Finite Group Databasebeta

← #13072158

Subgroups — #13072158

Order 1408.

922 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#121C211yesmaximal, characteristic, complemented
2C2×#66992C211yesmaximal, characteristic, complemented
3C2×#66990C211yesmaximal, characteristic, complemented
4C2×#66990C211yesmaximal, characteristic, complemented
5C2×D4×Dic11C211yesmaximal, characteristic, complemented
6C22×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
7#10622836C211yesmaximal, characteristic, complemented
8#10622833C211yesmaximal, characteristic, complemented
9#10622823C211yesmaximal, characteristic, complemented
10#10622607C211yesmaximal, characteristic, complemented
11#10622603C211yesmaximal, characteristic, complemented
12#10622574C211yesmaximal, characteristic, complemented
13#10622572C211yesmaximal, characteristic, complemented
14#10622571C211yesmaximal, characteristic, complemented
15#10622570C211yesmaximal, characteristic, complemented
16C24×D11C2211yescharacteristic
17C22×D4×C11C2211yescharacteristic
18C22×D4×C11C2211yescharacteristic
19C22×D4×C11C2211yescharacteristic, complemented
20C23×C4×C11C2211yescharacteristic
21C22×C22⋊D11C2211yescharacteristic
22C22×C22⋊D11C2211yescharacteristic
23C22×C22⋊D11C2211yescharacteristic
24C22×C22⋊D11C2211yescharacteristic
25C23×Dic11C2211yescharacteristic
26C23×Dic11C2211yescharacteristic, complemented
27C11×#121—24no—
28C2×C11×C4⋊C4C2211yescharacteristic, complemented
29C2×C11×C22⋊C4C2211yescharacteristic, complemented
30C2×C11×C22⋊C4C2211yescharacteristic, complemented
31C2×C22⋊Dic11C2211yescharacteristic
32C2×C22⋊Dic11C2211yescharacteristic
33C2×C22⋊Dic11C2211yescharacteristic, complemented
34C2×C22⋊Dic11C2211yescharacteristic, complemented
35C2×C22⋊Dic11C2211yescharacteristic, complemented
36#66992—24no—
37#66990—24no—
38#66990—24no—
39D4×Dic11—24no—
40C2×(C2×D11)⋊C4—24no—
41C2×(C2×D11)⋊C4C2211yescharacteristic
42C2×(C2×D11)⋊C4C2211yescharacteristic
43C2×(C2×D11)⋊C4C2211yescharacteristic
44C2×(C2×D11)⋊C4C2211yescharacteristic
45C2×(C2×D11)⋊C4C2211yescharacteristic
46C2×(C2×D11)⋊C4C2211yescharacteristic
47C2×(C2×D11)⋊C4C2211yescharacteristic
48C2×(C2×D11)⋊C4C2211yescharacteristic
49C2×C4⋊Dic11C2211yescharacteristic, complemented
50C2×Dic11⋊C4C2211yescharacteristic, complemented
51C2×Dic11⋊C4C2211yescharacteristic, complemented
52C2×C4×Dic11C2211yescharacteristic, complemented
53C11⋊#95C2211yescharacteristic, complemented
54C11⋊#95C2211yescharacteristic, complemented
55C11⋊#95C2211yescharacteristic, complemented
56C11⋊#95C2211yescharacteristic, complemented
57C24×C11C2311yescharacteristic
58C24×C11C2311yescharacteristic
59C24×C11C2311yescharacteristic
60C23×D11—22no—
61C23×D11—22no—
