Finite Group Databasebeta

← C11×#10465 #14587658

Subgroups — C11×#10465 #14587658

Order 2816.

452 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3036C211yesmaximal, characteristic
2C11×#1804C211yesmaximal, characteristic, complemented
3C11×#1570C211yesmaximal, characteristic, complemented
4C11×#1540C211yesmaximal, characteristic, complemented
5C11×#1517C211yesmaximal, characteristic, complemented
6C11×#1460C211yesmaximal, characteristic, complemented
7C11×#1286C211yesmaximal, characteristic, complemented
8C2×C11×AGL(1,ℤ/8)—21no—
9C11×#532C2211yescharacteristic
10C2×C4×D4×C11C2211yescharacteristic
11C11×#463—22no—
12C11×#461—21no—
13C11×#459—21no—
14C11×#431C2211yescharacteristic
15C11×#431C2211yescharacteristic
16C11×#423C2211yescharacteristic
17C2×C11×C4⋊C8C2211yescharacteristic
18C11×#417—21no—
19C2×C11×#102—21no—
20C11×#382C2211yescharacteristic
21C11×#340—21no—
22C11×#334—22no—
23C11×#332—21no—
24C11×#331—21no—
25C11×#327—22no—
26C11×#323—22no—
27C2×C11×#41—21no—
28C22×D4×C11D411yescharacteristic
29C23×C4×C11—21no—
30C11×AGL(1,ℤ/8)—42no—
31C11×AGL(1,ℤ/8)—42no—
32C2×C11×SD16—22no—
33C2×C11×D8—22no—
34C2×C11×M16—21no—
35C22×C8×C11—21no—
36C11×C4⋊Q8D411yescharacteristic
37C11×#127D411yescharacteristic
38C11×#124—21no—
39C11×#121—21no—
40C11×#121—21no—
41C4×D4×C11—21no—
42C4×D4×C11—21no—
43C4×D4×C11—21no—
44C4×D4×C11—21no—
45C4×D4×C11—21no—
46C4×D4×C11—21no—
47C2×C11×C4⋊C4—21no—
48C2×C11×C4⋊C4D411yescharacteristic
49C2×C11×C22⋊C4—21no—
50C2×C42×C11C2311yescharacteristic
51C11×C4⋊C8—21no—
52C11×C4⋊C8—21no—
53C11×C4⋊C8—21no—
54C11×C4⋊C8—21no—
55C11×C4⋊C8—21no—
56C11×C4⋊C8D412yes—
57C11×#103—22no—
58C11×#102—22no—
59C11×#102—42no—
60C11×C22⋊C8—21no—
61C11×C22⋊C8D412yes—
62C4×C8×C11—21no—
63C4×C8×C11—21no—
64C11×#95—21no—
65C11×#95—21no—
66#10465C1111yesmaximal, characteristic, direct product factor, Sylow
67C24×C11—21no—
68C11×#41—41no—
69C11×#41—41no—
70C11×#41—41no—
71C11×#41—41no—
72C2×Q8×C11—21no—
73C2×D4×C11—21no—
74C2×D4×C11—21no—
75C2×D4×C11—21no—
76C2×D4×C11—21no—
77C2×D4×C11—21no—
78C2×D4×C11—21no—
79C2×D4×C11—21no—
80C2×D4×C11—21no—
81C2×D4×C11—41no—
82C2×D4×C11SD1612yes—
83C22×C4×C11—21no—
84C22×C4×C11—41no—
85C22×C4×C11—41no—
86C22×C4×C11—41no—
87C22×C4×C11—41no—
88C22×C4×C11—82no—
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11#4111yescharacteristic
92C11×SD16—44no—
93C11×D8—44no—
94C11×M16—41no—
95C11×M16—41no—
96C2×C8×C11—22no—
97C2×C8×C11—22no—
98C2×C8×C11—41no—
99C2×C8×C11—41no—
100C2×C8×C11—41no—
101C2×C8×C11—41no—
102C11×C4⋊C4—21no—
103C11×C4⋊C4—21no—
104C11×C4⋊C4—21no—
105C11×C4⋊C4—21no—
106C11×C4⋊C4—41no—
107C11×C4⋊C4—41no—
108C11×C22⋊C4—41no—
109C11×C22⋊C4—41no—
110C11×C22⋊C4—41no—
111C11×C22⋊C4—41no—
112C42×C11C2×D411yescharacteristic
113C42×C11C2×D411yescharacteristic
114C42×C11#4111yescharacteristic
115C42×C11#4111yescharacteristic
116#3036C2×C1111yescharacteristic
117#1804C2×C1111yescharacteristic, complemented
118#1570C2×C1111yescharacteristic, complemented
119#1540C2×C1111yescharacteristic, complemented
