Finite Group Databasebeta

← #16848370

Subgroups — #16848370

Order 3968.

808 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11758514C211yesmaximal, characteristic
2C2×(C22⋊D31)⋊C4C211yesmaximal, characteristic, complemented
3C2×C22⋊C4×D31C211yesmaximal, characteristic, complemented
4#14520949C211yesmaximal, characteristic, complemented
5#14520943C211yesmaximal, characteristic, complemented
6#14520943C211yesmaximal, characteristic, complemented
7#14520940C211yesmaximal, characteristic, complemented
8#14520939C211yesmaximal, characteristic, complemented
9#14520929C211yesmaximal, characteristic, complemented
10#14520926C211yesmaximal, characteristic, complemented
11#14520925C211yesmaximal, characteristic, complemented
12#14520920C211yesmaximal, characteristic, complemented
13#14520904C211yesmaximal, characteristic, complemented
14C4×(C2×D31)⋊C4C211yesmaximal, characteristic, complemented
15C31×#390C211yesmaximal, characteristic, complemented
16C24×D31C2211yescharacteristic
17C22×D4×C31C2211yescharacteristic
18C22×C22⋊D31C2211yescharacteristic
19C22×C22⋊D31C2211yescharacteristic
20C23×Dic31C2211yescharacteristic, complemented
21C22×C4×D31C2211yescharacteristic
22C22×C4×D31C2211yescharacteristic
23C2×C4⋊C4×C31C2211yescharacteristic, complemented
24C2×C22⋊C4×C31C2211yescharacteristic
25C2×C22⋊C4×C31C2211yescharacteristic
26C2×C22⋊C4×C31C2211yescharacteristic, complemented
27C2×C22⋊C4×C31C2211yescharacteristic, complemented
28C2×C42×C31C2211yescharacteristic, complemented
29C2×C22⋊Dic31C2211yescharacteristic
30C2×C22⋊Dic31C2211yescharacteristic
31C2×C22⋊Dic31C2211yescharacteristic
32C2×C22⋊Dic31C2211yescharacteristic, complemented
33#11758514C418yescomplemented
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×Dic31⋊C4C2211yescharacteristic, complemented
43C2×Dic31⋊C4C2211yescharacteristic, complemented
44C2×C4×Dic31C2211yescharacteristic, complemented
45C2×C4×Dic31C2211yescharacteristic, complemented
46(C22⋊D31)⋊C4—24no—
47C22⋊C4×D31—24no—
48C31⋊#95C2211yescharacteristic, complemented
49C31⋊#95C2211yescharacteristic, complemented
50C31⋊#95C2211yescharacteristic, complemented
51C31⋊#95C2211yescharacteristic, complemented
52C31⋊#95C2211yescharacteristic, complemented
53C31⋊#95C2211yescharacteristic, complemented
54C24×C31C2311yescharacteristic
55C24×C31C2311yescharacteristic
56C23×D31—22no—
57C23×D31—22no—
58C23×D31—41no—
59C23×D31—41no—
60C23×D31—41no—
61C23×D31—41no—
62C23×D31C2×C414yescomplemented
63C23×D31C2311yescharacteristic
64C23×D31C2311yescharacteristic
65C2×D4×C31—41no—
66C2×D4×C31—41no—
67C2×D4×C31C2×C414yescomplemented
68C22×C4×C31C2311yescharacteristic
69C22×C4×C31C2311yescharacteristic
70C22×C4×C31C2311yescharacteristic
71C22×C4×C31C2311yescharacteristic
72C22×C4×C31C2311yescharacteristic
73C2×C22⋊D31—22no—
74C2×C22⋊D31—22no—
75C2×C22⋊D31—41no—
76C2×C22⋊D31—41no—
77C2×C22⋊D31C2×C414yes—
78C2×C22⋊D31C2×C414yescomplemented
79C22×Dic31—22no—
80C22×Dic31—41no—
81C22×Dic31—41no—
82C22×Dic31C2311yescharacteristic
83C22×Dic31C2311yescharacteristic
84C22×Dic31C2311yescharacteristic
