Finite Group Databasebeta

← #16848688

Subgroups — #16848688

Order 3968.

928 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11758514C211yesmaximal, characteristic
2C2×C4×C22⋊D31C211yesmaximal, characteristic, complemented
3C22×(C2×D31)⋊C4C211yesmaximal, characteristic, complemented
4C2×C22⋊C4×D31C211yesmaximal, characteristic, complemented
5#14520949C211yesmaximal, characteristic, complemented
6#14520940C211yesmaximal, characteristic, complemented
7#14520939C211yesmaximal, characteristic, complemented
8#14520929C211yesmaximal, characteristic, complemented
9#14520928C211yesmaximal, characteristic, complemented
10#14520925C211yesmaximal, characteristic, complemented
11#14520922C211yesmaximal, characteristic, complemented
12#14520920C211yesmaximal, characteristic, complemented
13C22⋊C4×Dic31C211yesmaximal, characteristic, complemented
14C4×(C2×D31)⋊C4C211yesmaximal, characteristic, complemented
15C2×C4×D4×C31C211yesmaximal, characteristic, complemented
16C24×D31C2211yescharacteristic
17C22×D4×C31C2211yescharacteristic
18C23×C4×C31C2211yescharacteristic
19C23×C4×C31C2211yescharacteristic, complemented
20C22×C22⋊D31C2211yescharacteristic
21C22×C22⋊D31C2211yescharacteristic
22C23×Dic31C2211yescharacteristic
23C22×C4×D31C2211yescharacteristic
24C22×C4×D31C2211yescharacteristic
25C4×D4×C31—24no—
26C2×C4⋊C4×C31C2211yescharacteristic, complemented
27C2×C22⋊C4×C31C2211yescharacteristic
28C2×C22⋊C4×C31C2211yescharacteristic, complemented
29C2×C42×C31C2211yescharacteristic, complemented
30C2×C22⋊Dic31C2211yescharacteristic
31C2×C22⋊Dic31C2211yescharacteristic
32C2×C22⋊Dic31C2211yescharacteristic, complemented
33C2×C22⋊Dic31C2211yescharacteristic, complemented
34#11758514C418yescomplemented
35C4×C22⋊D31—24no—
36C2×(C2×D31)⋊C4—24no—
37C2×(C2×D31)⋊C4C2211yescharacteristic
38C2×(C2×D31)⋊C4C2211yescharacteristic
39C2×(C2×D31)⋊C4C2211yescharacteristic
40C2×(C2×D31)⋊C4C2211yescharacteristic
41C2×(C2×D31)⋊C4C2211yescharacteristic
42C2×(C2×D31)⋊C4C2211yescharacteristic
43C2×(C2×D31)⋊C4C2211yescharacteristic
44C2×(C2×D31)⋊C4C2211yescharacteristic
45C2×Dic31⋊C4C2211yescharacteristic, complemented
46C2×Dic31⋊C4C2211yescharacteristic, complemented
47C2×C4×Dic31C2211yescharacteristic, complemented
48C2×C4×Dic31C2211yescharacteristic, complemented
49C22⋊C4×D31—24no—
50C31⋊#95C2211yescharacteristic, complemented
51C31⋊#95C2211yescharacteristic, complemented
52C31⋊#95C2211yescharacteristic, complemented
53C31⋊#95C2211yescharacteristic, complemented
54C31⋊#95C2211yescharacteristic, complemented
55C31⋊#95C2211yescharacteristic, complemented
56C24×C31C2311yescharacteristic
57C24×C31C2311yescharacteristic
58C23×D31—22no—
59C23×D31—22no—
60C23×D31—22no—
61C23×D31—22no—
62C23×D31—41no—
