Finite Group Databasebeta

← C11×#32953 #14610146

Subgroups — C11×#32953 #14610146

Order 2816.

1764 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D4×C11C211yesmaximal, characteristic
2C2×C11×#474C212yesmaximal, complemented
3C11×#2857C211yesmaximal, characteristic, complemented
4C11×#1862C214yesmaximal, complemented
5C11×#1852C212yesmaximal, complemented
6C11×#1802C212yesmaximal, complemented
7C11×#1797C211yesmaximal, characteristic, complemented
8C11×#1786C212yesmaximal
9C23×D4×C11C2211yescharacteristic
10C24×C4×C11—21no—
11C2×C11×C4⋊Q8C2211yescharacteristic, complemented
12C2×C11×C22⋊Q8—21no—
13C2×C4×D4×C11—28no—
14C2×C4×D4×C11—21no—
15C2×C4×D4×C11—21no—
16C2×C4×D4×C11C2212yes—
17C2×C4×D4×C11C2212yes—
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4—21no—
20C22×C42×C11C2211yescharacteristic
21C11×#474—28no—
22C2×C11×#107C2214yescomplemented
23C2×C11×C4⋊C8C2212yescomplemented
24C2×C11×#102C2214yes—
25C2×C11×#102C2214yes—
26C2×C11×C22⋊C8C2212yes—
27C11×#391—21no—
28C11×#389—21no—
29C11×#389C2212yescomplemented
30C11×#384C2211yescharacteristic, complemented
31C11×#380—21no—
32C11×#380C2212yes—
33C11×#340C2214yescomplemented
34C11×#336C2212yescomplemented
35C25×C11—21no—
36C22×Q8×C11—21no—
37C22×D4×C11—24no—
38C22×D4×C11—24no—
39C22×D4×C11—21no—
40C22×D4×C11—22no—
41C22×D4×C11Q814yescomplemented
42C22×D4×C11C2312yes—
43C23×C4×C11—28no—
44C23×C4×C11—21no—
45C23×C4×C11—22no—
46C23×C4×C11—22no—
47C23×C4×C11—44no—
48C23×C4×C11—44no—
49C23×C4×C11D411yescharacteristic
50C23×C4×C11D411yescharacteristic
51C23×C4×C11C2311yescharacteristic
52C22×C8×C11C2314yes—
53C11×C4⋊Q8—24no—
54C11×C22⋊Q8—44no—
55C4×D4×C11—28no—
56C4×D4×C11—28no—
57C4×D4×C11—24no—
58C4×D4×C11—24no—
59C4×D4×C11—24no—
60C4×D4×C11D418yes—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4—24no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—22no—
67C2×C11×C4⋊C4C2312yes—
68C2×C11×C4⋊C4C2312yes—
69C2×C11×C4⋊C4C2312yes—
70C2×C11×C22⋊C4—28no—
71C2×C11×C22⋊C4—22no—
72C2×C11×C22⋊C4—22no—
73C2×C11×C22⋊C4—22no—
74C2×C42×C11—24no—
75C2×C42×C11D411yescharacteristic
76C2×C42×C11D411yescharacteristic
77C2×C42×C11C2311yescharacteristic
78C2×C42×C11C2311yescharacteristic
79C11×#107—28no—
80C11×C4⋊C8—24no—
81C11×#102—28no—
82C11×#102—28no—
83C11×C22⋊C8—24no—
84C11×#95—22no—
85C11×#95—22no—
86#32953C1111yesmaximal, characteristic, direct product factor, Sylow
87C24×C11—24no—
88C24×C11—24no—
89C24×C11—24no—
90C24×C11—22no—
91C24×C11—42no—
92C24×C11—42no—
93C24×C11—42no—
94C24×C11—42no—
95C24×C11C2×D411yescharacteristic
96C2×Q8×C11—42no—
97C2×Q8×C11—42no—
98C2×Q8×C11—42no—
99C2×D4×C11—24no—
100C2×D4×C11—24no—
101C2×D4×C11—216no—
102C2×D4×C11—216no—
103C2×D4×C11—24no—
104C2×D4×C11—22no—
105C2×D4×C11—22no—
106C2×D4×C11—22no—
107C2×D4×C11C2×D414yes—
108C2×D4×C11C2×Q814yes—
109C2×D4×C11#4114yes—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—24no—
115C22×C4×C11—28no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—28no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—41no—
123C22×C4×C11—44no—
124C22×C4×C11—432no—
125C22×C4×C11—42no—
126C22×C4×C11—42no—
