Finite Group Databasebeta

← #16848559

Subgroups — #16848559

Order 3968.

792 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11758469C211yesmaximal, characteristic, complemented
2C2×C22⋊C4×D31C211yesmaximal, characteristic
3C2×C22⋊C4×D31C211yesmaximal, characteristic
4#14520943C211yesmaximal, characteristic, complemented
5#14520942C211yesmaximal, characteristic, complemented
6#14520937C211yesmaximal, characteristic, complemented
7#14520923C211yesmaximal, characteristic, complemented
8#14520920C211yesmaximal, characteristic, complemented
9#14520911C211yesmaximal, characteristic, complemented
10#14520908C211yesmaximal, characteristic, complemented
11#14520904C211yesmaximal, characteristic
12C4×(C2×D31)⋊C4C211yesmaximal, characteristic, complemented
13C4×(C2×D31)⋊C4C211yesmaximal, characteristic, complemented
14#14520896C211yesmaximal, characteristic, complemented
15C31×#388C211yesmaximal, characteristic, complemented
16C24×D31C2211yescharacteristic
17C22×C4×D31C2211yescharacteristic
18C22×C4×D31C2211yescharacteristic
19C22×C4×D31C2211yescharacteristic
20C22×C4×D31C2211yescharacteristic
21C2×C4⋊C4×C31C2211yescharacteristic, complemented
22C2×C22⋊C4×C31C2211yescharacteristic
23C2×C22⋊C4×C31C2211yescharacteristic
24C2×C22⋊C4×C31C2211yescharacteristic
25C2×C42×C31C2211yescharacteristic, complemented
26C2×C22⋊Dic31C2211yescharacteristic
27C2×C22⋊Dic31C2211yescharacteristic
28C2×C22⋊Dic31C2211yescharacteristic
29C2×(C2×D31)⋊C4C2211yescharacteristic
30C2×(C2×D31)⋊C4C2211yescharacteristic
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×C4⋊Dic31C2211yescharacteristic, complemented
38C2×Dic31⋊C4C2211yescharacteristic, complemented
39C2×Dic31⋊C4C2211yescharacteristic, complemented
40C2×C4×Dic31C2211yescharacteristic, complemented
41C2×C4×Dic31C2211yescharacteristic, complemented
42C2×C4×Dic31C2211yescharacteristic, complemented
43#11758469—24no—
44C22⋊C4×D31—24no—
45C22⋊C4×D31C418yescomplemented
46C31×#95C2211yescharacteristic, complemented
47C31×#95C2211yescharacteristic, complemented
48C31⋊#95C2211yescharacteristic, complemented
49C31⋊#95C2211yescharacteristic, complemented
50C31⋊#95C2211yescharacteristic, complemented
51C31⋊#95C2211yescharacteristic, complemented
52C31⋊#95C2211yescharacteristic, complemented
53C31⋊#95C2211yescharacteristic, complemented
54C24×C31C2311yescharacteristic
55C23×D31—22no—
56C23×D31—22no—
57C23×D31—22no—
58C23×D31—22no—
59C23×D31—41no—
60C23×D31—41no—
61C23×D31C2×C414yes—
62C23×D31C2311yescharacteristic
63C23×D31C2311yescharacteristic
64C22×C4×C31C2311yescharacteristic
65C22×C4×C31C2311yescharacteristic
66C22×C4×C31C2311yescharacteristic
67C22×C4×C31C2311yescharacteristic
68C22×C4×C31C2311yescharacteristic
69C22×C4×C31C2311yescharacteristic
70C22×Dic31C2311yescharacteristic
71C22×Dic31C2311yescharacteristic
72C22×Dic31C2311yescharacteristic
73C22×Dic31C2311yescharacteristic
74C22×Dic31C2311yescharacteristic
75C22×Dic31C2311yescharacteristic
76C2×C4×D31—22no—
