Finite Group Databasebeta

← C11×#20961 #14598154

Subgroups — C11×#20961 #14598154

Order 2816.

1998 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#535C211yesmaximal, characteristic
2C11×#3428C211yesmaximal, characteristic, complemented
3C2×C11×#410C211yesmaximal, characteristic, complemented
4C11×#2309C212yesmaximal, complemented
5C11×#1889C218yesmaximal, complemented
6C11×#1740C212yesmaximal, complemented
7C22×C11×#41C2211yescharacteristic
8C23×D4×C11C2211yescharacteristic
9C11×#535—24no—
10C11×#535C418yescomplemented
11C2×C11×#127—21no—
12C2×C11×#124—21no—
13C2×C11×#121—22no—
14C2×C11×#120C2214yes—
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×#390—24no—
27C11×#390—24no—
28C11×#379C2218yes—
29C11×#342C2218yes—
30C25×C11C2312yes—
31C2×C11×#41—22no—
32C2×C11×#41—22no—
33C2×C11×#41—24no—
34C2×C11×#41C2×C414yes—
35C2×C11×#41D414yes—
36C22×Q8×C11D411yescharacteristic
37C22×D4×C11—24no—
38C22×D4×C11—21no—
39C22×D4×C11—21no—
40C22×D4×C11—22no—
41C22×D4×C11—22no—
42C22×D4×C11—22no—
43C22×D4×C11—24no—
44C22×D4×C11C2×C414yescomplemented
45C22×D4×C11D411yescharacteristic
46C22×D4×C11C2312yes—
47C23×C4×C11D412yes—
48C23×C4×C11C2311yescharacteristic
49C11×#127—28no—
50C11×#124—28no—
51C11×#121—216no—
52C11×#120—28no—
53C11×#120C2×C4116yescomplemented
54C4×Q8×C11—28no—
55C4×D4×C11—28no—
56C4×D4×C11—216no—
57C11×#117—24no—
58C11×#117—24no—
59C11×#117—22no—
60C11×#117—24no—
61C11×#117—22no—
62C11×#117—22no—
63C11×#117—22no—
64C11×#117—22no—
65C11×#117—24no—
66C11×#117—24no—
67C11×#117C2×C414yescomplemented
68C2×C11×C4⋊C4—24no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—22no—
71C2×C11×C4⋊C4D414yescomplemented
72C2×C11×C22⋊C4—24no—
73C2×C11×C22⋊C4—24no—
74C2×C11×C22⋊C4—216no—
75C2×C11×C22⋊C4C2314yes—
76C2×C11×C22⋊C4C2314yes—
77C2×C11×C22⋊C4C2312yes—
78C2×C42×C11—24no—
79C2×C42×C11—21no—
80C2×C42×C11—22no—
81C2×C42×C11D414yescomplemented
82C11×#99—28no—
83#20961C1111yesmaximal, characteristic, direct product factor, Sylow
84C24×C11—24no—
85C24×C11—22no—
86C24×C11—22no—
87C24×C11—24no—
88C24×C11—84no—
89C24×C11C22×C414yes—
90C24×C11C2×D412yes—
91C24×C11C2411yescharacteristic
92C11×#41—28no—
93C11×#41—28no—
94C11×#41—28no—
95C11×#41—28no—
96C2×Q8×C11—22no—
97C2×Q8×C11—22no—
98C2×Q8×C11C22⋊C414yescomplemented
99C2×D4×C11—24no—
100C2×D4×C11—24no—
101C2×D4×C11—216no—
102C2×D4×C11—24no—
103C2×D4×C11—24no—
104C2×D4×C11—28no—
105C2×D4×C11—28no—
106C2×D4×C11—22no—
107C2×D4×C11—22no—
108C2×D4×C11—41no—
109C2×D4×C11—42no—
110C2×D4×C11—41no—
111C2×D4×C11—44no—
112C2×D4×C11—44no—
113C2×D4×C11—42no—
114C2×D4×C11—42no—
115C2×D4×C11—88no—
116C2×D4×C11C22⋊C414yescomplemented
117C2×D4×C11C22×C414yes—
118C2×D4×C11C2×D414yes—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—24no—
122C22×C4×C11—22no—
