Finite Group Databasebeta

← #13074830

Subgroups — #13074830

Order 1408.

932 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#120C211yesmaximal, characteristic, complemented
2C2×#67006C211yesmaximal, characteristic, complemented
3C2×#67006C211yesmaximal, characteristic, complemented
4C2×#66993C211yesmaximal, characteristic, complemented
5C2×#66991C211yesmaximal, characteristic, complemented
6C2×#66937C211yesmaximal, characteristic, complemented
7#10622836C211yesmaximal, characteristic, complemented
8#10622836C211yesmaximal, characteristic, complemented
9#10622836C211yesmaximal, characteristic, complemented
10#10622835C211yesmaximal, characteristic, complemented
11#10622574C211yesmaximal, characteristic, complemented
12#10622573C211yesmaximal, characteristic, complemented
13#10622569C211yesmaximal, characteristic, complemented
14#10622564C211yesmaximal, characteristic, complemented
15#10622558C211yesmaximal, characteristic, complemented
16C25×C11C2211yescharacteristic
17C22×D4×C11C2211yescharacteristic
18C22×D4×C11C2211yescharacteristic
19C22×D4×C11C2211yescharacteristic
20C22×C22⋊D11C2211yescharacteristic
21C22×C22⋊D11C2211yescharacteristic
22C22×C22⋊D11C2211yescharacteristic
23C22×C22⋊D11C2211yescharacteristic
24C22×C22⋊D11C2211yescharacteristic
25C22×C22⋊D11C2211yescharacteristic
26C22×C22⋊D11C2211yescharacteristic, complemented
27C22×C22⋊D11C2211yescharacteristic, complemented
28C22×D44C2211yescharacteristic, complemented
29C22×C4×D11C2211yescharacteristic, complemented
30C11×#120—24no—
31C2×C11×C22⋊C4C2211yescharacteristic
32C2×C11×C22⋊C4C2211yescharacteristic
33C2×C11×C22⋊C4C2211yescharacteristic
34#67006—24no—
35#67006—24no—
36C2×C22⋊Dic11C2211yescharacteristic
37C2×C22⋊Dic11C2211yescharacteristic
38C2×C22⋊Dic11C2211yescharacteristic
39C2×C22⋊Dic11C2211yescharacteristic
40C2×C22⋊Dic11C2211yescharacteristic
41C2×C22⋊Dic11C2211yescharacteristic
42C2×C22⋊Dic11C2211yescharacteristic, complemented
43C2×C22⋊Dic11C2211yescharacteristic, complemented
44#66993—24no—
45#66991—24no—
46C2×(C2×D11)⋊C4C2211yescharacteristic, complemented
47C2×(C2×D11)⋊C4C2211yescharacteristic, complemented
48C2×(C2×D11)⋊C4C2211yescharacteristic, complemented
49C2×C4⋊Dic11C2211yescharacteristic, complemented
50C2×Dic11⋊C4C2211yescharacteristic, complemented
51C2×C4×Dic11C2211yescharacteristic, complemented
52#66937—24no—
53C11⋊#95C2211yescharacteristic, complemented
54C11⋊#95C2211yescharacteristic, complemented
55C11⋊#95C2211yescharacteristic, complemented
56C11⋊#95C2211yescharacteristic, complemented
57C24×C11—22no—
58C24×C11—22no—
59C24×C11—22no—
60C24×C11—41no—
61C24×C11—41no—
62C24×C11—41no—
63C24×C11—41no—
64C24×C11C2311yescharacteristic
65C24×C11C2311yescharacteristic
