Finite Group Databasebeta

← #13072747

Subgroups — #13072747

Order 1408.

786 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66990C211yesmaximal, characteristic
2C22×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
3C2×#66977C211yesmaximal, characteristic, complemented
4C2×#66938C211yesmaximal, characteristic, complemented
5C11×#386C211yesmaximal, characteristic, complemented
6#10622833C211yesmaximal, characteristic, complemented
7#10622574C211yesmaximal, characteristic, complemented
8#10622572C211yesmaximal, characteristic, complemented
9#10622570C211yesmaximal, characteristic, complemented
10#10622568C211yesmaximal, characteristic, complemented
11C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
12#10622288C211yesmaximal, characteristic, complemented
13#10622286C211yesmaximal, characteristic, complemented
14#10622283C211yesmaximal, characteristic, complemented
15#10622282C211yesmaximal, characteristic, complemented
16C24×D11C2211yescharacteristic
17C22×D4×C11C2211yescharacteristic
18C23×C4×C11C2211yescharacteristic
19C22×C22⋊D11C2211yescharacteristic
20C22×C22⋊D11C2211yescharacteristic
21C23×Dic11C2211yescharacteristic
22C22×Dic22C2211yescharacteristic, complemented
23C2×C11×C22⋊C4C2211yescharacteristic
24C2×C11×C22⋊C4C2211yescharacteristic, complemented
25C2×C11×C22⋊C4C2211yescharacteristic, complemented
26C2×C22⋊Dic11C2211yescharacteristic
27C2×C22⋊Dic11C2211yescharacteristic
28C2×C22⋊Dic11C2211yescharacteristic, complemented
29C2×C22⋊Dic11C2211yescharacteristic, complemented
30#66990—24no—
31C2×(C2×D11)⋊C4—24no—
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
40C2×(C2×D11)⋊C4C2211yescharacteristic
41C2×(C2×D11)⋊C4C2211yescharacteristic
42C2×C4⋊Dic11C2211yescharacteristic, complemented
43#66977—24no—
44C2×Dic11⋊C4C2211yescharacteristic, complemented
45C2×Dic11⋊C4C2211yescharacteristic, complemented
46C2×C4×Dic11C2211yescharacteristic, complemented
47C2×C4×Dic11C2211yescharacteristic, complemented
48#66938—24no—
49C11×#95C2211yescharacteristic, complemented
50C11×#95C2211yescharacteristic, complemented
51C11⋊#95C2211yescharacteristic, complemented
52C11⋊#95C2211yescharacteristic, complemented
53C11⋊#95C2211yescharacteristic, complemented
54C11⋊#95C2211yescharacteristic, complemented
55C24×C11C2311yescharacteristic
56C24×C11C2311yescharacteristic
57C23×D11—22no—
58C23×D11—22no—
59C23×D11—22no—
60C23×D11—22no—
61C23×D11—22no—
62C23×D11—41no—
63C23×D11—41no—
64C23×D11C2311yescharacteristic
65C23×D11C2311yescharacteristic
66C2×D4×C11—22no—
67C2×D4×C11—22no—
68C2×D4×C11—22no—
69C22×C4×C11—22no—
70C22×C4×C11—22no—
71C22×C4×C11—41no—
72C22×C4×C11C2311yescharacteristic
73C22×C4×C11C2311yescharacteristic
74C22×C4×C11C2311yescharacteristic
75C22×C4×C11C2311yescharacteristic
76C22×C4×C11C2311yescharacteristic
77C2×C22⋊D11—22no—
78C2×C22⋊D11—22no—
79C2×C22⋊D11—22no—
80C2×C22⋊D11—22no—
81C2×C22⋊D11—41no—
82C2×C22⋊D11—41no—
83C22×Dic11—22no—
84C22×Dic11—22no—
85C22×Dic11—41no—
86C22×Dic11C2311yescharacteristic
