Finite Group Databasebeta

← #13074841

Subgroups — #13074841

Order 1408.

796 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66990C211yesmaximal, characteristic, complemented
2C2×#66990C211yesmaximal, characteristic, complemented
3C2×#66989C211yesmaximal, characteristic, complemented
4C2×#66938C211yesmaximal, characteristic, complemented
5C11×#392C211yesmaximal, characteristic, complemented
6#10622836C211yesmaximal, characteristic, complemented
7#10622836C211yesmaximal, characteristic, complemented
8#10622835C211yesmaximal, characteristic, complemented
9#10622572C211yesmaximal, characteristic, complemented
10#10622570C211yesmaximal, characteristic, complemented
11#10622570C211yesmaximal, characteristic, complemented
12#10622568C211yesmaximal, characteristic, complemented
13#10622558C211yesmaximal, characteristic, complemented
14#10622286C211yesmaximal, 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×Dic22C2211yescharacteristic, complemented
25C2×C11×C22⋊C4C2211yescharacteristic
26C2×C11×C22⋊C4C2211yescharacteristic, complemented
27C2×C11×C22⋊C4C2211yescharacteristic, complemented
28C2×C22⋊Dic11C2211yescharacteristic
29C2×C22⋊Dic11C2211yescharacteristic
30C2×C22⋊Dic11C2211yescharacteristic
31C2×C22⋊Dic11C2211yescharacteristic, complemented
32C2×C22⋊Dic11C2211yescharacteristic, complemented
33C2×C22⋊Dic11C2211yescharacteristic, complemented
34C2×C22⋊Dic11C2211yescharacteristic, complemented
35#66990—24no—
36#66990—24no—
37#66989—24no—
38C2×(C2×D11)⋊C4C2211yescharacteristic
39C2×(C2×D11)⋊C4C2211yescharacteristic
40C2×(C2×D11)⋊C4C2211yescharacteristic
41C2×(C2×D11)⋊C4C2211yescharacteristic
42C2×(C2×D11)⋊C4C2211yescharacteristic
43C2×(C2×D11)⋊C4C2211yescharacteristic
44C2×(C2×D11)⋊C4C2211yescharacteristic
45C2×(C2×D11)⋊C4C2211yescharacteristic
46C2×Dic11⋊C4C2211yescharacteristic, complemented
47C2×Dic11⋊C4C2211yescharacteristic, complemented
48C2×C4×Dic11C2211yescharacteristic, complemented
49C2×C4×Dic11C2211yescharacteristic, complemented
50#66938—24no—
51C11×#95C2211yescharacteristic, complemented
52C11⋊#95C2211yescharacteristic, complemented
53C11⋊#95C2211yescharacteristic, complemented
54C11⋊#95C2211yescharacteristic, complemented
55C24×C11C2311yescharacteristic
56C24×C11C2311yescharacteristic
57C24×C11C2311yescharacteristic
58C23×D11—22no—
59C23×D11—22no—
60C23×D11—22no—
61C23×D11—41no—
62C23×D11—41no—
63C23×D11—41no—
64C23×D11—41no—
65C23×D11C2311yescharacteristic
66C23×D11C2311yescharacteristic
67C2×D4×C11—22no—
68C2×D4×C11—22no—
69C2×D4×C11—22no—
70C2×D4×C11—41no—
71C2×D4×C11—41no—
72C2×D4×C11—41no—
73C2×D4×C11—41no—
74C2×D4×C11—41no—
75C2×D4×C11—41no—
76C22×C4×C11C2311yescharacteristic
77C22×C4×C11C2311yescharacteristic
78C22×C4×C11C2311yescharacteristic
79C22×C4×C11C2311yescharacteristic
80C2×C22⋊D11—22no—
81C2×C22⋊D11—22no—
82C2×C22⋊D11—22no—
83C2×C22⋊D11—22no—
84C2×C22⋊D11—22no—
85C2×C22⋊D11—22no—
86C2×C22⋊D11—22no—
87C2×C22⋊D11—41no—
