Finite Group Databasebeta

← C11×#32969 #14610162

Subgroups — C11×#32969 #14610162

Order 2816.

1350 conjugacy classes of subgroups.

The subgroup lattice has 498 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×#2542C211yesmaximal, characteristic, complemented
4C11×#1859C214yesmaximal, complemented
5C11×#1856C212yesmaximal, complemented
6C11×#1806C212yesmaximal, complemented
7C11×#1800C211yesmaximal, characteristic, complemented
8C11×#1792C212yesmaximal
9C2×C11×H(5,𝔽2)C2211yescharacteristic
10C2×C11×C4⋊Q8C2211yescharacteristic, complemented
11C2×C11×C22⋊Q8—22no—
12C11×#520—22no—
13C11×#520C2212yes—
14C11×#518—22no—
15C11×#518—22no—
16C11×#518C2211yescharacteristic
17C4×C11×#41—22no—
18C4×C11×#41C2212yes—
19C2×C4×D4×C11—22no—
20C2×C4×D4×C11—22no—
21C2×C4×D4×C11C2211yescharacteristic
22C11×#477—22no—
23C11×#476—22no—
24C11×#475—22no—
25C11×#474—22no—
26C11×#428C2214yescomplemented
27C11×#423C2212yescomplemented
28C2×C11×#104C2214yes—
29C11×#417C2214yes—
30C2×C11×#100C2212yes—
31C11×#399—22no—
32C11×#390C2212yes—
33C11×#384C2212yescomplemented
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—
51C11×C22⋊Q8—48no—
52C4×Q8×C11—22no—
53C4×Q8×C11D412yes—
54C4×Q8×C11D412yes—
55C4×D4×C11—24no—
56C4×D4×C11—24no—
57C4×D4×C11—24no—
58C4×D4×C11—24no—
59C4×D4×C11—22no—
60C4×D4×C11—22no—
61C4×D4×C11—24no—
62C4×D4×C11—22no—
63C4×D4×C11—22no—
64C4×D4×C11—22no—
65C4×D4×C11—22no—
66C4×D4×C11—22no—
67C4×D4×C11D412yes—
68C4×D4×C11D412yes—
69C11×#117—24no—
70C11×#117—22no—
71C11×#117—22no—
72C11×#117C2312yes—
73C2×C11×C4⋊C4—22no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—22no—
76C2×C11×C4⋊C4—24no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4C2312yes—
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C22⋊C4—22no—
81C2×C11×C22⋊C4—24no—
82C2×C11×C22⋊C4—22no—
83C2×C11×C22⋊C4—24no—
84C2×C11×C22⋊C4D412yes—
85C2×C42×C11—22no—
86C2×C42×C11—22no—
87C2×C42×C11C2312yes—
88C2×C42×C11C2311yescharacteristic
89C11×#107—24no—
90C11×#106—24no—
91C11×C4⋊C8—22no—
92C11×C4⋊C8—22no—
93C11×#104—28no—
94C11×#103—24no—
95C11×#102—24no—
96C11×#100—24no—
97C11×#95—21no—
98#32969C1111yesmaximal, characteristic, direct product factor, Sylow
99C24×C11—22no—
100C24×C11C2×D412yes—
101C11×#41—28no—
102C11×#41—28no—
103C11×#41—22no—
104C11×#41—22no—
105C11×#41C2×Q814yes—
106C11×#41#4114yes—
107C2×Q8×C11—44no—
108C2×Q8×C11—41no—
109C2×Q8×C11—41no—
110C2×Q8×C11C2×D412yes—
111C2×D4×C11—24no—
112C2×D4×C11—28no—
113C2×D4×C11—28no—
114C2×D4×C11—28no—
115C2×D4×C11—22no—
116C2×D4×C11—28no—
117C2×D4×C11—22no—
118C2×D4×C11—22no—
119C2×D4×C11C2×D412yes—
120C2×D4×C11C2×Q812yes—
121C2×D4×C11#4112yes—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—24no—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—44no—