123C22×C4×C11—28no—
124C22×C4×C11—24no—
125C22×C4×C11C22⋊C418yescomplemented
126C22×C4×C11C22×C412yes—
127C22×C4×C11C2×D412yes—
128C22×C4×C11C2×D418yes—
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×D412yes—
132C22×C4×C11C2×D412yes—
133C22×C4×C11C2×D412yes—
134C22×C4×C11#4114yes—
135C11×C4⋊C4—28no—
136C11×C4⋊C4—24no—
137C11×C4⋊C4—24no—
138C11×C4⋊C4—24no—
139C11×C4⋊C4—44no—
140C11×C22⋊C4—28no—
141C11×C22⋊C4—24no—
142C11×C22⋊C4—24no—
143C11×C22⋊C4—22no—
144C11×C22⋊C4—216no—
145C11×C22⋊C4—24no—
146C11×C22⋊C4—24no—
147C11×C22⋊C4—816no—
148C11×C22⋊C4C22×C414yes—
149C42×C11—28no—
150C42×C11—24no—
151C42×C11—24no—
152C42×C11—24no—
153C42×C11—44no—
154C2×#535C2×C1111yescharacteristic
155#3428C2×C1111yescharacteristic, complemented
156C2×#410C2×C1111yescharacteristic, complemented
157#2309C2×C1112yescomplemented
158#1889C2×C1118yescomplemented
159#1740C2×C1112yescomplemented
160C23×C11—22no—
161C23×C11—22no—
162C23×C11—24no—
163C23×C11—28no—
164C23×C11—42no—
165C23×C11—44no—
166C23×C11—416no—
167C23×C11—48no—
168C23×C11—42no—
169C23×C11—44no—
170C23×C11—42no—
171C23×C11—84no—
172C23×C11—84no—
173C23×C11—88no—
174C23×C11C2×C22⋊C414yes—
175C23×C11C23×C411yescharacteristic
176C23×C11C22×D411yescharacteristic
177C23×C11C22×D412yes—
178C23×C11C22×D411yescharacteristic
179C23×C11C2×#4112yes—
180Q8×C11—28no—
181D4×C11—28no—
182D4×C11—28no—
183D4×C11—28no—
184D4×C11—44no—
185D4×C11—44no—
186D4×C11—48no—
187D4×C11—816no—
188C2×C4×C11—22no—
189C2×C4×C11—22no—
190C2×C4×C11—28no—
191C2×C4×C11—28no—
192C2×C4×C11—24no—
193C2×C4×C11—28no—
194C2×C4×C11—44no—
195C2×C4×C11—48no—
196C2×C4×C11—48no—
197C2×C4×C11—44no—
198C2×C4×C11—88no—
199C2×C4×C11C2×C22⋊C414yes—
200C2×C4×C11C2×C22⋊C412yes—
201C2×C4×C11C2×C22⋊C412yes—
202C2×C4×C11C4×D414yes—
203C2×C4×C11C4×D414yes—
204C2×C4×C11#12011yescharacteristic
205C2×C4×C11#12012yes—
206C2×C4×C11#12011yescharacteristic
207C2×C4×C11#12114yes—
208C2×C4×C11#12114yes—
209C2×C4×C11#12312yes—
210C2×C4×C11#12312yes—
211C22×#41C22×C1111yescharacteristic
212C23×D4C22×C1111yescharacteristic
213#535—24no—
214#535C4×C1118yescomplemented
215C2×#127—21no—
216C2×#124—21no—
217C2×#121—22no—
218C2×#120C22×C1114yes—
219#520—24no—
220#519—21no—
221#518—21no—
222#518C22×C1114yes—
223C4×#41—24no—
224C2×#117—22no—
225C2×#117C22×C1112yes—
226C2×#117C22×C1111yescharacteristic
227C2×#117C22×C1112yes—
228#410—24no—
229C2×#99C22×C1114yes—
230#390—24no—
231#390—24no—
232#379C22×C1118yes—
233#342C22×C1118yes—
234C22×C11—24no—
235C22×C11—22no—
236C22×C11—24no—
237C22×C11—41no—
238C22×C11—41no—
239C22×C11—42no—
240C22×C11—44no—
241C22×C11—48no—
242C22×C11—416no—
243C22×C11—44no—
244C22×C11—44no—
245C22×C11—82no—
246C22×C11—88no—
247C22×C11—84no—
248C22×C11—84no—
249C22×C11C22×C22⋊C411yescharacteristic