88C2×C22⋊D11—41no—
89C2×C22⋊D11—41no—
90C2×C22⋊D11—41no—
91C2×C22⋊D11—41no—
92C22×Dic11C2311yescharacteristic
93C22×Dic11C2311yescharacteristic
94C22×Dic11C2311yescharacteristic
95C22×Dic11C2311yescharacteristic
96C22×Dic11C2311yescharacteristic
97C22×Dic11C2311yescharacteristic
98C2×Dic22—22no—
99C2×Dic22—22no—
100C2×Dic22—41no—
101C11×C22⋊C4—22no—
102C11×C22⋊C4—41no—
103C11×C22⋊C4—41no—
104C22⋊Dic11—22no—
105C22⋊Dic11—22no—
106C22⋊Dic11—22no—
107C22⋊Dic11—22no—
108C22⋊Dic11—22no—
109C22⋊Dic11—41no—
110C22⋊Dic11D414yescomplemented
111(C2×D11)⋊C4—22no—
112(C2×D11)⋊C4—22no—
113(C2×D11)⋊C4—22no—
114(C2×D11)⋊C4—22no—
115(C2×D11)⋊C4—41no—
116(C2×D11)⋊C4—41no—
117(C2×D11)⋊C4—41no—
118(C2×D11)⋊C4D414yescomplemented
119Dic11⋊C4—41no—
120Dic11⋊C4—41no—
121C4×Dic11—22no—
122C4×Dic11—22no—
123#2670—111nomaximal, Sylow
124C23×C11—21no—
125C23×C11—21no—
126C23×C11—21no—
127C23×C11—21no—
128C23×C11—21no—
129C23×C11—21no—
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×C11C2×D412yes—
145C23×C11C2411yescharacteristic
146C22×D11—21no—
147C22×D11—21no—
148C22×D11—21no—
149C22×D11—21no—
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—44no—
159C22×D11—44no—
160C22×D11—44no—
161C22×D11—44no—
162C22×D11—44no—
163C22×D11—44no—
164C22×D11—44no—
165C22×D11C2×D412yes—
166C22×D11#4112yes—
167D4×C11—44no—
168D4×C11—44no—
169D4×C11—44no—
170C2×C4×C11—21no—
171C2×C4×C11—21no—
172C2×C4×C11—21no—
173C2×C4×C11—21no—
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×C11C2×D412yes—
182C22⋊D11—44no—
183C22⋊D11—44no—
184C22⋊D11—44no—
185C22⋊D11—44no—
186C2×Dic11—21no—
187C2×Dic11—21no—
188C2×Dic11—21no—
189C2×Dic11—21no—
190C2×Dic11—21no—
191C2×Dic11—21no—
192C2×Dic11—21no—
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×Dic11C2×D412yes—
202C2×Dic11C2×D412yes—
203C2×Dic11C2×D412yes—
204Dic22—44no—
205C2×#124—111no—
206C2×#124—111no—
207C2×#120—111no—
208C2×#120—111no—
209#394—111no—
210#394—111no—
211#393—111no—
212#392—111no—
213#392—111no—
214#392D1111yescharacteristic, complemented
215#390—111no—
216#390—111no—
217#388—111no—
218#388—111no—
219#379—111no—
220C22×C11—22no—
221C22×C11—22no—
222C22×C11—22no—
223C22×C11—41no—
224C22×C11—41no—
225C22×C11—41no—
226C22×C11—41no—
227C22×C11—41no—
228C22×C11—41no—
229C22×C11—41no—
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×C11C2×#4111yescharacteristic
244C22×C11H(5,𝔽2)11yescharacteristic
245C22×C11H(5,𝔽2)11yescharacteristic
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—416no—
255C2×D11—41no—
256C2×D11—41no—
257C2×D11—41no—
258C2×D11—41no—
259C2×D11—41no—
260C2×D11—41no—
261C2×D11—41no—
262C2×D11—41no—
263C4×C11—22no—
264C4×C11—41no—
265C4×C11—41no—
266C4×C11—41no—
267Dic11—22no—
268Dic11—22no—
269Dic11—22no—
270Dic11—41no—
271Dic11—41no—
272Dic11—41no—
273C25—111no—
274C22×Q8—111no—
275C22×D4—111no—
276C22×D4—111no—
277C22×D4—111no—
278C22×D4—111no—
279C22×D4C2×D1111yescharacteristic
280C22×D4C2×D1111yescharacteristic
