Finite Group Databasebeta

← C11×#10247 #14587440

Subgroups — C11×#10247 #14587440

Order 2816.

556 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3229C211yesmaximal, characteristic, complemented
2C11×#3077C211yesmaximal, characteristic
3C11×#2547C211yesmaximal, characteristic
4C11×#1546C211yesmaximal, characteristic, complemented
5C11×#1503C211yesmaximal, characteristic, complemented
6C11×#1478C211yesmaximal, characteristic
7C11×#1303C211yesmaximal, characteristic, complemented
8C11×#533C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C11×#124—21no—
11C2×C4×D4×C11C2211yescharacteristic
12C11×#498—21no—
13C11×#487—21no—
14C11×#483—22no—
15C11×#478—22no—
16C11×#476—21no—
17C11×#475—22no—
18C11×#474—21no—
19C11×#431C2211yescharacteristic
20C11×#431C2211yescharacteristic
21C11×#428—21no—
22C11×#423C2211yescharacteristic
23C11×#418—21no—
24C11×#397—22no—
25C11×#391—21no—
26C11×#380—22no—
27C4×C11×C4⋊C4C2211yescharacteristic
28C11×#332—22no—
29C11×#328—22no—
30C11×D4⋊C8—22no—
31C22×Q8×C11—21no—
32C22×D4×C11D411yescharacteristic
33C23×C4×C11—21no—
34C2×C11×M16—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8—21no—
39C11×C4⋊Q8D411yescharacteristic
40C11×C4⋊Q8D411yescharacteristic
41C11×#125—21no—
42C11×#124—42no—
43C11×#124—42no—
44C11×C22⋊Q8—21no—
45C11×C22⋊Q8—21no—
46C4×Q8×C11—21no—
47C4×Q8×C11—21no—
48C4×D4×C11—21no—
49C4×D4×C11—21no—
50C4×D4×C11—21no—
51C4×D4×C11—21no—
52C11×#117—21no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4D411yescharacteristic
56C2×C11×C4⋊C4D412yes—
57C2×C11×C22⋊C4—24no—
58C2×C11×C22⋊C4—21no—
59C2×C42×C11—21no—
60C2×C42×C11C2311yescharacteristic
61C11×#107—22no—
62C11×#106—24no—
63C11×#106—22no—
64C11×C4⋊C8—21no—
65C11×C4⋊C8—21no—
66C11×C4⋊C8D412yes—
67C11×C4⋊C8D412yes—
68C11×#103—24no—
69C11×#102—22no—
70C11×#102—22no—
71C11×C22⋊C8—21no—
72C11×C22⋊C8—21no—
73C4×C8×C11—21no—
74C4×C8×C11—21no—
75C11×#95—24no—
76C11×#95D412yes—
77#10247C1111yesmaximal, characteristic, direct product factor, Sylow
78C24×C11—21no—
79C2×Q8×C11—21no—
80C2×Q8×C11—21no—
81C2×Q8×C11—41no—
82C2×Q8×C11—41no—
83C2×Q8×C11—41no—
84C2×Q8×C11—41no—
85C2×Q8×C11—41no—
86C2×Q8×C11—41no—
87C2×D4×C11—21no—
88C2×D4×C11—21no—
89C2×D4×C11—21no—
90C2×D4×C11—21no—
91C2×D4×C11—21no—
92C2×D4×C11SD1612yes—
93C22×C4×C11—21no—
94C22×C4×C11—22no—
95C22×C4×C11—22no—
96C22×C4×C11—44no—
97C22×C4×C11—41no—
98C22×C4×C11—41no—
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2×D411yescharacteristic
102C11×M16—41no—
103C11×M16—41no—
104C2×C8×C11—22no—
105C2×C8×C11—22no—
106C2×C8×C11—41no—
107C11×C4⋊C4—21no—
108C11×C4⋊C4—21no—
109C11×C4⋊C4—22no—
110C11×C4⋊C4—21no—
111C11×C4⋊C4—21no—
112C11×C4⋊C4—21no—
113C11×C4⋊C4—22no—
114C11×C4⋊C4—21no—
115C11×C4⋊C4—42no—
116C11×C4⋊C4—41no—
117C11×C4⋊C4—41no—
118C11×C4⋊C4—41no—
119C11×C4⋊C4—41no—
120C11×C22⋊C4—48no—
121C11×C22⋊C4—41no—
122C11×C22⋊C4—41no—
123C11×C22⋊C4—41no—
124C42×C11—41no—
125C42×C11—41no—
126C42×C11—41no—
127C42×C11C2×D411yescharacteristic
128C42×C11C2×D411yescharacteristic
129C42×C11C2×D411yescharacteristic
130C42×C11#4111yescharacteristic
131#3229C2×C1111yescharacteristic, complemented
