Finite Group Databasebeta

← #13072278

Subgroups — #13072278

Order 1408.

780 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66950C211yesmaximal, characteristic, complemented
2C2×#66949C211yesmaximal, characteristic, complemented
3C2×C22⋊C4×D11C211yesmaximal, characteristic
4C2×C22⋊C4×D11C211yesmaximal, characteristic
5C11×#396C211yesmaximal, characteristic, complemented
6#10622602C211yesmaximal, characteristic, complemented
7#10622602C211yesmaximal, characteristic, complemented
8#10622602C211yesmaximal, characteristic, complemented
9#10622600C211yesmaximal, characteristic, complemented
10#10622568C211yesmaximal, characteristic
11#10622562C211yesmaximal, characteristic, complemented
12#10622561C211yesmaximal, characteristic, complemented
13#10622560C211yesmaximal, characteristic, complemented
14#10622281C211yesmaximal, characteristic, complemented
15#10622280C211yesmaximal, characteristic, complemented
16C24×D11C2211yescharacteristic
17C22×C4×D11C2211yescharacteristic
18C22×C4×D11C2211yescharacteristic
19C22×C4×D11C2211yescharacteristic
20C22×C4×D11C2211yescharacteristic
21C22×Dic22C2211yescharacteristic, complemented
22C2×C11×C4⋊C4C2211yescharacteristic, complemented
23C2×C11×C4⋊C4C2211yescharacteristic, complemented
24C2×C11×C4⋊C4C2211yescharacteristic, complemented
25C2×C11×C22⋊C4C2211yescharacteristic
26C2×C11×C22⋊C4C2211yescharacteristic
27C2×C11×C22⋊C4C2211yescharacteristic
28C2×C22⋊Dic11C2211yescharacteristic
29C2×C22⋊Dic11C2211yescharacteristic
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×C4⋊Dic11C2211yescharacteristic, complemented
40C2×C4⋊Dic11C2211yescharacteristic, complemented
41C2×Dic11⋊C4C2211yescharacteristic, complemented
42C2×Dic11⋊C4C2211yescharacteristic, complemented
43C2×Dic11⋊C4C2211yescharacteristic, complemented
44C2×Dic11⋊C4C2211yescharacteristic, complemented
45#66950—24no—
46#66949—24no—
47C22⋊C4×D11—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
56C23×D11—22no—
57C23×D11—22no—
58C23×D11—22no—
59C23×D11—22no—
60C23×D11—41no—
61C23×D11—41no—
62C23×D11Q814yescomplemented
63C23×D11C2311yescharacteristic
64C23×D11C2311yescharacteristic
65C22×C4×C11C2311yescharacteristic
66C22×C4×C11C2311yescharacteristic
67C22×C4×C11C2311yescharacteristic
68C22×C4×C11C2311yescharacteristic
69C22×C4×C11C2311yescharacteristic
70C22×C4×C11C2311yescharacteristic
71C22×Dic11C2311yescharacteristic
72C22×Dic11C2311yescharacteristic
73C22×Dic11C2311yescharacteristic
74C22×Dic11C2311yescharacteristic
75C22×Dic11C2311yescharacteristic
76C22×Dic11C2311yescharacteristic
77C2×C4×D11—22no—
78C2×C4×D11—22no—
79C2×C4×D11—22no—
80C2×C4×D11—22no—
81C2×C4×D11—22no—
82C2×C4×D11—22no—
83C2×C4×D11—22no—
84C2×C4×D11—22no—
85C2×C4×D11—41no—
86C2×C4×D11—41no—
87C2×C4×D11—41no—
88C2×C4×D11—41no—
89C2×Dic22—22no—
90C2×Dic22—22no—
91C2×Dic22—41no—
92C11×C4⋊C4—22no—
93C11×C4⋊C4—22no—
94C11×C4⋊C4—41no—
95C11×C22⋊C4—22no—
96C11×C22⋊C4—22no—
97C11×C22⋊C4—41no—
98C22⋊Dic11—22no—
99C22⋊Dic11—22no—
100C22⋊Dic11—41no—
101(C2×D11)⋊C4—22no—
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)⋊C4D414yes—
108(C2×D11)⋊C4D414yes—
109C4⋊Dic11—22no—
110C4⋊Dic11—22no—
111Dic11⋊C4—22no—
112Dic11⋊C4—22no—
113Dic11⋊C4—41no—
114Dic11⋊C4—41no—
115#2437—111nomaximal, Sylow
116C23×C11—21no—
117C23×C11—21no—
118C23×C11—21no—
119C23×C11—21no—
120C23×C11—21no—
