Finite Group Databasebeta

← #16848690

Subgroups — #16848690

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×#11758530C211yesmaximal, characteristic
2C2×C4×C22⋊D31C211yesmaximal, characteristic, complemented
3C2×(C22⋊D31)⋊C4C211yesmaximal, characteristic, complemented
4C22×C22⋊Dic31C211yesmaximal, characteristic, complemented
5#14520949C211yesmaximal, characteristic, complemented
6#14520943C211yesmaximal, characteristic, complemented
7#14520937C211yesmaximal, characteristic, complemented
8#14520928C211yesmaximal, characteristic, complemented
9#14520926C211yesmaximal, characteristic, complemented
10#14520925C211yesmaximal, characteristic, complemented
11#14520922C211yesmaximal, characteristic, complemented
12#14520921C211yesmaximal, characteristic, complemented
13C22⋊C4×Dic31C211yesmaximal, characteristic, complemented
14C4×C22⋊Dic31C211yesmaximal, characteristic, complemented
15C22×C22⋊C4×C31C211yesmaximal, characteristic, complemented
16C25×C31C2211yescharacteristic
17C23×C4×C31C2211yescharacteristic
18C23×C4×C31C2211yescharacteristic
19C22×C22⋊D31C2211yescharacteristic
20C22×C22⋊D31C2211yescharacteristic
21C22×C22⋊D31C2211yescharacteristic
22C23×Dic31C2211yescharacteristic
23C23×Dic31C2211yescharacteristic
24C22×C4×D31C2211yescharacteristic, complemented
25C2×C22⋊C4×C31—24no—
26C2×C22⋊C4×C31C2211yescharacteristic
27C2×C22⋊C4×C31C2211yescharacteristic
28C2×C22⋊C4×C31C2211yescharacteristic
29C2×C22⋊C4×C31C2211yescharacteristic
30#11758530C418yescomplemented
31C2×C22⋊Dic31—24no—
32C2×C22⋊Dic31C2211yescharacteristic
33C2×C22⋊Dic31C2211yescharacteristic
34C2×C22⋊Dic31C2211yescharacteristic
35C2×C22⋊Dic31C2211yescharacteristic
36C2×C22⋊Dic31C2211yescharacteristic
37C2×C22⋊Dic31C2211yescharacteristic
38C2×C22⋊Dic31C2211yescharacteristic
39C4×C22⋊D31—24no—
40C2×(C2×D31)⋊C4C2211yescharacteristic, complemented
41C2×(C2×D31)⋊C4C2211yescharacteristic, complemented
42C2×(C2×D31)⋊C4C2211yescharacteristic, complemented
43C2×Dic31⋊C4C2211yescharacteristic, complemented
44C2×Dic31⋊C4C2211yescharacteristic, complemented
45C2×Dic31⋊C4C2211yescharacteristic, complemented
46C2×C4×Dic31C2211yescharacteristic, complemented
47C2×C4×Dic31C2211yescharacteristic, complemented
48C2×C4×Dic31C2211yescharacteristic, complemented
49(C22⋊D31)⋊C4—24no—
50C31⋊#95C2211yescharacteristic, complemented
51C31⋊#95C2211yescharacteristic, complemented
52C31⋊#95C2211yescharacteristic, complemented
53C31⋊#95C2211yescharacteristic, complemented
54C31⋊#95C2211yescharacteristic, complemented
55C31⋊#95C2211yescharacteristic, complemented
56C24×C31—22no—
57C24×C31—22no—
58C24×C31—22no—
59C24×C31—22no—
60C24×C31—41no—
61C24×C31—41no—
62C24×C31C2×C414yescomplemented
63C24×C31C2311yescharacteristic
64C24×C31C2311yescharacteristic
65C24×C31C2311yescharacteristic
66C23×D31C2311yescharacteristic