85C22×Dic31C2311yescharacteristic
86C22×Dic31C2311yescharacteristic
87C22×Dic31C2311yescharacteristic
88C2×C4×D31—22no—
89C2×C4×D31—41no—
90C2×C4×D31—41no—
91C2×C4×D31—41no—
92C2×C4×D31—41no—
93C2×C4×D31D414yescomplemented
94C4⋊C4×C31—41no—
95C22⋊C4×C31—22no—
96C22⋊C4×C31—22no—
97C22⋊C4×C31—41no—
98C22⋊C4×C31—41no—
99C42×C31—41no—
100C22⋊Dic31—22no—
101C22⋊Dic31—41no—
102C22⋊Dic31—41no—
103C22⋊Dic31C2×C414yescomplemented
104(C2×D31)⋊C4—22no—
105(C2×D31)⋊C4—22no—
106(C2×D31)⋊C4—22no—
107(C2×D31)⋊C4—22no—
108(C2×D31)⋊C4—41no—
109(C2×D31)⋊C4—41no—
110(C2×D31)⋊C4C2×C414yescomplemented
111(C2×D31)⋊C4C2×C414yescomplemented
112Dic31⋊C4—22no—
113Dic31⋊C4—41no—
114C4×Dic31—22no—
115C4×Dic31—41no—
116C23×C31—21no—
117C23×C31—21no—
118C23×C31—21no—
119C23×C31—21no—
120C23×C31—21no—
121C23×C31—21no—
122C23×C31—21no—
123C23×C31—21no—
124C23×C31—21no—
125C23×C31—21no—
126C23×C31—21no—
127C23×C31—21no—
128C23×C31C22×C412yes—
129C23×C31C22×C412yes—
130C23×C31C2411yescharacteristic
131C22×D31—21no—
132C22×D31—21no—
133C22×D31—21no—
134C22×D31—21no—
135C22×D31—21no—
136C22×D31—21no—
137C22×D31—21no—
138C22×D31—21no—
139C22×D31—21no—
140C22×D31—21no—
141C22×D31—28no—
142C22×D31—44no—
143C22×D31—44no—
144C22×D31—44no—
145C22×D31—44no—
146C22×D31—44no—
147C22×D31—44no—
148C22×D31C22×C412yes—
149C22×D31C22×C412yes—
150C22×D31C2×D412yes—
151C22×D31#4112yes—
152D4×C31—44no—
153C2×C4×C31—21no—
154C2×C4×C31—21no—
155C2×C4×C31—21no—
156C2×C4×C31—21no—
157C2×C4×C31—21no—
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×C31C22×C412yes—
167C2×C4×C31C2×D412yes—
168C22⋊D31—28no—
169C22⋊D31—44no—
170C2×Dic31—21no—
171C2×Dic31—21no—
172C2×Dic31—21no—
173C2×Dic31—21no—
174C2×Dic31—21no—
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—44no—
186C2×Dic31C22×C412yes—
187C2×Dic31C22×C412yes—
188C2×Dic31C2×D412yes—
189C4×D31—44no—
190C4×D31—44no—
191#2321—311nomaximal, Sylow
192C22×C31—22no—
193C22×C31—22no—
194C22×C31—22no—
195C22×C31—22no—
196C22×C31—22no—
197C22×C31—22no—
198C22×C31—41no—
199C22×C31—41no—
200C22×C31—41no—
201C22×C31—41no—
202C22×C31—41no—
203C22×C31—41no—
204C22×C31—41no—
205C22×C31—41no—
206C22×C31C23×C411yescharacteristic
207C22×C31C22×D411yescharacteristic
208C22×C31C2×#4111yescharacteristic
209C22×C31H(5,𝔽2)11yescharacteristic
210C22×C31H(5,𝔽2)11yescharacteristic
211C22×C31H(5,𝔽2)11yescharacteristic
212C22×C31H(5,𝔽2)11yescharacteristic
213C2×D31—22no—
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—416no—
223C2×D31—41no—
224C2×D31—41no—
225C2×D31—41no—
226C2×D31—41no—
227C2×D31C4×D414yes—
228C4×C31—22no—
229C4×C31—22no—
230C4×C31—41no—
231C4×C31—41no—
232C4×C31—41no—
233Dic31—22no—
234Dic31—22no—
235Dic31—22no—
236Dic31—41no—
237Dic31—41no—
238Dic31—41no—
239C2×#120—311no—
240C2×C4×D4—311no—
241C22×C22⋊C4—311no—
242#390—311no—
243#390D3111yescharacteristic, complemented
244#388—311no—
245#388—311no—
246#388—311no—
247#388—311no—
248#386—311no—
249#386—311no—
250#386—311no—
251#385—311no—
252#379—311no—
253C4×C22⋊C4—311no—
254C2×C31—42no—
255C2×C31—42no—
256C2×C31C2×C4×D411yescharacteristic
