Finite Group Databasebeta

← #13073545

Subgroups — #13073545

Order 1408.

900 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66990C211yesmaximal, characteristic, complemented
2C2×#66947C211yesmaximal, characteristic, complemented
3C2×#66937C211yesmaximal, characteristic, complemented
4C2×#66936C211yesmaximal, characteristic, complemented
5C2×#66935C211yesmaximal, characteristic, complemented
6C2×C22⋊C4×D11C211yesmaximal, characteristic, complemented
7C11×#390C211yesmaximal, characteristic, complemented
8#10622836C211yesmaximal, characteristic, complemented
9#10622605C211yesmaximal, characteristic, complemented
10#10622573C211yesmaximal, characteristic, complemented
11#10622570C211yesmaximal, characteristic, complemented
12#10622570C211yesmaximal, characteristic, complemented
13#10622562C211yesmaximal, characteristic, complemented
14#10622552C211yesmaximal, characteristic, complemented
15C4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
16C24×D11C2211yescharacteristic
17C22×D4×C11C2211yescharacteristic
18C22×C22⋊D11C2211yescharacteristic
19C22×C22⋊D11C2211yescharacteristic
20C22×C22⋊D11C2211yescharacteristic
21C22×C22⋊D11C2211yescharacteristic, complemented
22C22×D44C2211yescharacteristic
23C22×D44C2211yescharacteristic
24C22×C4×D11C2211yescharacteristic
25C22×C4×D11C2211yescharacteristic
26C2×C11×C4⋊C4C2211yescharacteristic, complemented
27C2×C11×C22⋊C4C2211yescharacteristic
28C2×C11×C22⋊C4C2211yescharacteristic
29C2×C11×C22⋊C4C2211yescharacteristic, complemented
30C2×C11×C22⋊C4C2211yescharacteristic, complemented
31C2×C42×C11C2211yescharacteristic, complemented
32C2×C22⋊Dic11C2211yescharacteristic
33C2×C22⋊Dic11C2211yescharacteristic
34C2×C22⋊Dic11C2211yescharacteristic, complemented
35#66990—24no—
36C2×(C2×D11)⋊C4C2211yescharacteristic
37C2×(C2×D11)⋊C4C2211yescharacteristic
38C2×(C2×D11)⋊C4C2211yescharacteristic
39C2×(C2×D11)⋊C4C2211yescharacteristic
40C2×(C2×D11)⋊C4C2211yescharacteristic
41C2×(C2×D11)⋊C4C2211yescharacteristic
42C2×(C2×D11)⋊C4C2211yescharacteristic, complemented
43C2×(C2×D11)⋊C4C2211yescharacteristic, complemented
44C2×(C2×D11)⋊C4C2211yescharacteristic, complemented
45C2×C4⋊Dic11C2211yescharacteristic, complemented
46C2×Dic11⋊C4C2211yescharacteristic, complemented
47C2×Dic11⋊C4C2211yescharacteristic, complemented
48C2×Dic11⋊C4C2211yescharacteristic, complemented
49C2×C4×Dic11C2211yescharacteristic, complemented
50#66947—24no—
51#66937—24no—
52#66936—24no—
53#66935—24no—
54C22⋊C4×D11—24no—
55C11⋊#95C2211yescharacteristic, complemented
56C11⋊#95C2211yescharacteristic, complemented
57C24×C11C2311yescharacteristic
58C24×C11C2311yescharacteristic
59C23×D11—22no—
60C23×D11—22no—
61C23×D11—22no—
62C23×D11—22no—
63C23×D11—22no—
64C23×D11—41no—
65C23×D11—41no—
66C23×D11C2311yescharacteristic
67C23×D11C2311yescharacteristic
68C23×D11C2311yescharacteristic
69C2×D4×C11—22no—
70C2×D4×C11—22no—
71C2×D4×C11—41no—
72C22×C4×C11C2311yescharacteristic
73C22×C4×C11C2311yescharacteristic
