Finite Group Databasebeta

← #13074827

Subgroups — #13074827

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×#66993C211yesmaximal, characteristic, complemented
2C2×#66992C211yesmaximal, characteristic, complemented
3C2×#66992C211yesmaximal, characteristic, complemented
4C2×#66990C211yesmaximal, characteristic, complemented
5C2×#66990C211yesmaximal, characteristic, complemented
6C2×#66935C211yesmaximal, characteristic, complemented
7C11×#392C211yesmaximal, characteristic, complemented
8#10622836C211yesmaximal, characteristic, complemented
9#10622573C211yesmaximal, characteristic, complemented
10#10622573C211yesmaximal, characteristic, complemented
11#10622572C211yesmaximal, characteristic, complemented
12#10622571C211yesmaximal, characteristic, complemented
13#10622558C211yesmaximal, characteristic, complemented
14#10622285C211yesmaximal, characteristic, complemented
15#10622282C211yesmaximal, characteristic, complemented
16C24×D11C2211yescharacteristic
17C22×D4×C11C2211yescharacteristic
18C22×D4×C11C2211yescharacteristic
19C22×D4×C11C2211yescharacteristic, complemented
20C22×C22⋊D11C2211yescharacteristic
21C22×C22⋊D11C2211yescharacteristic
22C22×C22⋊D11C2211yescharacteristic
23C22×C22⋊D11C2211yescharacteristic
24C22×C22⋊D11C2211yescharacteristic
25C22×C22⋊D11C2211yescharacteristic, complemented
26C22×C22⋊D11C2211yescharacteristic, complemented
27C23×Dic11C2211yescharacteristic, complemented
28C22×D44C2211yescharacteristic
29C22×D44C2211yescharacteristic
30C2×C11×C22⋊C4C2211yescharacteristic
31C2×C11×C22⋊C4C2211yescharacteristic, complemented
32C2×C11×C22⋊C4C2211yescharacteristic, complemented
33C2×C22⋊Dic11C2211yescharacteristic
34C2×C22⋊Dic11C2211yescharacteristic
35C2×C22⋊Dic11C2211yescharacteristic, complemented
36#66993—24no—
37#66992—24no—
38#66992—24no—
39#66990—24no—
40#66990—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, complemented
48C2×(C2×D11)⋊C4C2211yescharacteristic, complemented
49C2×Dic11⋊C4C2211yescharacteristic, complemented
50C2×Dic11⋊C4C2211yescharacteristic, complemented
51C2×C4×Dic11C2211yescharacteristic, complemented
52#66935—24no—
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—41no—
64C23×D11—41no—
65C23×D11—41no—
66C23×D11—41no—
67C23×D11C2311yescharacteristic
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
82C22×C4×C11C2311yescharacteristic
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⋊D11D414yescomplemented
104C22×Dic11—22no—
105C22×Dic11—22no—
106C22×Dic11—41no—
107C22×Dic11C2311yescharacteristic
108C22×Dic11C2311yescharacteristic
109C22×Dic11C2311yescharacteristic
110C22×Dic11C2311yescharacteristic
111C22×Dic11C2311yescharacteristic
112C2×D44—22no—
113C2×D44—22no—
114C2×D44—22no—
115C2×D44—41no—
116C2×D44—41no—
117C2×D44—41no—
118C11×C22⋊C4—22no—
119C11×C22⋊C4—41no—
120C11×C22⋊C4—41no—
121C22⋊Dic11—22no—
122C22⋊Dic11—22no—
123C22⋊Dic11D414yescomplemented
124(C2×D11)⋊C4—22no—
125(C2×D11)⋊C4—22no—
126(C2×D11)⋊C4—22no—
127(C2×D11)⋊C4—22no—
128(C2×D11)⋊C4—22no—
129(C2×D11)⋊C4—22no—
130(C2×D11)⋊C4—41no—
131(C2×D11)⋊C4D414yescomplemented
132Dic11⋊C4—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×C11C2×D412yes—
156C23×C11C2×D412yes—
157C23×C11C2411yescharacteristic
