Finite Group Databasebeta

← C11×#24645 #14601838

Subgroups — C11×#24645 #14601838

Order 2816.

848 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#462C211yesmaximal, characteristic, complemented
2C2×C11×#440C211yesmaximal, characteristic
3C11×#2547C211yesmaximal, characteristic
4C11×#2356C211yesmaximal, characteristic, complemented
5C11×#2056C212yesmaximal, complemented
6C11×#2015C212yesmaximal
7C11×#1983C212yesmaximal
8C11×#1960C211yesmaximal, characteristic, complemented
9C11×#1940C211yesmaximal, characteristic, complemented
10C11×#1928C212yesmaximal, complemented
11C11×#1804C211yesmaximal, characteristic
12C22×C11×Q16C2212yes—
13C22×C11×SD16C2211yescharacteristic
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C11×#124C2212yes—
16C2×C4×Q8×C11C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C11×#462—24no—
19C11×#440—24no—
20C2×C11×#107C2211yescharacteristic
21C2×C11×C4⋊C8C2211yescharacteristic
22C2×C11×C4⋊C8C2212yes—
23C2×C11×#103C2211yescharacteristic
24C2×C11×#103C2212yes—
25C2×C11×#103C2212yes—
26C2×C11×#103C2212yes—
27C2×C11×#102C2211yescharacteristic
28C2×C11×#102C2212yes—
29C2×C11×#97C2211yescharacteristic
30C11×#397—21no—
31C11×#397—21no—
32C11×#391C2212yes—
33C11×#391C2212yes—
34C11×#387—22no—
35C11×#383—21no—
36C11×#382C2211yescharacteristic
37C11×#380—22no—
38C4×C11×C4⋊C4C2212yes—
39C4×C11×C4⋊C4C2211yescharacteristic
40C11×#376—21no—
41C11×#340C2212yes—
42C11×#336C2212yes—
43C22×Q8×C11C2312yes—
44C22×Q8×C11C2311yescharacteristic
45C22×D4×C11C2311yescharacteristic
46C23×C4×C11—21no—
47C2×C11×Q16—24no—
48C2×C11×Q16—42no—
49C2×C11×Q16—42no—
50C2×C11×SD16—22no—
51C2×C11×SD16—22no—
52C2×C11×SD16—22no—
53C22×C8×C11C2312yes—
54C22×C8×C11C2311yescharacteristic
55C22×C8×C11C2311yescharacteristic
56C11×C4⋊Q8—22no—
57C11×C4⋊Q8—22no—
58C11×#124—24no—
59C11×#124—42no—
60C4×Q8×C11—22no—
61C4×Q8×C11D414yes—
62C4×D4×C11—22no—
63C4×D4×C11—22no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4D412yes—
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2312yes—
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C22⋊C4—21no—
72C2×C11×C22⋊C4—22no—
73C2×C11×C22⋊C4—22no—
74C2×C42×C11—21no—
75C2×C42×C11—22no—
76C2×C42×C11C2312yes—
77C2×C42×C11C2311yescharacteristic
78C11×#107—22no—
79C11×C4⋊C8—22no—
80C11×C4⋊C8—42no—
81C11×#103—22no—
82C11×#103—24no—
83C11×#103—24no—
84C11×#103—42no—
85C11×#102—22no—
86C11×#102—42no—
87C11×#97—22no—
88C11×#95—21no—
89C11×#95—22no—
90C11×#95—22no—
91C11×#95—22no—
92C11×#95—22no—
93C11×#95—21no—
94C11×#95—22no—
95C11×#95D411yescharacteristic
96C11×#95D411yescharacteristic
97#24645C1111yesmaximal, characteristic, direct product factor, Sylow
98C24×C11—21no—
99C2×Q8×C11—21no—
100C2×Q8×C11—22no—
101C2×Q8×C11—21no—