77C2×C4×D31—22no—
78C2×C4×D31—22no—
79C2×C4×D31—22no—
80C2×C4×D31—22no—
81C2×C4×D31—22no—
82C2×C4×D31—41no—
83C2×C4×D31—41no—
84C2×C4×D31—41no—
85C2×C4×D31—41no—
86C2×C4×D31C2×C414yescomplemented
87C2×C4×D31C2×C414yescomplemented
88C4⋊C4×C31—22no—
89C22⋊C4×C31—22no—
90C22⋊C4×C31—41no—
91C22⋊C4×C31C2×C414yescomplemented
92C42×C31—41no—
93C22⋊Dic31—22no—
94C22⋊Dic31—41no—
95C22⋊Dic31C2×C414yescomplemented
96(C2×D31)⋊C4—22no—
97(C2×D31)⋊C4—22no—
98(C2×D31)⋊C4—22no—
99(C2×D31)⋊C4—22no—
100(C2×D31)⋊C4—22no—
101(C2×D31)⋊C4C2×C414yes—
102(C2×D31)⋊C4C2×C414yes—
103(C2×D31)⋊C4D414yes—
104C4⋊Dic31—22no—
105Dic31⋊C4—41no—
106Dic31⋊C4—41no—
107C4×Dic31—22no—
108C4×Dic31—22no—
109C4×Dic31—41no—
110C23×C31—21no—
111C23×C31—21no—
112C23×C31—21no—
113C23×C31—21no—
114C23×C31—21no—
115C23×C31—21no—
116C23×C31C22×C412yes—
117C23×C31C2411yescharacteristic
118C22×D31—21no—
119C22×D31—21no—
120C22×D31—21no—
121C22×D31—21no—
122C22×D31—21no—
123C22×D31—21no—
124C22×D31—21no—
125C22×D31—21no—
126C22×D31—28no—
127C22×D31—28no—
128C22×D31—44no—
129C22×D31—44no—
130C22×D31—44no—
131C22×D31—44no—
132C22×D31—44no—
133C22×D31C22×C412yes—
134C22×D31C22×C412yes—
135C22×D31C2×D412yes—
136C22×D31#4112yes—
137C22×D31#4112yes—
138C22×D31#4112yes—
139C2×C4×C31—21no—
140C2×C4×C31—21no—
141C2×C4×C31—21no—
142C2×C4×C31—21no—
143C2×C4×C31—21no—
144C2×C4×C31—21no—
145C2×C4×C31—21no—
146C2×C4×C31—21no—
147C2×C4×C31—21no—
148C2×C4×C31—21no—
149C2×C4×C31—21no—
150C2×C4×C31—21no—
151C2×C4×C31—21no—
152C2×C4×C31—21no—
153C2×C4×C31—21no—
154C2×C4×C31C22×C412yes—
155C2×C4×C31C22×C412yes—
156C2×C4×C31C2×D412yes—
157C2×Dic31—21no—
158C2×Dic31—21no—
159C2×Dic31—21no—
160C2×Dic31—21no—
161C2×Dic31—21no—
162C2×Dic31—21no—
163C2×Dic31—21no—
164C2×Dic31—21no—
165C2×Dic31—21no—
166C2×Dic31—21no—
167C2×Dic31—21no—
168C2×Dic31—21no—
169C2×Dic31—21no—
170C2×Dic31—21no—
171C2×Dic31—21no—
172C2×Dic31C22×C412yes—
173C2×Dic31C22×C412yes—
174C2×Dic31C2×D412yes—
175C4×D31—28no—
176C4×D31—44no—
177C4×D31—44no—
178C4×D31—44no—
179#2342—311nomaximal, Sylow
180C22×C31—22no—
181C22×C31—22no—
182C22×C31—22no—
183C22×C31—41no—
184C22×C31—41no—
185C22×C31—41no—
186C22×C31—41no—
187C22×C31C23×C411yescharacteristic
188C22×C31C22×D411yescharacteristic
189C22×C31C2×#4111yescharacteristic
190C22×C31C2×#4111yescharacteristic
191C22×C31C2×#4111yescharacteristic
192C22×C31H(5,𝔽2)11yescharacteristic
193C22×C31H(5,𝔽2)11yescharacteristic
194C2×D31—22no—
195C2×D31—22no—
196C2×D31—22no—
197C2×D31—22no—
198C2×D31—22no—
199C2×D31—22no—
200C2×D31—22no—
201C2×D31—22no—
202C2×D31—22no—
203C2×D31—22no—
204C2×D31—22no—
205C2×D31—22no—
206C2×D31—416no—
207C2×D31#11714yescomplemented
208C2×D31C4×D414yes—
209C4×C31—22no—
210C4×C31—22no—
211C4×C31—22no—
212C4×C31—41no—
213C4×C31—41no—
214C4×C31—41no—
215Dic31—22no—
216Dic31—22no—
217Dic31—22no—
218Dic31—41no—
219Dic31—41no—
220Dic31—41no—
221C2×#117—311no—
222C22×C22⋊C4—311no—
223C22×C22⋊C4—311no—
224#388—311no—
225#388—311no—
226#388—311no—
