Finite Group Databasebeta

← C11×#9363 #14586556

Subgroups — C11×#9363 #14586556

Order 2816.

500 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3095C211yesmaximal, characteristic
2C11×#2346C211yesmaximal, characteristic
3C11×#1996C211yesmaximal, characteristic
4C11×#1826C211yesmaximal, characteristic
5C11×#1508C211yesmaximal, characteristic
6C11×#1305C211yesmaximal, characteristic
7C11×#1297C211yesmaximal, characteristic
8C2×C11×C22⋊Q8C2211yescharacteristic
9C2×C11×#117C2211yescharacteristic
10C11×#485—22no—
11C11×#484—21no—
12C11×#483—21no—
13C11×#428C412yescomplemented
14C11×#419C412yescomplemented
15C11×#407C2211yescharacteristic
16C11×#407C2211yescharacteristic
17C11×#389—21no—
18C11×#388—22no—
19C11×#382—21no—
20C11×#380C2211yescharacteristic
21C4×C11×C4⋊C4—21no—
22C4×C11×C22⋊C4C2211yescharacteristic
23C4×C11×C22⋊C4C2211yescharacteristic
24C11×#376—21no—
25C11×#342—22no—
26C11×#339—22no—
27C11×#328—21no—
28C11×#328—21no—
29C22×Q8×C11C2×C411yescharacteristic
30C23×C4×C11C2311yescharacteristic
31C2×C11×M16—21no—
32C2×C11×M16C2×C412yes—
33C11×C22⋊Q8—21no—
34C11×C22⋊Q8—21no—
35C11×C22⋊Q8—21no—
36C11×C22⋊Q8—21no—
37C11×#117—21no—
38C11×#117—21no—
39C11×#117C2×C412yes—
40C11×#117D412yes—
41C2×C11×C4⋊C4—21no—
42C2×C11×C4⋊C4—21no—
43C2×C11×C4⋊C4—22no—
44C2×C11×C4⋊C4C2×C411yescharacteristic
45C2×C11×C4⋊C4D411yescharacteristic
46C2×C11×C4⋊C4D411yescharacteristic
47C2×C11×C22⋊C4—21no—
48C2×C11×C22⋊C4—21no—
49C2×C11×C22⋊C4—21no—
50C2×C11×C22⋊C4—21no—
51C2×C11×C22⋊C4D412yes—
52C2×C42×C11—21no—
53C2×C42×C11—22no—
54C2×C42×C11—21no—
55C2×C42×C11—21no—
56C11×#107—22no—
57C11×#106—22no—
58C11×#103—22no—
59C11×#103—22no—
60C11×C22⋊C8—21no—
61C11×C22⋊C8—21no—
62C11×C22⋊C8—21no—
63C11×C22⋊C8—21no—
64C11×#95—22no—
65C11×#95—22no—
66C11×#95—21no—
67C11×#95—21no—
68C11×#95D411yescharacteristic
69C11×#95D411yescharacteristic
70#9363C1111yesmaximal, characteristic, direct product factor, Sylow
71C24×C11C2×D411yescharacteristic
72C2×Q8×C11—21no—
73C2×Q8×C11—21no—
74C2×Q8×C11—42no—
75C22×C4×C11—21no—
76C22×C4×C11—21no—
77C22×C4×C11—21no—
78C22×C4×C11—22no—
79C22×C4×C11—21no—
80C22×C4×C11—21no—
81C22×C4×C11—21no—
82C22×C4×C11—42no—
83C22×C4×C11—41no—
84C22×C4×C11C22×C411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11#4111yescharacteristic
89C22×C4×C11#4111yescharacteristic
90C11×M16—42no—
91C11×M16—42no—
92C2×C8×C11—22no—
93C2×C8×C11—41no—
94C11×C4⋊C4—21no—
95C11×C4⋊C4—21no—
96C11×C4⋊C4—21no—
97C11×C4⋊C4—21no—
98C11×C4⋊C4—42no—
99C11×C4⋊C4—41no—
100C11×C4⋊C4—41no—
101C11×C4⋊C4—82no—
102C11×C4⋊C4C22⋊C412yes—
103C11×C4⋊C4C22⋊C412yes—
104C11×C22⋊C4—22no—
105C11×C22⋊C4—22no—
106C11×C22⋊C4—22no—
107C11×C22⋊C4—42no—
108C11×C22⋊C4—41no—
109C11×C22⋊C4—41no—
110C11×C22⋊C4—41no—
111C11×C22⋊C4—42no—
112C42×C11—22no—
113C42×C11—22no—