67C22×C4×C31—22no—
68C22×C4×C31—22no—
69C22×C4×C31—22no—
70C22×C4×C31—22no—
71C22×C4×C31—41no—
72C22×C4×C31—41no—
73C22×C4×C31C2311yescharacteristic
74C22×C4×C31C2311yescharacteristic
75C22×C4×C31C2311yescharacteristic
76C22×C4×C31C2311yescharacteristic
77C2×C22⋊D31—22no—
78C2×C22⋊D31—22no—
79C2×C22⋊D31—22no—
80C2×C22⋊D31—22no—
81C2×C22⋊D31—41no—
82C2×C22⋊D31—41no—
83C2×C22⋊D31C2×C414yescomplemented
84C2×C22⋊D31C2×C414yescomplemented
85C2×C22⋊D31C2×C414yescomplemented
86C22×Dic31—22no—
87C22×Dic31—22no—
88C22×Dic31—22no—
89C22×Dic31—22no—
90C22×Dic31—41no—
91C22×Dic31—41no—
92C22×Dic31C2311yescharacteristic
93C22×Dic31C2311yescharacteristic
94C22×Dic31C2311yescharacteristic
95C22×Dic31C2311yescharacteristic
96C22×Dic31C2311yescharacteristic
97C22×Dic31C2311yescharacteristic
98C22×Dic31C2311yescharacteristic
99C2×C4×D31—22no—
100C2×C4×D31—22no—
101C2×C4×D31—41no—
102C22⋊C4×C31—22no—
103C22⋊C4×C31—22no—
104C22⋊C4×C31—22no—
105C22⋊C4×C31D414yescomplemented
106C22⋊Dic31—22no—
107C22⋊Dic31—22no—
108C22⋊Dic31—22no—
109C22⋊Dic31C2×C414yescomplemented
110C22⋊Dic31C2×C414yescomplemented
111C22⋊Dic31C2×C414yescomplemented
112C22⋊Dic31D414yescomplemented
113(C2×D31)⋊C4—22no—
114(C2×D31)⋊C4—22no—
115(C2×D31)⋊C4—41no—
116Dic31⋊C4—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—28no—
131C23×C31—28no—
132C23×C31—21no—
133C23×C31—21no—
134C23×C31—21no—
135C23×C31—21no—
136C23×C31—21no—
137C23×C31—21no—
138C23×C31—44no—
139C23×C31—44no—
140C23×C31—44no—
141C23×C31—44no—
142C23×C31—44no—
143C23×C31C22×C412yes—
144C23×C31C22×C412yes—
145C23×C31C22×C412yes—
146C23×C31C2×D412yes—
147C23×C31C2×D412yes—
148C23×C31#4112yes—
149C23×C31#4112yes—
150C23×C31C2411yescharacteristic
151C22×D31—21no—
152C22×D31—21no—
153C22×D31—21no—
154C22×D31—21no—
155C22×D31—21no—
156C22×D31—21no—
157C22×D31C22×C412yes—
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—44no—
169C2×C4×C31—44no—
170C2×C4×C31C2×D412yes—
171C2×C4×C31C2×D412yes—
172C22⋊D31—28no—
173C22⋊D31—28no—
174C22⋊D31—44no—
175C2×Dic31—21no—
176C2×Dic31—21no—
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—21no—
191C2×Dic31—44no—
192C2×Dic31—44no—
193C2×Dic31C22×C412yes—
194C2×Dic31C22×C412yes—
195C2×Dic31C22×C412yes—
196C2×Dic31C2×D412yes—
197C2×Dic31C2×D412yes—
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—22no—
210C22×C31—22no—
211C22×C31—22no—
212C22×C31—22no—
213C22×C31—22no—
214C22×C31—22no—
215C22×C31—416no—
216C22×C31—41no—
217C22×C31—41no—
218C22×C31—41no—
219C22×C31—41no—
220C22×C31C4×D414yescomplemented
221C22×C31C4×D414yescomplemented
222C22×C31C23×C411yescharacteristic
223C22×C31C22×D411yescharacteristic
224C22×C31C22×D411yescharacteristic
225C22×C31C2×#4111yescharacteristic
226C22×C31C2×#4111yescharacteristic
227C22×C31H(5,𝔽2)11yescharacteristic
228C22×C31H(5,𝔽2)11yescharacteristic
229C2×D31—22no—
