Finite Group Databasebeta

← #16848305

Subgroups — #16848305

Order 3968.

672 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊C4×D31C211yesmaximal, characteristic
2#14520943C211yesmaximal, characteristic, complemented
3#14520942C211yesmaximal, characteristic, complemented
4#14520941C211yesmaximal, characteristic, complemented
5#14520940C211yesmaximal, characteristic, complemented
6#14520939C211yesmaximal, characteristic, complemented
7#14520938C211yesmaximal, characteristic, complemented
8#14520937C211yesmaximal, characteristic, complemented
9#14520908C211yesmaximal, characteristic, complemented
10#14520906C211yesmaximal, characteristic, complemented
11#14520904C211yesmaximal, characteristic
12#14520904C211yesmaximal, characteristic
13C4×(C2×D31)⋊C4C211yesmaximal, characteristic, complemented
14#14520896C211yesmaximal, characteristic, complemented
15C31×#388C211yesmaximal, characteristic, complemented
16C24×D31C2211yescharacteristic
17C22×C4×D31C2211yescharacteristic
18C22×C4×D31C2211yescharacteristic
19C2×C4⋊C4×C31C2211yescharacteristic, complemented
20C2×C22⋊C4×C31C2211yescharacteristic
21C2×C22⋊C4×C31C2211yescharacteristic
22C2×C22⋊C4×C31C2211yescharacteristic
23C2×C42×C31C2211yescharacteristic, complemented
24C2×C22⋊Dic31C2211yescharacteristic
25C2×C22⋊Dic31C2211yescharacteristic
26C2×C22⋊Dic31C2211yescharacteristic
27C2×(C2×D31)⋊C4C2211yescharacteristic
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×C4⋊Dic31C2211yescharacteristic, complemented
38C2×Dic31⋊C4C2211yescharacteristic, complemented
39C2×Dic31⋊C4C2211yescharacteristic, complemented
40C2×C4×Dic31C2211yescharacteristic, complemented
41C2×C4×Dic31C2211yescharacteristic, complemented
42C2×C4×Dic31C2211yescharacteristic, complemented
43C22⋊C4×D31C418yescomplemented
44C31×#95C2211yescharacteristic, complemented
45C31×#95C2211yescharacteristic, complemented
46C31⋊#95C2211yescharacteristic, complemented
47C31⋊#95C2211yescharacteristic, complemented
48C31⋊#95C2211yescharacteristic, complemented
49C31⋊#95C2211yescharacteristic, complemented
50C31⋊#95C2211yescharacteristic, complemented
51C31⋊#95C2211yescharacteristic, complemented
52C24×C31C2311yescharacteristic
53C23×D31—22no—
54C23×D31—22no—
55C23×D31—41no—
56C23×D31—41no—
57C23×D31—41no—
58C23×D31—41no—
59C23×D31C2×C414yes—
60C23×D31C2311yescharacteristic
61C23×D31C2311yescharacteristic
62C22×C4×C31C2311yescharacteristic
63C22×C4×C31C2311yescharacteristic
64C22×C4×C31C2311yescharacteristic
65C22×C4×C31C2311yescharacteristic
66C22×C4×C31C2311yescharacteristic
67C22×C4×C31C2311yescharacteristic
68C22×Dic31C2311yescharacteristic
69C22×Dic31C2311yescharacteristic
70C22×Dic31C2311yescharacteristic
71C22×Dic31C2311yescharacteristic
72C22×Dic31C2311yescharacteristic
73C22×Dic31C2311yescharacteristic
74C2×C4×D31—41no—
75C2×C4×D31—41no—
76C2×C4×D31—41no—
77C2×C4×D31—41no—
78C2×C4×D31C2×C414yes—
79C2×C4×D31C2×C414yes—
80C4⋊C4×C31—41no—
81C22⋊C4×C31—41no—
82C22⋊C4×C31—41no—