120#1517C2×C1111yescharacteristic, complemented
121#1460C2×C1111yescharacteristic, complemented
122#1286C2×C1111yescharacteristic, complemented
123C23×C11—22no—
124C23×C11—41no—
125C23×C11—41no—
126C23×C11—41no—
127C23×C11—81no—
128C23×C11—81no—
129C23×C11#12111yescharacteristic
130Q8×C11—41no—
131Q8×C11—41no—
132D4×C11—22no—
133D4×C11—22no—
134D4×C11—41no—
135D4×C11—41no—
136D4×C11—41no—
137D4×C11—41no—
138D4×C11—81no—
139D4×C11—81no—
140D4×C11—81no—
141D4×C11—81no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11—82no—
147C2×C4×C11—82no—
148C2×C4×C11—81no—
149C2×C4×C11—81no—
150C2×C4×C11—81no—
151C2×C4×C11—81no—
152C2×C4×C11—81no—
153C2×C4×C11—81no—
154C2×C4×C11#12011yescharacteristic
155C2×C4×C11#12111yescharacteristic
156C2×C4×C11#12111yescharacteristic
157C2×C4×C11#12311yescharacteristic
158C2×C4×C11#12311yescharacteristic
159C2×C4×C11#12411yescharacteristic
160C2×C4×C11C2×SD1611yescharacteristic
161C2×C4×C11#13511yescharacteristic
162C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
163C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
164C8×C11—42no—
165C8×C11—42no—
166C8×C11—81no—
167C8×C11—81no—
168C2×AGL(1,ℤ/8)—21no—
169#532C22×C1111yescharacteristic
170C2×C4×D4C22×C1111yescharacteristic
171#463—22no—
172#461—21no—
173#459—21no—
174#431C22×C1111yescharacteristic
175#431C22×C1111yescharacteristic
176#423C22×C1111yescharacteristic
177C2×C4⋊C8C22×C1111yescharacteristic
178#417—21no—
179C2×#102—21no—
180#382C22×C1111yescharacteristic
181#340—21no—
182#334—22no—
183#332—21no—
184#331—21no—
185#327—22no—
186#323—22no—
187C22×C11—21no—
188C22×C11—21no—
189C22×C11—42no—
190C22×C11—82no—
191C22×C11—82no—
192C22×C11—81no—
193C22×C11—81no—
194C22×C11—81no—
195C22×C11—81no—
196C22×C11—81no—
197C22×C11#39411yescharacteristic
198C22×C11#46511yescharacteristic
199C22×C11#46911yescharacteristic
200C4×C11—21no—
201C4×C11—21no—
202C4×C11—21no—
203C4×C11—21no—
204C4×C11—81no—
205C4×C11—81no—
206C4×C11—161no—
207C4×C11#44911yescharacteristic
208C4×C11#45011yescharacteristic
209C4×C11#48111yescharacteristic
210C4×C11#48211yescharacteristic
211C2×#41—21no—
212C22×D4D4×C1111yescharacteristic
213C23×C4—21no—
214AGL(1,ℤ/8)—42no—
215AGL(1,ℤ/8)—42no—
216C2×SD16—22no—
217C2×D8—22no—
218C2×M16—21no—
219C22×C8—21no—
220C4⋊Q8D4×C1111yescharacteristic
221#127D4×C1111yescharacteristic
222#124—21no—
223#121—21no—
224#121—21no—
225C4×D4—21no—
226C4×D4—21no—
227C4×D4—21no—
228C4×D4—21no—
229C4×D4—21no—
230C4×D4—21no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4D4×C1111yescharacteristic
233C2×C22⋊C4—21no—
234C2×C42C23×C1111yescharacteristic
235C4⋊C8—21no—
236C4⋊C8—21no—
237C4⋊C8—21no—
238C4⋊C8—21no—
239C4⋊C8—21no—
240C4⋊C8D4×C1112yes—
241#103—22no—
242#102—22no—
243#102—42no—
244C22⋊C8—21no—
245C22⋊C8D4×C1112yes—
246C4×C8—21no—
247C4×C8—21no—
248#95—21no—
249#95—21no—
250C2×C11—21no—
251C2×C11—21no—
252C2×C11—82no—
253C2×C11—161no—
254C2×C11#203411yescharacteristic
255C2×C11#204811yescharacteristic
256C2×C11#205311yescharacteristic
257C24—21no—
258#41—41no—