114C42×C11—42no—
115C42×C11—44no—
116C42×C11—42no—
117#3095C2×C1111yescharacteristic
118#2346C2×C1111yescharacteristic
119#1996C2×C1111yescharacteristic
120#1826C2×C1111yescharacteristic
121#1508C2×C1111yescharacteristic
122#1305C2×C1111yescharacteristic
123#1297C2×C1111yescharacteristic
124C23×C11—21no—
125C23×C11—21no—
126C23×C11—41no—
127C23×C11—41no—
128C23×C11C4×D411yescharacteristic
129C23×C11#12011yescharacteristic
130C23×C11#12111yescharacteristic
131Q8×C11—42no—
132Q8×C11—81no—
133C2×C4×C11—22no—
134C2×C4×C11—22no—
135C2×C4×C11—22no—
136C2×C4×C11—22no—
137C2×C4×C11—22no—
138C2×C4×C11—22no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—42no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—42no—
149C2×C4×C11—42no—
150C2×C4×C11—41no—
151C2×C4×C11—42no—
152C2×C4×C11—41no—
153C2×C4×C11—41no—
154C2×C4×C11—42no—
155C2×C4×C11—41no—
156C2×C4×C11—81no—
157C2×C4×C11—81no—
158C2×C4×C11—81no—
159C2×C4×C11—81no—
160C2×C4×C11C2×C22⋊C411yescharacteristic
161C2×C4×C11C4×D411yescharacteristic
162C2×C4×C11#12111yescharacteristic
163C2×C4×C11#12311yescharacteristic
164C8×C11—42no—
165C8×C11—81no—
166C2×C22⋊Q8C22×C1111yescharacteristic
167C2×#117C22×C1111yescharacteristic
168#485—22no—
169#484—21no—
170#483—21no—
171#428C4×C1112yescomplemented
172#419C4×C1112yescomplemented
173#407C22×C1111yescharacteristic
174#407C22×C1111yescharacteristic
175#389—21no—
176#388—22no—
177#382—21no—
178#380C22×C1111yescharacteristic
179C4×C4⋊C4—21no—
180C4×C22⋊C4C22×C1111yescharacteristic
181C4×C22⋊C4C22×C1111yescharacteristic
182#376—21no—
183#342—22no—
184#339—22no—
185#328—21no—
186#328—21no—
187C22×C11—21no—
188C22×C11—21no—
189C22×C11—21no—
190C22×C11—21no—
191C22×C11—21no—
192C22×C11—21no—
193C22×C11—21no—
194C22×C11—21no—
195C22×C11—81no—
196C22×C11—81no—
197C22×C11#38611yescharacteristic
198C22×C11#45511yescharacteristic
199C22×C11#45611yescharacteristic
200C4×C11—21no—
201C4×C11—21no—
202C4×C11—21no—
203C4×C11—42no—
204C4×C11—42no—
205C4×C11—42no—
206C4×C11—81no—
207C4×C11—82no—
208C4×C11—82no—
209C4×C11—81no—
210C4×C11—81no—
211C4×C11#41012yes—
212C22×Q8C2×C4×C1111yescharacteristic
213C23×C4C23×C1111yescharacteristic
214C2×M16—21no—
215C2×M16C2×C4×C1112yes—
216C22⋊Q8—21no—
217C22⋊Q8—21no—
218C22⋊Q8—21no—
219C22⋊Q8—21no—
220#117—21no—
221#117—21no—
222#117C2×C4×C1112yes—
223#117D4×C1112yes—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—22no—
227C2×C4⋊C4C2×C4×C1111yescharacteristic
228C2×C4⋊C4D4×C1111yescharacteristic
229C2×C4⋊C4D4×C1111yescharacteristic
230C2×C22⋊C4—21no—
231C2×C22⋊C4—21no—
232C2×C22⋊C4—21no—
233C2×C22⋊C4—21no—
234C2×C22⋊C4D4×C1112yes—
235C2×C42—21no—
236C2×C42—22no—
237C2×C42—21no—
238C2×C42—21no—
239#107—22no—
240#106—22no—
241#103—22no—
242#103—22no—
243C22⋊C8—21no—
244C22⋊C8—21no—
245C22⋊C8—21no—