132#3077C2×C1111yescharacteristic
133#2547C2×C1111yescharacteristic
134#1546C2×C1111yescharacteristic, complemented
135#1503C2×C1111yescharacteristic, complemented
136#1478C2×C1111yescharacteristic
137#1303C2×C1111yescharacteristic, complemented
138C23×C11—22no—
139C23×C11—42no—
140C23×C11—42no—
141C23×C11—41no—
142C23×C11—41no—
143C23×C11#12011yescharacteristic
144Q8×C11—42no—
145Q8×C11—81no—
146Q8×C11—81no—
147Q8×C11—81no—
148Q8×C11—81no—
149Q8×C11—81no—
150D4×C11—22no—
151D4×C11—22no—
152D4×C11—41no—
153D4×C11—41no—
154C2×C4×C11—22no—
155C2×C4×C11—41no—
156C2×C4×C11—42no—
157C2×C4×C11—42no—
158C2×C4×C11—42no—
159C2×C4×C11—41no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11—42no—
163C2×C4×C11—42no—
164C2×C4×C11—42no—
165C2×C4×C11—42no—
166C2×C4×C11—82no—
167C2×C4×C11—82no—
168C2×C4×C11#12011yescharacteristic
169C2×C4×C11#12011yescharacteristic
170C2×C4×C11#12111yescharacteristic
171C2×C4×C11#12111yescharacteristic
172C2×C4×C11#12111yescharacteristic
173C2×C4×C11#12711yescharacteristic
174C2×C4×C11C2×SD1611yescharacteristic
175C2×C4×C11#13511yescharacteristic
176C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
177C2×C4×C11#13711yescharacteristic
178C8×C11—42no—
179C8×C11—42no—
180C8×C11—81no—
181#533C22×C1111yescharacteristic
182C2×C4⋊Q8C22×C1111yescharacteristic
183C2×#124—21no—
184C2×C4×D4C22×C1111yescharacteristic
185#498—21no—
186#487—21no—
187#483—22no—
188#478—22no—
189#476—21no—
190#475—22no—
191#474—21no—
192#431C22×C1111yescharacteristic
193#431C22×C1111yescharacteristic
194#428—21no—
195#423C22×C1111yescharacteristic
196#418—21no—
197#397—22no—
198#391—21no—
199#380—22no—
200C4×C4⋊C4C22×C1111yescharacteristic
201#332—22no—
202#328—22no—
203D4⋊C8—22no—
204C22×C11—21no—
205C22×C11—21no—
206C22×C11—44no—
207C22×C11—42no—
208C22×C11—82no—
209C22×C11—81no—
210C22×C11—81no—
211C22×C11#39211yescharacteristic
212C22×C11#45011yescharacteristic
213C22×C11#45211yescharacteristic
214C4×C11—21no—
215C4×C11—21no—
216C4×C11—21no—
217C4×C11—82no—
218C4×C11—82no—
219C4×C11—81no—
220C4×C11—81no—
221C4×C11—81no—
222C4×C11#44811yescharacteristic
223C4×C11#44911yescharacteristic
224C4×C11#45412yes—
225C4×C11#46511yescharacteristic
226C4×C11#46811yescharacteristic
227C22×Q8—21no—
228C22×D4D4×C1111yescharacteristic
229C23×C4—21no—
230C2×M16—21no—
231C4⋊Q8—21no—
232C4⋊Q8—21no—
233C4⋊Q8—21no—
234C4⋊Q8—21no—
235C4⋊Q8D4×C1111yescharacteristic
236C4⋊Q8D4×C1111yescharacteristic
237#125—21no—
238#124—42no—
239#124—42no—
240C22⋊Q8—21no—
241C22⋊Q8—21no—
242C4×Q8—21no—
243C4×Q8—21no—
244C4×D4—21no—
245C4×D4—21no—
246C4×D4—21no—
247C4×D4—21no—
248#117—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4D4×C1111yescharacteristic
252C2×C4⋊C4D4×C1112yes—
253C2×C22⋊C4—24no—
254C2×C22⋊C4—21no—
255C2×C42—21no—
256C2×C42C23×C1111yescharacteristic
257#107—22no—
258#106—22no—
259#106—24no—
260C4⋊C8—21no—
261C4⋊C8—21no—
262C4⋊C8D4×C1112yes—
263C4⋊C8D4×C1112yes—
264#103—24no—
265#102—22no—
266#102—22no—
267C22⋊C8—21no—
268C22⋊C8—21no—
269C4×C8—21no—
270C4×C8—21no—
271#95—24no—
272#95D4×C1112yes—
273C2×C11—21no—
274C2×C11—21no—
275C2×C11—82no—
