Finite Group Databasebeta

← C11×#10059 #14587252

Subgroups — C11×#10059 #14587252

Order 2816.

570 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
1C2×C11×#487C211yesmaximal, characteristic
2C2×C11×#477C211yesmaximal, characteristic
3C11×#2546C211yesmaximal, characteristic
4C11×#1987C211yesmaximal, characteristic
5C2×C11×#332C211yesmaximal, characteristic
6C2×C11×Q8⋊C8C211yesmaximal, characteristic
7C11×#1279C211yesmaximal, characteristic
8C2×C11×C4⋊Q8—21no—
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×C4×Q8×C11C2211yescharacteristic
12C11×#487—22no—
13C11×#487—22no—
14C11×#477—22no—
15C11×#477—22no—
16C2×C11×#107—21no—
17C2×C11×C4⋊C8C2211yescharacteristic
18C2×C11×C4⋊C8C2211yescharacteristic
19C2×C11×#103—21no—
20C2×C11×#103—22no—
21C2×C4×C8×C11C2211yescharacteristic
22C11×#398—22no—
23C11×#391—21no—
24C11×#389—22no—
25C4×C11×C4⋊C4C2211yescharacteristic
26C11×#340—22no—
27C11×#332—22no—
28C11×Q8⋊C8—22no—
29C22×Q8×C11—21no—
30C22×Q8×C11—21no—
31C22×Q8×C11D411yescharacteristic
32C22×C8×C11—21no—
33C22×C8×C11—21no—
34C22×C8×C11—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8—21no—
39C11×C4⋊Q8—21no—
40C11×C4⋊Q8—21no—
41C11×C4⋊Q8—21no—
42C11×C4⋊Q8—42no—
43C11×C4⋊Q8—42no—
44C11×C4⋊Q8D412yes—
45C4×Q8×C11—21no—
46C4×Q8×C11—21no—
47C4×Q8×C11—21no—
48C4×Q8×C11—21no—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4—24no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4D411yescharacteristic
55C2×C11×C4⋊C4D412yes—
56C2×C11×C4⋊C4D412yes—
57C2×C42×C11—21no—
58C2×C42×C11—21no—
59C2×C42×C11C2311yescharacteristic
60C11×#107—24no—
61C11×C4⋊C8—21no—
62C11×C4⋊C8—21no—
63C11×C4⋊C8—21no—
64C11×C4⋊C8D412yes—
65C11×#103—24no—
66C11×#103—28no—
67C4×C8×C11—21no—
68C4×C8×C11D412yes—
69C11×#95—24no—
70C11×#95—21no—
71#10059C1111yesmaximal, characteristic, direct product factor, Sylow
72C2×Q8×C11—21no—
73C2×Q8×C11—21no—
74C2×Q8×C11—22no—
75C2×Q8×C11—21no—
76C2×Q8×C11—21no—
77C2×Q8×C11—21no—
78C2×Q8×C11—44no—
79C2×Q8×C11—41no—
80C2×Q8×C11—41no—
81C2×Q8×C11—41no—
82C2×Q8×C11—41no—
83C2×Q8×C11—41no—
84C2×Q8×C11—41no—
85C2×Q8×C11—41no—
86C2×Q8×C11SD1612yes—
87C22×C4×C11—22no—
88C22×C4×C11—21no—
89C22×C4×C11—21no—
90C22×C4×C11—22no—
91C22×C4×C11—41no—
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11C2×D411yescharacteristic
95C2×C8×C11—22no—
96C2×C8×C11—22no—
97C2×C8×C11—42no—
98C2×C8×C11—41no—
99C2×C8×C11—41no—
100C2×C8×C11—41no—
101C2×C8×C11—42no—
102C11×C4⋊C4—22no—
103C11×C4⋊C4—22no—
104C11×C4⋊C4—22no—
105C11×C4⋊C4—21no—
106C11×C4⋊C4—22no—
107C11×C4⋊C4—21no—
108C11×C4⋊C4—22no—
109C11×C4⋊C4—48no—
110C11×C4⋊C4—41no—
111C11×C4⋊C4—41no—
112C11×C4⋊C4—41no—
113C11×C4⋊C4—41no—
114C11×C4⋊C4—41no—
115C11×C4⋊C4—41no—
116C11×C4⋊C4Q1614yes—
117C42×C11—41no—
118C42×C11—41no—
119C42×C11—41no—
120C42×C11—41no—
121C42×C11C2×D411yescharacteristic
122C42×C11C2×D411yescharacteristic
123C42×C11C2×D411yescharacteristic
124C42×C11#4111yescharacteristic