121C23×C11—21no—
122C23×C11C2×Q812yes—
123C23×C11C2411yescharacteristic
124C22×D11—21no—
125C22×D11—21no—
126C22×D11—21no—
127C22×D11—21no—
128C22×D11—21no—
129C22×D11—21no—
130C22×D11—21no—
131C22×D11—21no—
132C22×D11—28no—
133C22×D11—28no—
134C22×D11—44no—
135C22×D11—44no—
136C22×D11—44no—
137C22×D11—44no—
138C22×D11—44no—
139C22×D11C2×D412yes—
140C22×D11C2×D412yes—
141C22×D11C2×Q812yes—
142C22×D11C2×Q812yes—
143C22×D11#4112yes—
144C22×D11#4112yes—
145C2×C4×C11—21no—
146C2×C4×C11—21no—
147C2×C4×C11—21no—
148C2×C4×C11—21no—
149C2×C4×C11—21no—
150C2×C4×C11—21no—
151C2×C4×C11—21no—
152C2×C4×C11—21no—
153C2×C4×C11—21no—
154C2×C4×C11—21no—
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×C11C2×D412yes—
162C2×C4×C11C2×D412yes—
163C2×Dic11—21no—
164C2×Dic11—21no—
165C2×Dic11—21no—
166C2×Dic11—21no—
167C2×Dic11—21no—
168C2×Dic11—21no—
169C2×Dic11—21no—
170C2×Dic11—21no—
171C2×Dic11—21no—
172C2×Dic11—21no—
173C2×Dic11—21no—
174C2×Dic11—21no—
175C2×Dic11—21no—
176C2×Dic11—21no—
177C2×Dic11—21no—
178C2×Dic11—21no—
179C2×Dic11C2×D412yes—
180C2×Dic11C2×D412yes—
181C4×D11—44no—
182C4×D11—44no—
183C4×D11—44no—
184C4×D11—44no—
185Dic22—44no—
186C2×C22⋊Q8—111no—
187C2×C22⋊Q8—111no—
188C22×C22⋊C4—111no—
189C22×C22⋊C4—111no—
190#399—111no—
191#396—111no—
192#396D1111yescharacteristic, complemented
193#393—111no—
194#385—111no—
195#385—111no—
196#385—111no—
197#385—111no—
198#380—111no—
199#380—111no—
200#379—111no—
201C22×C11—22no—
202C22×C11—22no—
203C22×C11—22no—
204C22×C11—41no—
205C22×C11—41no—
206C22×C11—41no—
207C22×C11—41no—
208C22×C11C22×D411yescharacteristic
209C22×C11C22×D411yescharacteristic
210C22×C11C22×Q811yescharacteristic
211C22×C11C2×#4111yescharacteristic
212C22×C11C2×#4111yescharacteristic
213C22×C11H(5,𝔽2)11yescharacteristic
214C22×C11H(5,𝔽2)11yescharacteristic
215C2×D11—22no—
216C2×D11—22no—
217C2×D11—22no—
218C2×D11—22no—
219C2×D11—22no—
220C2×D11—22no—
221C2×D11—22no—
222C2×D11—22no—
223C2×D11—22no—
224C2×D11—22no—
225C2×D11—22no—
226C2×D11—22no—
227C2×D11—416no—
228C2×D11C22⋊Q814yescomplemented
229C2×D11C22⋊Q814yescomplemented
230C4×C11—22no—
231C4×C11—22no—
232C4×C11—41no—
233C4×C11—41no—
234C4×C11—41no—
235C4×C11—41no—
236Dic11—22no—
237Dic11—22no—
238Dic11—41no—
239Dic11—41no—
240Dic11—41no—
241Dic11—41no—
242C25—111no—
243C22×Q8—111no—
244C23×C4—111no—
245C23×C4—111no—
246C23×C4—111no—
247C23×C4—111no—
248C22⋊Q8—224no—
249C22⋊Q8—224no—
250C2×C4⋊C4—111no—
251C2×C4⋊C4—111no—
252C2×C4⋊C4—111no—
253C2×C4⋊C4—111no—
254C2×C4⋊C4—111no—
255C2×C4⋊C4—111no—
256C2×C4⋊C4C2×D1111yescharacteristic, complemented
257C2×C4⋊C4C2×D1111yescharacteristic, complemented
258C2×C4⋊C4C2×D1111yescharacteristic, complemented
259C2×C22⋊C4—111no—
260C2×C22⋊C4—111no—
261C2×C22⋊C4—111no—
262C2×C22⋊C4—111no—
263C2×C22⋊C4—111no—
264C2×C22⋊C4—111no—
265C2×C22⋊C4—111no—
266C2×C22⋊C4—111no—
267C2×C22⋊C4—111no—
268C2×C22⋊C4—111no—
269C2×C22⋊C4—111no—
270C2×C22⋊C4—224no—
271C2×C22⋊C4—224no—
272C2×C22⋊C4C2×D1111yescharacteristic
273C2×C22⋊C4C2×D1111yescharacteristic
274C2×C22⋊C4C2×D1111yescharacteristic
275#95—111no—
276#95—111no—
277#95—111no—
278#95—111no—
279#95—111no—
280#95C2×D1111yescharacteristic, complemented
281C2×C11—42no—
282C2×C11C2×C22⋊Q811yescharacteristic
283C2×C11C2×C22⋊Q811yescharacteristic
284C2×C11#54311yescharacteristic
285C2×C11D4211yescharacteristic