63C23×D31—41no—
64C23×D31C2×C414yescomplemented
65C23×D31C2311yescharacteristic
66C23×D31C2311yescharacteristic
67C2×D4×C31—22no—
68C2×D4×C31—22no—
69C2×D4×C31C2×C414yescomplemented
70C22×C4×C31—22no—
71C22×C4×C31—22no—
72C22×C4×C31—22no—
73C22×C4×C31—22no—
74C22×C4×C31—41no—
75C22×C4×C31—41no—
76C22×C4×C31C2311yescharacteristic
77C22×C4×C31C2311yescharacteristic
78C22×C4×C31C2311yescharacteristic
79C22×C4×C31C2311yescharacteristic
80C22×C4×C31C2311yescharacteristic
81C2×C22⋊D31—22no—
82C2×C22⋊D31—22no—
83C2×C22⋊D31—41no—
84C2×C22⋊D31—41no—
85C2×C22⋊D31C2×C414yescomplemented
86C2×C22⋊D31C2×C414yescomplemented
87C22×Dic31—22no—
88C22×Dic31—22no—
89C22×Dic31—41no—
90C22×Dic31C2311yescharacteristic
91C22×Dic31C2311yescharacteristic
92C22×Dic31C2311yescharacteristic
93C22×Dic31C2311yescharacteristic
94C22×Dic31C2311yescharacteristic
95C22×Dic31C2311yescharacteristic
96C2×C4×D31—22no—
97C2×C4×D31—22no—
98C2×C4×D31—22no—
99C2×C4×D31—22no—
100C2×C4×D31—41no—
101C2×C4×D31—41no—
102C4⋊C4×C31—22no—
103C22⋊C4×C31—22no—
104C22⋊C4×C31D414yescomplemented
105C42×C31—22no—
106C22⋊Dic31—22no—
107C22⋊Dic31—22no—
108C22⋊Dic31—41no—
109C22⋊Dic31C2×C414yescomplemented
110(C2×D31)⋊C4—22no—
111(C2×D31)⋊C4—22no—
112(C2×D31)⋊C4—22no—
113(C2×D31)⋊C4—22no—
114(C2×D31)⋊C4—22no—
115(C2×D31)⋊C4C2×C414yescomplemented
116(C2×D31)⋊C4C2×C414yescomplemented
117(C2×D31)⋊C4D414yescomplemented
118Dic31⋊C4—22no—
119Dic31⋊C4—41no—
120C4×Dic31—22no—
121C4×Dic31—41no—
122C23×C31—21no—
123C23×C31—21no—
124C23×C31—21no—
125C23×C31—21no—
126C23×C31—21no—
127C23×C31—21no—
128C23×C31—21no—
129C23×C31—21no—
130C23×C31—21no—
131C23×C31—21no—
132C23×C31C22×C412yes—
133C23×C31C22×C412yes—
134C23×C31C2×D412yes—
135C23×C31#4112yes—
136C23×C31C2411yescharacteristic
137C22×D31—21no—
138C22×D31—21no—
139C22×D31—21no—
140C22×D31—21no—
141C22×D31—28no—
142C22×D31—21no—
143C22×D31—21no—
144C22×D31—21no—
145C22×D31—21no—
146C22×D31—21no—
147C22×D31—21no—
148C22×D31—28no—
149C22×D31—44no—
150C22×D31—44no—
151C22×D31—44no—
152C22×D31—44no—
153C22×D31—44no—
154C22×D31C22×C412yes—
155C22×D31C22×C412yes—
156C22×D31C2×D412yes—
157C22×D31#4112yes—
158D4×C31—28no—
159C2×C4×C31—21no—
160C2×C4×C31—21no—
161C2×C4×C31—21no—
162C2×C4×C31—21no—
163C2×C4×C31—21no—
164C2×C4×C31—21no—
165C2×C4×C31—21no—
166C2×C4×C31—21no—
167C2×C4×C31—21no—
168C2×C4×C31—21no—
169C2×C4×C31—21no—
170C2×C4×C31—44no—
171C2×C4×C31—44no—
172C2×C4×C31C22×C412yes—
173C2×C4×C31C2×D412yes—
174C2×C4×C31C2×D412yes—
175C2×C4×C31C2×D412yes—
176C22⋊D31—28no—
177C22⋊D31—44no—
178C2×Dic31—21no—
179C2×Dic31—21no—
180C2×Dic31—21no—
181C2×Dic31—21no—
182C2×Dic31—21no—
183C2×Dic31—21no—
184C2×Dic31—21no—
185C2×Dic31—21no—
186C2×Dic31—21no—
187C2×Dic31—21no—
