Finite Group Databasebeta

← C11×#9133 #14586326

Subgroups — C11×#9133 #14586326

Order 2816.

784 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×C4⋊C8C211yesmaximal, characteristic, complemented
2C11×#2856C211yesmaximal, characteristic
3C11×#1797C211yesmaximal, characteristic, complemented
4C2×C11×#331C212yesmaximal, complemented
5C11×#1296C212yesmaximal, complemented
6C23×C8×C11—21no—
7C2×C11×#127C2211yescharacteristic
8C2×C11×#121—21no—
9C2×C11×#121—21no—
10C2×C11×#121C412yes—
11C22×C42×C11C2211yescharacteristic
12C2×C11×C4⋊C8—21no—
13C2×C11×C4⋊C8—24no—
14C2×C11×C4⋊C8C2212yes—
15C2×C11×C4⋊C8C2212yes—
16C2×C11×C22⋊C8—21no—
17C11×#390—21no—
18C11×#390—21no—
19C11×#390C412yes—
20C11×#384C2211yescharacteristic
21C11×#336—21no—
22C11×#331—24no—
23C22×D4×C11—22no—
24C22×D4×C11—21no—
25C22×D4×C11—21no—
26C22×D4×C11C2×C412yes—
27C23×C4×C11C2×C411yescharacteristic
28C23×C4×C11D411yescharacteristic
29C23×C4×C11D411yescharacteristic
30C22×C8×C11—24no—
31C22×C8×C11—22no—
32C22×C8×C11—22no—
33C22×C8×C11—42no—
34C22×C8×C11—42no—
35C11×#127—22no—
36C11×#127—22no—
37C11×#121—44no—
38C11×#121—42no—
39C11×#121—42no—
40C11×#121—42no—
41C11×#121—42no—
42C2×C11×C4⋊C4—21no—
43C2×C11×C4⋊C4—21no—
44C2×C11×C4⋊C4C2×C412yes—
45C2×C11×C22⋊C4—22no—
46C2×C11×C22⋊C4—22no—
47C2×C11×C22⋊C4—22no—
48C2×C42×C11—22no—
49C2×C42×C11—22no—
50C2×C42×C11C2×C411yescharacteristic
51C2×C42×C11D411yescharacteristic
52C2×C42×C11D411yescharacteristic
53C2×C42×C11C2311yescharacteristic
54C11×C4⋊C8—24no—
55C11×C4⋊C8—22no—
56C11×C4⋊C8—22no—
57C11×C4⋊C8—22no—
58C11×C4⋊C8D414yescomplemented
59C11×C22⋊C8—42no—
60#9133C1111yesmaximal, characteristic, direct product factor, Sylow
61C24×C11—22no—
62C24×C11C22⋊C411yescharacteristic
63C2×D4×C11—24no—
64C2×D4×C11—42no—
65C2×D4×C11—42no—
66C2×D4×C11—44no—
67C2×D4×C11—44no—
68C2×D4×C11—44no—
69C2×D4×C11—41no—
70C2×D4×C11—42no—
71C2×D4×C11—41no—
72C2×D4×C11—41no—
73C2×D4×C11—41no—
74C2×D4×C11—41no—
75C2×D4×C11—41no—
76C2×D4×C11—42no—
77C2×D4×C11—41no—
78C2×D4×C11—41no—
79C22×C4×C11—21no—
80C22×C4×C11—22no—
81C22×C4×C11—21no—
82C22×C4×C11—22no—
83C22×C4×C11—21no—
84C22×C4×C11—21no—
85C22×C4×C11—22no—
86C22×C4×C11—22no—
87C22×C4×C11—22no—
88C22×C4×C11—41no—
89C22×C4×C11C22⋊C411yescharacteristic
90C22×C4×C11C22⋊C411yescharacteristic
91C22×C4×C11C22⋊C411yescharacteristic
92C22×C4×C11D812yes—
93C22×C4×C11D812yes—
94C22×C4×C11SD1612yes—
95C22×C4×C11SD1612yes—
96C22×C4×C11C22×C411yescharacteristic
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C2×C8×C11—24no—
100C2×C8×C11—48no—
101C2×C8×C11—42no—
102C2×C8×C11—42no—
103C2×C8×C11—42no—
104C2×C8×C11—42no—