286C2×C11#54611yescharacteristic
287C2×C11#54611yescharacteristic
288C2×C11#55111yescharacteristic
289D11—24no—
290D11—24no—
291C24—111no—
292C24—111no—
293C24—114no—
294C24—222no—
295C24—222no—
296C24—222no—
297C24—222no—
298C24—441no—
299C24—441no—
300C24C22×D1111yescharacteristic
301C2×Q8—222no—
302C2×Q8—222no—
303C2×Q8—441no—
304C22×C4—111no—
305C22×C4—111no—
306C22×C4—111no—
307C22×C4—111no—
308C22×C4—111no—
309C22×C4—111no—
310C22×C4—222no—
311C22×C4—222no—
312C22×C4—222no—
313C22×C4—222no—
314C22×C4—222no—
315C22×C4—222no—
316C22×C4—222no—
317C22×C4—222no—
318C22×C4—441no—
319C22×C4—441no—
320C22×C4—441no—
321C22×C4—441no—
322C22×C4C22×D1111yescharacteristic
323C22×C4C22×D1111yescharacteristic
324C22×C4C22×D1111yescharacteristic
325C22×C4C22×D1111yescharacteristic
326C22×C4C22×D1111yescharacteristic
327C22×C4C22×D1111yescharacteristic
328C4⋊C4—22no—
329C4⋊C4—22no—
330C4⋊C4—41no—
331C4⋊C4—222no—
332C4⋊C4—222no—
333C4⋊C4—222no—
334C4⋊C4—222no—
335C4⋊C4—441no—
336C4⋊C4—441no—
337C22⋊C4—22no—
338C22⋊C4—22no—
339C22⋊C4—41no—
340C22⋊C4—114no—
341C22⋊C4—114no—
342C22⋊C4—222no—
343C22⋊C4—222no—
344C22⋊C4—222no—
345C22⋊C4—222no—
346C22⋊C4—222no—
347C22⋊C4—222no—
348C22⋊C4—222no—
349C22⋊C4—222no—
350C22⋊C4—441no—
351C11#243711yescharacteristic, complemented, Sylow
352C23—21no—
353C23—21no—
354C23—21no—
355C23—21no—
356C23—21no—
357C23—21no—
358C23—112no—
359C23—112no—
360C23—112no—
361C23—112no—
362C23—112no—
363C23—112no—
364C23—228no—
365C23—228no—
366C23—221no—
367C23—221no—
368C23—221no—
369C23—221no—
370C23—221no—
371C23—221no—
372C23—221no—
373C23—221no—
374C23—444no—
375C23—444no—
376C23—444no—
377C23—444no—
378C23—444no—
379C23Q8×D1112yes—
380C23C23×D1111yescharacteristic
381Q8—444no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—112no—
399C2×C4—112no—
400C2×C4—221no—
401C2×C4—221no—
402C2×C4—221no—
403C2×C4—221no—
404C2×C4—221no—
405C2×C4—221no—
406C2×C4—221no—
407C2×C4—221no—
408C2×C4—221no—
409C2×C4—221no—
410C2×C4—221no—
411C2×C4—221no—
412C2×C4—221no—
413C2×C4—221no—
414C2×C4—221no—
415C2×C4—221no—
416C2×C4—444no—
417C2×C4—444no—
418C2×C4—444no—
419C2×C4—444no—
420C2×C4D4×D1112yes—
421C2×C4D4×D1112yes—
422C22—22no—
423C22—22no—
424C22—22no—
425C22—41no—
426C22—41no—
427C22—41no—
428C22—41no—
429C22—114no—
430C22—114no—
431C22—222no—
432C22—222no—
433C22—222no—
434C22—222no—
435C22—222no—
436C22—222no—
437C22—222no—
438C22—222no—
439C22—222no—
440C22—222no—
441C22—222no—
442C22—222no—
443C22—4416no—
444C22C2×D4×D1111yescharacteristic
445C22C2×D4×D1111yescharacteristic
446C22#6703711yescharacteristic
447C22C2×Q8×D1111yescharacteristic
448C22#41×D1111yescharacteristic
449C22#41×D1111yescharacteristic
450C22#6704211yescharacteristic
451C4—22no—
452C4—22no—
453C4—41no—
454C4—41no—
455C4—41no—
456C4—41no—
457C4—222no—
458C4—222no—
459C4—441no—
460C4—441no—
461C4—441no—
462C4—441no—
463C2—42no—
464C2—224no—
465C2—224no—
466C2#1062314011yescharacteristic
467C2#1062314111yescharacteristic
468C2#1062314311yescharacteristic
469C2D11×C22⋊Q811yescharacteristic
470C2D11×C22⋊Q811yescharacteristic
471C2#1062316511yescharacteristic
472C2#1062323611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#396C2
prime radicalC24×D11C22
hypercenter#396D11
hypocenterC11#2437
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #396