66C24×C11C2311yescharacteristic
67C24×C11C2311yescharacteristic
68C23×D11C2311yescharacteristic
69C23×D11C2311yescharacteristic
70C2×D4×C11—22no—
71C2×D4×C11—22no—
72C2×D4×C11—22no—
73C2×D4×C11—22no—
74C2×D4×C11—22no—
75C2×D4×C11—41no—
76C2×D4×C11—41no—
77C2×D4×C11—41no—
78C2×D4×C11—41no—
79C22×C4×C11C2311yescharacteristic
80C22×C4×C11C2311yescharacteristic
81C22×C4×C11C2311yescharacteristic
82C2×C22⋊D11—22no—
83C2×C22⋊D11—22no—
84C2×C22⋊D11—22no—
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—22no—
94C2×C22⋊D11—41no—
95C2×C22⋊D11—41no—
96C2×C22⋊D11—41no—
97C2×C22⋊D11—41no—
98C2×C22⋊D11—41no—
99C2×C22⋊D11—41no—
100C2×C22⋊D11—41no—
101C2×C22⋊D11—41no—
102C2×C22⋊D11—41no—
103C2×C22⋊D11—41no—
104C2×C22⋊D11—41no—
105C2×C22⋊D11D414yescomplemented
106C22×Dic11C2311yescharacteristic
107C22×Dic11C2311yescharacteristic
108C22×Dic11C2311yescharacteristic
109C22×Dic11C2311yescharacteristic
110C22×Dic11C2311yescharacteristic
111C22×Dic11C2311yescharacteristic
112C2×D44—22no—
113C2×D44—22no—
114C2×D44—41no—
115C2×C4×D11—22no—
116C2×C4×D11—22no—
117C2×C4×D11—41no—
118C11×C22⋊C4—22no—
119C11×C22⋊C4—22no—
120C11×C22⋊C4D414yescomplemented
121C22⋊Dic11—22no—
122C22⋊Dic11—22no—
123C22⋊Dic11—22no—
124C22⋊Dic11—22no—
125C22⋊Dic11—22no—
126C22⋊Dic11—22no—
127C22⋊Dic11—41no—
128C22⋊Dic11D414yescomplemented
129(C2×D11)⋊C4—22no—
130(C2×D11)⋊C4—41no—
131(C2×D11)⋊C4—41no—
132C4⋊Dic11—22no—
133Dic11⋊C4—22no—
134C4×Dic11—22no—
135#2669—111nomaximal, Sylow
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×C11—21no—
148C23×C11—21no—
149C23×C11—21no—
150C23×C11—21no—
151C23×C11—21no—
152C23×C11—21no—
153C23×C11—21no—
154C23×C11—21no—
155C23×C11—21no—
156C23×C11—21no—
157C23×C11—21no—
158C23×C11—21no—
159C23×C11—21no—
160C23×C11—21no—
161C23×C11—44no—
162C23×C11—44no—
163C23×C11—44no—
164C23×C11—44no—
165C23×C11—44no—
166C23×C11—44no—
167C23×C11—44no—
168C23×C11C2×D412yes—
169C23×C11C2×D412yes—
170C23×C11C2×D412yes—
171C23×C11C2411yescharacteristic
172C22×D11—21no—
173C22×D11—21no—
174C22×D11—21no—
175C22×D11—21no—
176C22×D11—21no—
177C22×D11—21no—
178C22×D11—21no—
179C22×D11—21no—
180C22×D11—21no—
181C22×D11—21no—
182C22×D11—21no—
183C22×D11—21no—
184C22×D11—21no—
185C22×D11C2×D412yes—
186D4×C11—44no—
187D4×C11—44no—
188D4×C11—44no—
189C2×C4×C11—21no—
190C2×C4×C11—21no—
191C2×C4×C11—21no—
192C2×C4×C11—21no—
193C2×C4×C11—21no—
194C2×C4×C11—21no—
195C2×C4×C11—21no—
196C2×C4×C11C2×D412yes—
197C2×C4×C11C2×D412yes—
198C22⋊D11—44no—
199C22⋊D11—44no—
200C22⋊D11—44no—
201C22⋊D11—44no—
202C22⋊D11—44no—
203C22⋊D11—44no—
204C22⋊D11—44no—
205C22⋊D11—44no—
206C2×Dic11—21no—
207C2×Dic11—21no—
208C2×Dic11—21no—
209C2×Dic11—21no—
210C2×Dic11—21no—
211C2×Dic11—21no—
212C2×Dic11—21no—
