Finite Group Databasebeta

← C11×#9120 #14586313

Subgroups — C11×#9120 #14586313

Order 2816.

684 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C11×M16C211yesmaximal, characteristic, complemented
2C11×#2850C211yesmaximal, characteristic
3C11×#1749C211yesmaximal, characteristic, complemented
4C2×C11×#329C212yesmaximal, complemented
5C11×#1295C212yesmaximal, complemented
6C22×C11×M16—21no—
7C2×C11×#124C2211yescharacteristic
8C2×C11×C22⋊Q8C411yescharacteristic
9C2×C11×#121C411yescharacteristic
10C22×C42×C11C2211yescharacteristic
11C2×C11×C22⋊C8—21no—
12C4×C11×M16—24no—
13C2×C11×#97C2212yes—
14C2×C11×#97C2212yes—
15C2×C4×C8×C11—21no—
16C11×#391C411yescharacteristic
17C11×#390C411yescharacteristic
18C11×#388—21no—
19C11×#388—21no—
20C11×#386—21no—
21C11×#386—21no—
22C11×#382C2211yescharacteristic
23C11×#336—21no—
24C11×#329—24no—
25C22×Q8×C11C2×C411yescharacteristic
26C22×D4×C11—21no—
27C22×D4×C11C2×C411yescharacteristic
28C23×C4×C11C2×C411yescharacteristic
29C23×C4×C11D411yescharacteristic
30C23×C4×C11D411yescharacteristic
31C2×C11×M16—24no—
32C2×C11×M16—24no—
33C2×C11×M16—24no—
34C22×C8×C11—22no—
35C22×C8×C11—22no—
36C11×#124—22no—
37C11×#124—22no—
38C11×C22⋊Q8—42no—
39C11×#121—42no—
40C2×C11×C4⋊C4—21no—
41C2×C11×C4⋊C4C2×C411yescharacteristic
42C2×C11×C4⋊C4C2×C411yescharacteristic
43C2×C11×C22⋊C4—21no—
44C2×C11×C22⋊C4—21no—
45C2×C11×C22⋊C4—21no—
46C2×C11×C22⋊C4—21no—
47C2×C11×C22⋊C4—21no—
48C2×C11×C22⋊C4—21no—
49C2×C42×C11—22no—
50C2×C42×C11—22no—
51C2×C42×C11C2×C411yescharacteristic
52C2×C42×C11D411yescharacteristic
53C2×C42×C11D411yescharacteristic
54C2×C42×C11C2311yescharacteristic
55C11×C22⋊C8—24no—
56C11×#97—22no—
57C11×#97—22no—
58C11×#97—22no—
59C11×#97D414yescomplemented
60C4×C8×C11—24no—
61C11×#95—21no—
62C11×#95—21no—
63C11×#95—21no—
64C11×#95—21no—
65#9120C1111yesmaximal, characteristic, direct product factor, Sylow
66C24×C11—21no—
67C24×C11C22⋊C411yescharacteristic
68C2×Q8×C11—22no—
69C2×Q8×C11—41no—
70C2×Q8×C11—41no—
71C2×D4×C11—22no—
72C2×D4×C11—41no—
73C2×D4×C11—41no—
74C2×D4×C11—42no—
75C2×D4×C11—42no—
76C2×D4×C11—42no—
77C22×C4×C11—22no—
78C22×C4×C11—22no—
79C22×C4×C11—21no—
80C22×C4×C11—21no—
81C22×C4×C11—22no—
82C22×C4×C11—22no—
83C22×C4×C11—22no—
84C22×C4×C11—22no—
85C22×C4×C11—21no—
86C22×C4×C11—21no—
87C22×C4×C11—21no—
88C22×C4×C11—41no—
89C22×C4×C11—41no—
90C22×C4×C11C22⋊C411yescharacteristic
91C22×C4×C11C22⋊C411yescharacteristic
92C22×C4×C11C22⋊C411yescharacteristic
93C22×C4×C11C22×C411yescharacteristic
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11C2×D411yescharacteristic
96C11×M16—216no—
97C2×C8×C11—24no—
98C2×C8×C11—24no—
99C2×C8×C11—24no—
100C2×C8×C11—24no—
101C2×C8×C11—42no—
102C2×C8×C11—42no—
103C11×C4⋊C4—41no—
104C11×C4⋊C4—41no—
105C11×C4⋊C4—42no—
106C11×C22⋊C4—42no—
107C11×C22⋊C4—42no—
108C11×C22⋊C4—42no—
109C11×C22⋊C4—42no—
110C11×C22⋊C4—41no—
111C11×C22⋊C4—42no—
112C11×C22⋊C4—41no—
113C42×C11—22no—
114C42×C11—21no—
115C42×C11—22no—
116C42×C11—21no—
117C42×C11C2×D412yes—
118C42×C11#4112yes—
119C2×C4×M16C2×C1111yescharacteristic, complemented
120#2850C2×C1111yescharacteristic
121#1749C2×C1111yescharacteristic, complemented
122C2×#329C2×C1112yescomplemented