62C23×D11—22no—
63C23×D11—22no—
64C23×D11—22no—
65C23×D11—41no—
66C23×D11—41no—
67C23×D11C2311yescharacteristic
68C23×D11C2311yescharacteristic
69C2×D4×C11—22no—
70C2×D4×C11—22no—
71C2×D4×C11—22no—
72C2×D4×C11—22no—
73C2×D4×C11—22no—
74C2×D4×C11—22no—
75C2×D4×C11—22no—
76C2×D4×C11—41no—
77C2×D4×C11D414yescomplemented
78C22×C4×C11—22no—
79C22×C4×C11—22no—
80C22×C4×C11—41no—
81C22×C4×C11C2311yescharacteristic
82C22×C4×C11C2311yescharacteristic
83C22×C4×C11C2311yescharacteristic
84C22×C4×C11C2311yescharacteristic
85C2×C22⋊D11—22no—
86C2×C22⋊D11—22no—
87C2×C22⋊D11—22no—
88C2×C22⋊D11—22no—
89C2×C22⋊D11—22no—
90C2×C22⋊D11—22no—
91C2×C22⋊D11—22no—
92C2×C22⋊D11—22no—
93C2×C22⋊D11—41no—
94C2×C22⋊D11—41no—
95C2×C22⋊D11—41no—
96C2×C22⋊D11—41no—
97C22×Dic11—22no—
98C22×Dic11—22no—
99C22×Dic11—22no—
100C22×Dic11—22no—
101C22×Dic11—41no—
102C22×Dic11—41no—
103C22×Dic11C2311yescharacteristic
104C22×Dic11C2311yescharacteristic
105C22×Dic11C2311yescharacteristic
106C22×Dic11C2311yescharacteristic
107C22×Dic11C2311yescharacteristic
108C22×Dic11C2311yescharacteristic
109C11×C4⋊C4—22no—
110C11×C22⋊C4—22no—
111C11×C22⋊C4—22no—
112C22⋊Dic11—22no—
113C22⋊Dic11—22no—
114C22⋊Dic11—22no—
115C22⋊Dic11—41no—
116C22⋊Dic11D414yescomplemented
117(C2×D11)⋊C4—22no—
118(C2×D11)⋊C4—22no—
119(C2×D11)⋊C4—22no—
120(C2×D11)⋊C4—22no—
121(C2×D11)⋊C4—22no—
122(C2×D11)⋊C4—22no—
123(C2×D11)⋊C4—22no—
124(C2×D11)⋊C4D414yescomplemented
125C4⋊Dic11—22no—
126Dic11⋊C4—22no—
127Dic11⋊C4—41no—
128C4×Dic11—22no—
129#2424—111nomaximal, Sylow
130C23×C11—21no—
131C23×C11—21no—
132C23×C11—21no—
133C23×C11—21no—
134C23×C11—21no—
135C23×C11—21no—
136C23×C11—21no—
137C23×C11—21no—
138C23×C11—21no—
139C23×C11—21no—
140C23×C11—21no—
141C23×C11—21no—
142C23×C11—21no—
143C23×C11—21no—
144C23×C11—21no—
145C23×C11—21no—
146C23×C11—21no—
147C23×C11C2×D412yes—
148C23×C11C2×D412yes—
149C23×C11C2×D412yes—
150C23×C11#4112yes—
151C23×C11C2411yescharacteristic
152C22×D11—28no—
153C22×D11—21no—
154C22×D11—21no—
155C22×D11—21no—
156C22×D11—21no—
157C22×D11—21no—
158C22×D11—21no—
159C22×D11—21no—
160C22×D11—21no—
161C22×D11—21no—
162C22×D11—21no—
163C22×D11—21no—
164C22×D11—21no—
165C22×D11—44no—
166C22×D11—44no—
167C22×D11—44no—
168C22×D11—44no—
169C22×D11—44no—
170C22×D11—44no—
171C22×D11C2×D412yes—
172C22×D11#4112yes—
173D4×C11—28no—
174D4×C11—44no—
175D4×C11—44no—
176C2×C4×C11—21no—
177C2×C4×C11—21no—
178C2×C4×C11—21no—
179C2×C4×C11—21no—
180C2×C4×C11—21no—
181C2×C4×C11—21no—
182C2×C4×C11—21no—
183C2×C4×C11—21no—
184C2×C4×C11—21no—
185C2×C4×C11—21no—
186C2×C4×C11—44no—
187C2×C4×C11C2×D412yes—
188C2×C4×C11C2×D412yes—
189C22⋊D11—44no—
190C22⋊D11—44no—
191C22⋊D11—44no—
192C22⋊D11—44no—
193C2×Dic11—21no—