134C22×C4×C11—84no—
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D412yes—
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2411yescharacteristic
139C11×M16—24no—
140C11×M16—24no—
141C2×C8×C11—24no—
142C11×C4⋊C4—24no—
143C11×C4⋊C4—24no—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—22no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—24no—
148C11×C4⋊C4—48no—
149C11×C4⋊C4—42no—
150C11×C4⋊C4C2×D412yes—
151C11×C4⋊C4C2×D412yes—
152C11×C22⋊C4—24no—
153C11×C22⋊C4—24no—
154C11×C22⋊C4—22no—
155C11×C22⋊C4—22no—
156C11×C22⋊C4—22no—
157C11×C22⋊C4—24no—
158C11×C22⋊C4—48no—
159C42×C11—24no—
160C42×C11—22no—
161C42×C11—22no—
162C42×C11—22no—
163C42×C11—24no—
164C42×C11C2×D412yes—
165C42×C11C2×D412yes—
166C4×H(5,𝔽2)C2×C1111yescharacteristic
167#3079C2×C1112yescomplemented
168#2542C2×C1111yescharacteristic, complemented
169#1859C2×C1114yescomplemented
170#1856C2×C1112yescomplemented
171#1806C2×C1112yescomplemented
172#1800C2×C1111yescharacteristic, complemented
173#1792C2×C1112yes—
174C23×C11—28no—
175C23×C11—22no—
176C23×C11—22no—
177C23×C11—22no—
178C23×C11—42no—
179C23×C11—42no—
180C23×C11—82no—
181C23×C11—82no—
182C23×C11C22⋊Q814yes—
183C23×C11C22×D411yescharacteristic
184Q8×C11—22no—
185Q8×C11—82no—
186Q8×C11—82no—
187Q8×C11C22⋊Q814yescomplemented
188D4×C11—216no—
189D4×C11—24no—
190D4×C11—24no—
191D4×C11—24no—
192D4×C11—22no—
193D4×C11—24no—
194D4×C11C22⋊Q814yescomplemented
195C2×C4×C11—28no—
196C2×C4×C11—22no—
197C2×C4×C11—24no—
198C2×C4×C11—24no—
199C2×C4×C11—22no—
200C2×C4×C11—24no—
201C2×C4×C11—22no—
202C2×C4×C11—22no—
203C2×C4×C11—22no—
204C2×C4×C11—41no—
205C2×C4×C11—42no—
206C2×C4×C11—42no—
207C2×C4×C11—44no—
208C2×C4×C11—44no—
209C2×C4×C11—42no—
210C2×C4×C11—44no—
211C2×C4×C11—42no—
212C2×C4×C11—82no—
213C2×C4×C11—82no—
214C2×C4×C11—82no—
215C2×C4×C11—84no—
216C2×C4×C11—82no—
217C2×C4×C11#12012yes—
218C2×C4×C11#12011yescharacteristic
219C2×C4×C11#12011yescharacteristic
220C2×C4×C11C22×D412yes—
221C2×C4×C11C22×Q811yescharacteristic
222C2×C4×C11C2×#4112yes—
223C2×C4×C11C2×#4111yescharacteristic
224C8×C11—44no—
225C2×H(5,𝔽2)C22×C1111yescharacteristic
226C2×C4⋊Q8C22×C1111yescharacteristic, complemented
227C2×C22⋊Q8—22no—
228#520—22no—
229#520C22×C1112yes—
230#518—22no—
231#518—22no—
232#518C22×C1111yescharacteristic
233C4×#41—22no—
234C4×#41C22×C1112yes—
235C2×C4×D4—22no—
236C2×C4×D4—22no—
237C2×C4×D4C22×C1111yescharacteristic
238#477—22no—
239#476—22no—
240#475—22no—
241#474—22no—
242#428C22×C1114yescomplemented
243#423C22×C1112yescomplemented
244C2×#104C22×C1114yes—
245#417C22×C1114yes—
246C2×#100C22×C1112yes—
247#399—22no—
248#390C22×C1112yes—
249#384C22×C1112yescomplemented
250C4×C4⋊C4C22×C1111yescharacteristic, complemented
251#343C22×C1112yescomplemented
