Finite Group Databasebeta

← #13072000

Subgroups — #13072000

Order 1408.

786 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66947C211yesmaximal, characteristic, complemented
2C2×#66935C211yesmaximal, characteristic
3C2×C22⋊C4×D11C211yesmaximal, characteristic, complemented
4C2×#66925C211yesmaximal, characteristic, complemented
5C11×#388C211yesmaximal, characteristic, complemented
6#10622603C211yesmaximal, characteristic, complemented
7#10622572C211yesmaximal, characteristic, complemented
8#10622570C211yesmaximal, characteristic, complemented
9#10622568C211yesmaximal, characteristic, complemented
10#10622561C211yesmaximal, characteristic, complemented
11#10622552C211yesmaximal, characteristic, complemented
12#10622289C211yesmaximal, characteristic, complemented
13#10622285C211yesmaximal, characteristic, complemented
14#10622281C211yesmaximal, characteristic, complemented
15#10622278C211yesmaximal, characteristic, complemented
16C24×D11C2211yescharacteristic
17C22×C22⋊D11C2211yescharacteristic
18C22×D44C2211yescharacteristic
19C22×D44C2211yescharacteristic
20C22×C4×D11C2211yescharacteristic
21C22×C4×D11C2211yescharacteristic
22C2×C11×C4⋊C4C2211yescharacteristic, complemented
23C2×C11×C22⋊C4C2211yescharacteristic
24C2×C11×C22⋊C4C2211yescharacteristic
25C2×C11×C22⋊C4C2211yescharacteristic
26C2×C42×C11C2211yescharacteristic, complemented
27C2×C22⋊Dic11C2211yescharacteristic
28C2×C22⋊Dic11C2211yescharacteristic
29C2×(C2×D11)⋊C4C2211yescharacteristic
30C2×(C2×D11)⋊C4C2211yescharacteristic
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, complemented
38C2×(C2×D11)⋊C4C2211yescharacteristic, complemented
39C2×(C2×D11)⋊C4C2211yescharacteristic, complemented
40C2×(C2×D11)⋊C4C2211yescharacteristic, complemented
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#66947—24no—
48#66935—24no—
49C22⋊C4×D11—24no—
50#66925—24no—
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—22no—
61C23×D11—41no—
62C23×D11—41no—
63C23×D11C2311yescharacteristic
64C23×D11C2311yescharacteristic
65C23×D11C2311yescharacteristic
66C22×C4×C11C2311yescharacteristic
67C22×C4×C11C2311yescharacteristic
68C22×C4×C11C2311yescharacteristic
69C22×C4×C11C2311yescharacteristic
70C22×C4×C11C2311yescharacteristic
71C22×C4×C11C2311yescharacteristic
72C2×C22⋊D11—22no—
73C2×C22⋊D11—22no—
74C2×C22⋊D11—41no—
75C22×Dic11C2311yescharacteristic
76C22×Dic11C2311yescharacteristic
77C22×Dic11C2311yescharacteristic
78C22×Dic11C2311yescharacteristic
79C22×Dic11C2311yescharacteristic
80C2×D44—22no—
81C2×D44—22no—
82C2×D44—22no—
83C2×D44—22no—
84C2×D44—22no—
85C2×D44—41no—
86C2×C4×D11—22no—
87C2×C4×D11—22no—
88C2×C4×D11—22no—
89C2×C4×D11—41no—
90C2×C4×D11—41no—
91C2×C4×D11D414yescomplemented
92C11×C4⋊C4—22no—
93C11×C22⋊C4—22no—
94C11×C22⋊C4—22no—
95C11×C22⋊C4—22no—
96C42×C11—22no—
97C22⋊Dic11—22no—
98C22⋊Dic11—41no—
99(C2×D11)⋊C4—22no—
100(C2×D11)⋊C4—22no—
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)⋊C4—41no—
108(C2×D11)⋊C4—41no—
109(C2×D11)⋊C4—41no—
110(C2×D11)⋊C4D414yes—
111C4⋊Dic11—41no—
112Dic11⋊C4—22no—
113Dic11⋊C4—22no—
114Dic11⋊C4—22no—
115Dic11⋊C4—41no—
116C4×Dic11—22no—
117#2411—111nomaximal, Sylow
118C23×C11—21no—
119C23×C11—21no—
120C23×C11—21no—
121C23×C11—21no—
122C23×C11—21no—
123C23×C11—21no—
124C23×C11#4112yes—
125C23×C11C2411yescharacteristic
126C22×D11—21no—
127C22×D11—21no—
128C22×D11—21no—
129C22×D11—21no—
130C22×D11—28no—
131C22×D11—21no—
