Finite Group Databasebeta

← C11×#18287 #14595480

Subgroups — C11×#18287 #14595480

Order 2816.

1064 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
1C2×C11×#543C211yesmaximal, characteristic
2C11×#3189C212yesmaximal, complemented
3C11×#2626C211yesmaximal, characteristic
4C11×#1614C214yesmaximal, complemented
5C11×#1602C214yesmaximal, complemented
6C11×#1520C212yesmaximal, complemented
7C2×C11×#323C211yesmaximal, characteristic
8C11×#543—24no—
9C11×#543—22no—
10C11×#543C2214yes—
11C2×C11×C22⋊Q8—22no—
12C2×C11×C22⋊Q8—21no—
13C2×C11×C22⋊Q8—22no—
14C2×C11×C22⋊Q8C2212yes—
15C2×C11×C22⋊Q8C2211yescharacteristic
16C22×C11×C22⋊C4—21no—
17C22×C11×C22⋊C4C2211yescharacteristic
18C11×#484—22no—
19C11×#484C2214yescomplemented
20C11×#467—24no—
21C11×#451—22no—
22C11×#451C2214yescomplemented
23C2×C11×C22⋊C8C2212yes—
24C11×#399C2212yes—
25C11×#396—22no—
26C11×#393C2212yes—
27C11×#385—21no—
28C11×#380C2211yescharacteristic
29C11×#379—21no—
30C11×#328C2218yescomplemented
31C11×#323C2214yes—
32C25×C11D411yescharacteristic
33C22×Q8×C11—21no—
34C22×Q8×C11D412yes—
35C22×Q8×C11C2311yescharacteristic
36C23×C4×C11—21no—
37C23×C4×C11—21no—
38C23×C4×C11D411yescharacteristic
39C23×C4×C11C2311yescharacteristic
40C2×C11×Q16—24no—
41C22×C8×C11—22no—
42C11×C22⋊Q8—28no—
43C11×C22⋊Q8—28no—
44C11×C22⋊Q8—24no—
45C11×C22⋊Q8—28no—
46C11×C22⋊Q8—24no—
47C11×C22⋊Q8—22no—
48C11×C22⋊Q8—22no—
49C11×C22⋊Q8—28no—
50C11×C22⋊Q8—22no—
51C11×C22⋊Q8—22no—
52C11×C22⋊Q8D414yes—
53C11×C22⋊Q8C2314yes—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4—22no—
56C2×C11×C4⋊C4—22no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4—22no—
60C2×C11×C4⋊C4D412yes—
61C2×C11×C4⋊C4C2311yescharacteristic
62C2×C11×C22⋊C4—22no—
63C2×C11×C22⋊C4—24no—
64C2×C11×C22⋊C4—22no—
65C2×C11×C22⋊C4—24no—
66C2×C11×C22⋊C4—22no—
67C2×C11×C22⋊C4—22no—
68C2×C11×C22⋊C4—21no—
69C2×C11×C22⋊C4—21no—
70C2×C11×C22⋊C4—22no—
71C2×C11×C22⋊C4—22no—
72C2×C11×C22⋊C4D412yes—
73C2×C11×C22⋊C4C2312yes—
74C11×#107—24no—
75C11×#103—24no—
76C11×#103—24no—
77C11×C22⋊C8—22no—
78C11×C22⋊C8C2314yes—
79C11×#95—22no—
80C11×#95C2312yes—
81#18287C1111yesmaximal, characteristic, direct product factor, Sylow
82C24×C11—21no—
83C24×C11—21no—
84C24×C11—22no—
85C24×C11—81no—
86C24×C11—81no—
87C24×C11Q1614yescomplemented
88C24×C11C2×D412yes—
89C24×C11C2×D411yescharacteristic
90C2×Q8×C11—24no—
91C2×Q8×C11—22no—
92C2×Q8×C11—22no—
93C2×Q8×C11—81no—
94C2×Q8×C11—82no—
95C2×Q8×C11—82no—
96C2×Q8×C11C2×D414yes—
97C22×C4×C11—22no—
