Finite Group Databasebeta

← #13074840

Subgroups — #13074840

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×#66938C211yesmaximal, characteristic, complemented
2C2×#66935C211yesmaximal, characteristic, complemented
3C2×#66935C211yesmaximal, characteristic, complemented
4C2×#66928C211yesmaximal, characteristic, complemented
5C11×#388C211yesmaximal, characteristic, complemented
6#10622604C211yesmaximal, characteristic, complemented
7#10622601C211yesmaximal, characteristic, complemented
8#10622574C211yesmaximal, characteristic, complemented
9#10622573C211yesmaximal, characteristic, complemented
10#10622568C211yesmaximal, characteristic, complemented
11#10622552C211yesmaximal, characteristic, complemented
12#10622286C211yesmaximal, characteristic, complemented
13#10622284C211yesmaximal, characteristic, complemented
14#10622284C211yesmaximal, characteristic, complemented
15#10622283C211yesmaximal, characteristic, complemented
16C24×D11C2211yescharacteristic
17C22×C22⋊D11C2211yescharacteristic
18C22×C22⋊D11C2211yescharacteristic
19C22×D44C2211yescharacteristic
20C22×D44C2211yescharacteristic
21C22×D44C2211yescharacteristic
22C22×D44C2211yescharacteristic
23C22×D44C2211yescharacteristic, complemented
24C22×Dic22C2211yescharacteristic, complemented
25C2×C11×C4⋊C4C2211yescharacteristic, complemented
26C2×C11×C22⋊C4C2211yescharacteristic
27C2×C11×C22⋊C4C2211yescharacteristic
28C2×C11×C22⋊C4C2211yescharacteristic
29C2×C42×C11C2211yescharacteristic, complemented
30C2×C22⋊Dic11C2211yescharacteristic
31C2×(C2×D11)⋊C4C2211yescharacteristic
32C2×(C2×D11)⋊C4C2211yescharacteristic
33C2×(C2×D11)⋊C4C2211yescharacteristic
34C2×(C2×D11)⋊C4C2211yescharacteristic
35C2×(C2×D11)⋊C4C2211yescharacteristic
36C2×(C2×D11)⋊C4C2211yescharacteristic
37C2×(C2×D11)⋊C4C2211yescharacteristic
38C2×(C2×D11)⋊C4C2211yescharacteristic
39C2×(C2×D11)⋊C4C2211yescharacteristic, complemented
40C2×(C2×D11)⋊C4C2211yescharacteristic, complemented
41C2×(C2×D11)⋊C4C2211yescharacteristic, complemented
42C2×(C2×D11)⋊C4C2211yescharacteristic, complemented
43C2×(C2×D11)⋊C4C2211yescharacteristic, complemented
44C2×(C2×D11)⋊C4C2211yescharacteristic, complemented
45C2×C4⋊Dic11C2211yescharacteristic, complemented
46C2×C4×Dic11C2211yescharacteristic, complemented
47#66938—24no—
48#66935—24no—
49#66935—24no—
50#66928—24no—
51C11×#95C2211yescharacteristic, complemented
52C11×#95C2211yescharacteristic, complemented
53C11⋊#95C2211yescharacteristic, complemented
54C11⋊#95C2211yescharacteristic, complemented
55C24×C11C2311yescharacteristic
56C23×D11—22no—
57C23×D11—22no—
58C23×D11—22no—
59C23×D11—41no—
60C23×D11—41no—
61C23×D11—41no—
62C23×D11—41no—
63C23×D11C2311yescharacteristic
64C23×D11C2311yescharacteristic
65C23×D11C2311yescharacteristic
66C23×D11C2311yescharacteristic
67C22×C4×C11C2311yescharacteristic
68C22×C4×C11C2311yescharacteristic
69C22×C4×C11C2311yescharacteristic
70C22×C4×C11C2311yescharacteristic
71C22×C4×C11C2311yescharacteristic
72C22×C4×C11C2311yescharacteristic
73C2×C22⋊D11—22no—
74C2×C22⋊D11—22no—
75C2×C22⋊D11—22no—
76C2×C22⋊D11—41no—
77C2×C22⋊D11—41no—
78C2×C22⋊D11—41no—
79C22×Dic11C2311yescharacteristic
80C22×Dic11C2311yescharacteristic
81C22×Dic11C2311yescharacteristic
82C22×Dic11C2311yescharacteristic
83C2×D44—22no—