188C2×Dic31—21no—
189C2×Dic31—21no—
190C2×Dic31—21no—
191C2×Dic31—21no—
192C2×Dic31—21no—
193C2×Dic31—44no—
194C2×Dic31C22×C412yes—
195C2×Dic31C22×C412yes—
196C2×Dic31C2×D412yes—
197C4×D31—44no—
198C4×D31—44no—
199#2358—311nomaximal, Sylow
200C22×C31—22no—
201C22×C31—22no—
202C22×C31—22no—
203C22×C31—22no—
204C22×C31—22no—
205C22×C31—22no—
206C22×C31—22no—
207C22×C31—22no—
208C22×C31—22no—
209C22×C31—41no—
210C22×C31—41no—
211C22×C31—41no—
212C22×C31—41no—
213C22×C31C4×D414yescomplemented
214C22×C31C23×C411yescharacteristic
215C22×C31C22×D411yescharacteristic
216C22×C31C22×D411yescharacteristic
217C22×C31C2×#4111yescharacteristic
218C22×C31C2×#4111yescharacteristic
219C22×C31H(5,𝔽2)11yescharacteristic
220C22×C31H(5,𝔽2)11yescharacteristic
221C2×D31—22no—
222C2×D31—22no—
223C2×D31—22no—
224C2×D31—22no—
225C2×D31—22no—
226C2×D31—22no—
227C2×D31—22no—
228C2×D31—22no—
229C2×D31—22no—
230C2×D31—416no—
231C2×D31—41no—
232C2×D31—41no—
233C2×D31—41no—
234C2×D31—41no—
235C2×D31C4×D414yescomplemented
236C4×C31—22no—
237C4×C31—22no—
238C4×C31—22no—
239C4×C31—22no—
240C4×C31—41no—
241Dic31—22no—
242Dic31—22no—
243Dic31—22no—
244Dic31—41no—
245Dic31—41no—
246Dic31—41no—
247C2×#120—311no—
248C2×C4×D4—311no—
249C2×C4×D4D3111yescharacteristic, complemented
250C22×C22⋊C4—311no—
251C22×C22⋊C4—311no—
252#390—311no—
253#388—311no—
254#388—311no—
255#386—311no—
256#386—311no—
257#386—311no—
258#385—311no—
259#385—311no—
260C4×C22⋊C4—311no—
261C4×C22⋊C4—311no—
262C2×C31—24no—
263C2×C31—42no—
264C2×C31C2×C4×D411yescharacteristic
265C2×C31C2×C4×D411yescharacteristic
266C2×C31#51811yescharacteristic
267C2×C31D4211yescharacteristic
268C2×C31#54611yescharacteristic
269C2×C31#54611yescharacteristic
270C2×C31#55111yescharacteristic
271D31—24no—
272D31—42no—
273C25—311no—
274C22×D4—311no—
275C22×D4—311no—
276C22×D4C2×D3111yescharacteristic
277C23×C4—311no—
278C23×C4—311no—
279C23×C4—311no—
280C23×C4C2×D3111yescharacteristic
281C23×C4C2×D3111yescharacteristic, complemented
282#120—318no—
283C4×D4—24no—
284C4×D4—624no—
285C2×C4⋊C4—311no—
286C2×C4⋊C4—311no—
287C2×C4⋊C4C2×D3111yescharacteristic, complemented
288C2×C22⋊C4—311no—
289C2×C22⋊C4—311no—
290C2×C22⋊C4—311no—
291C2×C22⋊C4—311no—
292C2×C22⋊C4—311no—
293C2×C22⋊C4—311no—
294C2×C22⋊C4—311no—
295C2×C22⋊C4—311no—
296C2×C22⋊C4—311no—
297C2×C22⋊C4—311no—
298C2×C22⋊C4—311no—
299C2×C22⋊C4—311no—
300C2×C22⋊C4—624no—
301C2×C22⋊C4—624no—
302C2×C22⋊C4C2×D3111yescharacteristic
303C2×C22⋊C4C2×D3111yescharacteristic, complemented
304C2×C42—311no—
305C2×C42—311no—
306C2×C42C2×D3111yescharacteristic, complemented
307#95—311no—
308#95—311no—
309#95—311no—
310#95—311no—
311#95—311no—
312#95—311no—
313C31#235811yescharacteristic, complemented, Sylow
314C24—311no—