98C22×C4×C11—21no—
99C22×C4×C11—22no—
100C22×C4×C11—24no—
101C22×C4×C11—24no—
102C22×C4×C11—21no—
103C22×C4×C11—21no—
104C22×C4×C11—22no—
105C22×C4×C11—21no—
106C22×C4×C11—81no—
107C22×C4×C11—81no—
108C22×C4×C11—82no—
109C22×C4×C11—82no—
110C22×C4×C11C2×D412yes—
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2×D412yes—
113C22×C4×C11C2×D412yes—
114C22×C4×C11C2411yescharacteristic
115C11×Q16—84no—
116C2×C8×C11—24no—
117C2×C8×C11—82no—
118C11×C4⋊C4—24no—
119C11×C4⋊C4—28no—
120C11×C4⋊C4—24no—
121C11×C4⋊C4—22no—
122C11×C4⋊C4—24no—
123C11×C4⋊C4—22no—
124C11×C4⋊C4—42no—
125C11×C4⋊C4—81no—
126C11×C4⋊C4—82no—
127C11×C4⋊C4C2×D414yes—
128C11×C22⋊C4—28no—
129C11×C22⋊C4—24no—
130C11×C22⋊C4—24no—
131C11×C22⋊C4—24no—
132C11×C22⋊C4—24no—
133C11×C22⋊C4—41no—
134C11×C22⋊C4—41no—
135C11×C22⋊C4—42no—
136C11×C22⋊C4—82no—
137C11×C22⋊C4—82no—
138C2×#543C2×C1111yescharacteristic
139#3189C2×C1112yescomplemented
140#2626C2×C1111yescharacteristic
141#1614C2×C1114yescomplemented
142#1602C2×C1114yescomplemented
143#1520C2×C1112yescomplemented
144C2×#323C2×C1111yescharacteristic
145C23×C11—22no—
146C23×C11—24no—
147C23×C11—22no—
148C23×C11—24no—
149C23×C11—41no—
150C23×C11—41no—
151C23×C11—42no—
152C23×C11—42no—
153C23×C11—42no—
154C23×C11—42no—
155C23×C11—81no—
156C23×C11—81no—
157C23×C11—84no—
158C23×C11—84no—
159C23×C11#12011yescharacteristic
160C23×C11#12011yescharacteristic
161C23×C11C2×Q1614yes—
162C23×C11C2×Q1612yes—
163C23×C11#13712yes—
164C23×C11C22×D411yescharacteristic
165Q8×C11—44no—
166Q8×C11—44no—
167Q8×C11—82no—
168Q8×C11—84no—
169C2×C4×C11—24no—
170C2×C4×C11—22no—
171C2×C4×C11—24no—
172C2×C4×C11—41no—
173C2×C4×C11—42no—
174C2×C4×C11—42no—
175C2×C4×C11—41no—
176C2×C4×C11—42no—
177C2×C4×C11—44no—
178C2×C4×C11—44no—
179C2×C4×C11—42no—
180C2×C4×C11—42no—
181C2×C4×C11—42no—
182C2×C4×C11—42no—
183C2×C4×C11—42no—
184C2×C4×C11—41no—
185C2×C4×C11—41no—
186C2×C4×C11—42no—
187C2×C4×C11—81no—
188C2×C4×C11—84no—
189C2×C4×C11—84no—
190C2×C4×C11#12012yes—
191C2×C4×C11C22×D412yes—
192C8×C11—44no—
193#543—24no—
194#543—22no—
195#543C22×C1114yes—
196C2×C22⋊Q8—22no—
197C2×C22⋊Q8—21no—
198C2×C22⋊Q8—22no—
199C2×C22⋊Q8C22×C1112yes—
200C2×C22⋊Q8C22×C1111yescharacteristic
201C22×C22⋊C4—21no—
202C22×C22⋊C4C22×C1111yescharacteristic
203#484—22no—
204#484C22×C1114yescomplemented
205#467—24no—
206#451—22no—
207#451C22×C1114yescomplemented
208C2×C22⋊C8C22×C1112yes—
209#399C22×C1112yes—
210#396—22no—
211#393C22×C1112yes—
212#385—21no—