127C22×C4×C11—44no—
128C22×C4×C11—44no—
129C22×C4×C11—44no—
130C22×C4×C11D814yes—
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×Q812yes—
137C22×C4×C11#4112yes—
138C22×C4×C11C2411yescharacteristic
139C2×C8×C11—24no—
140C2×C8×C11—24no—
141C2×C8×C11—24no—
142C11×C4⋊C4—24no—
143C11×C4⋊C4—22no—
144C11×C4⋊C4—24no—
145C11×C4⋊C4—24no—
146C11×C4⋊C4—42no—
147C11×C4⋊C4—42no—
148C11×C4⋊C4—42no—
149C11×C4⋊C4—44no—
150C11×C4⋊C4C2×D414yes—
151C11×C22⋊C4—28no—
152C11×C22⋊C4—28no—
153C11×C22⋊C4—44no—
154C42×C11—22no—
155C42×C11—22no—
156C42×C11—22no—
157C42×C11C2×D414yes—
158C22×C4×D4C2×C1111yescharacteristic
159C2×#474C2×C1112yescomplemented
160#2857C2×C1111yescharacteristic, complemented
161#1862C2×C1114yescomplemented
162#1852C2×C1112yescomplemented
163#1802C2×C1112yescomplemented
164#1797C2×C1111yescharacteristic, complemented
165#1786C2×C1112yes—
166C23×C11—21no—
167C23×C11—21no—
168C23×C11—21no—
169C23×C11—21no—
170C23×C11—216no—
171C23×C11—24no—
172C23×C11—24no—
173C23×C11—24no—
174C23×C11—48no—
175C23×C11—48no—
176C23×C11—48no—
177C23×C11—48no—
178C23×C11—48no—
179C23×C11—42no—
180C23×C11—42no—
181C23×C11—42no—
182C23×C11—42no—
183C23×C11—48no—
184C23×C11C22⋊Q812yes—
185C23×C11C2×D812yes—
186C23×C11#13712yes—
187C23×C11C22×D411yescharacteristic
188Q8×C11—84no—
189D4×C11—216no—
190D4×C11—24no—
191D4×C11—24no—
192D4×C11—24no—
193D4×C11C22⋊Q818yescomplemented
194C2×C4×C11—21no—
195C2×C4×C11—21no—
196C2×C4×C11—21no—
197C2×C4×C11—21no—
198C2×C4×C11—21no—
199C2×C4×C11—21no—
200C2×C4×C11—24no—
201C2×C4×C11—24no—
202C2×C4×C11—28no—
203C2×C4×C11—21no—
204C2×C4×C11—24no—
205C2×C4×C11—21no—
206C2×C4×C11—21no—
207C2×C4×C11—44no—
208C2×C4×C11—416no—
209C2×C4×C11—48no—
210C2×C4×C11—42no—
211C2×C4×C11—42no—
212C2×C4×C11—416no—
213C2×C4×C11—42no—
214C2×C4×C11—42no—
215C2×C4×C11—42no—
216C2×C4×C11—42no—
217C2×C4×C11—42no—
218C2×C4×C11—42no—
219C2×C4×C11#12012yes—
220C2×C4×C11#12012yes—
221C2×C4×C11C22⋊Q812yes—
222C2×C4×C11C2×D812yes—
223C2×C4×C11C2×D812yes—
224C2×C4×C11AGL(1,ℤ/8)12yes—
225C2×C4×C11C22×D412yes—
226C2×C4×C11C22×Q811yescharacteristic
227C2×C4×C11C2×#4112yes—
228C2×C4×C11C2×#4111yescharacteristic
229C8×C11—44no—
230C23×D4C22×C1111yescharacteristic
231C24×C4—21no—
232C2×C4⋊Q8C22×C1111yescharacteristic, complemented
233C2×C22⋊Q8—21no—
234C2×C4×D4—28no—
235C2×C4×D4—21no—
236C2×C4×D4—21no—
237C2×C4×D4C22×C1112yes—
238C2×C4×D4C22×C1112yes—
239C22×C4⋊C4C22×C1111yescharacteristic
240C22×C22⋊C4—21no—
241C22×C42C22×C1111yescharacteristic
242#474—28no—
243C2×#107C22×C1114yescomplemented
244C2×C4⋊C8C22×C1112yescomplemented
245C2×#102C22×C1114yes—
246C2×#102C22×C1114yes—
247C2×C22⋊C8C22×C1112yes—
248#391—21no—
249#389—21no—
250#389C22×C1112yescomplemented
251#384C22×C1111yescharacteristic, complemented
252#380—21no—
253#380C22×C1112yes—
254#340C22×C1114yescomplemented
255#336C22×C1112yescomplemented
256C22×C11—22no—
257C22×C11—22no—
258C22×C11—22no—
259C22×C11—22no—
260C22×C11—22no—
261C22×C11—22no—
262C22×C11—28no—
263C22×C11—432no—
264C22×C11—44no—
265C22×C11—44no—
266C22×C11—44no—
267C22×C11—44no—
268C22×C11—44no—
269C22×C11—44no—