87C22×Dic11C2311yescharacteristic
88C22×Dic11C2311yescharacteristic
89C22×Dic11C2311yescharacteristic
90C22×Dic11C2311yescharacteristic
91C22×Dic11C2311yescharacteristic
92C2×Dic22—22no—
93C2×Dic22—22no—
94C2×Dic22—41no—
95C11×C22⋊C4—22no—
96C11×C22⋊C4—22no—
97C11×C22⋊C4—41no—
98C22⋊Dic11—22no—
99C22⋊Dic11—22no—
100C22⋊Dic11—41no—
101C22⋊Dic11D414yes—
102(C2×D11)⋊C4—22no—
103(C2×D11)⋊C4—22no—
104(C2×D11)⋊C4—22no—
105(C2×D11)⋊C4—22no—
106(C2×D11)⋊C4—22no—
107(C2×D11)⋊C4—22no—
108(C2×D11)⋊C4—22no—
109(C2×D11)⋊C4—41no—
110(C2×D11)⋊C4—41no—
111(C2×D11)⋊C4D414yescomplemented
112C4⋊Dic11—22no—
113Dic11⋊C4—22no—
114Dic11⋊C4—22no—
115C4×Dic11—22no—
116C4×Dic11—41no—
117#2472—111nomaximal, Sylow
118C23×C11—21no—
119C23×C11—21no—
120C23×C11—21no—
121C23×C11—21no—
122C23×C11—21no—
123C23×C11—21no—
124C23×C11—21no—
125C23×C11—21no—
126C23×C11—21no—
127C23×C11—21no—
128C23×C11—21no—
129C23×C11C2×D412yes—
130C23×C11#4112yes—
131C23×C11#4112yes—
132C23×C11C2411yescharacteristic
133C22×D11—28no—
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—44no—
147C22×D11—44no—
148C22×D11—44no—
149C22×D11—44no—
150C22×D11—44no—
151C22×D11—44no—
152C22×D11C2×D412yes—
153C22×D11#4112yes—
154D4×C11—44no—
155C2×C4×C11—21no—
156C2×C4×C11—21no—
157C2×C4×C11—21no—
158C2×C4×C11—21no—
159C2×C4×C11—21no—
160C2×C4×C11—21no—
161C2×C4×C11—21no—
162C2×C4×C11—21no—
163C2×C4×C11—21no—
164C2×C4×C11—21no—
165C2×C4×C11—21no—
166C2×C4×C11—21no—
167C2×C4×C11—21no—
168C2×C4×C11—21no—
169C2×C4×C11—44no—
170C2×C4×C11C2×D412yes—
171C22⋊D11—44no—
172C22⋊D11—44no—
173C2×Dic11—21no—
174C2×Dic11—21no—
175C2×Dic11—21no—
176C2×Dic11—21no—
177C2×Dic11—21no—
178C2×Dic11—21no—
179C2×Dic11—21no—
180C2×Dic11—21no—
181C2×Dic11—21no—
182C2×Dic11—21no—
183C2×Dic11—21no—
184C2×Dic11—21no—
185C2×Dic11—21no—
186C2×Dic11—21no—
187C2×Dic11—21no—
188C2×Dic11—44no—
189C2×Dic11C2×D412yes—
190C2×Dic11C2×D412yes—
191C2×Dic11C2×D412yes—
192Dic22—44no—
193C2×#124—111no—
194C2×C22⋊Q8—111no—
195C2×#120—111no—
196C22×C22⋊C4—111no—
197#397—111no—
198#394—111no—
199#394—111no—
200#393—111no—
201#390—111no—
202#388—111no—
203#388—111no—
204#386—111no—
205#386D1111yescharacteristic, complemented
206#379—111no—
207C4×C22⋊C4—111no—
208C22×C11—22no—
209C22×C11—22no—
210C22×C11—22no—
211C22×C11—22no—
212C22×C11—22no—
213C22×C11—22no—
214C22×C11—41no—
215C22×C11—41no—
216C22×C11—41no—
217C22×C11—41no—
218C22×C11—41no—
219C22×C11—41no—
220C22×C11—41no—
221C22×C11#12414yescomplemented
222C22×C11C22×D411yescharacteristic
223C22×C11C22×D411yescharacteristic
224C22×C11C2×#4111yescharacteristic
225C22×C11C2×#4111yescharacteristic
226C22×C11C2×#4111yescharacteristic
227C22×C11H(5,𝔽2)11yescharacteristic
228C22×C11H(5,𝔽2)11yescharacteristic
229C2×D11—22no—
230C2×D11—22no—
231C2×D11—22no—
232C2×D11—22no—
233C2×D11—22no—
234C2×D11—22no—
235C2×D11—416no—
236C2×D11—41no—
237C2×D11—41no—
238C2×D11—41no—
239C2×D11—41no—
240C2×D11—41no—
241C2×D11—41no—
242C2×D11—41no—
243C2×D11—41no—
244C4×C11—22no—
245C4×C11—41no—
246C4×C11—41no—