194C2×Dic11—21no—
195C2×Dic11—21no—
196C2×Dic11—21no—
197C2×Dic11—21no—
198C2×Dic11—21no—
199C2×Dic11—21no—
200C2×Dic11—21no—
201C2×Dic11—21no—
202C2×Dic11—21no—
203C2×Dic11—21no—
204C2×Dic11—21no—
205C2×Dic11—21no—
206C2×Dic11—21no—
207C2×Dic11—21no—
208C2×Dic11—44no—
209C2×Dic11—44no—
210C2×Dic11C2×D412yes—
211C2×Dic11C2×D412yes—
212C2×Dic11C2×D412yes—
213C2×#121—111no—
214C2×#121D1111yescharacteristic, complemented
215C2×#120—111no—
216C2×#120—111no—
217C2×C4×D4—111no—
218C22×C22⋊C4—111no—
219#396—111no—
220#394—111no—
221#394—111no—
222#392—111no—
223#390—111no—
224#388—111no—
225#386—111no—
226#386—111no—
227#385—111no—
228C22×C11—22no—
229C22×C11—22no—
230C22×C11—22no—
231C22×C11—22no—
232C22×C11—22no—
233C22×C11—22no—
234C22×C11—22no—
235C22×C11—22no—
236C22×C11—22no—
237C22×C11—41no—
238C22×C11—41no—
239C22×C11—41no—
240C22×C11—41no—
241C22×C11—41no—
242C22×C11—41no—
243C22×C11—41no—
244C22×C11—41no—
245C22×C11—41no—
246C22×C11—41no—
247C22×C11—41no—
248C22×C11#12114yescomplemented
249C22×C11C22×D411yescharacteristic
250C22×C11C22×D411yescharacteristic
251C22×C11C22×D411yescharacteristic
252C22×C11C2×#4111yescharacteristic
253C22×C11C2×#4111yescharacteristic
254C22×C11H(5,𝔽2)11yescharacteristic
255C22×C11H(5,𝔽2)11yescharacteristic
256C2×D11—22no—
257C2×D11—22no—
258C2×D11—22no—
259C2×D11—22no—
260C2×D11—22no—
261C2×D11—22no—
262C2×D11—416no—
263C2×D11—41no—
264C2×D11—41no—
265C2×D11—41no—
266C2×D11—41no—
267C2×D11—41no—
268C2×D11—41no—
269C2×D11—41no—
270C2×D11—41no—
271C4×C11—22no—
272C4×C11—22no—
273C4×C11—41no—
274C4×C11—41no—
275Dic11—22no—
276Dic11—22no—
277Dic11—22no—
278Dic11—41no—
279Dic11—41no—
280Dic11—41no—
281C25—111no—
282C22×D4—111no—
283C22×D4—111no—
284C22×D4—111no—
285C22×D4—111no—
286C22×D4C2×D1111yescharacteristic
287C22×D4C2×D1111yescharacteristic
288C22×D4C2×D1111yescharacteristic, complemented
289C23×C4—111no—
290C23×C4—111no—
291C23×C4C2×D1111yescharacteristic
292#121—24no—
293#121—224no—
294#120—224no—
295#120—224no—
296C4×D4—224no—
297C2×C4⋊C4—111no—
298C2×C4⋊C4—111no—
299C2×C4⋊C4—111no—
300C2×C4⋊C4C2×D1111yescharacteristic, complemented
301C2×C22⋊C4—111no—
302C2×C22⋊C4—111no—
303C2×C22⋊C4—111no—
304C2×C22⋊C4—111no—
305C2×C22⋊C4—111no—
306C2×C22⋊C4—111no—
307C2×C22⋊C4—111no—
308C2×C22⋊C4—111no—
309C2×C22⋊C4—111no—
310C2×C22⋊C4—111no—
311C2×C22⋊C4—111no—
312C2×C22⋊C4—111no—
313C2×C22⋊C4—111no—
314C2×C22⋊C4—224no—
315C2×C22⋊C4C2×D1111yescharacteristic, complemented
316C2×C22⋊C4C2×D1111yescharacteristic, complemented
317C2×C42—111no—
318#95—111no—
319#95—111no—
320#95—111no—
321#95—111no—
322C2×C11—24no—
323C2×C11—42no—
324C2×C11—81no—
325C2×C11C2×#12111yescharacteristic
326C2×C11#52511yescharacteristic