102C2×Q8×C11—21no—
103C2×Q8×C11—22no—
104C2×Q8×C11—22no—
105C2×Q8×C11—22no—
106C2×Q8×C11—21no—
107C2×Q8×C11—21no—
108C2×Q8×C11—22no—
109C2×Q8×C11—22no—
110C2×Q8×C11C2×D412yes—
111C2×D4×C11—21no—
112C2×D4×C11—21no—
113C2×D4×C11—21no—
114C2×D4×C11—21no—
115C2×D4×C11—21no—
116C2×D4×C11#4112yes—
117C22×C4×C11—21no—
118C22×C4×C11—21no—
119C22×C4×C11—22no—
120C22×C4×C11—21no—
121C22×C4×C11—22no—
122C22×C4×C11—44no—
123C22×C4×C11—42no—
124C22×C4×C11C2×D412yes—
125C22×C4×C11C2×D412yes—
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2411yescharacteristic
129C11×Q16—48no—
130C11×SD16—28no—
131C2×C8×C11—21no—
132C2×C8×C11—21no—
133C2×C8×C11—22no—
134C2×C8×C11—21no—
135C2×C8×C11—22no—
136C2×C8×C11—21no—
137C2×C8×C11—21no—
138C2×C8×C11—22no—
139C2×C8×C11#4112yes—
140C11×C4⋊C4—24no—
141C11×C4⋊C4—21no—
142C11×C4⋊C4—21no—
143C11×C4⋊C4—22no—
144C11×C4⋊C4—21no—
145C11×C4⋊C4—22no—
146C11×C4⋊C4—42no—
147C11×C4⋊C4—42no—
148C11×C4⋊C4—42no—
149C11×C4⋊C4C2×D412yes—
150C11×C22⋊C4—44no—
151C11×C22⋊C4—44no—
152C11×C22⋊C4—42no—
153C42×C11—24no—
154C42×C11—22no—
155C42×C11—22no—
156C42×C11—44no—
157C42×C11C2×D412yes—
158C42×C11#4112yes—
159C2×#462C2×C1111yescharacteristic, complemented
160C2×#440C2×C1111yescharacteristic
161#2547C2×C1111yescharacteristic
162#2356C2×C1111yescharacteristic, complemented
163#2056C2×C1112yescomplemented
164#2015C2×C1112yes—
165#1983C2×C1112yes—
166#1960C2×C1111yescharacteristic, complemented
167#1940C2×C1111yescharacteristic, complemented
168#1928C2×C1112yescomplemented
169#1804C2×C1111yescharacteristic
170C23×C11—22no—
171C23×C11—41no—
172C23×C11—41no—
173C23×C11—42no—
174C23×C11—42no—
175C23×C11C22×D411yescharacteristic
176Q8×C11—22no—
177Q8×C11—22no—
178Q8×C11—41no—
179Q8×C11—41no—
180Q8×C11—42no—
181Q8×C11—42no—
182Q8×C11—42no—
183Q8×C11—42no—
184D4×C11—22no—
185D4×C11—22no—
186D4×C11—41no—
187D4×C11—41no—
188C2×C4×C11—22no—
189C2×C4×C11—22no—
190C2×C4×C11—22no—
191C2×C4×C11—22no—
192C2×C4×C11—22no—
193C2×C4×C11—22no—
194C2×C4×C11—22no—
195C2×C4×C11—22no—
196C2×C4×C11—22no—
197C2×C4×C11—22no—
198C2×C4×C11—41no—
199C2×C4×C11—41no—
200C2×C4×C11—42no—
201C2×C4×C11—41no—
202C2×C4×C11—42no—
203C2×C4×C11—42no—
204C2×C4×C11—42no—
205C2×C4×C11—42no—
206C2×C4×C11—42no—
207C2×C4×C11—42no—
208C2×C4×C11—42no—
209C2×C4×C11—84no—
210C2×C4×C11#12112yes—
211C2×C4×C11#12112yes—
212C2×C4×C11C22×D411yescharacteristic
213C2×C4×C11C2×#4111yescharacteristic
214C2×C4×C11C2×#4111yescharacteristic
215C2×C4×C11C2×#4111yescharacteristic
216C2×C4×C11H(5,𝔽2)11yescharacteristic
217C2×C4×C11H(5,𝔽2)11yescharacteristic
218C8×C11—22no—
219C8×C11—41no—
220C8×C11—42no—
221C22×Q16C22×C1112yes—
222C22×SD16C22×C1111yescharacteristic
223C2×C4⋊Q8C22×C1111yescharacteristic
224C2×#124C22×C1112yes—