158C22×D11—21no—
159C22×D11—21no—
160C22×D11—21no—
161C22×D11—21no—
162C22×D11—21no—
163C22×D11—21no—
164C22×D11—21no—
165C22×D11—21no—
166C22×D11—21no—
167C22×D11—21no—
168C22×D11—21no—
169C22×D11—21no—
170C22×D11—21no—
171C22×D11—21no—
172C22×D11—21no—
173C22×D11—21no—
174C22×D11—21no—
175C22×D11—21no—
176C22×D11—21no—
177C22×D11—44no—
178C22×D11—44no—
179C22×D11—44no—
180C22×D11—44no—
181C22×D11—44no—
182C22×D11—44no—
183C22×D11—44no—
184C22×D11C2×D412yes—
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×C11—21no—
197C2×C4×C11—21no—
198C2×C4×C11—21no—
199C2×C4×C11—21no—
200C2×C4×C11C2×D412yes—
201C22⋊D11—44no—
202C22⋊D11—44no—
203C22⋊D11—44no—
204C22⋊D11—44no—
205C22⋊D11—44no—
206C22⋊D11—44no—
207C22⋊D11—44no—
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—44no—
220C2×Dic11C2×D412yes—
221C2×Dic11C2×D412yes—
222C2×Dic11C2×D412yes—
223C2×Dic11C2×D412yes—
224D44—44no—
225D44—44no—
226C2×#127—111no—
227C2×#121—111no—
228C2×#121—111no—
229C2×#120—111no—
230C2×#120—111no—
231C2×#120—111no—
232#394—111no—
233#394—111no—
234#392—111no—
235#392—111no—
236#392—111no—
237#392D1111yescharacteristic, complemented
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—41no—
248C22×C11—41no—
249C22×C11—41no—
250C22×C11—41no—
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×C11C22×D411yescharacteristic
263C22×C11C22×D411yescharacteristic
264C22×C11C22×D411yescharacteristic
265C22×C11H(5,𝔽2)11yescharacteristic
266C22×C11H(5,𝔽2)11yescharacteristic
267C22×C11H(5,𝔽2)11yescharacteristic
268C22×C11H(5,𝔽2)11yescharacteristic
269C2×D11—22no—
270C2×D11—22no—
271C2×D11—22no—
272C2×D11—22no—
273C2×D11—22no—
274C2×D11—22no—
275C2×D11—416no—
276C2×D11—41no—
277C2×D11—41no—
278C2×D11—41no—
279C2×D11—41no—
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—41no—
293C4×C11—41no—
294C4×C11—41no—
295Dic11—22no—
296Dic11—22no—
297Dic11—22no—
298Dic11—22no—
299Dic11—41no—
300C25—111no—
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, complemented
313C23×C4—111no—
314#127—224no—
315#121—224no—
316#121—224no—
317#120—224no—
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, complemented
335C2×C22⋊C4C2×D1111yescharacteristic, complemented
336C2×C42—111no—
337#95—111no—
338#95—111no—
339#95—111no—
340#95C2×D1111yescharacteristic, complemented
341C2×C11—42no—
342C2×C11—42no—
343C2×C11—81no—
344C2×C11#53411yescharacteristic
345C2×C11#53511yescharacteristic
346C2×C11#53511yescharacteristic
347C2×C11D4211yescharacteristic
348C2×C11D4211yescharacteristic
349C2×C11D4211yescharacteristic
350C2×C11#56011yescharacteristic
351D11—42no—
352D11—42no—
353D11—81no—
354C24—111no—
355C24—111no—
356C24—111no—
357C24—222no—
358C24—222no—
359C24—222no—
360C24—441no—
361C24—441no—
362C24—441no—
363C24—441no—
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—222no—
409C22×C4—222no—
410C22×C4—441no—
411C22×C4C22×D1111yescharacteristic
412C22×C4C22×D1111yescharacteristic
413C22×C4C22×D1111yescharacteristic
414C22×C4C22×D1111yescharacteristic
415C4⋊C4—222no—
416C4⋊C4—222no—
417C22⋊C4—22no—
418C22⋊C4—41no—
419C22⋊C4—41no—
420C22⋊C4—114no—
421C22⋊C4—114no—
422C22⋊C4—222no—
423C22⋊C4—222no—
424C22⋊C4—222no—
425C22⋊C4—222no—
426C22⋊C4—222no—
427C22⋊C4—222no—
428C22⋊C4—222no—