327C2×C11#53811yescharacteristic
328C2×C11D4211yescharacteristic
329C2×C11D4211yescharacteristic
330C2×C11#54611yescharacteristic
331C2×C11#54611yescharacteristic
332D11—42no—
333D11—42no—
334C24—111no—
335C24—111no—
336C24—222no—
337C24—222no—
338C24—222no—
339C24—222no—
340C24—222no—
341C24—441no—
342C24—441no—
343C24C22×D1111yescharacteristic
344C24C22×D1111yescharacteristic
345C24C22×D1111yescharacteristic
346C2×D4—22no—
347C2×D4—22no—
348C2×D4—22no—
349C2×D4—22no—
350C2×D4—22no—
351C2×D4—22no—
352C2×D4—22no—
353C2×D4—41no—
354C2×D4—222no—
355C2×D4—222no—
356C2×D4—222no—
357C2×D4—222no—
358C2×D4—222no—
359C2×D4—222no—
360C2×D4—222no—
361C2×D4—222no—
362C2×D4—441no—
363C2×D4—441no—
364C2×D4—441no—
365C2×D4—441no—
366C2×D4C22⋊D1114yescomplemented
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—41no—
370C22×C4—111no—
371C22×C4—111no—
372C22×C4—111no—
373C22×C4—111no—
374C22×C4—111no—
375C22×C4—111no—
376C22×C4—222no—
377C22×C4—222no—
378C22×C4—222no—
379C22×C4—222no—
380C22×C4—441no—
381C22×C4—441no—
382C22×C4C22×D1111yescharacteristic
383C22×C4C22×D1111yescharacteristic
384C22×C4C22×D1111yescharacteristic
385C22×C4C22×D1111yescharacteristic
386C4⋊C4—22no—
387C4⋊C4—222no—
388C4⋊C4—222no—
389C4⋊C4—441no—
390C22⋊C4—22no—
391C22⋊C4—22no—
392C22⋊C4—114no—
393C22⋊C4—114no—
394C22⋊C4—222no—
395C22⋊C4—222no—
396C22⋊C4—222no—
397C22⋊C4—222no—
398C22⋊C4—222no—
399C22⋊C4—222no—
400C22⋊C4—222no—
401C22⋊C4—222no—
402C22⋊C4—222no—
403C22⋊C4—222no—
404C22⋊C4—441no—
405C42—222no—
406C11#242411yescharacteristic, complemented, Sylow
407C23—21no—
408C23—21no—
409C23—21no—
410C23—21no—
411C23—21no—
412C23—21no—
413C23—21no—
414C23—21no—
415C23—21no—
416C23—21no—
417C23—21no—
418C23—21no—
419C23—21no—
420C23—21no—
421C23—21no—
422C23—21no—
423C23—21no—
424C23—112no—
425C23—112no—
426C23—228no—
427C23—221no—
428C23—221no—
429C23—221no—
430C23—221no—
431C23—221no—
432C23—221no—
433C23—221no—
434C23—221no—
435C23—221no—
436C23—221no—
437C23—221no—
438C23—221no—
439C23—444no—
440C23—444no—
441C23—444no—
442C23—444no—
443C23—444no—
444C23—444no—
445C23D4×D1112yes—
446C23#434112yes—
447C23C2×C22⋊D1112yes—
448C23C2×C22⋊D1112yes—
449C23C23×D1111yescharacteristic
450D4—28no—
451D4—44no—
452D4—44no—
453D4—444no—
454D4—444no—
455D4—444no—
456D4—444no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—44no—
468C2×C4—112no—
469C2×C4—112no—
470C2×C4—112no—
471C2×C4—221no—
472C2×C4—221no—
473C2×C4—221no—
474C2×C4—221no—
475C2×C4—221no—
476C2×C4—221no—
477C2×C4—221no—
478C2×C4—221no—
479C2×C4—221no—
480C2×C4—221no—
481C2×C4—221no—
482C2×C4—221no—
483C2×C4—221no—
484C2×C4—221no—
485C2×C4—221no—
486C2×C4—444no—
487C2×C4—444no—
488C2×C4D4×D1112yes—
489C2×C4C2×C22⋊D1112yes—
