Finite Group Databasebeta

← C11×#10069 #14587262

Subgroups — C11×#10069 #14587262

Order 2816.

566 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
1C2×C11×#498C211yesmaximal, characteristic
2C2×C11×#462C211yesmaximal, characteristic
3C11×#2568C211yesmaximal, characteristic
4C11×#1988C211yesmaximal, characteristic
5C2×C11×#332C211yesmaximal, characteristic
6C2×C11×Q8⋊C8C211yesmaximal, characteristic
7C11×#1279C211yesmaximal, characteristic
8C22×C11×Q16—21no—
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×C4×Q8×C11C2211yescharacteristic
12C11×#498—22no—
13C11×#498—22no—
14C11×#462—22no—
15C11×#462—22no—
16C2×C11×#106—22no—
17C2×C11×C4⋊C8C2211yescharacteristic
18C2×C11×C4⋊C8C2211yescharacteristic
19C2×C11×#103—21no—
20C2×C4×C8×C11C2211yescharacteristic
21C11×#400—22no—
22C11×#391—21no—
23C11×#391—22no—
24C11×#382—21no—
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
32C2×C11×Q16—24no—
33C2×C11×Q16—42no—
34C2×C11×Q16—42no—
35C22×C8×C11—21no—
36C22×C8×C11—21no—
37C22×C8×C11—21no—
38C11×C4⋊Q8—21no—
39C11×C4⋊Q8—21no—
40C11×C4⋊Q8—21no—
41C11×C4⋊Q8—21no—
42C11×C4⋊Q8—21no—
43C11×C4⋊Q8—21no—
44C11×C4⋊Q8—21no—
45C11×C4⋊Q8D412yes—
46C4×Q8×C11—21no—
47C4×Q8×C11—21no—
48C4×Q8×C11—21no—
49C4×Q8×C11—21no—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4D412yes—
55C2×C11×C4⋊C4D411yescharacteristic
56C2×C11×C4⋊C4D412yes—
57C2×C42×C11—21no—
58C2×C42×C11—21no—
59C2×C42×C11C2311yescharacteristic
60C11×#106—28no—
61C11×C4⋊C8—21no—
62C11×C4⋊C8—21no—
63C11×C4⋊C8—21no—
64C11×C4⋊C8D412yes—
65C11×#103—24no—
66C4×C8×C11—21no—
67C4×C8×C11D412yes—
68C11×#95—24no—
69C11×#95—24no—
70C11×#95—21no—
71#10069C1111yesmaximal, 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—41no—
79C2×Q8×C11—41no—
80C2×Q8×C11—41no—
81C2×Q8×C11—42no—
82C2×Q8×C11—42no—
83C2×Q8×C11—41no—
84C2×Q8×C11—41no—
85C2×Q8×C11—41no—
86C2×Q8×C11—41no—
87C2×Q8×C11SD1612yes—
88C22×C4×C11—21no—
89C22×C4×C11—22no—
90C22×C4×C11—21no—
91C22×C4×C11—22no—
92C22×C4×C11—41no—
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11C2×D411yescharacteristic
96C11×Q16—48no—
97C2×C8×C11—24no—
98C2×C8×C11—22no—
99C2×C8×C11—22no—
100C2×C8×C11—41no—
101C2×C8×C11—41no—
102C2×C8×C11—42no—
103C2×C8×C11—41no—
104C11×C4⋊C4—21no—
105C11×C4⋊C4—22no—
106C11×C4⋊C4—22no—
107C11×C4⋊C4—22no—
108C11×C4⋊C4—21no—
109C11×C4⋊C4—22no—
110C11×C4⋊C4—22no—
111C11×C4⋊C4—22no—
112C11×C4⋊C4—41no—
113C11×C4⋊C4—41no—
114C11×C4⋊C4—41no—
115C11×C4⋊C4—41no—
116C11×C4⋊C4—41no—
117C11×C4⋊C4—41no—
118C42×C11—41no—
119C42×C11—41no—
120C42×C11—41no—
121C42×C11—41no—
122C42×C11C2×D411yescharacteristic
123C42×C11C2×D411yescharacteristic
124C42×C11C2×D411yescharacteristic
125C42×C11#4111yescharacteristic
126C2×#498C2×C1111yescharacteristic
127C2×#462C2×C1111yescharacteristic