230C2×D31—22no—
231C2×D31—22no—
232C2×D31—41no—
233C2×D31—41no—
234C2×D31—41no—
235C2×D31—41no—
236C4×C31—22no—
237C4×C31—22no—
238C4×C31—41no—
239C4×C31—41no—
240Dic31—22no—
241Dic31—22no—
242Dic31—22no—
243Dic31—22no—
244Dic31—22no—
245Dic31—41no—
246Dic31—41no—
247C2×#120—311no—
248C2×C4×D4—311no—
249C2×C4×D4—311no—
250C22×C22⋊C4—311no—
251C22×C22⋊C4D3111yescharacteristic, complemented
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—24no—
264C2×C31—42no—
265C2×C31C2×C4×D411yescharacteristic
266C2×C31C2×C4×D411yescharacteristic
267C2×C31#51811yescharacteristic
268C2×C31D4211yescharacteristic
269C2×C31#54611yescharacteristic
270C2×C31#54611yescharacteristic
271C2×C31#55111yescharacteristic
272D31—42no—
273C25C2×D3111yescharacteristic
274C22×D4—311no—
275C22×D4—311no—
276C22×D4—311no—
277C23×C4—311no—
278C23×C4—311no—
279C23×C4—311no—
280C23×C4C2×D3111yescharacteristic
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—24no—
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⋊C4C2×D3111yescharacteristic
301C2×C22⋊C4C2×D3111yescharacteristic
302C2×C22⋊C4C2×D3111yescharacteristic
303C2×C22⋊C4C2×D3111yescharacteristic
304C2×C42—311no—
305C2×C42—311no—
306C2×C42—311no—
307#95—311no—
308#95—311no—
309#95—311no—
310#95—311no—
311#95—311no—
312#95—311no—
313C31#235811yescharacteristic, complemented, Sylow
314C24—22no—
315C24—22no—
316C24—22no—
317C24—22no—
318C24—41no—
319C24—41no—
320C24—311no—
321C24C4×D3114yescomplemented
322C24C22×D3111yescharacteristic
323C24C22×D3111yescharacteristic
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—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—311no—
347C22×C4—622no—
348C22×C4—622no—
349C22×C4—622no—
350C22×C4—622no—
351C22×C4—622no—
352C22×C4—622no—
353C22×C4—1241no—
354C22×C4—1241no—
355C22×C4—1241no—
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—22no—
366C22⋊C4—314no—
367C22⋊C4—314no—
368C22⋊C4—314no—
369C22⋊C4—314no—
370C22⋊C4—622no—
371C22⋊C4—622no—
372C22⋊C4—622no—
373C22⋊C4—622no—
374C22⋊C4—622no—
375C22⋊C4—1241no—
376C22⋊C4C22⋊D3114yescomplemented
377C42—622no—
378C42—622no—
379C42—1241no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—21no—
385C23—21no—
386C23—21no—
387C23—21no—
388C23—28no—
389C23—28no—
390C23—21no—
391C23—21no—
392C23—21no—
393C23—21no—
394C23—21no—
395C23—21no—
396C23—44no—
397C23—44no—
398C23—44no—
399C23—44no—
400C23—44no—
401C23—312no—
402C23—621no—
403C23—621no—
404C23—621no—
405C23—621no—
406C23—621no—
407C23—621no—
408C23C2×C4×D3112yes—
409C23C2×C4×D3112yes—
410C23C2×C4×D3112yes—
411C23#9249512yes—
412C23D4×D3112yes—
413C23#9249712yes—
414C23C2×C22⋊D3112yes—
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—44no—
430C2×C4—44no—
431C2×C4—312no—
432C2×C4—312no—
433C2×C4—312no—
434C2×C4—312no—
435C2×C4—312no—
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—621no—
