Finite Group Databasebeta

← #16848558

Subgroups — #16848558

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
2C22×(C2×D31)⋊C4C211yesmaximal, characteristic
3C2×C22⋊C4×D31C211yesmaximal, characteristic
4#14520941C211yesmaximal, characteristic, complemented
5#14520941C211yesmaximal, characteristic, complemented
6#14520939C211yesmaximal, characteristic, complemented
7#14520939C211yesmaximal, characteristic, complemented
8#14520924C211yesmaximal, characteristic, complemented
9#14520911C211yesmaximal, characteristic, complemented
10#14520906C211yesmaximal, characteristic, complemented
11#14520904C211yesmaximal, characteristic
12C22⋊C4×Dic31C211yesmaximal, characteristic, complemented
13C4×C22⋊Dic31C211yesmaximal, characteristic, complemented
14#14520896C211yesmaximal, characteristic, complemented
15C31×#385C211yesmaximal, characteristic, complemented
16C24×D31C2211yescharacteristic
17C23×C4×C31C2211yescharacteristic
18C23×Dic31C2211yescharacteristic
19C22×C4×D31C2211yescharacteristic
20C22×C4×D31C2211yescharacteristic
21C2×C4⋊C4×C31C2211yescharacteristic, complemented
22C2×C4⋊C4×C31C2211yescharacteristic, complemented
23C2×C22⋊C4×C31C2211yescharacteristic
24C2×C22⋊C4×C31C2211yescharacteristic
25C2×C22⋊Dic31C2211yescharacteristic
26C2×C22⋊Dic31C2211yescharacteristic
27C2×(C2×D31)⋊C4—24no—
28C2×(C2×D31)⋊C4C2211yescharacteristic
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×(C2×D31)⋊C4C2211yescharacteristic
38C2×C4⋊Dic31C2211yescharacteristic, complemented
39C2×C4⋊Dic31C2211yescharacteristic, complemented
40C2×C4×Dic31C2211yescharacteristic, complemented
41C2×C4×Dic31C2211yescharacteristic, complemented
42C2×C4×Dic31C2211yescharacteristic, complemented
43C2×C4×Dic31C2211yescharacteristic, complemented
44#11758469—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×C31—22no—
65C22×C4×C31—22no—
66C22×C4×C31—41no—
67C22×C4×C31C2311yescharacteristic
68C22×C4×C31C2311yescharacteristic
69C22×C4×C31C2311yescharacteristic
70C22×C4×C31C2311yescharacteristic
71C22×C4×C31C2311yescharacteristic
72C22×C4×C31C2311yescharacteristic
73C22×Dic31—22no—
74C22×Dic31—22no—
75C22×Dic31—41no—
76C22×Dic31C2311yescharacteristic
77C22×Dic31C2311yescharacteristic
78C22×Dic31C2311yescharacteristic
79C22×Dic31C2311yescharacteristic
80C22×Dic31C2311yescharacteristic
81C22×Dic31C2311yescharacteristic
82C2×C4×D31—22no—
83C2×C4×D31—22no—
84C2×C4×D31—41no—
85C2×C4×D31—41no—
86C2×C4×D31C2×C414yescomplemented
87C2×C4×D31C2×C414yescomplemented
88C4⋊C4×C31—22no—
89C4⋊C4×C31—41no—
90C22⋊C4×C31—22no—
91C22⋊C4×C31C2×C414yes—
92C22⋊Dic31—22no—
93C22⋊Dic31C2×C414yes—
94(C2×D31)⋊C4—22no—
95(C2×D31)⋊C4—22no—
96(C2×D31)⋊C4—22no—
97(C2×D31)⋊C4—22no—
98(C2×D31)⋊C4—22no—
99(C2×D31)⋊C4—41no—
100(C2×D31)⋊C4—41no—
101(C2×D31)⋊C4C2×C414yescomplemented
102(C2×D31)⋊C4C2×C414yescomplemented
103(C2×D31)⋊C4D414yes—
104C4⋊Dic31—22no—
105C4⋊Dic31—41no—
106C4×Dic31—22no—
107C4×Dic31—22no—
108C4×Dic31—41no—
109C4×Dic31—41no—
110C23×C31—21no—
111C23×C31—21no—
112C23×C31—21no—
113C23×C31—21no—
114C23×C31C22×C412yes—
115C23×C31#4112yes—
116C23×C31#4112yes—
117C23×C31C2411yescharacteristic
118C22×D31—21no—
119C22×D31—21no—
120C22×D31—21no—
121C22×D31—21no—
122C22×D31—28no—
123C22×D31—21no—
124C22×D31—21no—
125C22×D31—21no—
126C22×D31—21no—
127C22×D31—21no—
128C22×D31—21no—
129C22×D31—28no—
130C22×D31—44no—
131C22×D31—44no—
132C22×D31—44no—
133C22×D31—44no—
134C22×D31—44no—
135C22×D31C22×C412yes—
136C22×D31C22×C412yes—
137C22×D31C2×D412yes—
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×C31—44no—
155C2×C4×C31C22×C412yes—
156C2×C4×C31C22×C412yes—
157C2×C4×C31C2×D412yes—
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×Dic31—21no—
173C2×Dic31—44no—
174C2×Dic31C22×C412yes—
175C2×Dic31C22×C412yes—
176C2×Dic31C2×D412yes—
177C4×D31—28no—
178C4×D31—44no—
179#2342—311nomaximal, Sylow
180C22×C31—22no—
181C22×C31—22no—
182C22×C31—22no—
183C22×C31—22no—
184C22×C31—22no—
185C22×C31—22no—
186C22×C31#11714yescomplemented
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—416no—
204C2×D31—41no—
205C2×D31—41no—
206C2×D31—41no—
207C2×D31—41no—
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#388—311no—
228#385—311no—
229#385D3111yescharacteristic, complemented