74C22×C4×C11C2311yescharacteristic
75C22×C4×C11C2311yescharacteristic
76C22×C4×C11C2311yescharacteristic
77C2×C22⋊D11—22no—
78C2×C22⋊D11—22no—
79C2×C22⋊D11—22no—
80C2×C22⋊D11—22no—
81C2×C22⋊D11—22no—
82C2×C22⋊D11—22no—
83C2×C22⋊D11—22no—
84C2×C22⋊D11—22no—
85C2×C22⋊D11—41no—
86C2×C22⋊D11—41no—
87C2×C22⋊D11—41no—
88C2×C22⋊D11—41no—
89C22×Dic11C2311yescharacteristic
90C22×Dic11C2311yescharacteristic
91C22×Dic11C2311yescharacteristic
92C22×Dic11C2311yescharacteristic
93C22×Dic11C2311yescharacteristic
94C2×D44—22no—
95C2×D44—22no—
96C2×D44—22no—
97C2×D44—22no—
98C2×D44—22no—
99C2×D44—41no—
100C2×C4×D11—22no—
101C2×C4×D11—22no—
102C2×C4×D11—22no—
103C2×C4×D11—41no—
104C2×C4×D11—41no—
105C2×C4×D11D414yescomplemented
106C11×C4⋊C4—22no—
107C11×C22⋊C4—22no—
108C11×C22⋊C4—22no—
109C11×C22⋊C4—22no—
110C11×C22⋊C4—22no—
111C42×C11—41no—
112C22⋊Dic11—22no—
113C22⋊Dic11—22no—
114C22⋊Dic11—22no—
115(C2×D11)⋊C4—22no—
116(C2×D11)⋊C4—22no—
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)⋊C4D414yescomplemented
123(C2×D11)⋊C4D414yescomplemented
124C4⋊Dic11—22no—
125Dic11⋊C4—22no—
126Dic11⋊C4—22no—
127Dic11⋊C4—22no—
128C4×Dic11—41no—
129#2539—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#4112yes—
144C23×C11C2411yescharacteristic
145C22×D11—21no—
146C22×D11—21no—
147C22×D11—21no—
148C22×D11—21no—
149C22×D11—28no—
150C22×D11—21no—
151C22×D11—21no—
152C22×D11—21no—
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—44no—
164C22×D11—44no—
165C22×D11—44no—
166C22×D11—44no—
167C22×D11—44no—
168C22×D11—44no—
169C22×D11C2×D412yes—
170C22×D11C2×D412yes—
171C22×D11C2×D412yes—
172C22×D11#4112yes—
173D4×C11—44no—
174C2×C4×C11—21no—
175C2×C4×C11—21no—
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×C11C2×D412yes—
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×Dic11C2×D412yes—
206C2×Dic11C2×D412yes—
207C2×Dic11C2×D412yes—
208D44—44no—
209D44—44no—
210C4×D11—44no—
211C4×D11—44no—
212C2×#123—111no—
213C2×#123—111no—
214C2×#121—111no—
215C2×#120—111no—
216C2×#120—111no—
217C22×C22⋊C4—111no—
218#399—111no—
219#399—111no—
220#392—111no—
221#392—111no—
222#390—111no—
223#390—111no—
224#390—111no—
225#390D1111yescharacteristic, complemented
226C4×C22⋊C4—111no—
227C22×C11—22no—
228C22×C11—22no—
229C22×C11—22no—
230C22×C11—41no—
231C22×C11—41no—
232C22×C11—41no—
233C22×C11—41no—
234C22×C11—41no—
235C22×C11—41no—
236C22×C11—41no—
237C22×C11—41no—
238C22×C11—41no—
239C22×C11—41no—
240C22×C11—41no—
241C22×C11C22×D411yescharacteristic
242C22×C11C22×D411yescharacteristic
243C22×C11C22×D411yescharacteristic
244C22×C11C2×#4111yescharacteristic
245C22×C11C2×#4111yescharacteristic
246C22×C11H(5,𝔽2)11yescharacteristic
247C22×C11H(5,𝔽2)11yescharacteristic
248C2×D11—22no—
249C2×D11—22no—
250C2×D11—22no—
251C2×D11—22no—
252C2×D11—22no—
253C2×D11—22no—
254C2×D11—22no—
255C2×D11—22no—
256C2×D11—22no—
257C2×D11—416no—
258C2×D11—41no—
259C2×D11—41no—
260C2×D11—41no—
261C2×D11—41no—
262C2×D11—41no—
263C2×D11—41no—
