Finite Group Databasebeta

← #13074820

Subgroups — #13074820

Order 1408.

816 conjugacy classes of subgroups.

The subgroup lattice has 542 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×#66992C211yesmaximal, characteristic, complemented
4C2×#66991C211yesmaximal, characteristic, complemented
5#10622860C211yesmaximal, characteristic, complemented
6#10622836C211yesmaximal, characteristic, complemented
7#10622835C211yesmaximal, characteristic, complemented
8#10622833C211yesmaximal, characteristic, complemented
9#10622833C211yesmaximal, characteristic, complemented
10#10622572C211yesmaximal, characteristic, complemented
11#10622569C211yesmaximal, characteristic, complemented
12#10622569C211yesmaximal, characteristic, complemented
13#10622566C211yesmaximal, characteristic, complemented
14#10622565C211yesmaximal, characteristic, complemented
15#10622562C211yesmaximal, 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
24C23×Dic11C2211yescharacteristic, complemented
25C22×C4×D11C2211yescharacteristic, complemented
26C11×#120—24no—
27C2×C11×C22⋊C4C2211yescharacteristic
28C2×C11×C22⋊C4C2211yescharacteristic
29C2×C11×C22⋊C4C2211yescharacteristic
30#67006—24no—
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
40C2×C22⋊Dic11C2211yescharacteristic, complemented
41C2×C22⋊Dic11C2211yescharacteristic, complemented
42#66992—24no—
43#66991—24no—
44C2×(C2×D11)⋊C4C2211yescharacteristic, complemented
45C2×(C2×D11)⋊C4C2211yescharacteristic, complemented
46C2×C4⋊Dic11C2211yescharacteristic, complemented
47C2×Dic11⋊C4C2211yescharacteristic, complemented
48C2×Dic11⋊C4C2211yescharacteristic, complemented
49C11⋊#95C2211yescharacteristic, complemented
50C11⋊#95C2211yescharacteristic, complemented
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—41no—
72C2×D4×C11—41no—
73C2×D4×C11—41no—
74C2×D4×C11—41no—
75C2×D4×C11D414yescomplemented
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—22no—
85C2×C22⋊D11—41no—
86C2×C22⋊D11—41no—
87C2×C22⋊D11—41no—
88C2×C22⋊D11—41no—
89C2×C22⋊D11—41no—
90C2×C22⋊D11D414yescomplemented
91C22×Dic11—22no—
92C22×Dic11—41no—
93C22×Dic11—41no—
94C22×Dic11C2311yescharacteristic
95C22×Dic11C2311yescharacteristic
96C22×Dic11C2311yescharacteristic
97C22×Dic11C2311yescharacteristic
98C22×Dic11C2311yescharacteristic
99C22×Dic11C2311yescharacteristic
100C22×Dic11C2311yescharacteristic
101C2×C4×D11—22no—
102C2×C4×D11—41no—
103C2×C4×D11—41no—
104C11×C22⋊C4—22no—
105C11×C22⋊C4—22no—
106C11×C22⋊C4—22no—
107C22⋊Dic11—22no—
108C22⋊Dic11—22no—
109C22⋊Dic11—22no—
110C22⋊Dic11—22no—
111C22⋊Dic11—22no—
112C22⋊Dic11—22no—
113C22⋊Dic11—41no—
114C22⋊Dic11—41no—
115C22⋊Dic11—41no—
116C22⋊Dic11—41no—
117C22⋊Dic11—41no—
118(C2×D11)⋊C4—22no—
119(C2×D11)⋊C4—41no—
120C4⋊Dic11—22no—
121Dic11⋊C4—22no—
122Dic11⋊C4—41no—
123#2668—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—44no—
149C23×C11—44no—
150C23×C11—44no—
151C23×C11—44no—
152C23×C11—44no—
153C23×C11—44no—
154C23×C11—44no—
155C23×C11C2×D412yes—
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×D11C2×D412yes—
