Finite Group Databasebeta

← #13072005

Subgroups — #13072005

Order 1408.

814 conjugacy classes of subgroups.

The subgroup lattice has 504 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×C22⋊C4×D11C211yesmaximal, characteristic, complemented
5C11×#397C211yesmaximal, characteristic, complemented
6#10622600C211yesmaximal, characteristic, complemented
7#10622574C211yesmaximal, characteristic, complemented
8#10622572C211yesmaximal, characteristic, complemented
9#10622565C211yesmaximal, characteristic, complemented
10#10622281C211yesmaximal, characteristic, complemented
11#10622280C211yesmaximal, characteristic, complemented
12#10622278C211yesmaximal, characteristic, complemented
13#10622278C211yesmaximal, characteristic, complemented
14#10622278C211yesmaximal, characteristic, complemented
15#10622277C211yesmaximal, characteristic, complemented
16C24×D11C2211yescharacteristic
17C22×C22⋊D11C2211yescharacteristic
18C22×D44C2211yescharacteristic
19C22×D44C2211yescharacteristic
20C22×C4×D11C2211yescharacteristic
21C22×C4×D11C2211yescharacteristic
22C22×C4×D11C2211yescharacteristic
23C22×C4×D11C2211yescharacteristic
24C2×C11×C4⋊C4C2211yescharacteristic, complemented
25C2×C11×C22⋊C4C2211yescharacteristic
26C2×C11×C22⋊C4C2211yescharacteristic
27C2×C11×C22⋊C4C2211yescharacteristic
28C2×C22⋊Dic11C2211yescharacteristic
29C2×C22⋊Dic11C2211yescharacteristic
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, complemented
37C2×(C2×D11)⋊C4C2211yescharacteristic, complemented
38C2×(C2×D11)⋊C4C2211yescharacteristic, complemented
39C2×(C2×D11)⋊C4C2211yescharacteristic, complemented
40C2×C4⋊Dic11C2211yescharacteristic, complemented
41C2×Dic11⋊C4C2211yescharacteristic, complemented
42C2×Dic11⋊C4C2211yescharacteristic, complemented
43#66947—24no—
44#66935—24no—
45C22⋊C4×D11—24no—
46C22⋊C4×D11—24no—
47C11×#95C2211yescharacteristic, complemented
48C11×#95C2211yescharacteristic, complemented
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×D11D414yes—
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—41no—
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—22no—
86C2×C4×D11—22no—
87C2×C4×D11—22no—
88C2×C4×D11—22no—
89C2×C4×D11—22no—
90C2×C4×D11—22no—
91C2×C4×D11—22no—
92C2×C4×D11—22no—
93C2×C4×D11—22no—
94C2×C4×D11—41no—
95C2×C4×D11—41no—
96C2×C4×D11—41no—
97C2×C4×D11—41no—
98C11×C4⋊C4—22no—
99C11×C22⋊C4—22no—
100C11×C22⋊C4—22no—
101C11×C22⋊C4—22no—
102C22⋊Dic11—22no—
103C22⋊Dic11—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—22no—
111(C2×D11)⋊C4—41no—
112(C2×D11)⋊C4—41no—
113(C2×D11)⋊C4D414yescomplemented
114C4⋊Dic11—41no—
115Dic11⋊C4—22no—
116Dic11⋊C4—41no—
117#2412—111nomaximal, Sylow
118C23×C11—21no—
119C23×C11—21no—
120C23×C11—21no—
121C23×C11—21no—
122C23×C11—21no—
123C23×C11—21no—
124C23×C11C2×D412yes—
125C23×C11C2411yescharacteristic
126C22×D11—21no—
127C22×D11—21no—
128C22×D11—21no—
129C22×D11—21no—
130C22×D11—21no—
131C22×D11—21no—
132C22×D11—21no—
133C22×D11—21no—
134C22×D11—28no—
135C22×D11—28no—
136C22×D11—21no—
137C22×D11—21no—
138C22×D11—21no—
139C22×D11—21no—
140C22×D11—21no—
141C22×D11—21no—
142C22×D11—21no—
143C22×D11—44no—
144C22×D11—44no—
145C22×D11—44no—
146C22×D11—44no—
147C22×D11—44no—
148C22×D11C2×D412yes—
