Finite Group Databasebeta

← C11×#20962 #14598155

Subgroups — C11×#20962 #14598155

Order 2816.

1742 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#536C211yesmaximal, characteristic
2C11×#3428C211yesmaximal, characteristic
3C2×C11×#410C211yesmaximal, characteristic
4C11×#2310C212yesmaximal, complemented
5C11×#1890C218yesmaximal, complemented
6C11×#1740C212yesmaximal, complemented
7C22×C11×#41C2211yescharacteristic
8C23×Q8×C11C2211yescharacteristic
9C11×#536—24no—
10C11×#536C418yescomplemented
11C2×C11×C4⋊Q8—21no—
12C2×C11×#124—21no—
13C2×C11×#123C2214yes—
14C2×C11×C22⋊Q8—22no—
15C11×#520—24no—
16C11×#519—21no—
17C11×#518—21no—
18C11×#518C2214yes—
19C4×C11×#41—24no—
20C2×C11×#117—22no—
21C2×C11×#117C2212yes—
22C2×C11×#117C2211yescharacteristic
23C2×C11×#117C2212yes—
24C11×#410—24no—
25C2×C11×#99C2214yes—
26C11×#391—24no—
27C11×#391—24no—
28C11×#381C2218yes—
29C11×#342C2218yes—
30C2×C11×#41—22no—
31C2×C11×#41—22no—
32C2×C11×#41—24no—
33C2×C11×#41C2×C414yes—
34C2×C11×#41D414yes—
35C22×Q8×C11—21no—
36C22×Q8×C11—21no—
37C22×Q8×C11—22no—
38C22×Q8×C11—22no—
39C22×Q8×C11—22no—
40C22×Q8×C11—24no—
41C22×Q8×C11C2×C414yescomplemented
42C22×Q8×C11D411yescharacteristic
43C22×D4×C11D411yescharacteristic
44C22×D4×C11C2312yes—
45C23×C4×C11D412yes—
46C23×C4×C11C2312yes—
47C23×C4×C11C2311yescharacteristic
48C11×C4⋊Q8—28no—
49C11×#124—28no—
50C11×#123—28no—
51C11×#123C2×C4116yescomplemented
52C11×C22⋊Q8—216no—
53C4×Q8×C11—28no—
54C4×D4×C11—28no—
55C4×D4×C11—216no—
56C11×#117—24no—
57C11×#117—24no—
58C11×#117—22no—
59C11×#117—24no—
60C11×#117—22no—
61C11×#117—22no—
62C11×#117—22no—
63C11×#117—22no—
64C11×#117—24no—
65C11×#117—24no—
66C11×#117C2×C414yescomplemented
67C2×C11×C4⋊C4—24no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—24no—
70C2×C11×C4⋊C4—22no—
71C2×C11×C4⋊C4D414yes—
72C2×C11×C22⋊C4—24no—
73C2×C11×C22⋊C4—24no—
74C2×C11×C22⋊C4C2314yes—
75C2×C11×C22⋊C4C2314yes—
76C2×C11×C22⋊C4C2312yes—
77C2×C42×C11—24no—
78C2×C42×C11—21no—
79C2×C42×C11—22no—
80C2×C42×C11D414yes—
81C11×#99—28no—
82C11×#95—216no—
83#20962C1111yesmaximal, characteristic, direct product factor, Sylow
84C24×C11C2×D412yes—
85C24×C11C2411yescharacteristic
86C11×#41—28no—
87C11×#41—28no—
88C11×#41—28no—
89C11×#41—28no—
90C2×Q8×C11—24no—
91C2×Q8×C11—24no—
92C2×Q8×C11—28no—
93C2×Q8×C11—28no—
94C2×Q8×C11—22no—
95C2×Q8×C11—22no—
96C2×Q8×C11—41no—
97C2×Q8×C11—42no—
98C2×Q8×C11—41no—
99C2×Q8×C11—44no—
100C2×Q8×C11—44no—
101C2×Q8×C11—42no—
102C2×Q8×C11—42no—
103C2×Q8×C11C22⋊C414yes—
104C2×D4×C11—24no—
105C2×D4×C11—24no—
106C2×D4×C11—22no—
