Finite Group Databasebeta

← #16848691

Subgroups — #16848691

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×D4×Dic31C211yesmaximal, characteristic, complemented
3C2×(C22⋊D31)⋊C4C211yesmaximal, characteristic, complemented
4C22×(C2×D31)⋊C4C211yesmaximal, characteristic, complemented
5C2×C22⋊C4×D31C211yesmaximal, characteristic, complemented
6#14520949C211yesmaximal, characteristic, complemented
7#14520941C211yesmaximal, characteristic, complemented
8#14520938C211yesmaximal, characteristic, complemented
9#14520926C211yesmaximal, characteristic, complemented
10#14520925C211yesmaximal, characteristic, complemented
11#14520923C211yesmaximal, characteristic, complemented
12#14520921C211yesmaximal, characteristic, complemented
13C4×C22⋊Dic31C211yesmaximal, characteristic, complemented
14#14520896C211yesmaximal, characteristic, complemented
15C31×#386C211yesmaximal, characteristic, complemented
16C24×D31C2211yescharacteristic
17C22×D4×C31C2211yescharacteristic
18C23×C4×C31C2211yescharacteristic
19C22×C22⋊D31C2211yescharacteristic
20C22×C22⋊D31C2211yescharacteristic
21C23×Dic31C2211yescharacteristic
22C23×Dic31C2211yescharacteristic, complemented
23C22×C4×D31C2211yescharacteristic
24C22×C4×D31C2211yescharacteristic
25C2×C22⋊C4×C31C2211yescharacteristic
26C2×C22⋊C4×C31C2211yescharacteristic, complemented
27C2×C22⋊C4×C31C2211yescharacteristic, complemented
28C2×C22⋊Dic31C2211yescharacteristic
29C2×C22⋊Dic31C2211yescharacteristic
30C2×C22⋊Dic31C2211yescharacteristic, complemented
31#11758514C418yescomplemented
32D4×Dic31—24no—
33C2×(C2×D31)⋊C4—24no—
34C2×(C2×D31)⋊C4C2211yescharacteristic
35C2×(C2×D31)⋊C4C2211yescharacteristic
36C2×(C2×D31)⋊C4C2211yescharacteristic
37C2×(C2×D31)⋊C4C2211yescharacteristic
38C2×(C2×D31)⋊C4C2211yescharacteristic
39C2×(C2×D31)⋊C4C2211yescharacteristic
40C2×(C2×D31)⋊C4C2211yescharacteristic
41C2×(C2×D31)⋊C4C2211yescharacteristic
42C2×C4⋊Dic31C2211yescharacteristic, complemented
43C2×Dic31⋊C4C2211yescharacteristic, complemented
44C2×Dic31⋊C4C2211yescharacteristic, complemented
45C2×C4×Dic31C2211yescharacteristic, complemented
46C2×C4×Dic31C2211yescharacteristic, complemented
47C2×C4×Dic31C2211yescharacteristic, complemented
48(C22⋊D31)⋊C4—24no—
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—41no—
73C22×C4×C31C2311yescharacteristic
74C22×C4×C31C2311yescharacteristic
75C22×C4×C31C2311yescharacteristic
76C22×C4×C31C2311yescharacteristic
77C22×C4×C31C2311yescharacteristic
78C2×C22⋊D31—22no—
79C2×C22⋊D31—22no—
80C2×C22⋊D31—41no—
81C2×C22⋊D31—41no—
82C2×C22⋊D31C2×C414yescomplemented
83C2×C22⋊D31C2×C414yescomplemented
84C22×Dic31—22no—
85C22×Dic31—22no—
86C22×Dic31—22no—
87C22×Dic31—22no—
88C22×Dic31—41no—
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—
102C22⋊C4×C31—22no—
103C22⋊C4×C31—22no—
104C22⋊C4×C31—41no—
105C22⋊Dic31—22no—
106C22⋊Dic31C2×C414yescomplemented
107C22⋊Dic31D414yescomplemented
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)⋊C4C2×C414yescomplemented
114(C2×D31)⋊C4C2×C414yescomplemented
115(C2×D31)⋊C4D414yescomplemented
116C4⋊Dic31—22no—
117Dic31⋊C4—22no—
118Dic31⋊C4—41no—
119C4×Dic31—22no—
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—21no—
171C2×C4×C31—21no—
172C2×C4×C31—44no—
173C2×C4×C31C22×C412yes—
174C2×C4×C31C2×D412yes—
175C22⋊D31—28no—
176C22⋊D31—44no—
177C2×Dic31—21no—
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—44no—
191C2×Dic31—44no—
192C2×Dic31C22×C412yes—
193C2×Dic31C22×C412yes—
194C2×Dic31C2×D412yes—
195C2×Dic31C2×D412yes—
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—41no—
239C4×C31—41no—
240C4×C31—41no—
241Dic31—22no—
242Dic31—22no—
243Dic31—22no—
244Dic31—22no—
245Dic31—22no—
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#386D3111yescharacteristic, complemented
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×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—624no—
