Finite Group Databasebeta

← #16848693

Subgroups — #16848693

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×#11758459C211yesmaximal, characteristic
2C2×C4×D124C211yesmaximal, characteristic, complemented
3C2×(C22⋊D31)⋊C4C211yesmaximal, characteristic, complemented
4C22×(C2×D31)⋊C4C211yesmaximal, characteristic, complemented
5C2×C22⋊C4×D31C211yesmaximal, characteristic, complemented
6#14520951C211yesmaximal, characteristic, complemented
7#14520941C211yesmaximal, characteristic, complemented
8#14520940C211yesmaximal, characteristic, complemented
9#14520928C211yesmaximal, characteristic, complemented
10#14520927C211yesmaximal, characteristic, complemented
11#14520927C211yesmaximal, characteristic, complemented
12#14520924C211yesmaximal, characteristic, complemented
13#14520923C211yesmaximal, characteristic, complemented
14C4×(C2×D31)⋊C4C211yesmaximal, characteristic, complemented
15C4×C22⋊C4×C31C211yesmaximal, characteristic, complemented
16C24×D31C2211yescharacteristic
17C23×C4×C31C2211yescharacteristic
18C22×C22⋊D31C2211yescharacteristic
19C23×Dic31C2211yescharacteristic
20C22×D124C2211yescharacteristic
21C22×D124C2211yescharacteristic
22C22×C4×D31C2211yescharacteristic
23C22×C4×D31C2211yescharacteristic
24C22×C4×D31C2211yescharacteristic, complemented
25C2×C22⋊C4×C31C2211yescharacteristic
26C2×C22⋊C4×C31C2211yescharacteristic
27C2×C42×C31C2211yescharacteristic, complemented
28C2×C42×C31C2211yescharacteristic, complemented
29C2×C22⋊Dic31C2211yescharacteristic
30C2×(C2×D31)⋊C4—24no—
31C2×(C2×D31)⋊C4C2211yescharacteristic
32C2×(C2×D31)⋊C4C2211yescharacteristic
33C2×(C2×D31)⋊C4C2211yescharacteristic
34C2×(C2×D31)⋊C4C2211yescharacteristic
35C2×(C2×D31)⋊C4C2211yescharacteristic
36C2×(C2×D31)⋊C4C2211yescharacteristic
37C2×(C2×D31)⋊C4C2211yescharacteristic
38C2×(C2×D31)⋊C4C2211yescharacteristic
39C2×(C2×D31)⋊C4C2211yescharacteristic, complemented
40C2×(C2×D31)⋊C4C2211yescharacteristic, complemented
41C2×(C2×D31)⋊C4C2211yescharacteristic, complemented
42C2×C4⋊Dic31C2211yescharacteristic, complemented
43C2×C4⋊Dic31C2211yescharacteristic, complemented
44C2×Dic31⋊C4C2211yescharacteristic, complemented
45C2×C4×Dic31C2211yescharacteristic, complemented
46#11758459C418yescomplemented
47(C22⋊D31)⋊C4—24no—
48C22⋊C4×D31—24no—
49C4×D124—24no—
50C31×#95C2211yescharacteristic, complemented
51C31×#95C2211yescharacteristic, complemented
52C31⋊#95C2211yescharacteristic, complemented
53C31⋊#95C2211yescharacteristic, complemented
54C31⋊#95C2211yescharacteristic, complemented
55C31⋊#95C2211yescharacteristic, complemented
56C24×C31C2311yescharacteristic
57C23×D31—22no—
58C23×D31—22no—
59C23×D31—22no—
60C23×D31—22no—
61C23×D31—41no—
62C23×D31—41no—
63C23×D31C2×C414yescomplemented
64C23×D31C2311yescharacteristic
65C23×D31C2311yescharacteristic
66C23×D31C2311yescharacteristic
67C22×C4×C31—22no—
68C22×C4×C31—22no—
69C22×C4×C31—41no—
70C22×C4×C31C2311yescharacteristic
71C22×C4×C31C2311yescharacteristic
72C22×C4×C31C2311yescharacteristic
73C22×C4×C31C2311yescharacteristic
74C22×C4×C31C2311yescharacteristic