264C2×D11—41no—
265C2×D11—41no—
266C2×D11—41no—
267C2×D11—41no—
268C2×D11—41no—
269C2×D11#12714yes—
270C4×C11—22no—
271C4×C11—22no—
272C4×C11—22no—
273C4×C11—41no—
274C4×C11—41no—
275Dic11—22no—
276Dic11—22no—
277Dic11—22no—
278Dic11—41no—
279Dic11—41no—
280C25—111no—
281C22×D4—111no—
282C22×D4—111no—
283C22×D4—111no—
284C22×D4—111no—
285C22×D4—111no—
286C22×D4—111no—
287C22×D4C2×D1111yescharacteristic
288C23×C4—111no—
289C23×C4—111no—
290#123—224no—
291#123—224no—
292#121—224no—
293#120—224no—
294#120—224no—
295C2×C4⋊C4—111no—
296C2×C4⋊C4—111no—
297C2×C4⋊C4—111no—
298C2×C4⋊C4—111no—
299C2×C4⋊C4C2×D1111yescharacteristic, complemented
300C2×C22⋊C4—111no—
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—224no—
313C2×C22⋊C4C2×D1111yescharacteristic
314C2×C22⋊C4C2×D1111yescharacteristic
315C2×C22⋊C4C2×D1111yescharacteristic, complemented
316C2×C22⋊C4C2×D1111yescharacteristic, complemented
317C2×C42—111no—
318C2×C42C2×D1111yescharacteristic, complemented
319#95—111no—
320#95—111no—
321C2×C11—42no—
322C2×C11—81no—
323C2×C11#52511yescharacteristic
324C2×C11C2×#12711yescharacteristic
325C2×C11#53411yescharacteristic
326C2×C11#54611yescharacteristic
327C2×C11#54611yescharacteristic
328C2×C11#54611yescharacteristic
329C2×C11#54611yescharacteristic
330D11—24no—
331D11—42no—
332D11—81no—
333C24—111no—
334C24—111no—
335C24—111no—
336C24—222no—
337C24—222no—
338C24—222no—
339C24—222no—
340C24—222no—
341C24—441no—
342C24—441no—
343C24C22×D1111yescharacteristic
344C24C22×D1111yescharacteristic
345C2×D4—22no—
346C2×D4—22no—
347C2×D4—41no—
348C2×D4—222no—
349C2×D4—222no—
350C2×D4—222no—
351C2×D4—222no—
352C2×D4—222no—
353C2×D4—222no—
354C2×D4—222no—
355C2×D4—222no—
356C2×D4—222no—
357C2×D4—222no—
358C2×D4—222no—
359C2×D4—222no—
360C2×D4—222no—
361C2×D4—441no—
362C2×D4—441no—
363C2×D4—441no—
364C2×D4—441no—
365C2×D4—441no—
366C22×C4—111no—
367C22×C4—111no—
368C22×C4—111no—
369C22×C4—114no—
370C22×C4—111no—
371C22×C4—111no—
372C22×C4—222no—
373C22×C4—222no—
374C22×C4—222no—
375C22×C4—441no—
376C22×C4—441no—
377C22×C4C22×D1111yescharacteristic
378C22×C4C22×D1111yescharacteristic
379C22×C4C22×D1111yescharacteristic
380C22×C4C22×D1111yescharacteristic
381C22×C4C22×D1111yescharacteristic
382C4⋊C4—22no—
383C4⋊C4—222no—
384C4⋊C4—222no—
385C4⋊C4—222no—
386C4⋊C4—222no—
387C22⋊C4—22no—
388C22⋊C4—22no—
389C22⋊C4—22no—
390C22⋊C4—22no—
391C22⋊C4—114no—
392C22⋊C4—114no—
393C22⋊C4—222no—
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—
403C42—41no—
404C42—441no—
405C11#253911yescharacteristic, complemented, Sylow
406C23—21no—
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—112no—
420C23—112no—
421C23—112no—
422C23—112no—
423C23—228no—
424C23—221no—
425C23—221no—
426C23—221no—
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—221no—
440C23—221no—
441C23—444no—
442C23—444no—
443C23—444no—
444C23—444no—
445C23—444no—
446C23—444no—
447C23#433912yes—
448C23C23×D1111yescharacteristic
449D4—44no—