270C22×C11#47414yescomplemented
271C22×C11C2×#12011yescharacteristic
272C22×C11C2×C22⋊Q811yescharacteristic
273C22×C11#52511yescharacteristic
274C22×C11C22×D811yescharacteristic
275C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
276C22×C11C2×#13711yescharacteristic
277C22×C11#57511yescharacteristic
278C4×C11—22no—
279C4×C11—22no—
280C4×C11—22no—
281C4×C11—44no—
282C4×C11—41no—
283C4×C11—82no—
284C4×C11—82no—
285C4×C11#44714yes—
286C4×C11C2×C22⋊Q812yes—
287C4×C11#52512yes—
288C25—21no—
289C22×Q8—21no—
290C22×D4—24no—
291C22×D4—24no—
292C22×D4—21no—
293C22×D4—22no—
294C22×D4Q8×C1114yescomplemented
295C22×D4C23×C1112yes—
296C23×C4—28no—
297C23×C4—21no—
298C23×C4—22no—
299C23×C4—22no—
300C23×C4—44no—
301C23×C4—44no—
302C23×C4D4×C1111yescharacteristic
303C23×C4D4×C1111yescharacteristic
304C23×C4C23×C1111yescharacteristic
305C22×C8C23×C1114yes—
306C4⋊Q8—24no—
307C22⋊Q8—44no—
308C4×D4—28no—
309C4×D4—28no—
310C4×D4—24no—
311C4×D4—24no—
312C4×D4—24no—
313C4×D4D4×C1118yes—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4C23×C1112yes—
321C2×C4⋊C4C23×C1112yes—
322C2×C4⋊C4C23×C1112yes—
323C2×C22⋊C4—28no—
324C2×C22⋊C4—22no—
325C2×C22⋊C4—22no—
326C2×C22⋊C4—22no—
327C2×C42—24no—
328C2×C42D4×C1111yescharacteristic
329C2×C42D4×C1111yescharacteristic
330C2×C42C23×C1111yescharacteristic
331C2×C42C23×C1111yescharacteristic
332#107—28no—
333C4⋊C8—24no—
334#102—28no—
335#102—28no—
336C22⋊C8—24no—
337#95—22no—
338#95—22no—
339C2×C11—24no—
340C2×C11—48no—
341C2×C11#284811yescharacteristic
342C2×C11C2×#44711yescharacteristic
343C2×C11#300711yescharacteristic
344C2×C11C2×#47411yescharacteristic
345C2×C11#307711yescharacteristic
346C2×C11#310011yescharacteristic
347C2×C11#311011yescharacteristic
348C24—24no—
349C24—24no—
350C24—24no—
351C24—22no—
352C24—42no—
353C24—42no—
354C24—42no—
355C24—42no—
356C24C2×D4×C1111yescharacteristic
357C2×Q8—42no—
358C2×Q8—42no—
359C2×Q8—42no—
360C2×D4—24no—
361C2×D4—24no—
362C2×D4—216no—
363C2×D4—216no—
364C2×D4—24no—
365C2×D4—22no—
366C2×D4—22no—
367C2×D4—22no—
368C2×D4C2×D4×C1114yes—
369C2×D4C2×Q8×C1114yes—
370C2×D4C11×#4114yes—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—24no—
376C22×C4—28no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—28no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—41no—
384C22×C4—44no—
385C22×C4—432no—
386C22×C4—42no—
387C22×C4—42no—
388C22×C4—44no—
389C22×C4—44no—
390C22×C4—44no—
391C22×C4C11×D814yes—
392C22×C4C2×D4×C1111yescharacteristic
393C22×C4C2×D4×C1111yescharacteristic
394C22×C4C2×D4×C1111yescharacteristic
395C22×C4C2×D4×C1111yescharacteristic
396C22×C4C2×D4×C1111yescharacteristic
397C22×C4C2×Q8×C1112yes—
398C22×C4C11×#4112yes—
399C22×C4C24×C1111yescharacteristic
400C2×C8—24no—
401C2×C8—24no—
402C2×C8—24no—
403C4⋊C4—24no—
404C4⋊C4—22no—
405C4⋊C4—24no—
406C4⋊C4—24no—
407C4⋊C4—42no—
408C4⋊C4—42no—
409C4⋊C4—42no—
410C4⋊C4—44no—
411C4⋊C4C2×D4×C1114yes—
412C22⋊C4—28no—
413C22⋊C4—28no—
414C22⋊C4—44no—
415C42—22no—
416C42—22no—
417C42—22no—
418C42C2×D4×C1114yes—
419C11#3295311yescharacteristic, direct product factor, Sylow
420C23—21no—
421C23—21no—
