Finite Group Databasebeta

← #107×C22⋊D11 #14771888

Subgroups — #107×C22⋊D11 #14771888

Order 2816.

1126 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C8×C22⋊D11C211yesmaximal, characteristic
2C2×D11×#107C211yesmaximal, characteristic, complemented
3C4⋊C4×C22⋊D11C212yesmaximal
4#13069371C212yesmaximal, complemented
5#13068804C212yesmaximal, complemented
6#13068802C212yesmaximal, complemented
7#13068774C211yesmaximal, characteristic, complemented
8#13068645C211yesmaximal, characteristic, complemented
9#13068642C211yesmaximal, characteristic, complemented
10#107×Dic11C211yesmaximal, characteristic, complemented
11C22×C11×#107C211yesmaximal, characteristic, complemented
12C23×C8×C11C2211yescharacteristic
13C22×C11×C4⋊C4C2212yes—
14C2×C4×C22⋊D11—22no—
15C2×C4×C22⋊D11C2211yescharacteristic
16C22×C8×D11C2211yescharacteristic
17C2×C4⋊C4×D11C2212yes—
18C2×C11×#107—24no—
19C2×C11×#107C2212yes—
20C2×C11×#107C2211yescharacteristic
21C2×C11×#107C2211yescharacteristic
22#10622825C2212yes—
23#10622823—22no—
24C2×C22⋊(C11⋊C8)C2211yescharacteristic
25C8×C22⋊D11C418yescomplemented
26C2×(C2×D11)⋊C8C2211yescharacteristic
27C2×#66882C2211yescharacteristic
28C2×#66882C2211yescharacteristic
29C2×Dic11⋊C8C2211yescharacteristic
30C2×C8×Dic11C2211yescharacteristic
31#10622602—22no—
32#10622600C2212yes—
33#10622589C2212yes—
34C4⋊C4×Dic11C2212yes—
35#10622585—22no—
36C2×#66871C2212yes—
37C2×#66871C2212yes—
38D11×#107—24no—
39#10622189C2212yes—
40#10622167C2212yes—
41#10622167C2212yes—
42C23×C4×C11—22no—
43C23×C4×C11C2311yescharacteristic
44C22×C22⋊D11D411yescharacteristic
45C22×C4×D11—22no—
46C22×C4×D11C2311yescharacteristic
47C22×C8×C11—22no—
48C22×C8×C11—22no—
49C22×C8×C11C2×C414yescomplemented
50C22×C8×C11C2311yescharacteristic
51C22×C8×C11C2311yescharacteristic
52C2×C11×C4⋊C4—24no—
53C2×C11×C4⋊C4—22no—
54C2×C11×C4⋊C4—42no—
55C2×C11×C4⋊C4C2312yes—
56C2×C11×C4⋊C4C2312yes—
57C2×C22⋊Dic11—22no—
58C2×C22⋊Dic11D411yescharacteristic
59C4×C22⋊D11—48no—
60C4×C22⋊D11C2×C414yes—
61C4×C22⋊D11Q814yes—
62C2×(C2×D11)⋊C4—22no—
63C2×(C2×D11)⋊C4D411yescharacteristic
64C2×C4⋊Dic11C2312yes—
65C2×C4⋊Dic11C2312yes—
66C2×Dic11⋊C4—22no—
67C2×Dic11⋊C4—22no—
68C2×Dic11⋊C4—22no—
69C2×Dic11⋊C4D411yescharacteristic
70C2×C4×Dic11—22no—
71C2×C4×Dic11C2311yescharacteristic
72C22×C11⋊C8C2311yescharacteristic
73C22×C11⋊C8C2311yescharacteristic
74C2×C8×D11—22no—
75C2×C8×D11—22no—
76C2×C8×D11C2×C414yescomplemented
77C4⋊C4×D11—24no—
78C4⋊C4×D11—42no—
79C11×#107—22no—
80C11×#107—24no—
81C11×#107D414yescomplemented
82C11⋊#95—22no—
83C11⋊#95—22no—
84C11⋊#95—22no—
85C22⋊(C11⋊C8)C2×C414yescomplemented
86(C2×D11)⋊C8C2×C414yescomplemented
87#66882—22no—
88#66882—22no—
89Dic11⋊C8C2×C414yescomplemented
90C8×Dic11C2×C414yescomplemented
91#66871—24no—
92#66871—42no—
93D4×#107—111nomaximal, Sylow
94C24×C11C2×D411yescharacteristic
95C23×D11C2×D411yescharacteristic
96C22×C4×C11—21no—
97C22×C4×C11—21no—
98C22×C4×C11—21no—
99C22×C4×C11—21no—
100C22×C4×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11—44no—