213C2×Dic11—21no—
214C2×Dic11—21no—
215C2×Dic11—21no—
216C2×Dic11—21no—
217C2×Dic11—21no—
218C2×Dic11—21no—
219C2×Dic11—21no—
220C2×Dic11—21no—
221C2×Dic11C2×D412yes—
222C2×Dic11C2×D412yes—
223C2×Dic11C2×D412yes—
224D44—44no—
225C4×D11—44no—
226C2×#127—111no—
227C2×#121—111no—
228C2×#121—111no—
229C2×#120—111no—
230C2×#120—111no—
231C2×#120D1111yescharacteristic, complemented
232#394—111no—
233#394—111no—
234#392—111no—
235#392—111no—
236#392—111no—
237#392—111no—
238#388—111no—
239#388—111no—
240#386—111no—
241C22×C11—22no—
242C22×C11—22no—
243C22×C11—22no—
244C22×C11—22no—
245C22×C11—22no—
246C22×C11—22no—
247C22×C11—22no—
248C22×C11—22no—
249C22×C11—22no—
250C22×C11—416no—
251C22×C11—41no—
252C22×C11—41no—
253C22×C11—41no—
254C22×C11—41no—
255C22×C11—41no—
256C22×C11—41no—
257C22×C11—41no—
258C22×C11—41no—
259C22×C11—41no—
260C22×C11—41no—
261C22×C11—41no—
262C22×C11—41no—
263C22×C11—41no—
264C22×C11—41no—
265C22×C11—41no—
266C22×C11—41no—
267C22×C11—41no—
268C22×C11—41no—
269C22×C11—41no—
270C22×C11C22×D411yescharacteristic
271C22×C11C22×D411yescharacteristic
272C22×C11C22×D411yescharacteristic
273C22×C11H(5,𝔽2)11yescharacteristic
274C22×C11H(5,𝔽2)11yescharacteristic
275C22×C11H(5,𝔽2)11yescharacteristic
276C22×C11H(5,𝔽2)11yescharacteristic
277C2×D11—22no—
278C2×D11—22no—
279C2×D11—22no—
280C2×D11—41no—
281C2×D11—41no—
282C2×D11—41no—
283C2×D11—41no—
284C2×D11—41no—
285C2×D11—41no—
286C2×D11—41no—
287C2×D11—41no—
288C2×D11—41no—
289C2×D11—41no—
290C2×D11—41no—
291C4×C11—22no—
292C4×C11—22no—
293C4×C11—41no—
294Dic11—22no—
295Dic11—22no—
296Dic11—22no—
297Dic11—41no—
298Dic11—41no—
299Dic11—41no—
300C25C2×D1111yescharacteristic
301C22×D4—111no—
302C22×D4—111no—
303C22×D4—111no—
304C22×D4—111no—
305C22×D4—111no—
306C22×D4—111no—
307C22×D4—111no—
308C22×D4—111no—
309C22×D4—111no—
310C22×D4C2×D1111yescharacteristic
311C22×D4C2×D1111yescharacteristic
312C22×D4C2×D1111yescharacteristic
313C23×C4—111no—
314#127—224no—
315#121—224no—
316#121—224no—
317#120—24no—
318#120—224no—
319#120—224no—
320C2×C4⋊C4—111no—
321C2×C4⋊C4—111no—
322C2×C22⋊C4—111no—
323C2×C22⋊C4—111no—
324C2×C22⋊C4—111no—
325C2×C22⋊C4—111no—
326C2×C22⋊C4—111no—
327C2×C22⋊C4—111no—
328C2×C22⋊C4—111no—
329C2×C22⋊C4—111no—
330C2×C22⋊C4—111no—
331C2×C22⋊C4—111no—
332C2×C22⋊C4—111no—
333C2×C22⋊C4C2×D1111yescharacteristic
334C2×C22⋊C4C2×D1111yescharacteristic
335C2×C22⋊C4C2×D1111yescharacteristic
336C2×C42—111no—
337#95—111no—
338#95—111no—
339#95—111no—
340#95—111no—
341C2×C11—42no—
342C2×C11—42no—
343C2×C11—42no—
344C2×C11—81no—
345C2×C11#53411yescharacteristic
346C2×C11#53511yescharacteristic
347C2×C11#53511yescharacteristic
348C2×C11D4211yescharacteristic
349C2×C11D4211yescharacteristic
