24no—
165D4×C11—42no—
166C2×C4×C11—22no—
167C2×C4×C11—22no—
168C2×C4×C11—22no—
169C2×C4×C11—22no—
170C2×C4×C11—24no—
171C2×C4×C11—24no—
172C2×C4×C11—22no—
173C2×C4×C11—22no—
174C2×C4×C11—41no—
175C2×C4×C11—41no—
176C2×C4×C11—41no—
177C2×C4×C11—41no—
178C2×C4×C11—41no—
179C2×C4×C11—42no—
180C2×C4×C11—42no—
181C2×C4×C11—41no—
182C2×C4×C11—82no—
183C2×C4×C11—82no—
184C2×C4×C11#12011yescharacteristic
185C2×C4×C11#12012yes—
186C2×C4×C11#12011yescharacteristic
187C2×C4×C11C22⋊Q814yes—
188C2×C4×C11C22×D412yes—
189C2×C4×C11C22×Q811yescharacteristic
190C2×C4×C11C2×#4111yescharacteristic
191C2×C4×C112−1+412yes—
192C8×C11—44no—
193Q82—22no—
194#557—22no—
195#557—24no—
196#544—22no—
197#544C22×C1112yes—
198#533—22no—
199#533C22×C1112yes—
200C2×#124C22×C1111yescharacteristic
201#519C22×C1112yes—
202C2×C4×Q8C22×C1111yescharacteristic
203C2×C4×D4C22×C1111yescharacteristic
204#478—24no—
205#476—22no—
206#474—22no—
207#428C22×C1114yes—
208#423C22×C1112yes—
209#418C22×C1114yes—
210C2×#101C22×C1112yes—
211#391C22×C1111yescharacteristic
212#390C22×C1111yescharacteristic
213#388—22no—
214#382C22×C1111yescharacteristic
215C4×C22⋊C4—22no—
216C43C22×C1111yescharacteristic
217#343C22×C1112yes—
218#339C22×C1114yes—
219#339C22×C1114yes—
220C22×C11—21no—
221C22×C11—21no—
222C22×C11—44no—
223C22×C11—42no—
224C22×C11—82no—
225C22×C11—81no—
226C22×C11—81no—
227C22×C11C2×#12011yescharacteristic
228C22×C11C2×C22⋊Q811yescharacteristic
229C22×C11#53611yescharacteristic
230C4×C11—24no—
231C4×C11—21no—
232C4×C11—22no—
233C4×C11—42no—
234C4×C11—42no—
235C4×C11—44no—
236C4×C11—42no—
237C4×C11—44no—
238C4×C11—81no—
239C4×C11#45412yes—
240C4×C11#54812yes—
241C4×C11D4×Q812yes—
242C22×Q8C23×C1111yescharacteristic
243C22×D4C23×C1111yescharacteristic
244C23×C4—21no—
245C2×M16C23×C1114yes—
246C4⋊Q8—22no—
247C4⋊Q8—22no—
248C4⋊Q8—28no—
249C4⋊Q8—24no—
250C4⋊Q8D4×C1112yes—
251C4⋊Q8D4×C1112yes—
252#125—24no—
253#125—28no—
254#125—24no—
255#125D4×C1114yes—
256#124—22no—
257#124Q8×C1114yescomplemented
258C22⋊Q8—22no—
259C22⋊Q8—24no—
260C22⋊Q8—22no—
261C4×Q8—24no—
262C4×Q8—24no—
263C4×Q8—24no—
264C4×Q8—24no—
265C4×Q8—22no—
266C4×Q8—22no—
267C4×Q8—22no—
268C4×Q8—22no—
269C4×D4—22no—
270C4×D4—22no—
271#117—24no—
272#117C23×C1114yes—
273C2×C4⋊C4D4×C1112yes—
274C2×C4⋊C4C23×C1111yescharacteristic
275C2×C4⋊C4C23×C1111yescharacteristic
276C2×C22⋊C4—22no—
277C2×C22⋊C4—21no—
278C2×C22⋊C4—22no—
279C2×C42—21no—
280C2×C42—21no—
281C2×C42D4×C1112yes—
282C2×C42C23×C1111yescharacteristic
283C2×C42C23×C1111yescharacteristic
284C2×C42C23×C1111yescharacteristic
285#107—24no—
286#106—24no—
287C4⋊C8—22no—
288C4⋊C8—22no—
289#102—24no—
290#102—24no—
291#101—24no—
292#95—22no—
293#95—22no—
294C2×C11—21no—
295C2×C11—21no—
296C2×C11—82no—
297C2×C11#240911yescharacteristic
298C2×C11C2×#45411yescharacteristic