105C2×C8×C11—42no—
106C11×C4⋊C4—42no—
107C11×C4⋊C4—41no—
108C11×C4⋊C4—41no—
109C11×C4⋊C4—41no—
110C11×C4⋊C4—41no—
111C11×C22⋊C4—44no—
112C11×C22⋊C4—44no—
113C11×C22⋊C4—44no—
114C42×C11—22no—
115C42×C11—21no—
116C42×C11—22no—
117C42×C11—21no—
118C42×C11C2×D412yes—
119C42×C11#4112yes—
120C22×C4⋊C8C2×C1111yescharacteristic, complemented
121#2856C2×C1111yescharacteristic
122#1797C2×C1111yescharacteristic, complemented
123C2×#331C2×C1112yescomplemented
124#1296C2×C1112yescomplemented
125C23×C11—21no—
126C23×C11—21no—
127C23×C11—21no—
128C23×C11—21no—
129C23×C11—42no—
130C23×C11—42no—
131C23×C11—42no—
132C23×C11—42no—
133C23×C11—42no—
134C23×C11—42no—
135C23×C11—42no—
136C23×C11#10012yes—
137C23×C11#10212yes—
138C23×C11#10212yes—
139C23×C11C2×C22⋊C411yescharacteristic
140D4×C11—84no—
141D4×C11—88no—
142D4×C11—81no—
143D4×C11—81no—
144D4×C11—82no—
145D4×C11—82no—
146D4×C11—81no—
147D4×C11—81no—
148C2×C4×C11—21no—
149C2×C4×C11—21no—
150C2×C4×C11—21no—
151C2×C4×C11—21no—
152C2×C4×C11—21no—
153C2×C4×C11—21no—
154C2×C4×C11—22no—
155C2×C4×C11—22no—
156C2×C4×C11—24no—
157C2×C4×C11—24no—
158C2×C4×C11—22no—
159C2×C4×C11—22no—
160C2×C4×C11—21no—
161C2×C4×C11—21no—
162C2×C4×C11—21no—
163C2×C4×C11—44no—
164C2×C4×C11—42no—
165C2×C4×C11—42no—
166C2×C4×C11—42no—
167C2×C4×C11#10212yes—
168C2×C4×C11#10212yes—
169C2×C4×C11C4×D412yes—
170C2×C4×C11#12011yescharacteristic
171C2×C4×C11#12112yes—
172C2×C4×C11#12311yescharacteristic
173C2×C4×C11C2×D811yescharacteristic
174C2×C4×C11C2×D811yescharacteristic
175C2×C4×C11C2×SD1611yescharacteristic
176C2×C4×C11C2×SD1611yescharacteristic
177C2×C4×C11#13512yes—
178C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
179C2×C4×C11#13711yescharacteristic
180C8×C11—44no—
181C8×C11—82no—
182C23×C8—21no—
183C2×#127C22×C1111yescharacteristic
184C2×#121—21no—
185C2×#121—21no—
186C2×#121C4×C1112yes—
187C22×C42C22×C1111yescharacteristic
188C2×C4⋊C8—21no—
189C2×C4⋊C8—24no—
190C2×C4⋊C8C22×C1112yes—
191C2×C4⋊C8C22×C1112yes—
192C2×C22⋊C8—21no—
193#390—21no—
194#390—21no—
195#390C4×C1112yes—
196#384C22×C1111yescharacteristic
197#336—21no—
198#331—24no—
199C22×C11—22no—
200C22×C11—22no—
201C22×C11—22no—
202C22×C11—22no—
203C22×C11—22no—
204C22×C11—22no—
205C22×C11—82no—
206C22×C11—82no—
207C22×C11—82no—
208C22×C11—82no—
209C22×C11—82no—
210C22×C11—82no—
211C22×C11—82no—
212C22×C11#33114yescomplemented
213C22×C11#38611yescharacteristic
214C22×C11C2×#10011yescharacteristic
215C22×C11#41311yescharacteristic
216C22×C11C2×#10211yescharacteristic
217C22×C11C2×#10211yescharacteristic
218C22×C11#41611yescharacteristic
219C22×C11#41711yescharacteristic
