Finite Group Databasebeta

← #13074945

Subgroups — #13074945

Order 1408.

802 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×#67006C211yesmaximal, characteristic, complemented
2C2×#67006C211yesmaximal, characteristic, complemented
3C2×#66937C211yesmaximal, characteristic, complemented
4C2×#66936C211yesmaximal, characteristic, complemented
5C11×#379C211yesmaximal, characteristic, complemented
6#10622574C211yesmaximal, characteristic, complemented
7#10622573C211yesmaximal, characteristic, complemented
8#10622573C211yesmaximal, characteristic, complemented
9#10622572C211yesmaximal, characteristic, complemented
10#10622570C211yesmaximal, characteristic, complemented
11#10622570C211yesmaximal, characteristic, complemented
12#10622569C211yesmaximal, characteristic, complemented
13#10622565C211yesmaximal, characteristic, complemented
14#10622561C211yesmaximal, characteristic, complemented
15#10622557C211yesmaximal, characteristic, complemented
16C25×C11C2211yescharacteristic
17C22×C22⋊D11C2211yescharacteristic
18C22×C22⋊D11C2211yescharacteristic
19C22×C22⋊D11C2211yescharacteristic
20C22×C22⋊D11C2211yescharacteristic
21C22×C22⋊D11C2211yescharacteristic
22C22×C22⋊D11C2211yescharacteristic
23C22×D44C2211yescharacteristic, complemented
24C22×C4×D11C2211yescharacteristic, complemented
25C2×C11×C22⋊C4C2211yescharacteristic
26C2×C11×C22⋊C4C2211yescharacteristic
27C2×C11×C22⋊C4C2211yescharacteristic
28C2×C11×C22⋊C4C2211yescharacteristic
29C2×C11×C22⋊C4C2211yescharacteristic
30C2×C11×C22⋊C4C2211yescharacteristic
31#67006—24no—
32#67006—24no—
33C2×C22⋊Dic11C2211yescharacteristic
34C2×C22⋊Dic11C2211yescharacteristic
35C2×C22⋊Dic11C2211yescharacteristic
36C2×C22⋊Dic11C2211yescharacteristic
37C2×C22⋊Dic11C2211yescharacteristic
38C2×C22⋊Dic11C2211yescharacteristic
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×C4⋊Dic11C2211yescharacteristic, complemented
45C2×Dic11⋊C4C2211yescharacteristic, complemented
46C2×Dic11⋊C4C2211yescharacteristic, complemented
47C2×Dic11⋊C4C2211yescharacteristic, complemented
48C2×C4×Dic11C2211yescharacteristic, complemented
49#66937—24no—
50#66936—24no—
51C11⋊#95C2211yescharacteristic, complemented
52C11⋊#95C2211yescharacteristic, complemented
53C11⋊#95C2211yescharacteristic, complemented
54C11⋊#95C2211yescharacteristic, complemented
55C24×C11—22no—
56C24×C11—22no—
57C24×C11—22no—
58C24×C11—41no—
59C24×C11—41no—
60C24×C11—41no—
61C24×C11—41no—
62C24×C11C2311yescharacteristic
63C24×C11C2311yescharacteristic
64C24×C11C2311yescharacteristic
65C23×D11C2311yescharacteristic
66C23×D11C2311yescharacteristic
67C22×C4×C11C2311yescharacteristic
68C22×C4×C11C2311yescharacteristic
69C22×C4×C11C2311yescharacteristic
70C22×C4×C11C2311yescharacteristic
71C2×C22⋊D11—22no—
72C2×C22⋊D11—22no—
73C2×C22⋊D11—22no—
74C2×C22⋊D11—22no—
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—
87C2×C22⋊D11—41no—
88C2×C22⋊D11D414yescomplemented
89C22×Dic11C2311yescharacteristic
90C22×Dic11C2311yescharacteristic
91C22×Dic11C2311yescharacteristic
92C22×Dic11C2311yescharacteristic
93C22×Dic11C2311yescharacteristic
94C22×Dic11C2311yescharacteristic
95C2×D44—22no—
96C2×D44—41no—
97C2×D44—41no—
98C2×C4×D11—22no—
99C2×C4×D11—22no—
100C2×C4×D11—41no—
101C11×C22⋊C4—22no—
102C11×C22⋊C4—22no—
103C11×C22⋊C4—41no—
104C11×C22⋊C4—41no—
105C11×C22⋊C4—41no—
106C11×C22⋊C4—41no—
107C22⋊Dic11—22no—
108C22⋊Dic11—22no—
109C22⋊Dic11—22no—
110C22⋊Dic11—22no—
111C22⋊Dic11—22no—
112C22⋊Dic11D414yescomplemented
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—
118C4⋊Dic11—22no—
119Dic11⋊C4—22no—
120Dic11⋊C4—22no—
121Dic11⋊C4—41no—
122C4×Dic11—41no—
123#2678—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—44no—
143C23×C11—44no—
144C23×C11—44no—
145C23×C11—44no—
146C23×C11—44no—
147C23×C11—44no—
148C23×C11—44no—
149C23×C11C2×D412yes—
150C23×C11C2×D412yes—
151C23×C11#4112yes—
152C23×C11C2411yescharacteristic
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—21no—
164C22×D11—21no—
165C22×D11—21no—
166C22×D11C2×D412yes—
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—
179C22⋊D11—44no—
180C22⋊D11—44no—
181C22⋊D11—44no—
182C22⋊D11—44no—
183C22⋊D11—44no—
184C22⋊D11—44no—
185C2×Dic11—21no—
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×Dic11C2×D412yes—
201C2×Dic11C2×D412yes—
202C2×Dic11C2×D412yes—
203D44—44no—
204C4×D11—44no—
205C2×#123—111no—
206C2×#121—111no—
207C2×#120—111no—
208C2×#120—111no—
209#397—111no—
210#396—111no—
211#394—111no—
212#394—111no—
213#392—111no—
214#392—111no—
215#390—111no—
216#390—111no—
217#388—111no—
