Finite Group Databasebeta

← #13072742

Subgroups — #13072742

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
1C22×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
2C2×#66935C211yesmaximal, characteristic
3C2×#66931C211yesmaximal, characteristic, complemented
4C2×#66928C211yesmaximal, characteristic, complemented
5C4×C11×C22⋊C4C211yesmaximal, characteristic, complemented
6#10622826C211yesmaximal, characteristic, complemented
7#10622571C211yesmaximal, characteristic, complemented
8#10622568C211yesmaximal, characteristic, complemented
9#10622553C211yesmaximal, characteristic, complemented
10#10622553C211yesmaximal, characteristic, complemented
11#10622552C211yesmaximal, characteristic, complemented
12#10622287C211yesmaximal, characteristic, complemented
13#10622286C211yesmaximal, characteristic, complemented
14#10622285C211yesmaximal, characteristic, complemented
15#10622285C211yesmaximal, characteristic, complemented
16C24×D11C2211yescharacteristic
17C23×C4×C11C2211yescharacteristic
18C22×C22⋊D11C2211yescharacteristic
19C23×Dic11C2211yescharacteristic
20C22×D44C2211yescharacteristic
21C22×D44C2211yescharacteristic
22C22×Dic22C2211yescharacteristic, complemented
23C2×C11×C22⋊C4C2211yescharacteristic
24C2×C11×C22⋊C4C2211yescharacteristic
25C2×C42×C11C2211yescharacteristic, complemented
26C2×C42×C11C2211yescharacteristic, complemented
27C2×C22⋊Dic11C2211yescharacteristic
28C2×(C2×D11)⋊C4—24no—
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
38C2×(C2×D11)⋊C4C2211yescharacteristic
39C2×(C2×D11)⋊C4C2211yescharacteristic, complemented
40C2×(C2×D11)⋊C4C2211yescharacteristic, complemented
41C2×(C2×D11)⋊C4C2211yescharacteristic, complemented
42C2×(C2×D11)⋊C4C2211yescharacteristic, complemented
43C2×C4⋊Dic11C2211yescharacteristic, complemented
44C2×Dic11⋊C4C2211yescharacteristic, complemented
45C2×Dic11⋊C4C2211yescharacteristic, complemented
46#66935—24no—
47#66931—24no—
48#66928—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—22no—
61C23×D11—41no—
62C23×D11—41no—
63C23×D11C2311yescharacteristic
64C23×D11C2311yescharacteristic
65C23×D11C2311yescharacteristic
66C22×C4×C11—22no—
67C22×C4×C11—22no—
68C22×C4×C11—41no—
69C22×C4×C11C2311yescharacteristic
70C22×C4×C11C2311yescharacteristic
71C22×C4×C11C2311yescharacteristic
72C22×C4×C11C2311yescharacteristic
73C22×C4×C11C2311yescharacteristic
74C22×C4×C11C2311yescharacteristic
75C2×C22⋊D11—22no—
76C2×C22⋊D11—22no—
77C2×C22⋊D11—22no—
78C22×Dic11—22no—
79C22×Dic11—22no—
80C22×Dic11—41no—
81C22×Dic11C2311yescharacteristic
82C22×Dic11C2311yescharacteristic
83C22×Dic11C2311yescharacteristic
84C22×Dic11C2311yescharacteristic
85C22×Dic11C2311yescharacteristic
86C2×D44—22no—
87C2×D44—22no—
88C2×D44—22no—
89C2×D44—22no—
90C2×D44—41no—
91C2×D44—41no—
92C2×Dic22—22no—
93C2×Dic22—22no—
94C2×Dic22—41no—
95C11×C22⋊C4—22no—
96C11×C22⋊C4D414yes—
97C42×C11—22no—
98C42×C11—41no—
99C22⋊Dic11—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—22no—
108(C2×D11)⋊C4—22no—
109(C2×D11)⋊C4—41no—
110(C2×D11)⋊C4—41no—
111(C2×D11)⋊C4—41no—