350C2×C11D4211yescharacteristic
351C2×C11#56011yescharacteristic
352D11—42no—
353D11—81no—
354C24—22no—
355C24—22no—
356C24—22no—
357C24—41no—
358C24—41no—
359C24—41no—
360C24—41no—
361C24—111no—
362C24—111no—
363C24C22×D1111yescharacteristic
364C24C22×D1111yescharacteristic
365C24C22×D1111yescharacteristic
366C24C22×D1111yescharacteristic
367C2×D4—22no—
368C2×D4—22no—
369C2×D4—22no—
370C2×D4—22no—
371C2×D4—22no—
372C2×D4—41no—
373C2×D4—41no—
374C2×D4—41no—
375C2×D4—41no—
376C2×D4—114no—
377C2×D4—222no—
378C2×D4—222no—
379C2×D4—222no—
380C2×D4—222no—
381C2×D4—222no—
382C2×D4—222no—
383C2×D4—222no—
384C2×D4—222no—
385C2×D4—222no—
386C2×D4—222no—
387C2×D4—222no—
388C2×D4—222no—
389C2×D4—222no—
390C2×D4—222no—
391C2×D4—441no—
392C2×D4—441no—
393C2×D4—441no—
394C2×D4—441no—
395C2×D4—441no—
396C2×D4—441no—
397C2×D4—441no—
398C2×D4—441no—
399C2×D4—441no—
400C2×D4—441no—
401C2×D4—441no—
402C2×D4—441no—
403C22×C4—111no—
404C22×C4—111no—
405C22×C4—111no—
406C22×C4—111no—
407C22×C4—111no—
408C22×C4—111no—
409C22×C4—222no—
410C22×C4—222no—
411C22×C4—441no—
412C22×C4C22×D1111yescharacteristic
413C22×C4C22×D1111yescharacteristic
414C22×C4C22×D1111yescharacteristic
415C4⋊C4—222no—
416C4⋊C4—222no—
417C22⋊C4—22no—
418C22⋊C4—22no—
419C22⋊C4—114no—
420C22⋊C4—222no—
421C22⋊C4—222no—
422C22⋊C4—222no—
423C22⋊C4—222no—
424C22⋊C4—222no—
425C22⋊C4—222no—
426C22⋊C4—222no—
427C22⋊C4—441no—
428C22⋊C4—441no—
429C22⋊C4—441no—
430C22⋊C4C22⋊D1114yescomplemented
431C42—222no—
432C11#266911yescharacteristic, complemented, Sylow
433C23—21no—
434C23—21no—
435C23—21no—
436C23—21no—
437C23—21no—
438C23—21no—
439C23—21no—
440C23—21no—
441C23—21no—
442C23—21no—
443C23—21no—
444C23—21no—
445C23—21no—
446C23—21no—
447C23—21no—
448C23—21no—
449C23—21no—
450C23—21no—
451C23—21no—
452C23—21no—
453C23—21no—
454C23—21no—
455C23—21no—
456C23—21no—
457C23—21no—
458C23—44no—
459C23—44no—
460C23—44no—
461C23—44no—
462C23—44no—
463C23—44no—
464C23—44no—
465C23—112no—
466C23—221no—
467C23—221no—
468C23—221no—
469C23—221no—
470C23—221no—
471C23—221no—
472C23—221no—
473C23—221no—
474C23—221no—
475C23—221no—
476C23—221no—
477C23—221no—
478C23—221no—
479C23D4×D1112yes—
480C23D4×D1112yes—
481C23C2×C22⋊D1112yes—
482C23C23×D1111yescharacteristic
483D4—44no—
484D4—44no—
485D4—44no—
486D4—444no—
487D4—444no—
488D4—444no—
489D4—444no—
490D4—444no—
491D4—444no—
492D4—444no—
493D4—444no—
494D4—444no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—112no—
503C2×C4—112no—
504C2×C4—112no—
505C2×C4—221no—
506C2×C4—221no—
507C2×C4—221no—
508C2×C4—221no—
509C2×C4—221no—
510C2×C4—221no—
511C2×C4—221no—
512C2×C4—221no—
513C2×C4—221no—
514C2×C4—221no—
515C2×C4—221no—
516C2×C4—221no—
517C2×C4—221no—
518C2×C4—221no—
519C2×C4—221no—