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×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×Dic11—21no—
203C2×Dic11—44no—
204C2×Dic11C2×D412yes—
205C4×D11—44no—
206C2×#121—111no—
207C2×#121—111no—
208C2×#120—111no—
209C2×#120D1111yescharacteristic, complemented
210#399—111no—
211#397—111no—
212#397—111no—
213#394—111no—
214#394—111no—
215#392—111no—
216#386—111no—
217#386—111no—
218#386—111no—
219#386—111no—
220#379—111no—
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—22no—
230C22×C11—22no—
231C22×C11—22no—
232C22×C11—22no—
233C22×C11—416no—
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×C11—41no—
250C22×C11C22×D411yescharacteristic
251C22×C11C22×D411yescharacteristic
252C22×C11C2×#4111yescharacteristic
253C22×C11H(5,𝔽2)11yescharacteristic
254C22×C11H(5,𝔽2)11yescharacteristic
255C22×C11H(5,𝔽2)11yescharacteristic
256C22×C11H(5,𝔽2)11yescharacteristic
257C2×D11—22no—
258C2×D11—22no—
259C2×D11—22no—
260C2×D11—41no—
261C2×D11—41no—
262C2×D11—41no—
263C2×D11—41no—
264C4×C11—22no—
265C4×C11—41no—
266C4×C11—41no—
267Dic11—22no—
268Dic11—41no—
269Dic11—41no—
270Dic11—41no—
271Dic11—41no—
272Dic11—41no—
273Dic11—41no—
274C25C2×D1111yescharacteristic
275C22×D4—111no—
276C22×D4—111no—
277C22×D4—111no—
278C22×D4—111no—
279C22×D4C2×D1111yescharacteristic
280C22×D4C2×D1111yescharacteristic
281C22×D4C2×D1111yescharacteristic
282C23×C4—111no—
283C23×C4—111no—
284#121—224no—
285#121—224no—
286#120—24no—
287#120—224no—
288C2×C4⋊C4—111no—
289C2×C4⋊C4—111no—
290C2×C4⋊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⋊C4—111no—
304C2×C22⋊C4C2×D1111yescharacteristic
305C2×C22⋊C4C2×D1111yescharacteristic
306C2×C22⋊C4C2×D1111yescharacteristic
307#95—111no—
308#95—111no—
309#95—111no—
310#95—111no—
311#95—111no—
312#95—111no—
313C2×C11—42no—
314C2×C11—42no—
315C2×C11—42no—
316C2×C11—42no—
317C2×C11#53411yescharacteristic
318C2×C11#53411yescharacteristic
319C2×C11#53811yescharacteristic
320C2×C11D4211yescharacteristic
321C2×C11#54611yescharacteristic
322C2×C11#54611yescharacteristic
323C2×C11#56011yescharacteristic
324D11—42no—
325C24—22no—
326C24—22no—
327C24—22no—
328C24—41no—
329C24—41no—
330C24—41no—
331C24—41no—
332C24—111no—
333C24C22×D1111yescharacteristic
334C24C22×D1111yescharacteristic
335C24C22×D1111yescharacteristic
336C24C22×D1111yescharacteristic
337C2×D4—22no—
338C2×D4—22no—
339C2×D4—22no—
340C2×D4—22no—
341C2×D4—41no—
342C2×D4—41no—
343C2×D4—41no—
344C2×D4—41no—
345C2×D4—114no—
346C2×D4—222no—
347C2×D4—222no—
348C2×D4—222no—
349C2×D4—222no—
350C2×D4—222no—
351C2×D4—222no—
352C2×D4—441no—
353C2×D4—441no—
354C2×D4—441no—
355C2×D4—441no—
356C2×D4—441no—
357C2×D4C22⋊D1114yescomplemented
358C22×C4—111no—
359C22×C4—111no—
360C22×C4—111no—
361C22×C4—111no—
362C22×C4—111no—
363C22×C4—111no—
364C22×C4—111no—
365C22×C4—222no—
366C22×C4—222no—
367C22×C4—441no—
368C22×C4—441no—
369C22×C4—441no—
370C22×C4—441no—
371C22×C4C22×D1111yescharacteristic
372C22×C4C22×D1111yescharacteristic
373C22×C4C22×D1111yescharacteristic
374C4⋊C4—222no—