128#2568C2×C1111yescharacteristic
129#1988C2×C1111yescharacteristic
130C2×#332C2×C1111yescharacteristic
131C2×Q8⋊C8C2×C1111yescharacteristic
132#1279C2×C1111yescharacteristic
133C23×C11#12011yescharacteristic
134Q8×C11—22no—
135Q8×C11—22no—
136Q8×C11—41no—
137Q8×C11—41no—
138Q8×C11—42no—
139Q8×C11—42no—
140Q8×C11—82no—
141Q8×C11—81no—
142Q8×C11—81no—
143Q8×C11—81no—
144Q8×C11—81no—
145C2×C4×C11—22no—
146C2×C4×C11—22no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—42no—
151C2×C4×C11—42no—
152C2×C4×C11—42no—
153C2×C4×C11—42no—
154C2×C4×C11—44no—
155C2×C4×C11—42no—
156C2×C4×C11—42no—
157C2×C4×C11—81no—
158C2×C4×C11—81no—
159C2×C4×C11#12011yescharacteristic
160C2×C4×C11#12011yescharacteristic
161C2×C4×C11#12111yescharacteristic
162C2×C4×C11#12111yescharacteristic
163C2×C4×C11#12111yescharacteristic
164C2×C4×C11#12711yescharacteristic
165C2×C4×C11C2×SD1611yescharacteristic
166C2×C4×C11#13511yescharacteristic
167C2×C4×C11#13512yes—
168C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
169C2×C4×C11#13711yescharacteristic
170C2×C4×C11#13712yes—
171C8×C11—24no—
172C8×C11—42no—
173C8×C11—81no—
174C22×Q16—21no—
175C2×C4⋊Q8C22×C1111yescharacteristic
176C2×C4⋊Q8C22×C1111yescharacteristic
177C2×C4×Q8C22×C1111yescharacteristic
178#498—22no—
179#498—22no—
180#462—22no—
181#462—22no—
182C2×#106—22no—
183C2×C4⋊C8C22×C1111yescharacteristic
184C2×C4⋊C8C22×C1111yescharacteristic
185C2×#103—21no—
186C2×C4×C8C22×C1111yescharacteristic
187#400—22no—
188#391—21no—
189#391—22no—
190#382—21no—
191C4×C4⋊C4C22×C1111yescharacteristic
192#340—22no—
193#332—22no—
194Q8⋊C8—22no—
195C22×C11#39211yescharacteristic
196C22×C11#44811yescharacteristic
197C22×C11#44911yescharacteristic
198C22×C11#45212yes—
199C22×C11#45612yes—
200C4×C11—21no—
201C4×C11—21no—
202C4×C11—42no—
203C4×C11—82no—
204C4×C11—82no—
205C4×C11—81no—
206C4×C11—82no—
207C4×C11#45011yescharacteristic
208C4×C11#45211yescharacteristic
209C4×C11#46412yes—
210C4×C11#46511yescharacteristic
211C4×C11#46811yescharacteristic
212C4×C11#49511yescharacteristic
213C4×C11#49711yescharacteristic
214C22×Q8—21no—
215C22×Q8—21no—
216C22×Q8D4×C1111yescharacteristic
217C2×Q16—24no—
218C2×Q16—42no—
219C2×Q16—42no—
220C22×C8—21no—
221C22×C8—21no—
222C22×C8—21no—
223C4⋊Q8—21no—
224C4⋊Q8—21no—
225C4⋊Q8—21no—
226C4⋊Q8—21no—
227C4⋊Q8—21no—
228C4⋊Q8—21no—
229C4⋊Q8—21no—
230C4⋊Q8D4×C1112yes—
231C4×Q8—21no—
232C4×Q8—21no—
233C4×Q8—21no—
234C4×Q8—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4D4×C1111yescharacteristic
240C2×C4⋊C4D4×C1112yes—
241C2×C4⋊C4D4×C1112yes—
242C2×C42—21no—
243C2×C42—21no—
244C2×C42C23×C1111yescharacteristic
245#106—28no—
246C4⋊C8—21no—
247C4⋊C8—21no—
248C4⋊C8—21no—
249C4⋊C8D4×C1112yes—
250#103—24no—
251C4×C8—21no—
252C4×C8D4×C1112yes—
253#95—24no—
254#95—24no—
