Finite Group Databasebeta

← C11×#19433 #14596626

Subgroups — C11×#19433 #14596626

Order 2816.

636 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×#3206C211yesmaximal, characteristic
2C2×C11×#475C211yesmaximal, characteristic, complemented
3C11×#3037C211yesmaximal, characteristic
4C11×#2983C211yesmaximal, characteristic, complemented
5C11×#1700C214yesmaximal, complemented
6C11×#1686C214yesmaximal, complemented
7C11×#1571C211yesmaximal, characteristic, complemented
8C11×#1549C211yesmaximal, characteristic, complemented
9C11×#1540C211yesmaximal, characteristic
10C2×C11×#137—21no—
11C11×#532C2211yescharacteristic
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C4×Q8×C11C2211yescharacteristic
14C11×#492C2212yes—
15C11×#487C2212yes—
16C11×#475—22no—
17C11×#475C2214yes—
18C11×#464—22no—
19C11×#462C2212yes—
20C11×#461—22no—
21C11×#460C2212yes—
22C11×#448—22no—
23C11×#446—22no—
24C11×#446C2214yes—
25C11×#432—22no—
26C11×#431C2211yescharacteristic
27C11×#431C2211yescharacteristic
28C2×C11×#106—21no—
29C11×#423C2211yescharacteristic
30C2×C11×C4⋊C8C2211yescharacteristic
31C11×#417—21no—
32C2×C11×#103—21no—
33C11×#335C2214yes—
34C11×#332C2214yes—
35C11×#332C2212yes—
36C11×#331C2212yes—
37C2×C11×#41—21no—
38C22×Q8×C11—21no—
39C22×Q8×C11D411yescharacteristic
40C11×#137—44no—
41C2×C11×Q16—22no—
42C2×C11×SD16—22no—
43C2×C11×SD16—24no—
44C2×C11×M16—21no—
45C22×C8×C11—21no—
46C11×C4⋊Q8—21no—
47C11×C4⋊Q8—21no—
48C11×C4⋊Q8—21no—
49C11×C4⋊Q8C2312yes—
50C11×C4⋊Q8C2311yescharacteristic
51C11×#127C2311yescharacteristic
52C11×#124—21no—
53C11×#121—21no—
54C11×#121—21no—
55C4×Q8×C11—21no—
56C4×Q8×C11—21no—
57C4×Q8×C11D412yes—
58C4×Q8×C11C2312yes—
59C4×D4×C11—21no—
60C4×D4×C11—21no—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4D411yescharacteristic
65C2×C42×C11—21no—
66C2×C42×C11C2311yescharacteristic
67C11×#106—24no—
68C11×C4⋊C8—24no—
69C11×C4⋊C8—21no—
70C11×C4⋊C8—21no—
71C11×C4⋊C8D412yes—
72C11×C4⋊C8C2312yes—
73C11×C4⋊C8C2312yes—
74C11×C4⋊C8C2312yes—
75C11×#103—24no—
76C11×#103—24no—
77C11×#103—22no—
78C11×#102—22no—
79C11×C22⋊C8—21no—
80C11×C22⋊C8D412yes—
81C11×#97—24no—
82C4×C8×C11—21no—
83C4×C8×C11C2312yes—
84#19433C1111yesmaximal, characteristic, direct product factor, Sylow
85C11×#41—42no—
86C11×#41—42no—
87C2×Q8×C11—21no—
88C2×Q8×C11—22no—
89C2×Q8×C11—22no—
90C2×Q8×C11—21no—
91C2×Q8×C11—22no—
92C2×Q8×C11—41no—
93C2×Q8×C11—82no—
94C2×Q8×C11C2×D412yes—
95C2×D4×C11—21no—
96C2×D4×C11—21no—
97C2×D4×C11—21no—
98C2×D4×C11—41no—
99C22×C4×C11—21no—
100C22×C4×C11—21no—
101C22×C4×C11—41no—
102C22×C4×C11—41no—
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11#4111yescharacteristic
106C11×Q16—44no—
107C11×SD16—44no—
108C11×SD16—84no—
109C11×M16—42no—
110C2×C8×C11—22no—
111C2×C8×C11—22no—
112C2×C8×C11—22no—
113C2×C8×C11—42no—
114C2×C8×C11C2×D414yes—
115C11×C4⋊C4—22no—
116C11×C4⋊C4—21no—
117C11×C4⋊C4—22no—
118C11×C4⋊C4—21no—
119C11×C4⋊C4—22no—
120C11×C4⋊C4—22no—
121C11×C4⋊C4—21no—
122C11×C4⋊C4—41no—
123C11×C4⋊C4—41no—
124C11×C4⋊C4C2×D412yes—
125C11×C22⋊C4—41no—
126C11×C22⋊C4—41no—
