Finite Group Databasebeta

← C11×#10062 #14587255

Subgroups — C11×#10062 #14587255

Order 2816.

806 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#486C211yesmaximal, characteristic, complemented
2C2×C11×#461C211yesmaximal, characteristic, complemented
3C11×#2541C211yesmaximal, characteristic
4C11×#1988C211yesmaximal, characteristic, complemented
5C2×C11×#331C211yesmaximal, characteristic, complemented
6C2×C11×D4⋊C8C211yesmaximal, characteristic, complemented
7C11×#1279C211yesmaximal, characteristic, complemented
8C22×C11×SD16—21no—
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C11×#127—21no—
11C2×C11×#127C2211yescharacteristic
12C2×C11×#121—22no—
13C2×C4×D4×C11C2211yescharacteristic
14C11×#486—22no—
15C11×#486—22no—
16C11×#461—22no—
17C11×#461—22no—
18C2×C11×C4⋊C8C2211yescharacteristic
19C2×C11×C4⋊C8C2211yescharacteristic
20C2×C11×#103—21no—
21C2×C11×#102—22no—
22C2×C4×C8×C11C2211yescharacteristic
23C11×#392—22no—
24C11×#390—21no—
25C4×C11×C4⋊C4C2211yescharacteristic
26C11×#340—22no—
27C11×#331—22no—
28C11×D4⋊C8—22no—
29C22×Q8×C11—21no—
30C22×D4×C11—24no—
31C22×D4×C11—21no—
32C22×D4×C11—21no—
33C22×D4×C11D411yescharacteristic
34C22×D4×C11D412yes—
35C23×C4×C11—21no—
36C2×C11×SD16—24no—
37C2×C11×SD16—42no—
38C2×C11×SD16—42no—
39C22×C8×C11—21no—
40C22×C8×C11—21no—
41C22×C8×C11—21no—
42C11×C4⋊Q8—21no—
43C11×C4⋊Q8—21no—
44C11×C4⋊Q8—21no—
45C11×C4⋊Q8D412yescomplemented
46C11×#127—21no—
47C11×#127—21no—
48C11×#127—21no—
49C11×#127—21no—
50C11×#127—42no—
51C11×#127—42no—
52C11×#121—44no—
53C11×#121—44no—
54C4×D4×C11—21no—
55C4×D4×C11—21no—
56C4×D4×C11—21no—
57C4×D4×C11—21no—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4D411yescharacteristic
61C2×C11×C4⋊C4D412yes—
62C2×C11×C22⋊C4—24no—
63C2×C11×C22⋊C4—21no—
64C2×C42×C11—21no—
65C2×C42×C11C2311yescharacteristic
66C11×C4⋊C8—21no—
67C11×C4⋊C8—21no—
68C11×C4⋊C8—21no—
69C11×C4⋊C8D412yescomplemented
70C11×#103—24no—
71C11×#102—28no—
72C4×C8×C11—21no—
73C4×C8×C11D412yescomplemented
74C11×#95—21no—
75#10062C1111yesmaximal, characteristic, direct product factor, Sylow
76C24×C11—21no—
77C24×C11—22no—
78C2×Q8×C11—22no—
79C2×Q8×C11—41no—
80C2×Q8×C11—41no—
81C2×Q8×C11—41no—
82C2×Q8×C11—41no—
83C2×Q8×C11—41no—
84C2×D4×C11—21no—
85C2×D4×C11—22no—
86C2×D4×C11—21no—
87C2×D4×C11—22no—
88C2×D4×C11—21no—
89C2×D4×C11—21no—
90C2×D4×C11—21no—
91C2×D4×C11—44no—
92C2×D4×C11—48no—
93C2×D4×C11—48no—
94C2×D4×C11—41no—
95C2×D4×C11—41no—
96C2×D4×C11—41no—
97C2×D4×C11—41no—
98C2×D4×C11—41no—
99C2×D4×C11—42no—
100C2×D4×C11—41no—
101C2×D4×C11—42no—
102C2×D4×C11—41no—
103C2×D4×C11—41no—
104C2×D4×C11—84no—
105C2×D4×C11D812yes—
106C22×C4×C11—22no—
107C22×C4×C11—21no—
108C22×C4×C11—41no—
109C22×C4×C11—41no—
110C22×C4×C11—41no—
111C22×C4×C11—42no—
112C22×C4×C11—42no—