213#380C22×C1111yescharacteristic
214#379—21no—
215#328C22×C1118yescomplemented
216#323C22×C1114yes—
217C22×C11—21no—
218C22×C11—21no—
219C22×C11—21no—
220C22×C11—21no—
221C22×C11—21no—
222C22×C11—21no—
223C22×C11—24no—
224C22×C11—42no—
225C22×C11—42no—
226C22×C11—44no—
227C22×C11—48no—
228C22×C11—42no—
229C22×C11—42no—
230C22×C11—82no—
231C22×C11—84no—
232C22×C11#45112yes—
233C22×C11#45112yes—
234C22×C11C2×#12011yescharacteristic
235C22×C11C22×Q1611yescharacteristic
236C22×C11C2×#13711yescharacteristic
237C4×C11—22no—
238C4×C11—22no—
239C4×C11—42no—
240C4×C11—44no—
241C4×C11—44no—
242C4×C11—82no—
243C4×C11—81no—
244C4×C11—81no—
245C25D4×C1111yescharacteristic
246C22×Q8—21no—
247C22×Q8D4×C1112yes—
248C22×Q8C23×C1111yescharacteristic
249C23×C4—21no—
250C23×C4—21no—
251C23×C4D4×C1111yescharacteristic
252C23×C4C23×C1111yescharacteristic
253C2×Q16—24no—
254C22×C8—22no—
255C22⋊Q8—28no—
256C22⋊Q8—28no—
257C22⋊Q8—24no—
258C22⋊Q8—28no—
259C22⋊Q8—24no—
260C22⋊Q8—22no—
261C22⋊Q8—22no—
262C22⋊Q8—28no—
263C22⋊Q8—22no—
264C22⋊Q8—22no—
265C22⋊Q8D4×C1114yes—
266C22⋊Q8C23×C1114yes—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—22no—
269C2×C4⋊C4—22no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—22no—
273C2×C4⋊C4D4×C1112yes—
274C2×C4⋊C4C23×C1111yescharacteristic
275C2×C22⋊C4—22no—
276C2×C22⋊C4—24no—
277C2×C22⋊C4—22no—
278C2×C22⋊C4—24no—
279C2×C22⋊C4—22no—
280C2×C22⋊C4—22no—
281C2×C22⋊C4—21no—
282C2×C22⋊C4—21no—
283C2×C22⋊C4—22no—
284C2×C22⋊C4—22no—
285C2×C22⋊C4D4×C1112yes—
286C2×C22⋊C4C23×C1112yes—
287#107—24no—
288#103—24no—
289#103—24no—
290C22⋊C8—22no—
291C22⋊C8C23×C1114yes—
292#95—22no—
293#95C23×C1112yes—
294C2×C11—21no—
295C2×C11—21no—
296C2×C11—22no—
297C2×C11—22no—
298C2×C11—44no—
299C2×C11C2×#45111yescharacteristic
300C2×C11#301911yescharacteristic
301C2×C11#302611yescharacteristic
302C24—21no—
303C24—21no—
304C24—22no—
305C24—81no—
306C24—81no—
307C24C11×Q1614yescomplemented
308C24C2×D4×C1112yes—
309C24C2×D4×C1111yescharacteristic
310C2×Q8—24no—
311C2×Q8—22no—
312C2×Q8—22no—
313C2×Q8—81no—
314C2×Q8—82no—
315C2×Q8—82no—
316C2×Q8C2×D4×C1114yes—
317C22×C4—22no—
318C22×C4—21no—
319C22×C4—22no—
320C22×C4—24no—
321C22×C4—24no—
322C22×C4—21no—
323C22×C4—21no—
324C22×C4—22no—
325C22×C4—21no—
326C22×C4—81no—
327C22×C4—81no—
328C22×C4—82no—
329C22×C4—82no—
330C22×C4C2×D4×C1112yes—
331C22×C4C2×D4×C1111yescharacteristic
332C22×C4C2×D4×C1112yes—
333C22×C4C2×D4×C1112yes—
334C22×C4C24×C1111yescharacteristic
335Q16—84no—