84C2×D44—22no—
85C2×D44—22no—
86C2×D44—22no—
87C2×D44—22no—
88C2×D44—22no—
89C2×D44—22no—
90C2×D44—41no—
91C2×D44—41no—
92C2×D44—41no—
93C2×D44—41no—
94C2×D44—41no—
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—41no—
104C11×C22⋊C4D414yescomplemented
105C42×C11—22no—
106C22⋊Dic11—22no—
107(C2×D11)⋊C4—22no—
108(C2×D11)⋊C4—22no—
109(C2×D11)⋊C4—22no—
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—41no—
116(C2×D11)⋊C4—41no—
117(C2×D11)⋊C4—41no—
118(C2×D11)⋊C4—41no—
119(C2×D11)⋊C4—41no—
120(C2×D11)⋊C4D414yescomplemented
121C4⋊Dic11—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×C11C2×D412yes—
131C23×C11C2411yescharacteristic
132C22×D11—21no—
133C22×D11—21no—
134C22×D11—21no—
135C22×D11—21no—
136C22×D11—21no—
137C22×D11—21no—
138C22×D11—21no—
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×D11#4112yes—
167C2×C4×C11—21no—
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×C11—21no—
182C2×C4×C11C2×D412yes—
183C2×C4×C11C2×D412yes—
184C2×C4×C11C2×D412yes—
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×Dic11C2×D412yes—
199D44—44no—
200D44—44no—
201D44—44no—
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#390—111no—
217#388—111no—
218#388D1111yescharacteristic, complemented
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×C11C22×D411yescharacteristic
228C22×C11C22×D411yescharacteristic
229C22×C11C2×#4111yescharacteristic
230C22×C11H(5,𝔽2)11yescharacteristic
231C22×C11H(5,𝔽2)11yescharacteristic
232C22×C11H(5,𝔽2)11yescharacteristic
233C22×C11H(5,𝔽2)11yescharacteristic
234C2×D11—22no—
235C2×D11—22no—
236C2×D11—22no—
237C2×D11—22no—
238C2×D11—22no—
239C2×D11—22no—
240C2×D11—416no—
241C2×D11—41no—
242C2×D11—41no—
243C2×D11—41no—
244C2×D11—41no—
245C2×D11—41no—
246C2×D11—41no—
247C2×D11—41no—
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—22no—
266C4×C11—41no—
267C4×C11—41no—
268C4×C11—41no—
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×D4—111no—
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⋊C4—111no—
303C2×C22⋊C4C2×D1111yescharacteristic
304C2×C22⋊C4C2×D1111yescharacteristic
305C2×C22⋊C4C2×D1111yescharacteristic
306C2×C42—111no—
307C2×C42C2×D1111yescharacteristic, complemented
308#95—111no—
309#95—111no—
310#95C2×D1111yescharacteristic, complemented
311#95C2×D1111yescharacteristic, complemented
312C2×C11—42no—
313C2×C11#53511yescharacteristic
314C2×C11#53511yescharacteristic
315C2×C11#53811yescharacteristic
316C2×C11D4211yescharacteristic
317C2×C11#54611yescharacteristic
318C2×C11#54611yescharacteristic
319C2×C11H(3,𝔽4)11yescharacteristic
320D11—42no—
321D11—42no—
322D11—81no—
323D11—81no—
324C24—111no—
325C24—111no—
326C24—111no—
327C24—111no—
328C24—222no—
329C24—222no—
330C24—222no—
331C24—441no—
332C24—441no—
333C24—441no—
334C24—441no—
335C24C22×D1111yescharacteristic
336C2×Q8—222no—
337C2×Q8—222no—
338C2×Q8—441no—
339C2×D4—222no—
340C2×D4—222no—
341C2×D4—222no—
342C2×D4—222no—
343C2×D4—222no—
344C2×D4—222no—
345C2×D4—222no—
346C2×D4—222no—
347C2×D4—222no—
348C2×D4—222no—
349C2×D4—441no—
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×C4C22×D1111yescharacteristic
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—41no—
374C22⋊C4—114no—
375C22⋊C4—222no—
376C22⋊C4—222no—
377C22⋊C4—222no—
378C22⋊C4—222no—
379C22⋊C4—222no—