520C2×C4—444no—
521C2×C4C2×C22⋊D1112yes—
522C2×C4C2×C22⋊D1112yes—
523C22—22no—
524C22—22no—
525C22—22no—
526C22—22no—
527C22—22no—
528C22—22no—
529C22—22no—
530C22—22no—
531C22—22no—
532C22—416no—
533C22—41no—
534C22—41no—
535C22—41no—
536C22—41no—
537C22—41no—
538C22—41no—
539C22—41no—
540C22—41no—
541C22—41no—
542C22—41no—
543C22—41no—
544C22—41no—
545C22—41no—
546C22—41no—
547C22—41no—
548C22—41no—
549C22—41no—
550C22—41no—
551C22—41no—
552C22—222no—
553C22—222no—
554C22—222no—
555C22—441no—
556C22—441no—
557C22—441no—
558C22—441no—
559C22—441no—
560C22—441no—
561C22—441no—
562C22—441no—
563C22—441no—
564C22—441no—
565C22—441no—
566C22C2×D4×D1111yescharacteristic
567C22C2×D4×D1111yescharacteristic
568C22#6703711yescharacteristic
569C22#6703711yescharacteristic
570C22#6703711yescharacteristic
571C22#6703711yescharacteristic
572C22C22×C22⋊D1111yescharacteristic
573C4—22no—
574C4—22no—
575C4—41no—
576C4—222no—
577C4—222no—
578C4—222no—
579C4—441no—
580C4—441no—
581C4—441no—
582C2—42no—
583C2—42no—
584C2—42no—
585C2—81no—
586C2—442no—
587C2—881no—
588C2#1062312011yescharacteristic
589C2#1062312111yescharacteristic
590C2#1062312311yescharacteristic
591C2#1062312611yescharacteristic
592C2D4×C22⋊D1111yescharacteristic
593C2D4×C22⋊D1111yescharacteristic
594C2#1062333611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC2×C11×#120C2
hypercenterC2×#120D11
hypocenterC11#2669
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#120

Complements

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

NH ≅ G/Ntype
1. C2×C11×#120C2semidirect
2. C2×#67006C2semidirect
3. C2×#67006C2semidirect
4. C2×#66993C2semidirect
5. C2×#66991C2semidirect
6. C2×#66937C2semidirect
7. #10622836C2semidirect
8. #10622836C2semidirect
9. #10622836C2semidirect
10. #10622835C2semidirect
11. #10622574C2semidirect
12. #10622573C2semidirect
13. #10622569C2semidirect
14. #10622564C2semidirect
15. #10622558C2semidirect
26. C22×C22⋊D11C22semidirect
27. C22×C22⋊D11C22semidirect
28. C22×D44C22semidirect
29. C22×C4×D11C22semidirect
42. C2×C22⋊Dic11C22semidirect
43. C2×C22⋊Dic11C22semidirect
46. C2×(C2×D11)⋊C4C22semidirect
47. C2×(C2×D11)⋊C4C22semidirect
48. C2×(C2×D11)⋊C4C22semidirect
49. C2×C4⋊Dic11C22semidirect
50. C2×Dic11⋊C4C22semidirect
51. C2×C4×Dic11C22semidirect
53. C11⋊#95C22semidirect
54. C11⋊#95C22semidirect
55. C11⋊#95C22semidirect
56. C11⋊#95C22semidirect
105. C2×C22⋊D11D4semidirect
120. C11×C22⋊C4D4semidirect
128. C22⋊Dic11D4semidirect
231. C2×#120D11semidirect
430. C22⋊C4C22⋊D11semidirect
432. C11#2669semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#1202
C2×#670062
C2×#669932
C2×#669912
C2×#669372
#106228362
#106228352
#106225742
#106225732
#106225692
#106225642
#106225582
#266911