Finite Group Databasebeta

← C11×#10476 #14587669

Subgroups — C11×#10476 #14587669

Order 2816.

506 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#461C211yesmaximal, characteristic
2C11×#1990C211yesmaximal, characteristic, complemented
3C11×#1954C211yesmaximal, characteristic
4C11×#1802C211yesmaximal, characteristic
5C2×C11×#335C211yesmaximal, characteristic, complemented
6C2×C11×#332C211yesmaximal, characteristic, complemented
7C11×#1296C211yesmaximal, characteristic, complemented
8C22×C11×SD16—21no—
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C4×D4×C11C2211yescharacteristic
11C11×#461—22no—
12C11×#461—22no—
13C2×C11×C4⋊C8C2211yescharacteristic
14C2×C11×C4⋊C8C2211yescharacteristic
15C2×C11×C4⋊C8C2211yescharacteristic
16C2×C11×#103—21no—
17C2×C11×#102—21no—
18C2×C11×C22⋊C8—21no—
19C2×C11×C22⋊C8—21no—
20C2×C4×C8×C11C2211yescharacteristic
21C11×#384C2211yescharacteristic
22C11×#340—21no—
23C11×#340—21no—
24C11×#340—21no—
25C11×#335—22no—
26C11×#332—22no—
27C22×Q8×C11—21no—
28C22×D4×C11D411yescharacteristic
29C23×C4×C11—21no—
30C2×C11×SD16—24no—
31C2×C11×SD16—42no—
32C2×C11×SD16—42no—
33C22×C8×C11—21no—
34C22×C8×C11—21no—
35C22×C8×C11—21no—
36C22×C8×C11D411yescharacteristic
37C22×C8×C11D411yescharacteristic
38C11×C4⋊Q8—21no—
39C11×C4⋊Q8—21no—
40C11×C4⋊Q8—21no—
41C11×C4⋊Q8D412yes—
42C4×D4×C11—21no—
43C4×D4×C11—21no—
44C4×D4×C11—21no—
45C4×D4×C11—21no—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4—21no—
48C2×C11×C4⋊C4—21no—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4D411yescharacteristic
52C2×C11×C22⋊C4—21no—
53C2×C42×C11C2311yescharacteristic
54C11×C4⋊C8—21no—
55C11×C4⋊C8—21no—
56C11×C4⋊C8—21no—
57C11×C4⋊C8—21no—
58C11×C4⋊C8—21no—
59C11×C4⋊C8D412yes—
60C11×#103—24no—
61C11×#102—42no—
62C11×C22⋊C8—42no—
63C11×C22⋊C8—42no—
64C4×C8×C11—21no—
65C4×C8×C11—21no—
66#10476C1111yesmaximal, characteristic, direct product factor, Sylow
67C24×C11—21no—
68C2×Q8×C11—22no—
69C2×Q8×C11—41no—
70C2×Q8×C11—41no—
71C2×Q8×C11—41no—
72C2×Q8×C11—41no—
73C2×Q8×C11—41no—
74C2×D4×C11—21no—
75C2×D4×C11—21no—
76C2×D4×C11—21no—
77C2×D4×C11—21no—
78C2×D4×C11—21no—
79C2×D4×C11D812yes—
80C22×C4×C11—21no—
81C22×C4×C11—41no—
82C22×C4×C11—41no—
83C22×C4×C11—41no—
84C22×C4×C11—41no—
85C22×C4×C11—41no—
86C22×C4×C11—41no—
87C22×C4×C11—41no—
88C22×C4×C11—41no—
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11#4111yescharacteristic
92C11×SD16—48no—
93C2×C8×C11—22no—
94C2×C8×C11—21no—
95C2×C8×C11—21no—
96C2×C8×C11—21no—
97C2×C8×C11—21no—
98C2×C8×C11—21no—
99C2×C8×C11—41no—
100C2×C8×C11—41no—
101C2×C8×C11—41no—
102C2×C8×C11—41no—
103C2×C8×C11—41no—
104C2×C8×C11—41no—
105C2×C8×C11—41no—
106C2×C8×C11—41no—
107C2×C8×C11SD1612yescomplemented
108C11×C4⋊C4—21no—
109C11×C4⋊C4—22no—
110C11×C4⋊C4—22no—
111C11×C4⋊C4—21no—
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—81no—
119C11×C22⋊C4—41no—
120C11×C22⋊C4—41no—
121C42×C11C2×D411yescharacteristic
122C42×C11C2×D411yescharacteristic
123C42×C11#4111yescharacteristic
124C42×C11#4111yescharacteristic
125C2×#461C2×C1111yescharacteristic
126#1990C2×C1111yescharacteristic, complemented
127#1954C2×C1111yescharacteristic
128#1802C2×C1111yescharacteristic
129C2×#335C2×C1111yescharacteristic, complemented
130C2×#332C2×C1111yescharacteristic, complemented
131#1296C2×C1111yescharacteristic, complemented
132C23×C11—22no—
133C23×C11—41no—
134C23×C11—41no—
135C23×C11—41no—
136C23×C11—41no—
137C23×C11—41no—
138C23×C11—41no—