123#1295C2×C1112yescomplemented
124C23×C11—21no—
125C23×C11—21no—
126C23×C11—21no—
127C23×C11—21no—
128C23×C11—21no—
129C23×C11—21no—
130C23×C11—41no—
131C23×C11—41no—
132C23×C11—41no—
133C23×C11—41no—
134C23×C11—41no—
135C23×C11—41no—
136C23×C11—41no—
137C23×C11#10412yes—
138C23×C11C2×C22⋊C411yescharacteristic
139Q8×C11—82no—
140D4×C11—82no—
141D4×C11—84no—
142C2×C4×C11—24no—
143C2×C4×C11—24no—
144C2×C4×C11—21no—
145C2×C4×C11—21no—
146C2×C4×C11—21no—
147C2×C4×C11—21no—
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—21no—
155C2×C4×C11—21no—
156C2×C4×C11—44no—
157C2×C4×C11—44no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11—41no—
163C2×C4×C11—41no—
164C2×C4×C11—41no—
165C2×C4×C11—41no—
166C2×C4×C11—41no—
167C2×C4×C11#10012yes—
168C2×C4×C11#10412yes—
169C2×C4×C11#10412yes—
170C2×C4×C11C4×D412yes—
171C2×C4×C11#12011yescharacteristic
172C2×C4×C11#12112yes—
173C2×C4×C11#12311yescharacteristic
174C8×C11—28no—
175C8×C11—44no—
176C22×M16—21no—
177C2×#124C22×C1111yescharacteristic
178C2×C22⋊Q8C4×C1111yescharacteristic
179C2×#121C4×C1111yescharacteristic
180C22×C42C22×C1111yescharacteristic
181C2×C22⋊C8—21no—
182C4×M16—24no—
183C2×#97C22×C1112yes—
184C2×#97C22×C1112yes—
185C2×C4×C8—21no—
186#391C4×C1111yescharacteristic
187#390C4×C1111yescharacteristic
188#388—21no—
189#388—21no—
190#386—21no—
191#386—21no—
192#382C22×C1111yescharacteristic
193#336—21no—
194#329—24no—
195C22×C11—22no—
196C22×C11—22no—
197C22×C11—22no—
198C22×C11—41no—
199C22×C11—41no—
200C22×C11—41no—
201C22×C11—41no—
202C22×C11—81no—
203C22×C11—81no—
204C22×C11—81no—
205C22×C11—81no—
206C22×C11—81no—
207C22×C11—81no—
208C22×C11—81no—
209C22×C11#38611yescharacteristic
210C22×C11C2×#10011yescharacteristic
211C22×C11#41311yescharacteristic
212C22×C11C2×#10411yescharacteristic
213C22×C11C2×#10411yescharacteristic
214C22×C11C2×#10411yescharacteristic
215C22×C11#42111yescharacteristic
216C4×C11—22no—
217C4×C11—22no—
218C4×C11—22no—
219C4×C11—21no—
220C4×C11—21no—
221C4×C11—22no—
222C4×C11—22no—
223C4×C11—81no—
224C4×C11—81no—
225C4×C11—81no—
226C22×Q8C2×C4×C1111yescharacteristic
227C22×D4—21no—
228C22×D4C2×C4×C1111yescharacteristic
229C23×C4C2×C4×C1111yescharacteristic
230C23×C4D4×C1111yescharacteristic
231C23×C4D4×C1111yescharacteristic
232C2×M16—24no—
233C2×M16—24no—
234C2×M16—24no—
235C22×C8—22no—
236C22×C8—22no—
237#124—22no—
238#124—22no—
239C22⋊Q8—42no—
240#121—42no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4C2×C4×C1111yescharacteristic
243C2×C4⋊C4C2×C4×C1111yescharacteristic
244C2×C22⋊C4—21no—
245C2×C22⋊C4—21no—
246C2×C22⋊C4—21no—
247C2×C22⋊C4—21no—
248C2×C22⋊C4—21no—
249C2×C22⋊C4—21no—
250C2×C42—22no—
251C2×C42—22no—
252C2×C42C2×C4×C1111yescharacteristic
253C2×C42D4×C1111yescharacteristic
254C2×C42D4×C1111yescharacteristic
255C2×C42C23×C1111yescharacteristic
256C22⋊C8—24no—
257#97—22no—
258#97—22no—
259#97—22no—
260#97D4×C1114yescomplemented
261C4×C8—24no—
262#95—21no—
263#95—21no—
264#95—21no—
265#95—21no—
266C2×C11—42no—
267C2×C11—161no—
268C2×C11#152411yescharacteristic
269C2×C11#152511yescharacteristic
270C2×C11#152711yescharacteristic
271C2×C11#152911yescharacteristic
272C2×C11#187111yescharacteristic
