Finite Group Databasebeta

← C11×#32971 #14610164

Subgroups — C11×#32971 #14610164

Order 2816.

1294 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C11×H(5,𝔽2)C211yesmaximal, characteristic
2C11×#3079C212yesmaximal, complemented
3C11×#2563C211yesmaximal, characteristic, complemented
4C11×#1860C214yesmaximal, complemented
5C11×#1856C212yesmaximal, complemented
6C11×#1806C212yesmaximal, complemented
7C11×#1800C211yesmaximal, characteristic, complemented
8C11×#1792C212yesmaximal
9C2×C11×H(5,𝔽2)C2211yescharacteristic
10C2×C11×C4⋊Q8C2211yescharacteristic, complemented
11C11×#520—22no—
12C11×#520C2212yes—
13C11×#518—22no—
14C11×#518—22no—
15C11×#518C2211yescharacteristic
16C4×C11×#41—22no—
17C4×C11×#41C2212yes—
18C2×C4×D4×C11—22no—
19C2×C4×D4×C11—22no—
20C2×C4×D4×C11C2211yescharacteristic
21C11×#477—22no—
22C11×#476—22no—
23C11×#475—22no—
24C11×#474—22no—
25C11×#428C2214yescomplemented
26C11×#423C2212yescomplemented
27C2×C11×#104C2214yes—
28C11×#417C2214yes—
29C2×C11×#100C2212yes—
30C11×#393—22no—
31C11×#390C2212yes—
32C11×#382C2212yescomplemented
33C11×#380—22no—
34C4×C11×C4⋊C4C2211yescharacteristic, complemented
35C11×#343C2212yescomplemented
36C11×#339C2214yescomplemented
37C11×H(5,𝔽2)—24no—
38C11×H(5,𝔽2)—22no—
39C11×H(5,𝔽2)Q814yescomplemented
40C2×C11×#41—22no—
41C2×C11×#41C2312yes—
42C22×Q8×C11—21no—
43C22×D4×C11—22no—
44C22×D4×C11—22no—
45C22×D4×C11C2311yescharacteristic
46C23×C4×C11—22no—
47C23×C4×C11D412yes—
48C2×C11×M16C2314yes—
49C11×C4⋊Q8—22no—
50C11×C4⋊Q8—22no—
51C4×Q8×C11—22no—
52C4×Q8×C11D412yes—
53C4×Q8×C11D412yes—
54C4×D4×C11—24no—
55C4×D4×C11—24no—
56C4×D4×C11—24no—
57C4×D4×C11—24no—
58C4×D4×C11—22no—
59C4×D4×C11—22no—
60C4×D4×C11—24no—
61C4×D4×C11—22no—
62C4×D4×C11—22no—
63C4×D4×C11—22no—
64C4×D4×C11—22no—
65C4×D4×C11—22no—
66C4×D4×C11D412yes—
67C4×D4×C11D412yes—
68C11×#117—24no—
69C11×#117—22no—
70C11×#117—22no—
71C11×#117C2312yes—
72C2×C11×C4⋊C4—22no—
73C2×C11×C4⋊C4—22no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4C2312yes—
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C22⋊C4—22no—
79C2×C11×C22⋊C4—24no—
80C2×C11×C22⋊C4—22no—
81C2×C11×C22⋊C4—24no—
82C2×C11×C22⋊C4D412yes—
83C2×C42×C11—22no—
84C2×C42×C11—22no—
85C2×C42×C11C2312yes—
86C2×C42×C11C2311yescharacteristic
87C11×#107—24no—
88C11×#106—24no—
89C11×C4⋊C8—22no—
90C11×C4⋊C8—22no—
91C11×#104—28no—
92C11×#103—24no—
93C11×#102—24no—
94C11×#100—24no—
95C11×#95—21no—
96C11×#95—24no—
97#32971C1111yesmaximal, characteristic, direct product factor, Sylow
98C24×C11—22no—
99C24×C11C2×D412yes—
100C11×#41—28no—
101C11×#41—28no—
102C11×#41—22no—
103C11×#41—22no—
104C11×#41C2×Q814yes—
105C11×#41#4114yes—
106C2×Q8×C11—42no—
107C2×Q8×C11—82no—
108C2×Q8×C11C2×D412yes—
109C2×D4×C11—24no—
110C2×D4×C11—28no—
111C2×D4×C11—28no—
112C2×D4×C11—28no—