75C22×C4×C31C2311yescharacteristic
76C2×C22⋊D31—22no—
77C2×C22⋊D31—22no—
78C2×C22⋊D31C2×C414yescomplemented
79C22×Dic31—22no—
80C22×Dic31—22no—
81C22×Dic31—41no—
82C22×Dic31C2311yescharacteristic
83C22×Dic31C2311yescharacteristic
84C22×Dic31C2311yescharacteristic
85C22×Dic31C2311yescharacteristic
86C22×Dic31C2311yescharacteristic
87C2×D124—22no—
88C2×D124—22no—
89C2×D124—41no—
90C2×D124—41no—
91C2×D124C2×C414yescomplemented
92C2×D124C2×C414yescomplemented
93C2×C4×D31—22no—
94C2×C4×D31—22no—
95C2×C4×D31—22no—
96C2×C4×D31—22no—
97C2×C4×D31—22no—
98C2×C4×D31—22no—
99C2×C4×D31—41no—
100C2×C4×D31—41no—
101C2×C4×D31—41no—
102C22⋊C4×C31C2×C414yescomplemented
103C22⋊C4×C31D414yescomplemented
104C42×C31—22no—
105C42×C31—41no—
106C22⋊Dic31—22no—
107(C2×D31)⋊C4—22no—
108(C2×D31)⋊C4—22no—
109(C2×D31)⋊C4—22no—
110(C2×D31)⋊C4—22no—
111(C2×D31)⋊C4—22no—
112(C2×D31)⋊C4—22no—
113(C2×D31)⋊C4—22no—
114(C2×D31)⋊C4—41no—
115(C2×D31)⋊C4C2×C414yescomplemented
116(C2×D31)⋊C4C2×C414yescomplemented
117(C2×D31)⋊C4D414yescomplemented
118C4⋊Dic31—22no—
119C4⋊Dic31—41no—
120Dic31⋊C4—22no—
121C4×Dic31—22no—
122C23×C31—21no—
123C23×C31—21no—
124C23×C31—21no—
125C23×C31—21no—
126C23×C31C22×C412yes—
127C23×C31C2×D412yes—
128C23×C31#4112yes—
129C23×C31C2411yescharacteristic
130C22×D31—21no—
131C22×D31—21no—
132C22×D31—21no—
133C22×D31—21no—
134C22×D31—28no—
135C22×D31—21no—
136C22×D31—21no—
137C22×D31—21no—
138C22×D31—21no—
139C22×D31—21no—
140C22×D31—21no—
141C22×D31—21no—
142C22×D31—21no—
143C22×D31—21no—
144C22×D31—21no—
145C22×D31—21no—
146C22×D31—21no—
147C22×D31—28no—
148C22×D31—44no—
149C22×D31—44no—
150C22×D31—44no—
151C22×D31—44no—
152C22×D31—44no—
153C22×D31C22×C412yes—
154C22×D31C22×C412yes—
155C22×D31C22×C412yes—
156C22×D31C2×D412yes—
157C22×D31#4112yes—
158C2×C4×C31—21no—
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—21no—
171C2×C4×C31—44no—
172C2×C4×C31C22×C412yes—
173C2×C4×C31C22×C412yes—
174C2×C4×C31C2×D412yes—
175C2×C4×C31C2×D412yes—
176C2×C4×C31C2×D412yes—
177C22⋊D31—28no—
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—44no—
192C2×Dic31C22×C412yes—
193C2×Dic31C2×D412yes—
194D124—28no—
195D124—44no—
196C4×D31—44no—
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×C31C4×D414yescomplemented
207C22×C31C23×C411yescharacteristic
208C22×C31C22×D411yescharacteristic
209C22×C31C22×D411yescharacteristic
210C22×C31C2×#4111yescharacteristic
211C22×C31C2×#4111yescharacteristic
212C22×C31H(5,𝔽2)11yescharacteristic
213C22×C31H(5,𝔽2)11yescharacteristic
214C2×D31—22no—
215C2×D31—22no—
216C2×D31—22no—
217C2×D31—22no—
218C2×D31—22no—
219C2×D31—22no—
220C2×D31—22no—
221C2×D31—22no—
222C2×D31—22no—
223C2×D31—22no—
224C2×D31—22no—
225C2×D31—22no—
226C2×D31—416no—
227C2×D31—41no—
228C2×D31—41no—
229C2×D31—41no—
230C2×D31—41no—
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—22no—
241C4×C31—41no—
242Dic31—22no—
243Dic31—22no—
244Dic31—41no—
245Dic31—41no—
246Dic31—41no—
247C2×#120—311no—
248C2×C4×D4—311no—
249C2×C4×D4—311no—
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⋊C4D3111yescharacteristic, complemented