257C2×C31#51811yescharacteristic
258C2×C31#51811yescharacteristic
259C2×C31#53411yescharacteristic
260C2×C31#53511yescharacteristic
261C2×C31#53811yescharacteristic
262C2×C31#53811yescharacteristic
263D31—24no—
264D31—42no—
265C25—311no—
266C22×D4—311no—
267C22×D4—311no—
268C22×D4C2×D3111yescharacteristic
269C23×C4—311no—
270C23×C4—311no—
271C23×C4—311no—
272#120—318no—
273C4×D4—624no—
274C2×C4⋊C4—311no—
275C2×C4⋊C4—311no—
276C2×C4⋊C4C2×D3111yescharacteristic, complemented
277C2×C22⋊C4—311no—
278C2×C22⋊C4—311no—
279C2×C22⋊C4—311no—
280C2×C22⋊C4—311no—
281C2×C22⋊C4—311no—
282C2×C22⋊C4—311no—
283C2×C22⋊C4—311no—
284C2×C22⋊C4—311no—
285C2×C22⋊C4—311no—
286C2×C22⋊C4—311no—
287C2×C22⋊C4—311no—
288C2×C22⋊C4—311no—
289C2×C22⋊C4—624no—
290C2×C22⋊C4C2×D3111yescharacteristic
291C2×C22⋊C4C2×D3111yescharacteristic
292C2×C22⋊C4C2×D3111yescharacteristic, complemented
293C2×C22⋊C4C2×D3111yescharacteristic, complemented
294C2×C42—311no—
295C2×C42—311no—
296C2×C42C2×D3111yescharacteristic, complemented
297#95—311no—
298#95—311no—
299#95—311no—
300#95—311no—
301#95—311no—
302#95—311no—
303C31#232111yescharacteristic, complemented, Sylow
304C24—311no—
305C24—311no—
306C24—314no—
307C24—622no—
308C24—622no—
309C24—1241no—
310C24—1241no—
311C24—1241no—
312C24—1241no—
313C24C22×D3111yescharacteristic
314C24C22×D3111yescharacteristic
315C2×D4—41no—
316C2×D4—41no—
317C2×D4—314no—
318C2×D4—314no—
319C2×D4—622no—
320C2×D4—622no—
321C2×D4—1241no—
322C2×D4—1241no—
323C2×D4C4×D3114yescomplemented
324C22×C4—311no—
325C22×C4—311no—
326C22×C4—311no—
327C22×C4—314no—
328C22×C4—311no—
329C22×C4—311no—
330C22×C4—311no—
331C22×C4—622no—
332C22×C4—622no—
333C22×C4—1241no—
334C22×C4—1241no—
335C22×C4—1241no—
336C22×C4—1241no—
337C22×C4—1241no—
338C22×C4—1241no—
339C22×C4C22×D3111yescharacteristic
340C22×C4C22×D3111yescharacteristic
341C22×C4C22×D3111yescharacteristic
342C22×C4C22×D3111yescharacteristic
343C22×C4C22×D3111yescharacteristic
344C4⋊C4—41no—
345C4⋊C4—622no—
346C4⋊C4—1241no—
347C22⋊C4—22no—
348C22⋊C4—22no—
349C22⋊C4—41no—
350C22⋊C4—41no—
351C22⋊C4—314no—
352C22⋊C4—314no—
353C22⋊C4—314no—
354C22⋊C4—622no—
355C22⋊C4—622no—
356C22⋊C4—622no—
357C22⋊C4—622no—
358C22⋊C4—622no—
359C22⋊C4—1241no—
360C22⋊C4—1241no—
361C22⋊C4—1241no—
362C22⋊C4—1241no—
363C42—41no—
364C42—622no—
365C42—1241no—
366C23—21no—
367C23—21no—
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—21no—
373C23—21no—
374C23—21no—
375C23—21no—
376C23—21no—
377C23—21no—
378C23—312no—
379C23—312no—
380C23—312no—
381C23—312no—
382C23—628no—
383C23—621no—
384C23—621no—
385C23—621no—
386C23—621no—
387C23—621no—
388C23—621no—
389C23—621no—
390C23—621no—
391C23—621no—
392C23—621no—
393C23—1244no—
394C23—1244no—
395C23—1244no—
396C23—1244no—
397C23—1244no—
398C23—1244no—
399C23C2×C4×D3112yes—
400C23C2×C4×D3112yes—
401C23C23×D3111yescharacteristic
402D4—44no—
403D4—628no—
404D4—1244no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—312no—
419C2×C4—312no—
420C2×C4—312no—
421C2×C4—621no—
422C2×C4—621no—
423C2×C4—621no—
424C2×C4—621no—
425C2×C4—621no—
426C2×C4—621no—
427C2×C4—621no—
