Finite Group Databasebeta

← C11×#10568 #14587761

Subgroups — C11×#10568 #14587761

Order 2816.

560 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×#2659C211yesmaximal, characteristic
2C11×#1853C212yesmaximal
3C11×#1442C211yesmaximal, characteristic
4C11×#1294C212yesmaximal
5C11×#1280C211yesmaximal, characteristic
6C2×C11×C22⋊Q8—21no—
7C22×C11×C4⋊C4C2211yescharacteristic
8C2×C11×#106—22no—
9C2×C11×C22⋊C8C2212yes—
10C11×#398—22no—
11C11×#395—22no—
12C11×#380—21no—
13C11×#380C2212yes—
14C2×C11×#95—21no—
15C2×C11×#95—21no—
16C2×C11×#95C2211yescharacteristic
17C2×C11×#95C2211yescharacteristic
18C11×#340—22no—
19C22×Q8×C11—21no—
20C23×C4×C11—21no—
21C23×C4×C11—21no—
22C23×C4×C11D411yescharacteristic
23C23×C4×C11D411yescharacteristic
24C23×C4×C11C2311yescharacteristic
25C22×C8×C11—22no—
26C11×C22⋊Q8—42no—
27C11×C22⋊Q8—42no—
28C2×C11×C4⋊C4—22no—
29C2×C11×C4⋊C4—22no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4—42no—
34C2×C11×C4⋊C4D412yes—
35C2×C11×C4⋊C4D412yes—
36C2×C11×C22⋊C4—22no—
37C11×#106—44no—
38C11×C22⋊C8—22no—
39C11×C22⋊C8Q814yescomplemented
40C11×#95—22no—
41C11×#95—22no—
42C11×#95—22no—
43C11×#95—21no—
44C11×#95—42no—
45C11×#95—42no—
46C11×#95Q812yescomplemented
47#10568C1111yesmaximal, characteristic, direct product factor, Sylow
48C24×C11C2×D411yescharacteristic
49C2×Q8×C11—42no—
50C2×Q8×C11—81no—
51C2×Q8×C11—81no—
52C22×C4×C11—21no—
53C22×C4×C11—21no—
54C22×C4×C11—21no—
55C22×C4×C11—21no—
56C22×C4×C11—22no—
57C22×C4×C11—22no—
58C22×C4×C11—22no—
59C22×C4×C11—22no—
60C22×C4×C11—41no—
61C22×C4×C11—41no—
62C22×C4×C11—41no—
63C22×C4×C11—41no—
64C22×C4×C11—41no—
65C22×C4×C11—41no—
66C22×C4×C11—41no—
67C22×C4×C11—41no—
68C22×C4×C11—41no—
69C22×C4×C11—41no—
70C22×C4×C11—41no—
71C22×C4×C11—41no—
72C22×C4×C11—41no—
73C22×C4×C11—41no—
74C22×C4×C11—41no—
75C22×C4×C11—41no—
76C22×C4×C11—41no—
77C22×C4×C11—41no—
78C22×C4×C11SD1612yes—
79C22×C4×C11SD1612yes—
80C22×C4×C11C2×D412yes—
81C22×C4×C11C2×Q812yes—
82C22×C4×C11C2×Q811yescharacteristic
83C22×C4×C11#4111yescharacteristic
84C2×C8×C11—24no—
85C2×C8×C11—42no—
86C2×C8×C11—42no—
87C11×C4⋊C4—24no—
88C11×C4⋊C4—42no—
89C11×C4⋊C4—42no—
90C11×C4⋊C4—44no—
91C11×C4⋊C4—42no—
92C11×C4⋊C4—42no—
93C11×C4⋊C4—81no—
94C11×C4⋊C4—81no—
95C11×C22⋊C4—42no—
96C11×C22⋊C4—42no—
97#2659C2×C1111yescharacteristic
98#1853C2×C1112yes—
99#1442C2×C1111yescharacteristic
100#1294C2×C1112yes—
101#1280C2×C1111yescharacteristic
102C23×C11—21no—
103C23×C11—21no—
104C23×C11—21no—
105C23×C11—21no—
106C23×C11#12011yescharacteristic
107C23×C11C22⋊Q811yescharacteristic
108C23×C11C4⋊Q811yescharacteristic
109C23×C11C2×SD1611yescharacteristic
110C23×C11C2×SD1611yescharacteristic
111C23×C11AGL(1,ℤ/8)11yescharacteristic
112C23×C11#13711yescharacteristic
113Q8×C11—84no—