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2×D411yescharacteristic
116C11×SD16—48no—
117C2×C8×C11—22no—
118C2×C8×C11—22no—
119C2×C8×C11—42no—
120C2×C8×C11—41no—
121C2×C8×C11—41no—
122C2×C8×C11—41no—
123C2×C8×C11—42no—
124C11×C4⋊C4—22no—
125C11×C4⋊C4—22no—
126C11×C4⋊C4—21no—
127C11×C4⋊C4—22no—
128C11×C4⋊C4—21no—
129C11×C4⋊C4—41no—
130C11×C4⋊C4—41no—
131C11×C4⋊C4SD1614yescomplemented
132C11×C22⋊C4—48no—
133C11×C22⋊C4—41no—
134C11×C22⋊C4—41no—
135C42×C11—41no—
136C42×C11—41no—
137C42×C11C2×D411yescharacteristic
138C42×C11C2×D411yescharacteristic
139C42×C11C2×D411yescharacteristic
140C42×C11#4111yescharacteristic
141C2×#486C2×C1111yescharacteristic, complemented
142C2×#461C2×C1111yescharacteristic, complemented
143#2541C2×C1111yescharacteristic
144#1988C2×C1111yescharacteristic, complemented
145C2×#331C2×C1111yescharacteristic, complemented
146C2×D4⋊C8C2×C1111yescharacteristic, complemented
147#1279C2×C1111yescharacteristic, complemented
148C23×C11—22no—
149C23×C11—41no—
150C23×C11—41no—
151C23×C11—42no—
152C23×C11—42no—
153C23×C11—42no—
154C23×C11—42no—
155C23×C11—42no—
156C23×C11—44no—
157C23×C11—44no—
158C23×C11#12011yescharacteristic
159Q8×C11—42no—
160Q8×C11—42no—
161Q8×C11—81no—
162Q8×C11—81no—
163D4×C11—22no—
164D4×C11—22no—
165D4×C11—44no—
166D4×C11—41no—
167D4×C11—41no—
168D4×C11—82no—
169D4×C11—816no—
170D4×C11—81no—
171D4×C11—81no—
172D4×C11—82no—
173D4×C11—81no—
174D4×C11—81no—
175D4×C11—81no—
176D4×C11—81no—
177C2×C4×C11—22no—
178C2×C4×C11—24no—
179C2×C4×C11—42no—
180C2×C4×C11—42no—
181C2×C4×C11—41no—
182C2×C4×C11—42no—
183C2×C4×C11—42no—
184C2×C4×C11—81no—
185C2×C4×C11—81no—
186C2×C4×C11—82no—
187C2×C4×C11—81no—
188C2×C4×C11—81no—
189C2×C4×C11#12011yescharacteristic
190C2×C4×C11#12011yescharacteristic
191C2×C4×C11#12111yescharacteristic
192C2×C4×C11#12111yescharacteristic
193C2×C4×C11#12111yescharacteristic
194C2×C4×C11#12711yescharacteristic
195C2×C4×C11C2×D811yescharacteristic
196C2×C4×C11C2×SD1612yes—
197C2×C4×C11#13511yescharacteristic
198C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
199C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
200C2×C4×C11AGL(1,ℤ/8)12yes—
201C8×C11—42no—
202C8×C11—42no—
203C8×C11—81no—
204C22×SD16—21no—
205C2×C4⋊Q8C22×C1111yescharacteristic
206C2×#127—21no—
207C2×#127C22×C1111yescharacteristic
208C2×#121—22no—
209C2×C4×D4C22×C1111yescharacteristic
210#486—22no—
211#486—22no—
212#461—22no—
213#461—22no—
214C2×C4⋊C8C22×C1111yescharacteristic
215C2×C4⋊C8C22×C1111yescharacteristic
216C2×#103—21no—
217C2×#102—22no—
218C2×C4×C8C22×C1111yescharacteristic
219#392—22no—
220#390—21no—
221C4×C4⋊C4C22×C1111yescharacteristic
222#340—22no—
223#331—22no—
224D4⋊C8—22no—
225C22×C11—44no—
226C22×C11—42no—
227C22×C11—82no—
228C22×C11—81no—
