Finite Group Databasebeta

← #13074826

Subgroups — #13074826

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×#66948C211yesmaximal, characteristic, complemented
2C2×#66937C211yesmaximal, characteristic, complemented
3C2×#66935C211yesmaximal, characteristic, complemented
4C2×#66935C211yesmaximal, characteristic, complemented
5C11×#397C211yesmaximal, characteristic, complemented
6#10622605C211yesmaximal, characteristic, complemented
7#10622572C211yesmaximal, characteristic, complemented
8#10622569C211yesmaximal, characteristic, complemented
9#10622568C211yesmaximal, characteristic, complemented
10#10622288C211yesmaximal, characteristic, complemented
11#10622285C211yesmaximal, characteristic, complemented
12#10622284C211yesmaximal, characteristic, complemented
13#10622278C211yesmaximal, characteristic, complemented
14#10622278C211yesmaximal, characteristic, complemented
15#10622278C211yesmaximal, characteristic, complemented
16C24×D11C2211yescharacteristic
17C22×C22⋊D11C2211yescharacteristic
18C22×C22⋊D11C2211yescharacteristic
19C22×D44C2211yescharacteristic
20C22×D44C2211yescharacteristic
21C22×D44C2211yescharacteristic
22C22×D44C2211yescharacteristic
23C22×D44C2211yescharacteristic, complemented
24C22×C4×D11C2211yescharacteristic, complemented
25C22×C4×D11C2211yescharacteristic, complemented
26C2×C11×C4⋊C4C2211yescharacteristic, complemented
27C2×C11×C22⋊C4C2211yescharacteristic
28C2×C11×C22⋊C4C2211yescharacteristic
29C2×C11×C22⋊C4C2211yescharacteristic
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×Dic11⋊C4C2211yescharacteristic, complemented
44C2×Dic11⋊C4C2211yescharacteristic, complemented
45#66948—24no—
46#66937—24no—
47#66935—24no—
48#66935—24no—
49C11×#95C2211yescharacteristic, complemented
50C11×#95C2211yescharacteristic, complemented
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—41no—
76C2×C22⋊D11—41no—
77C2×C22⋊D11—41no—
78C2×C22⋊D11D414yescomplemented
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—22no—
91C2×D44—41no—
92C2×D44—41no—
93C2×D44—41no—
94C2×D44—41no—
95C2×D44—41no—
96C2×D44—41no—
97C2×D44D414yescomplemented
98C2×C4×D11—22no—
99C2×C4×D11—22no—
100C2×C4×D11—41no—
101C2×C4×D11—41no—
102C2×C4×D11—41no—
103C2×C4×D11—41no—
104C11×C4⋊C4—22no—
105C11×C22⋊C4—22no—
106C11×C22⋊C4—22no—
107C11×C22⋊C4—22no—
108C22⋊Dic11—41no—
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—22no—
116(C2×D11)⋊C4—41no—
117(C2×D11)⋊C4—41no—
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×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—44no—
157C22×D11—44no—
158C22×D11—44no—
159C22×D11—44no—
160C22×D11—44no—
161C22×D11—44no—
162C22×D11—44no—
163C22×D11C2×D412yes—
164C22×D11C2×D412yes—
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×C11—21no—
183C2×C4×C11—21no—
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—
204C4×D11—44no—
205C4×D11—44no—
206C2×#121—111no—
207C2×#121—111no—
208C2×#120—111no—
209C2×#120—111no—
210#399—111no—
211#397—111no—
212#397D1111yescharacteristic, complemented
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—41no—
225C22×C11—41no—
226C22×C11—41no—
227C22×C11—41no—
228C22×C11C22×D411yescharacteristic
229C22×C11C22×D411yescharacteristic
230C22×C11C2×#4111yescharacteristic
231C22×C11H(5,𝔽2)11yescharacteristic
232C22×C11H(5,𝔽2)11yescharacteristic
233C22×C11H(5,𝔽2)11yescharacteristic
234C22×C11H(5,𝔽2)11yescharacteristic
235C2×D11—22no—
236C2×D11—22no—
237C2×D11—22no—
238C2×D11—22no—
239C2×D11—22no—
240C2×D11—22no—
241C2×D11—22no—
242C2×D11—22no—
243C2×D11—22no—
244C2×D11—22no—
245C2×D11—22no—
246C2×D11—22no—
247C2×D11—416no—
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—
263C2×D11—41no—
264C4×C11—22no—
265C4×C11—41no—
266C4×C11—41no—
267C4×C11—41no—
268C4×C11—41no—
269C4×C11—41no—
270Dic11—22no—
271Dic11—41no—
272Dic11—41no—
273Dic11—41no—
274C25—111no—
275C22×D4—111no—
276C22×D4—111no—
277C22×D4—111no—
278C22×D4—111no—
279C22×D4—111no—
280C22×D4—111no—
281C22×D4—111no—
282C23×C4—111no—
283C23×C4—111no—
284#121—224no—