315C24—311no—
316C24—314no—
317C24—622no—
318C24—622no—
319C24—622no—
320C24—622no—
321C24—1241no—
322C24—1241no—
323C24C22×D3111yescharacteristic
324C24C22×D3111yescharacteristic
325C2×D4—22no—
326C2×D4—22no—
327C2×D4—314no—
328C2×D4—314no—
329C2×D4—622no—
330C2×D4—622no—
331C2×D4—1241no—
332C2×D4—1241no—
333C2×D4C4×D3114yescomplemented
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—22no—
337C22×C4—22no—
338C22×C4—41no—
339C22×C4—41no—
340C22×C4—311no—
341C22×C4—311no—
342C22×C4—311no—
343C22×C4—311no—
344C22×C4—311no—
345C22×C4—311no—
346C22×C4—622no—
347C22×C4—622no—
348C22×C4—622no—
349C22×C4—622no—
350C22×C4—622no—
351C22×C4—622no—
352C22×C4—1241no—
353C22×C4—1241no—
354C22×C4—1241no—
355C22×C4C22×D3111yescharacteristic
356C22×C4C22×D3111yescharacteristic
357C22×C4C22×D3111yescharacteristic
358C22×C4C22×D3111yescharacteristic
359C22×C4C22×D3111yescharacteristic
360C4⋊C4—22no—
361C4⋊C4—622no—
362C4⋊C4—1241no—
363C22⋊C4—22no—
364C22⋊C4—314no—
365C22⋊C4—314no—
366C22⋊C4—314no—
367C22⋊C4—314no—
368C22⋊C4—622no—
369C22⋊C4—622no—
370C22⋊C4—622no—
371C22⋊C4—622no—
372C22⋊C4—622no—
373C22⋊C4—622no—
374C22⋊C4—622no—
375C22⋊C4—1241no—
376C22⋊C4C22⋊D3114yescomplemented
377C42—22no—
378C42—622no—
379C42—1241no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—21no—
385C23—21no—
386C23—21no—
387C23—21no—
388C23—21no—
389C23—21no—
390C23—312no—
391C23—312no—
392C23—312no—
393C23—312no—
394C23—628no—
395C23—621no—
396C23—621no—
397C23—621no—
398C23—621no—
399C23—628no—
400C23—621no—
401C23—621no—
402C23—621no—
403C23—621no—
404C23—621no—
405C23—621no—
406C23—1244no—
407C23—1244no—
408C23—1244no—
409C23—1244no—
410C23—1244no—
411C23C2×C4×D3112yes—
412C23C2×C4×D3112yes—
413C23#9249512yes—
414C23C2×C22⋊D3112yes—
415C23C23×D3111yescharacteristic
416D4—28no—
417D4—628no—
418D4—1244no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—44no—
431C2×C4—44no—
432C2×C4—312no—
433C2×C4—312no—
434C2×C4—312no—
435C2×C4—621no—
436C2×C4—621no—
437C2×C4—621no—
438C2×C4—621no—
439C2×C4—621no—
440C2×C4—621no—
441C2×C4—621no—
442C2×C4—621no—
443C2×C4—621no—
444C2×C4—621no—
445C2×C4—621no—
446C2×C4—621no—
447C2×C4—621no—
448C2×C4—621no—
449C2×C4—621no—
450C2×C4—1244no—
451C2×C4—1244no—
452C2×C4—1244no—
453C2×C4C2×C4×D3112yes—
454C2×C4D4×D3112yes—
455C2×C4C2×C22⋊D3112yes—
456C2×C4C2×C22⋊D3112yes—
457C22—22no—
458C22—22no—
459C22—22no—
460C22—22no—
461C22—22no—
462C22—22no—
463C22—22no—
464C22—22no—
465C22—22no—
466C22—41no—
467C22—41no—
468C22—41no—
469C22—41no—
470C22—314no—
471C22—622no—
472C22—622no—
473C22—622no—
474C22—622no—
475C22—622no—
476C22—622no—
477C22—622no—
478C22—622no—
479C22—622no—
480C22—12416no—
481C22—1241no—
482C22—1241no—
483C22—1241no—
484C22—1241no—
