Finite Group Databasebeta

← C11×#9146 #14586339

Subgroups — C11×#9146 #14586339

Order 2816.

1010 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2848C211yesmaximal, characteristic
2C2×C4×C11×C22⋊C4C211yesmaximal, characteristic
3C11×#1779C211yesmaximal, characteristic
4C2×C11×#328C212yesmaximal, complemented
5C11×#1294C212yesmaximal, complemented
6C24×C4×C11C2211yescharacteristic
7C2×C11×C22⋊Q8C412yescomplemented
8C2×C11×C22⋊Q8C2211yescharacteristic
9C22×C11×C22⋊C4—21no—
10C22×C42×C11—21no—
11C2×C11×C22⋊C8—22no—
12C2×C11×C22⋊C8C2212yes—
13C11×#385—21no—
14C11×#385—22no—
15C11×#380C412yescomplemented
16C11×#380C2211yescharacteristic
17C11×#379—21no—
18C4×C11×C22⋊C4—24no—
19C2×C11×#95C2212yes—
20C11×#328—24no—
21C25×C11D411yescharacteristic
22C22×Q8×C11C2×C411yescharacteristic
23C23×C4×C11—22no—
24C23×C4×C11—22no—
25C23×C4×C11—22no—
26C23×C4×C11—44no—
27C23×C4×C11C2×C412yes—
28C23×C4×C11D411yescharacteristic
29C23×C4×C11D412yes—
30C23×C4×C11C2311yescharacteristic
31C22×C8×C11—22no—
32C11×C22⋊Q8—22no—
33C11×C22⋊Q8—22no—
34C11×C22⋊Q8—44no—
35C2×C11×C4⋊C4—22no—
36C2×C11×C4⋊C4—21no—
37C2×C11×C4⋊C4C2×C411yescharacteristic
38C2×C11×C4⋊C4C2×C412yes—
39C2×C11×C22⋊C4—28no—
40C2×C11×C22⋊C4—24no—
41C2×C11×C22⋊C4—22no—
42C2×C11×C22⋊C4—22no—
43C2×C11×C22⋊C4—21no—
44C2×C11×C22⋊C4—21no—
45C2×C42×C11—24no—
46C2×C42×C11—44no—
47C11×C22⋊C8—22no—
48C11×C22⋊C8—22no—
49C11×C22⋊C8—44no—
50C11×#95—22no—
51C11×#95—22no—
52C11×#95—21no—
53C11×#95D414yes—
54#9146C1111yesmaximal, characteristic, direct product factor, Sylow
55C24×C11—24no—
56C24×C11—21no—
57C24×C11—21no—
58C24×C11—22no—
59C24×C11—22no—
60C24×C11—42no—
61C24×C11C22⋊C412yes—
62C24×C11C2×D411yescharacteristic
63C2×Q8×C11—22no—
64C2×Q8×C11—42no—
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11—24no—
68C22×C4×C11—28no—
69C22×C4×C11—24no—
70C22×C4×C11—24no—
71C22×C4×C11—24no—
72C22×C4×C11—24no—
73C22×C4×C11—24no—
74C22×C4×C11—21no—
75C22×C4×C11—22no—
76C22×C4×C11—21no—
77C22×C4×C11—42no—
78C22×C4×C11—42no—
79C22×C4×C11—42no—
80C22×C4×C11—48no—
81C22×C4×C11—48no—
82C22×C4×C11—44no—
83C22×C4×C11—42no—
84C22×C4×C11—42no—
85C22×C4×C11C22⋊C412yes—
86C22×C4×C11C22×C411yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×D412yes—
89C22×C4×C11#4112yes—
90C2×C8×C11—44no—
91C2×C8×C11—42no—
92C11×C4⋊C4—22no—
93C11×C4⋊C4—42no—
94C11×C4⋊C4—44no—
95C11×C4⋊C4—42no—
96C11×C22⋊C4—216no—
97C11×C22⋊C4—44no—
98C11×C22⋊C4—44no—
99C11×C22⋊C4—41no—
100C11×C22⋊C4—41no—
101C11×C22⋊C4—42no—
102C42×C11—48no—
103#2848C2×C1111yescharacteristic
104C2×C4×C22⋊C4C2×C1111yescharacteristic
105#1779C2×C1111yescharacteristic
106C2×#328C2×C1112yescomplemented
107#1294C2×C1112yescomplemented
108C23×C11—22no—
109C23×C11—22no—
110C23×C11—24no—
111C23×C11—24no—
112C23×C11—22no—
113C23×C11—22no—
114C23×C11—22no—