220C4×C11—22no—
221C4×C11—22no—
222C4×C11—22no—
223C4×C11—41no—
224C4×C11—82no—
225C4×C11#44711yescharacteristic
226C4×C11#44811yescharacteristic
227C4×C11#46512yes—
228C4×C11#46612yes—
229C4×C11#48011yescharacteristic
230C4×C11#48111yescharacteristic
231C22×D4—22no—
232C22×D4—21no—
233C22×D4—21no—
234C22×D4C2×C4×C1112yes—
235C23×C4C2×C4×C1111yescharacteristic
236C23×C4D4×C1111yescharacteristic
237C23×C4D4×C1111yescharacteristic
238C22×C8—24no—
239C22×C8—22no—
240C22×C8—22no—
241C22×C8—42no—
242C22×C8—42no—
243#127—22no—
244#127—22no—
245#121—44no—
246#121—42no—
247#121—42no—
248#121—42no—
249#121—42no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4C2×C4×C1112yes—
253C2×C22⋊C4—22no—
254C2×C22⋊C4—22no—
255C2×C22⋊C4—22no—
256C2×C42—22no—
257C2×C42—22no—
258C2×C42C2×C4×C1111yescharacteristic
259C2×C42D4×C1111yescharacteristic
260C2×C42D4×C1111yescharacteristic
261C2×C42C23×C1111yescharacteristic
262C4⋊C8—24no—
263C4⋊C8—22no—
264C4⋊C8—22no—
265C4⋊C8—22no—
266C4⋊C8D4×C1114yescomplemented
267C22⋊C8—42no—
268C2×C11—24no—
269C2×C11—162no—
270C2×C11C2×#33111yescharacteristic
271C2×C11#154011yescharacteristic
272C2×C11#154711yescharacteristic
273C2×C11#155111yescharacteristic
274C2×C11#187411yescharacteristic
275C2×C11#189311yescharacteristic
276C2×C11#190011yescharacteristic
277C24—22no—
278C24C11×C22⋊C411yescharacteristic
279C2×D4—24no—
280C2×D4—42no—
281C2×D4—42no—
282C2×D4—44no—
283C2×D4—44no—
284C2×D4—44no—
285C2×D4—41no—
286C2×D4—42no—
287C2×D4—41no—
288C2×D4—41no—
289C2×D4—41no—
290C2×D4—41no—
291C2×D4—41no—
292C2×D4—42no—
293C2×D4—41no—
294C2×D4—41no—
295C22×C4—21no—
296C22×C4—22no—
297C22×C4—21no—
298C22×C4—22no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—22no—
302C22×C4—22no—
303C22×C4—22no—
304C22×C4—41no—
305C22×C4C11×C22⋊C411yescharacteristic
306C22×C4C11×C22⋊C411yescharacteristic
307C22×C4C11×C22⋊C411yescharacteristic
308C22×C4C11×D812yes—
309C22×C4C11×D812yes—
310C22×C4C11×SD1612yes—
311C22×C4C11×SD1612yes—
312C22×C4C22×C4×C1111yescharacteristic
313C22×C4C2×D4×C1111yescharacteristic
314C22×C4C2×D4×C1111yescharacteristic
315C2×C8—24no—
316C2×C8—48no—
317C2×C8—42no—
318C2×C8—42no—
319C2×C8—42no—
320C2×C8—42no—
321C2×C8—42no—
322C4⋊C4—42no—
323C4⋊C4—41no—
324C4⋊C4—41no—
325C4⋊C4—41no—
326C4⋊C4—41no—
327C22⋊C4—44no—
328C22⋊C4—44no—
329C22⋊C4—44no—
330C42—22no—
331C42—21no—
332C42—22no—
333C42—21no—
334C42C2×D4×C1112yes—
335C42C11×#4112yes—
336C11#913311yescharacteristic, direct product factor, Sylow
337C23—21no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—42no—
342C23—42no—
343C23—42no—
344C23—42no—
345C23—42no—