247C4×C11—41no—
248C4×C11—41no—
249Dic11—22no—
250Dic11—22no—
251Dic11—22no—
252Dic11—41no—
253Dic11—41no—
254Dic11—41no—
255C25—111no—
256C22×Q8—111no—
257C22×D4—111no—
258C22×D4—111no—
259C22×D4C2×D1111yescharacteristic
260C23×C4—111no—
261C23×C4C2×D1111yescharacteristic
262#124—224no—
263C22⋊Q8—224no—
264#120—224no—
265C2×C4⋊C4—111no—
266C2×C4⋊C4—111no—
267C2×C4⋊C4—111no—
268C2×C22⋊C4—111no—
269C2×C22⋊C4—111no—
270C2×C22⋊C4—111no—
271C2×C22⋊C4—111no—
272C2×C22⋊C4—111no—
273C2×C22⋊C4—111no—
274C2×C22⋊C4—111no—
275C2×C22⋊C4—111no—
276C2×C22⋊C4—111no—
277C2×C22⋊C4—111no—
278C2×C22⋊C4—111no—
279C2×C22⋊C4—111no—
280C2×C22⋊C4—111no—
281C2×C22⋊C4—111no—
282C2×C22⋊C4—224no—
283C2×C22⋊C4C2×D1111yescharacteristic
284C2×C22⋊C4C2×D1111yescharacteristic, complemented
285C2×C22⋊C4C2×D1111yescharacteristic, complemented
286C2×C42—111no—
287C2×C42—111no—
288#95—111no—
289#95—111no—
290#95—111no—
291#95—111no—
292#95C2×D1111yescharacteristic, complemented
293#95C2×D1111yescharacteristic, complemented
294C2×C11—24no—
295C2×C11—81no—
296C2×C11#52511yescharacteristic
297C2×C11C2×#12411yescharacteristic
298C2×C11#53811yescharacteristic
299C2×C11D4211yescharacteristic
300C2×C11#54611yescharacteristic
301C2×C11#54611yescharacteristic
302C2×C11#55111yescharacteristic
303D11—42no—
304D11—42no—
305C24—111no—
306C24—111no—
307C24—222no—
308C24—222no—
309C24—222no—
310C24—222no—
311C24—222no—
312C24—441no—
313C24—441no—
314C24C22×D1111yescharacteristic
315C24C22×D1111yescharacteristic
316C2×Q8—222no—
317C2×Q8—222no—
318C2×Q8—441no—
319C2×D4—22no—
320C2×D4—22no—
321C2×D4—22no—
322C2×D4—222no—
323C2×D4—222no—
324C2×D4—222no—
325C2×D4—222no—
326C2×D4—441no—
327C2×D4—441no—
328C22×C4—22no—
329C22×C4—22no—
330C22×C4—41no—
331C22×C4—111no—
332C22×C4—111no—
333C22×C4—111no—
334C22×C4—111no—
335C22×C4—111no—
336C22×C4—111no—
337C22×C4—222no—
338C22×C4—222no—
339C22×C4—441no—
340C22×C4C22×D1111yescharacteristic
341C22×C4C22×D1111yescharacteristic
342C22×C4C22×D1111yescharacteristic
343C22×C4C22×D1111yescharacteristic
344C22×C4C22×D1111yescharacteristic
345C4⋊C4—222no—
346C4⋊C4—222no—
347C4⋊C4—222no—
348C22⋊C4—22no—
349C22⋊C4—22no—
350C22⋊C4—41no—
351C22⋊C4—114no—
352C22⋊C4—114no—
353C22⋊C4—222no—
354C22⋊C4—222no—
355C22⋊C4—222no—
356C22⋊C4—222no—
357C22⋊C4—222no—
358C22⋊C4—222no—
359C22⋊C4—222no—
360C22⋊C4—222no—
361C22⋊C4—222no—
362C22⋊C4—441no—
363C22⋊C4—441no—
364C22⋊C4—441no—
365C42—222no—
366C42—441no—
367C11#247211yescharacteristic, complemented, Sylow
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—21no—
373C23—21no—
374C23—21no—
375C23—21no—
376C23—21no—
377C23—21no—
378C23—21no—
379C23—112no—
380C23—112no—
381C23—228no—
382C23—221no—
383C23—221no—
384C23—221no—
385C23—221no—
386C23—221no—
387C23—221no—
388C23—221no—
389C23—221no—
390C23—221no—
391C23—221no—
392C23—221no—
393C23—221no—
394C23—444no—
395C23—444no—
396C23—444no—
397C23—444no—
398C23—444no—
399C23—444no—
400C23#433912yes—
401C23D4×D1112yes—
402C23#434112yes—
403C23C23×D1111yescharacteristic