139C23×C11#12111yescharacteristic
140Q8×C11—42no—
141Q8×C11—42no—
142Q8×C11—81no—
143Q8×C11—81no—
144D4×C11—22no—
145D4×C11—22no—
146D4×C11—41no—
147D4×C11—41no—
148C2×C4×C11—21no—
149C2×C4×C11—21no—
150C2×C4×C11—41no—
151C2×C4×C11—42no—
152C2×C4×C11—41no—
153C2×C4×C11—41no—
154C2×C4×C11—81no—
155C2×C4×C11—81no—
156C2×C4×C11—81no—
157C2×C4×C11—81no—
158C2×C4×C11—81no—
159C2×C4×C11—81no—
160C2×C4×C11—81no—
161C2×C4×C11—81no—
162C2×C4×C11—81no—
163C2×C4×C11#12011yescharacteristic
164C2×C4×C11#12111yescharacteristic
165C2×C4×C11#12111yescharacteristic
166C2×C4×C11#12311yescharacteristic
167C2×C4×C11#12311yescharacteristic
168C2×C4×C11#12411yescharacteristic
169C2×C4×C11C2×D811yescharacteristic
170C2×C4×C11C2×SD1611yescharacteristic
171C2×C4×C11#13511yescharacteristic
172C2×C4×C11#13511yescharacteristic
173C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
174C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
175C2×C4×C11#13711yescharacteristic
176C2×C4×C11#13711yescharacteristic
177C8×C11—22no—
178C8×C11—42no—
179C8×C11—41no—
180C8×C11—81no—
181C8×C11—81no—
182C22×SD16—21no—
183C2×C4⋊Q8C22×C1111yescharacteristic
184C2×C4×D4C22×C1111yescharacteristic
185#461—22no—
186#461—22no—
187C2×C4⋊C8C22×C1111yescharacteristic
188C2×C4⋊C8C22×C1111yescharacteristic
189C2×C4⋊C8C22×C1111yescharacteristic
190C2×#103—21no—
191C2×#102—21no—
192C2×C22⋊C8—21no—
193C2×C22⋊C8—21no—
194C2×C4×C8C22×C1111yescharacteristic
195#384C22×C1111yescharacteristic
196#340—21no—
197#340—21no—
198#340—21no—
199#335—22no—
200#332—22no—
201C22×C11—42no—
202C22×C11—42no—
203C22×C11—42no—
204C22×C11—81no—
205C22×C11—81no—
206C22×C11—81no—
207C22×C11—81no—
208C22×C11#39411yescharacteristic
209C22×C11#46111yescharacteristic
210C22×C11#46311yescharacteristic
211C22×C11#46611yescharacteristic
212C22×C11#46811yescharacteristic
213C22×C11#47111yescharacteristic
214C22×C11#47311yescharacteristic
215C4×C11—21no—
216C4×C11—21no—
217C4×C11—81no—
218C4×C11—82no—
219C4×C11—161no—
220C4×C11#44711yescharacteristic
221C4×C11#45211yescharacteristic
222C4×C11#46011yescharacteristic
223C4×C11#46411yescharacteristic
224C4×C11#46511yescharacteristic
225C4×C11#46811yescharacteristic
226C4×C11#48011yescharacteristic
227C4×C11#48211yescharacteristic
228C22×Q8—21no—
229C22×D4D4×C1111yescharacteristic
230C23×C4—21no—
231C2×SD16—24no—
232C2×SD16—42no—
233C2×SD16—42no—
234C22×C8—21no—
235C22×C8—21no—
236C22×C8—21no—
237C22×C8D4×C1111yescharacteristic
238C22×C8D4×C1111yescharacteristic
239C4⋊Q8—21no—
240C4⋊Q8—21no—
241C4⋊Q8—21no—
242C4⋊Q8D4×C1112yes—
243C4×D4—21no—
244C4×D4—21no—
245C4×D4—21no—
246C4×D4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4D4×C1111yescharacteristic
253C2×C22⋊C4—21no—
254C2×C42C23×C1111yescharacteristic
255C4⋊C8—21no—
256C4⋊C8—21no—
257C4⋊C8—21no—
258C4⋊C8—21no—
259C4⋊C8—21no—
260C4⋊C8D4×C1112yes—
261#103—24no—
262#102—42no—
263C22⋊C8—42no—
264C22⋊C8—42no—
265C4×C8—21no—
266C4×C8—21no—
267C2×C11—82no—
268C2×C11#167311yescharacteristic
269C2×C11#168111yescharacteristic
270C2×C11#169111yescharacteristic
271C2×C11#169911yescharacteristic
272C2×C11#203311yescharacteristic
273C2×C11#205211yescharacteristic
274C2×C11#205511yescharacteristic
275C24—21no—
276C2×Q8—22no—
277C2×Q8—41no—
278C2×Q8—41no—
279C2×Q8—41no—
280C2×Q8—41no—
281C2×Q8—41no—
282C2×D4—21no—
283C2×D4—21no—
284C2×D4—21no—
285C2×D4—21no—
286C2×D4—21no—
287C2×D4C11×D812yes—
288C22×C4—21no—
289C22×C4—41no—
290C22×C4—41no—