428C2×C4—621no—
429C2×C4—621no—
430C2×C4—621no—
431C2×C4—621no—
432C2×C4—621no—
433C2×C4—621no—
434C2×C4—621no—
435C2×C4—621no—
436C2×C4—1244no—
437C2×C4—1244no—
438C2×C4—1244no—
439C2×C4C2×C4×D3112yes—
440C2×C4D4×D3112yes—
441C22—22no—
442C22—22no—
443C22—22no—
444C22—22no—
445C22—22no—
446C22—22no—
447C22—41no—
448C22—41no—
449C22—41no—
450C22—41no—
451C22—41no—
452C22—41no—
453C22—41no—
454C22—41no—
455C22—314no—
456C22—622no—
457C22—622no—
458C22—622no—
459C22—622no—
460C22—622no—
461C22—622no—
462C22—622no—
463C22—622no—
464C22—622no—
465C22—12416no—
466C22—1241no—
467C22—1241no—
468C22—1241no—
469C22—1241no—
470C22C22×C4×D3111yescharacteristic
471C22C2×D4×D3111yescharacteristic
472C22#1175856111yescharacteristic
473C22#1175856111yescharacteristic
474C22#1175856111yescharacteristic
475C22#41×D3111yescharacteristic
476C22#1175856611yescharacteristic
477C4—22no—
478C4—22no—
479C4—41no—
480C4—41no—
481C4—41no—
482C4—622no—
483C4—622no—
484C4—622no—
485C4—1241no—
486C4—1241no—
487C4—1241no—
488C2—42no—
489C2—42no—
490C2—624no—
491C2—1242no—
492C2C4×D4×D3111yescharacteristic
493C2#1452152111yescharacteristic
494C2#1452152211yescharacteristic
495C2#1452160711yescharacteristic
496C2#1452161211yescharacteristic
497C2#1452163111yescharacteristic
498C2#1452163311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D31
commutatorC22×C31C23×C4
FittingC31×#390C2
socle, cosocleC23×C31C24
prime radicalC2×#11758514C2
hypercenter#390D31
hypocenterC31#2321
LCSG ▷ C22×C31 ▷ C31
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
2. C2×(C22⋊D31)⋊C4C2semidirect
3. C2×C22⋊C4×D31C2semidirect
4. #14520949C2semidirect
5. #14520943C2semidirect
6. #14520943C2semidirect
7. #14520940C2semidirect
8. #14520939C2semidirect
9. #14520929C2semidirect
10. #14520926C2semidirect
11. #14520925C2semidirect
12. #14520920C2semidirect
13. #14520904C2semidirect
14. C4×(C2×D31)⋊C4C2semidirect
15. C31×#390C2semidirect
20. C23×Dic31C22semidirect
23. C2×C4⋊C4×C31C22semidirect
26. C2×C22⋊C4×C31C22semidirect
27. C2×C22⋊C4×C31C22semidirect
28. C2×C42×C31C22semidirect
32. C2×C22⋊Dic31C22semidirect
33. #11758514C4semidirect
42. C2×Dic31⋊C4C22semidirect
43. C2×Dic31⋊C4C22semidirect
44. C2×C4×Dic31C22semidirect
45. C2×C4×Dic31C22semidirect
48. C31⋊#95C22semidirect
49. C31⋊#95C22semidirect
50. C31⋊#95C22semidirect
51. C31⋊#95C22semidirect
52. C31⋊#95C22semidirect
53. C31⋊#95C22semidirect
62. C23×D31C2×C4semidirect
67. C2×D4×C31C2×C4semidirect
78. C2×C22⋊D31C2×C4semidirect
93. C2×C4×D31D4semidirect
103. C22⋊Dic31C2×C4semidirect
110. (C2×D31)⋊C4C2×C4semidirect
111. (C2×D31)⋊C4C2×C4semidirect
243. #390D31semidirect
276. C2×C4⋊C4C2×D31semidirect
292. C2×C22⋊C4C2×D31semidirect
293. C2×C22⋊C4C2×D31semidirect
296. C2×C42C2×D31semidirect
303. C31#2321semidirect
323. C2×D4C4×D31semidirect

Maximal subgroups

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

subgroupindex
C2×#117585142
C2×(C22⋊D31)⋊C42
C2×C22⋊C4×D312
#145209492
#145209432
#145209402
#145209392
#145209292
#145209262
#145209252
#145209202
#145209042
C4×(C2×D31)⋊C42
C31×#3902
#232131