125C2×#487C2×C1111yescharacteristic
126C2×#477C2×C1111yescharacteristic
127#2546C2×C1111yescharacteristic
128#1987C2×C1111yescharacteristic
129C2×#332C2×C1111yescharacteristic
130C2×Q8⋊C8C2×C1111yescharacteristic
131#1279C2×C1111yescharacteristic
132C23×C11#12011yescharacteristic
133Q8×C11—22no—
134Q8×C11—22no—
135Q8×C11—44no—
136Q8×C11—41no—
137Q8×C11—41no—
138Q8×C11—82no—
139Q8×C11—81no—
140Q8×C11—81no—
141Q8×C11—81no—
142Q8×C11—81no—
143C2×C4×C11—22no—
144C2×C4×C11—22no—
145C2×C4×C11—24no—
146C2×C4×C11—41no—
147C2×C4×C11—42no—
148C2×C4×C11—41no—
149C2×C4×C11—42no—
150C2×C4×C11—41no—
151C2×C4×C11—42no—
152C2×C4×C11—42no—
153C2×C4×C11—42no—
154C2×C4×C11—42no—
155C2×C4×C11—42no—
156C2×C4×C11—82no—
157C2×C4×C11#12011yescharacteristic
158C2×C4×C11#12011yescharacteristic
159C2×C4×C11#12111yescharacteristic
160C2×C4×C11#12111yescharacteristic
161C2×C4×C11#12111yescharacteristic
162C2×C4×C11#12711yescharacteristic
163C2×C4×C11C2×SD1611yescharacteristic
164C2×C4×C11C2×Q1612yes—
165C2×C4×C11#13511yescharacteristic
166C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
167C2×C4×C11#13711yescharacteristic
168C2×C4×C11#13712yes—
169C8×C11—42no—
170C8×C11—42no—
171C8×C11—81no—
172C2×C4⋊Q8—21no—
173C2×C4⋊Q8C22×C1111yescharacteristic
174C2×C4⋊Q8C22×C1111yescharacteristic
175C2×C4×Q8C22×C1111yescharacteristic
176#487—22no—
177#487—22no—
178#477—22no—
179#477—22no—
180C2×#107—21no—
181C2×C4⋊C8C22×C1111yescharacteristic
182C2×C4⋊C8C22×C1111yescharacteristic
183C2×#103—21no—
184C2×#103—22no—
185C2×C4×C8C22×C1111yescharacteristic
186#398—22no—
187#391—21no—
188#389—22no—
189C4×C4⋊C4C22×C1111yescharacteristic
190#340—22no—
191#332—22no—
192Q8⋊C8—22no—
193C22×C11#39211yescharacteristic
194C22×C11#45011yescharacteristic
195C22×C11#45112yes—
196C22×C11#45211yescharacteristic
197C22×C11#45412yes—
198C4×C11—21no—
199C4×C11—21no—
200C4×C11—44no—
201C4×C11—42no—
202C4×C11—82no—
203C4×C11—81no—
204C4×C11—82no—
205C4×C11#44811yescharacteristic
206C4×C11#44911yescharacteristic
207C4×C11#46212yes—
208C4×C11#46511yescharacteristic
209C4×C11#46811yescharacteristic
210C4×C11#49411yescharacteristic
211C4×C11#49711yescharacteristic
212C22×Q8—21no—
213C22×Q8—21no—
214C22×Q8D4×C1111yescharacteristic
215C22×C8—21no—
216C22×C8—21no—
217C22×C8—21no—
218C4⋊Q8—21no—
219C4⋊Q8—21no—
220C4⋊Q8—21no—
221C4⋊Q8—21no—
222C4⋊Q8—21no—
223C4⋊Q8—21no—
224C4⋊Q8—21no—
225C4⋊Q8—42no—
226C4⋊Q8—42no—
227C4⋊Q8D4×C1112yes—
228C4×Q8—21no—
229C4×Q8—21no—
230C4×Q8—21no—
231C4×Q8—21no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—24no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4D4×C1111yescharacteristic
238C2×C4⋊C4D4×C1112yes—
239C2×C4⋊C4D4×C1112yes—
240C2×C42—21no—
241C2×C42—21no—
242C2×C42C23×C1111yescharacteristic
243#107—24no—
244C4⋊C8—21no—
245C4⋊C8—21no—
246C4⋊C8—21no—
247C4⋊C8D4×C1112yes—
248#103—24no—
249#103—28no—
250C4×C8—21no—
251C4×C8D4×C1112yes—
252#95—24no—