281C22×D4C2×D1111yescharacteristic, complemented
282#124—224no—
283#124—224no—
284#120—224no—
285#120—224no—
286C2×C4⋊C4—111no—
287C2×C4⋊C4—111no—
288C2×C22⋊C4—111no—
289C2×C22⋊C4—111no—
290C2×C22⋊C4—111no—
291C2×C22⋊C4—111no—
292C2×C22⋊C4—111no—
293C2×C22⋊C4—111no—
294C2×C22⋊C4—111no—
295C2×C22⋊C4—111no—
296C2×C22⋊C4—111no—
297C2×C22⋊C4—111no—
298C2×C22⋊C4—111no—
299C2×C22⋊C4—111no—
300C2×C22⋊C4—111no—
301C2×C22⋊C4—111no—
302C2×C22⋊C4—111no—
303C2×C22⋊C4C2×D1111yescharacteristic
304C2×C22⋊C4C2×D1111yescharacteristic, complemented
305C2×C22⋊C4C2×D1111yescharacteristic, complemented
306C2×C42—111no—
307C2×C42—111no—
308#95—111no—
309#95—111no—
310#95—111no—
311#95C2×D1111yescharacteristic, complemented
312C2×C11—42no—
313C2×C11—81no—
314C2×C11—81no—
315C2×C11#53511yescharacteristic
316C2×C11#53511yescharacteristic
317C2×C11#53811yescharacteristic
318C2×C11D4211yescharacteristic
319C2×C11#54611yescharacteristic
320C2×C11#54611yescharacteristic
321C2×C11H(3,𝔽4)11yescharacteristic
322D11—42no—
323D11—42no—
324C24—111no—
325C24—111no—
326C24—222no—
327C24—222no—
328C24—222no—
329C24—441no—
330C24—441no—
331C24—441no—
332C24—441no—
333C24C22×D1111yescharacteristic
334C24C22×D1111yescharacteristic
335C24C22×D1111yescharacteristic
336C2×Q8—222no—
337C2×Q8—222no—
338C2×Q8—441no—
339C2×D4—22no—
340C2×D4—22no—
341C2×D4—22no—
342C2×D4—41no—
343C2×D4—41no—
344C2×D4—41no—
345C2×D4—41no—
346C2×D4—41no—
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—441no—
356C2×D4—441no—
357C2×D4—441no—
358C2×D4—441no—
359C2×D4—441no—
360C22×C4—111no—
361C22×C4—111no—
362C22×C4—111no—
363C22×C4—111no—
364C22×C4—111no—
365C22×C4—111no—
366C22×C4C22×D1111yescharacteristic
367C22×C4C22×D1111yescharacteristic
368C22×C4C22×D1111yescharacteristic
369C22×C4C22×D1111yescharacteristic
370C4⋊C4—441no—
371C4⋊C4—441no—
372C22⋊C4—22no—
373C22⋊C4—41no—
374C22⋊C4—41no—
375C22⋊C4—114no—
376C22⋊C4—114no—
377C22⋊C4—222no—
378C22⋊C4—222no—
379C22⋊C4—222no—
380C22⋊C4—222no—
381C22⋊C4—222no—
382C22⋊C4—222no—
383C22⋊C4—222no—
384C22⋊C4—222no—
385C22⋊C4—222no—
386C22⋊C4—441no—
387C22⋊C4—441no—
388C22⋊C4—441no—
389C22⋊C4—441no—
390C42—222no—
391C42—222no—
392C11#267011yescharacteristic, complemented, Sylow
393C23—21no—
394C23—21no—
395C23—21no—
396C23—21no—
397C23—21no—
398C23—21no—
399C23—21no—
400C23—21no—
401C23—21no—
402C23—21no—
403C23—21no—
404C23—21no—
405C23—21no—
406C23—21no—
407C23—21no—
408C23—21no—
409C23—21no—
410C23—21no—
411C23—21no—
412C23—21no—
413C23—112no—
414C23—112no—
415C23—221no—
416C23—221no—
417C23—221no—
418C23—221no—
419C23—221no—
420C23—221no—
421C23—221no—
422C23—221no—
423C23—221no—
424C23—221no—
425C23—221no—
426C23—221no—
427C23—444no—
428C23—444no—
429C23—444no—
430C23—444no—
431C23—444no—
432C23—444no—
433C23—444no—
434C23D4×D1112yes—
435C23C23×D1111yescharacteristic
436Q8—444no—
437D4—44no—
438D4—44no—
439D4—44no—
440D4—444no—
441D4—444no—
442D4—444no—