262C2×C31—24no—
263C2×C31C2×C4×D411yescharacteristic
264C2×C31C2×C4×D411yescharacteristic
265C2×C31#51811yescharacteristic
266C2×C31D4211yescharacteristic
267C2×C31#54611yescharacteristic
268C2×C31#54611yescharacteristic
269C2×C31#55111yescharacteristic
270D31—24no—
271D31—42no—
272D31—42no—
273C25—311no—
274C22×D4—311no—
275C22×D4—311no—
276C22×D4—311no—
277C23×C4—311no—
278C23×C4—311no—
279C23×C4—311no—
280C23×C4—311no—
281C23×C4C2×D3111yescharacteristic
282#120—318no—
283C4×D4—624no—
284C4×D4—624no—
285C2×C4⋊C4—311no—
286C2×C4⋊C4—311no—
287C2×C4⋊C4—311no—
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
304C2×C42—311no—
305C2×C42C2×D3111yescharacteristic, complemented
306C2×C42C2×D3111yescharacteristic, complemented
307#95—311no—
308#95—311no—
309#95—311no—
310#95—311no—
311#95C2×D3111yescharacteristic, complemented
312#95C2×D3111yescharacteristic, complemented
313C31#235811yescharacteristic, complemented, Sylow
314C24—311no—
315C24—311no—
316C24—311no—
317C24—314no—
318C24—622no—
319C24—622no—
320C24—622no—
321C24—622no—
322C24—1241no—
323C24—1241no—
324C24C22×D3111yescharacteristic
325C2×D4—314no—
326C2×D4—314no—
327C2×D4—314no—
328C2×D4—622no—
329C2×D4—622no—
330C2×D4—622no—
331C2×D4—622no—
332C2×D4—1241no—
333C2×D4—1241no—
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—41no—
337C22×C4—311no—
338C22×C4—311no—
339C22×C4—311no—
340C22×C4—311no—
341C22×C4—311no—
342C22×C4—622no—
343C22×C4—622no—
344C22×C4—622no—
345C22×C4—622no—
346C22×C4—622no—
347C22×C4—622no—
348C22×C4—622no—
349C22×C4—622no—
350C22×C4—1241no—
351C22×C4—1241no—
352C22×C4—1241no—
353C22×C4—1241no—
354C22×C4C22×D3111yescharacteristic
355C22×C4C22×D3111yescharacteristic
356C22×C4C22×D3111yescharacteristic
357C22×C4C22×D3111yescharacteristic
358C22×C4C22×D3111yescharacteristic
359C22×C4C22×D3111yescharacteristic
360C4⋊C4—622no—
361C4⋊C4—622no—
362C4⋊C4—1241no—
363C22⋊C4—314no—
364C22⋊C4—314no—
365C22⋊C4—314no—
366C22⋊C4—622no—
367C22⋊C4—622no—
368C22⋊C4—622no—
369C22⋊C4—622no—
370C22⋊C4—622no—
371C22⋊C4—622no—
372C22⋊C4—622no—
373C22⋊C4—622no—
374C22⋊C4—1241no—
375C22⋊C4C4×D3114yescomplemented
376C22⋊C4D12414yescomplemented
377C42—22no—
378C42—41no—
379C42—622no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—312no—
385C23—312no—
386C23—312no—
387C23—312no—
388C23—312no—
389C23—628no—
390C23—621no—
391C23—621no—
392C23—621no—
393C23—621no—
394C23—628no—
395C23—621no—
396C23—621no—
397C23—621no—
398C23—621no—
399C23—621no—
400C23—621no—
401C23—621no—
402C23—621no—
403C23—621no—
404C23—621no—
405C23—621no—
406C23—621no—
407C23—1244no—
408C23—1244no—
409C23—1244no—
410C23—1244no—
411C23—1244no—
412C23C2×C4×D3112yes—
413C23C2×D12412yes—
414C23#9249512yes—
415C23C23×D3111yescharacteristic
416D4—628no—
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—21no—
431C2×C4—21no—
432C2×C4—44no—
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—1244no—
449C2×C4—1244no—
450C2×C4—1244no—
451C2×C4—1244no—
452C2×C4C2×C4×D3112yes—
453C2×C4C2×C4×D3112yes—
454C2×C4C2×D12412yes—
455C2×C4C2×D12412yes—
456C2×C4D4×D3112yes—