255#95—21no—
256C2×C11#165212yes—
257C2×C11#165312yes—
258C2×C11#200011yescharacteristic
259C2×C11#200511yescharacteristic
260C2×C11#201511yescharacteristic
261C2×Q8—21no—
262C2×Q8—21no—
263C2×Q8—22no—
264C2×Q8—21no—
265C2×Q8—21no—
266C2×Q8—21no—
267C2×Q8—41no—
268C2×Q8—41no—
269C2×Q8—41no—
270C2×Q8—42no—
271C2×Q8—42no—
272C2×Q8—41no—
273C2×Q8—41no—
274C2×Q8—41no—
275C2×Q8—41no—
276C2×Q8C11×SD1612yes—
277C22×C4—21no—
278C22×C4—22no—
279C22×C4—21no—
280C22×C4—22no—
281C22×C4—41no—
282C22×C4C2×D4×C1111yescharacteristic
283C22×C4C2×D4×C1111yescharacteristic
284C22×C4C2×D4×C1111yescharacteristic
285Q16—48no—
286C2×C8—24no—
287C2×C8—22no—
288C2×C8—22no—
289C2×C8—41no—
290C2×C8—41no—
291C2×C8—41no—
292C2×C8—42no—
293C4⋊C4—21no—
294C4⋊C4—22no—
295C4⋊C4—22no—
296C4⋊C4—22no—
297C4⋊C4—21no—
298C4⋊C4—22no—
299C4⋊C4—22no—
300C4⋊C4—22no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C4⋊C4—41no—
307C42—41no—
308C42—41no—
309C42—41no—
310C42—41no—
311C42C2×D4×C1111yescharacteristic
312C42C2×D4×C1111yescharacteristic
313C42C2×D4×C1111yescharacteristic
314C42C11×#4111yescharacteristic
315C11#1006911yescharacteristic, direct product factor, Sylow
316C23C11×#12011yescharacteristic
317Q8—22no—
318Q8—22no—
319Q8—41no—
320Q8—41no—
321Q8—42no—
322Q8—42no—
323Q8—81no—
324Q8—81no—
325Q8—82no—
326Q8—81no—
327Q8—81no—
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—44no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—81no—
341C2×C4—81no—
342C2×C4C11×#12011yescharacteristic
343C2×C4C11×#12011yescharacteristic
344C2×C4C11×#12111yescharacteristic
345C2×C4C11×#12111yescharacteristic
346C2×C4C11×#12111yescharacteristic
347C2×C4C11×#12711yescharacteristic
348C2×C4C2×C11×SD1611yescharacteristic
349C2×C4C11×#13512yes—
350C2×C4C11×#13511yescharacteristic
351C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
352C2×C4C11×#13712yes—
353C2×C4C11×#13711yescharacteristic
354C8—24no—
355C8—42no—
356C8—81no—
357C22C11×#39211yescharacteristic
358C22C11×#44811yescharacteristic
359C22C11×#44911yescharacteristic
360C22C11×#45212yes—
361C22C11×#45612yes—
362C4—21no—
363C4—21no—
364C4—42no—
365C4—82no—
366C4—82no—
367C4—81no—
368C4—82no—
369C4C11×#45011yescharacteristic
370C4C11×#45211yescharacteristic
371C4C11×#46412yes—
372C4C11×#46511yescharacteristic
373C4C11×#46811yescharacteristic
374C4C11×#49511yescharacteristic
375C4C11×#49711yescharacteristic
376C2C11×#165212yes—
377C2C11×#165312yes—
378C2C11×#200011yescharacteristic
379C2C11×#200511yescharacteristic
380C2C11×#201511yescharacteristic
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. #10069C11direct (N × H)
315. C11#10069direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4982
C2×C11×#4622
C11×#25682
C11×#19882
C2×C11×#3322
C2×C11×Q8⋊C82
C11×#12792
#1006911