225C2×C4×Q8C22×C1111yescharacteristic
226C2×C4×D4C22×C1111yescharacteristic
227#462—24no—
228#440—24no—
229C2×#107C22×C1111yescharacteristic
230C2×C4⋊C8C22×C1111yescharacteristic
231C2×C4⋊C8C22×C1112yes—
232C2×#103C22×C1111yescharacteristic
233C2×#103C22×C1112yes—
234C2×#103C22×C1112yes—
235C2×#103C22×C1112yes—
236C2×#102C22×C1111yescharacteristic
237C2×#102C22×C1112yes—
238C2×#97C22×C1111yescharacteristic
239#397—21no—
240#397—21no—
241#391C22×C1112yes—
242#391C22×C1112yes—
243#387—22no—
244#383—21no—
245#382C22×C1111yescharacteristic
246#380—22no—
247C4×C4⋊C4C22×C1112yes—
248C4×C4⋊C4C22×C1111yescharacteristic
249#376—21no—
250#340C22×C1112yes—
251#336C22×C1112yes—
252C22×C11—42no—
253C22×C11—44no—
254C22×C11—82no—
255C22×C11—81no—
256C22×C11—81no—
257C22×C11C2×#12111yescharacteristic
258C22×C11#54611yescharacteristic
259C22×C11#55011yescharacteristic
260C22×C11#57512yes—
261C22×C11#57812yes—
262C4×C11—22no—
263C4×C11—22no—
264C4×C11—42no—
265C4×C11—42no—
266C4×C11—42no—
267C4×C11—42no—
268C4×C11—82no—
269C4×C11—82no—
270C4×C11—81no—
271C4×C11#52511yescharacteristic
272C4×C11#53511yescharacteristic
273C4×C11#55311yescharacteristic
274C4×C11#55511yescharacteristic
275C22×Q8C23×C1112yes—
276C22×Q8C23×C1111yescharacteristic
277C22×D4C23×C1111yescharacteristic
278C23×C4—21no—
279C2×Q16—24no—
280C2×Q16—42no—
281C2×Q16—42no—
282C2×SD16—22no—
283C2×SD16—22no—
284C2×SD16—22no—
285C22×C8C23×C1112yes—
286C22×C8C23×C1111yescharacteristic
287C22×C8C23×C1111yescharacteristic
288C4⋊Q8—22no—
289C4⋊Q8—22no—
290#124—24no—
291#124—42no—
292C4×Q8—22no—
293C4×Q8D4×C1114yes—
294C4×D4—22no—
295C4×D4—22no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4D4×C1112yes—
300C2×C4⋊C4C23×C1111yescharacteristic
301C2×C4⋊C4C23×C1112yes—
302C2×C4⋊C4C23×C1111yescharacteristic
303C2×C22⋊C4—21no—
304C2×C22⋊C4—22no—
305C2×C22⋊C4—22no—
306C2×C42—21no—
307C2×C42—22no—
308C2×C42C23×C1112yes—
309C2×C42C23×C1111yescharacteristic
310#107—22no—
311C4⋊C8—22no—
312C4⋊C8—42no—
313#103—22no—
314#103—24no—
315#103—24no—
316#103—42no—
317#102—22no—
318#102—42no—
319#97—22no—
320#95—21no—
321#95—22no—
322#95—22no—
323#95—22no—
324#95—22no—
325#95—21no—
326#95—22no—
327#95D4×C1111yescharacteristic
328#95D4×C1111yescharacteristic
329C2×C11—82no—
330C2×C11#241411yescharacteristic
331C2×C11#304011yescharacteristic
332C2×C11#304411yescharacteristic
333C2×C11#331512yes—
334C2×C11#340212yes—
335C24—21no—
336C2×Q8—21no—
337C2×Q8—22no—
338C2×Q8—21no—
339C2×Q8—21no—
340C2×Q8—22no—
341C2×Q8—22no—
342C2×Q8—22no—
343C2×Q8—21no—
344C2×Q8—21no—
345C2×Q8—22no—
346C2×Q8—22no—
347C2×Q8C2×D4×C1112yes—
348C2×D4—21no—
349C2×D4—21no—
350C2×D4—21no—
351C2×D4—21no—
352C2×D4—21no—
353C2×D4C11×#4112yes—
354C22×C4—21no—
355C22×C4—21no—
356C22×C4—22no—