443D4—444no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—112no—
456C2×C4—112no—
457C2×C4—112no—
458C2×C4—221no—
459C2×C4—221no—
460C2×C4—221no—
461C2×C4—221no—
462C2×C4—221no—
463C2×C4—221no—
464C2×C4—221no—
465C2×C4—221no—
466C2×C4—221no—
467C2×C4—221no—
468C2×C4—221no—
469C2×C4—221no—
470C2×C4—221no—
471C2×C4—221no—
472C2×C4—221no—
473C2×C4D4×D1112yes—
474C22—22no—
475C22—22no—
476C22—22no—
477C22—41no—
478C22—41no—
479C22—41no—
480C22—41no—
481C22—41no—
482C22—41no—
483C22—41no—
484C22—41no—
485C22—41no—
486C22—41no—
487C22—41no—
488C22—41no—
489C22—41no—
490C22—41no—
491C22—41no—
492C22—41no—
493C22—41no—
494C22—41no—
495C22—222no—
496C22—222no—
497C22—222no—
498C22—222no—
499C22—222no—
500C22—222no—
501C22—4416no—
502C22—441no—
503C22—441no—
504C22—441no—
505C22—441no—
506C22—441no—
507C22—441no—
508C22—441no—
509C22—441no—
510C22C2×D4×D1111yescharacteristic
511C22C2×D4×D1111yescharacteristic
512C22#6703711yescharacteristic
513C22#6703711yescharacteristic
514C22#6703711yescharacteristic
515C22#6703711yescharacteristic
516C22#41×D1111yescharacteristic
517C4—22no—
518C4—41no—
519C4—41no—
520C4—41no—
521C4—222no—
522C4—222no—
523C4—222no—
524C4—441no—
525C4—441no—
526C4—441no—
527C2—42no—
528C2—81no—
529C2—81no—
530C2—442no—
531C2—442no—
532C2#1062312111yescharacteristic
533C2#1062312311yescharacteristic
534C2#1062312511yescharacteristic
535C2#1062314111yescharacteristic
536C2#1062314311yescharacteristic
537C2#1062314411yescharacteristic
538C2#1062324611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#392C2
hypercenter#392D11
hypocenterC11#2670
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C2×#66990C2semidirect
2. C2×#66990C2semidirect
3. C2×#66989C2semidirect
4. C2×#66938C2semidirect
5. C11×#392C2semidirect
6. #10622836C2semidirect
7. #10622836C2semidirect
8. #10622835C2semidirect
9. #10622572C2semidirect
10. #10622570C2semidirect
11. #10622570C2semidirect
12. #10622568C2semidirect
13. #10622558C2semidirect
14. #10622286C2semidirect
15. #10622282C2semidirect
19. C22×D4×C11C22semidirect
24. C22×Dic22C22semidirect
26. C2×C11×C22⋊C4C22semidirect
27. C2×C11×C22⋊C4C22semidirect
31. C2×C22⋊Dic11C22semidirect
32. C2×C22⋊Dic11C22semidirect
33. C2×C22⋊Dic11C22semidirect
34. C2×C22⋊Dic11C22semidirect
46. C2×Dic11⋊C4C22semidirect
47. C2×Dic11⋊C4C22semidirect
48. C2×C4×Dic11C22semidirect
49. C2×C4×Dic11C22semidirect
51. C11×#95C22semidirect
52. C11⋊#95C22semidirect
53. C11⋊#95C22semidirect
54. C11⋊#95C22semidirect
110. C22⋊Dic11D4semidirect
118. (C2×D11)⋊C4D4semidirect
214. #392D11semidirect
281. C22×D4C2×D11semidirect
304. C2×C22⋊C4C2×D11semidirect
305. C2×C22⋊C4C2×D11semidirect
311. #95C2×D11semidirect
392. C11#2670semidirect

Maximal subgroups

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

subgroupindex
C2×#669902
C2×#669892
C2×#669382
C11×#3922
#106228362
#106228352
#106225722
#106225702
#106225682
#106225582
#106222862
#106222822
#267011