Finite Group Databasebeta

← #13074838

Subgroups — #13074838

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×C11×#120C211yesmaximal, characteristic, complemented
2C2×#67006C211yesmaximal, characteristic, complemented
3C2×#66989C211yesmaximal, characteristic, complemented
4C2×#66938C211yesmaximal, characteristic, complemented
5#10622860C211yesmaximal, characteristic, complemented
6#10622836C211yesmaximal, characteristic, complemented
7#10622836C211yesmaximal, characteristic, complemented
8#10622836C211yesmaximal, characteristic, complemented
9#10622835C211yesmaximal, characteristic, complemented
10#10622834C211yesmaximal, characteristic, complemented
11#10622574C211yesmaximal, characteristic, complemented
12#10622570C211yesmaximal, characteristic, complemented
13#10622564C211yesmaximal, characteristic, complemented
14#10622560C211yesmaximal, characteristic, complemented
15#10622557C211yesmaximal, characteristic, complemented
16C25×C11C2211yescharacteristic
17C22×D4×C11C2211yescharacteristic
18C22×D4×C11C2211yescharacteristic
19C22×D4×C11C2211yescharacteristic
20C22×C22⋊D11C2211yescharacteristic
21C22×C22⋊D11C2211yescharacteristic
22C22×C22⋊D11C2211yescharacteristic
23C22×C22⋊D11C2211yescharacteristic, complemented
24C22×Dic22C2211yescharacteristic, complemented
25C11×#120—24no—
26C2×C11×C22⋊C4C2211yescharacteristic
27C2×C11×C22⋊C4C2211yescharacteristic
28C2×C11×C22⋊C4C2211yescharacteristic
29#67006—24no—
30C2×C22⋊Dic11C2211yescharacteristic
31C2×C22⋊Dic11C2211yescharacteristic
32C2×C22⋊Dic11C2211yescharacteristic
33C2×C22⋊Dic11C2211yescharacteristic
34C2×C22⋊Dic11C2211yescharacteristic
35C2×C22⋊Dic11C2211yescharacteristic
36C2×C22⋊Dic11C2211yescharacteristic
37C2×C22⋊Dic11C2211yescharacteristic
38C2×C22⋊Dic11C2211yescharacteristic
39C2×C22⋊Dic11C2211yescharacteristic, complemented
40C2×C22⋊Dic11C2211yescharacteristic, complemented
41C2×C22⋊Dic11C2211yescharacteristic, complemented
42#66989—24no—
43C2×(C2×D11)⋊C4C2211yescharacteristic, complemented
44C2×(C2×D11)⋊C4C2211yescharacteristic, complemented
45C2×(C2×D11)⋊C4C2211yescharacteristic, complemented
46C2×C4⋊Dic11C2211yescharacteristic, 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×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
65C24×C11C2311yescharacteristic
66C23×D11C2311yescharacteristic
67C2×D4×C11—22no—
68C2×D4×C11—22no—
69C2×D4×C11—22no—
70C2×D4×C11—22no—
71C2×D4×C11—22no—
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
79C2×C22⋊D11—22no—
80C2×C22⋊D11—22no—
81C2×C22⋊D11—22no—
82C2×C22⋊D11—22no—
83C2×C22⋊D11—22no—
84C2×C22⋊D11—41no—
85C2×C22⋊D11—41no—
86C2×C22⋊D11—41no—
87C2×C22⋊D11—41no—
88C2×C22⋊D11—41no—
89C2×C22⋊D11—41no—
90C2×C22⋊D11—41no—
91C22×Dic11C2311yescharacteristic
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—22no—
103C11×C22⋊C4D414yescomplemented
104C22⋊Dic11—22no—
105C22⋊Dic11—22no—
106C22⋊Dic11—22no—
107C22⋊Dic11—22no—
108C22⋊Dic11—22no—
109C22⋊Dic11—22no—
110C22⋊Dic11—41no—
111C22⋊Dic11—41no—
112C22⋊Dic11—41no—
113C22⋊Dic11—41no—
114C22⋊Dic11—41no—
115C22⋊Dic11D414yescomplemented
116(C2×D11)⋊C4—22no—
117(C2×D11)⋊C4—22no—
118(C2×D11)⋊C4—41no—
119C4⋊Dic11—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×C11—21no—
145C23×C11—21no—
146C23×C11—21no—
147C23×C11—21no—
148C23×C11—21no—
149C23×C11—44no—
150C23×C11—44no—
151C23×C11—44no—
152C23×C11—44no—
153C23×C11—44no—
154C23×C11—44no—
155C23×C11—44no—
156C23×C11C2×D412yes—
157C23×C11C2×D412yes—
158C23×C11#4112yes—
159C23×C11C2411yescharacteristic
160C22×D11—21no—
161C22×D11—21no—
162C22×D11—21no—
163C22×D11—21no—
164C22×D11—21no—
165C22×D11—21no—
166C22×D11—21no—
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×C11C2×D412yes—
178C2×C4×C11C2×D412yes—
179C22⋊D11—44no—
180C22⋊D11—44no—
181C22⋊D11—44no—
182C22⋊D11—44no—
183C2×Dic11—21no—
184C2×Dic11—21no—
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×Dic11—21no—
201C2×Dic11—21no—