291C22×C4—41no—
292C22×C4—41no—
293C22×C4—41no—
294C22×C4—41no—
295C22×C4—41no—
296C22×C4—41no—
297C22×C4C2×D4×C1111yescharacteristic
298C22×C4C2×D4×C1111yescharacteristic
299C22×C4C11×#4111yescharacteristic
300SD16—48no—
301C2×C8—21no—
302C2×C8—21no—
303C2×C8—22no—
304C2×C8—21no—
305C2×C8—21no—
306C2×C8—21no—
307C2×C8—41no—
308C2×C8—41no—
309C2×C8—41no—
310C2×C8—41no—
311C2×C8—41no—
312C2×C8—41no—
313C2×C8—41no—
314C2×C8—41no—
315C2×C8C11×SD1612yescomplemented
316C4⋊C4—21no—
317C4⋊C4—22no—
318C4⋊C4—22no—
319C4⋊C4—21no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C4⋊C4—41no—
323C4⋊C4—41no—
324C4⋊C4—41no—
325C4⋊C4—41no—
326C4⋊C4—81no—
327C22⋊C4—41no—
328C22⋊C4—41no—
329C42C2×D4×C1111yescharacteristic
330C42C2×D4×C1111yescharacteristic
331C42C11×#4111yescharacteristic
332C42C11×#4111yescharacteristic
333C11#1047611yescharacteristic, direct product factor, Sylow
334C23—22no—
335C23—41no—
336C23—41no—
337C23—41no—
338C23—41no—
339C23—41no—
340C23—41no—
341C23C11×#12111yescharacteristic
342Q8—42no—
343Q8—42no—
344Q8—81no—
345Q8—81no—
346D4—22no—
347D4—22no—
348D4—41no—
349D4—41no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—41no—
353C2×C4—42no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—81no—
357C2×C4—81no—
358C2×C4—81no—
359C2×C4—81no—
360C2×C4—81no—
361C2×C4—81no—
362C2×C4—81no—
363C2×C4—81no—
364C2×C4—81no—
365C2×C4C11×#12011yescharacteristic
366C2×C4C11×#12111yescharacteristic
367C2×C4C11×#12111yescharacteristic
368C2×C4C11×#12311yescharacteristic
369C2×C4C11×#12311yescharacteristic
370C2×C4C11×#12411yescharacteristic
371C2×C4C2×C11×D811yescharacteristic
372C2×C4C2×C11×SD1611yescharacteristic
373C2×C4C11×#13511yescharacteristic
374C2×C4C11×#13511yescharacteristic
375C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
376C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
377C2×C4C11×#13711yescharacteristic
378C2×C4C11×#13711yescharacteristic
379C8—22no—
380C8—42no—
381C8—41no—
382C8—81no—
383C8—81no—
384C22—42no—
385C22—42no—
386C22—42no—
387C22—81no—
388C22—81no—
389C22—81no—
390C22—81no—
391C22C11×#39411yescharacteristic
392C22C11×#46111yescharacteristic
393C22C11×#46311yescharacteristic
394C22C11×#46611yescharacteristic
395C22C11×#46811yescharacteristic
396C22C11×#47111yescharacteristic
397C22C11×#47311yescharacteristic
398C4—21no—
399C4—21no—
400C4—82no—
401C4—81no—
402C4—161no—
403C4C11×#44711yescharacteristic
404C4C11×#45211yescharacteristic
405C4C11×#46011yescharacteristic
406C4C11×#46411yescharacteristic
407C4C11×#46511yescharacteristic
408C4C11×#46811yescharacteristic
409C4C11×#48011yescharacteristic
410C4C11×#48211yescharacteristic
411C2—82no—
412C2C11×#167311yescharacteristic
413C2C11×#168111yescharacteristic
414C2C11×#169111yescharacteristic
415C2C11×#169911yescharacteristic
416C2C11×#203311yescharacteristic
417C2C11×#205211yescharacteristic
418C2C11×#205511yescharacteristic
subgroupG/H
center, socleC23×C11#121
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×#1990C2semidirect
5. C2×C11×#335C2semidirect
6. C2×C11×#332C2semidirect
7. C11×#1296C2semidirect
66. #10476C11direct (N × H)
107. C2×C8×C11SD16semidirect
126. #1990C2×C11semidirect
129. C2×#335C2×C11semidirect
130. C2×#332C2×C11semidirect
131. #1296C2×C11semidirect
315. C2×C8C11×SD16semidirect
333. C11#10476direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4612
C11×#19902
C11×#19542
C11×#18022
C2×C11×#3352
C2×C11×#3322
C11×#12962
#1047611