103C22×C4×C11—44no—
104C22×C4×C11—82no—
105C22×C4×C11C22×C412yes—
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11C2×Q812yes—
108C22×C4×C11C2411yescharacteristic
109C2×C22⋊D11C4⋊C414yes—
110C2×C22⋊D11D814yes—
111C2×C22⋊D11Q1614yes—
112C22×Dic11—22no—
113C22×Dic11—22no—
114C22×Dic11C2×D411yescharacteristic
115C22×Dic11C2×D411yescharacteristic
116C22×Dic11C2×D411yescharacteristic
117C2×C4×D11—21no—
118C2×C4×D11—21no—
119C2×C4×D11—21no—
120C2×C4×D11—21no—
121C2×C4×D11—44no—
122C2×C4×D11—44no—
123C2×C4×D11—82no—
124C2×C4×D11C22×C412yes—
125C2×C4×D11C2×Q812yes—
126C2×C8×C11—28no—
127C2×C8×C11—21no—
128C2×C8×C11—21no—
129C2×C8×C11C22×C412yes—
130C2×C8×C11C22×C412yes—
131C2×C8×C11C2×D412yes—
132C2×C8×C11#4112yes—
133C11×C4⋊C4—22no—
134C11×C4⋊C4—22no—
135C11×C4⋊C4—22no—
136C11×C4⋊C4—44no—
137C11×C4⋊C4C2×D414yes—
138C22⋊Dic11—44no—
139C22⋊Dic11C4⋊C414yes—
140(C2×D11)⋊C4—44no—
141(C2×D11)⋊C4C4⋊C414yes—
142C4⋊Dic11—22no—
143C4⋊Dic11—22no—
144C4⋊Dic11—22no—
145C4⋊Dic11—22no—
146Dic11⋊C4—44no—
147Dic11⋊C4—44no—
148Dic11⋊C4—82no—
149Dic11⋊C4C4⋊C414yes—
150C4×Dic11—44no—
151C4×Dic11C22×C412yes—
152C4×Dic11C2×Q812yes—
153C2×C11⋊C8—21no—
154C2×C11⋊C8—21no—
155C2×C11⋊C8—21no—
156C2×C11⋊C8—21no—
157C2×C11⋊C8C22×C412yes—
158C2×C11⋊C8C22×C412yes—
159C8×D11—28no—
160C2×C8×D4—111no—
161C22×#107—111no—
162C22×#107D1111yescharacteristic, complemented
163D4×C4⋊C4—112no—
164#1947—112no—
165#1852—112no—
166#1852—112no—
167#1845—111no—
168#1808—111no—
169#1808—111no—
170C4×#107—111no—
171C23×C11—21no—
172C23×C11—21no—
173C23×C11—21no—
174C23×C11—21no—
175C23×C11C2×C4⋊C412yes—
176C23×C11C2×D812yes—
177C23×C11C2×Q1612yes—
178C23×C11C22×D411yescharacteristic
179C22×D11—21no—
180C22×D11—21no—
181C22×D11—21no—
182C22×D11—21no—
183C22×D11C2×C4⋊C412yes—
184C22×D11C2×D812yes—
185C22×D11C2×Q1612yes—
186C2×C4×C11—21no—
187C2×C4×C11—21no—
188C2×C4×C11—22no—
189C2×C4×C11—22no—
190C2×C4×C11—22no—
191C2×C4×C11—22no—
192C2×C4×C11—24no—
193C2×C4×C11—42no—
194C2×C4×C11—42no—
195C2×C4×C11—42no—
196C2×C4×C11—42no—
197C2×C4×C11—42no—
198C2×C4×C11—88no—
199C2×C4×C11C2×C4⋊C412yes—
200C2×C4×C11C23×C411yescharacteristic
201C2×C4×C11C22×D411yescharacteristic
202C2×C4×C11C22×Q811yescharacteristic
203C2×C4×C11C2×#4111yescharacteristic
204C2×C4×C11H(5,𝔽2)11yescharacteristic
205C2×C4×C112−1+411yescharacteristic
206C22⋊D11#107116yesdirect product factor
207C2×Dic11—21no—
208C2×Dic11—21no—
209C2×Dic11—21no—
210C2×Dic11—21no—
211C2×Dic11—42no—
212C2×Dic11—42no—
213C2×Dic11—42no—
214C2×Dic11—42no—
215C2×Dic11—42no—
216C2×Dic11—42no—
217C2×Dic11C2×C4⋊C412yes—
218C2×Dic11C2×C4⋊C412yes—
219C2×Dic11C2×C4⋊C412yes—
220C2×Dic11C2×D812yes—
221C2×Dic11C2×Q1612yes—
222C4×D11—22no—
223C4×D11—22no—
224C4×D11—22no—
225C4×D11—22no—
226C4×D11—88no—
227C8×C11—22no—
228C8×C11C4×D414yescomplemented
229C11⋊C8—22no—
230C11⋊C8—22no—
231C23×C8—111no—
232C23×C8C2×D1111yescharacteristic
233C2×C4×D4—111no—
234C2×C4×D4—222no—
235C22×C4⋊C4—112no—
236C22×C4⋊C4C2×D1112yes—
237C8×D4—118no—
238C2×#107—24no—
239C2×#107—111no—