230#381—311no—
231#380—311no—
232#379—311no—
233C4×C22⋊C4—311no—
234C4×C22⋊C4—311no—
235C4×C22⋊C4—311no—
236C2×C31—24no—
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—42no—
246C25—311no—
247C23×C4—311no—
248C23×C4—311no—
249C23×C4—311no—
250C23×C4C2×D3111yescharacteristic
251#117—624no—
252C2×C4⋊C4—311no—
253C2×C4⋊C4—311no—
254C2×C4⋊C4C2×D3111yescharacteristic, complemented
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—311no—
269C2×C22⋊C4—624no—
270C2×C22⋊C4C2×D3111yescharacteristic
271C2×C22⋊C4C2×D3111yescharacteristic
272C2×C42—311no—
273C2×C42—311no—
274C2×C42—311no—
275C2×C42—311no—
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—22no—
296C22×C4—22no—
297C22×C4—41no—
298C22×C4—311no—
299C22×C4—311no—
300C22×C4—311no—
301C22×C4—314no—
302C22×C4—314no—
303C22×C4—311no—
304C22×C4—311no—
305C22×C4—311no—
306C22×C4—622no—
307C22×C4—622no—
308C22×C4—622no—
309C22×C4—622no—
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—41no—
321C4⋊C4—622no—
322C4⋊C4—1241no—
323C22⋊C4—22no—
324C22⋊C4—314no—
325C22⋊C4—314no—
326C22⋊C4—314no—
327C22⋊C4—314no—
328C22⋊C4—622no—
329C22⋊C4—622no—
330C22⋊C4—622no—
331C22⋊C4—622no—
332C22⋊C4—622no—
333C22⋊C4—622no—
334C22⋊C4—1241no—
335C22⋊C4—1241no—
336C22⋊C4C4×D3114yes—
337C42—622no—
338C42—622no—
339C42—1241no—
340C42—1241no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—21no—
345C23—312no—
346C23—312no—
347C23—312no—
348C23—312no—
349C23—628no—
350C23—621no—
351C23—621no—
352C23—621no—
353C23—621no—
354C23—628no—
355C23—621no—
356C23—621no—
357C23—621no—
358C23—621no—
359C23—621no—
360C23—621no—
361C23—1244no—
362C23—1244no—
363C23—1244no—
364C23—1244no—
365C23—1244no—
366C23C2×C4×D3112yes—
367C23#9249712yes—
368C23#9249912yes—
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—44no—
386C2×C4—312no—
387C2×C4—312no—
388C2×C4—312no—
389C2×C4—628no—
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—621no—
405C2×C4—1244no—
406C2×C4—1244no—
407C2×C4C2×C4×D3112yes—
408C2×C4C2×C4×D3112yes—
409C2×C4D4×D3112yes—
410C22—22no—
411C22—22no—
412C22—22no—
413C22—22no—
414C22—22no—
415C22—22no—
416C22—314no—
417C22—622no—
418C22—622no—
419C22—622no—
420C22—622no—
421C22—622no—
422C22—622no—
423C22—622no—
424C22—622no—
425C22—622no—
426C22—12416no—
427C22—1241no—
428C22—1241no—
429C22—1241no—
430C22—1241no—
431C22#1175846914yescomplemented
432C22C22×C4×D3111yescharacteristic
433C22C2×D4×D3111yescharacteristic
434C22C2×#9249711yescharacteristic
435C22#1175856111yescharacteristic
436C22C2×#9249911yescharacteristic
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—24no—
452C2—624no—
453C2—1242no—
454C2C2×#1175846911yescharacteristic
455C2C4×D4×D3111yescharacteristic
456C2#1452152111yescharacteristic
457C2#1452168611yescharacteristic
458C2#1452169011yescharacteristic
459C2#1452172211yescharacteristic
460C2#1452172611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D31
commutatorC22×C31C23×C4
FittingC31×#385C2
socle, cosocleC23×C31C24
prime radicalC24×D31C22
hypercenter#385D31
hypocenterC31#2342
LCSG ▷ C22×C31 ▷ C31
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
1. C2×#11758469C2semidirect
4. #14520941C2semidirect
5. #14520941C2semidirect
6. #14520939C2semidirect
7. #14520939C2semidirect
8. #14520924C2semidirect
9. #14520911C2semidirect
10. #14520906C2semidirect
12. C22⋊C4×Dic31C2semidirect
13. C4×C22⋊Dic31C2semidirect
14. #14520896C2semidirect
15. C31×#385C2semidirect
21. C2×C4⋊C4×C31C22semidirect
22. C2×C4⋊C4×C31C22semidirect
38. C2×C4⋊Dic31C22semidirect
39. C2×C4⋊Dic31C22semidirect
40. C2×C4×Dic31C22semidirect
41. C2×C4×Dic31C22semidirect
42. C2×C4×Dic31C22semidirect
43. 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
101. (C2×D31)⋊C4C2×C4semidirect
102. (C2×D31)⋊C4C2×C4semidirect
186. C22×C31#117semidirect
229. #385D31semidirect
254. C2×C4⋊C4C2×D31semidirect
255. C2×C4⋊C4C2×D31semidirect
282. #95C2×D31semidirect
283. #95C2×D31semidirect
284. C31#2342semidirect
431. C22#11758469semidirect

Maximal subgroups

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

subgroupindex
C2×#117584692
C22×(C2×D31)⋊C42
C2×C22⋊C4×D312
#145209412
#145209392
#145209242
#145209112
#145209062
#145209042
C22⋊C4×Dic312
C4×C22⋊Dic312
#145208962
C31×#3852
#234231