Finite Group Databasebeta

← C11×#10436 #14587629

Subgroups — C11×#10436 #14587629

Order 2816.

530 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2538C211yesmaximal, characteristic
2C11×#1834C211yesmaximal, characteristic, complemented
3C11×#1803C211yesmaximal, characteristic, complemented
4C11×#1802C211yesmaximal, characteristic
5C2×C11×Q8⋊C8C211yesmaximal, characteristic, complemented
6C2×C11×D4⋊C8C211yesmaximal, characteristic
7C11×#1296C211yesmaximal, characteristic, complemented
8C2×C11×C22⋊Q8—21no—
9C2×C4×Q8×C11C2211yescharacteristic
10C2×C4×D4×C11C2211yescharacteristic
11C2×C11×C4⋊C8C2211yescharacteristic
12C2×C11×C4⋊C8C2211yescharacteristic
13C2×C11×#103—21no—
14C2×C11×#102—21no—
15C2×C4×C8×C11C2211yescharacteristic
16C11×#396—22no—
17C11×#390—21no—
18C11×#389—21no—
19C11×#384C2211yescharacteristic
20C11×#384C2211yescharacteristic
21C11×#380—21no—
22C11×#340—21no—
23C11×#340—21no—
24C11×#340—22no—
25C11×Q8⋊C8—22no—
26C11×D4⋊C8—22no—
27C22×Q8×C11D411yescharacteristic
28C22×D4×C11D411yescharacteristic
29C23×C4×C11—21no—
30C22×C8×C11—21no—
31C22×C8×C11—21no—
32C22×C8×C11—21no—
33C11×C22⋊Q8—42no—
34C11×C22⋊Q8—42no—
35C4×Q8×C11—21no—
36C4×Q8×C11—21no—
37C4×Q8×C11—21no—
38C4×Q8×C11—21no—
39C4×D4×C11—21no—
40C4×D4×C11—21no—
41C4×D4×C11—21no—
42C4×D4×C11—21no—
43C2×C11×C4⋊C4—22no—
44C2×C11×C4⋊C4—21no—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4—21no—
48C2×C11×C4⋊C4—21no—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4D411yescharacteristic
51C2×C11×C4⋊C4D411yescharacteristic
52C2×C11×C4⋊C4D412yes—
53C2×C11×C22⋊C4—22no—
54C2×C11×C22⋊C4—21no—
55C2×C11×C22⋊C4—22no—
56C2×C42×C11—21no—
57C2×C42×C11C2311yescharacteristic
58C11×C4⋊C8—21no—
59C11×C4⋊C8—21no—
60C11×C4⋊C8—21no—
61C11×C4⋊C8—21no—
62C11×#103—42no—
63C11×#102—42no—
64C4×C8×C11—21no—
65C4×C8×C11D412yes—
66C11×#95—22no—
67#10436C1111yesmaximal, characteristic, direct product factor, Sylow
68C24×C11—21no—
69C2×Q8×C11—21no—
70C2×Q8×C11—21no—
71C2×Q8×C11—21no—
72C2×Q8×C11—21no—
73C2×Q8×C11—21no—
74C2×Q8×C11SD1612yes—
75C2×D4×C11—21no—
76C2×D4×C11—21no—
77C2×D4×C11—21no—
78C2×D4×C11—21no—
79C2×D4×C11—21no—
80C2×D4×C11Q1612yes—
81C22×C4×C11—21no—
82C22×C4×C11—21no—
83C22×C4×C11—21no—
84C22×C4×C11—22no—
85C22×C4×C11—41no—
86C22×C4×C11—41no—
87C22×C4×C11—41no—
88C22×C4×C11—41no—
89C22×C4×C11—41no—
90C22×C4×C11—41no—
91C22×C4×C11—41no—
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11C2×D411yescharacteristic
95C2×C8×C11—22no—
96C2×C8×C11—41no—
97C2×C8×C11—41no—
98C2×C8×C11—41no—
99C2×C8×C11—41no—
100C2×C8×C11—41no—
101C2×C8×C11—41no—
102C2×C8×C11—41no—
103C2×C8×C11—41no—
104C11×C4⋊C4—21no—
105C11×C4⋊C4—21no—
106C11×C4⋊C4—21no—
107C11×C4⋊C4—21no—
