Finite Group Databasebeta

← C11×#10249 #14587442

Subgroups — C11×#10249 #14587442

Order 2816.

536 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3230C211yesmaximal, characteristic, complemented
2C11×#3077C211yesmaximal, characteristic
3C11×#2563C211yesmaximal, characteristic
4C11×#1549C211yesmaximal, characteristic, complemented
5C11×#1503C211yesmaximal, characteristic, complemented
6C11×#1478C211yesmaximal, characteristic
7C11×#1303C211yesmaximal, characteristic, complemented
8C11×#533C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C4×D4×C11C2211yescharacteristic
11C11×#500—21no—
12C11×#487—21no—
13C11×#484—22no—
14C11×#478—22no—
15C11×#477—22no—
16C11×#476—21no—
17C11×#474—21no—
18C11×#431C2211yescharacteristic
19C11×#431C2211yescharacteristic
20C11×#428—21no—
21C11×#423C2211yescharacteristic
22C11×#418—21no—
23C11×#393—22no—
24C11×#390—21no—
25C11×#382—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×C22⋊Q8—21no—
43C11×C22⋊Q8—21no—
44C4×Q8×C11—21no—
45C4×Q8×C11—21no—
46C4×D4×C11—21no—
47C4×D4×C11—21no—
48C4×D4×C11—21no—
49C4×D4×C11—21no—
50C11×#117—21no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4D411yescharacteristic
54C2×C11×C4⋊C4D412yes—
55C2×C11×C22⋊C4—21no—
56C2×C11×C22⋊C4—24no—
57C2×C42×C11—21no—
58C2×C42×C11C2311yescharacteristic
59C11×#107—24no—
60C11×#107—22no—
61C11×#106—22no—
62C11×C4⋊C8—21no—
63C11×C4⋊C8—21no—
64C11×C4⋊C8D412yes—
65C11×C4⋊C8D412yes—
66C11×#103—24no—
67C11×#102—22no—
68C11×#102—22no—
69C11×C22⋊C8—21no—
70C11×C22⋊C8—21no—
71C4×C8×C11—21no—
72C4×C8×C11—21no—
73C11×#95—24no—
74C11×#95D412yes—
75#10249C1111yesmaximal, characteristic, direct product factor, Sylow
76C24×C11—21no—
77C2×Q8×C11—21no—
78C2×Q8×C11—21no—
79C2×Q8×C11—41no—
80C2×Q8×C11—41no—
81C2×Q8×C11—82no—
82C2×D4×C11—21no—
83C2×D4×C11—21no—
84C2×D4×C11—21no—
85C2×D4×C11—21no—
86C2×D4×C11—21no—
87C2×D4×C11Q1612yes—
88C22×C4×C11—21no—
89C22×C4×C11—22no—
90C22×C4×C11—22no—
91C22×C4×C11—44no—
92C22×C4×C11—41no—
93C22×C4×C11—41no—
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C11×M16—41no—
98C11×M16—41no—
99C2×C8×C11—22no—
100C2×C8×C11—22no—
101C2×C8×C11—41no—
102C11×C4⋊C4—21no—
103C11×C4⋊C4—21no—
104C11×C4⋊C4—22no—
105C11×C4⋊C4—21no—
106C11×C4⋊C4—21no—
107C11×C4⋊C4—21no—
108C11×C4⋊C4—22no—
109C11×C4⋊C4—21no—
110C11×C4⋊C4—42no—
111C11×C4⋊C4—41no—
112C11×C4⋊C4—41no—
113C11×C4⋊C4—41no—
114C11×C4⋊C4—41no—
115C11×C22⋊C4—41no—
116C11×C22⋊C4—41no—
117C11×C22⋊C4—41no—
118C11×C22⋊C4—84no—
119C42×C11—41no—
120C42×C11—41no—
121C42×C11—41no—
122C42×C11C2×D411yescharacteristic
123C42×C11C2×D411yescharacteristic
124C42×C11C2×D411yescharacteristic
125C42×C11#4111yescharacteristic
126#3230C2×C1111yescharacteristic, complemented
127#3077C2×C1111yescharacteristic
128#2563C2×C1111yescharacteristic
129#1549C2×C1111yescharacteristic, complemented
130#1503C2×C1111yescharacteristic, complemented
