Finite Group Databasebeta

← C11×#18138 #14595331

Subgroups — C11×#18138 #14595331

Order 2816.

1054 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#543C211yesmaximal, characteristic
2C11×#3095C212yesmaximal, complemented
3C11×#2482C211yesmaximal, characteristic
4C11×#1614C214yesmaximal, complemented
5C11×#1608C214yesmaximal, complemented
6C11×#1511C212yesmaximal, complemented
7C11×#1462C211yesmaximal, 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×#117C2211yescharacteristic
16C22×C11×C22⋊C4—21no—
17C22×C11×C22⋊C4C2211yescharacteristic
18C11×#485—24no—
19C11×#484C2214yescomplemented
20C11×#483C2214yescomplemented
21C11×#428—22no—
22C11×#419—22no—
23C11×#407C2212yes—
24C11×#399C2212yes—
25C11×#397C2212yes—
26C11×#388—22no—
27C11×#385—21no—
28C11×#381C2211yescharacteristic
29C11×#379—21no—
30C11×#328C2218yescomplemented
31C11×#323C2214yes—
32C25×C11D411yescharacteristic
33C22×Q8×C11—21no—
34C22×Q8×C11D412yes—
35C23×C4×C11—21no—
36C23×C4×C11—21no—
37C23×C4×C11D411yescharacteristic
38C23×C4×C11C2311yescharacteristic
39C2×C11×M16—22no—
40C11×C22⋊Q8—28no—
41C11×C22⋊Q8—28no—
42C11×C22⋊Q8—24no—
43C11×C22⋊Q8—28no—
44C11×C22⋊Q8—24no—
45C11×C22⋊Q8—22no—
46C11×C22⋊Q8—22no—
47C11×C22⋊Q8—28no—
48C11×C22⋊Q8D414yes—
49C11×C22⋊Q8C2314yes—
50C11×#117—22no—
51C11×#117—22no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—22no—
54C2×C11×C4⋊C4—22no—
55C2×C11×C4⋊C4—22no—
56C2×C11×C4⋊C4D412yes—
57C2×C11×C4⋊C4C2311yescharacteristic
58C2×C11×C4⋊C4C2311yescharacteristic
59C2×C11×C22⋊C4—22no—
60C2×C11×C22⋊C4—24no—
61C2×C11×C22⋊C4—22no—
62C2×C11×C22⋊C4—24no—
63C2×C11×C22⋊C4—22no—
64C2×C11×C22⋊C4—22no—
65C2×C11×C22⋊C4—21no—
66C2×C11×C22⋊C4—21no—
67C2×C11×C22⋊C4—22no—
68C2×C11×C22⋊C4—22no—
69C2×C11×C22⋊C4D412yes—
70C2×C11×C22⋊C4C2312yes—
71C2×C42×C11—21no—
72C11×#107—24no—
73C11×#106—24no—
74C11×#103—24no—
75C11×#103—24no—
76C11×C22⋊C8—22no—
77C11×C22⋊C8C2314yes—
78C11×#95—21no—
79C11×#95—22no—
80C11×#95C2312yes—
81#18138C1111yesmaximal, characteristic, direct product factor, Sylow
82C24×C11—21no—
83C24×C11—21no—
84C24×C11—24no—
85C24×C11—42no—
86C24×C11—81no—
87C24×C11C2×D411yescharacteristic
88C24×C11C2×D412yes—
89C2×Q8×C11—24no—
90C2×Q8×C11—22no—
91C2×Q8×C11—44no—
92C2×Q8×C11—82no—
93C2×Q8×C11C2×D414yes—
94C22×C4×C11—22no—
95C22×C4×C11—21no—
96C22×C4×C11—22no—
97C22×C4×C11—24no—
98C22×C4×C11—24no—
99C22×C4×C11—21no—
100C22×C4×C11—22no—
101C22×C4×C11—21no—
102C22×C4×C11—21no—
103C22×C4×C11—42no—
104C22×C4×C11—81no—
105C22×C4×C11—82no—
106C22×C4×C11—82no—
107C22×C4×C11C2×D412yes—
108C22×C4×C11C2×D412yes—
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11C2×D412yes—
111C22×C4×C11C2411yescharacteristic
112C11×M16—44no—
113C2×C8×C11—24no—
114C11×C4⋊C4—24no—
115C11×C4⋊C4—28no—
116C11×C4⋊C4—24no—
117C11×C4⋊C4—22no—
118C11×C4⋊C4—24no—
119C11×C4⋊C4—22no—
120C11×C4⋊C4—22no—
121C11×C4⋊C4—82no—
122C11×C4⋊C4C2×D414yes—
123C11×C22⋊C4—28no—
124C11×C22⋊C4—24no—
125C11×C22⋊C4—24no—
126C11×C22⋊C4—24no—
127C11×C22⋊C4—24no—
128C11×C22⋊C4—42no—
129C11×C22⋊C4—41no—
130C11×C22⋊C4—41no—
