Finite Group Databasebeta

← C11×#10181 #14587374

Subgroups — C11×#10181 #14587374

Order 2816.

530 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3206C211yesmaximal, characteristic
2C2×C11×#477C211yesmaximal, characteristic, complemented
3C11×#3037C211yesmaximal, characteristic
4C11×#1549C211yesmaximal, characteristic, complemented
5C11×#1480C211yesmaximal, characteristic
6C11×#1461C211yesmaximal, characteristic, complemented
7C11×#1301C211yesmaximal, characteristic, complemented
8C2×C11×#137—21no—
9C11×#532C2211yescharacteristic
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×C4×Q8×C11C2211yescharacteristic
12C11×#492—21no—
13C11×#487—21no—
14C11×#477—22no—
15C11×#477—22no—
16C11×#464—22no—
17C11×#462—21no—
18C11×#461—22no—
19C11×#460—21no—
20C11×#448—22no—
21C11×#431C2211yescharacteristic
22C11×#431C2211yescharacteristic
23C2×C11×#107—21no—
24C11×#423C2211yescharacteristic
25C2×C11×C4⋊C8C2211yescharacteristic
26C11×#417—21no—
27C2×C11×#103—21no—
28C11×#332—22no—
29C11×D4⋊C8—22no—
30C11×#324—22no—
31C2×C11×#41—21no—
32C22×Q8×C11—21no—
33C22×Q8×C11D411yescharacteristic
34C11×#137—42no—
35C11×#137—42no—
36C2×C11×Q16—22no—
37C2×C11×SD16—22no—
38C2×C11×SD16—24no—
39C2×C11×M16—21no—
40C22×C8×C11—21no—
41C11×C4⋊Q8—21no—
42C11×C4⋊Q8—21no—
43C11×C4⋊Q8—21no—
44C11×C4⋊Q8D412yes—
45C11×C4⋊Q8D411yescharacteristic
46C11×#127D411yescharacteristic
47C11×#124—21no—
48C11×#121—21no—
49C11×#121—21no—
50C4×Q8×C11—21no—
51C4×Q8×C11—21no—
52C4×Q8×C11—21no—
53C4×Q8×C11—21no—
54C4×D4×C11—21no—
55C4×D4×C11—21no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4D411yescharacteristic
60C2×C42×C11—21no—
61C2×C42×C11C2311yescharacteristic
62C11×#107—24no—
63C11×C4⋊C8—21no—
64C11×C4⋊C8—21no—
65C11×C4⋊C8—21no—
66C11×C4⋊C8—21no—
67C11×C4⋊C8D412yes—
68C11×C4⋊C8D412yes—
69C11×#103—24no—
70C11×#103—22no—
71C11×#103—24no—
72C11×#102—22no—
73C11×C22⋊C8—21no—
74C11×C22⋊C8D412yes—
75C4×C8×C11—21no—
76C4×C8×C11—21no—
77#10181C1111yesmaximal, characteristic, direct product factor, Sylow
78C11×#41—41no—
79C11×#41—41no—
80C11×#41—41no—
81C11×#41—41no—
82C2×Q8×C11—21no—
83C2×Q8×C11—21no—
84C2×Q8×C11—21no—
85C2×Q8×C11—21no—
86C2×Q8×C11—22no—
87C2×Q8×C11—21no—
88C2×Q8×C11—21no—
89C2×Q8×C11—41no—
90C2×Q8×C11—82no—
91C2×Q8×C11SD1612yescomplemented
92C2×D4×C11—21no—
93C2×D4×C11—21no—
94C2×D4×C11—21no—
95C2×D4×C11—41no—
96C22×C4×C11—21no—
97C22×C4×C11—21no—
98C22×C4×C11—41no—
99C22×C4×C11—41no—
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11#4111yescharacteristic
103C11×Q16—44no—
104C11×SD16—44no—
105C11×SD16—84no—
106C11×M16—41no—
107C11×M16—41no—
108C2×C8×C11—22no—
109C2×C8×C11—22no—
110C2×C8×C11—22no—
111C2×C8×C11—41no—
112C2×C8×C11—41no—
113C2×C8×C11—41no—
114C11×C4⋊C4—21no—
115C11×C4⋊C4—21no—
116C11×C4⋊C4—22no—
117C11×C4⋊C4—21no—
118C11×C4⋊C4—22no—
119C11×C4⋊C4—21no—
120C11×C4⋊C4—41no—
121C11×C4⋊C4—41no—
122C11×C4⋊C4—41no—
123C11×C4⋊C4—41no—
124C11×C22⋊C4—41no—
125C11×C22⋊C4—41no—
126C42×C11—41no—
127C42×C11—41no—
128C42×C11C2×D411yescharacteristic
129C42×C11C2×D411yescharacteristic
130C42×C11C2×D411yescharacteristic