227#388D3111yescharacteristic, complemented
228#385—311no—
229#385—311no—
230#381—311no—
231#380—311no—
232#379—311no—
233C4×C22⋊C4—311no—
234C4×C22⋊C4—311no—
235C4×C22⋊C4—311no—
236C2×C31—42no—
237C2×C31C2×#11711yescharacteristic
238C2×C31C2×C4×D411yescharacteristic
239C2×C31#51811yescharacteristic
240C2×C31#54611yescharacteristic
241C2×C31#54611yescharacteristic
242C2×C31#55111yescharacteristic
243C2×C31#55111yescharacteristic
244D31—24no—
245D31—24no—
246C25—311no—
247C23×C4—311no—
248C23×C4—311no—
249C23×C4—311no—
250C23×C4—311no—
251#117—624no—
252C2×C4⋊C4—311no—
253C2×C4⋊C4—311no—
254C2×C4⋊C4—311no—
255C2×C4⋊C4C2×D3111yescharacteristic, complemented
256C2×C22⋊C4—311no—
257C2×C22⋊C4—311no—
258C2×C22⋊C4—311no—
259C2×C22⋊C4—311no—
260C2×C22⋊C4—318no—
261C2×C22⋊C4—311no—
262C2×C22⋊C4—311no—
263C2×C22⋊C4—311no—
264C2×C22⋊C4—311no—
265C2×C22⋊C4—311no—
266C2×C22⋊C4—311no—
267C2×C22⋊C4—311no—
268C2×C22⋊C4—624no—
269C2×C22⋊C4C2×D3111yescharacteristic
270C2×C22⋊C4C2×D3111yescharacteristic
271C2×C22⋊C4C2×D3111yescharacteristic
272C2×C42—311no—
273C2×C42—311no—
274C2×C42—311no—
275C2×C42C2×D3111yescharacteristic, complemented
276#95—311no—
277#95—311no—
278#95—311no—
279#95—311no—
280#95—311no—
281#95—311no—
282#95C2×D3111yescharacteristic, complemented
283#95C2×D3111yescharacteristic, complemented
284C31#234211yescharacteristic, complemented, Sylow
285C24—311no—
286C24—311no—
287C24—314no—
288C24—622no—
289C24—622no—
290C24—622no—
291C24—622no—
292C24—1241no—
293C24—1241no—
294C24C22×D3111yescharacteristic
295C22×C4—311no—
296C22×C4—311no—
297C22×C4—311no—
298C22×C4—314no—
299C22×C4—314no—
300C22×C4—311no—
301C22×C4—311no—
302C22×C4—311no—
303C22×C4—622no—
304C22×C4—622no—
305C22×C4—622no—
306C22×C4—622no—
307C22×C4—622no—
308C22×C4—622no—
309C22×C4—1241no—
310C22×C4—1241no—
311C22×C4—1241no—
312C22×C4—1241no—
313C22×C4C22×D3111yescharacteristic
314C22×C4C22×D3111yescharacteristic
315C22×C4C22×D3111yescharacteristic
316C22×C4C22×D3111yescharacteristic
317C22×C4C22×D3111yescharacteristic
318C22×C4C22×D3111yescharacteristic
319C4⋊C4—22no—
320C4⋊C4—622no—
321C4⋊C4—1241no—
322C4⋊C4—1241no—
323C22⋊C4—22no—
324C22⋊C4—41no—
325C22⋊C4—314no—
326C22⋊C4—314no—
327C22⋊C4—314no—
328C22⋊C4—314no—
329C22⋊C4—622no—
330C22⋊C4—622no—
331C22⋊C4—622no—
332C22⋊C4—622no—
333C22⋊C4—622no—
334C22⋊C4—622no—
335C22⋊C4—1241no—
336C22⋊C4C4×D3114yescomplemented
337C42—41no—
338C42—622no—
339C42—622no—
340C42—1241no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—21no—
345C23—21no—
346C23—21no—
347C23—312no—
348C23—312no—
349C23—312no—
350C23—312no—
351C23—312no—
352C23—312no—
353C23—628no—
354C23—628no—
355C23—621no—
356C23—621no—
357C23—621no—
358C23—621no—
359C23—621no—
360C23—621no—
361C23—621no—
362C23—621no—
363C23—1244no—
364C23—1244no—
365C23—1244no—
366C23—1244no—
367C23—1244no—
368C23C2×C4×D3112yes—
369C23C23×D3111yescharacteristic
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—312no—
386C2×C4—312no—
387C2×C4—312no—