131C11×C22⋊C4—44no—
132C11×C22⋊C4—82no—
133C42×C11—42no—
134C2×#543C2×C1111yescharacteristic
135#3095C2×C1112yescomplemented
136#2482C2×C1111yescharacteristic
137#1614C2×C1114yescomplemented
138#1608C2×C1114yescomplemented
139#1511C2×C1112yescomplemented
140#1462C2×C1111yescharacteristic
141C23×C11—24no—
142C23×C11—24no—
143C23×C11—22no—
144C23×C11—22no—
145C23×C11—22no—
146C23×C11—22no—
147C23×C11—41no—
148C23×C11—42no—
149C23×C11—42no—
150C23×C11—42no—
151C23×C11—42no—
152C23×C11—81no—
153C23×C11—81no—
154C23×C11—88no—
155C23×C11#12011yescharacteristic
156C23×C11#12011yescharacteristic
157C23×C11#13714yes—
158C23×C11C22×D411yescharacteristic
159Q8×C11—44no—
160Q8×C11—82no—
161Q8×C11—84no—
162C2×C4×C11—24no—
163C2×C4×C11—24no—
164C2×C4×C11—22no—
165C2×C4×C11—24no—
166C2×C4×C11—41no—
167C2×C4×C11—42no—
168C2×C4×C11—41no—
169C2×C4×C11—42no—
170C2×C4×C11—44no—
171C2×C4×C11—44no—
172C2×C4×C11—42no—
173C2×C4×C11—42no—
174C2×C4×C11—42no—
175C2×C4×C11—42no—
176C2×C4×C11—41no—
177C2×C4×C11—41no—
178C2×C4×C11—42no—
179C2×C4×C11—42no—
180C2×C4×C11—81no—
181C2×C4×C11—84no—
182C2×C4×C11—84no—
183C2×C4×C11#12012yes—
184C2×C4×C11C22×D412yes—
185C8×C11—44no—
186#543—24no—
187#543—22no—
188#543C22×C1114yes—
189C2×C22⋊Q8—22no—
190C2×C22⋊Q8—21no—
191C2×C22⋊Q8—22no—
192C2×C22⋊Q8C22×C1112yes—
193C2×#117C22×C1111yescharacteristic
194C22×C22⋊C4—21no—
195C22×C22⋊C4C22×C1111yescharacteristic
196#485—24no—
197#484C22×C1114yescomplemented
198#483C22×C1114yescomplemented
199#428—22no—
200#419—22no—
201#407C22×C1112yes—
202#399C22×C1112yes—
203#397C22×C1112yes—
204#388—22no—
205#385—21no—
206#381C22×C1111yescharacteristic
207#379—21no—
208#328C22×C1118yescomplemented
209#323C22×C1114yes—
210C22×C11—21no—
211C22×C11—21no—
212C22×C11—21no—
213C22×C11—21no—
214C22×C11—21no—
215C22×C11—24no—
216C22×C11—21no—
217C22×C11—21no—
218C22×C11—44no—
219C22×C11—44no—
220C22×C11—48no—
221C22×C11—42no—
222C22×C11—42no—
223C22×C11—82no—
224C22×C11—84no—
225C22×C11#45812yes—
226C22×C11C2×#12011yescharacteristic
227C22×C11C2×#13712yes—
228C4×C11—22no—
229C4×C11—22no—
230C4×C11—42no—
231C4×C11—44no—
232C4×C11—44no—
233C4×C11—82no—
234C4×C11—81no—
235C4×C11—81no—
236C25D4×C1111yescharacteristic
237C22×Q8—21no—
238C22×Q8D4×C1112yes—
239C23×C4—21no—
240C23×C4—21no—
241C23×C4D4×C1111yescharacteristic
242C23×C4C23×C1111yescharacteristic
243C2×M16—22no—
244C22⋊Q8—28no—
245C22⋊Q8—28no—
246C22⋊Q8—24no—
247C22⋊Q8—28no—
248C22⋊Q8—24no—
249C22⋊Q8—22no—
250C22⋊Q8—22no—
251C22⋊Q8—28no—
252C22⋊Q8D4×C1114yes—
253C22⋊Q8C23×C1114yes—
254#117—22no—
255#117—22no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—22no—
258C2×C4⋊C4—22no—
259C2×C4⋊C4—22no—
260C2×C4⋊C4D4×C1112yes—
261C2×C4⋊C4C23×C1111yescharacteristic
262C2×C4⋊C4C23×C1111yescharacteristic
263C2×C22⋊C4—22no—
264C2×C22⋊C4—24no—
265C2×C22⋊C4—22no—
266C2×C22⋊C4—24no—
267C2×C22⋊C4—22no—
268C2×C22⋊C4—22no—
269C2×C22⋊C4—21no—
270C2×C22⋊C4—21no—
271C2×C22⋊C4—22no—
272C2×C22⋊C4—22no—
273C2×C22⋊C4D4×C1112yes—
274C2×C22⋊C4C23×C1112yes—
275C2×C42—21no—
276#107—24no—