112(C2×D11)⋊C4—41no—
113(C2×D11)⋊C4D414yescomplemented
114C4⋊Dic11—22no—
115Dic11⋊C4—22no—
116Dic11⋊C4—22no—
117#2472—111nomaximal, Sylow
118C23×C11—21no—
119C23×C11—21no—
120C23×C11—21no—
121C23×C11—21no—
122C23×C11C2×D412yes—
123C23×C11#4112yes—
124C23×C11#4112yes—
125C23×C11C2411yescharacteristic
126C22×D11—28no—
127C22×D11—21no—
128C22×D11—21no—
129C22×D11—21no—
130C22×D11—21no—
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—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—
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—44no—
170C2×C4×C11C2×D412yes—
171C2×C4×C11C2×D412yes—
172C2×C4×C11C2×D412yes—
173C22⋊D11—44no—
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—
190D44—44no—
191D44—44no—
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#386—111no—
206#379—111no—
207C4×C22⋊C4D1111yescharacteristic, complemented
208C22×C11—22no—
209C22×C11—22no—
210C22×C11—22no—
211C22×C11—22no—
212C22×C11—22no—
213C22×C11—22no—
214C22×C11#12414yescomplemented
215C22×C11C22×D411yescharacteristic
216C22×C11C22×D411yescharacteristic
217C22×C11C2×#4111yescharacteristic
218C22×C11C2×#4111yescharacteristic
219C22×C11C2×#4111yescharacteristic
220C22×C11H(5,𝔽2)11yescharacteristic
221C22×C11H(5,𝔽2)11yescharacteristic
222C2×D11—22no—
223C2×D11—22no—
224C2×D11—22no—
225C2×D11—22no—
226C2×D11—22no—
227C2×D11—22no—
228C2×D11—416no—
229C2×D11—41no—
230C2×D11—41no—
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—41no—
243C2×D11—41no—
244C4×C11—22no—
245C4×C11—22no—
246C4×C11—22no—
247C4×C11—41no—
248C4×C11—41no—
249C4×C11—41no—
250Dic11—22no—
251Dic11—41no—
252Dic11—41no—
253Dic11—41no—
254Dic11—41no—
255C25—111no—
256C22×Q8—111no—
257C22×D4—111no—
258C22×D4—111no—
259C22×D4—111no—
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—111no—
283C2×C22⋊C4—224no—
284C2×C22⋊C4C2×D1111yescharacteristic
285C2×C22⋊C4C2×D1111yescharacteristic
286C2×C42C2×D1111yescharacteristic, complemented
287C2×C42C2×D1111yescharacteristic, complemented
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#52511yescharacteristic
296C2×C11C2×#12411yescharacteristic
297C2×C11#53811yescharacteristic
298C2×C11D4211yescharacteristic
299C2×C11#54611yescharacteristic
300C2×C11#54611yescharacteristic
301C2×C11#55111yescharacteristic
302D11—42no—
303D11—42no—
304D11—81no—
305C24—111no—
306C24—111no—
307C24—111no—
308C24—222no—
309C24—222no—
310C24—222no—
311C24—222no—
312C24—222no—
313C24—441no—
314C24—441no—
315C24C22×D1111yescharacteristic
316C2×Q8—222no—
317C2×Q8—222no—
318C2×Q8—441no—
319C2×D4—222no—
320C2×D4—222no—
321C2×D4—222no—
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—222no—
337C22×C4—222no—
338C22×C4—441no—
339C22×C4C22×D1111yescharacteristic
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—114no—
350C22⋊C4—222no—
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—
364C22⋊C4D4414yes—
365C42—22no—
366C42—41no—
367C11#247211yescharacteristic, complemented, Sylow
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—112no—
373C23—112no—
374C23—228no—