336C2×C8—24no—
337C2×C8—82no—
338C4⋊C4—24no—
339C4⋊C4—28no—
340C4⋊C4—24no—
341C4⋊C4—22no—
342C4⋊C4—24no—
343C4⋊C4—22no—
344C4⋊C4—42no—
345C4⋊C4—81no—
346C4⋊C4—82no—
347C4⋊C4C2×D4×C1114yes—
348C22⋊C4—28no—
349C22⋊C4—24no—
350C22⋊C4—24no—
351C22⋊C4—24no—
352C22⋊C4—24no—
353C22⋊C4—41no—
354C22⋊C4—41no—
355C22⋊C4—42no—
356C22⋊C4—82no—
357C22⋊C4—82no—
358C11#1828711yescharacteristic, direct product factor, Sylow
359C23—22no—
360C23—24no—
361C23—22no—
362C23—24no—
363C23—41no—
364C23—41no—
365C23—42no—
366C23—42no—
367C23—42no—
368C23—42no—
369C23—81no—
370C23—81no—
371C23—84no—
372C23—84no—
373C23C11×#12011yescharacteristic
374C23C11×#12011yescharacteristic
375C23C2×C11×Q1614yes—
376C23C2×C11×Q1612yes—
377C23C11×#13712yes—
378C23C22×D4×C1111yescharacteristic
379Q8—44no—
380Q8—44no—
381Q8—82no—
382Q8—84no—
383C2×C4—24no—
384C2×C4—22no—
385C2×C4—24no—
386C2×C4—41no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—41no—
390C2×C4—42no—
391C2×C4—44no—
392C2×C4—44no—
393C2×C4—42no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—42no—
401C2×C4—81no—
402C2×C4—84no—
403C2×C4—84no—
404C2×C4C11×#12012yes—
405C2×C4C22×D4×C1112yes—
406C8—44no—
407C22—21no—
408C22—21no—
409C22—21no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—24no—
414C22—42no—
415C22—42no—
416C22—44no—
417C22—48no—
418C22—42no—
419C22—42no—
420C22—82no—
421C22—84no—
422C22C11×#45112yes—
423C22C11×#45112yes—
424C22C2×C11×#12011yescharacteristic
425C22C22×C11×Q1611yescharacteristic
426C22C2×C11×#13711yescharacteristic
427C4—22no—
428C4—22no—
429C4—42no—
430C4—44no—
431C4—44no—
432C4—82no—
433C4—81no—
434C4—81no—
435C2—21no—
436C2—21no—
437C2—22no—
438C2—22no—
439C2—44no—
440C2C2×C11×#45111yescharacteristic
441C2C11×#301911yescharacteristic
442C2C11×#302611yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC25×C11D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#3189C2semidirect
4. C11×#1614C2semidirect
5. C11×#1602C2semidirect
6. C11×#1520C2semidirect
19. C11×#484C22semidirect
22. C11×#451C22semidirect
30. C11×#328C22semidirect
81. #18287C11direct (N × H)
87. C24×C11Q16semidirect
139. #3189C2×C11semidirect
141. #1614C2×C11semidirect
142. #1602C2×C11semidirect
143. #1520C2×C11semidirect
204. #484C22×C11semidirect
207. #451C22×C11semidirect
215. #328C22×C11semidirect
307. C24C11×Q16semidirect
358. C11#18287direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5432
C11×#31892
C11×#26262
C11×#16142
C11×#16022
C11×#15202
C2×C11×#3232
#1828711