277#106—24no—
278#103—24no—
279#103—24no—
280C22⋊C8—22no—
281C22⋊C8C23×C1114yes—
282#95—21no—
283#95—22no—
284#95C23×C1112yes—
285C2×C11—22no—
286C2×C11—22no—
287C2×C11—41no—
288C2×C11—44no—
289C2×C11#300411yescharacteristic
290C2×C11#301911yescharacteristic
291C2×C11C2×#45811yescharacteristic
292C24—21no—
293C24—21no—
294C24—24no—
295C24—42no—
296C24—81no—
297C24C2×D4×C1111yescharacteristic
298C24C2×D4×C1112yes—
299C2×Q8—24no—
300C2×Q8—22no—
301C2×Q8—44no—
302C2×Q8—82no—
303C2×Q8C2×D4×C1114yes—
304C22×C4—22no—
305C22×C4—21no—
306C22×C4—22no—
307C22×C4—24no—
308C22×C4—24no—
309C22×C4—21no—
310C22×C4—22no—
311C22×C4—21no—
312C22×C4—21no—
313C22×C4—42no—
314C22×C4—81no—
315C22×C4—82no—
316C22×C4—82no—
317C22×C4C2×D4×C1112yes—
318C22×C4C2×D4×C1112yes—
319C22×C4C2×D4×C1111yescharacteristic
320C22×C4C2×D4×C1112yes—
321C22×C4C24×C1111yescharacteristic
322M16—44no—
323C2×C8—24no—
324C4⋊C4—24no—
325C4⋊C4—28no—
326C4⋊C4—24no—
327C4⋊C4—22no—
328C4⋊C4—24no—
329C4⋊C4—22no—
330C4⋊C4—22no—
331C4⋊C4—82no—
332C4⋊C4C2×D4×C1114yes—
333C22⋊C4—28no—
334C22⋊C4—24no—
335C22⋊C4—24no—
336C22⋊C4—24no—
337C22⋊C4—24no—
338C22⋊C4—42no—
339C22⋊C4—41no—
340C22⋊C4—41no—
341C22⋊C4—44no—
342C22⋊C4—82no—
343C42—42no—
344C11#1813811yescharacteristic, direct product factor, Sylow
345C23—24no—
346C23—24no—
347C23—22no—
348C23—22no—
349C23—22no—
350C23—22no—
351C23—41no—
352C23—42no—
353C23—42no—
354C23—42no—
355C23—42no—
356C23—81no—
357C23—81no—
358C23—88no—
359C23C11×#12011yescharacteristic
360C23C11×#12011yescharacteristic
361C23C11×#13714yes—
362C23C22×D4×C1111yescharacteristic
363Q8—44no—
364Q8—82no—
365Q8—84no—
366C2×C4—24no—
367C2×C4—24no—
368C2×C4—22no—
369C2×C4—24no—
370C2×C4—42no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—42no—
374C2×C4—44no—
375C2×C4—44no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—81no—
385C2×C4—84no—
386C2×C4—84no—
387C2×C4C11×#12012yes—
388C2×C4C22×D4×C1112yes—
389C8—44no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—24no—
396C22—21no—
397C22—21no—
398C22—44no—
399C22—44no—
400C22—48no—
401C22—42no—
402C22—42no—
403C22—82no—
404C22—84no—
405C22C11×#45812yes—
406C22C2×C11×#12011yescharacteristic
407C22C2×C11×#13712yes—
408C4—22no—
409C4—22no—
410C4—42no—
411C4—44no—
412C4—44no—
413C4—82no—
414C4—81no—
415C4—81no—
416C2—22no—
417C2—22no—
418C2—41no—
419C2—44no—
420C2C11×#300411yescharacteristic
421C2C11×#301911yescharacteristic
422C2C2×C11×#45811yescharacteristic
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×#3095C2semidirect
4. C11×#1614C2semidirect
5. C11×#1608C2semidirect
6. C11×#1511C2semidirect
19. C11×#484C22semidirect
20. C11×#483C22semidirect
30. C11×#328C22semidirect
81. #18138C11direct (N × H)
135. #3095C2×C11semidirect
137. #1614C2×C11semidirect
138. #1608C2×C11semidirect
139. #1511C2×C11semidirect
197. #484C22×C11semidirect
198. #483C22×C11semidirect
208. #328C22×C11semidirect
344. C11#18138direct (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×#30952
C11×#24822
C11×#16142
C11×#16082
C11×#15112
C11×#14622
#1813811