375C4⋊C4—222no—
376C4⋊C4—441no—
377C22⋊C4—22no—
378C22⋊C4—22no—
379C22⋊C4—22no—
380C22⋊C4—222no—
381C22⋊C4—222no—
382C22⋊C4—222no—
383C22⋊C4—222no—
384C22⋊C4—222no—
385C22⋊C4—222no—
386C22⋊C4—222no—
387C22⋊C4—441no—
388C22⋊C4—441no—
389C22⋊C4—441no—
390C22⋊C4—441no—
391C22⋊C4—441no—
392C22⋊C4—441no—
393C11#266811yescharacteristic, complemented, Sylow
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—112no—
426C23—221no—
427C23—221no—
428C23—221no—
429C23—221no—
430C23—221no—
431C23—221no—
432C23D4×D1112yes—
433C23#434112yes—
434C23C2×C22⋊D1112yes—
435C23C2×C22⋊D1112yes—
436C23C23×D1111yescharacteristic
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—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×C4—221no—
473C2×C4—444no—
474C2×C4—444no—
475C2×C4C2×C22⋊D1112yes—
476C22—22no—
477C22—22no—
478C22—22no—
479C22—22no—
480C22—22no—
481C22—22no—
482C22—22no—
483C22—22no—
484C22—22no—
485C22—22no—
486C22—22no—
487C22—22no—
488C22—416no—
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—41no—
504C22—41no—
505C22—222no—
506C22—222no—
507C22—222no—
508C22—441no—
509C22—441no—
510C22—441no—
511C22—441no—
512C22C2×D4×D1111yescharacteristic
513C22C2×#434111yescharacteristic
514C22#6703711yescharacteristic
515C22#6703711yescharacteristic
516C22#6703711yescharacteristic
517C22#6703711yescharacteristic
518C22C22×C22⋊D1111yescharacteristic
519C4—22no—
520C4—41no—
521C4—41no—
522C4—222no—
523C4—441no—
524C4—441no—
525C4—441no—
526C4—441no—
527C4—441no—
528C4—441no—
529C2—42no—
530C2—42no—
531C2—42no—
532C2—42no—
533C2—442no—
534C2#1062312011yescharacteristic
535C2#1062312211yescharacteristic
536C2#1062312411yescharacteristic
537C2#1062312611yescharacteristic
538C2D4×C22⋊D1111yescharacteristic
539C2#1062333511yescharacteristic
540C2#1062333711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC2×C11×#120C2
hypercenterC2×#120D11
hypocenterC11#2668
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×#66992C2semidirect
4. C2×#66991C2semidirect
5. #10622860C2semidirect
6. #10622836C2semidirect
7. #10622835C2semidirect
8. #10622833C2semidirect
9. #10622833C2semidirect
10. #10622572C2semidirect
11. #10622569C2semidirect
12. #10622569C2semidirect
13. #10622566C2semidirect
14. #10622565C2semidirect
15. #10622562C2semidirect
23. C22×C22⋊D11C22semidirect
24. C23×Dic11C22semidirect
25. C22×C4×D11C22semidirect
40. C2×C22⋊Dic11C22semidirect
41. C2×C22⋊Dic11C22semidirect
44. C2×(C2×D11)⋊C4C22semidirect
45. C2×(C2×D11)⋊C4C22semidirect
46. C2×C4⋊Dic11C22semidirect
47. C2×Dic11⋊C4C22semidirect
48. C2×Dic11⋊C4C22semidirect
49. C11⋊#95C22semidirect
50. C11⋊#95C22semidirect
51. C11⋊#95C22semidirect
52. C11⋊#95C22semidirect
53. C11⋊#95C22semidirect
54. C11⋊#95C22semidirect
75. C2×D4×C11D4semidirect
90. C2×C22⋊D11D4semidirect
209. C2×#120D11semidirect
357. C2×D4C22⋊D11semidirect
393. C11#2668semidirect

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×#669922
C2×#669912
#106228602
#106228362
#106228352
#106228332
#106225722
#106225692
#106225662
#106225652
#106225622
#266811