115C23×C11—22no—
116C23×C11—22no—
117C23×C11—22no—
118C23×C11—48no—
119C23×C11—48no—
120C23×C11—42no—
121C23×C11—42no—
122C23×C11—42no—
123C23×C11—42no—
124C23×C11#10414yes—
125C23×C11C2×C22⋊C411yescharacteristic
126C23×C11#12011yescharacteristic
127C23×C11#12311yescharacteristic
128C23×C11#13512yes—
129C23×C11#13712yes—
130Q8×C11—82no—
131C2×C4×C11—24no—
132C2×C4×C11—24no—
133C2×C4×C11—22no—
134C2×C4×C11—22no—
135C2×C4×C11—22no—
136C2×C4×C11—22no—
137C2×C4×C11—28no—
138C2×C4×C11—42no—
139C2×C4×C11—42no—
140C2×C4×C11—48no—
141C2×C4×C11—48no—
142C2×C4×C11—44no—
143C2×C4×C11—48no—
144C2×C4×C11—48no—
145C2×C4×C11—44no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—42no—
149C2×C4×C11—42no—
150C2×C4×C11—42no—
151C2×C4×C11—42no—
152C2×C4×C11—42no—
153C2×C4×C11#9914yes—
154C2×C4×C11C4×D412yes—
155C2×C4×C11#12112yes—
156C8×C11—82no—
157C24×C4C22×C1111yescharacteristic
158C2×C22⋊Q8C4×C1112yescomplemented
159C2×C22⋊Q8C22×C1111yescharacteristic
160C22×C22⋊C4—21no—
161C22×C42—21no—
162C2×C22⋊C8—22no—
163C2×C22⋊C8C22×C1112yes—
164#385—21no—
165#385—22no—
166#380C4×C1112yescomplemented
167#380C22×C1111yescharacteristic
168#379—21no—
169C4×C22⋊C4—24no—
170C2×#95C22×C1112yes—
171#328—24no—
172C22×C11—21no—
173C22×C11—21no—
174C22×C11—21no—
175C22×C11—21no—
176C22×C11—24no—
177C22×C11—24no—
178C22×C11—24no—
179C22×C11—24no—
180C22×C11—24no—
181C22×C11—48no—
182C22×C11—48no—
183C22×C11—42no—
184C22×C11—42no—
185C22×C11—42no—
186C22×C11—42no—
187C22×C11#38611yescharacteristic
188C22×C11C2×#9912yes—
189C22×C11#41611yescharacteristic
190C22×C11#41911yescharacteristic
191C22×C11C2×#10412yes—
192C22×C11#45212yes—
193C22×C11#48512yes—
194C4×C11—24no—
195C4×C11—22no—
196C4×C11—22no—
197C4×C11—48no—
198C4×C11—81no—
199C4×C11—81no—
200C4×C11—82no—
201C25D4×C1111yescharacteristic
202C22×Q8C2×C4×C1111yescharacteristic
203C23×C4—22no—
204C23×C4—22no—
205C23×C4—22no—
206C23×C4—44no—
207C23×C4C2×C4×C1112yes—
208C23×C4D4×C1111yescharacteristic
209C23×C4D4×C1112yes—
210C23×C4C23×C1111yescharacteristic
211C22×C8—22no—
212C22⋊Q8—22no—
213C22⋊Q8—22no—
214C22⋊Q8—44no—
215C2×C4⋊C4—22no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4C2×C4×C1111yescharacteristic
218C2×C4⋊C4C2×C4×C1112yes—
219C2×C22⋊C4—24no—
220C2×C22⋊C4—28no—
221C2×C22⋊C4—22no—
222C2×C22⋊C4—22no—
223C2×C22⋊C4—21no—
224C2×C22⋊C4—21no—
225C2×C42—24no—
226C2×C42—44no—
227C22⋊C8—22no—
228C22⋊C8—22no—
229C22⋊C8—44no—
230#95—22no—
231#95—22no—
232#95—21no—
233#95D4×C1114yes—
234C2×C11—22no—
235C2×C11—22no—
236C2×C11—44no—
237C2×C11#150112yes—
238C2×C11#150812yes—
239C2×C11#187311yescharacteristic
240C2×C11#189611yescharacteristic
241C2×C11#189811yescharacteristic
242C24—24no—
243C24—21no—
244C24—21no—
245C24—22no—
246C24—22no—
247C24—42no—
248C24C11×C22⋊C412yes—
249C24C2×D4×C1111yescharacteristic