229C22×C11—81no—
230C22×C11—84no—
231C22×C11—84no—
232C22×C11—82no—
233C22×C11—82no—
234C22×C11—82no—
235C22×C11#39211yescharacteristic
236C22×C11#44711yescharacteristic
237C22×C11#44911yescharacteristic
238C22×C11#45012yes—
239C22×C11#45512yes—
240C4×C11—21no—
241C4×C11—21no—
242C4×C11—44no—
243C4×C11—82no—
244C4×C11—81no—
245C4×C11#44711yescharacteristic
246C4×C11#44911yescharacteristic
247C4×C11#46012yes—
248C4×C11#46611yescharacteristic
249C4×C11#46911yescharacteristic
250C4×C11#49211yescharacteristic
251C4×C11#49611yescharacteristic
252C22×Q8—21no—
253C22×D4—24no—
254C22×D4—21no—
255C22×D4—21no—
256C22×D4D4×C1111yescharacteristic
257C22×D4D4×C1112yes—
258C23×C4—21no—
259C2×SD16—24no—
260C2×SD16—42no—
261C2×SD16—42no—
262C22×C8—21no—
263C22×C8—21no—
264C22×C8—21no—
265C4⋊Q8—21no—
266C4⋊Q8—21no—
267C4⋊Q8—21no—
268C4⋊Q8D4×C1112yescomplemented
269#127—21no—
270#127—21no—
271#127—21no—
272#127—21no—
273#127—42no—
274#127—42no—
275#121—44no—
276#121—44no—
277C4×D4—21no—
278C4×D4—21no—
279C4×D4—21no—
280C4×D4—21no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4D4×C1111yescharacteristic
284C2×C4⋊C4D4×C1112yes—
285C2×C22⋊C4—24no—
286C2×C22⋊C4—21no—
287C2×C42—21no—
288C2×C42C23×C1111yescharacteristic
289C4⋊C8—21no—
290C4⋊C8—21no—
291C4⋊C8—21no—
292C4⋊C8D4×C1112yescomplemented
293#103—24no—
294#102—28no—
295C4×C8—21no—
296C4×C8D4×C1112yescomplemented
297#95—21no—
298C2×C11—82no—
299C2×C11—162no—
300C2×C11#163912yes—
301C2×C11#164212yes—
302C2×C11#199911yescharacteristic
303C2×C11#200411yescharacteristic
304C2×C11#201411yescharacteristic
305C24—21no—
306C24—22no—
307C2×Q8—22no—
308C2×Q8—41no—
309C2×Q8—41no—
310C2×Q8—41no—
311C2×Q8—41no—
312C2×Q8—41no—
313C2×D4—21no—
314C2×D4—22no—
315C2×D4—21no—
316C2×D4—22no—
317C2×D4—21no—
318C2×D4—21no—
319C2×D4—21no—
320C2×D4—44no—
321C2×D4—48no—
322C2×D4—48no—
323C2×D4—41no—
324C2×D4—41no—
325C2×D4—41no—
326C2×D4—41no—
327C2×D4—41no—
328C2×D4—42no—
329C2×D4—41no—
330C2×D4—42no—
331C2×D4—41no—
332C2×D4—41no—
333C2×D4—84no—
334C2×D4C11×D812yes—
335C22×C4—22no—
336C22×C4—21no—
337C22×C4—41no—
338C22×C4—41no—
339C22×C4—41no—
340C22×C4—42no—
341C22×C4—42no—
342C22×C4C2×D4×C1111yescharacteristic
343C22×C4C2×D4×C1111yescharacteristic
344C22×C4C2×D4×C1111yescharacteristic
345SD16—48no—
346C2×C8—22no—
347C2×C8—22no—
348C2×C8—42no—
349C2×C8—41no—
350C2×C8—41no—
351C2×C8—41no—
352C2×C8—42no—
353C4⋊C4—22no—
354C4⋊C4—22no—
355C4⋊C4—21no—
356C4⋊C4—22no—
357C4⋊C4—21no—
358C4⋊C4—41no—
359C4⋊C4—41no—
360C4⋊C4C11×SD1614yescomplemented
361C22⋊C4—48no—
362C22⋊C4—41no—
363C22⋊C4—41no—
364C42—41no—
365C42—41no—
366C42C2×D4×C1111yescharacteristic
367C42C2×D4×C1111yescharacteristic
368C42C2×D4×C1111yescharacteristic
369C42C11×#4111yescharacteristic