380C22⋊C4—222no—
381C22⋊C4—222no—
382C22⋊C4—222no—
383C22⋊C4—222no—
384C22⋊C4—441no—
385C22⋊C4—441no—
386C22⋊C4—441no—
387C22⋊C4—441no—
388C22⋊C4—441no—
389C22⋊C4D4414yescomplemented
390C42—22no—
391C42—222no—
392C11#267011yescharacteristic, complemented, Sylow
393C23—21no—
394C23—21no—
395C23—21no—
396C23—21no—
397C23—21no—
398C23—21no—
399C23—112no—
400C23—112no—
401C23—221no—
402C23—221no—
403C23—221no—
404C23—221no—
405C23—221no—
406C23—221no—
407C23—221no—
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—
434C23C2×D4412yes—
435C23C23×D1111yescharacteristic
436Q8—444no—
437D4—444no—
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—21no—
458C2×C4—21no—
459C2×C4—112no—
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×C4C2×D4412yes—
472C2×C4C2×D4412yes—
473C2×C4D4×D1112yes—
474C22—22no—
475C22—22no—
476C22—22no—
477C22—41no—
478C22—41no—
479C22—41no—
480C22—41no—
481C22—222no—
482C22—222no—
483C22—222no—
484C22—222no—
485C22—222no—
486C22—222no—
487C22—4416no—
488C22—441no—
489C22—441no—
490C22—441no—
491C22—441no—
492C22—441no—
493C22—441no—
494C22—441no—
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—
510C22C22×D4411yescharacteristic
511C22C2×D4×D1111yescharacteristic
512C22#6703711yescharacteristic
513C22#41×D1111yescharacteristic
514C22#6704211yescharacteristic
515C22#6704211yescharacteristic
516C22#6704211yescharacteristic
517C4—22no—
518C4—22no—
519C4—22no—
520C4—41no—
521C4—41no—
522C4—41no—
523C4—222no—
524C4—441no—
525C4—441no—
526C4—441no—
527C2—42no—
528C2—442no—
529C2—442no—
530C2—881no—
531C2—881no—
532C2#1062305611yescharacteristic
533C2D4×D4411yescharacteristic
534C2#1062308511yescharacteristic
535C2#1062313811yescharacteristic
536C2#1062318511yescharacteristic
537C2#1062321411yescharacteristic
538C2#1062323511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#388C2
hypercenter#388D11
hypocenterC11#2670
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. C2×#66938C2semidirect
2. C2×#66935C2semidirect
3. C2×#66935C2semidirect
4. C2×#66928C2semidirect
5. C11×#388C2semidirect
6. #10622604C2semidirect
7. #10622601C2semidirect
8. #10622574C2semidirect
9. #10622573C2semidirect
10. #10622568C2semidirect
11. #10622552C2semidirect
12. #10622286C2semidirect
13. #10622284C2semidirect
14. #10622284C2semidirect
15. #10622283C2semidirect
23. C22×D44C22semidirect
24. C22×Dic22C22semidirect
25. C2×C11×C4⋊C4C22semidirect
29. C2×C42×C11C22semidirect
39. C2×(C2×D11)⋊C4C22semidirect
40. C2×(C2×D11)⋊C4C22semidirect
41. C2×(C2×D11)⋊C4C22semidirect
42. C2×(C2×D11)⋊C4C22semidirect
43. C2×(C2×D11)⋊C4C22semidirect
44. C2×(C2×D11)⋊C4C22semidirect
45. C2×C4⋊Dic11C22semidirect
46. C2×C4×Dic11C22semidirect
51. C11×#95C22semidirect
52. C11×#95C22semidirect
53. C11⋊#95C22semidirect
54. C11⋊#95C22semidirect
104. C11×C22⋊C4D4semidirect
120. (C2×D11)⋊C4D4semidirect
218. #388D11semidirect
287. C2×C4⋊C4C2×D11semidirect
307. C2×C42C2×D11semidirect
310. #95C2×D11semidirect
311. #95C2×D11semidirect
389. C22⋊C4D44semidirect
392. C11#2670semidirect

Maximal subgroups

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

subgroupindex
C2×#669382
C2×#669352
C2×#669282
C11×#3882
#106226042
#106226012
#106225742
#106225732
#106225682
#106225522
#106222862
#106222842
#106222832
#267011