131#1478C2×C1111yescharacteristic
132#1303C2×C1111yescharacteristic, complemented
133C23×C11—22no—
134C23×C11—42no—
135C23×C11—42no—
136C23×C11—41no—
137C23×C11—41no—
138C23×C11#12011yescharacteristic
139Q8×C11—42no—
140Q8×C11—81no—
141Q8×C11—82no—
142Q8×C11—82no—
143D4×C11—22no—
144D4×C11—22no—
145D4×C11—41no—
146D4×C11—41no—
147C2×C4×C11—22no—
148C2×C4×C11—41no—
149C2×C4×C11—42no—
150C2×C4×C11—44no—
151C2×C4×C11—42no—
152C2×C4×C11—42no—
153C2×C4×C11—41no—
154C2×C4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11—42no—
157C2×C4×C11—42no—
158C2×C4×C11—82no—
159C2×C4×C11—82no—
160C2×C4×C11#12011yescharacteristic
161C2×C4×C11#12011yescharacteristic
162C2×C4×C11#12111yescharacteristic
163C2×C4×C11#12111yescharacteristic
164C2×C4×C11#12111yescharacteristic
165C2×C4×C11#12711yescharacteristic
166C2×C4×C11C2×Q1611yescharacteristic
167C2×C4×C11#13511yescharacteristic
168C2×C4×C11#13711yescharacteristic
169C2×C4×C11#13711yescharacteristic
170C8×C11—42no—
171C8×C11—42no—
172C8×C11—81no—
173#533C22×C1111yescharacteristic
174C2×C4⋊Q8C22×C1111yescharacteristic
175C2×C4×D4C22×C1111yescharacteristic
176#500—21no—
177#487—21no—
178#484—22no—
179#478—22no—
180#477—22no—
181#476—21no—
182#474—21no—
183#431C22×C1111yescharacteristic
184#431C22×C1111yescharacteristic
185#428—21no—
186#423C22×C1111yescharacteristic
187#418—21no—
188#393—22no—
189#390—21no—
190#382—21no—
191#380—22no—
192C4×C4⋊C4C22×C1111yescharacteristic
193#332—22no—
194#328—22no—
195D4⋊C8—22no—
196C22×C11—21no—
197C22×C11—21no—
198C22×C11—44no—
199C22×C11—42no—
200C22×C11—82no—
201C22×C11—81no—
202C22×C11—81no—
203C22×C11#39211yescharacteristic
204C22×C11#45111yescharacteristic
205C22×C11#45211yescharacteristic
206C4×C11—21no—
207C4×C11—21no—
208C4×C11—21no—
209C4×C11—82no—
210C4×C11—81no—
211C4×C11—81no—
212C4×C11—82no—
213C4×C11—81no—
214C4×C11#45111yescharacteristic
215C4×C11#45211yescharacteristic
216C4×C11#45412yes—
217C4×C11#46711yescharacteristic
218C4×C11#47011yescharacteristic
219C22×Q8—21no—
220C22×D4D4×C1111yescharacteristic
221C23×C4—21no—
222C2×M16—21no—
223C4⋊Q8—21no—
224C4⋊Q8—21no—
225C4⋊Q8—21no—
226C4⋊Q8—21no—
227C4⋊Q8D4×C1111yescharacteristic
228C4⋊Q8D4×C1111yescharacteristic
229#125—21no—
230C22⋊Q8—21no—
231C22⋊Q8—21no—
232C4×Q8—21no—
233C4×Q8—21no—
234C4×D4—21no—
235C4×D4—21no—
236C4×D4—21no—
237C4×D4—21no—
238#117—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4D4×C1111yescharacteristic
242C2×C4⋊C4D4×C1112yes—
243C2×C22⋊C4—21no—
244C2×C22⋊C4—24no—
245C2×C42—21no—
246C2×C42C23×C1111yescharacteristic
247#107—22no—
248#107—24no—
249#106—22no—
250C4⋊C8—21no—
251C4⋊C8—21no—
252C4⋊C8D4×C1112yes—
253C4⋊C8D4×C1112yes—
254#103—24no—
255#102—22no—
256#102—22no—
257C22⋊C8—21no—
258C22⋊C8—21no—
259C4×C8—21no—
260C4×C8—21no—
261#95—24no—
262#95D4×C1112yes—
263C2×C11—21no—
264C2×C11—21no—
265C2×C11—82no—