202C2×Dic11C2×D412yes—
203C2×Dic11C2×D412yes—
204Dic22—44no—
205C2×#124—111no—
206C2×#124—111no—
207C2×#120—111no—
208C2×#120D1111yescharacteristic, complemented
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#388—111no—
219#379—111no—
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×C11—41no—
243C22×C11—41no—
244C22×C11—41no—
245C22×C11—41no—
246C22×C11—41no—
247C22×C11—41no—
248C22×C11—41no—
249C22×C11C22×D411yescharacteristic
250C22×C11C22×D411yescharacteristic
251C22×C11C2×#4111yescharacteristic
252C22×C11H(5,𝔽2)11yescharacteristic
253C22×C11H(5,𝔽2)11yescharacteristic
254C22×C11H(5,𝔽2)11yescharacteristic
255C22×C11H(5,𝔽2)11yescharacteristic
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—
266Dic11—22no—
267Dic11—22no—
268Dic11—41no—
269Dic11—41no—
270Dic11—41no—
271Dic11—41no—
272Dic11—41no—
273C25C2×D1111yescharacteristic
274C22×Q8—111no—
275C22×D4—111no—
276C22×D4—111no—
277C22×D4—111no—
278C22×D4—111no—
279C22×D4C2×D1111yescharacteristic
280C22×D4C2×D1111yescharacteristic
281C22×D4C2×D1111yescharacteristic
282#124—224no—
283#124—224no—
284#120—24no—
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
305C2×C22⋊C4C2×D1111yescharacteristic
306C2×C42—111no—
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—81no—
316C2×C11#53511yescharacteristic
317C2×C11#53511yescharacteristic
318C2×C11#53811yescharacteristic
319C2×C11D4211yescharacteristic
320C2×C11#54611yescharacteristic
321C2×C11#54611yescharacteristic
322C2×C11H(3,𝔽4)11yescharacteristic
323D11—81no—
324C24—22no—
325C24—22no—
326C24—22no—
327C24—41no—
328C24—41no—
329C24—41no—
330C24—41no—
331C24—111no—
332C24C22×D1111yescharacteristic
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—22no—
343C2×D4—22no—
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—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×C4—111no—
366C22×C4—111no—
367C22×C4C22×D1111yescharacteristic
368C22×C4C22×D1111yescharacteristic
369C22×C4C22×D1111yescharacteristic
370C4⋊C4—441no—
371C4⋊C4—441no—
372C22⋊C4—22no—
373C22⋊C4—22no—
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—441no—
384C22⋊C4—441no—
385C22⋊C4—441no—
386C22⋊C4—441no—
387C22⋊C4—441no—
388C22⋊C4—441no—
389C22⋊C4C22⋊D1114yescomplemented
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—21no—
414C23—21no—
415C23—21no—
416C23—21no—
417C23—21no—
418C23—44no—
419C23—44no—
420C23—44no—
421C23—44no—
422C23—44no—
423C23—44no—
424C23—44no—
425C23—221no—
426C23—221no—
427C23—221no—
428C23—221no—
429C23—221no—
430C23—221no—
431C23—221no—
432C23D4×D1112yes—
433C23#434112yes—
434C23C2×C22⋊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—112no—
452C2×C4—112no—
453C2×C4—221no—
454C2×C4—221no—
455C2×C4—221no—
456C2×C4—221no—
457C2×C4—221no—
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×C4C2×C22⋊D1112yes—
473C2×C4C2×C22⋊D1112yes—
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—41no—
497C22—41no—
498C22—41no—
499C22—41no—
500C22—41no—
501C22—41no—
502C22—41no—
503C22—441no—
504C22—441no—
505C22—441no—
506C22—441no—
507C22—441no—
508C22—441no—
509C22—441no—
510C22C2×D4×D1111yescharacteristic
511C22C2×#434111yescharacteristic
512C22#6703711yescharacteristic
513C22#6703711yescharacteristic
514C22#6703711yescharacteristic
515C22#6703711yescharacteristic
516C22C22×C22⋊D1111yescharacteristic
517C4—22no—
518C4—22no—
519C4—41no—
520C4—222no—
521C4—222no—
522C4—441no—
523C4—441no—
524C4—441no—
525C4—441no—
526C4—441no—
527C2—42no—
528C2—42no—
529C2—42no—
530C2—81no—
531C2—881no—
532C2#1062312211yescharacteristic
533C2#1062312311yescharacteristic
534C2#1062312411yescharacteristic
535C2#1062312511yescharacteristic
536C2D4×C22⋊D1111yescharacteristic
537C2#1062333611yescharacteristic
538C2#1062333711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC2×C11×#120C2
hypercenterC2×#120D11
hypocenterC11#2670
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#120