250C22×C11C2×C4×D412yes—
251C22×C11C2×#12011yescharacteristic
252C22×C11C2×#12112yes—
253C22×C11C2×#12311yescharacteristic
254C4×C11—24no—
255C4×C11—44no—
256C4×C11—48no—
257C4×C11—84no—
258C4×C11#38612yes—
259C4×C11#38612yes—
260C4×C11#38614yes—
261C25C23×C1112yes—
262C2×#41—22no—
263C2×#41—22no—
264C2×#41—24no—
265C2×#41C2×C4×C1114yes—
266C2×#41D4×C1114yes—
267C22×Q8D4×C1111yescharacteristic
268C22×D4—24no—
269C22×D4—21no—
270C22×D4—21no—
271C22×D4—22no—
272C22×D4—22no—
273C22×D4—22no—
274C22×D4—24no—
275C22×D4C2×C4×C1114yescomplemented
276C22×D4D4×C1111yescharacteristic
277C22×D4C23×C1112yes—
278C23×C4D4×C1112yes—
279C23×C4C23×C1111yescharacteristic
280#127—28no—
281#124—28no—
282#121—216no—
283#120—28no—
284#120C2×C4×C11116yescomplemented
285C4×Q8—28no—
286C4×D4—28no—
287C4×D4—216no—
288#117—24no—
289#117—24no—
290#117—22no—
291#117—24no—
292#117—22no—
293#117—22no—
294#117—22no—
295#117—22no—
296#117—24no—
297#117—24no—
298#117C2×C4×C1114yescomplemented
299C2×C4⋊C4—24no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4D4×C1114yescomplemented
303C2×C22⋊C4—24no—
304C2×C22⋊C4—24no—
305C2×C22⋊C4—216no—
306C2×C22⋊C4C23×C1114yes—
307C2×C22⋊C4C23×C1114yes—
308C2×C22⋊C4C23×C1112yes—
309C2×C42—24no—
310C2×C42—21no—
311C2×C42—22no—
312C2×C42D4×C1114yescomplemented
313#99—28no—
314C2×C11—21no—
315C2×C11—22no—
316C2×C11—22no—
317C2×C11—21no—
318C2×C11—44no—
319C2×C11—84no—
320C2×C11C2×#38611yescharacteristic
321C2×C11#302712yes—
322C24—24no—
323C24—22no—
324C24—22no—
325C24—24no—
326C24—84no—
327C24C22×C4×C1114yes—
328C24C2×D4×C1112yes—
329C24C24×C1111yescharacteristic
330#41—28no—
331#41—28no—
332#41—28no—
333#41—28no—
334C2×Q8—22no—
335C2×Q8—22no—
336C2×Q8C11×C22⋊C414yescomplemented
337C2×D4—24no—
338C2×D4—24no—
339C2×D4—216no—
340C2×D4—24no—
341C2×D4—24no—
342C2×D4—28no—
343C2×D4—28no—
344C2×D4—22no—
345C2×D4—22no—
346C2×D4—41no—
347C2×D4—42no—
348C2×D4—41no—
349C2×D4—44no—
350C2×D4—44no—
351C2×D4—42no—
352C2×D4—42no—
353C2×D4—88no—
354C2×D4C11×C22⋊C414yescomplemented
355C2×D4C22×C4×C1114yes—
356C2×D4C2×D4×C1114yes—
357C22×C4—22no—
358C22×C4—22no—
359C22×C4—24no—
360C22×C4—22no—
361C22×C4—28no—
362C22×C4—24no—
363C22×C4C11×C22⋊C418yescomplemented
364C22×C4C22×C4×C1112yes—
365C22×C4C2×D4×C1112yes—
366C22×C4C2×D4×C1118yes—
367C22×C4C2×D4×C1111yescharacteristic
368C22×C4C2×D4×C1111yescharacteristic
369C22×C4C2×D4×C1112yes—
370C22×C4C2×D4×C1112yes—
371C22×C4C2×D4×C1112yes—
372C22×C4C11×#4114yes—
373C4⋊C4—28no—
374C4⋊C4—24no—
375C4⋊C4—24no—
376C4⋊C4—24no—
377C4⋊C4—44no—
378C22⋊C4—28no—
379C22⋊C4—24no—
380C22⋊C4—24no—
381C22⋊C4—22no—
382C22⋊C4—216no—
383C22⋊C4—24no—
384C22⋊C4—24no—
385C22⋊C4—816no—
386C22⋊C4C22×C4×C1114yes—
387C42—28no—
388C42—24no—
389C42—24no—
390C42—24no—
391C42—44no—