240C2×#107—111no—
241C2×#107—112no—
242C2×#107—112no—
243C2×#107—224no—
244C2×#107C2×D1111yescharacteristic
245C2×#107C2×D1112yes—
246C2×#107C2×D1111yescharacteristic
247C2×C4⋊C8—111no—
248C2×C22⋊C8—111no—
249C2×C22⋊C8—111no—
250C2×C4×C8—111no—
251#389—222no—
252#385—222no—
253#385—222no—
254#384—112no—
255#380—112no—
256#380—112no—
257C4×C4⋊C4—112no—
258#340—112no—
259#340—112no—
260#340—112no—
261C22×C11—22no—
262C22×C11—22no—
263C22×C11—22no—
264C22×C11—22no—
265C22×C11—22no—
266C22×C11—22no—
267C22×C11C2×#10714yescomplemented
268C22×C11C22×C4⋊C411yescharacteristic
269C22×C11D4211yescharacteristic
270C22×C11#54711yescharacteristic
271C22×C11C22×D811yescharacteristic
272C22×C11C22×Q1611yescharacteristic
273C22×C11#57611yescharacteristic
274C22×C11#57811yescharacteristic
275C2×D11—22no—
276C2×D11—22no—
277C2×D11—22no—
278C2×D11—22no—
279C2×D11—22no—
280C2×D11—22no—
281C2×D11C2×#10714yescomplemented
282C4×C11—22no—
283C4×C11—44no—
284C4×C11—82no—
285C4×C11C2×C4×D411yescharacteristic
286C4×C11#52011yescharacteristic
287C4×C11D4×Q811yescharacteristic
288C4×C11#55411yescharacteristic
289Dic11—22no—
290Dic11—22no—
291Dic11—82no—
292Dic11—82no—
293Dic11C2×#10714yescomplemented
294C22×D4—111no—
295C23×C4—22no—
296C23×C4—111no—
297C23×C4—222no—
298C23×C4C22×D1111yescharacteristic
299C22×C8—22no—
300C22×C8—22no—
301C22×C8—111no—
302C22×C8—111no—
303C22×C8—114no—
304C22×C8—222no—
305C22×C8—222no—
306C22×C8C4×D1114yescomplemented
307C22×C8C22×D1111yescharacteristic
308C22×C8C22×D1111yescharacteristic
309C4×D4—114no—
310C4×D4—114no—
311C4×D4—448no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—42no—
315C2×C4⋊C4—111no—
316C2×C4⋊C4—112no—
317C2×C4⋊C4—112no—
318C2×C4⋊C4—224no—
319C2×C4⋊C4—222no—
320C2×C4⋊C4—222no—
321C2×C4⋊C4—222no—
322C2×C4⋊C4—442no—
323C2×C4⋊C4C22×D1112yes—
324C2×C4⋊C4C22×D1112yes—
325C2×C22⋊C4—111no—
326C2×C22⋊C4—111no—
327C2×C22⋊C4—222no—
328C2×C22⋊C4—222no—
329C2×C42—111no—
330C2×C42—222no—
331#107—22no—
332#107—24no—
333#107—222no—
334#107—222no—
335#107—224no—
336#107—442no—
337#107C22⋊D1114yesdirect product factor
338C4⋊C8—114no—
339C22⋊C8—114no—
340C22⋊C8—114no—
341C4×C8—114no—
342#95—222no—
343#95—222no—
344#95—222no—
345C2×C11—24no—
346C2×C11D4×C4⋊C411yescharacteristic
347C2×C11C22×#10711yescharacteristic
348C2×C11#291311yescharacteristic
349C2×C11D4×D811yescharacteristic
350C2×C11D4×Q1611yescharacteristic
351C2×C11#333411yescharacteristic
352C2×C11#333811yescharacteristic
353D11—24no—
354C24—111no—
355C24D4×D1111yescharacteristic
356C2×D4—114no—
357C2×D4—114no—
358C2×D4—114no—
359C22×C4—21no—
360C22×C4—21no—
361C22×C4—21no—
362C22×C4—21no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—44no—
366C22×C4—44no—
367C22×C4—82no—
368C22×C4—111no—
369C22×C4—111no—
370C22×C4—111no—
371C22×C4—112no—
372C22×C4—112no—
373C22×C4—221no—
374C22×C4—221no—
375C22×C4—221no—
376C22×C4—221no—
377C22×C4—222no—
378C22×C4—222no—
379C22×C4—444no—
380C22×C4—444no—
381C22×C4—882no—
382C22×C4C2×C4×D1112yes—
383C22×C4D4×D1111yescharacteristic
384C22×C4Q8×D1112yes—