299C2×C11#301811yescharacteristic
300C24—21no—
301C2×Q8—24no—
302C2×Q8—22no—
303C2×Q8—22no—
304C2×Q8—22no—
305C2×Q8—22no—
306C2×Q8C2×Q8×C1112yes—
307C2×Q8C11×#4112yes—
308C2×D4—22no—
309C2×D4—21no—
310C2×D4—22no—
311C2×D4C2×Q8×C1112yes—
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—44no—
316C22×C4—41no—
317C22×C4—41no—
318C22×C4C2×D4×C1111yescharacteristic
319C22×C4C2×D4×C1112yes—
320C22×C4C2×D4×C1112yes—
321C22×C4C2×D4×C1111yescharacteristic
322C22×C4C24×C1111yescharacteristic
323M16—24no—
324M16—24no—
325C2×C8—24no—
326C4⋊C4—24no—
327C4⋊C4—24no—
328C4⋊C4—24no—
329C4⋊C4—28no—
330C4⋊C4—24no—
331C4⋊C4—24no—
332C4⋊C4—22no—
333C4⋊C4—22no—
334C4⋊C4—24no—
335C4⋊C4—22no—
336C4⋊C4—22no—
337C4⋊C4C2×D4×C1114yes—
338C4⋊C4C2×D4×C1114yes—
339C22⋊C4—24no—
340C22⋊C4—28no—
341C22⋊C4—44no—
342C22⋊C4—42no—
343C42—28no—
344C42—22no—
345C42—22no—
346C42—24no—
347C42—21no—
348C42—22no—
349C42—42no—
350C42—42no—
351C42C2×D4×C1112yes—
352C42C2×D4×C1112yes—
353C42C2×Q8×C1112yes—
354C11#2431311yescharacteristic, direct product factor, Sylow
355C23—22no—
356C23—42no—
357C23—42no—
358C23—41no—
359C23—41no—
360C23C22×D4×C1111yescharacteristic
361Q8—24no—
362Q8—24no—
363Q8—44no—
364Q8—82no—
365Q8—84no—
366D4—24no—
367D4—42no—
368C2×C4—22no—
369C2×C4—22no—
370C2×C4—22no—
371C2×C4—22no—
372C2×C4—24no—
373C2×C4—24no—
374C2×C4—22no—
375C2×C4—22no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—41no—
384C2×C4—82no—
385C2×C4—82no—
386C2×C4C11×#12011yescharacteristic
387C2×C4C11×#12012yes—
388C2×C4C11×#12011yescharacteristic
389C2×C4C11×C22⋊Q814yes—
390C2×C4C22×D4×C1112yes—
391C2×C4C22×Q8×C1111yescharacteristic
392C2×C4C2×C11×#4111yescharacteristic
393C2×C4C11×2−1+412yes—
394C8—44no—
395C22—21no—
396C22—21no—
397C22—44no—
398C22—42no—
399C22—82no—
400C22—81no—
401C22—81no—
402C22C2×C11×#12011yescharacteristic
403C22C2×C11×C22⋊Q811yescharacteristic
404C22C11×#53611yescharacteristic
405C4—24no—
406C4—21no—
407C4—22no—
408C4—42no—
409C4—42no—
410C4—44no—
411C4—42no—
412C4—44no—
413C4—81no—
414C4C11×#45412yes—
415C4C11×#54812yes—
416C4D4×Q8×C1112yes—
417C2—21no—
418C2—21no—
419C2—82no—
420C2C11×#240911yescharacteristic
421C2C2×C11×#45411yescharacteristic
422C2C11×#301811yescharacteristic
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
1. C11×#3502C2semidirect
4. C11×#2061C2semidirect
6. C11×#1994C2semidirect
8. C11×#1857C2semidirect
9. C11×#1801C2semidirect
52. C11×#124Q8semidirect
89. #24313C11direct (N × H)
144. #3502C2×C11semidirect
147. #2061C2×C11semidirect
149. #1994C2×C11semidirect
151. #1857C2×C11semidirect
152. #1801C2×C11semidirect
257. #124Q8×C11semidirect
354. C11#24313direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35022
C11×#30772
C4×C11×#1242
C11×#20612
C11×#20272
C11×#19942
C11×#18882
C11×#18572
C11×#18012
#2431311