113C2×D4×C11—22no—
114C2×D4×C11—28no—
115C2×D4×C11—22no—
116C2×D4×C11—22no—
117C2×D4×C11C2×D412yes—
118C2×D4×C11C2×Q812yes—
119C2×D4×C11#4112yes—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—24no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—44no—
132C22×C4×C11—84no—
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D412yes—
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2411yescharacteristic
137C11×M16—24no—
138C11×M16—24no—
139C2×C8×C11—24no—
140C11×C4⋊C4—24no—
141C11×C4⋊C4—22no—
142C11×C4⋊C4—22no—
143C11×C4⋊C4—22no—
144C11×C4⋊C4—24no—
145C11×C4⋊C4—42no—
146C11×C4⋊C4—41no—
147C11×C4⋊C4—41no—
148C11×C4⋊C4C2×D412yes—
149C11×C4⋊C4C2×D412yes—
150C11×C22⋊C4—24no—
151C11×C22⋊C4—24no—
152C11×C22⋊C4—22no—
153C11×C22⋊C4—22no—
154C11×C22⋊C4—22no—
155C11×C22⋊C4—24no—
156C11×C22⋊C4—84no—
157C42×C11—24no—
158C42×C11—22no—
159C42×C11—22no—
160C42×C11—22no—
161C42×C11—24no—
162C42×C11C2×D412yes—
163C42×C11C2×D412yes—
164C4×H(5,𝔽2)C2×C1111yescharacteristic
165#3079C2×C1112yescomplemented
166#2563C2×C1111yescharacteristic, complemented
167#1860C2×C1114yescomplemented
168#1856C2×C1112yescomplemented
169#1806C2×C1112yescomplemented
170#1800C2×C1111yescharacteristic, complemented
171#1792C2×C1112yes—
172C23×C11—28no—
173C23×C11—22no—
174C23×C11—22no—
175C23×C11—22no—
176C23×C11—42no—
177C23×C11—42no—
178C23×C11—82no—
179C23×C11—82no—
180C23×C11C22⋊Q814yes—
181C23×C11C22×D411yescharacteristic
182Q8×C11—22no—
183Q8×C11—84no—
184Q8×C11C22⋊Q814yes—
185D4×C11—216no—
186D4×C11—24no—
187D4×C11—24no—
188D4×C11—24no—
189D4×C11—22no—
190D4×C11—24no—
191D4×C11C22⋊Q814yes—
192C2×C4×C11—28no—
193C2×C4×C11—22no—
194C2×C4×C11—24no—
195C2×C4×C11—24no—
196C2×C4×C11—22no—
197C2×C4×C11—22no—
198C2×C4×C11—22no—
199C2×C4×C11—22no—
200C2×C4×C11—41no—
201C2×C4×C11—44no—
202C2×C4×C11—44no—
203C2×C4×C11—42no—
204C2×C4×C11—42no—
205C2×C4×C11—44no—
206C2×C4×C11—42no—
207C2×C4×C11—42no—
208C2×C4×C11—42no—
209C2×C4×C11—82no—
210C2×C4×C11—82no—
211C2×C4×C11—82no—
212C2×C4×C11—84no—
213C2×C4×C11—82no—
214C2×C4×C11#12012yes—
215C2×C4×C11#12011yescharacteristic
216C2×C4×C11#12011yescharacteristic
217C2×C4×C11C22×D412yes—
218C2×C4×C11C22×Q811yescharacteristic
219C2×C4×C11C2×#4112yes—
220C2×C4×C11C2×#4111yescharacteristic
221C8×C11—44no—
222C2×H(5,𝔽2)C22×C1111yescharacteristic
223C2×C4⋊Q8C22×C1111yescharacteristic, complemented
224#520—22no—
225#520C22×C1112yes—
226#518—22no—
227#518—22no—
228#518C22×C1111yescharacteristic
229C4×#41—22no—
230C4×#41C22×C1112yes—
231C2×C4×D4—22no—
232C2×C4×D4—22no—
233C2×C4×D4C22×C1111yescharacteristic
234#477—22no—
235#476—22no—
236#475—22no—
237#474—22no—
238#428C22×C1114yescomplemented
239#423C22×C1112yescomplemented
240C2×#104C22×C1114yes—
241#417C22×C1114yes—
242C2×#100C22×C1112yes—
243#393—22no—
244#390C22×C1112yes—