107C2×D4×C11—22no—
108C2×D4×C11C22⋊C414yes—
109C2×D4×C11C22×C414yes—
110C2×D4×C11C2×D414yes—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—24no—
114C22×C4×C11—24no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—24no—
119C22×C4×C11—28no—
120C22×C4×C11—24no—
121C22×C4×C11C22⋊C418yes—
122C22×C4×C11C22×C414yes—
123C22×C4×C11C22×C412yes—
124C22×C4×C11C2×D412yes—
125C22×C4×C11C2×D418yes—
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2×D412yes—
129C22×C4×C11C2×D412yes—
130C22×C4×C11C2×D412yes—
131C22×C4×C11#4114yes—
132C11×C4⋊C4—28no—
133C11×C4⋊C4—24no—
134C11×C4⋊C4—216no—
135C11×C4⋊C4—24no—
136C11×C4⋊C4—24no—
137C11×C4⋊C4—44no—
138C11×C22⋊C4—28no—
139C11×C22⋊C4—216no—
140C11×C22⋊C4—24no—
141C11×C22⋊C4—24no—
142C11×C22⋊C4—22no—
143C11×C22⋊C4—24no—
144C11×C22⋊C4—24no—
145C11×C22⋊C4C22×C414yes—
146C42×C11—28no—
147C42×C11—24no—
148C42×C11—24no—
149C42×C11—24no—
150C42×C11—44no—
151C2×#536C2×C1111yescharacteristic
152#3428C2×C1111yescharacteristic
153C2×#410C2×C1111yescharacteristic
154#2310C2×C1112yescomplemented
155#1890C2×C1118yescomplemented
156#1740C2×C1112yescomplemented
157C23×C11—22no—
158C23×C11—22no—
159C23×C11—42no—
160C23×C11—44no—
161C23×C11C2×C22⋊C414yes—
162C23×C11C23×C411yescharacteristic
163C23×C11C22×D411yescharacteristic
164C23×C11C22×D412yes—
165C23×C11C22×D411yescharacteristic
166C23×C11C2×#4112yes—
167Q8×C11—28no—
168Q8×C11—44no—
169Q8×C11—44no—
170Q8×C11—48no—
171D4×C11—28no—
172D4×C11—28no—
173D4×C11—28no—
174C2×C4×C11—22no—
175C2×C4×C11—22no—
176C2×C4×C11—28no—
177C2×C4×C11—28no—
178C2×C4×C11—24no—
179C2×C4×C11—24no—
180C2×C4×C11—28no—
181C2×C4×C11—28no—
182C2×C4×C11—44no—
183C2×C4×C11—42no—
184C2×C4×C11—44no—
185C2×C4×C11—42no—
186C2×C4×C11—48no—
187C2×C4×C11—48no—
188C2×C4×C11—44no—
189C2×C4×C11—88no—
190C2×C4×C11C2×C22⋊C414yes—
191C2×C4×C11C2×C22⋊C412yes—
192C2×C4×C11C2×C22⋊C412yes—
193C2×C4×C11C4×D414yes—
194C2×C4×C11C4×D414yes—
195C2×C4×C11#12011yescharacteristic
196C2×C4×C11#12012yes—
197C2×C4×C11#12011yescharacteristic
198C2×C4×C11#12114yes—
199C2×C4×C11#12114yes—
200C2×C4×C11#12312yes—
201C2×C4×C11#12312yes—
202C22×#41C22×C1111yescharacteristic
203C23×Q8C22×C1111yescharacteristic
204#536—24no—
205#536C4×C1118yescomplemented
206C2×C4⋊Q8—21no—
207C2×#124—21no—
208C2×#123C22×C1114yes—
209C2×C22⋊Q8—22no—
210#520—24no—
211#519—21no—
212#518—21no—
213#518C22×C1114yes—
214C4×#41—24no—
215C2×#117—22no—
216C2×#117C22×C1112yes—
217C2×#117C22×C1111yescharacteristic
218C2×#117C22×C1112yes—
219#410—24no—
220C2×#99C22×C1114yes—
221#391—24no—
222#391—24no—
223#381C22×C1118yes—