108C11×C4⋊C4—44no—
109C11×C4⋊C4—42no—
110C11×C4⋊C4—42no—
111C11×C4⋊C4—41no—
112C11×C4⋊C4—41no—
113C11×C4⋊C4—41no—
114C11×C4⋊C4—41no—
115C11×C4⋊C4—41no—
116C11×C4⋊C4—41no—
117C11×C4⋊C4—41no—
118C11×C4⋊C4—41no—
119C11×C4⋊C4—41no—
120C11×C4⋊C4—41no—
121C11×C22⋊C4—44no—
122C11×C22⋊C4—41no—
123C11×C22⋊C4—41no—
124C11×C22⋊C4—82no—
125C42×C11—41no—
126C42×C11—41no—
127C42×C11C2×D411yescharacteristic
128C42×C11#4111yescharacteristic
129C42×C11#4111yescharacteristic
130C42×C11#4111yescharacteristic
131#2538C2×C1111yescharacteristic
132#1834C2×C1111yescharacteristic, complemented
133#1803C2×C1111yescharacteristic, complemented
134#1802C2×C1111yescharacteristic
135C2×Q8⋊C8C2×C1111yescharacteristic, complemented
136C2×D4⋊C8C2×C1111yescharacteristic
137#1296C2×C1111yescharacteristic, complemented
138C23×C11—22no—
139C23×C11—41no—
140C23×C11—41no—
141C23×C11—41no—
142C23×C11—41no—
143C23×C11—41no—
144C23×C11—41no—
145C23×C11#12011yescharacteristic
146Q8×C11—22no—
147Q8×C11—22no—
148Q8×C11—41no—
149Q8×C11—41no—
150D4×C11—22no—
151D4×C11—22no—
152D4×C11—41no—
153D4×C11—41no—
154C2×C4×C11—21no—
155C2×C4×C11—21no—
156C2×C4×C11—22no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—41no—
161C2×C4×C11—42no—
162C2×C4×C11—41no—
163C2×C4×C11—42no—
164C2×C4×C11—41no—
165C2×C4×C11—41no—
166C2×C4×C11—41no—
167C2×C4×C11—42no—
168C2×C4×C11—81no—
169C2×C4×C11—81no—
170C2×C4×C11—81no—
171C2×C4×C11—81no—
172C2×C4×C11—81no—
173C2×C4×C11—81no—
174C2×C4×C11—81no—
175C2×C4×C11#12111yescharacteristic
176C2×C4×C11#12111yescharacteristic
177C2×C4×C11#12111yescharacteristic
178C2×C4×C11#12311yescharacteristic
179C2×C4×C11#12311yescharacteristic
180C2×C4×C11#12411yescharacteristic
181C2×C4×C11C2×SD1611yescharacteristic
182C2×C4×C11C2×Q1611yescharacteristic
183C2×C4×C11#13511yescharacteristic
184C2×C4×C11#13511yescharacteristic
185C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
186C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
187C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
188C2×C4×C11#13711yescharacteristic
189C8×C11—42no—
190C8×C11—81no—
191C8×C11—81no—
192C2×C22⋊Q8—21no—
193C2×C4×Q8C22×C1111yescharacteristic
194C2×C4×D4C22×C1111yescharacteristic
195C2×C4⋊C8C22×C1111yescharacteristic
196C2×C4⋊C8C22×C1111yescharacteristic
197C2×#103—21no—
198C2×#102—21no—
199C2×C4×C8C22×C1111yescharacteristic
200#396—22no—
201#390—21no—
202#389—21no—
203#384C22×C1111yescharacteristic
204#384C22×C1111yescharacteristic
205#380—21no—
206#340—21no—
207#340—21no—
208#340—22no—
209Q8⋊C8—22no—
210D4⋊C8—22no—
211C22×C11—42no—
212C22×C11—42no—
213C22×C11—42no—
214C22×C11—81no—
215C22×C11—81no—
216C22×C11—81no—
217C22×C11—81no—
218C22×C11#39411yescharacteristic