450D4—444no—
451D4—444no—
452D4—444no—
453D4—444no—
454D4—444no—
455D4—444no—
456C2×C4—21no—
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—21no—
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—444no—
484C2×C4—444no—
485C2×C4D4×D1112yes—
486C2×C4D4×D1112yes—
487C2×C4D4×D1112yes—
488C22—22no—
489C22—22no—
490C22—22no—
491C22—41no—
492C22—41no—
493C22—41no—
494C22—41no—
495C22—41no—
496C22—41no—
497C22—41no—
498C22—41no—
499C22—41no—
500C22—41no—
501C22—41no—
502C22—114no—
503C22—222no—
504C22—222no—
505C22—222no—
506C22—222no—
507C22—222no—
508C22—222no—
509C22—222no—
510C22—222no—
511C22—222no—
512C22—4416no—
513C22—441no—
514C22—441no—
515C22—441no—
516C22—441no—
517C22—441no—
518C22—441no—
519C22—441no—
520C22—441no—
521C22—441no—
522C22—441no—
523C22—441no—
524C22C2×#433911yescharacteristic
525C22C2×D4×D1111yescharacteristic
526C22C2×D4×D1111yescharacteristic
527C22C2×D4×D1111yescharacteristic
528C22#6703711yescharacteristic
529C22#41×D1111yescharacteristic
530C22#6704211yescharacteristic
531C4—22no—
532C4—22no—
533C4—22no—
534C4—41no—
535C4—41no—
536C4—222no—
537C4—222no—
538C4—222no—
539C4—441no—
540C4—441no—
541C2—42no—
542C2—81no—
543C2—224no—
544C2—442no—
545C2—881no—
546C2#1062302111yescharacteristic
547C2#1062307811yescharacteristic
548C2#1062308111yescharacteristic
549C2#1062313611yescharacteristic
550C2#1062314111yescharacteristic
551C2#1062320711yescharacteristic
552C2D11×#12711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#390C2
hypercenter#390D11
hypocenterC11#2539
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
1. C2×#66990C2semidirect
2. C2×#66947C2semidirect
3. C2×#66937C2semidirect
4. C2×#66936C2semidirect
5. C2×#66935C2semidirect
6. C2×C22⋊C4×D11C2semidirect
7. C11×#390C2semidirect
8. #10622836C2semidirect
9. #10622605C2semidirect
10. #10622573C2semidirect
11. #10622570C2semidirect
12. #10622570C2semidirect
13. #10622562C2semidirect
14. #10622552C2semidirect
15. C4×(C2×D11)⋊C4C2semidirect
21. C22×C22⋊D11C22semidirect
26. C2×C11×C4⋊C4C22semidirect
29. C2×C11×C22⋊C4C22semidirect
30. C2×C11×C22⋊C4C22semidirect
31. C2×C42×C11C22semidirect
34. C2×C22⋊Dic11C22semidirect
42. C2×(C2×D11)⋊C4C22semidirect
43. C2×(C2×D11)⋊C4C22semidirect
44. C2×(C2×D11)⋊C4C22semidirect
45. C2×C4⋊Dic11C22semidirect
46. C2×Dic11⋊C4C22semidirect
47. C2×Dic11⋊C4C22semidirect
48. C2×Dic11⋊C4C22semidirect
49. C2×C4×Dic11C22semidirect
55. C11⋊#95C22semidirect
56. C11⋊#95C22semidirect
105. C2×C4×D11D4semidirect
122. (C2×D11)⋊C4D4semidirect
123. (C2×D11)⋊C4D4semidirect
225. #390D11semidirect
299. C2×C4⋊C4C2×D11semidirect
315. C2×C22⋊C4C2×D11semidirect
316. C2×C22⋊C4C2×D11semidirect
318. C2×C42C2×D11semidirect
405. C11#2539semidirect

Maximal subgroups

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

subgroupindex
C2×#669902
C2×#669472
C2×#669372
C2×#669362
C2×#669352
C2×C22⋊C4×D112
C11×#3902
#106228362
#106226052
#106225732
#106225702
#106225622
#106225522
C4×(C2×D11)⋊C42
#253911