370C11#1006211yescharacteristic, direct product factor, Sylow
371C23—22no—
372C23—41no—
373C23—41no—
374C23—42no—
375C23—42no—
376C23—42no—
377C23—42no—
378C23—42no—
379C23—44no—
380C23—44no—
381C23C11×#12011yescharacteristic
382Q8—42no—
383Q8—42no—
384Q8—81no—
385Q8—81no—
386D4—22no—
387D4—22no—
388D4—44no—
389D4—41no—
390D4—41no—
391D4—82no—
392D4—816no—
393D4—81no—
394D4—81no—
395D4—81no—
396D4—81no—
397D4—82no—
398D4—81no—
399D4—81no—
400C2×C4—22no—
401C2×C4—24no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—41no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—81no—
408C2×C4—81no—
409C2×C4—81no—
410C2×C4—81no—
411C2×C4—82no—
412C2×C4C11×#12011yescharacteristic
413C2×C4C11×#12011yescharacteristic
414C2×C4C11×#12111yescharacteristic
415C2×C4C11×#12111yescharacteristic
416C2×C4C11×#12111yescharacteristic
417C2×C4C11×#12711yescharacteristic
418C2×C4C2×C11×D811yescharacteristic
419C2×C4C2×C11×SD1612yes—
420C2×C4C11×#13511yescharacteristic
421C2×C4C11×AGL(1,ℤ/8)12yes—
422C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
423C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
424C8—42no—
425C8—42no—
426C8—81no—
427C22—44no—
428C22—42no—
429C22—82no—
430C22—81no—
431C22—81no—
432C22—84no—
433C22—84no—
434C22—82no—
435C22—82no—
436C22—82no—
437C22C11×#39211yescharacteristic
438C22C11×#44711yescharacteristic
439C22C11×#44911yescharacteristic
440C22C11×#45012yes—
441C22C11×#45512yes—
442C4—21no—
443C4—21no—
444C4—44no—
445C4—82no—
446C4—81no—
447C4C11×#44711yescharacteristic
448C4C11×#44911yescharacteristic
449C4C11×#46012yes—
450C4C11×#46611yescharacteristic
451C4C11×#46911yescharacteristic
452C4C11×#49211yescharacteristic
453C4C11×#49611yescharacteristic
454C2—82no—
455C2—162no—
456C2C11×#163912yes—
457C2C11×#164212yes—
458C2C11×#199911yescharacteristic
459C2C11×#200411yescharacteristic
460C2C11×#201411yescharacteristic
subgroupG/H
center, socleC23×C11#120
commutator, Frattini, cosocleC2×C42C23×C11
prime radicalC11×#2541C2
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
1. C2×C11×#486C2semidirect
2. C2×C11×#461C2semidirect
4. C11×#1988C2semidirect
5. C2×C11×#331C2semidirect
6. C2×C11×D4⋊C8C2semidirect
7. C11×#1279C2semidirect
45. C11×C4⋊Q8D4semidirect
69. C11×C4⋊C8D4semidirect
73. C4×C8×C11D4semidirect
75. #10062C11direct (N × H)
131. C11×C4⋊C4SD16semidirect
141. C2×#486C2×C11semidirect
142. C2×#461C2×C11semidirect
144. #1988C2×C11semidirect
145. C2×#331C2×C11semidirect
146. C2×D4⋊C8C2×C11semidirect
147. #1279C2×C11semidirect
268. C4⋊Q8D4×C11semidirect
292. C4⋊C8D4×C11semidirect
296. C4×C8D4×C11semidirect
360. C4⋊C4C11×SD16semidirect
370. C11#10062direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4862
C2×C11×#4612
C11×#25412
C11×#19882
C2×C11×#3312
C2×C11×D4⋊C82
C11×#12792
#1006211