246C22⋊C8—21no—
247#95—22no—
248#95—22no—
249#95—21no—
250#95—21no—
251#95D4×C1111yescharacteristic
252#95D4×C1111yescharacteristic
253C2×C11—21no—
254C2×C11—21no—
255C2×C11—41no—
256C2×C11—41no—
257C2×C11#188211yescharacteristic
258C2×C11#189911yescharacteristic
259C2×C11#190611yescharacteristic
260C24C2×D4×C1111yescharacteristic
261C2×Q8—21no—
262C2×Q8—21no—
263C2×Q8—42no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—22no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—42no—
272C22×C4—41no—
273C22×C4C22×C4×C1111yescharacteristic
274C22×C4C2×D4×C1111yescharacteristic
275C22×C4C2×D4×C1111yescharacteristic
276C22×C4C2×D4×C1111yescharacteristic
277C22×C4C11×#4111yescharacteristic
278C22×C4C11×#4111yescharacteristic
279M16—42no—
280M16—42no—
281C2×C8—22no—
282C2×C8—41no—
283C4⋊C4—21no—
284C4⋊C4—21no—
285C4⋊C4—21no—
286C4⋊C4—21no—
287C4⋊C4—42no—
288C4⋊C4—41no—
289C4⋊C4—41no—
290C4⋊C4—82no—
291C4⋊C4C11×C22⋊C412yes—
292C4⋊C4C11×C22⋊C412yes—
293C22⋊C4—22no—
294C22⋊C4—22no—
295C22⋊C4—22no—
296C22⋊C4—42no—
297C22⋊C4—41no—
298C22⋊C4—41no—
299C22⋊C4—41no—
300C22⋊C4—42no—
301C42—22no—
302C42—22no—
303C42—42no—
304C42—44no—
305C42—42no—
306C11#936311yescharacteristic, direct product factor, Sylow
307C23—21no—
308C23—21no—
309C23—41no—
310C23—41no—
311C23C4×D4×C1111yescharacteristic
312C23C11×#12011yescharacteristic
313C23C11×#12111yescharacteristic
314Q8—42no—
315Q8—81no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—42no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4—41no—
334C2×C4—42no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—42no—
338C2×C4—41no—
339C2×C4—81no—
340C2×C4—81no—
341C2×C4—81no—
342C2×C4—81no—
343C2×C4C2×C11×C22⋊C411yescharacteristic
344C2×C4C4×D4×C1111yescharacteristic
345C2×C4C11×#12111yescharacteristic
346C2×C4C11×#12311yescharacteristic
347C8—42no—
348C8—81no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—81no—
358C22—81no—
359C22C11×#38611yescharacteristic
360C22C11×#45511yescharacteristic
361C22C11×#45611yescharacteristic
362C4—21no—
363C4—21no—
364C4—21no—
365C4—42no—
366C4—42no—
367C4—42no—
368C4—81no—
369C4—82no—
370C4—82no—
371C4—81no—
372C4—81no—
373C4C11×#41012yes—
374C2—21no—
375C2—21no—
376C2—41no—
377C2—41no—
378C2C11×#188211yescharacteristic
379C2C11×#189911yescharacteristic
380C2C11×#190611yescharacteristic
subgroupG/H
center, socleC22×C11#386
commutatorC22×C4C22×C4×C11
Frattini, cosocleC23×C4C23×C11
prime radicalC24×C11C2×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
13. C11×#428C4semidirect
14. C11×#419C4semidirect
70. #9363C11direct (N × H)
171. #428C4×C11semidirect
172. #419C4×C11semidirect
306. C11#9363direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#30952
C11×#23462
C11×#19962
C11×#18262
C11×#15082
C11×#13052
C11×#12972
#936311