Finite Group Databasebeta

← #13074839

Subgroups — #13074839

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×#66938C211yesmaximal, characteristic, complemented
3C2×#66935C211yesmaximal, characteristic, complemented
4C2×#66928C211yesmaximal, characteristic, complemented
5C11×#390C211yesmaximal, characteristic, complemented
6#10622836C211yesmaximal, characteristic, complemented
7#10622604C211yesmaximal, characteristic, complemented
8#10622603C211yesmaximal, characteristic, complemented
9#10622573C211yesmaximal, characteristic, complemented
10#10622573C211yesmaximal, characteristic, complemented
11#10622572C211yesmaximal, characteristic, complemented
12#10622570C211yesmaximal, characteristic, complemented
13#10622568C211yesmaximal, characteristic, complemented
14#10622560C211yesmaximal, characteristic, complemented
15#10622553C211yesmaximal, 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×Dic22C2211yescharacteristic, complemented
25C2×C11×C4⋊C4C2211yescharacteristic, complemented
26C2×C11×C22⋊C4C2211yescharacteristic
27C2×C11×C22⋊C4C2211yescharacteristic
28C2×C11×C22⋊C4C2211yescharacteristic, complemented
29C2×C11×C22⋊C4C2211yescharacteristic, complemented
30C2×C42×C11C2211yescharacteristic, complemented
31C2×C22⋊Dic11C2211yescharacteristic
32C2×C22⋊Dic11C2211yescharacteristic
33C2×C22⋊Dic11C2211yescharacteristic, complemented
34#66990—24no—
35C2×(C2×D11)⋊C4C2211yescharacteristic
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
43C2×(C2×D11)⋊C4C2211yescharacteristic, complemented
44C2×(C2×D11)⋊C4C2211yescharacteristic, complemented
45C2×(C2×D11)⋊C4C2211yescharacteristic, complemented
46C2×Dic11⋊C4C2211yescharacteristic, complemented
47C2×C4×Dic11C2211yescharacteristic, complemented
48#66938—24no—
49#66935—24no—
50#66928—24no—
51C11⋊#95C2211yescharacteristic, complemented
52C11⋊#95C2211yescharacteristic, complemented
53C11⋊#95C2211yescharacteristic, complemented
54C11⋊#95C2211yescharacteristic, complemented
55C24×C11C2311yescharacteristic
56C24×C11C2311yescharacteristic
57C23×D11—22no—
58C23×D11—22no—
59C23×D11—22no—
60C23×D11—41no—
61C23×D11—41no—
62C23×D11—41no—
63C23×D11—41no—
64C23×D11C2311yescharacteristic
65C23×D11C2311yescharacteristic
66C23×D11C2311yescharacteristic
67C2×D4×C11—22no—
68C2×D4×C11—22no—
69C2×D4×C11—41no—
70C22×C4×C11C2311yescharacteristic
71C22×C4×C11C2311yescharacteristic
72C22×C4×C11C2311yescharacteristic
73C22×C4×C11C2311yescharacteristic
74C22×C4×C11C2311yescharacteristic
75C2×C22⋊D11—22no—
76C2×C22⋊D11—22no—
77C2×C22⋊D11—22no—
78C2×C22⋊D11—22no—
79C2×C22⋊D11—22no—
80C2×C22⋊D11—41no—
81C2×C22⋊D11—41no—
82C2×C22⋊D11—41no—
83C2×C22⋊D11—41no—
84C2×C22⋊D11—41no—
85C2×C22⋊D11—41no—
86C2×C22⋊D11—41no—
87C22×Dic11C2311yescharacteristic
88C22×Dic11C2311yescharacteristic
89C22×Dic11C2311yescharacteristic
90C22×Dic11C2311yescharacteristic
91C22×Dic11C2311yescharacteristic
92C2×D44—22no—
93C2×D44—22no—
94C2×D44—22no—
95C2×D44—41no—
96C2×D44—41no—
97C2×D44—41no—
98C2×Dic22—22no—
99C2×Dic22—22no—
100C2×Dic22—41no—
101C11×C4⋊C4—41no—
102C11×C22⋊C4—22no—
103C11×C22⋊C4—22no—
104C11×C22⋊C4—41no—
105C11×C22⋊C4—41no—
106C42×C11—22no—
107C22⋊Dic11—22no—
108C22⋊Dic11—22no—