131C42×C11C2×D411yescharacteristic
132#3206C2×C1111yescharacteristic
133C2×#477C2×C1111yescharacteristic, complemented
134#3037C2×C1111yescharacteristic
135#1549C2×C1111yescharacteristic, complemented
136#1480C2×C1111yescharacteristic
137#1461C2×C1111yescharacteristic, complemented
138#1301C2×C1111yescharacteristic, complemented
139C23×C11—41no—
140C23×C11#12111yescharacteristic
141Q8×C11—22no—
142Q8×C11—22no—
143Q8×C11—44no—
144Q8×C11—41no—
145Q8×C11—41no—
146Q8×C11—41no—
147Q8×C11—41no—
148Q8×C11—82no—
149D4×C11—42no—
150D4×C11—41no—
151D4×C11—41no—
152D4×C11—42no—
153D4×C11—81no—
154D4×C11—81no—
155C2×C4×C11—22no—
156C2×C4×C11—22no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11—42no—
163C2×C4×C11—82no—
164C2×C4×C11—81no—
165C2×C4×C11—81no—
166C2×C4×C11—81no—
167C2×C4×C11#12011yescharacteristic
168C2×C4×C11#12011yescharacteristic
169C2×C4×C11#12011yescharacteristic
170C2×C4×C11#12111yescharacteristic
171C2×C4×C11#12111yescharacteristic
172C2×C4×C11#12711yescharacteristic
173C2×C4×C11C2×SD1611yescharacteristic
174C2×C4×C11#13511yescharacteristic
175C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
176C2×C4×C11#13711yescharacteristic
177C8×C11—42no—
178C8×C11—42no—
179C8×C11—42no—
180C8×C11—81no—
181C2×#137—21no—
182#532C22×C1111yescharacteristic
183C2×C4⋊Q8C22×C1111yescharacteristic
184C2×C4×Q8C22×C1111yescharacteristic
185#492—21no—
186#487—21no—
187#477—22no—
188#477—22no—
189#464—22no—
190#462—21no—
191#461—22no—
192#460—21no—
193#448—22no—
194#431C22×C1111yescharacteristic
195#431C22×C1111yescharacteristic
196C2×#107—21no—
197#423C22×C1111yescharacteristic
198C2×C4⋊C8C22×C1111yescharacteristic
199#417—21no—
200C2×#103—21no—
201#332—22no—
202D4⋊C8—22no—
203#324—22no—
204C22×C11—21no—
205C22×C11—21no—
206C22×C11—81no—
207C22×C11—81no—
208C22×C11—81no—
209C22×C11#39211yescharacteristic
210C22×C11#46511yescharacteristic
211C22×C11#46811yescharacteristic
212C4×C11—21no—
213C4×C11—21no—
214C4×C11—21no—
215C4×C11—42no—
216C4×C11—81no—
217C4×C11—81no—
218C4×C11—82no—
219C4×C11#44811yescharacteristic
220C4×C11#44911yescharacteristic
221C4×C11#45011yescharacteristic
222C4×C11#45211yescharacteristic
223C4×C11#47312yes—
224C2×#41—21no—
225C22×Q8—21no—
226C22×Q8D4×C1111yescharacteristic
227#137—42no—
228#137—42no—
229C2×Q16—22no—
230C2×SD16—22no—
231C2×SD16—24no—
232C2×M16—21no—
233C22×C8—21no—
234C4⋊Q8—21no—
235C4⋊Q8—21no—
236C4⋊Q8—21no—
237C4⋊Q8D4×C1112yes—
238C4⋊Q8D4×C1111yescharacteristic
239#127D4×C1111yescharacteristic
240#124—21no—
241#121—21no—
242#121—21no—
243C4×Q8—21no—
244C4×Q8—21no—
245C4×Q8—21no—
246C4×Q8—21no—
247C4×D4—21no—
248C4×D4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4D4×C1111yescharacteristic
253C2×C42—21no—
254C2×C42C23×C1111yescharacteristic
255#107—24no—
256C4⋊C8—21no—
257C4⋊C8—21no—
258C4⋊C8—21no—
259C4⋊C8—21no—
260C4⋊C8D4×C1112yes—
261C4⋊C8D4×C1112yes—
262#103—24no—
263#103—22no—
264#103—24no—
265#102—22no—
266C22⋊C8—21no—
267C22⋊C8D4×C1112yes—
268C4×C8—21no—
269C4×C8—21no—
270C2×C11—21no—
271C2×C11—21no—
272C2×C11—161no—