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—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—
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×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—21no—
170C2×C4×C11C2×D412yes—
171C2×C4×C11C2×D412yes—
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×Dic11C2×D412yes—
187C2×Dic11C2×D412yes—
188D44—44no—
189D44—44no—
190C4×D11—28no—
191C4×D11—44no—
192C2×#123—111no—
193C2×#120—111no—
194C2×#117—111no—
195C22×C22⋊C4—111no—
196#396—111no—
197#396—111no—
198#394—111no—
199#394—111no—
200#390—111no—
201#390—111no—
202#388—111no—
203#388D1111yescharacteristic, complemented
204#386—111no—
205#385—111no—
206#379—111no—
207C22×C11—22no—
208C22×C11—22no—
209C22×C11—22no—
210C22×C11—41no—
211C22×C11—41no—
212C22×C11—41no—
213C22×C11—41no—
214C22×C11C22×D411yescharacteristic
215C22×C11C22×D411yescharacteristic
216C22×C11C2×#4111yescharacteristic
217C22×C11C2×#4111yescharacteristic
218C22×C11C2×#4111yescharacteristic
219C22×C11H(5,𝔽2)11yescharacteristic
220C22×C11H(5,𝔽2)11yescharacteristic
221C2×D11—22no—
222C2×D11—22no—
223C2×D11—22no—
224C2×D11—22no—
225C2×D11—22no—
226C2×D11—22no—
227C2×D11—22no—
228C2×D11—22no—
229C2×D11—22no—
230C2×D11—416no—
231C2×D11—41no—
232C2×D11—41no—
233C2×D11—41no—
234C2×D11—41no—
235C2×D11—41no—
236C2×D11—41no—
237C2×D11—41no—
238C2×D11—41no—
239C2×D11—41no—
240C2×D11—41no—
241C2×D11—41no—
242C2×D11#12114yes—
243C4×C11—22no—
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—
254C25—111no—
255C22×D4—111no—
256C22×D4—111no—
257C22×D4—111no—
258C23×C4—111no—
259C23×C4—111no—
260#123—224no—
261#120—224no—
262#117—224no—
263C2×C4⋊C4—111no—
264C2×C4⋊C4—111no—
265C2×C4⋊C4—111no—
266C2×C4⋊C4—111no—
267C2×C4⋊C4—111no—
268C2×C4⋊C4C2×D1111yescharacteristic, complemented
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—111no—
283C2×C22⋊C4—224no—
284C2×C22⋊C4C2×D1111yescharacteristic
285C2×C22⋊C4C2×D1111yescharacteristic
286C2×C22⋊C4C2×D1111yescharacteristic
287C2×C42—111no—
288C2×C42C2×D1111yescharacteristic, complemented
289#95—111no—
290#95—111no—
291#95C2×D1111yescharacteristic, complemented
292#95C2×D1111yescharacteristic, complemented
293C2×C11—42no—
294C2×C11C2×#12111yescharacteristic
295C2×C11#52511yescharacteristic
296C2×C11#53511yescharacteristic
297C2×C11#54611yescharacteristic
298C2×C11#54611yescharacteristic
299C2×C11#55111yescharacteristic
300C2×C11#55111yescharacteristic
301D11—24no—
302D11—42no—
303D11—81no—
304C24—111no—
305C24—111no—
306C24—111no—
307C24—222no—
308C24—222no—
309C24—222no—
310C24—222no—
311C24—222no—
312C24—441no—
313C24—441no—
314C24C22×D1111yescharacteristic
315C2×D4—222no—
316C2×D4—222no—
317C2×D4—222no—
318C2×D4—222no—
319C2×D4—222no—
320C2×D4—222no—
321C2×D4—222no—
322C2×D4—441no—
323C2×D4—441no—
324C22×C4—111no—
325C22×C4—111no—
326C22×C4—114no—
327C22×C4—111no—
328C22×C4—111no—
329C22×C4—111no—
330C22×C4—222no—
331C22×C4—222no—
332C22×C4—222no—
333C22×C4—441no—
334C22×C4—441no—
335C22×C4C22×D1111yescharacteristic
336C22×C4C22×D1111yescharacteristic
337C22×C4C22×D1111yescharacteristic
338C22×C4C22×D1111yescharacteristic
339C22×C4C22×D1111yescharacteristic
340C22×C4C22×D1111yescharacteristic
341C4⋊C4—22no—
342C4⋊C4—222no—
343C4⋊C4—222no—
344C4⋊C4—222no—
345C4⋊C4—441no—
346C4⋊C4—441no—
347C22⋊C4—22no—
348C22⋊C4—22no—
349C22⋊C4—22no—
350C22⋊C4—114no—
351C22⋊C4—222no—
352C22⋊C4—222no—
353C22⋊C4—222no—