149C22×D11C2×D412yes—
150C22×D11C2×D412yes—
151C22×D11#4112yes—
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×C11—21no—
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×Dic11—21no—
187C2×Dic11C2×D412yes—
188D44—44no—
189D44—44no—
190C4×D11—44no—
191C4×D11—44no—
192C4×D11—44no—
193C4×D11—44no—
194C2×#123—111no—
195C2×#120—111no—
196C22×C22⋊C4—111no—
197C22×C22⋊C4—111no—
198#397—111no—
199#397D1111yescharacteristic, complemented
200#394—111no—
201#394—111no—
202#386—111no—
203#386—111no—
204#386—111no—
205#385—111no—
206#381—111no—
207#380—111no—
208#380—111no—
209C22×C11—22no—
210C22×C11—22no—
211C22×C11—22no—
212C22×C11—41no—
213C22×C11—41no—
214C22×C11—41no—
215C22×C11—41no—
216C22×C11C22×D411yescharacteristic
217C22×C11C22×D411yescharacteristic
218C22×C11C2×#4111yescharacteristic
219C22×C11C2×#4111yescharacteristic
220C22×C11C2×#4111yescharacteristic
221C22×C11H(5,𝔽2)11yescharacteristic
222C22×C11H(5,𝔽2)11yescharacteristic
223C2×D11—22no—
224C2×D11—22no—
225C2×D11—22no—
226C2×D11—22no—
227C2×D11—22no—
228C2×D11—22no—
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#12114yes—
244C2×D11#12314yescomplemented
245C4×C11—22no—
246C4×C11—41no—
247C4×C11—41no—
248C4×C11—41no—
249C4×C11—41no—
250C4×C11—41no—
251Dic11—22no—
252Dic11—41no—
253Dic11—41no—
254Dic11—41no—
255Dic11—41no—
256C25—111no—
257C22×D4—111no—
258C22×D4—111no—
259C22×D4—111no—
260C23×C4—111no—
261C23×C4—111no—
262C23×C4—111no—
263C23×C4—111no—
264#123—224no—
265#120—224no—
266C2×C4⋊C4—111no—
267C2×C4⋊C4—111no—
268C2×C4⋊C4—111no—
269C2×C4⋊C4C2×D1111yescharacteristic, complemented
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⋊C4—224no—
284C2×C22⋊C4C2×D1111yescharacteristic
285C2×C22⋊C4C2×D1111yescharacteristic
286C2×C22⋊C4C2×D1111yescharacteristic
287#95—111no—
288#95—111no—
289#95—111no—
290#95—111no—
291#95—111no—
292#95C2×D1111yescharacteristic, complemented
293#95C2×D1111yescharacteristic, complemented
294#95C2×D1111yescharacteristic, complemented
295C2×C11—42no—
296C2×C11C2×#12111yescharacteristic
297C2×C11C2×#12311yescharacteristic
298C2×C11#53411yescharacteristic
299C2×C11#54611yescharacteristic
300C2×C11#54611yescharacteristic
301C2×C11#55111yescharacteristic
302C2×C11#55111yescharacteristic
303D11—24no—
304D11—24no—
305D11—81no—
306C24—111no—
307C24—111no—
308C24—114no—
309C24—111no—
310C24—222no—
311C24—222no—
312C24—222no—
313C24—222no—
314C24—441no—
315C24—441no—
316C24C22×D1111yescharacteristic
317C2×D4—222no—
318C2×D4—222no—
319C2×D4—222no—
320C2×D4—222no—
321C2×D4—222no—
322C2×D4—222no—
323C2×D4—222no—
324C2×D4—441no—
325C2×D4—441no—
326C22×C4—111no—
327C22×C4—111no—
328C22×C4—111no—
329C22×C4—111no—
330C22×C4—111no—
331C22×C4—222no—
332C22×C4—222no—
333C22×C4—222no—
334C22×C4—222no—
335C22×C4—222no—
336C22×C4—222no—
337C22×C4—222no—
338C22×C4—222no—
339C22×C4—441no—
340C22×C4—441no—
341C22×C4—441no—
342C22×C4—441no—
343C22×C4C22×D1111yescharacteristic
344C22×C4C22×D1111yescharacteristic
345C22×C4C22×D1111yescharacteristic
346C22×C4C22×D1111yescharacteristic
347C22×C4C22×D1111yescharacteristic
348C22×C4C22×D1111yescharacteristic
349C4⋊C4—22no—
350C4⋊C4—222no—
351C4⋊C4—441no—
352C4⋊C4—441no—
353C22⋊C4—22no—
354C22⋊C4—22no—
355C22⋊C4—22no—