388C2×C4—628no—
389C2×C4—621no—
390C2×C4—621no—
391C2×C4—621no—
392C2×C4—621no—
393C2×C4—621no—
394C2×C4—621no—
395C2×C4—621no—
396C2×C4—621no—
397C2×C4—621no—
398C2×C4—621no—
399C2×C4—621no—
400C2×C4—621no—
401C2×C4—621no—
402C2×C4—621no—
403C2×C4—621no—
404C2×C4—1244no—
405C2×C4—1244no—
406C2×C4—1244no—
407C2×C4C2×C4×D3112yes—
408C2×C4C2×C4×D3112yes—
409C2×C4D4×D3112yes—
410C22—22no—
411C22—22no—
412C22—22no—
413C22—41no—
414C22—41no—
415C22—41no—
416C22—41no—
417C22—314no—
418C22—314no—
419C22—622no—
420C22—622no—
421C22—622no—
422C22—622no—
423C22—622no—
424C22—622no—
425C22—622no—
426C22—622no—
427C22—622no—
428C22—622no—
429C22—622no—
430C22—622no—
431C22—12416no—
432C22C22×C4×D3111yescharacteristic
433C22C2×D4×D3111yescharacteristic
434C22#1175856111yescharacteristic
435C22#41×D3111yescharacteristic
436C22#41×D3111yescharacteristic
437C22#41×D3111yescharacteristic
438C22#1175856611yescharacteristic
439C4—22no—
440C4—22no—
441C4—22no—
442C4—41no—
443C4—41no—
444C4—41no—
445C4—622no—
446C4—622no—
447C4—622no—
448C4—1241no—
449C4—1241no—
450C4—1241no—
451C2—42no—
452C2—624no—
453C2—624no—
454C2#117×D3111yescharacteristic
455C2C4×D4×D3111yescharacteristic
456C2#1452152111yescharacteristic
457C2#1452168811yescharacteristic
458C2#1452169211yescharacteristic
459C2#1452172411yescharacteristic
460C2#1452172711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D31
commutatorC22×C31C23×C4
FittingC31×#388C2
socle, cosocleC23×C31C24
prime radicalC24×D31C22
hypercenter#388D31
hypocenterC31#2342
LCSG ▷ C22×C31 ▷ C31
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. C2×#11758469C2semidirect
4. #14520943C2semidirect
5. #14520942C2semidirect
6. #14520937C2semidirect
7. #14520923C2semidirect
8. #14520920C2semidirect
9. #14520911C2semidirect
10. #14520908C2semidirect
12. C4×(C2×D31)⋊C4C2semidirect
13. C4×(C2×D31)⋊C4C2semidirect
14. #14520896C2semidirect
15. C31×#388C2semidirect
21. C2×C4⋊C4×C31C22semidirect
25. C2×C42×C31C22semidirect
37. C2×C4⋊Dic31C22semidirect
38. C2×Dic31⋊C4C22semidirect
39. C2×Dic31⋊C4C22semidirect
40. C2×C4×Dic31C22semidirect
41. C2×C4×Dic31C22semidirect
42. C2×C4×Dic31C22semidirect
45. C22⋊C4×D31C4semidirect
46. C31×#95C22semidirect
47. C31×#95C22semidirect
48. C31⋊#95C22semidirect
49. C31⋊#95C22semidirect
50. C31⋊#95C22semidirect
51. C31⋊#95C22semidirect
52. C31⋊#95C22semidirect
53. C31⋊#95C22semidirect
86. C2×C4×D31C2×C4semidirect
87. C2×C4×D31C2×C4semidirect
91. C22⋊C4×C31C2×C4semidirect
95. C22⋊Dic31C2×C4semidirect
207. C2×D31#117semidirect
227. #388D31semidirect
255. C2×C4⋊C4C2×D31semidirect
275. C2×C42C2×D31semidirect
282. #95C2×D31semidirect
283. #95C2×D31semidirect
284. C31#2342semidirect
336. C22⋊C4C4×D31semidirect

Maximal subgroups

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

subgroupindex
C2×#117584692
C2×C22⋊C4×D312
#145209432
#145209422
#145209372
#145209232
#145209202
#145209112
#145209082
#145209042
C4×(C2×D31)⋊C42
#145208962
C31×#3882
#234231