114C2×C4×C11—22no—
115C2×C4×C11—22no—
116C2×C4×C11—22no—
117C2×C4×C11—22no—
118C2×C4×C11—42no—
119C2×C4×C11—41no—
120C2×C4×C11—41no—
121C2×C4×C11—41no—
122C2×C4×C11—41no—
123C2×C4×C11—41no—
124C2×C4×C11—41no—
125C2×C4×C11—42no—
126C2×C4×C11—42no—
127C2×C4×C11—42no—
128C2×C4×C11—42no—
129C2×C4×C11—42no—
130C2×C4×C11—42no—
131C2×C4×C11—42no—
132C2×C4×C11—42no—
133C2×C4×C11—42no—
134C2×C4×C11—42no—
135C2×C4×C11—42no—
136C2×C4×C11—42no—
137C2×C4×C11—42no—
138C2×C4×C11—42no—
139C2×C4×C11—81no—
140C2×C4×C11—81no—
141C2×C4×C11—81no—
142C2×C4×C11—81no—
143C2×C4×C11—81no—
144C2×C4×C11—81no—
145C2×C4×C11—81no—
146C2×C4×C11—81no—
147C2×C4×C11—81no—
148C2×C4×C11—81no—
149C2×C4×C11C22⋊Q812yes—
150C2×C4×C11C4⋊Q812yes—
151C8×C11—44no—
152C2×C22⋊Q8—21no—
153C22×C4⋊C4C22×C1111yescharacteristic
154C2×#106—22no—
155C2×C22⋊C8C22×C1112yes—
156#398—22no—
157#395—22no—
158#380—21no—
159#380C22×C1112yes—
160C2×#95—21no—
161C2×#95—21no—
162C2×#95C22×C1111yescharacteristic
163C2×#95C22×C1111yescharacteristic
164#340—22no—
165C22×C11—21no—
166C22×C11—21no—
167C22×C11—21no—
168C22×C11—21no—
169C22×C11—21no—
170C22×C11—21no—
171C22×C11—21no—
172C22×C11—21no—
173C22×C11—21no—
174C22×C11—21no—
175C22×C11—21no—
176C22×C11—21no—
177C22×C11#39511yescharacteristic
178C22×C11#44811yescharacteristic
179C22×C11#45011yescharacteristic
180C22×C11#45411yescharacteristic
181C22×C11#45511yescharacteristic
182C22×C11B(4,𝔽2)11yescharacteristic
183C22×C11#45811yescharacteristic
184C22×C11#47511yescharacteristic
185C22×C11#47611yescharacteristic
186C22×C11#49811yescharacteristic
187C22×C11#50111yescharacteristic
188C4×C11—22no—
189C4×C11—22no—
190C4×C11—42no—
191C4×C11—42no—
192C4×C11—82no—
193C4×C11—82no—
194C4×C11—82no—
195C4×C11—82no—
196C22×Q8—21no—
197C23×C4—21no—
198C23×C4—21no—
199C23×C4D4×C1111yescharacteristic
200C23×C4D4×C1111yescharacteristic
201C23×C4C23×C1111yescharacteristic
202C22×C8—22no—
203C22⋊Q8—42no—
204C22⋊Q8—42no—
205C2×C4⋊C4—22no—
206C2×C4⋊C4—22no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4—42no—
211C2×C4⋊C4D4×C1112yes—
212C2×C4⋊C4D4×C1112yes—
213C2×C22⋊C4—22no—
214#106—44no—
215C22⋊C8—22no—
216C22⋊C8Q8×C1114yescomplemented
217#95—22no—
218#95—22no—
219#95—22no—
220#95—21no—
221#95—42no—
222#95—42no—
223#95Q8×C1112yescomplemented
224C2×C11—21no—
225C2×C11—21no—
226C2×C11—21no—
227C2×C11—21no—
228C2×C11#159911yescharacteristic
229C2×C11#160111yescharacteristic
230C2×C11#160811yescharacteristic
231C2×C11#161611yescharacteristic
232C2×C11#205811yescharacteristic
233C2×C11#206111yescharacteristic
234C2×C11#206211yescharacteristic
235C24C2×D4×C1111yescharacteristic
236C2×Q8—42no—
237C2×Q8—81no—
238C2×Q8—81no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—22no—
244C22×C4—22no—
245C22×C4—22no—