356C22⋊C4—114no—
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—222no—
366C22⋊C4—441no—
367C22⋊C4—441no—
368C11#241211yescharacteristic, complemented, Sylow
369C23—21no—
370C23—21no—
371C23—21no—
372C23—21no—
373C23—21no—
374C23—21no—
375C23—112no—
376C23—112no—
377C23—112no—
378C23—112no—
379C23—112no—
380C23—112no—
381C23—228no—
382C23—228no—
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—221no—
396C23—221no—
397C23—221no—
398C23—444no—
399C23—444no—
400C23—444no—
401C23—444no—
402C23—444no—
403C23D4×D1112yes—
404C23C23×D1111yescharacteristic
405D4—444no—
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—21no—
423C2×C4—21no—
424C2×C4—21no—
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—444no—
441C2×C4—444no—
442C2×C4—444no—
443C2×C4—444no—
444C2×C4D4×D1112yes—
445C22—22no—
446C22—22no—
447C22—22no—
448C22—41no—
449C22—41no—
450C22—41no—
451C22—41no—
452C22—114no—
453C22—114no—
454C22—222no—
455C22—222no—
456C22—222no—
457C22—222no—
458C22—222no—
459C22—222no—
460C22—222no—
461C22—222no—
462C22—222no—
463C22—222no—
464C22—222no—
465C22—222no—
466C22—4416no—
467C22—441no—
468C22—441no—
469C22—441no—
470C22—441no—
471C22—441no—
472C22—441no—
473C22—441no—
474C22C2×D4×D1111yescharacteristic
475C22C2×D4×D1111yescharacteristic
476C22#41×D1111yescharacteristic
477C22#41×D1111yescharacteristic
478C22#41×D1111yescharacteristic
479C22#6704211yescharacteristic
480C22#6704211yescharacteristic
481C4—22no—
482C4—41no—
483C4—41no—
484C4—41no—
485C4—41no—
486C4—41no—
487C4—222no—
488C4—441no—
489C4—441no—
490C4—441no—
491C4—441no—
492C2—42no—
493C2—224no—
494C2—224no—
495C2—881no—
496C2D11×#12111yescharacteristic
497C2D11×#12311yescharacteristic
498C2#1062318411yescharacteristic
499C2#1062318511yescharacteristic
500C2#1062320711yescharacteristic
501C2#1062323611yescharacteristic
502C2#1062323611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#397C2
prime radicalC2×#66935C2
hypercenter#397D11
hypocenterC11#2412
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
1. C2×#66947C2semidirect
3. C2×C22⋊C4×D11C2semidirect
4. C2×C22⋊C4×D11C2semidirect
5. C11×#397C2semidirect
6. #10622600C2semidirect
7. #10622574C2semidirect
8. #10622572C2semidirect
9. #10622565C2semidirect
10. #10622281C2semidirect
11. #10622280C2semidirect
12. #10622278C2semidirect
13. #10622278C2semidirect
14. #10622278C2semidirect
15. #10622277C2semidirect
24. C2×C11×C4⋊C4C22semidirect
36. C2×(C2×D11)⋊C4C22semidirect
37. C2×(C2×D11)⋊C4C22semidirect
38. C2×(C2×D11)⋊C4C22semidirect
39. C2×(C2×D11)⋊C4C22semidirect
40. C2×C4⋊Dic11C22semidirect
41. C2×Dic11⋊C4C22semidirect
42. C2×Dic11⋊C4C22semidirect
47. C11×#95C22semidirect
48. C11×#95C22semidirect
49. C11×#95C22semidirect
50. C11⋊#95C22semidirect
51. C11⋊#95C22semidirect
52. C11⋊#95C22semidirect
53. C11⋊#95C22semidirect
54. C11⋊#95C22semidirect
113. (C2×D11)⋊C4D4semidirect
199. #397D11semidirect
244. C2×D11#123semidirect
269. C2×C4⋊C4C2×D11semidirect
292. #95C2×D11semidirect
293. #95C2×D11semidirect
294. #95C2×D11semidirect
368. C11#2412semidirect

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
C11×#3972
#106226002
#106225742
#106225722
#106225652
#106222812
#106222802
#106222782
#106222772
#241211