385C22×C4C23×D1111yescharacteristic
386C2×C8—21no—
387C2×C8—21no—
388C2×C8—28no—
389C2×C8—112no—
390C2×C8—112no—
391C2×C8—221no—
392C2×C8—221no—
393C2×C8—221no—
394C2×C8—221no—
395C2×C8—228no—
396C2×C8C2×C4×D1112yes—
397C2×C8C2×C4×D1112yes—
398C2×C8#433912yes—
399C2×C8C2×C22⋊D1112yes—
400C4⋊C4—22no—
401C4⋊C4—22no—
402C4⋊C4—22no—
403C4⋊C4—44no—
404C4⋊C4—114no—
405C4⋊C4—222no—
406C4⋊C4—222no—
407C4⋊C4—222no—
408C4⋊C4—222no—
409C4⋊C4—444no—
410C4⋊C4—444no—
411C4⋊C4—882no—
412C4⋊C4C2×C22⋊D1114yes—
413C22⋊C4—114no—
414C22⋊C4—114no—
415C22⋊C4—444no—
416C22⋊C4—444no—
417C42—112no—
418C42—112no—
419C42—444no—
420C11D4×#10711yescharacteristic, complemented, Sylow
421C23—21no—
422C23—21no—
423C23—21no—
424C23—21no—
425C23—112no—
426C23—112no—
427C23—112no—
428C23—221no—
429C23—221no—
430C23—221no—
431C23—221no—
432C23C4⋊C4×D1112yes—
433C23D8×D1112yes—
434C23Q16×D1112yes—
435C23C2×D4×D1111yescharacteristic
436D4—1116no—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—22no—
440C2×C4—22no—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—24no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—42no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—88no—
450C2×C4—112no—
451C2×C4—112no—
452C2×C4—112no—
453C2×C4—112no—
454C2×C4—112no—
455C2×C4—221no—
456C2×C4—221no—
457C2×C4—221no—
458C2×C4—221no—
459C2×C4—222no—
460C2×C4—222no—
461C2×C4—222no—
462C2×C4—222no—
463C2×C4—442no—
464C2×C4—442no—
465C2×C4—442no—
466C2×C4—442no—
467C2×C4—442no—
468C2×C4—442no—
469C2×C4—888no—
470C2×C4C4⋊C4×D1112yes—
471C2×C4C22×C4×D1111yescharacteristic
472C2×C4C2×#433911yescharacteristic
473C2×C4#6703711yescharacteristic
474C2×C4C2×Q8×D1111yescharacteristic
475C2×C4#6704011yescharacteristic
476C2×C4C22×C22⋊D1111yescharacteristic
477C8—22no—
478C8—222no—
479C8—222no—
480C8C4×C22⋊D1114yescomplemented
481C22—22no—
482C22—22no—
483C22—22no—
484C22—22no—
485C22—22no—
486C22—22no—
487C22—114no—
488C22—222no—
489C22—222no—
490C22—222no—
491C22—222no—
492C22—222no—
493C22—222no—
494C22D11×#10714yescomplemented
495C22C2×C4⋊C4×D1111yescharacteristic
496C22#1062303811yescharacteristic
497C22C2×D8×D1111yescharacteristic
498C22#1062328811yescharacteristic
499C22C2×Q16×D1111yescharacteristic
500C22#1062329711yescharacteristic
501C22D4×C22⋊D1111yescharacteristic
502C4—22no—
503C4—44no—
504C4—82no—
505C4—114no—
506C4—222no—
507C4—222no—
508C4—882no—
509C4—882no—
510C4#1062303511yescharacteristic
511C4#1062304211yescharacteristic
512C4C2×C4×C22⋊D1111yescharacteristic
513C4Q8×C22⋊D1111yescharacteristic
514C2—24no—
515C2—224no—
516C2C4⋊C4×C22⋊D1111yescharacteristic
517C2C2×D11×#10711yescharacteristic
518C2#1307721211yescharacteristic
519C2D8×C22⋊D1111yescharacteristic
520C2Q16×C22⋊D1111yescharacteristic
521C2#1308096111yescharacteristic
522C2#1308100611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC22×C11×#107C2
socleC23×C11C22×D4
prime radicalC22×C22⋊D11D4
cosocleC22×C4×C11C24
hypercenterC22×#107D11
hypocenterC11D4×#107
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#107