392C11#2096111yescharacteristic, direct product factor, Sylow
393C23—22no—
394C23—22no—
395C23—24no—
396C23—28no—
397C23—42no—
398C23—44no—
399C23—416no—
400C23—48no—
401C23—42no—
402C23—44no—
403C23—42no—
404C23—84no—
405C23—84no—
406C23—88no—
407C23C2×C11×C22⋊C414yes—
408C23C23×C4×C1111yescharacteristic
409C23C22×D4×C1111yescharacteristic
410C23C22×D4×C1112yes—
411C23C22×D4×C1111yescharacteristic
412C23C2×C11×#4112yes—
413Q8—28no—
414D4—28no—
415D4—28no—
416D4—28no—
417D4—44no—
418D4—44no—
419D4—48no—
420D4—816no—
421C2×C4—22no—
422C2×C4—22no—
423C2×C4—28no—
424C2×C4—28no—
425C2×C4—24no—
426C2×C4—28no—
427C2×C4—44no—
428C2×C4—48no—
429C2×C4—48no—
430C2×C4—44no—
431C2×C4—88no—
432C2×C4C2×C11×C22⋊C414yes—
433C2×C4C2×C11×C22⋊C412yes—
434C2×C4C2×C11×C22⋊C412yes—
435C2×C4C4×D4×C1114yes—
436C2×C4C4×D4×C1114yes—
437C2×C4C11×#12011yescharacteristic
438C2×C4C11×#12012yes—
439C2×C4C11×#12011yescharacteristic
440C2×C4C11×#12114yes—
441C2×C4C11×#12114yes—
442C2×C4C11×#12312yes—
443C2×C4C11×#12312yes—
444C22—24no—
445C22—22no—
446C22—24no—
447C22—41no—
448C22—41no—
449C22—42no—
450C22—44no—
451C22—48no—
452C22—416no—
453C22—44no—
454C22—44no—
455C22—82no—
456C22—88no—
457C22—84no—
458C22—84no—
459C22C22×C11×C22⋊C411yescharacteristic
460C22C2×C4×D4×C1112yes—
461C22C2×C11×#12011yescharacteristic
462C22C2×C11×#12112yes—
463C22C2×C11×#12311yescharacteristic
464C4—24no—
465C4—44no—
466C4—48no—
467C4—84no—
468C4C11×#38612yes—
469C4C11×#38612yes—
470C4C11×#38614yes—
471C2—21no—
472C2—22no—
473C2—22no—
474C2—21no—
475C2—44no—
476C2—84no—
477C2C2×C11×#38611yescharacteristic
478C2C11×#302712yes—
subgroupG/H
center, socleC22×C11C2×#120
commutatorC23C23×C4×C11
Frattini, cosocleC24C24×C11
prime radicalC2×C11×#535C2
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
2. C11×#3428C2semidirect
3. C2×C11×#410C2semidirect
4. C11×#2309C2semidirect
5. C11×#1889C2semidirect
6. C11×#1740C2semidirect
10. C11×#535C4semidirect
44. C22×D4×C11C2×C4semidirect
53. C11×#120C2×C4semidirect
67. C11×#117C2×C4semidirect
71. C2×C11×C4⋊C4D4semidirect
81. C2×C42×C11D4semidirect
83. #20961C11direct (N × H)
98. C2×Q8×C11C22⋊C4semidirect
116. C2×D4×C11C22⋊C4semidirect
125. C22×C4×C11C22⋊C4semidirect
155. #3428C2×C11semidirect
156. C2×#410C2×C11semidirect
157. #2309C2×C11semidirect
158. #1889C2×C11semidirect
159. #1740C2×C11semidirect
214. #535C4×C11semidirect
275. C22×D4C2×C4×C11semidirect
284. #120C2×C4×C11semidirect
298. #117C2×C4×C11semidirect
302. C2×C4⋊C4D4×C11semidirect
312. C2×C42D4×C11semidirect
336. C2×Q8C11×C22⋊C4semidirect
354. C2×D4C11×C22⋊C4semidirect
363. C22×C4C11×C22⋊C4semidirect
392. C11#20961direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5352
C11×#34282
C2×C11×#4102
C11×#23092
C11×#18892
C11×#17402
#2096111