127C42×C11—22no—
128C42×C11—22no—
129C42×C11C2×D411yescharacteristic
130C42×C11C2×D411yescharacteristic
131C42×C11#4111yescharacteristic
132C42×C11C2411yescharacteristic
133#3206C2×C1111yescharacteristic
134C2×#475C2×C1111yescharacteristic, complemented
135#3037C2×C1111yescharacteristic
136#2983C2×C1111yescharacteristic, complemented
137#1700C2×C1114yescomplemented
138#1686C2×C1114yescomplemented
139#1571C2×C1111yescharacteristic, complemented
140#1549C2×C1111yescharacteristic, complemented
141#1540C2×C1111yescharacteristic
142C23×C11—41no—
143C23×C11#12111yescharacteristic
144Q8×C11—22no—
145Q8×C11—22no—
146Q8×C11—42no—
147Q8×C11—41no—
148Q8×C11—41no—
149Q8×C11—44no—
150Q8×C11—82no—
151D4×C11—41no—
152D4×C11—41no—
153D4×C11—42no—
154D4×C11—81no—
155D4×C11—82no—
156C2×C4×C11—22no—
157C2×C4×C11—22no—
158C2×C4×C11—22no—
159C2×C4×C11—41no—
160C2×C4×C11—42no—
161C2×C4×C11—41no—
162C2×C4×C11—42no—
163C2×C4×C11—81no—
164C2×C4×C11—82no—
165C2×C4×C11—82no—
166C2×C4×C11#12111yescharacteristic
167C2×C4×C11#12111yescharacteristic
168C2×C4×C11#12111yescharacteristic
169C2×C4×C11AGL(1,ℤ/8)12yes—
170C2×C4×C11#13712yes—
171C2×C4×C11C22×D411yescharacteristic
172C2×C4×C11C22×D411yescharacteristic
173C2×C4×C11C2×#4111yescharacteristic
174C8×C11—24no—
175C8×C11—42no—
176C8×C11—42no—
177C8×C11—42no—
178C2×#137—21no—
179#532C22×C1111yescharacteristic
180C2×C4⋊Q8C22×C1111yescharacteristic
181C2×C4×Q8C22×C1111yescharacteristic
182#492C22×C1112yes—
183#487C22×C1112yes—
184#475—22no—
185#475C22×C1114yes—
186#464—22no—
187#462C22×C1112yes—
188#461—22no—
189#460C22×C1112yes—
190#448—22no—
191#446—22no—
192#446C22×C1114yes—
193#432—22no—
194#431C22×C1111yescharacteristic
195#431C22×C1111yescharacteristic
196C2×#106—21no—
197#423C22×C1111yescharacteristic
198C2×C4⋊C8C22×C1111yescharacteristic
199#417—21no—
200C2×#103—21no—
201#335C22×C1114yes—
202#332C22×C1112yes—
203#332C22×C1114yes—
204#331C22×C1112yes—
205C22×C11—21no—
206C22×C11—21no—
207C22×C11—81no—
208C22×C11—81no—
209C22×C11—81no—
210C22×C11#46812yes—
211C22×C11C2×#12111yescharacteristic
212C4×C11—21no—
213C4×C11—21no—
214C4×C11—21no—
215C4×C11—42no—
216C4×C11—42no—
217C4×C11—82no—
218C4×C11—81no—
219C4×C11#46812yes—
220C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
221C4×C11C2×#13711yescharacteristic
222C4×C11#57712yes—
223C2×#41—21no—
224C22×Q8—21no—
225C22×Q8D4×C1111yescharacteristic
226#137—44no—
227C2×Q16—22no—
228C2×SD16—22no—
229C2×SD16—24no—
230C2×M16—21no—
231C22×C8—21no—
232C4⋊Q8—21no—
233C4⋊Q8—21no—
234C4⋊Q8—21no—
235C4⋊Q8C23×C1112yes—
236C4⋊Q8C23×C1111yescharacteristic
237#127C23×C1111yescharacteristic
238#124—21no—
239#121—21no—
240#121—21no—
241C4×Q8—21no—
242C4×Q8—21no—
243C4×Q8D4×C1112yes—
244C4×Q8C23×C1112yes—
245C4×D4—21no—
246C4×D4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4D4×C1111yescharacteristic
251C2×C42—21no—
252C2×C42C23×C1111yescharacteristic
253#106—24no—
254C4⋊C8—24no—
255C4⋊C8—21no—
256C4⋊C8—21no—
257C4⋊C8D4×C1112yes—
258C4⋊C8C23×C1112yes—
259C4⋊C8C23×C1112yes—
260C4⋊C8C23×C1112yes—
261#103—24no—