357C22×C4—21no—
358C22×C4—22no—
359C22×C4—44no—
360C22×C4—42no—
361C22×C4C2×D4×C1112yes—
362C22×C4C2×D4×C1112yes—
363C22×C4C2×D4×C1111yescharacteristic
364C22×C4C2×D4×C1111yescharacteristic
365C22×C4C24×C1111yescharacteristic
366Q16—48no—
367SD16—28no—
368C2×C8—21no—
369C2×C8—21no—
370C2×C8—21no—
371C2×C8—22no—
372C2×C8—22no—
373C2×C8—21no—
374C2×C8—21no—
375C2×C8—22no—
376C2×C8C11×#4112yes—
377C4⋊C4—24no—
378C4⋊C4—21no—
379C4⋊C4—21no—
380C4⋊C4—22no—
381C4⋊C4—21no—
382C4⋊C4—22no—
383C4⋊C4—42no—
384C4⋊C4—42no—
385C4⋊C4—42no—
386C4⋊C4C2×D4×C1112yes—
387C22⋊C4—44no—
388C22⋊C4—44no—
389C22⋊C4—42no—
390C42—24no—
391C42—22no—
392C42—22no—
393C42—44no—
394C42C2×D4×C1112yes—
395C42C11×#4112yes—
396C11#2464511yescharacteristic, direct product factor, Sylow
397C23—22no—
398C23—41no—
399C23—41no—
400C23—42no—
401C23—42no—
402C23C22×D4×C1111yescharacteristic
403Q8—22no—
404Q8—22no—
405Q8—41no—
406Q8—41no—
407Q8—42no—
408Q8—42no—
409Q8—42no—
410Q8—42no—
411D4—22no—
412D4—22no—
413D4—41no—
414D4—41no—
415C2×C4—22no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—42no—
428C2×C4—41no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—84no—
437C2×C4C11×#12112yes—
438C2×C4C11×#12112yes—
439C2×C4C22×D4×C1111yescharacteristic
440C2×C4C2×C11×#4111yescharacteristic
441C2×C4C2×C11×#4111yescharacteristic
442C2×C4C2×C11×#4111yescharacteristic
443C2×C4C11×H(5,𝔽2)11yescharacteristic
444C2×C4C11×H(5,𝔽2)11yescharacteristic
445C8—22no—
446C8—42no—
447C8—41no—
448C22—42no—
449C22—44no—
450C22—82no—
451C22—81no—
452C22—81no—
453C22C2×C11×#12111yescharacteristic
454C22C11×#54611yescharacteristic
455C22C11×#55011yescharacteristic
456C22C11×#57512yes—
457C22C11×#57812yes—
458C4—22no—
459C4—22no—
460C4—42no—
461C4—42no—
462C4—42no—
463C4—42no—
464C4—82no—
465C4—82no—
466C4—81no—
467C4C11×#52511yescharacteristic
468C4C11×#53511yescharacteristic
469C4C11×#55311yescharacteristic
470C4C11×#55511yescharacteristic
471C2—82no—
472C2C11×#241411yescharacteristic
473C2C11×#304011yescharacteristic
474C2C11×#304411yescharacteristic
475C2C11×#331512yes—
476C2C11×#340212yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C4×C11×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#462C2semidirect
4. C11×#2356C2semidirect
5. C11×#2056C2semidirect
8. C11×#1960C2semidirect
9. C11×#1940C2semidirect
10. C11×#1928C2semidirect
97. #24645C11direct (N × H)
159. C2×#462C2×C11semidirect
162. #2356C2×C11semidirect
163. #2056C2×C11semidirect
166. #1960C2×C11semidirect
167. #1940C2×C11semidirect
168. #1928C2×C11semidirect
396. C11#24645direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4622
C2×C11×#4402
C11×#25472
C11×#23562
C11×#20562
C11×#20152
C11×#19832
C11×#19602
C11×#19402
C11×#19282
C11×#18042
#2464511