429C22⋊C4—222no—
430C22⋊C4—441no—
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—112no—
453C23—112no—
454C23—221no—
455C23—221no—
456C23—221no—
457C23—221no—
458C23—221no—
459C23—221no—
460C23—221no—
461C23—221no—
462C23—221no—
463C23—221no—
464C23—221no—
465C23—221no—
466C23—221no—
467C23—221no—
468C23—221no—
469C23—221no—
470C23—221no—
471C23—221no—
472C23—221no—
473C23—444no—
474C23—444no—
475C23—444no—
476C23—444no—
477C23—444no—
478C23—444no—
479C23—444no—
480C23D4×D1112yes—
481C23D4×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—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—112no—
507C2×C4—112no—
508C2×C4—112no—
509C2×C4—112no—
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—221no—
521C2×C4—444no—
522C2×C4D4×D1112yes—
523C22—22no—
524C22—22no—
525C22—22no—
526C22—22no—
527C22—22no—
528C22—22no—
529C22—41no—
530C22—41no—
531C22—41no—
532C22—41no—
533C22—41no—
534C22—41no—
535C22—41no—
536C22—41no—
537C22—41no—
538C22—41no—
539C22—41no—
540C22—41no—
541C22—41no—
542C22—41no—
543C22—41no—
544C22—222no—
545C22—222no—
546C22—222no—
547C22—222no—
548C22—222no—
549C22—222no—
550C22—4416no—
551C22—441no—
552C22—441no—
553C22—441no—
554C22—441no—
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
568C22C2×D4×D1111yescharacteristic
569C22#6703711yescharacteristic
570C22#6703711yescharacteristic
571C22#6703711yescharacteristic
572C22#6704211yescharacteristic
573C4—22no—
574C4—41no—
575C4—41no—
576C4—41no—
577C4—222no—
578C4—222no—
579C4—222no—
580C4—222no—
581C4—441no—
582C2—42no—
583C2—42no—
584C2—81no—
585C2—442no—
586C2—442no—
587C2—881no—
588C2#1062312111yescharacteristic
589C2#1062312111yescharacteristic
590C2#1062312311yescharacteristic
591C2#1062313611yescharacteristic
592C2#1062314011yescharacteristic
593C2#1062315111yescharacteristic
594C2#1062324611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#392C2
hypercenter#392D11
hypocenterC11#2669
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C2×#66993C2semidirect
2. C2×#66992C2semidirect
3. C2×#66992C2semidirect
4. C2×#66990C2semidirect
5. C2×#66990C2semidirect
6. C2×#66935C2semidirect
7. C11×#392C2semidirect
8. #10622836C2semidirect
9. #10622573C2semidirect
10. #10622573C2semidirect
11. #10622572C2semidirect
12. #10622571C2semidirect
13. #10622558C2semidirect
14. #10622285C2semidirect
15. #10622282C2semidirect
19. C22×D4×C11C22semidirect
25. C22×C22⋊D11C22semidirect
26. C22×C22⋊D11C22semidirect
27. C23×Dic11C22semidirect
31. C2×C11×C22⋊C4C22semidirect
32. C2×C11×C22⋊C4C22semidirect
35. C2×C22⋊Dic11C22semidirect
47. C2×(C2×D11)⋊C4C22semidirect
48. C2×(C2×D11)⋊C4C22semidirect
49. C2×Dic11⋊C4C22semidirect
50. C2×Dic11⋊C4C22semidirect
51. C2×C4×Dic11C22semidirect
53. C11×#95C22semidirect
54. C11⋊#95C22semidirect
55. C11⋊#95C22semidirect
56. C11⋊#95C22semidirect
103. C2×C22⋊D11D4semidirect
123. C22⋊Dic11D4semidirect
131. (C2×D11)⋊C4D4semidirect
237. #392D11semidirect
312. C22×D4C2×D11semidirect
334. C2×C22⋊C4C2×D11semidirect
335. C2×C22⋊C4C2×D11semidirect
340. #95C2×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×#669932
C2×#669922
C2×#669902
C2×#669352
C11×#3922
#106228362
#106225732
#106225722
#106225712
#106225582
#106222852
#106222822
#266911