Finite Group Databasebeta

← #13073504

Subgroups — #13073504

Order 1408.

800 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
2C2×C4×C22⋊D11C211yesmaximal, characteristic, complemented
3C2×#66936C211yesmaximal, characteristic, complemented
4C2×C22⋊C4×D11C211yesmaximal, characteristic, complemented
5C11×#386C211yesmaximal, characteristic, complemented
6#10622835C211yesmaximal, characteristic, complemented
7#10622826C211yesmaximal, characteristic, complemented
8#10622572C211yesmaximal, characteristic, complemented
9#10622568C211yesmaximal, characteristic, complemented
10#10622561C211yesmaximal, characteristic, complemented
11#10622557C211yesmaximal, characteristic, complemented
12#10622289C211yesmaximal, characteristic, complemented
13#10622283C211yesmaximal, characteristic, complemented
14#10622280C211yesmaximal, characteristic, complemented
15#10622277C211yesmaximal, characteristic, complemented
16C24×D11C2211yescharacteristic
17C22×D4×C11C2211yescharacteristic
18C23×C4×C11C2211yescharacteristic, complemented
19C22×C22⋊D11C2211yescharacteristic
20C22×C22⋊D11C2211yescharacteristic
21C22×C4×D11C2211yescharacteristic
22C22×C4×D11C2211yescharacteristic
23C2×C11×C22⋊C4C2211yescharacteristic
24C2×C11×C22⋊C4C2211yescharacteristic
25C2×C11×C22⋊C4C2211yescharacteristic, complemented
26C2×C22⋊Dic11C2211yescharacteristic
27C2×C22⋊Dic11C2211yescharacteristic
28C2×C22⋊Dic11C2211yescharacteristic
29C2×C22⋊Dic11C2211yescharacteristic, complemented
30C2×C22⋊Dic11C2211yescharacteristic, complemented
31#66990—24no—
32C4×C22⋊D11—24no—
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×C4⋊Dic11C2211yescharacteristic, complemented
42C2×Dic11⋊C4C2211yescharacteristic, complemented
43C2×Dic11⋊C4C2211yescharacteristic, complemented
44C2×Dic11⋊C4C2211yescharacteristic, complemented
45C2×Dic11⋊C4C2211yescharacteristic, complemented
46C2×C4×Dic11C2211yescharacteristic, complemented
47#66936—24no—
48C22⋊C4×D11—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—41no—
69C22×C4×C11—22no—
70C22×C4×C11—41no—
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⋊D11D414yes—
83C22×Dic11C2311yescharacteristic
84C22×Dic11C2311yescharacteristic
85C22×Dic11C2311yescharacteristic
86C22×Dic11C2311yescharacteristic
87C22×Dic11C2311yescharacteristic
88C22×Dic11C2311yescharacteristic
89C2×C4×D11—22no—
90C2×C4×D11—22no—
91C2×C4×D11—22no—
92C2×C4×D11—41no—
93C2×C4×D11—41no—
94C2×C4×D11D414yescomplemented
95C11×C22⋊C4—22no—
96C11×C22⋊C4—22no—
97C11×C22⋊C4—41no—
98C22⋊Dic11—22no—
99C22⋊Dic11—22no—
100C22⋊Dic11—22no—
101C22⋊Dic11—22no—
102C22⋊Dic11—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—22no—
110(C2×D11)⋊C4—41no—
111C4⋊Dic11—22no—
112Dic11⋊C4—22no—
113Dic11⋊C4—22no—
114Dic11⋊C4—41no—
115Dic11⋊C4—41no—
116C4×Dic11—22no—
117#2534—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×C11—21no—
130C23×C11C2×D412yes—
131C23×C11#4112yes—
132C23×C11C2411yescharacteristic
133C22×D11—21no—
134C22×D11—21no—
135C22×D11—21no—
136C22×D11—21no—
137C22×D11—28no—
138C22×D11—21no—
139C22×D11—21no—
140C22×D11—21no—
141C22×D11—21no—
142C22×D11—21no—
143C22×D11—21no—
144C22×D11—44no—
145C22×D11—44no—
146C22×D11—44no—
147C22×D11—44no—
148C22×D11—44no—
149C22×D11—44no—
150C22×D11C2×D412yes—
151C22×D11C2×D412yes—
152C22×D11#4112yes—
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—28no—
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—21no—
189C2×Dic11C2×D412yes—
190C2×Dic11C2×D412yes—
191C4×D11—44no—
192C4×D11—44no—
193C2×#123—111no—
194C2×#120—111no—
195C2×C4×D4—111no—
196C22×C22⋊C4—111no—
197#396—111no—
198#396—111no—
199#394—111no—
200#394—111no—
201#388—111no—
202#388—111no—
203#386—111no—
204#386D1111yescharacteristic, complemented
205#381—111no—
206#380—111no—
207#379—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—41no—
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—22no—
236C2×D11—22no—
237C2×D11—22no—
238C2×D11—416no—
239C2×D11—41no—
240C2×D11—41no—
241C2×D11—41no—
242C2×D11—41no—
243C2×D11#12114yes—
244C4×C11—22no—
245C4×C11—41no—
246C4×C11—41no—
247C4×C11—41no—
248C4×C11—41no—
249Dic11—22no—
250Dic11—22no—
251Dic11—41no—
252Dic11—41no—
253Dic11—41no—
254Dic11—41no—
255C25—111no—
256C22×D4—111no—
257C22×D4—111no—
258C22×D4C2×D1111yescharacteristic
259C23×C4—111no—
260C23×C4—111no—
261C23×C4C2×D1111yescharacteristic, complemented
262#123—224no—
263#120—224no—
264C4×D4—224no—