109C22⋊Dic11—41no—
110(C2×D11)⋊C4—22no—
111(C2×D11)⋊C4—22no—
112(C2×D11)⋊C4—22no—
113(C2×D11)⋊C4—22no—
114(C2×D11)⋊C4—22no—
115(C2×D11)⋊C4—22no—
116(C2×D11)⋊C4—41no—
117(C2×D11)⋊C4—41no—
118(C2×D11)⋊C4—41no—
119(C2×D11)⋊C4D414yescomplemented
120(C2×D11)⋊C4D414yescomplemented
121Dic11⋊C4—41no—
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#4112yes—
138C23×C11C2411yescharacteristic
139C22×D11—21no—
140C22×D11—21no—
141C22×D11—21no—
142C22×D11—21no—
143C22×D11—21no—
144C22×D11—21no—
145C22×D11—21no—
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×D11C2×D412yes—
167D4×C11—44no—
168C2×C4×C11—21no—
169C2×C4×C11—21no—
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—
182C2×C4×C11C2×D412yes—
183C22⋊D11—44no—
184C22⋊D11—44no—
185C22⋊D11—44no—
186C22⋊D11—44no—
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×Dic11C2×D412yes—
201C2×Dic11C2×D412yes—
202D44—44no—
203D44—44no—
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#392—111no—
215#390—111no—
216#390D1111yescharacteristic, complemented
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×C11C22×D411yescharacteristic
235C22×C11C22×D411yescharacteristic
236C22×C11C2×#4111yescharacteristic
237C22×C11H(5,𝔽2)11yescharacteristic
238C22×C11H(5,𝔽2)11yescharacteristic
239C22×C11H(5,𝔽2)11yescharacteristic
240C22×C11H(5,𝔽2)11yescharacteristic
241C2×D11—22no—
242C2×D11—22no—
243C2×D11—22no—
244C2×D11—22no—
245C2×D11—22no—
246C2×D11—22no—
247C2×D11—416no—
248C2×D11—41no—
249C2×D11—41no—
250C2×D11—41no—
251C2×D11—41no—
252C2×D11—41no—
253C2×D11—41no—
254C2×D11—41no—
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—22no—
265C4×C11—41no—
266C4×C11—41no—
267C4×C11—41no—
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×D4—111no—
280C22×D4—111no—
281C22×D4C2×D1111yescharacteristic
282#124—224no—
283#124—224no—
284#120—224no—
285#120—224no—
286C2×C4⋊C4—111no—
287C2×C4⋊C4C2×D1111yescharacteristic, complemented
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⋊C4C2×D1111yescharacteristic
303C2×C22⋊C4C2×D1111yescharacteristic
304C2×C22⋊C4C2×D1111yescharacteristic, complemented
305C2×C22⋊C4C2×D1111yescharacteristic, complemented
306C2×C42—111no—
307C2×C42C2×D1111yescharacteristic, complemented
308#95—111no—
309#95—111no—
310#95—111no—
311#95—111no—
312C2×C11—42no—
313C2×C11—81no—
314C2×C11#53511yescharacteristic
315C2×C11#53511yescharacteristic
316C2×C11#53811yescharacteristic
317C2×C11D4211yescharacteristic
318C2×C11#54611yescharacteristic
319C2×C11#54611yescharacteristic
320C2×C11H(3,𝔽4)11yescharacteristic
321D11—42no—
322D11—42no—
323D11—81no—
324C24—111no—
325C24—111no—
326C24—111no—
327C24—222no—
328C24—222no—
329C24—222no—
330C24—441no—
331C24—441no—
332C24—441no—
333C24—441no—
334C24C22×D1111yescharacteristic
335C24C22×D1111yescharacteristic
336C2×Q8—222no—
337C2×Q8—222no—
338C2×Q8—441no—
339C2×D4—22no—
340C2×D4—22no—
341C2×D4—41no—
342C2×D4—222no—
343C2×D4—222no—
344C2×D4—222no—
345C2×D4—222no—
346C2×D4—222no—
347C2×D4—222no—
348C2×D4—222no—
349C2×D4—222no—
350C2×D4—441no—
351C2×D4—441no—
352C2×D4—441no—
353C2×D4—441no—
354C2×D4—441no—
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×C4C22×D1111yescharacteristic
366C22×C4C22×D1111yescharacteristic