253#95—21no—
254C2×C11#163612yes—
255C2×C11#163712yes—
256C2×C11#200011yescharacteristic
257C2×C11#200311yescharacteristic
258C2×C11#201611yescharacteristic
259C2×Q8—21no—
260C2×Q8—21no—
261C2×Q8—22no—
262C2×Q8—21no—
263C2×Q8—21no—
264C2×Q8—21no—
265C2×Q8—44no—
266C2×Q8—41no—
267C2×Q8—41no—
268C2×Q8—41no—
269C2×Q8—41no—
270C2×Q8—41no—
271C2×Q8—41no—
272C2×Q8—41no—
273C2×Q8C11×SD1612yes—
274C22×C4—22no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—22no—
278C22×C4—41no—
279C22×C4C2×D4×C1111yescharacteristic
280C22×C4C2×D4×C1111yescharacteristic
281C22×C4C2×D4×C1111yescharacteristic
282C2×C8—22no—
283C2×C8—22no—
284C2×C8—42no—
285C2×C8—41no—
286C2×C8—41no—
287C2×C8—41no—
288C2×C8—42no—
289C4⋊C4—22no—
290C4⋊C4—22no—
291C4⋊C4—22no—
292C4⋊C4—21no—
293C4⋊C4—22no—
294C4⋊C4—21no—
295C4⋊C4—22no—
296C4⋊C4—48no—
297C4⋊C4—41no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4C11×Q1614yes—
304C42—41no—
305C42—41no—
306C42—41no—
307C42—41no—
308C42C2×D4×C1111yescharacteristic
309C42C2×D4×C1111yescharacteristic
310C42C2×D4×C1111yescharacteristic
311C42C11×#4111yescharacteristic
312C11#1005911yescharacteristic, direct product factor, Sylow
313C23C11×#12011yescharacteristic
314Q8—22no—
315Q8—22no—
316Q8—44no—
317Q8—41no—
318Q8—41no—
319Q8—82no—
320Q8—81no—
321Q8—81no—
322Q8—81no—
323Q8—81no—
324C2×C4—22no—
325C2×C4—22no—
326C2×C4—24no—
327C2×C4—41no—
328C2×C4—42no—
329C2×C4—41no—
330C2×C4—42no—
331C2×C4—41no—
332C2×C4—42no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—82no—
338C2×C4C11×#12011yescharacteristic
339C2×C4C11×#12011yescharacteristic
340C2×C4C11×#12111yescharacteristic
341C2×C4C11×#12111yescharacteristic
342C2×C4C11×#12111yescharacteristic
343C2×C4C11×#12711yescharacteristic
344C2×C4C2×C11×SD1611yescharacteristic
345C2×C4C2×C11×Q1612yes—
346C2×C4C11×#13511yescharacteristic
347C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
348C2×C4C11×#13712yes—
349C2×C4C11×#13711yescharacteristic
350C8—42no—
351C8—42no—
352C8—81no—
353C22C11×#39211yescharacteristic
354C22C11×#45011yescharacteristic
355C22C11×#45112yes—
356C22C11×#45211yescharacteristic
357C22C11×#45412yes—
358C4—21no—
359C4—21no—
360C4—44no—
361C4—42no—
362C4—82no—
363C4—81no—
364C4—82no—
365C4C11×#44811yescharacteristic
366C4C11×#44911yescharacteristic
367C4C11×#46212yes—
368C4C11×#46511yescharacteristic
369C4C11×#46811yescharacteristic
370C4C11×#49411yescharacteristic
371C4C11×#49711yescharacteristic
372C2C11×#163612yes—
373C2C11×#163712yes—
374C2C11×#200011yescharacteristic
375C2C11×#200311yescharacteristic
376C2C11×#201611yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C11#120
commutator, Frattini, cosocleC2×C42C23×C11
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
71. #10059C11direct (N × H)
312. C11#10059direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4872
C2×C11×#4772
C11×#25462
C11×#19872
C2×C11×#3322
C2×C11×Q8⋊C82
C11×#12792
#1005911