259#41—41no—
260#41—41no—
261#41—41no—
262C2×Q8—21no—
263C2×D4—21no—
264C2×D4—21no—
265C2×D4—21no—
266C2×D4—21no—
267C2×D4—21no—
268C2×D4—21no—
269C2×D4—21no—
270C2×D4—21no—
271C2×D4—41no—
272C2×D4C11×SD1612yes—
273C22×C4—21no—
274C22×C4—41no—
275C22×C4—41no—
276C22×C4—41no—
277C22×C4—41no—
278C22×C4—82no—
279C22×C4C2×D4×C1111yescharacteristic
280C22×C4C2×D4×C1111yescharacteristic
281C22×C4C11×#4111yescharacteristic
282SD16—44no—
283D8—44no—
284M16—41no—
285M16—41no—
286C2×C8—22no—
287C2×C8—22no—
288C2×C8—41no—
289C2×C8—41no—
290C2×C8—41no—
291C2×C8—41no—
292C4⋊C4—21no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C22⋊C4—41no—
299C22⋊C4—41no—
300C22⋊C4—41no—
301C22⋊C4—41no—
302C42C2×D4×C1111yescharacteristic
303C42C2×D4×C1111yescharacteristic
304C42C11×#4111yescharacteristic
305C42C11×#4111yescharacteristic
306C11#1046511yescharacteristic, direct product factor, Sylow
307C23—22no—
308C23—41no—
309C23—41no—
310C23—41no—
311C23—81no—
312C23—81no—
313C23C11×#12111yescharacteristic
314Q8—41no—
315Q8—41no—
316D4—22no—
317D4—22no—
318D4—41no—
319D4—41no—
320D4—41no—
321D4—41no—
322D4—81no—
323D4—81no—
324D4—81no—
325D4—81no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—82no—
331C2×C4—82no—
332C2×C4—81no—
333C2×C4—81no—
334C2×C4—81no—
335C2×C4—81no—
336C2×C4—81no—
337C2×C4—81no—
338C2×C4C11×#12011yescharacteristic
339C2×C4C11×#12111yescharacteristic
340C2×C4C11×#12111yescharacteristic
341C2×C4C11×#12311yescharacteristic
342C2×C4C11×#12311yescharacteristic
343C2×C4C11×#12411yescharacteristic
344C2×C4C2×C11×SD1611yescharacteristic
345C2×C4C11×#13511yescharacteristic
346C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
347C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
348C8—42no—
349C8—42no—
350C8—81no—
351C8—81no—
352C22—21no—
353C22—21no—
354C22—42no—
355C22—82no—
356C22—82no—
357C22—81no—
358C22—81no—
359C22—81no—
360C22—81no—
361C22—81no—
362C22C11×#39411yescharacteristic
363C22C11×#46511yescharacteristic
364C22C11×#46911yescharacteristic
365C4—21no—
366C4—21no—
367C4—21no—
368C4—21no—
369C4—81no—
370C4—81no—
371C4—161no—
372C4C11×#44911yescharacteristic
373C4C11×#45011yescharacteristic
374C4C11×#48111yescharacteristic
375C4C11×#48211yescharacteristic
376C2—21no—
377C2—21no—
378C2—82no—
379C2—161no—
380C2C11×#203411yescharacteristic
381C2C11×#204811yescharacteristic
382C2C11×#205311yescharacteristic
subgroupG/H
center, socleC22×C11#394
commutator, Frattini, cosocleC2×C42C23×C11
prime radicalC11×#3036C2
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#1804C2semidirect
3. C11×#1570C2semidirect
4. C11×#1540C2semidirect
5. C11×#1517C2semidirect
6. C11×#1460C2semidirect
7. C11×#1286C2semidirect
66. #10465C11direct (N × H)
117. #1804C2×C11semidirect
118. #1570C2×C11semidirect
119. #1540C2×C11semidirect
120. #1517C2×C11semidirect
121. #1460C2×C11semidirect
122. #1286C2×C11semidirect
306. C11#10465direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#30362
C11×#18042
C11×#15702
C11×#15402
C11×#15172
C11×#14602
C11×#12862
#1046511