354C22⋊C4—222no—
355C22⋊C4—222no—
356C22⋊C4—222no—
357C22⋊C4—222no—
358C22⋊C4—222no—
359C22⋊C4—222no—
360C22⋊C4—441no—
361C22⋊C4—441no—
362C22⋊C4—441no—
363C22⋊C4—441no—
364C42—22no—
365C42—222no—
366C11#241111yescharacteristic, complemented, Sylow
367C23—21no—
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—21no—
373C23—112no—
374C23—112no—
375C23—112no—
376C23—112no—
377C23—228no—
378C23—221no—
379C23—221no—
380C23—221no—
381C23—221no—
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—221no—
395C23—444no—
396C23—444no—
397C23—444no—
398C23—444no—
399C23—444no—
400C23—444no—
401C23#433912yes—
402C23C23×D1111yescharacteristic
403D4—444no—
404D4—444no—
405D4—444no—
406C2×C4—21no—
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—21no—
422C2×C4—112no—
423C2×C4—112no—
424C2×C4—228no—
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—444no—
439C2×C4D4×D1112yes—
440C2×C4D4×D1112yes—
441C22—22no—
442C22—22no—
443C22—22no—
444C22—41no—
445C22—41no—
446C22—41no—
447C22—41no—
448C22—114no—
449C22—222no—
450C22—222no—
451C22—222no—
452C22—222no—
453C22—222no—
454C22—222no—
455C22—222no—
456C22—222no—
457C22—222no—
458C22—4416no—
459C22—441no—
460C22—441no—
461C22—441no—
462C22—441no—
463C22—441no—
464C22—441no—
465C22—441no—
466C22—441no—
467C22—441no—
468C22—441no—
469C22—441no—
470C22C2×#433911yescharacteristic
471C22C2×D4×D1111yescharacteristic
472C22C2×D4×D1111yescharacteristic
473C22#41×D1111yescharacteristic
474C22#41×D1111yescharacteristic
475C22#6704211yescharacteristic
476C22#6704211yescharacteristic
477C4—22no—
478C4—22no—
479C4—41no—
480C4—41no—
481C4—41no—
482C4—41no—
483C4—222no—
484C4—222no—
485C4—441no—
486C4—441no—
487C4—441no—
488C2—42no—
489C2—224no—
490C2—442no—
491C2—881no—
492C2#1062305811yescharacteristic
493C2#1062307811yescharacteristic
494C2#1062308111yescharacteristic
495C2D11×#12111yescharacteristic
496C2#1062318511yescharacteristic
497C2#1062320511yescharacteristic
498C2#1062323611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#388C2
prime radicalC2×#66935C2
hypercenter#388D11
hypocenterC11#2411
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. C2×#66947C2semidirect
3. C2×C22⋊C4×D11C2semidirect
4. C2×#66925C2semidirect
5. C11×#388C2semidirect
6. #10622603C2semidirect
7. #10622572C2semidirect
8. #10622570C2semidirect
9. #10622568C2semidirect
10. #10622561C2semidirect
11. #10622552C2semidirect
12. #10622289C2semidirect
13. #10622285C2semidirect
14. #10622281C2semidirect
15. #10622278C2semidirect
22. C2×C11×C4⋊C4C22semidirect
26. C2×C42×C11C22semidirect
37. C2×(C2×D11)⋊C4C22semidirect
38. C2×(C2×D11)⋊C4C22semidirect
39. C2×(C2×D11)⋊C4C22semidirect
40. C2×(C2×D11)⋊C4C22semidirect
41. C2×C4⋊Dic11C22semidirect
42. C2×Dic11⋊C4C22semidirect
43. C2×Dic11⋊C4C22semidirect
44. C2×Dic11⋊C4C22semidirect
45. C2×Dic11⋊C4C22semidirect
46. C2×C4×Dic11C22semidirect
51. C11×#95C22semidirect
52. C11×#95C22semidirect
53. C11⋊#95C22semidirect
54. C11⋊#95C22semidirect
91. C2×C4×D11D4semidirect
203. #388D11semidirect
268. C2×C4⋊C4C2×D11semidirect
288. C2×C42C2×D11semidirect
291. #95C2×D11semidirect
292. #95C2×D11semidirect
366. C11#2411semidirect

Maximal subgroups

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

subgroupindex
C2×#669472
C2×#669352
C2×C22⋊C4×D112
C2×#669252
C11×#3882
#106226032
#106225722
#106225702
#106225682
#106225612
#106225522
#106222892
#106222852
#106222812
#106222782
#241111