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⋊C4C2×D1111yescharacteristic
305C2×C22⋊C4C2×D1111yescharacteristic
306C2×C22⋊C4C2×D1111yescharacteristic
307#95—111no—
308#95—111no—
309#95—111no—
310#95C2×D1111yescharacteristic, complemented
311#95C2×D1111yescharacteristic, complemented
312#95C2×D1111yescharacteristic, complemented
313C2×C11—42no—
314C2×C11#53411yescharacteristic
315C2×C11#53411yescharacteristic
316C2×C11#53811yescharacteristic
317C2×C11D4211yescharacteristic
318C2×C11#54611yescharacteristic
319C2×C11#54611yescharacteristic
320C2×C11#56011yescharacteristic
321D11—42no—
322D11—42no—
323D11—42no—
324D11—42no—
325C24—111no—
326C24—111no—
327C24—111no—
328C24—111no—
329C24—222no—
330C24—222no—
331C24—222no—
332C24—441no—
333C24—441no—
334C24—441no—
335C24—441no—
336C24C22×D1111yescharacteristic
337C2×D4—114no—
338C2×D4—114no—
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—
358C22×C4—111no—
359C22×C4—111no—
360C22×C4—111no—
361C22×C4—111no—
362C22×C4—222no—
363C22×C4—222no—
364C22×C4—441no—
365C22×C4—441no—
366C22×C4—441no—
367C22×C4—441no—
368C22×C4C22×D1111yescharacteristic
369C22×C4C22×D1111yescharacteristic
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—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—112no—
401C23—112no—
402C23—112no—
403C23—112no—
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—221no—
428C23—444no—
429C23—444no—
430C23—444no—
431C23—444no—
432C23—444no—
433C23—444no—
434C23—444no—
435C23D4×D1112yes—
436C23C23×D1111yescharacteristic
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—21no—
460C2×C4—21no—
461C2×C4—112no—
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×C4D4×D1112yes—
476C22—22no—
477C22—22no—
478C22—22no—
479C22—41no—
480C22—41no—
481C22—41no—
482C22—41no—
483C22—222no—
484C22—222no—
485C22—222no—
486C22—222no—
487C22—222no—
488C22—222no—
489C22—222no—
490C22—222no—
491C22—222no—
492C22—222no—
493C22—222no—
494C22—222no—
495C22—4416no—
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—
510C22—441no—
511C22—441no—
512C22C2×D4×D1111yescharacteristic
513C22C2×D4×D1111yescharacteristic
514C22#41×D1111yescharacteristic
515C22#6704211yescharacteristic
516C22#6704211yescharacteristic
517C22#6704211yescharacteristic
518C22#6704211yescharacteristic
519C4—22no—
520C4—41no—
521C4—41no—
522C4—41no—
523C4—41no—
524C4—41no—
525C4—222no—
526C4—441no—
527C4—441no—
528C4—441no—
529C2—42no—
530C2—442no—
531C2—442no—
532C2—442no—
533C2—442no—
534C2#1062314011yescharacteristic
535C2#1062318411yescharacteristic
536C2#1062318411yescharacteristic
537C2#1062318511yescharacteristic
538C2#1062320711yescharacteristic
539C2#1062323511yescharacteristic
540C2#1062324211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#397C2
hypercenter#397D11
hypocenterC11#2668
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
1. C2×#66948C2semidirect
2. C2×#66937C2semidirect
3. C2×#66935C2semidirect
4. C2×#66935C2semidirect
5. C11×#397C2semidirect
6. #10622605C2semidirect
7. #10622572C2semidirect
8. #10622569C2semidirect
9. #10622568C2semidirect
10. #10622288C2semidirect
11. #10622285C2semidirect
12. #10622284C2semidirect
13. #10622278C2semidirect
14. #10622278C2semidirect
15. #10622278C2semidirect
23. C22×D44C22semidirect
24. C22×C4×D11C22semidirect
25. C22×C4×D11C22semidirect
26. C2×C11×C4⋊C4C22semidirect
39. C2×(C2×D11)⋊C4C22semidirect
40. C2×(C2×D11)⋊C4C22semidirect
41. C2×(C2×D11)⋊C4C22semidirect
42. C2×(C2×D11)⋊C4C22semidirect
43. C2×Dic11⋊C4C22semidirect
44. C2×Dic11⋊C4C22semidirect
49. C11×#95C22semidirect
50. C11×#95C22semidirect
51. C11×#95C22semidirect
52. C11⋊#95C22semidirect
53. C11⋊#95C22semidirect
54. C11⋊#95C22semidirect
78. C2×C22⋊D11D4semidirect
97. C2×D44D4semidirect
212. #397D11semidirect
290. C2×C4⋊C4C2×D11semidirect
310. #95C2×D11semidirect
311. #95C2×D11semidirect
312. #95C2×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×#669482
C2×#669372
C2×#669352
C11×#3972
#106226052
#106225722
#106225692
#106225682
#106222882
#106222852
#106222842
#106222782
#266811