218#386—111no—
219#379D1111yescharacteristic, complemented
220C22×C11—22no—
221C22×C11—22no—
222C22×C11—22no—
223C22×C11—22no—
224C22×C11—22no—
225C22×C11—22no—
226C22×C11—22no—
227C22×C11—22no—
228C22×C11—22no—
229C22×C11—416no—
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×C11—41no—
242C22×C11C22×D411yescharacteristic
243C22×C11C22×D411yescharacteristic
244C22×C11C2×#4111yescharacteristic
245C22×C11H(5,𝔽2)11yescharacteristic
246C22×C11H(5,𝔽2)11yescharacteristic
247C22×C11H(5,𝔽2)11yescharacteristic
248C22×C11H(5,𝔽2)11yescharacteristic
249C2×D11—22no—
250C2×D11—22no—
251C2×D11—22no—
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—41no—
264C4×C11—41no—
265C4×C11—41no—
266C4×C11—41no—
267Dic11—22no—
268Dic11—22no—
269Dic11—22no—
270Dic11—41no—
271Dic11—41no—
272Dic11—41no—
273C25C2×D1111yescharacteristic
274C22×D4—111no—
275C22×D4—111no—
276C22×D4—111no—
277C22×D4—111no—
278C22×D4—111no—
279C22×D4—111no—
280C22×D4—111no—
281C23×C4—111no—
282#123—224no—
283#121—224no—
284#120—224no—
285#120—224no—
286C2×C4⋊C4—111no—
287C2×C4⋊C4—111no—
288C2×C4⋊C4—111no—
289C2×C4⋊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⋊C4C2×D1111yescharacteristic
302C2×C22⋊C4C2×D1111yescharacteristic
303C2×C22⋊C4C2×D1111yescharacteristic
304C2×C22⋊C4C2×D1111yescharacteristic
305C2×C22⋊C4C2×D1111yescharacteristic
306C2×C22⋊C4C2×D1111yescharacteristic
307C2×C42—111no—
308#95—111no—
309#95—111no—
310#95—111no—
311#95—111no—
312C2×C11—42no—
313C2×C11—42no—
314C2×C11—42no—
315C2×C11#53411yescharacteristic
316C2×C11#53511yescharacteristic
317C2×C11#53811yescharacteristic
318C2×C11D4211yescharacteristic
319C2×C11#54611yescharacteristic
320C2×C11#54611yescharacteristic
321C2×C11#56011yescharacteristic
322D11—42no—
323D11—81no—
324C24—22no—
325C24—22no—
326C24—22no—
327C24—41no—
328C24—41no—
329C24—41no—
330C24—41no—
331C24—111no—
332C24—111no—
333C24C22×D1111yescharacteristic
334C24C22×D1111yescharacteristic
335C24C22×D1111yescharacteristic
336C2×D4—114no—
337C2×D4—222no—
338C2×D4—222no—
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—441no—
348C2×D4—441no—
349C2×D4—441no—
350C2×D4—441no—
351C2×D4—441no—
352C2×D4—441no—
353C2×D4—441no—
354C2×D4—441no—
355C2×D4—441no—
356C2×D4—441no—
357C22×C4—111no—
358C22×C4—111no—
359C22×C4—111no—
360C22×C4—111no—
361C22×C4—111no—
362C22×C4—111no—
363C22×C4—222no—
364C22×C4—222no—
365C22×C4—441no—
366C22×C4C22×D1111yescharacteristic
367C22×C4C22×D1111yescharacteristic
368C22×C4C22×D1111yescharacteristic
369C22×C4C22×D1111yescharacteristic
370C4⋊C4—222no—
371C4⋊C4—222no—
372C4⋊C4—222no—
373C4⋊C4—441no—
374C22⋊C4—22no—
375C22⋊C4—22no—
376C22⋊C4—41no—
377C22⋊C4—41no—
378C22⋊C4—41no—
379C22⋊C4—41no—
380C22⋊C4—114no—
381C22⋊C4—222no—
382C22⋊C4—222no—
383C22⋊C4—222no—
384C22⋊C4—222no—
385C22⋊C4—222no—
386C22⋊C4—222no—
387C22⋊C4—222no—
388C22⋊C4—441no—
389C22⋊C4—441no—
390C22⋊C4—441no—
391C42—441no—
392C11#267811yescharacteristic, 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—44no—
412C23—44no—
413C23—44no—
414C23—44no—
415C23—44no—
416C23—44no—
417C23—44no—
418C23—112no—
419C23—221no—
420C23—221no—
421C23—221no—
422C23—221no—
423C23—221no—
424C23—221no—
425C23—221no—
426C23—221no—
427C23—221no—
428C23—221no—
429C23—221no—
430C23—221no—
431C23—221no—
432C23#433912yes—
433C23D4×D1112yes—
434C23D4×D1112yes—
435C23C23×D1111yescharacteristic
436D4—444no—
437D4—444no—
438D4—444no—
439D4—444no—
440D4—444no—
441D4—444no—
442D4—444no—
443C2×C4—21no—
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×C4—444no—
474C22—22no—
475C22—22no—
476C22—22no—
477C22—22no—
478C22—22no—
479C22—22no—
480C22—22no—
481C22—22no—
482C22—22no—
483C22—416no—
484C22—41no—
485C22—41no—
486C22—41no—
487C22—41no—
488C22—41no—
489C22—41no—
490C22—41no—
491C22—41no—
492C22—41no—
493C22—41no—
494C22—41no—
495C22—41no—
496C22—222no—
497C22—222no—
498C22—222no—
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#6703711yescharacteristic
516C22#6703711yescharacteristic
517C4—41no—
518C4—41no—
519C4—41no—
520C4—41no—
521C4—222no—
522C4—222no—
523C4—222no—
524C4—441no—
525C4—441no—
526C4—441no—
527C2—42no—
528C2—42no—
529C2—42no—
530C2—442no—
531C2—881no—
532C2#1062302111yescharacteristic
533C2#1062302111yescharacteristic
534C2#1062302511yescharacteristic
535C2#1062312011yescharacteristic
536C2#1062312111yescharacteristic
537C2#1062312311yescharacteristic
538C2#1062312611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#379C2
hypercenter#379D11
hypocenterC11#2678
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #379