245#382C22×C1112yescomplemented
246#380—22no—
247C4×C4⋊C4C22×C1111yescharacteristic, complemented
248#343C22×C1112yescomplemented
249#339C22×C1114yescomplemented
250C22×C11—21no—
251C22×C11—21no—
252C22×C11—24no—
253C22×C11—24no—
254C22×C11—44no—
255C22×C11—42no—
256C22×C11—42no—
257C22×C11—42no—
258C22×C11—42no—
259C22×C11—82no—
260C22×C11—88no—
261C22×C11C2×#12011yescharacteristic
262C22×C11C2×C22⋊Q811yescharacteristic
263C22×C11#52511yescharacteristic
264C4×C11—24no—
265C4×C11—21no—
266C4×C11—22no—
267C4×C11—42no—
268C4×C11—42no—
269C4×C11—42no—
270C4×C11—82no—
271C4×C11—82no—
272C4×C11#45512yes—
273C4×C11C2×C22⋊Q812yes—
274C4×C11#52512yes—
275H(5,𝔽2)—24no—
276H(5,𝔽2)—22no—
277H(5,𝔽2)Q8×C1114yescomplemented
278C2×#41—22no—
279C2×#41C23×C1112yes—
280C22×Q8—21no—
281C22×D4—22no—
282C22×D4—22no—
283C22×D4C23×C1111yescharacteristic
284C23×C4—22no—
285C23×C4D4×C1112yes—
286C2×M16C23×C1114yes—
287C4⋊Q8—22no—
288C4⋊Q8—22no—
289C4×Q8—22no—
290C4×Q8D4×C1112yes—
291C4×Q8D4×C1112yes—
292C4×D4—24no—
293C4×D4—24no—
294C4×D4—24no—
295C4×D4—24no—
296C4×D4—22no—
297C4×D4—22no—
298C4×D4—24no—
299C4×D4—22no—
300C4×D4—22no—
301C4×D4—22no—
302C4×D4—22no—
303C4×D4—22no—
304C4×D4D4×C1112yes—
305C4×D4D4×C1112yes—
306#117—24no—
307#117—22no—
308#117—22no—
309#117C23×C1112yes—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4C23×C1112yes—
315C2×C4⋊C4C23×C1111yescharacteristic
316C2×C22⋊C4—22no—
317C2×C22⋊C4—24no—
318C2×C22⋊C4—22no—
319C2×C22⋊C4—24no—
320C2×C22⋊C4D4×C1112yes—
321C2×C42—22no—
322C2×C42—22no—
323C2×C42C23×C1112yes—
324C2×C42C23×C1111yescharacteristic
325#107—24no—
326#106—24no—
327C4⋊C8—22no—
328C4⋊C8—22no—
329#104—28no—
330#103—24no—
331#102—24no—
332#100—24no—
333#95—21no—
334#95—24no—
335C2×C11—21no—
336C2×C11—21no—
337C2×C11—44no—
338C2×C11—44no—
339C2×C11#284811yescharacteristic
340C2×C11C2×#45511yescharacteristic
341C2×C11#302111yescharacteristic
342C24—22no—
343C24C2×D4×C1112yes—
344#41—28no—
345#41—28no—
346#41—22no—
347#41—22no—
348#41C2×Q8×C1114yes—
349#41C11×#4114yes—
350C2×Q8—42no—
351C2×Q8—82no—
352C2×Q8C2×D4×C1112yes—
353C2×D4—24no—
354C2×D4—28no—
355C2×D4—28no—
356C2×D4—28no—
357C2×D4—22no—
358C2×D4—28no—
359C2×D4—22no—
360C2×D4—22no—
361C2×D4C2×D4×C1112yes—
362C2×D4C2×Q8×C1112yes—
363C2×D4C11×#4112yes—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—24no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—44no—
376C22×C4—84no—
377C22×C4C2×D4×C1111yescharacteristic
378C22×C4C2×D4×C1112yes—
379C22×C4C2×D4×C1111yescharacteristic
380C22×C4C24×C1111yescharacteristic
381M16—24no—
382M16—24no—
383C2×C8—24no—
384C4⋊C4—24no—
385C4⋊C4—22no—
386C4⋊C4—22no—
387C4⋊C4—22no—
388C4⋊C4—24no—
389C4⋊C4—42no—
390C4⋊C4—41no—
391C4⋊C4—41no—
392C4⋊C4C2×D4×C1112yes—
393C4⋊C4C2×D4×C1112yes—
394C22⋊C4—24no—
395C22⋊C4—24no—