Complements

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

NH ≅ G/Ntype
2. C2×D11×#107C2semidirect
4. #13069371C2semidirect
5. #13068804C2semidirect
6. #13068802C2semidirect
7. #13068774C2semidirect
8. #13068645C2semidirect
9. #13068642C2semidirect
10. #107×Dic11C2semidirect
11. C22×C11×#107C2semidirect
25. C8×C22⋊D11C4semidirect
49. C22×C8×C11C2×C4semidirect
76. C2×C8×D11C2×C4semidirect
81. C11×#107D4semidirect
85. C22⋊(C11⋊C8)C2×C4semidirect
86. (C2×D11)⋊C8C2×C4semidirect
89. Dic11⋊C8C2×C4semidirect
90. C8×Dic11C2×C4semidirect
162. C22×#107D11semidirect
206. C22⋊D11#107direct (N × H)
228. C8×C11C4×D4semidirect
267. C22×C11C2×#107semidirect
281. C2×D11C2×#107semidirect
293. Dic11C2×#107semidirect
306. C22×C8C4×D11semidirect
337. #107C22⋊D11direct (N × H)
420. C11D4×#107semidirect
480. C8C4×C22⋊D11semidirect
494. C22D11×#107semidirect

Maximal subgroups

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

subgroupindex
C2×C8×C22⋊D112
C2×D11×#1072
C4⋊C4×C22⋊D112
#130693712
#130688042
#130688022
#130687742
#130686452
#130686422
#107×Dic112
C22×C11×#1072
D4×#10711