262#103—24no—
263#103—22no—
264#102—22no—
265C22⋊C8—21no—
266C22⋊C8D4×C1112yes—
267#97—24no—
268C4×C8—21no—
269C4×C8C23×C1112yes—
270C2×C11—22no—
271C2×C11—161no—
272C2×C11#304311yescharacteristic
273C2×C11C2×#46811yescharacteristic
274C2×C11#306911yescharacteristic
275#41—42no—
276#41—42no—
277C2×Q8—21no—
278C2×Q8—22no—
279C2×Q8—22no—
280C2×Q8—21no—
281C2×Q8—22no—
282C2×Q8—41no—
283C2×Q8—82no—
284C2×Q8C2×D4×C1112yes—
285C2×D4—21no—
286C2×D4—21no—
287C2×D4—21no—
288C2×D4—41no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—41no—
292C22×C4—41no—
293C22×C4C2×D4×C1111yescharacteristic
294C22×C4C2×D4×C1111yescharacteristic
295C22×C4C11×#4111yescharacteristic
296Q16—44no—
297SD16—44no—
298SD16—84no—
299M16—42no—
300C2×C8—22no—
301C2×C8—22no—
302C2×C8—22no—
303C2×C8—42no—
304C2×C8C2×D4×C1114yes—
305C4⋊C4—22no—
306C4⋊C4—21no—
307C4⋊C4—22no—
308C4⋊C4—21no—
309C4⋊C4—22no—
310C4⋊C4—22no—
311C4⋊C4—21no—
312C4⋊C4—41no—
313C4⋊C4—41no—
314C4⋊C4C2×D4×C1112yes—
315C22⋊C4—41no—
316C22⋊C4—41no—
317C42—22no—
318C42—22no—
319C42C2×D4×C1111yescharacteristic
320C42C2×D4×C1111yescharacteristic
321C42C11×#4111yescharacteristic
322C42C24×C1111yescharacteristic
323C11#1943311yescharacteristic, direct product factor, Sylow
324C23—41no—
325C23C11×#12111yescharacteristic
326Q8—22no—
327Q8—22no—
328Q8—42no—
329Q8—41no—
330Q8—41no—
331Q8—44no—
332Q8—82no—
333D4—41no—
334D4—41no—
335D4—42no—
336D4—81no—
337D4—82no—
338C2×C4—22no—
339C2×C4—22no—
340C2×C4—22no—
341C2×C4—41no—
342C2×C4—42no—
343C2×C4—41no—
344C2×C4—42no—
345C2×C4—81no—
346C2×C4—82no—
347C2×C4—82no—
348C2×C4C11×#12111yescharacteristic
349C2×C4C11×#12111yescharacteristic
350C2×C4C11×#12111yescharacteristic
351C2×C4C11×AGL(1,ℤ/8)12yes—
352C2×C4C11×#13712yes—
353C2×C4C22×D4×C1111yescharacteristic
354C2×C4C22×D4×C1111yescharacteristic
355C2×C4C2×C11×#4111yescharacteristic
356C8—24no—
357C8—42no—
358C8—42no—
359C8—42no—
360C22—21no—
361C22—21no—
362C22—81no—
363C22—81no—
364C22—81no—
365C22C11×#46812yes—
366C22C2×C11×#12111yescharacteristic
367C4—21no—
368C4—21no—
369C4—21no—
370C4—42no—
371C4—42no—
372C4—82no—
373C4—81no—
374C4C11×#46812yes—
375C4C2×C11×AGL(1,ℤ/8)11yescharacteristic
376C4C2×C11×#13711yescharacteristic
377C4C11×#57712yes—
378C2—22no—
379C2—161no—
380C2C11×#304311yescharacteristic
381C2C2×C11×#46811yescharacteristic
382C2C11×#306911yescharacteristic
subgroupG/H
center, socleC22×C11C2×#121
commutator, Frattini, cosocleC42C24×C11
prime radicalC11×#532C22
LCSG ▷ 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. C2×C11×#475C2semidirect
4. C11×#2983C2semidirect
5. C11×#1700C2semidirect
6. C11×#1686C2semidirect
7. C11×#1571C2semidirect
8. C11×#1549C2semidirect
84. #19433C11direct (N × H)
134. C2×#475C2×C11semidirect
136. #2983C2×C11semidirect
137. #1700C2×C11semidirect
138. #1686C2×C11semidirect
139. #1571C2×C11semidirect
140. #1549C2×C11semidirect
323. C11#19433direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32062
C2×C11×#4752
C11×#30372
C11×#29832
C11×#17002
C11×#16862
C11×#15712
C11×#15492
C11×#15402
#1943311