457C22—22no—
458C22—22no—
459C22—22no—
460C22—22no—
461C22—22no—
462C22—22no—
463C22—314no—
464C22—622no—
465C22—622no—
466C22—622no—
467C22—622no—
468C22—622no—
469C22—622no—
470C22—622no—
471C22—622no—
472C22—622no—
473C22—622no—
474C22—622no—
475C22—622no—
476C22—12416no—
477C22—1241no—
478C22—1241no—
479C22—1241no—
480C22—1241no—
481C22—1241no—
482C22—1241no—
483C22—1241no—
484C22—1241no—
485C22C4×D12414yescomplemented
486C22C22×C4×D3111yescharacteristic
487C22C22×D12411yescharacteristic
488C22C2×#9249511yescharacteristic
489C22C2×D4×D3111yescharacteristic
490C22#1175856111yescharacteristic
491C22#41×D3111yescharacteristic
492C22#1175856611yescharacteristic
493C4—22no—
494C4—22no—
495C4—22no—
496C4—22no—
497C4—22no—
498C4—41no—
499C4—622no—
500C4—622no—
501C4—1241no—
502C4—1241no—
503C4—1241no—
504C2—24no—
505C2—624no—
506C2—1242no—
507C2—1242no—
508C2C4×D4×D3111yescharacteristic
509C2C2×C4×D12411yescharacteristic
510C2#1452152111yescharacteristic
511C2D4×D12411yescharacteristic
512C2#1452168911yescharacteristic
513C2#1452169411yescharacteristic
514C2#1452172311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D31
commutatorC22×C31C23×C4
FittingC4×C22⋊C4×C31C2
socle, cosocleC23×C31C24
prime radicalC2×#11758459C2
hypercenterC4×C22⋊C4D31
hypocenterC31#2358
LCSG ▷ C22×C31 ▷ C31
UCSC1 ◁ C23 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×D124C2semidirect
3. C2×(C22⋊D31)⋊C4C2semidirect
4. C22×(C2×D31)⋊C4C2semidirect
5. C2×C22⋊C4×D31C2semidirect
6. #14520951C2semidirect
7. #14520941C2semidirect
8. #14520940C2semidirect
9. #14520928C2semidirect
10. #14520927C2semidirect
11. #14520927C2semidirect
12. #14520924C2semidirect
13. #14520923C2semidirect
14. C4×(C2×D31)⋊C4C2semidirect
15. C4×C22⋊C4×C31C2semidirect
24. C22×C4×D31C22semidirect
27. C2×C42×C31C22semidirect
28. C2×C42×C31C22semidirect
39. C2×(C2×D31)⋊C4C22semidirect
40. C2×(C2×D31)⋊C4C22semidirect
41. C2×(C2×D31)⋊C4C22semidirect
42. C2×C4⋊Dic31C22semidirect
43. C2×C4⋊Dic31C22semidirect
44. C2×Dic31⋊C4C22semidirect
45. C2×C4×Dic31C22semidirect
46. #11758459C4semidirect
50. C31×#95C22semidirect
51. C31×#95C22semidirect
52. C31⋊#95C22semidirect
53. C31⋊#95C22semidirect
54. C31⋊#95C22semidirect
55. C31⋊#95C22semidirect
63. C23×D31C2×C4semidirect
78. C2×C22⋊D31C2×C4semidirect
91. C2×D124C2×C4semidirect
92. C2×D124C2×C4semidirect
102. C22⋊C4×C31C2×C4semidirect
103. C22⋊C4×C31D4semidirect
115. (C2×D31)⋊C4C2×C4semidirect
116. (C2×D31)⋊C4C2×C4semidirect
117. (C2×D31)⋊C4D4semidirect
206. C22×C31C4×D4semidirect
235. C2×D31C4×D4semidirect
261. C4×C22⋊C4D31semidirect
305. C2×C42C2×D31semidirect
306. C2×C42C2×D31semidirect
311. #95C2×D31semidirect
312. #95C2×D31semidirect
313. C31#2358semidirect
375. C22⋊C4C4×D31semidirect
376. C22⋊C4D124semidirect
485. C22C4×D124semidirect

Maximal subgroups

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

subgroupindex
C2×#117584592
C2×C4×D1242
C2×(C22⋊D31)⋊C42
C22×(C2×D31)⋊C42
C2×C22⋊C4×D312
#145209512
#145209412
#145209402
#145209282
#145209272
#145209242
#145209232
C4×(C2×D31)⋊C42
C4×C22⋊C4×C312
#235831