451C2×C4—621no—
452C2×C4—1244no—
453C2×C4—1244no—
454C2×C4—1244no—
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—22no—
467C22—22no—
468C22—22no—
469C22—22no—
470C22—22no—
471C22—22no—
472C22—416no—
473C22—41no—
474C22—41no—
475C22—41no—
476C22—41no—
477C22—622no—
478C22—622no—
479C22—622no—
480C22—1241no—
481C22—1241no—
482C22—1241no—
483C22—1241no—
484C22(C22⋊D31)⋊C414yescomplemented
485C22C4×C22⋊D3114yescomplemented
486C22C22×C4×D3111yescharacteristic
487C22C2×#9249511yescharacteristic
488C22C2×D4×D3111yescharacteristic
489C22C2×#9249711yescharacteristic
490C22#1175856111yescharacteristic
491C22#1175856111yescharacteristic
492C22C22×C22⋊D3111yescharacteristic
493C4—22no—
494C4—22no—
495C4—41no—
496C4—41no—
497C4—622no—
498C4—622no—
499C4—622no—
500C4—622no—
501C4—622no—
502C4—1241no—
503C4—1241no—
504C2—24no—
505C2—24no—
506C2—42no—
507C2—1242no—
508C2C2×(C22⋊D31)⋊C411yescharacteristic
509C2C2×C4×C22⋊D3111yescharacteristic
510C2#1452152211yescharacteristic
511C2D4×C22⋊D3111yescharacteristic
512C2#1452168911yescharacteristic
513C2#1452169311yescharacteristic
514C2#1452172511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D31
commutatorC22×C31C23×C4
FittingC22×C22⋊C4×C31C2
socle, cosocleC23×C31C24
prime radicalC2×#11758530C2
hypercenterC22×C22⋊C4D31
hypocenterC31#2358
LCSG ▷ C22×C31 ▷ C31
UCSC1 ◁ C23 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×C22⋊D31C2semidirect
3. C2×(C22⋊D31)⋊C4C2semidirect
4. C22×C22⋊Dic31C2semidirect
5. #14520949C2semidirect
6. #14520943C2semidirect
7. #14520937C2semidirect
8. #14520928C2semidirect
9. #14520926C2semidirect
10. #14520925C2semidirect
11. #14520922C2semidirect
12. #14520921C2semidirect
13. C22⋊C4×Dic31C2semidirect
14. C4×C22⋊Dic31C2semidirect
15. C22×C22⋊C4×C31C2semidirect
24. C22×C4×D31C22semidirect
30. #11758530C4semidirect
40. C2×(C2×D31)⋊C4C22semidirect
41. C2×(C2×D31)⋊C4C22semidirect
42. C2×(C2×D31)⋊C4C22semidirect
43. C2×Dic31⋊C4C22semidirect
44. C2×Dic31⋊C4C22semidirect
45. C2×Dic31⋊C4C22semidirect
46. C2×C4×Dic31C22semidirect
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
62. C24×C31C2×C4semidirect
83. C2×C22⋊D31C2×C4semidirect
84. C2×C22⋊D31C2×C4semidirect
85. C2×C22⋊D31C2×C4semidirect
105. C22⋊C4×C31D4semidirect
109. C22⋊Dic31C2×C4semidirect
110. C22⋊Dic31C2×C4semidirect
111. C22⋊Dic31C2×C4semidirect
112. C22⋊Dic31D4semidirect
220. C22×C31C4×D4semidirect
221. C22×C31C4×D4semidirect
251. C22×C22⋊C4D31semidirect
313. C31#2358semidirect
321. C24C4×D31semidirect
376. C22⋊C4C22⋊D31semidirect
484. C22(C22⋊D31)⋊C4semidirect
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×#117585302
C2×C4×C22⋊D312
C2×(C22⋊D31)⋊C42
C22×C22⋊Dic312
#145209492
#145209432
#145209372
#145209282
#145209262
#145209252
#145209222
#145209212
C22⋊C4×Dic312
C4×C22⋊Dic312
C22×C22⋊C4×C312
#235831