Complements

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

NH ≅ G/Ntype
1. C2×#67006C2semidirect
2. C2×#67006C2semidirect
3. C2×#66937C2semidirect
4. C2×#66936C2semidirect
5. C11×#379C2semidirect
6. #10622574C2semidirect
7. #10622573C2semidirect
8. #10622573C2semidirect
9. #10622572C2semidirect
10. #10622570C2semidirect
11. #10622570C2semidirect
12. #10622569C2semidirect
13. #10622565C2semidirect
14. #10622561C2semidirect
15. #10622557C2semidirect
23. C22×D44C22semidirect
24. C22×C4×D11C22semidirect
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×C4⋊Dic11C22semidirect
45. C2×Dic11⋊C4C22semidirect
46. C2×Dic11⋊C4C22semidirect
47. C2×Dic11⋊C4C22semidirect
48. C2×C4×Dic11C22semidirect
51. C11⋊#95C22semidirect
52. C11⋊#95C22semidirect
53. C11⋊#95C22semidirect
54. C11⋊#95C22semidirect
88. C2×C22⋊D11D4semidirect
112. C22⋊Dic11D4semidirect
219. #379D11semidirect
392. C11#2678semidirect

Maximal subgroups

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

subgroupindex
C2×#670062
C2×#669372
C2×#669362
C11×#3792
#106225742
#106225732
#106225722
#106225702
#106225692
#106225652
#106225612
#106225572
#267811