273C2×C11#200011yescharacteristic
274C2×C11#200811yescharacteristic
275C2×C11#202011yescharacteristic
276#41—41no—
277#41—41no—
278#41—41no—
279#41—41no—
280C2×Q8—21no—
281C2×Q8—21no—
282C2×Q8—21no—
283C2×Q8—21no—
284C2×Q8—22no—
285C2×Q8—21no—
286C2×Q8—21no—
287C2×Q8—41no—
288C2×Q8—82no—
289C2×Q8C11×SD1612yescomplemented
290C2×D4—21no—
291C2×D4—21no—
292C2×D4—21no—
293C2×D4—41no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—41no—
297C22×C4—41no—
298C22×C4C2×D4×C1111yescharacteristic
299C22×C4C2×D4×C1111yescharacteristic
300C22×C4C11×#4111yescharacteristic
301Q16—44no—
302SD16—44no—
303SD16—84no—
304M16—41no—
305M16—41no—
306C2×C8—22no—
307C2×C8—22no—
308C2×C8—22no—
309C2×C8—41no—
310C2×C8—41no—
311C2×C8—41no—
312C4⋊C4—21no—
313C4⋊C4—21no—
314C4⋊C4—22no—
315C4⋊C4—21no—
316C4⋊C4—22no—
317C4⋊C4—21no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C22⋊C4—41no—
323C22⋊C4—41no—
324C42—41no—
325C42—41no—
326C42C2×D4×C1111yescharacteristic
327C42C2×D4×C1111yescharacteristic
328C42C2×D4×C1111yescharacteristic
329C42C2×D4×C1111yescharacteristic
330C11#1018111yescharacteristic, direct product factor, Sylow
331C23—41no—
332C23C11×#12111yescharacteristic
333Q8—22no—
334Q8—22no—
335Q8—44no—
336Q8—41no—
337Q8—41no—
338Q8—41no—
339Q8—41no—
340Q8—82no—
341D4—42no—
342D4—41no—
343D4—41no—
344D4—42no—
345D4—81no—
346D4—81no—
347C2×C4—22no—
348C2×C4—22no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—42no—
355C2×C4—82no—
356C2×C4—81no—
357C2×C4—81no—
358C2×C4—81no—
359C2×C4C11×#12011yescharacteristic
360C2×C4C11×#12011yescharacteristic
361C2×C4C11×#12011yescharacteristic
362C2×C4C11×#12111yescharacteristic
363C2×C4C11×#12111yescharacteristic
364C2×C4C11×#12711yescharacteristic
365C2×C4C2×C11×SD1611yescharacteristic
366C2×C4C11×#13511yescharacteristic
367C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
368C2×C4C11×#13711yescharacteristic
369C8—42no—
370C8—42no—
371C8—42no—
372C8—81no—
373C22—21no—
374C22—21no—
375C22—81no—
376C22—81no—
377C22—81no—
378C22C11×#39211yescharacteristic
379C22C11×#46511yescharacteristic
380C22C11×#46811yescharacteristic
381C4—21no—
382C4—21no—
383C4—21no—
384C4—42no—
385C4—81no—
386C4—82no—
387C4—81no—
388C4C11×#44811yescharacteristic
389C4C11×#44911yescharacteristic
390C4C11×#45011yescharacteristic
391C4C11×#45211yescharacteristic
392C4C11×#47312yes—
393C2—21no—
394C2—21no—
395C2—161no—
396C2C11×#200011yescharacteristic
397C2C11×#200811yescharacteristic
398C2C11×#202011yescharacteristic
subgroupG/H
center, socleC22×C11#392
commutator, Frattini, cosocleC2×C42C23×C11
prime radicalC11×#532C22
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. C2×C11×#477C2semidirect
4. C11×#1549C2semidirect
6. C11×#1461C2semidirect
7. C11×#1301C2semidirect
77. #10181C11direct (N × H)
91. C2×Q8×C11SD16semidirect
133. C2×#477C2×C11semidirect
135. #1549C2×C11semidirect
137. #1461C2×C11semidirect
138. #1301C2×C11semidirect
289. C2×Q8C11×SD16semidirect
330. C11#10181direct (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×#4772
C11×#30372
C11×#15492
C11×#14802
C11×#14612
C11×#13012
#1018111