246C22×C4—22no—
247C22×C4—41no—
248C22×C4—41no—
249C22×C4—41no—
250C22×C4—41no—
251C22×C4—41no—
252C22×C4—41no—
253C22×C4—41no—
254C22×C4—41no—
255C22×C4—41no—
256C22×C4—41no—
257C22×C4—41no—
258C22×C4—41no—
259C22×C4—41no—
260C22×C4—41no—
261C22×C4—41no—
262C22×C4—41no—
263C22×C4—41no—
264C22×C4—41no—
265C22×C4C11×SD1612yes—
266C22×C4C11×SD1612yes—
267C22×C4C2×D4×C1112yes—
268C22×C4C2×Q8×C1112yes—
269C22×C4C2×Q8×C1111yescharacteristic
270C22×C4C11×#4111yescharacteristic
271C2×C8—24no—
272C2×C8—42no—
273C2×C8—42no—
274C4⋊C4—24no—
275C4⋊C4—42no—
276C4⋊C4—42no—
277C4⋊C4—42no—
278C4⋊C4—42no—
279C4⋊C4—44no—
280C4⋊C4—81no—
281C4⋊C4—81no—
282C22⋊C4—42no—
283C22⋊C4—42no—
284C11#1056811yescharacteristic, direct product factor, Sylow
285C23—21no—
286C23—21no—
287C23—21no—
288C23—21no—
289C23C11×#12011yescharacteristic
290C23C11×C22⋊Q811yescharacteristic
291C23C11×C4⋊Q811yescharacteristic
292C23C2×C11×SD1611yescharacteristic
293C23C2×C11×SD1611yescharacteristic
294C23C11×AGL(1,ℤ/8)11yescharacteristic
295C23C11×#13711yescharacteristic
296Q8—84no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—22no—
301C2×C4—42no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—42no—
309C2×C4—42no—
310C2×C4—42no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—81no—
323C2×C4—81no—
324C2×C4—81no—
325C2×C4—81no—
326C2×C4—81no—
327C2×C4—81no—
328C2×C4—81no—
329C2×C4—81no—
330C2×C4—81no—
331C2×C4—81no—
332C2×C4C11×C22⋊Q812yes—
333C2×C4C11×C4⋊Q812yes—
334C8—44no—
335C22—21no—
336C22—21no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22C11×#39511yescharacteristic
348C22C11×#44811yescharacteristic
349C22C11×#45011yescharacteristic
350C22C11×#45411yescharacteristic
351C22C11×#45511yescharacteristic
352C22C11×B(4,𝔽2)11yescharacteristic
353C22C11×#45811yescharacteristic
354C22C11×#47511yescharacteristic
355C22C11×#47611yescharacteristic
356C22C11×#49811yescharacteristic
357C22C11×#50111yescharacteristic
358C4—22no—
359C4—22no—
360C4—42no—
361C4—42no—
362C4—82no—
363C4—82no—
364C4—82no—
365C4—82no—
366C2—21no—
367C2—21no—
368C2—21no—
369C2—21no—
370C2C11×#159911yescharacteristic
371C2C11×#160111yescharacteristic
372C2C11×#160811yescharacteristic
373C2C11×#161611yescharacteristic
374C2C11×#205811yescharacteristic
375C2C11×#206111yescharacteristic
376C2C11×#206211yescharacteristic
subgroupG/H
center, socleC23×C11#120
commutator, Frattini, cosocleC23×C4C23×C11
prime radicalC24×C11C2×D4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
39. C11×C22⋊C8Q8semidirect
46. C11×#95Q8semidirect
47. #10568C11direct (N × H)
216. C22⋊C8Q8×C11semidirect
223. #95Q8×C11semidirect
284. C11#10568direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#26592
C11×#18532
C11×#14422
C11×#12942
C11×#12802
#1056811