252#339C22×C1114yescomplemented
253C22×C11—21no—
254C22×C11—21no—
255C22×C11—24no—
256C22×C11—24no—
257C22×C11—44no—
258C22×C11—42no—
259C22×C11—42no—
260C22×C11—42no—
261C22×C11—42no—
262C22×C11—82no—
263C22×C11—88no—
264C22×C11C2×#12011yescharacteristic
265C22×C11C2×C22⋊Q811yescharacteristic
266C22×C11#52511yescharacteristic
267C4×C11—24no—
268C4×C11—21no—
269C4×C11—22no—
270C4×C11—44no—
271C4×C11—42no—
272C4×C11—42no—
273C4×C11—42no—
274C4×C11—82no—
275C4×C11#45312yes—
276C4×C11C2×C22⋊Q812yes—
277C4×C11#52512yes—
278H(5,𝔽2)—24no—
279H(5,𝔽2)—22no—
280H(5,𝔽2)Q8×C1114yescomplemented
281C2×#41—22no—
282C2×#41C23×C1112yes—
283C22×Q8—21no—
284C22×D4—22no—
285C22×D4—22no—
286C22×D4C23×C1111yescharacteristic
287C23×C4—22no—
288C23×C4D4×C1112yes—
289C2×M16C23×C1114yes—
290C4⋊Q8—22no—
291C4⋊Q8—22no—
292C22⋊Q8—48no—
293C4×Q8—22no—
294C4×Q8D4×C1112yes—
295C4×Q8D4×C1112yes—
296C4×D4—24no—
297C4×D4—24no—
298C4×D4—24no—
299C4×D4—24no—
300C4×D4—22no—
301C4×D4—22no—
302C4×D4—24no—
303C4×D4—22no—
304C4×D4—22no—
305C4×D4—22no—
306C4×D4—22no—
307C4×D4—22no—
308C4×D4D4×C1112yes—
309C4×D4D4×C1112yes—
310#117—24no—
311#117—22no—
312#117—22no—
313#117C23×C1112yes—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4C23×C1112yes—
320C2×C4⋊C4C23×C1111yescharacteristic
321C2×C22⋊C4—22no—
322C2×C22⋊C4—24no—
323C2×C22⋊C4—22no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4D4×C1112yes—
326C2×C42—22no—
327C2×C42—22no—
328C2×C42C23×C1112yes—
329C2×C42C23×C1111yescharacteristic
330#107—24no—
331#106—24no—
332C4⋊C8—22no—
333C4⋊C8—22no—
334#104—28no—
335#103—24no—
336#102—24no—
337#100—24no—
338#95—21no—
339C2×C11—21no—
340C2×C11—21no—
341C2×C11—44no—
342C2×C11—44no—
343C2×C11#284811yescharacteristic
344C2×C11C2×#45311yescharacteristic
345C2×C11#302211yescharacteristic
346C24—22no—
347C24C2×D4×C1112yes—
348#41—28no—
349#41—28no—
350#41—22no—
351#41—22no—
352#41C2×Q8×C1114yes—
353#41C11×#4114yes—
354C2×Q8—44no—
355C2×Q8—41no—
356C2×Q8—41no—
357C2×Q8C2×D4×C1112yes—
358C2×D4—24no—
359C2×D4—28no—
360C2×D4—28no—
361C2×D4—28no—
362C2×D4—22no—
363C2×D4—28no—
364C2×D4—22no—
365C2×D4—22no—
366C2×D4C2×D4×C1112yes—
367C2×D4C2×Q8×C1112yes—
368C2×D4C11×#4112yes—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—24no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—44no—
381C22×C4—84no—
382C22×C4C2×D4×C1111yescharacteristic
383C22×C4C2×D4×C1112yes—
384C22×C4C2×D4×C1111yescharacteristic
385C22×C4C24×C1111yescharacteristic
386M16—24no—
387M16—24no—
388C2×C8—24no—
389C4⋊C4—24no—
390C4⋊C4—24no—
391C4⋊C4—22no—
392C4⋊C4—22no—
393C4⋊C4—22no—
394C4⋊C4—24no—
395C4⋊C4—48no—
396C4⋊C4—42no—
397C4⋊C4C2×D4×C1112yes—
398C4⋊C4C2×D4×C1112yes—
399C22⋊C4—24no—
400C22⋊C4—24no—
401C22⋊C4—22no—
402C22⋊C4—22no—
403C22⋊C4—22no—
404C22⋊C4—24no—
