Finite Group Databasebeta

← #13074819

Subgroups — #13074819

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×#121C211yesmaximal, characteristic, complemented
2C2×#66992C211yesmaximal, characteristic, complemented
3C2×#66990C211yesmaximal, characteristic, complemented
4C2×#66990C211yesmaximal, characteristic, complemented
5#10622836C211yesmaximal, characteristic, complemented
6#10622835C211yesmaximal, characteristic, complemented
7#10622833C211yesmaximal, characteristic, complemented
8#10622826C211yesmaximal, characteristic, complemented
9#10622826C211yesmaximal, characteristic, complemented
10#10622606C211yesmaximal, characteristic, complemented
11#10622605C211yesmaximal, characteristic, complemented
12#10622572C211yesmaximal, characteristic, complemented
13#10622571C211yesmaximal, characteristic, complemented
14#10622568C211yesmaximal, characteristic, complemented
15#10622565C211yesmaximal, characteristic, complemented
16C24×D11C2211yescharacteristic
17C22×D4×C11C2211yescharacteristic
18C22×D4×C11C2211yescharacteristic
19C22×D4×C11C2211yescharacteristic, complemented
20C23×C4×C11C2211yescharacteristic, complemented
21C22×C22⋊D11C2211yescharacteristic
22C22×C22⋊D11C2211yescharacteristic
23C22×C22⋊D11C2211yescharacteristic
24C22×C22⋊D11C2211yescharacteristic
25C23×Dic11C2211yescharacteristic, complemented
26C11×#121—24no—
27C2×C11×C4⋊C4C2211yescharacteristic, complemented
28C2×C11×C22⋊C4C2211yescharacteristic
29C2×C11×C22⋊C4C2211yescharacteristic, complemented
30C2×C22⋊Dic11C2211yescharacteristic
31C2×C22⋊Dic11C2211yescharacteristic
32C2×C22⋊Dic11C2211yescharacteristic
33C2×C22⋊Dic11C2211yescharacteristic, complemented
34C2×C22⋊Dic11C2211yescharacteristic, complemented
35C2×C22⋊Dic11C2211yescharacteristic, complemented
36#66992—24no—
37#66990—24no—
38#66990—24no—
39C2×(C2×D11)⋊C4C2211yescharacteristic
40C2×(C2×D11)⋊C4C2211yescharacteristic
41C2×(C2×D11)⋊C4C2211yescharacteristic
42C2×(C2×D11)⋊C4C2211yescharacteristic
43C2×(C2×D11)⋊C4C2211yescharacteristic
44C2×(C2×D11)⋊C4C2211yescharacteristic
45C2×(C2×D11)⋊C4C2211yescharacteristic
46C2×(C2×D11)⋊C4C2211yescharacteristic
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×C11C2311yescharacteristic
56C24×C11C2311yescharacteristic
57C24×C11C2311yescharacteristic
58C23×D11—22no—
59C23×D11—22no—
60C23×D11—22no—
61C23×D11—41no—
62C23×D11—41no—
63C23×D11—41no—
64C23×D11—41no—
65C23×D11C2311yescharacteristic
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×C11—22no—
77C22×C4×C11—41no—
78C22×C4×C11—41no—
79C22×C4×C11C2311yescharacteristic
80C22×C4×C11C2311yescharacteristic
81C22×C4×C11C2311yescharacteristic
82C22×C4×C11C2311yescharacteristic
83C2×C22⋊D11—22no—
84C2×C22⋊D11—22no—
85C2×C22⋊D11—22no—
86C2×C22⋊D11—22no—
87C2×C22⋊D11—22no—
88C2×C22⋊D11—22no—
89C2×C22⋊D11—41no—
90C2×C22⋊D11—41no—
91C2×C22⋊D11—41no—
92C2×C22⋊D11—41no—
93C2×C22⋊D11—41no—
94C2×C22⋊D11D414yescomplemented
95C22×Dic11—22no—
96C22×Dic11—41no—
97C22×Dic11—41no—
98C22×Dic11C2311yescharacteristic
99C22×Dic11C2311yescharacteristic
100C22×Dic11C2311yescharacteristic
101C22×Dic11C2311yescharacteristic
102C22×Dic11C2311yescharacteristic
103C22×Dic11C2311yescharacteristic
104C11×C4⋊C4—22no—
105C11×C22⋊C4—22no—
106C11×C22⋊C4—22no—
107C22⋊Dic11—22no—
108C22⋊Dic11—22no—
109C22⋊Dic11—22no—
110C22⋊Dic11—41no—
111C22⋊Dic11—41no—
112C22⋊Dic11—41no—
113(C2×D11)⋊C4—22no—
114(C2×D11)⋊C4—22no—
115(C2×D11)⋊C4—22no—
116(C2×D11)⋊C4—22no—
117(C2×D11)⋊C4—22no—
118(C2×D11)⋊C4—41no—
119(C2×D11)⋊C4—41no—
120(C2×D11)⋊C4—41no—
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×C11C2×D412yes—
143C23×C11C2×D412yes—
144C23×C11C2×D412yes—
145C23×C11C2411yescharacteristic
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—
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×C11—21no—
179C2×C4×C11—21no—
180C2×C4×C11—21no—
181C2×C4×C11—44no—
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×Dic11—21no—
201C2×Dic11—21no—
202C2×Dic11—21no—
203C2×Dic11—21no—
204C2×Dic11—44no—
205C2×Dic11C2×D412yes—
206C2×#121—111no—
207C2×#121D1111yescharacteristic, complemented
208C2×#120—111no—
209C2×#120—111no—
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—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—22no—
253C2×D11—22no—
254C2×D11—22no—
255C2×D11—416no—
256C2×D11—41no—
257C2×D11—41no—
258C2×D11—41no—
259C2×D11—41no—
260C2×D11—41no—
261C2×D11—41no—