346C23—42no—
347C23—42no—
348C23C11×#10012yes—
349C23C11×#10212yes—
350C23C11×#10212yes—
351C23C2×C11×C22⋊C411yescharacteristic
352D4—84no—
353D4—88no—
354D4—81no—
355D4—81no—
356D4—82no—
357D4—82no—
358D4—81no—
359D4—81no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—22no—
367C2×C4—22no—
368C2×C4—24no—
369C2×C4—24no—
370C2×C4—22no—
371C2×C4—22no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—44no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—42no—
379C2×C4C11×#10212yes—
380C2×C4C11×#10212yes—
381C2×C4C4×D4×C1112yes—
382C2×C4C11×#12011yescharacteristic
383C2×C4C11×#12112yes—
384C2×C4C11×#12311yescharacteristic
385C2×C4C2×C11×D811yescharacteristic
386C2×C4C2×C11×D811yescharacteristic
387C2×C4C2×C11×SD1611yescharacteristic
388C2×C4C2×C11×SD1611yescharacteristic
389C2×C4C11×#13512yes—
390C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
391C2×C4C11×#13711yescharacteristic
392C8—44no—
393C8—82no—
394C22—22no—
395C22—22no—
396C22—22no—
397C22—22no—
398C22—22no—
399C22—22no—
400C22—82no—
401C22—82no—
402C22—82no—
403C22—82no—
404C22—82no—
405C22—82no—
406C22—82no—
407C22C11×#33114yescomplemented
408C22C11×#38611yescharacteristic
409C22C2×C11×#10011yescharacteristic
410C22C11×#41311yescharacteristic
411C22C2×C11×#10211yescharacteristic
412C22C2×C11×#10211yescharacteristic
413C22C11×#41611yescharacteristic
414C22C11×#41711yescharacteristic
415C4—22no—
416C4—22no—
417C4—22no—
418C4—41no—
419C4—82no—
420C4C11×#44711yescharacteristic
421C4C11×#44811yescharacteristic
422C4C11×#46512yes—
423C4C11×#46612yes—
424C4C11×#48011yescharacteristic
425C4C11×#48111yescharacteristic
426C2—24no—
427C2—162no—
428C2C2×C11×#33111yescharacteristic
429C2C11×#154011yescharacteristic
430C2C11×#154711yescharacteristic
431C2C11×#155111yescharacteristic
432C2C11×#187411yescharacteristic
433C2C11×#189311yescharacteristic
434C2C11×#190011yescharacteristic
subgroupG/H
center, socleC23×C11C2×C22⋊C4
commutatorC22×C4C22×C4×C11
Frattini, cosocleC2×C42C23×C11
prime radicalC11×#2856C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C11×C4⋊C8C2semidirect
3. C11×#1797C2semidirect
4. C2×C11×#331C2semidirect
5. C11×#1296C2semidirect
58. C11×C4⋊C8D4semidirect
60. #9133C11direct (N × H)
120. C22×C4⋊C8C2×C11semidirect
122. #1797C2×C11semidirect
123. C2×#331C2×C11semidirect
124. #1296C2×C11semidirect
212. C22×C11#331semidirect
266. C4⋊C8D4×C11semidirect
336. C11#9133direct (N × H)
407. C22C11×#331semidirect

Maximal subgroups

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

subgroupindex
C22×C11×C4⋊C82
C11×#28562
C11×#17972
C2×C11×#3312
C11×#12962
#913311