219C22×C11#44911yescharacteristic
220C22×C11#44911yescharacteristic
221C22×C11#45011yescharacteristic
222C22×C11#45111yescharacteristic
223C22×C11#45411yescharacteristic
224C22×C11#45511yescharacteristic
225C4×C11—21no—
226C4×C11—21no—
227C4×C11—42no—
228C4×C11—82no—
229C4×C11—81no—
230C4×C11—81no—
231C4×C11—161no—
232C4×C11#46511yescharacteristic
233C4×C11#46711yescharacteristic
234C4×C11#46811yescharacteristic
235C4×C11#46911yescharacteristic
236C4×C11#48111yescharacteristic
237C4×C11#48211yescharacteristic
238C4×C11#48411yescharacteristic
239C4×C11#48511yescharacteristic
240C22×Q8D4×C1111yescharacteristic
241C22×D4D4×C1111yescharacteristic
242C23×C4—21no—
243C22×C8—21no—
244C22×C8—21no—
245C22×C8—21no—
246C22⋊Q8—42no—
247C22⋊Q8—42no—
248C4×Q8—21no—
249C4×Q8—21no—
250C4×Q8—21no—
251C4×Q8—21no—
252C4×D4—21no—
253C4×D4—21no—
254C4×D4—21no—
255C4×D4—21no—
256C2×C4⋊C4—22no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4D4×C1111yescharacteristic
264C2×C4⋊C4D4×C1111yescharacteristic
265C2×C4⋊C4D4×C1112yes—
266C2×C22⋊C4—22no—
267C2×C22⋊C4—21no—
268C2×C22⋊C4—22no—
269C2×C42—21no—
270C2×C42C23×C1111yescharacteristic
271C4⋊C8—21no—
272C4⋊C8—21no—
273C4⋊C8—21no—
274C4⋊C8—21no—
275#103—42no—
276#102—42no—
277C4×C8—21no—
278C4×C8D4×C1112yes—
279#95—22no—
280C2×C11—82no—
281C2×C11#162811yescharacteristic
282C2×C11#163711yescharacteristic
283C2×C11#164211yescharacteristic
284C2×C11#164411yescharacteristic
285C2×C11#203411yescharacteristic
286C2×C11#203611yescharacteristic
287C2×C11#204011yescharacteristic
288C24—21no—
289C2×Q8—21no—
290C2×Q8—21no—
291C2×Q8—21no—
292C2×Q8—21no—
293C2×Q8—21no—
294C2×Q8C11×SD1612yes—
295C2×D4—21no—
296C2×D4—21no—
297C2×D4—21no—
298C2×D4—21no—
299C2×D4—21no—
300C2×D4C11×Q1612yes—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—22no—
305C22×C4—41no—
306C22×C4—41no—
307C22×C4—41no—
308C22×C4—41no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4—41no—
312C22×C4C2×D4×C1111yescharacteristic
313C22×C4C2×D4×C1111yescharacteristic
314C22×C4C2×D4×C1111yescharacteristic
315C2×C8—22no—
316C2×C8—41no—
317C2×C8—41no—
318C2×C8—41no—
319C2×C8—41no—
320C2×C8—41no—
321C2×C8—41no—
322C2×C8—41no—
323C2×C8—41no—
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—21no—
327C4⋊C4—21no—
328C4⋊C4—42no—
329C4⋊C4—44no—
330C4⋊C4—42no—
331C4⋊C4—41no—
332C4⋊C4—41no—
333C4⋊C4—41no—
334C4⋊C4—41no—
335C4⋊C4—41no—
336C4⋊C4—41no—
337C4⋊C4—41no—
338C4⋊C4—41no—
339C4⋊C4—41no—
340C4⋊C4—41no—
341C22⋊C4—44no—
342C22⋊C4—41no—
343C22⋊C4—41no—
344C22⋊C4—82no—
345C42—41no—
346C42—41no—
347C42C2×D4×C1111yescharacteristic
348C42C11×#4111yescharacteristic
349C42C11×#4111yescharacteristic
350C42C11×#4111yescharacteristic