273C2×C11#189611yescharacteristic
274C2×C11#190011yescharacteristic
275C24—21no—
276C24C11×C22⋊C411yescharacteristic
277C2×Q8—22no—
278C2×Q8—41no—
279C2×Q8—41no—
280C2×D4—22no—
281C2×D4—41no—
282C2×D4—41no—
283C2×D4—42no—
284C2×D4—42no—
285C2×D4—42no—
286C22×C4—22no—
287C22×C4—22no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—22no—
291C22×C4—22no—
292C22×C4—22no—
293C22×C4—22no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—41no—
298C22×C4—41no—
299C22×C4C11×C22⋊C411yescharacteristic
300C22×C4C11×C22⋊C411yescharacteristic
301C22×C4C11×C22⋊C411yescharacteristic
302C22×C4C22×C4×C1111yescharacteristic
303C22×C4C2×D4×C1111yescharacteristic
304C22×C4C2×D4×C1111yescharacteristic
305M16—216no—
306C2×C8—24no—
307C2×C8—24no—
308C2×C8—24no—
309C2×C8—24no—
310C2×C8—42no—
311C2×C8—42no—
312C4⋊C4—41no—
313C4⋊C4—41no—
314C4⋊C4—42no—
315C22⋊C4—42no—
316C22⋊C4—42no—
317C22⋊C4—42no—
318C22⋊C4—42no—
319C22⋊C4—41no—
320C22⋊C4—42no—
321C22⋊C4—41no—
322C42—22no—
323C42—21no—
324C42—22no—
325C42—21no—
326C42C2×D4×C1112yes—
327C42C11×#4112yes—
328C11#912011yescharacteristic, direct product factor, Sylow
329C23—21no—
330C23—21no—
331C23—21no—
332C23—21no—
333C23—21no—
334C23—21no—
335C23—41no—
336C23—41no—
337C23—41no—
338C23—41no—
339C23—41no—
340C23—41no—
341C23—41no—
342C23C11×#10412yes—
343C23C2×C11×C22⋊C411yescharacteristic
344Q8—82no—
345D4—82no—
346D4—84no—
347C2×C4—24no—
348C2×C4—24no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—44no—
362C2×C4—44no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4C11×#10012yes—
373C2×C4C11×#10412yes—
374C2×C4C11×#10412yes—
375C2×C4C4×D4×C1112yes—
376C2×C4C11×#12011yescharacteristic
377C2×C4C11×#12112yes—
378C2×C4C11×#12311yescharacteristic
379C8—28no—
380C8—44no—
381C22—22no—
382C22—22no—
383C22—22no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—81no—
389C22—81no—
390C22—81no—
391C22—81no—
392C22—81no—
393C22—81no—
394C22—81no—
395C22C11×#38611yescharacteristic
396C22C2×C11×#10011yescharacteristic
397C22C11×#41311yescharacteristic
398C22C2×C11×#10411yescharacteristic
399C22C2×C11×#10411yescharacteristic
400C22C2×C11×#10411yescharacteristic
401C22C11×#42111yescharacteristic
402C4—22no—
403C4—22no—
404C4—21no—
405C4—22no—
406C4—21no—
407C4—22no—
408C4—22no—
409C4—81no—
410C4—81no—
411C4—81no—
412C2—42no—
413C2—161no—
414C2C11×#152411yescharacteristic
415C2C11×#152511yescharacteristic
416C2C11×#152711yescharacteristic
417C2C11×#152911yescharacteristic
418C2C11×#187111yescharacteristic
419C2C11×#189611yescharacteristic
420C2C11×#190011yescharacteristic
subgroupG/H
center, socleC23×C11C2×C22⋊C4
commutatorC22×C4C22×C4×C11
Frattini, cosocleC2×C42C23×C11
prime radicalC2×C11×#121C4
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. C2×C4×C11×M16C2semidirect
3. C11×#1749C2semidirect
4. C2×C11×#329C2semidirect
5. C11×#1295C2semidirect
59. C11×#97D4semidirect
65. #9120C11direct (N × H)
119. C2×C4×M16C2×C11semidirect
121. #1749C2×C11semidirect
122. C2×#329C2×C11semidirect
123. #1295C2×C11semidirect
260. #97D4×C11semidirect
328. C11#9120direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×C11×M162
C11×#28502
C11×#17492
C2×C11×#3292
C11×#12952
#912011