224#342C22×C1118yes—
225C22×C11—24no—
226C22×C11—22no—
227C22×C11—24no—
228C22×C11—41no—
229C22×C11—41no—
230C22×C11—42no—
231C22×C11—44no—
232C22×C11—44no—
233C22×C11—82no—
234C22×C11C22×C22⋊C411yescharacteristic
235C22×C11C2×C4×D412yes—
236C22×C11C2×#12011yescharacteristic
237C22×C11C2×#12112yes—
238C22×C11C2×#12311yescharacteristic
239C4×C11—24no—
240C4×C11—44no—
241C4×C11—48no—
242C4×C11—44no—
243C4×C11—84no—
244C4×C11#38612yes—
245C4×C11#38612yes—
246C4×C11#38614yes—
247C2×#41—22no—
248C2×#41—22no—
249C2×#41—24no—
250C2×#41C2×C4×C1114yes—
251C2×#41D4×C1114yes—
252C22×Q8—21no—
253C22×Q8—21no—
254C22×Q8—22no—
255C22×Q8—22no—
256C22×Q8—22no—
257C22×Q8—24no—
258C22×Q8C2×C4×C1114yescomplemented
259C22×Q8D4×C1111yescharacteristic
260C22×D4D4×C1111yescharacteristic
261C22×D4C23×C1112yes—
262C23×C4D4×C1112yes—
263C23×C4C23×C1112yes—
264C23×C4C23×C1111yescharacteristic
265C4⋊Q8—28no—
266#124—28no—
267#123—28no—
268#123C2×C4×C11116yescomplemented
269C22⋊Q8—216no—
270C4×Q8—28no—
271C4×D4—28no—
272C4×D4—216no—
273#117—24no—
274#117—24no—
275#117—22no—
276#117—24no—
277#117—22no—
278#117—22no—
279#117—22no—
280#117—22no—
281#117—24no—
282#117—24no—
283#117C2×C4×C1114yescomplemented
284C2×C4⋊C4—24no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—24no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4D4×C1114yes—
289C2×C22⋊C4—24no—
290C2×C22⋊C4—24no—
291C2×C22⋊C4C23×C1114yes—
292C2×C22⋊C4C23×C1114yes—
293C2×C22⋊C4C23×C1112yes—
294C2×C42—24no—
295C2×C42—21no—
296C2×C42—22no—
297C2×C42D4×C1114yes—
298#99—28no—
299#95—216no—
300C2×C11—21no—
301C2×C11—22no—
302C2×C11—21no—
303C2×C11—22no—
304C2×C11—44no—
305C2×C11C2×#38611yescharacteristic
306C2×C11#302812yes—
307C24C2×D4×C1112yes—
308C24C24×C1111yescharacteristic
309#41—28no—
310#41—28no—
311#41—28no—
312#41—28no—
313C2×Q8—24no—
314C2×Q8—24no—
315C2×Q8—28no—
316C2×Q8—28no—
317C2×Q8—22no—
318C2×Q8—22no—
319C2×Q8—41no—
320C2×Q8—42no—
321C2×Q8—41no—
322C2×Q8—44no—
323C2×Q8—44no—
324C2×Q8—42no—
325C2×Q8—42no—
326C2×Q8C11×C22⋊C414yes—
327C2×D4—24no—
328C2×D4—24no—
329C2×D4—22no—
330C2×D4—22no—
331C2×D4C11×C22⋊C414yes—
332C2×D4C22×C4×C1114yes—
333C2×D4C2×D4×C1114yes—
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—24no—
337C22×C4—24no—
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—24no—
342C22×C4—28no—
343C22×C4—24no—
344C22×C4C11×C22⋊C418yes—
345C22×C4C22×C4×C1114yes—
346C22×C4C22×C4×C1112yes—
347C22×C4C2×D4×C1112yes—
348C22×C4C2×D4×C1118yes—
349C22×C4C2×D4×C1111yescharacteristic
350C22×C4C2×D4×C1111yescharacteristic
351C22×C4C2×D4×C1112yes—