351C11#1043611yescharacteristic, direct product factor, Sylow
352C23—22no—
353C23—41no—
354C23—41no—
355C23—41no—
356C23—41no—
357C23—41no—
358C23—41no—
359C23C11×#12011yescharacteristic
360Q8—22no—
361Q8—22no—
362Q8—41no—
363Q8—41no—
364D4—22no—
365D4—22no—
366D4—41no—
367D4—41no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—22no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—42no—
376C2×C4—41no—
377C2×C4—42no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—42no—
382C2×C4—81no—
383C2×C4—81no—
384C2×C4—81no—
385C2×C4—81no—
386C2×C4—81no—
387C2×C4—81no—
388C2×C4—81no—
389C2×C4C11×#12111yescharacteristic
390C2×C4C11×#12111yescharacteristic
391C2×C4C11×#12111yescharacteristic
392C2×C4C11×#12311yescharacteristic
393C2×C4C11×#12311yescharacteristic
394C2×C4C11×#12411yescharacteristic
395C2×C4C2×C11×SD1611yescharacteristic
396C2×C4C2×C11×Q1611yescharacteristic
397C2×C4C11×#13511yescharacteristic
398C2×C4C11×#13511yescharacteristic
399C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
400C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
401C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
402C2×C4C11×#13711yescharacteristic
403C8—42no—
404C8—81no—
405C8—81no—
406C22—42no—
407C22—42no—
408C22—42no—
409C22—81no—
410C22—81no—
411C22—81no—
412C22—81no—
413C22C11×#39411yescharacteristic
414C22C11×#44911yescharacteristic
415C22C11×#44911yescharacteristic
416C22C11×#45011yescharacteristic
417C22C11×#45111yescharacteristic
418C22C11×#45411yescharacteristic
419C22C11×#45511yescharacteristic
420C4—21no—
421C4—21no—
422C4—42no—
423C4—82no—
424C4—81no—
425C4—81no—
426C4—161no—
427C4C11×#46511yescharacteristic
428C4C11×#46711yescharacteristic
429C4C11×#46811yescharacteristic
430C4C11×#46911yescharacteristic
431C4C11×#48111yescharacteristic
432C4C11×#48211yescharacteristic
433C4C11×#48411yescharacteristic
434C4C11×#48511yescharacteristic
435C2—82no—
436C2C11×#162811yescharacteristic
437C2C11×#163711yescharacteristic
438C2C11×#164211yescharacteristic
439C2C11×#164411yescharacteristic
440C2C11×#203411yescharacteristic
441C2C11×#203611yescharacteristic
442C2C11×#204011yescharacteristic
subgroupG/H
center, socleC23×C11#120
commutator, Frattini, cosocleC2×C42C23×C11
prime radicalC22×D4×C11D4
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#1834C2semidirect
3. C11×#1803C2semidirect
5. C2×C11×Q8⋊C8C2semidirect
7. C11×#1296C2semidirect
67. #10436C11direct (N × H)
132. #1834C2×C11semidirect
133. #1803C2×C11semidirect
135. C2×Q8⋊C8C2×C11semidirect
137. #1296C2×C11semidirect
351. C11#10436direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#25382
C11×#18342
C11×#18032
C11×#18022
C2×C11×Q8⋊C82
C2×C11×D4⋊C82
C11×#12962
#1043611