375C23—221no—
376C23—221no—
377C23—221no—
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—444no—
395C23—444no—
396C23—444no—
397C23—444no—
398C23—444no—
399C23—444no—
400C23C2×D4412yes—
401C23#433912yes—
402C23#433912yes—
403C23C23×D1111yescharacteristic
404Q8—444no—
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—44no—
424C2×C4—112no—
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—444no—
440C2×C4C2×D4412yes—
441C2×C4C2×D4412yes—
442C2×C4D4×D1112yes—
443C22—22no—
444C22—22no—
445C22—22no—
446C22—22no—
447C22—22no—
448C22—22no—
449C22—222no—
450C22—222no—
451C22—222no—
452C22—222no—
453C22—222no—
454C22—222no—
455C22—4416no—
456C22—441no—
457C22—441no—
458C22—441no—
459C22—441no—
460C22—441no—
461C22—441no—
462C22—441no—
463C22—441no—
464C22—441no—
465C22—441no—
466C22—441no—
467C22—441no—
468C22—441no—
469C22—441no—
470C22—441no—
471C22#6692814yescomplemented
472C22C22×D4411yescharacteristic
473C22C2×#433911yescharacteristic
474C22C2×#433911yescharacteristic
475C22C2×D4×D1111yescharacteristic
476C22#6703711yescharacteristic
477C22#41×D1111yescharacteristic
478C22#6704211yescharacteristic
479C4—22no—
480C4—22no—
481C4—22no—
482C4—41no—
483C4—41no—
484C4—41no—
485C4—222no—
486C4—441no—
487C4—441no—
488C4—441no—
489C4—441no—
490C2—24no—
491C2—442no—
492C2—442no—
493C2—881no—
494C2C2×#6692811yescharacteristic
495C2#1062302111yescharacteristic
496C2#1062305811yescharacteristic
497C2#1062307811yescharacteristic
498C2D4×D4411yescharacteristic
499C2#1062308511yescharacteristic
500C2#1062309111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC4×C11×C22⋊C4C2
prime radicalC2×#66935C2
hypercenterC4×C22⋊C4D11
hypocenterC11#2472
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×(C2×D11)⋊C4C2semidirect
3. C2×#66931C2semidirect
4. C2×#66928C2semidirect
5. C4×C11×C22⋊C4C2semidirect
6. #10622826C2semidirect
7. #10622571C2semidirect
8. #10622568C2semidirect
9. #10622553C2semidirect
10. #10622553C2semidirect
11. #10622552C2semidirect
12. #10622287C2semidirect
13. #10622286C2semidirect
14. #10622285C2semidirect
15. #10622285C2semidirect
22. C22×Dic22C22semidirect
25. C2×C42×C11C22semidirect
26. C2×C42×C11C22semidirect
39. C2×(C2×D11)⋊C4C22semidirect
40. C2×(C2×D11)⋊C4C22semidirect
41. C2×(C2×D11)⋊C4C22semidirect
42. C2×(C2×D11)⋊C4C22semidirect
43. C2×C4⋊Dic11C22semidirect
44. C2×Dic11⋊C4C22semidirect
45. C2×Dic11⋊C4C22semidirect
49. C11×#95C22semidirect
50. C11×#95C22semidirect
51. C11⋊#95C22semidirect
52. C11⋊#95C22semidirect
53. C11⋊#95C22semidirect
54. C11⋊#95C22semidirect
113. (C2×D11)⋊C4D4semidirect
207. C4×C22⋊C4D11semidirect
214. C22×C11#124semidirect
286. C2×C42C2×D11semidirect
287. C2×C42C2×D11semidirect
292. #95C2×D11semidirect
293. #95C2×D11semidirect
367. C11#2472semidirect
471. C22#66928semidirect

Maximal subgroups

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

subgroupindex
C22×(C2×D11)⋊C42
C2×#669352
C2×#669312
C2×#669282
C4×C11×C22⋊C42
#106228262
#106225712
#106225682
#106225532
#106225522
#106222872
#106222862
#106222852
#247211