485C22C4×C22⋊D3114yescomplemented
486C22C22×C4×D3111yescharacteristic
487C22C2×#9249511yescharacteristic
488C22C2×D4×D3111yescharacteristic
489C22#1175856111yescharacteristic
490C22#41×D3111yescharacteristic
491C22#1175856611yescharacteristic
492C22C22×C22⋊D3111yescharacteristic
493C4—22no—
494C4—22no—
495C4—22no—
496C4—22no—
497C4—41no—
498C4—622no—
499C4—622no—
500C4—622no—
501C4—1241no—
502C4—1241no—
503C4—1241no—
504C2—24no—
505C2—42no—
506C2—624no—
507C2—1242no—
508C2C4×D4×D3111yescharacteristic
509C2C2×C4×C22⋊D3111yescharacteristic
510C2#1452152111yescharacteristic
511C2D4×C22⋊D3111yescharacteristic
512C2#1452168711yescharacteristic
513C2#1452169511yescharacteristic
514C2#1452172811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D31
commutatorC22×C31C23×C4
FittingC2×C4×D4×C31C2
socle, cosocleC23×C31C24
prime radicalC2×#11758514C2
hypercenterC2×C4×D4D31
hypocenterC31#2358
LCSG ▷ C22×C31 ▷ C31
UCSC1 ◁ C23 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
2. C2×C4×C22⋊D31C2semidirect
3. C22×(C2×D31)⋊C4C2semidirect
4. C2×C22⋊C4×D31C2semidirect
5. #14520949C2semidirect
6. #14520940C2semidirect
7. #14520939C2semidirect
8. #14520929C2semidirect
9. #14520928C2semidirect
10. #14520925C2semidirect
11. #14520922C2semidirect
12. #14520920C2semidirect
13. C22⋊C4×Dic31C2semidirect
14. C4×(C2×D31)⋊C4C2semidirect
15. C2×C4×D4×C31C2semidirect
19. C23×C4×C31C22semidirect
26. C2×C4⋊C4×C31C22semidirect
28. C2×C22⋊C4×C31C22semidirect
29. C2×C42×C31C22semidirect
32. C2×C22⋊Dic31C22semidirect
33. C2×C22⋊Dic31C22semidirect
34. #11758514C4semidirect
45. C2×Dic31⋊C4C22semidirect
46. C2×Dic31⋊C4C22semidirect
47. C2×C4×Dic31C22semidirect
48. C2×C4×Dic31C22semidirect
50. C31⋊#95C22semidirect
51. C31⋊#95C22semidirect
52. C31⋊#95C22semidirect
53. C31⋊#95C22semidirect
54. C31⋊#95C22semidirect
55. C31⋊#95C22semidirect
64. C23×D31C2×C4semidirect
69. C2×D4×C31C2×C4semidirect
85. C2×C22⋊D31C2×C4semidirect
86. C2×C22⋊D31C2×C4semidirect
104. C22⋊C4×C31D4semidirect
109. C22⋊Dic31C2×C4semidirect
115. (C2×D31)⋊C4C2×C4semidirect
116. (C2×D31)⋊C4C2×C4semidirect
117. (C2×D31)⋊C4D4semidirect
213. C22×C31C4×D4semidirect
235. C2×D31C4×D4semidirect
249. C2×C4×D4D31semidirect
281. C23×C4C2×D31semidirect
287. C2×C4⋊C4C2×D31semidirect
303. C2×C22⋊C4C2×D31semidirect
306. C2×C42C2×D31semidirect
313. C31#2358semidirect
333. C2×D4C4×D31semidirect
376. C22⋊C4C22⋊D31semidirect
485. C22C4×C22⋊D31semidirect

Maximal subgroups

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

subgroupindex
C2×#117585142
C2×C4×C22⋊D312
C22×(C2×D31)⋊C42
C2×C22⋊C4×D312
#145209492
#145209402
#145209392
#145209292
#145209282
#145209252
#145209222
#145209202
C22⋊C4×Dic312
C4×(C2×D31)⋊C42
C2×C4×D4×C312
#235831