276C2×C11#200011yescharacteristic
277C2×C11#200311yescharacteristic
278C2×C11#200911yescharacteristic
279C24—21no—
280C2×Q8—21no—
281C2×Q8—21no—
282C2×Q8—41no—
283C2×Q8—41no—
284C2×Q8—41no—
285C2×Q8—41no—
286C2×Q8—41no—
287C2×Q8—41no—
288C2×D4—21no—
289C2×D4—21no—
290C2×D4—21no—
291C2×D4—21no—
292C2×D4—21no—
293C2×D4C11×SD1612yes—
294C22×C4—21no—
295C22×C4—22no—
296C22×C4—22no—
297C22×C4—44no—
298C22×C4—41no—
299C22×C4—41no—
300C22×C4C2×D4×C1111yescharacteristic
301C22×C4C2×D4×C1111yescharacteristic
302C22×C4C2×D4×C1111yescharacteristic
303M16—41no—
304M16—41no—
305C2×C8—22no—
306C2×C8—22no—
307C2×C8—41no—
308C4⋊C4—21no—
309C4⋊C4—21no—
310C4⋊C4—22no—
311C4⋊C4—21no—
312C4⋊C4—21no—
313C4⋊C4—21no—
314C4⋊C4—22no—
315C4⋊C4—21no—
316C4⋊C4—42no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—41no—
321C22⋊C4—48no—
322C22⋊C4—41no—
323C22⋊C4—41no—
324C22⋊C4—41no—
325C42—41no—
326C42—41no—
327C42—41no—
328C42C2×D4×C1111yescharacteristic
329C42C2×D4×C1111yescharacteristic
330C42C2×D4×C1111yescharacteristic
331C42C11×#4111yescharacteristic
332C11#1024711yescharacteristic, direct product factor, Sylow
333C23—22no—
334C23—42no—
335C23—42no—
336C23—41no—
337C23—41no—
338C23C11×#12011yescharacteristic
339Q8—42no—
340Q8—81no—
341Q8—81no—
342Q8—81no—
343Q8—81no—
344Q8—81no—
345D4—22no—
346D4—22no—
347D4—41no—
348D4—41no—
349C2×C4—22no—
350C2×C4—41no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—42no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—42no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—42no—
361C2×C4—82no—
362C2×C4—82no—
363C2×C4C11×#12011yescharacteristic
364C2×C4C11×#12011yescharacteristic
365C2×C4C11×#12111yescharacteristic
366C2×C4C11×#12111yescharacteristic
367C2×C4C11×#12111yescharacteristic
368C2×C4C11×#12711yescharacteristic
369C2×C4C2×C11×SD1611yescharacteristic
370C2×C4C11×#13511yescharacteristic
371C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
372C2×C4C11×#13711yescharacteristic
373C8—42no—
374C8—42no—
375C8—81no—
376C22—21no—
377C22—21no—
378C22—44no—
379C22—42no—
380C22—82no—
381C22—81no—
382C22—81no—
383C22C11×#39211yescharacteristic
384C22C11×#45011yescharacteristic
385C22C11×#45211yescharacteristic
386C4—21no—
387C4—21no—
388C4—21no—
389C4—82no—
390C4—82no—
391C4—81no—
392C4—81no—
393C4—81no—
394C4C11×#44811yescharacteristic
395C4C11×#44911yescharacteristic
396C4C11×#45412yes—
397C4C11×#46511yescharacteristic
398C4C11×#46811yescharacteristic
399C2—21no—
400C2—21no—
401C2—82no—
402C2C11×#200011yescharacteristic
403C2C11×#200311yescharacteristic
404C2C11×#200911yescharacteristic
subgroupG/H
center, socleC22×C11#392
commutator, Frattini, cosocleC2×C42C23×C11
prime radicalC22×D4×C11D4
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
1. C11×#3229C2semidirect
4. C11×#1546C2semidirect
5. C11×#1503C2semidirect
7. C11×#1303C2semidirect
77. #10247C11direct (N × H)
131. #3229C2×C11semidirect
134. #1546C2×C11semidirect
135. #1503C2×C11semidirect
137. #1303C2×C11semidirect
332. C11#10247direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32292
C11×#30772
C11×#25472
C11×#15462
C11×#15032
C11×#14782
C11×#13032
#1024711