Complements

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

NH ≅ G/Ntype
1. C2×#66950C2semidirect
2. C2×#66949C2semidirect
5. C11×#396C2semidirect
6. #10622602C2semidirect
7. #10622602C2semidirect
8. #10622602C2semidirect
9. #10622600C2semidirect
11. #10622562C2semidirect
12. #10622561C2semidirect
13. #10622560C2semidirect
14. #10622281C2semidirect
15. #10622280C2semidirect
21. C22×Dic22C22semidirect
22. C2×C11×C4⋊C4C22semidirect
23. C2×C11×C4⋊C4C22semidirect
24. C2×C11×C4⋊C4C22semidirect
39. C2×C4⋊Dic11C22semidirect
40. C2×C4⋊Dic11C22semidirect
41. C2×Dic11⋊C4C22semidirect
42. C2×Dic11⋊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
62. C23×D11Q8semidirect
192. #396D11semidirect
228. C2×D11C22⋊Q8semidirect
229. C2×D11C22⋊Q8semidirect
256. C2×C4⋊C4C2×D11semidirect
257. C2×C4⋊C4C2×D11semidirect
258. C2×C4⋊C4C2×D11semidirect
280. #95C2×D11semidirect
351. C11#2437semidirect

Maximal subgroups

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

subgroupindex
C2×#669502
C2×#669492
C2×C22⋊C4×D112
C11×#3962
#106226022
#106226002
#106225682
#106225622
#106225612
#106225602
#106222812
#106222802
#243711