404Q8—444no—
405D4—44no—
406D4—444no—
407D4—444no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—44no—
423C2×C4—112no—
424C2×C4—112no—
425C2×C4—112no—
426C2×C4—221no—
427C2×C4—221no—
428C2×C4—221no—
429C2×C4—221no—
430C2×C4—221no—
431C2×C4—221no—
432C2×C4—221no—
433C2×C4—221no—
434C2×C4—221no—
435C2×C4—221no—
436C2×C4—221no—
437C2×C4—221no—
438C2×C4—221no—
439C2×C4—221no—
440C2×C4—221no—
441C2×C4—444no—
442C2×C4D4×D1112yes—
443C22—22no—
444C22—22no—
445C22—22no—
446C22—22no—
447C22—22no—
448C22—22no—
449C22—41no—
450C22—41no—
451C22—41no—
452C22—41no—
453C22—41no—
454C22—41no—
455C22—41no—
456C22—222no—
457C22—222no—
458C22—222no—
459C22—222no—
460C22—222no—
461C22—222no—
462C22—4416no—
463C22—441no—
464C22—441no—
465C22—441no—
466C22—441no—
467C22—441no—
468C22—441no—
469C22—441no—
470C22—441no—
471C22#6693814yescomplemented
472C22C2×#433911yescharacteristic
473C22C2×D4×D1111yescharacteristic
474C22C2×D4×D1111yescharacteristic
475C22C2×#434111yescharacteristic
476C22#6703711yescharacteristic
477C22#41×D1111yescharacteristic
478C22#6704211yescharacteristic
479C4—22no—
480C4—41no—
481C4—41no—
482C4—41no—
483C4—41no—
484C4—222no—
485C4—222no—
486C4—222no—
487C4—441no—
488C4—441no—
489C4—441no—
490C2—24no—
491C2—81no—
492C2—442no—
493C2—442no—
494C2C2×#6693811yescharacteristic
495C2#1062308111yescharacteristic
496C2#1062308711yescharacteristic
497C2#1062312111yescharacteristic
498C2#1062313711yescharacteristic
499C2#1062314811yescharacteristic
500C2#1062318511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#386C2
prime radicalC2×#66990C2
hypercenter#386D11
hypocenterC11#2472
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
2. C22×(C2×D11)⋊C4C2semidirect
3. C2×#66977C2semidirect
4. C2×#66938C2semidirect
5. C11×#386C2semidirect
6. #10622833C2semidirect
7. #10622574C2semidirect
8. #10622572C2semidirect
9. #10622570C2semidirect
10. #10622568C2semidirect
11. C22⋊C4×Dic11C2semidirect
12. #10622288C2semidirect
13. #10622286C2semidirect
14. #10622283C2semidirect
15. #10622282C2semidirect
22. C22×Dic22C22semidirect
24. C2×C11×C22⋊C4C22semidirect
25. C2×C11×C22⋊C4C22semidirect
28. C2×C22⋊Dic11C22semidirect
29. C2×C22⋊Dic11C22semidirect
42. C2×C4⋊Dic11C22semidirect
44. C2×Dic11⋊C4C22semidirect
45. C2×Dic11⋊C4C22semidirect
46. C2×C4×Dic11C22semidirect
47. C2×C4×Dic11C22semidirect
49. C11×#95C22semidirect
50. C11×#95C22semidirect
51. C11⋊#95C22semidirect
52. C11⋊#95C22semidirect
53. C11⋊#95C22semidirect
54. C11⋊#95C22semidirect
111. (C2×D11)⋊C4D4semidirect
205. #386D11semidirect
221. C22×C11#124semidirect
284. C2×C22⋊C4C2×D11semidirect
285. C2×C22⋊C4C2×D11semidirect
292. #95C2×D11semidirect
293. #95C2×D11semidirect
367. C11#2472semidirect
471. C22#66938semidirect

Maximal subgroups

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

subgroupindex
C2×#669902
C22×(C2×D11)⋊C42
C2×#669772
C2×#669382
C11×#3862
#106228332
#106225742
#106225722
#106225702
#106225682
C22⋊C4×Dic112
#106222882
#106222862
#106222832
#106222822
#247211