367C22×C4C22×D1111yescharacteristic
368C22×C4C22×D1111yescharacteristic
369C22×C4C22×D1111yescharacteristic
370C4⋊C4—41no—
371C4⋊C4—441no—
372C22⋊C4—22no—
373C22⋊C4—22no—
374C22⋊C4—41no—
375C22⋊C4—41no—
376C22⋊C4—114no—
377C22⋊C4—114no—
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—22no—
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—112no—
407C23—112no—
408C23—221no—
409C23—221no—
410C23—221no—
411C23—221no—
412C23—221no—
413C23—221no—
414C23—221no—
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—
434C23#433912yes—
435C23C23×D1111yescharacteristic
436Q8—444no—
437D4—44no—
438D4—444no—
439D4—444no—
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—21no—
456C2×C4—21no—
457C2×C4—112no—
458C2×C4—112no—
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×C4D4×D1112yes—
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—222no—
489C22—222no—
490C22—222no—
491C22—222no—
492C22—222no—
493C22—222no—
494C22—4416no—
495C22—441no—
496C22—441no—
497C22—441no—
498C22—441no—
499C22—441no—
500C22—441no—
501C22—441no—
502C22—441no—
503C22—441no—
504C22—441no—
505C22—441no—
506C22—441no—
507C22—441no—
508C22—441no—
509C22—441no—
510C22C2×#433911yescharacteristic
511C22C2×D4×D1111yescharacteristic
512C22C2×D4×D1111yescharacteristic
513C22#6703711yescharacteristic
514C22#6703711yescharacteristic
515C22#6704211yescharacteristic
516C22#6704211yescharacteristic
517C4—22no—
518C4—22no—
519C4—41no—
520C4—41no—
521C4—41no—
522C4—222no—
523C4—222no—
524C4—441no—
525C4—441no—
526C4—441no—
527C2—42no—
528C2—81no—
529C2—442no—
530C2—442no—
531C2—881no—
532C2#1062302111yescharacteristic
533C2#1062308111yescharacteristic
534C2#1062309111yescharacteristic
535C2#1062313811yescharacteristic
536C2#1062314011yescharacteristic
537C2#1062321411yescharacteristic
538C2#1062324611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#390C2
hypercenter#390D11
hypocenterC11#2670
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×#66938C2semidirect
3. C2×#66935C2semidirect
4. C2×#66928C2semidirect
5. C11×#390C2semidirect
6. #10622836C2semidirect
7. #10622604C2semidirect
8. #10622603C2semidirect
9. #10622573C2semidirect
10. #10622573C2semidirect
11. #10622572C2semidirect
12. #10622570C2semidirect
13. #10622568C2semidirect
14. #10622560C2semidirect
15. #10622553C2semidirect
21. C22×C22⋊D11C22semidirect
24. C22×Dic22C22semidirect
25. C2×C11×C4⋊C4C22semidirect
28. C2×C11×C22⋊C4C22semidirect
29. C2×C11×C22⋊C4C22semidirect
30. C2×C42×C11C22semidirect
33. C2×C22⋊Dic11C22semidirect
43. C2×(C2×D11)⋊C4C22semidirect
44. C2×(C2×D11)⋊C4C22semidirect
45. C2×(C2×D11)⋊C4C22semidirect
46. C2×Dic11⋊C4C22semidirect
47. C2×C4×Dic11C22semidirect
51. C11⋊#95C22semidirect
52. C11⋊#95C22semidirect
53. C11⋊#95C22semidirect
54. C11⋊#95C22semidirect
119. (C2×D11)⋊C4D4semidirect
120. (C2×D11)⋊C4D4semidirect
216. #390D11semidirect
287. C2×C4⋊C4C2×D11semidirect
304. C2×C22⋊C4C2×D11semidirect
305. C2×C22⋊C4C2×D11semidirect
307. C2×C42C2×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×#669382
C2×#669352
C2×#669282
C11×#3902
#106228362
#106226042
#106226032
#106225732
#106225722
#106225702
#106225682
#106225602
#106225532
#267011