262C2×D11—41no—
263C2×D11—41no—
264C4×C11—22no—
265C4×C11—41no—
266C4×C11—41no—
267C4×C11—41no—
268Dic11—22no—
269Dic11—41no—
270Dic11—41no—
271Dic11—41no—
272Dic11—41no—
273Dic11—41no—
274C25—111no—
275C22×D4—111no—
276C22×D4—111no—
277C22×D4—111no—
278C22×D4—111no—
279C22×D4C2×D1111yescharacteristic
280C22×D4C2×D1111yescharacteristic
281C22×D4C2×D1111yescharacteristic, complemented
282C23×C4—111no—
283C23×C4C2×D1111yescharacteristic, complemented
284#121—24no—
285#121—224no—
286#120—224no—
287#120—224no—
288C2×C4⋊C4—111no—
289C2×C4⋊C4—111no—
290C2×C4⋊C4C2×D1111yescharacteristic, complemented
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⋊C4—111no—
305C2×C22⋊C4C2×D1111yescharacteristic
306C2×C22⋊C4C2×D1111yescharacteristic, complemented
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#53411yescharacteristic
317C2×C11#53411yescharacteristic
318C2×C11#53811yescharacteristic
319C2×C11D4211yescharacteristic
320C2×C11#54611yescharacteristic
321C2×C11#54611yescharacteristic
322C2×C11#56011yescharacteristic
323D11—42no—
324D11—42no—
325C24—111no—
326C24—111no—
327C24—222no—
328C24—222no—
329C24—222no—
330C24—441no—
331C24—441no—
332C24—441no—
333C24—441no—
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—22no—
359C22×C4—41no—
360C22×C4—41no—
361C22×C4—111no—
362C22×C4—111no—
363C22×C4—111no—
364C22×C4—111no—
365C22×C4—111no—
366C22×C4—111no—
367C22×C4—222no—
368C22×C4—441no—
369C22×C4—441no—
370C22×C4C22×D1111yescharacteristic
371C22×C4C22×D1111yescharacteristic
372C22×C4C22×D1111yescharacteristic
373C22×C4C22×D1111yescharacteristic
374C4⋊C4—22no—
375C4⋊C4—222no—
376C4⋊C4—441no—
377C22⋊C4—22no—
378C22⋊C4—22no—
379C22⋊C4—222no—
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—112no—
413C23—112no—
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—444no—
427C23—444no—
428C23—444no—
429C23—444no—
430C23—444no—
431C23—444no—
432C23—444no—
433C23D4×D1112yes—
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—21no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—44no—
456C2×C4—112no—
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—221no—
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—41no—
486C22—41no—
487C22—41no—
488C22—41no—
489C22—41no—
490C22—41no—
491C22—41no—
492C22—41no—
493C22—41no—
494C22—41no—
495C22—41no—
496C22—41no—
497C22—222no—
498C22—222no—
499C22—222no—
500C22—222no—
501C22—222no—
502C22—222no—
503C22—4416no—
504C22—441no—
505C22—441no—
506C22—441no—
507C22—441no—
508C22—441no—
509C22—441no—
510C22—441no—
511C22—441no—
512C22C2×D4×D1111yescharacteristic
513C22#6703711yescharacteristic
514C22#6703711yescharacteristic
515C22#6703711yescharacteristic
516C22#41×D1111yescharacteristic
517C22#6704211yescharacteristic
518C22C22×C22⋊D1111yescharacteristic
519C4—22no—
520C4—41no—
521C4—41no—
522C4—41no—
523C4—222no—
524C4—441no—
525C4—441no—
526C4—441no—
527C4—441no—
528C4—441no—
529C2—42no—
530C2—42no—
531C2—42no—
532C2—442no—
533C2—442no—
534C2#1062313611yescharacteristic
535C2#1062314111yescharacteristic
536C2#1062314411yescharacteristic
537C2#1062315111yescharacteristic
538C2D4×C22⋊D1111yescharacteristic
539C2#1062333511yescharacteristic
540C2#1062336011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC2×C11×#121C2
hypercenterC2×#121D11
hypocenterC11#2668
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C2×C11×#121C2semidirect
2. C2×#66992C2semidirect
3. C2×#66990C2semidirect
4. C2×#66990C2semidirect
5. #10622836C2semidirect
6. #10622835C2semidirect
7. #10622833C2semidirect
8. #10622826C2semidirect
9. #10622826C2semidirect
10. #10622606C2semidirect
11. #10622605C2semidirect
12. #10622572C2semidirect
13. #10622571C2semidirect
14. #10622568C2semidirect
15. #10622565C2semidirect
19. C22×D4×C11C22semidirect
20. C23×C4×C11C22semidirect
25. C23×Dic11C22semidirect
27. C2×C11×C4⋊C4C22semidirect
29. C2×C11×C22⋊C4C22semidirect
33. C2×C22⋊Dic11C22semidirect
34. C2×C22⋊Dic11C22semidirect
35. C2×C22⋊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
94. C2×C22⋊D11D4semidirect
207. C2×#121D11semidirect
281. C22×D4C2×D11semidirect
283. C23×C4C2×D11semidirect
290. C2×C4⋊C4C2×D11semidirect
306. C2×C22⋊C4C2×D11semidirect
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×#1212
C2×#669922
C2×#669902
#106228362
#106228352
#106228332
#106228262
#106226062
#106226052
#106225722
#106225712
#106225682
#106225652
#266811