250C2×Q8—22no—
251C2×Q8—42no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—24no—
255C22×C4—28no—
256C22×C4—24no—
257C22×C4—24no—
258C22×C4—24no—
259C22×C4—24no—
260C22×C4—24no—
261C22×C4—21no—
262C22×C4—22no—
263C22×C4—21no—
264C22×C4—42no—
265C22×C4—42no—
266C22×C4—42no—
267C22×C4—48no—
268C22×C4—48no—
269C22×C4—44no—
270C22×C4—42no—
271C22×C4—42no—
272C22×C4C11×C22⋊C412yes—
273C22×C4C22×C4×C1111yescharacteristic
274C22×C4C2×D4×C1111yescharacteristic
275C22×C4C2×D4×C1112yes—
276C22×C4C11×#4112yes—
277C2×C8—44no—
278C2×C8—42no—
279C4⋊C4—22no—
280C4⋊C4—42no—
281C4⋊C4—44no—
282C4⋊C4—42no—
283C22⋊C4—216no—
284C22⋊C4—44no—
285C22⋊C4—44no—
286C22⋊C4—41no—
287C22⋊C4—41no—
288C22⋊C4—42no—
289C42—48no—
290C11#914611yescharacteristic, direct product factor, Sylow
291C23—22no—
292C23—22no—
293C23—24no—
294C23—24no—
295C23—22no—
296C23—22no—
297C23—22no—
298C23—22no—
299C23—22no—
300C23—22no—
301C23—48no—
302C23—48no—
303C23—42no—
304C23—42no—
305C23—42no—
306C23—42no—
307C23C11×#10414yes—
308C23C2×C11×C22⋊C411yescharacteristic
309C23C11×#12011yescharacteristic
310C23C11×#12311yescharacteristic
311C23C11×#13512yes—
312C23C11×#13712yes—
313Q8—82no—
314C2×C4—24no—
315C2×C4—24no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—28no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—48no—
324C2×C4—48no—
325C2×C4—44no—
326C2×C4—48no—
327C2×C4—48no—
328C2×C4—44no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4C11×#9914yes—
337C2×C4C4×D4×C1112yes—
338C2×C4C11×#12112yes—
339C8—82no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—24no—
345C22—24no—
346C22—24no—
347C22—24no—
348C22—24no—
349C22—48no—
350C22—48no—
351C22—42no—
352C22—42no—
353C22—42no—
354C22—42no—
355C22C11×#38611yescharacteristic
356C22C2×C11×#9912yes—
357C22C11×#41611yescharacteristic
358C22C11×#41911yescharacteristic
359C22C2×C11×#10412yes—
360C22C11×#45212yes—
361C22C11×#48512yes—
362C4—22no—
363C4—24no—
364C4—22no—
365C4—48no—
366C4—81no—
367C4—81no—
368C4—82no—
369C2—22no—
370C2—22no—
371C2—44no—
372C2C11×#150112yes—
373C2C11×#150812yes—
374C2C11×#187311yescharacteristic
375C2C11×#189611yescharacteristic
376C2C11×#189811yescharacteristic
subgroupG/H
center, socleC23×C11C2×C22⋊C4
commutatorC22×C4C22×C4×C11
Frattini, cosocleC23×C4C23×C11
prime radicalC25×C11D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C11 ◁ C24×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×C11×#328C2semidirect
5. C11×#1294C2semidirect
7. C2×C11×C22⋊Q8C4semidirect
15. C11×#380C4semidirect
54. #9146C11direct (N × H)
106. C2×#328C2×C11semidirect
107. #1294C2×C11semidirect
158. C2×C22⋊Q8C4×C11semidirect
166. #380C4×C11semidirect
290. C11#9146direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#28482
C2×C4×C11×C22⋊C42
C11×#17792
C2×C11×#3282
C11×#12942
#914611