490C22—22no—
491C22—22no—
492C22—22no—
493C22—22no—
494C22—22no—
495C22—22no—
496C22—22no—
497C22—22no—
498C22—22no—
499C22—41no—
500C22—41no—
501C22—41no—
502C22—41no—
503C22—41no—
504C22—41no—
505C22—41no—
506C22—41no—
507C22—41no—
508C22—41no—
509C22—41no—
510C22—222no—
511C22—222no—
512C22—222no—
513C22—222no—
514C22—222no—
515C22—222no—
516C22—4416no—
517C22—441no—
518C22—441no—
519C22—441no—
520C22—441no—
521C22—441no—
522C22—441no—
523C22—441no—
524C22—441no—
525C22#6699214yescomplemented
526C22C2×D4×D1111yescharacteristic
527C22C2×D4×D1111yescharacteristic
528C22C2×#434111yescharacteristic
529C22#6703711yescharacteristic
530C22#41×D1111yescharacteristic
531C22#6704211yescharacteristic
532C22C22×C22⋊D1111yescharacteristic
533C4—22no—
534C4—22no—
535C4—41no—
536C4—41no—
537C4—222no—
538C4—222no—
539C4—222no—
540C4—441no—
541C4—441no—
542C4—441no—
543C2—24no—
544C2—42no—
545C2—81no—
546C2—442no—
547C2—442no—
548C2#1062313711yescharacteristic
549C2#1062314011yescharacteristic
550C2#1062314111yescharacteristic
551C2#1062314811yescharacteristic
552C2D4×C22⋊D1111yescharacteristic
553C2C2×#6699211yescharacteristic
554C2#1062336011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC2×C11×#121C2
hypercenterC2×#121D11
hypocenterC11#2424
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C2×C11×#121C2semidirect
2. C2×#66992C2semidirect
3. C2×#66990C2semidirect
4. C2×#66990C2semidirect
5. C2×D4×Dic11C2semidirect
6. C22×(C2×D11)⋊C4C2semidirect
7. #10622836C2semidirect
8. #10622833C2semidirect
9. #10622823C2semidirect
10. #10622607C2semidirect
11. #10622603C2semidirect
12. #10622574C2semidirect
13. #10622572C2semidirect
14. #10622571C2semidirect
15. #10622570C2semidirect
19. C22×D4×C11C22semidirect
26. C23×Dic11C22semidirect
28. C2×C11×C4⋊C4C22semidirect
29. C2×C11×C22⋊C4C22semidirect
30. C2×C11×C22⋊C4C22semidirect
33. C2×C22⋊Dic11C22semidirect
34. C2×C22⋊Dic11C22semidirect
35. C2×C22⋊Dic11C22semidirect
49. C2×C4⋊Dic11C22semidirect
50. C2×Dic11⋊C4C22semidirect
51. C2×Dic11⋊C4C22semidirect
52. C2×C4×Dic11C22semidirect
53. C11⋊#95C22semidirect
54. C11⋊#95C22semidirect
55. C11⋊#95C22semidirect
56. C11⋊#95C22semidirect
77. C2×D4×C11D4semidirect
116. C22⋊Dic11D4semidirect
124. (C2×D11)⋊C4D4semidirect
214. C2×#121D11semidirect
248. C22×C11#121semidirect
288. C22×D4C2×D11semidirect
300. C2×C4⋊C4C2×D11semidirect
315. C2×C22⋊C4C2×D11semidirect
316. C2×C22⋊C4C2×D11semidirect
366. C2×D4C22⋊D11semidirect
406. C11#2424semidirect
525. C22#66992semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#1212
C2×#669922
C2×#669902
C2×D4×Dic112
C22×(C2×D11)⋊C42
#106228362
#106228332
#106228232
#106226072
#106226032
#106225742
#106225722
#106225712
#106225702
#242411