300C2×C22⋊C4—624no—
301C2×C22⋊C4C2×D3111yescharacteristic
302C2×C22⋊C4C2×D3111yescharacteristic, complemented
303C2×C22⋊C4C2×D3111yescharacteristic, complemented
304C2×C42—311no—
305C2×C42—311no—
306C2×C42—311no—
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—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—41no—
337C22×C4—311no—
338C22×C4—311no—
339C22×C4—311no—
340C22×C4—311no—
341C22×C4—311no—
342C22×C4—311no—
343C22×C4—622no—
344C22×C4—622no—
345C22×C4—622no—
346C22×C4—622no—
347C22×C4—622no—
348C22×C4—622no—
349C22×C4—622no—
350C22×C4—622no—
351C22×C4—1241no—
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—622no—
361C4⋊C4—622no—
362C4⋊C4—1241no—
363C22⋊C4—22no—
364C22⋊C4—22no—
365C22⋊C4—41no—
366C22⋊C4—314no—
367C22⋊C4—314no—
368C22⋊C4—314no—
369C22⋊C4—314no—
370C22⋊C4—314no—
371C22⋊C4—622no—
372C22⋊C4—622no—
373C22⋊C4—622no—
374C22⋊C4—622no—
375C22⋊C4—622no—
376C22⋊C4—622no—
377C42—622no—
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—
413C23D4×D3112yes—
414C23#9249712yes—
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—21no—
431C2×C4—21no—
432C2×C4—44no—
433C2×C4—312no—
434C2×C4—312no—
435C2×C4—312no—
436C2×C4—312no—
437C2×C4—312no—
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—621no—
451C2×C4—1244no—
452C2×C4—1244no—
453C2×C4—1244no—
454C2×C4—1244no—
455C2×C4C2×C4×D3112yes—
456C2×C4D4×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—
485C22(C22⋊D31)⋊C414yescomplemented
486C22C22×C4×D3111yescharacteristic
487C22C2×D4×D3111yescharacteristic
488C22C2×D4×D3111yescharacteristic
489C22C2×#9249711yescharacteristic
490C22#1175856111yescharacteristic
491C22#41×D3111yescharacteristic
492C22#1175856611yescharacteristic
493C4—22no—
494C4—22no—
495C4—41no—
496C4—41no—
497C4—41no—
498C4—622no—
499C4—622no—
500C4—622no—
501C4—622no—
502C4—622no—
503C4—1241no—
504C2—24no—
505C2—42no—
506C2—624no—
507C2—1242no—
508C2C4×D4×D3111yescharacteristic
509C2C2×(C22⋊D31)⋊C411yescharacteristic
510C2#1452152111yescharacteristic
511C2#1452168311yescharacteristic
512C2#1452168611yescharacteristic
513C2#1452168811yescharacteristic
514C2#1452172211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D31
commutatorC22×C31C23×C4
FittingC31×#386C2
socle, cosocleC23×C31C24
prime radicalC2×#11758514C2
hypercenter#386D31
hypocenterC31#2358
LCSG ▷ C22×C31 ▷ C31
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
2. C2×D4×Dic31C2semidirect
3. C2×(C22⋊D31)⋊C4C2semidirect
4. C22×(C2×D31)⋊C4C2semidirect
5. C2×C22⋊C4×D31C2semidirect
6. #14520949C2semidirect
7. #14520941C2semidirect
8. #14520938C2semidirect
9. #14520926C2semidirect
10. #14520925C2semidirect
11. #14520923C2semidirect
12. #14520921C2semidirect
13. C4×C22⋊Dic31C2semidirect
14. #14520896C2semidirect
15. C31×#386C2semidirect
22. C23×Dic31C22semidirect
26. C2×C22⋊C4×C31C22semidirect
27. C2×C22⋊C4×C31C22semidirect
30. C2×C22⋊Dic31C22semidirect
31. #11758514C4semidirect
42. C2×C4⋊Dic31C22semidirect
43. C2×Dic31⋊C4C22semidirect
44. C2×Dic31⋊C4C22semidirect
45. C2×C4×Dic31C22semidirect
46. C2×C4×Dic31C22semidirect
47. 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
82. C2×C22⋊D31C2×C4semidirect
83. C2×C22⋊D31C2×C4semidirect
106. C22⋊Dic31C2×C4semidirect
107. C22⋊Dic31D4semidirect
113. (C2×D31)⋊C4C2×C4semidirect
114. (C2×D31)⋊C4C2×C4semidirect
115. (C2×D31)⋊C4D4semidirect
213. C22×C31C4×D4semidirect
235. C2×D31C4×D4semidirect
257. #386D31semidirect
302. C2×C22⋊C4C2×D31semidirect
303. C2×C22⋊C4C2×D31semidirect
311. #95C2×D31semidirect
312. #95C2×D31semidirect
313. C31#2358semidirect
333. C2×D4C4×D31semidirect
485. C22(C22⋊D31)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×#117585142
C2×D4×Dic312
C2×(C22⋊D31)⋊C42
C22×(C2×D31)⋊C42
C2×C22⋊C4×D312
#145209492
#145209412
#145209382
#145209262
#145209252
#145209232
#145209212
C4×C22⋊Dic312
#145208962
C31×#3862
#235831