422C23—21no—
423C23—21no—
424C23—216no—
425C23—24no—
426C23—24no—
427C23—24no—
428C23—48no—
429C23—48no—
430C23—48no—
431C23—48no—
432C23—48no—
433C23—42no—
434C23—42no—
435C23—42no—
436C23—42no—
437C23—48no—
438C23C11×C22⋊Q812yes—
439C23C2×C11×D812yes—
440C23C11×#13712yes—
441C23C22×D4×C1111yescharacteristic
442Q8—84no—
443D4—216no—
444D4—24no—
445D4—24no—
446D4—24no—
447D4C11×C22⋊Q818yescomplemented
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—24no—
455C2×C4—24no—
456C2×C4—28no—
457C2×C4—21no—
458C2×C4—24no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—44no—
462C2×C4—416no—
463C2×C4—48no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—416no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4C11×#12012yes—
474C2×C4C11×#12012yes—
475C2×C4C11×C22⋊Q812yes—
476C2×C4C2×C11×D812yes—
477C2×C4C2×C11×D812yes—
478C2×C4C11×AGL(1,ℤ/8)12yes—
479C2×C4C22×D4×C1112yes—
480C2×C4C22×Q8×C1111yescharacteristic
481C2×C4C2×C11×#4112yes—
482C2×C4C2×C11×#4111yescharacteristic
483C8—44no—
484C22—22no—
485C22—22no—
486C22—22no—
487C22—22no—
488C22—22no—
489C22—22no—
490C22—28no—
491C22—432no—
492C22—44no—
493C22—44no—
494C22—44no—
495C22—44no—
496C22—44no—
497C22—44no—
498C22C11×#47414yescomplemented
499C22C2×C11×#12011yescharacteristic
500C22C2×C11×C22⋊Q811yescharacteristic
501C22C11×#52511yescharacteristic
502C22C22×C11×D811yescharacteristic
503C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
504C22C2×C11×#13711yescharacteristic
505C22C11×#57511yescharacteristic
506C4—22no—
507C4—22no—
508C4—22no—
509C4—44no—
510C4—41no—
511C4—82no—
512C4—82no—
513C4C11×#44714yes—
514C4C2×C11×C22⋊Q812yes—
515C4C11×#52512yes—
516C2—24no—
517C2—48no—
518C2C11×#284811yescharacteristic
519C2C2×C11×#44711yescharacteristic
520C2C11×#300711yescharacteristic
521C2C2×C11×#47411yescharacteristic
522C2C11×#307711yescharacteristic
523C2C11×#310011yescharacteristic
524C2C11×#311011yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC23×D4×C11C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#474C2semidirect
3. C11×#2857C2semidirect
4. C11×#1862C2semidirect
5. C11×#1852C2semidirect
6. C11×#1802C2semidirect
7. C11×#1797C2semidirect
11. C2×C11×C4⋊Q8C22semidirect
22. C2×C11×#107C22semidirect
23. C2×C11×C4⋊C8C22semidirect
29. C11×#389C22semidirect
30. C11×#384C22semidirect
33. C11×#340C22semidirect
34. C11×#336C22semidirect
41. C22×D4×C11Q8semidirect
86. #32953C11direct (N × H)
159. C2×#474C2×C11semidirect
160. #2857C2×C11semidirect
161. #1862C2×C11semidirect
162. #1852C2×C11semidirect
163. #1802C2×C11semidirect
164. #1797C2×C11semidirect
193. D4×C11C22⋊Q8semidirect
232. C2×C4⋊Q8C22×C11semidirect
243. C2×#107C22×C11semidirect
244. C2×C4⋊C8C22×C11semidirect
250. #389C22×C11semidirect
251. #384C22×C11semidirect
254. #340C22×C11semidirect
255. #336C22×C11semidirect
270. C22×C11#474semidirect
294. C22×D4Q8×C11semidirect
419. C11#32953direct (N × H)
447. D4C11×C22⋊Q8semidirect
498. C22C11×#474semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D4×C112
C2×C11×#4742
C11×#28572
C11×#18622
C11×#18522
C11×#18022
C11×#17972
C11×#17862
#3295311