396C22⋊C4—22no—
397C22⋊C4—22no—
398C22⋊C4—22no—
399C22⋊C4—24no—
400C22⋊C4—84no—
401C42—24no—
402C42—22no—
403C42—22no—
404C42—22no—
405C42—24no—
406C42C2×D4×C1112yes—
407C42C2×D4×C1112yes—
408C11#3297111yescharacteristic, direct product factor, Sylow
409C23—28no—
410C23—22no—
411C23—22no—
412C23—22no—
413C23—42no—
414C23—42no—
415C23—82no—
416C23—82no—
417C23C11×C22⋊Q814yes—
418C23C22×D4×C1111yescharacteristic
419Q8—22no—
420Q8—84no—
421Q8C11×C22⋊Q814yes—
422D4—216no—
423D4—24no—
424D4—24no—
425D4—24no—
426D4—22no—
427D4—24no—
428D4C11×C22⋊Q814yes—
429C2×C4—28no—
430C2×C4—22no—
431C2×C4—24no—
432C2×C4—24no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—41no—
438C2×C4—44no—
439C2×C4—44no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—44no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—82no—
447C2×C4—82no—
448C2×C4—82no—
449C2×C4—84no—
450C2×C4—82no—
451C2×C4C11×#12012yes—
452C2×C4C11×#12011yescharacteristic
453C2×C4C11×#12011yescharacteristic
454C2×C4C22×D4×C1112yes—
455C2×C4C22×Q8×C1111yescharacteristic
456C2×C4C2×C11×#4112yes—
457C2×C4C2×C11×#4111yescharacteristic
458C8—44no—
459C22—21no—
460C22—21no—
461C22—24no—
462C22—24no—
463C22—44no—
464C22—42no—
465C22—42no—
466C22—42no—
467C22—42no—
468C22—82no—
469C22—88no—
470C22C2×C11×#12011yescharacteristic
471C22C2×C11×C22⋊Q811yescharacteristic
472C22C11×#52511yescharacteristic
473C4—21no—
474C4—22no—
475C4—24no—
476C4—42no—
477C4—42no—
478C4—42no—
479C4—82no—
480C4—82no—
481C4C11×#45512yes—
482C4C2×C11×C22⋊Q812yes—
483C4C11×#52512yes—
484C2—21no—
485C2—21no—
486C2—44no—
487C2—44no—
488C2C11×#284811yescharacteristic
489C2C2×C11×#45511yescharacteristic
490C2C11×#302111yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×H(5,𝔽2)C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#3079C2semidirect
3. C11×#2563C2semidirect
4. C11×#1860C2semidirect
5. C11×#1856C2semidirect
6. C11×#1806C2semidirect
7. C11×#1800C2semidirect
10. C2×C11×C4⋊Q8C22semidirect
25. C11×#428C22semidirect
26. C11×#423C22semidirect
32. C11×#382C22semidirect
34. C4×C11×C4⋊C4C22semidirect
35. C11×#343C22semidirect
36. C11×#339C22semidirect
39. C11×H(5,𝔽2)Q8semidirect
97. #32971C11direct (N × H)
165. #3079C2×C11semidirect
166. #2563C2×C11semidirect
167. #1860C2×C11semidirect
168. #1856C2×C11semidirect
169. #1806C2×C11semidirect
170. #1800C2×C11semidirect
223. C2×C4⋊Q8C22×C11semidirect
238. #428C22×C11semidirect
239. #423C22×C11semidirect
245. #382C22×C11semidirect
247. C4×C4⋊C4C22×C11semidirect
248. #343C22×C11semidirect
249. #339C22×C11semidirect
277. H(5,𝔽2)Q8×C11semidirect
408. C11#32971direct (N × H)

Maximal subgroups

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

subgroupindex
C4×C11×H(5,𝔽2)2
C11×#30792
C11×#25632
C11×#18602
C11×#18562
C11×#18062
C11×#18002
C11×#17922
#3297111