405C22⋊C4—48no—
406C42—24no—
407C42—22no—
408C42—22no—
409C42—22no—
410C42—24no—
411C42C2×D4×C1112yes—
412C42C2×D4×C1112yes—
413C11#3296911yescharacteristic, direct product factor, Sylow
414C23—28no—
415C23—22no—
416C23—22no—
417C23—22no—
418C23—42no—
419C23—42no—
420C23—82no—
421C23—82no—
422C23C11×C22⋊Q814yes—
423C23C22×D4×C1111yescharacteristic
424Q8—22no—
425Q8—82no—
426Q8—82no—
427Q8C11×C22⋊Q814yescomplemented
428D4—216no—
429D4—24no—
430D4—24no—
431D4—24no—
432D4—22no—
433D4—24no—
434D4C11×C22⋊Q814yescomplemented
435C2×C4—28no—
436C2×C4—22no—
437C2×C4—24no—
438C2×C4—24no—
439C2×C4—22no—
440C2×C4—24no—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—41no—
445C2×C4—42no—
446C2×C4—42no—
447C2×C4—44no—
448C2×C4—44no—
449C2×C4—42no—
450C2×C4—44no—
451C2×C4—42no—
452C2×C4—82no—
453C2×C4—82no—
454C2×C4—82no—
455C2×C4—84no—
456C2×C4—82no—
457C2×C4C11×#12012yes—
458C2×C4C11×#12011yescharacteristic
459C2×C4C11×#12011yescharacteristic
460C2×C4C22×D4×C1112yes—
461C2×C4C22×Q8×C1111yescharacteristic
462C2×C4C2×C11×#4112yes—
463C2×C4C2×C11×#4111yescharacteristic
464C8—44no—
465C22—21no—
466C22—21no—
467C22—24no—
468C22—24no—
469C22—44no—
470C22—42no—
471C22—42no—
472C22—42no—
473C22—42no—
474C22—82no—
475C22—88no—
476C22C2×C11×#12011yescharacteristic
477C22C2×C11×C22⋊Q811yescharacteristic
478C22C11×#52511yescharacteristic
479C4—21no—
480C4—22no—
481C4—24no—
482C4—44no—
483C4—42no—
484C4—42no—
485C4—42no—
486C4—82no—
487C4C11×#45312yes—
488C4C2×C11×C22⋊Q812yes—
489C4C11×#52512yes—
490C2—21no—
491C2—21no—
492C2—44no—
493C2—44no—
494C2C11×#284811yescharacteristic
495C2C2×C11×#45311yescharacteristic
496C2C11×#302211yescharacteristic
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×#2542C2semidirect
4. C11×#1859C2semidirect
5. C11×#1856C2semidirect
6. C11×#1806C2semidirect
7. C11×#1800C2semidirect
10. C2×C11×C4⋊Q8C22semidirect
26. C11×#428C22semidirect
27. C11×#423C22semidirect
33. C11×#384C22semidirect
34. C4×C11×C4⋊C4C22semidirect
35. C11×#343C22semidirect
36. C11×#339C22semidirect
39. C11×H(5,𝔽2)Q8semidirect
98. #32969C11direct (N × H)
167. #3079C2×C11semidirect
168. #2542C2×C11semidirect
169. #1859C2×C11semidirect
170. #1856C2×C11semidirect
171. #1806C2×C11semidirect
172. #1800C2×C11semidirect
187. Q8×C11C22⋊Q8semidirect
194. D4×C11C22⋊Q8semidirect
226. C2×C4⋊Q8C22×C11semidirect
242. #428C22×C11semidirect
243. #423C22×C11semidirect
249. #384C22×C11semidirect
250. C4×C4⋊C4C22×C11semidirect
251. #343C22×C11semidirect
252. #339C22×C11semidirect
280. H(5,𝔽2)Q8×C11semidirect
413. C11#32969direct (N × H)
427. Q8C11×C22⋊Q8semidirect
434. D4C11×C22⋊Q8semidirect

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×#25422
C11×#18592
C11×#18562
C11×#18062
C11×#18002
C11×#17922
#3296911