352C22×C4C2×D4×C1112yes—
353C22×C4C2×D4×C1112yes—
354C22×C4C11×#4114yes—
355C4⋊C4—28no—
356C4⋊C4—24no—
357C4⋊C4—216no—
358C4⋊C4—24no—
359C4⋊C4—24no—
360C4⋊C4—44no—
361C22⋊C4—28no—
362C22⋊C4—216no—
363C22⋊C4—24no—
364C22⋊C4—24no—
365C22⋊C4—22no—
366C22⋊C4—24no—
367C22⋊C4—24no—
368C22⋊C4C22×C4×C1114yes—
369C42—28no—
370C42—24no—
371C42—24no—
372C42—24no—
373C42—44no—
374C11#2096211yescharacteristic, direct product factor, Sylow
375C23—22no—
376C23—22no—
377C23—42no—
378C23—44no—
379C23C2×C11×C22⋊C414yes—
380C23C23×C4×C1111yescharacteristic
381C23C22×D4×C1111yescharacteristic
382C23C22×D4×C1112yes—
383C23C22×D4×C1111yescharacteristic
384C23C2×C11×#4112yes—
385Q8—28no—
386Q8—44no—
387Q8—44no—
388Q8—48no—
389D4—28no—
390D4—28no—
391D4—28no—
392C2×C4—22no—
393C2×C4—22no—
394C2×C4—28no—
395C2×C4—28no—
396C2×C4—24no—
397C2×C4—24no—
398C2×C4—28no—
399C2×C4—28no—
400C2×C4—44no—
401C2×C4—42no—
402C2×C4—44no—
403C2×C4—42no—
404C2×C4—48no—
405C2×C4—48no—
406C2×C4—44no—
407C2×C4—88no—
408C2×C4C2×C11×C22⋊C414yes—
409C2×C4C2×C11×C22⋊C412yes—
410C2×C4C2×C11×C22⋊C412yes—
411C2×C4C4×D4×C1114yes—
412C2×C4C4×D4×C1114yes—
413C2×C4C11×#12011yescharacteristic
414C2×C4C11×#12012yes—
415C2×C4C11×#12011yescharacteristic
416C2×C4C11×#12114yes—
417C2×C4C11×#12114yes—
418C2×C4C11×#12312yes—
419C2×C4C11×#12312yes—
420C22—24no—
421C22—22no—
422C22—24no—
423C22—41no—
424C22—41no—
425C22—42no—
426C22—44no—
427C22—44no—
428C22—82no—
429C22C22×C11×C22⋊C411yescharacteristic
430C22C2×C4×D4×C1112yes—
431C22C2×C11×#12011yescharacteristic
432C22C2×C11×#12112yes—
433C22C2×C11×#12311yescharacteristic
434C4—24no—
435C4—44no—
436C4—48no—
437C4—44no—
438C4—84no—
439C4C11×#38612yes—
440C4C11×#38612yes—
441C4C11×#38614yes—
442C2—21no—
443C2—22no—
444C2—21no—
445C2—22no—
446C2—44no—
447C2C2×C11×#38611yescharacteristic
448C2C11×#302812yes—
subgroupG/H
center, socleC22×C11C2×#120
commutatorC23C23×C4×C11
Frattini, cosocleC24C24×C11
prime radicalC22×C11×#41C22
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
4. C11×#2310C2semidirect
5. C11×#1890C2semidirect
6. C11×#1740C2semidirect
10. C11×#536C4semidirect
41. C22×Q8×C11C2×C4semidirect
51. C11×#123C2×C4semidirect
66. C11×#117C2×C4semidirect
83. #20962C11direct (N × H)
154. #2310C2×C11semidirect
155. #1890C2×C11semidirect
156. #1740C2×C11semidirect
205. #536C4×C11semidirect
258. C22×Q8C2×C4×C11semidirect
268. #123C2×C4×C11semidirect
283. #117C2×C4×C11semidirect
374. C11#20962direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5362
C11×#34282
C2×C11×#4102
C11×#23102
C11×#18902
C11×#17402
#2096211