266C2×C11#200111yescharacteristic
267C2×C11#200311yescharacteristic
268C2×C11#200811yescharacteristic
269C24—21no—
270C2×Q8—21no—
271C2×Q8—21no—
272C2×Q8—41no—
273C2×Q8—41no—
274C2×Q8—82no—
275C2×D4—21no—
276C2×D4—21no—
277C2×D4—21no—
278C2×D4—21no—
279C2×D4—21no—
280C2×D4C11×Q1612yes—
281C22×C4—21no—
282C22×C4—22no—
283C22×C4—22no—
284C22×C4—44no—
285C22×C4—41no—
286C22×C4—41no—
287C22×C4C2×D4×C1111yescharacteristic
288C22×C4C2×D4×C1111yescharacteristic
289C22×C4C2×D4×C1111yescharacteristic
290M16—41no—
291M16—41no—
292C2×C8—22no—
293C2×C8—22no—
294C2×C8—41no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—22no—
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—21no—
301C4⋊C4—22no—
302C4⋊C4—21no—
303C4⋊C4—42no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C4⋊C4—41no—
307C4⋊C4—41no—
308C22⋊C4—41no—
309C22⋊C4—41no—
310C22⋊C4—41no—
311C22⋊C4—84no—
312C42—41no—
313C42—41no—
314C42—41no—
315C42C2×D4×C1111yescharacteristic
316C42C2×D4×C1111yescharacteristic
317C42C2×D4×C1111yescharacteristic
318C42C11×#4111yescharacteristic
319C11#1024911yescharacteristic, direct product factor, Sylow
320C23—22no—
321C23—42no—
322C23—42no—
323C23—41no—
324C23—41no—
325C23C11×#12011yescharacteristic
326Q8—42no—
327Q8—81no—
328Q8—82no—
329Q8—82no—
330D4—22no—
331D4—22no—
332D4—41no—
333D4—41no—
334C2×C4—22no—
335C2×C4—41no—
336C2×C4—42no—
337C2×C4—44no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—82no—
346C2×C4—82no—
347C2×C4C11×#12011yescharacteristic
348C2×C4C11×#12011yescharacteristic
349C2×C4C11×#12111yescharacteristic
350C2×C4C11×#12111yescharacteristic
351C2×C4C11×#12111yescharacteristic
352C2×C4C11×#12711yescharacteristic
353C2×C4C2×C11×Q1611yescharacteristic
354C2×C4C11×#13511yescharacteristic
355C2×C4C11×#13711yescharacteristic
356C2×C4C11×#13711yescharacteristic
357C8—42no—
358C8—42no—
359C8—81no—
360C22—21no—
361C22—21no—
362C22—44no—
363C22—42no—
364C22—82no—
365C22—81no—
366C22—81no—
367C22C11×#39211yescharacteristic
368C22C11×#45111yescharacteristic
369C22C11×#45211yescharacteristic
370C4—21no—
371C4—21no—
372C4—21no—
373C4—82no—
374C4—81no—
375C4—81no—
376C4—82no—
377C4—81no—
378C4C11×#45111yescharacteristic
379C4C11×#45211yescharacteristic
380C4C11×#45412yes—
381C4C11×#46711yescharacteristic
382C4C11×#47011yescharacteristic
383C2—21no—
384C2—21no—
385C2—82no—
386C2C11×#200111yescharacteristic
387C2C11×#200311yescharacteristic
388C2C11×#200811yescharacteristic
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×#3230C2semidirect
4. C11×#1549C2semidirect
5. C11×#1503C2semidirect
7. C11×#1303C2semidirect
75. #10249C11direct (N × H)
126. #3230C2×C11semidirect
129. #1549C2×C11semidirect
130. #1503C2×C11semidirect
132. #1303C2×C11semidirect
319. C11#10249direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32302
C11×#30772
C11×#25632
C11×#15492
C11×#15032
C11×#14782
C11×#13032
#1024911