Complements

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

NH ≅ G/Ntype
1. C2×C11×#120C2semidirect
2. C2×#67006C2semidirect
3. C2×#66989C2semidirect
4. C2×#66938C2semidirect
5. #10622860C2semidirect
6. #10622836C2semidirect
7. #10622836C2semidirect
8. #10622836C2semidirect
9. #10622835C2semidirect
10. #10622834C2semidirect
11. #10622574C2semidirect
12. #10622570C2semidirect
13. #10622564C2semidirect
14. #10622560C2semidirect
15. #10622557C2semidirect
23. C22×C22⋊D11C22semidirect
24. C22×Dic22C22semidirect
39. C2×C22⋊Dic11C22semidirect
40. C2×C22⋊Dic11C22semidirect
41. C2×C22⋊Dic11C22semidirect
43. C2×(C2×D11)⋊C4C22semidirect
44. C2×(C2×D11)⋊C4C22semidirect
45. C2×(C2×D11)⋊C4C22semidirect
46. C2×C4⋊Dic11C22semidirect
47. C2×Dic11⋊C4C22semidirect
48. C2×C4×Dic11C22semidirect
49. C2×C4×Dic11C22semidirect
51. C11⋊#95C22semidirect
52. C11⋊#95C22semidirect
53. C11⋊#95C22semidirect
54. C11⋊#95C22semidirect
103. C11×C22⋊C4D4semidirect
115. C22⋊Dic11D4semidirect
208. C2×#120D11semidirect
389. C22⋊C4C22⋊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×C11×#1202
C2×#670062
C2×#669892
C2×#669382
#106228602
#106228362
#106228352
#106228342
#106225742
#106225702
#106225642
#106225602
#106225572
#267011