265C2×C4⋊C4—111no—
266C2×C4⋊C4—111no—
267C2×C4⋊C4—111no—
268C2×C4⋊C4—111no—
269C2×C4⋊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—111no—
283C2×C22⋊C4—224no—
284C2×C22⋊C4C2×D1111yescharacteristic
285C2×C22⋊C4C2×D1111yescharacteristic
286C2×C22⋊C4C2×D1111yescharacteristic, complemented
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—42no—
295C2×C11—42no—
296C2×C11C2×#12111yescharacteristic
297C2×C11#52511yescharacteristic
298C2×C11#53411yescharacteristic
299C2×C11#54611yescharacteristic
300C2×C11#54611yescharacteristic
301C2×C11#55111yescharacteristic
302C2×C11#55111yescharacteristic
303D11—24no—
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×D4—22no—
317C2×D4—22no—
318C2×D4—41no—
319C2×D4—114no—
320C2×D4—222no—
321C2×D4—222no—
322C2×D4—222no—
323C2×D4—222no—
324C2×D4—441no—
325C22×C4—22no—
326C22×C4—41no—
327C22×C4—41no—
328C22×C4—111no—
329C22×C4—111no—
330C22×C4—114no—
331C22×C4—111no—
332C22×C4—111no—
333C22×C4—111no—
334C22×C4—111no—
335C22×C4—222no—
336C22×C4—222no—
337C22×C4—222no—
338C22×C4—441no—
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—
348C4⋊C4—441no—
349C4⋊C4—441no—
350C22⋊C4—22no—
351C22⋊C4—22no—
352C22⋊C4—41no—
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—222no—
363C22⋊C4—222no—
364C22⋊C4—222no—
365C22⋊C4—441no—
366C42—222no—
367C11#253411yescharacteristic, 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—21no—
380C23—112no—
381C23—112no—
382C23—112no—
383C23—112no—
384C23—228no—
385C23—221no—
386C23—221no—
387C23—221no—
388C23—221no—
389C23—221no—
390C23—221no—
391C23—221no—
392C23—221no—
393C23—221no—
394C23—221no—
395C23—444no—
396C23—444no—
397C23—444no—
398C23—444no—
399C23—444no—
400C23—444no—
401C23#433912yes—
402C23D4×D1112yes—
403C23C23×D1111yescharacteristic
404D4—44no—
405D4—228no—
406D4—444no—
407C2×C4—21no—
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—44no—
422C2×C4—112no—
423C2×C4—112no—
424C2×C4—221no—
425C2×C4—221no—
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—444no—
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—41no—
457C22—114no—
458C22—222no—
459C22—222no—
460C22—222no—
461C22—222no—
462C22—222no—
463C22—222no—
464C22—222no—
465C22—222no—
466C22—222no—
467C22—4416no—
468C22—441no—
469C22—441no—
470C22—441no—
471C22—441no—
472C22C2×#433911yescharacteristic
473C22C2×D4×D1111yescharacteristic
474C22C2×D4×D1111yescharacteristic
475C22#6703711yescharacteristic
476C22#6703711yescharacteristic
477C22#41×D1111yescharacteristic
478C22#41×D1111yescharacteristic
479C4—22no—
480C4—41no—
481C4—41no—
482C4—41no—
483C4—41no—
484C4—222no—
485C4—222no—
486C4—441no—
487C4—441no—
488C4—441no—
489C4—441no—
490C2—42no—
491C2—42no—
492C2—224no—
493C2—442no—
494C2#1062302111yescharacteristic
495C2#1062307811yescharacteristic
496C2#1062308711yescharacteristic
497C2#1062312011yescharacteristic
498C2D11×#12111yescharacteristic
499C2#1062314111yescharacteristic
500C2#1062319011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#386C2
prime radicalC2×#66990C2
hypercenter#386D11
hypocenterC11#2534
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
2. C2×C4×C22⋊D11C2semidirect
3. C2×#66936C2semidirect
4. C2×C22⋊C4×D11C2semidirect
5. C11×#386C2semidirect
6. #10622835C2semidirect
7. #10622826C2semidirect
8. #10622572C2semidirect
9. #10622568C2semidirect
10. #10622561C2semidirect
11. #10622557C2semidirect
12. #10622289C2semidirect
13. #10622283C2semidirect
14. #10622280C2semidirect
15. #10622277C2semidirect
18. C23×C4×C11C22semidirect
25. C2×C11×C22⋊C4C22semidirect
29. C2×C22⋊Dic11C22semidirect
30. C2×C22⋊Dic11C22semidirect
41. C2×C4⋊Dic11C22semidirect
42. C2×Dic11⋊C4C22semidirect
43. C2×Dic11⋊C4C22semidirect
44. C2×Dic11⋊C4C22semidirect
45. C2×Dic11⋊C4C22semidirect
46. C2×C4×Dic11C22semidirect
49. C11×#95C22semidirect
50. C11×#95C22semidirect
51. C11⋊#95C22semidirect
52. C11⋊#95C22semidirect
53. C11⋊#95C22semidirect
54. C11⋊#95C22semidirect
94. C2×C4×D11D4semidirect
204. #386D11semidirect
261. C23×C4C2×D11semidirect
286. C2×C22⋊C4C2×D11semidirect
292. #95C2×D11semidirect
293. #95C2×D11semidirect
367. C11#2534semidirect

Maximal subgroups

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

subgroupindex
C2×#669902
C2×C4×C22⋊D112
C2×#669362
C2×C22⋊C4×D112
C11×#3862
#106228352
#106228262
#106225722
#106225682
#106225612
#106225572
#106222892
#106222832
#106222802
#106222772
#253411