83C22⋊C4×C31C2×C414yes—
84C42×C31—41no—
85C22⋊Dic31—41no—
86C22⋊Dic31—41no—
87C22⋊Dic31C2×C414yes—
88(C2×D31)⋊C4—22no—
89(C2×D31)⋊C4—22no—
90(C2×D31)⋊C4—22no—
91(C2×D31)⋊C4—22no—
92(C2×D31)⋊C4—41no—
93(C2×D31)⋊C4—41no—
94(C2×D31)⋊C4—41no—
95(C2×D31)⋊C4—41no—
96(C2×D31)⋊C4C2×C414yes—
97(C2×D31)⋊C4C2×C414yes—
98C4⋊Dic31—41no—
99Dic31⋊C4—41no—
100Dic31⋊C4—41no—
101C4×Dic31—41no—
102C4×Dic31—41no—
103C4×Dic31—41no—
104C23×C31—21no—
105C23×C31—21no—
106C23×C31—21no—
107C23×C31—21no—
108C23×C31—21no—
109C23×C31—21no—
110C23×C31C22×C412yes—
111C23×C31C2411yescharacteristic
112C22×D31—21no—
113C22×D31—21no—
114C22×D31—21no—
115C22×D31—21no—
116C22×D31—21no—
117C22×D31—21no—
118C22×D31—21no—
119C22×D31—21no—
120C22×D31—21no—
121C22×D31—21no—
122C22×D31—28no—
123C22×D31—44no—
124C22×D31—44no—
125C22×D31—44no—
126C22×D31—44no—
127C22×D31—44no—
128C22×D31—44no—
129C22×D31C22×C412yes—
130C22×D31C22×C412yes—
131C22×D31#4112yes—
132C22×D31#4112yes—
133C2×C4×C31—21no—
134C2×C4×C31—21no—
135C2×C4×C31—21no—
136C2×C4×C31—21no—
137C2×C4×C31—21no—
138C2×C4×C31—21no—
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×C31C22×C412yes—
150C2×C4×C31C22×C412yes—
151C2×Dic31—21no—
152C2×Dic31—21no—
153C2×Dic31—21no—
154C2×Dic31—21no—
155C2×Dic31—21no—
156C2×Dic31—21no—
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×Dic31C22×C412yes—
168C2×Dic31C22×C412yes—
169C4×D31—44no—
170C4×D31—44no—
171#2312—311nomaximal, Sylow
172C22×C31—22no—
173C22×C31—22no—
174C22×C31—22no—
175C22×C31—41no—
176C22×C31—41no—
177C22×C31—41no—
178C22×C31—41no—
179C22×C31C23×C411yescharacteristic
180C22×C31C2×#4111yescharacteristic
181C22×C31C2×#4111yescharacteristic
182C22×C31H(5,𝔽2)11yescharacteristic
183C22×C31H(5,𝔽2)11yescharacteristic
184C22×C31H(5,𝔽2)11yescharacteristic
185C22×C31H(5,𝔽2)11yescharacteristic
186C2×D31—22no—
187C2×D31—22no—
188C2×D31—22no—
189C2×D31—22no—
190C2×D31—22no—
191C2×D31—22no—
192C2×D31—22no—
193C2×D31—22no—
194C2×D31—22no—
195C2×D31—416no—
196C2×D31—41no—
197C2×D31—41no—
198C2×D31—41no—
199C2×D31—41no—
200C2×D31#11714yes—
201C4×C31—22no—
202C4×C31—22no—
203C4×C31—41no—
204C4×C31—41no—
205C4×C31—41no—
206C4×C31—41no—
207Dic31—22no—
208Dic31—22no—
209Dic31—41no—
210Dic31—41no—
211Dic31—41no—
212Dic31—41no—
213C22×C22⋊C4—311no—
214#388—311no—
215#388—311no—
216#388—311no—
217#388—311no—
218#388—311no—
219#388—311no—
220#388—311no—
221#388D3111yescharacteristic, complemented
222#380—311no—
223#380—311no—
224#379—311no—
225#379—311no—
226C4×C22⋊C4—311no—
227C4×C22⋊C4—311no—
228C2×C31—42no—
229C2×C31C2×#11711yescharacteristic
230C2×C31#51811yescharacteristic
231C2×C31#51811yescharacteristic
232C2×C31#53811yescharacteristic
233C2×C31#53811yescharacteristic
234C2×C31#53811yescharacteristic
235C2×C31#53811yescharacteristic
236D31—24no—
237D31—42no—
238C25—311no—
239C23×C4—311no—
240C23×C4—311no—
241C2×C4⋊C4—311no—
242C2×C4⋊C4—311no—
243C2×C4⋊C4—311no—
244C2×C4⋊C4C2×D3111yescharacteristic, complemented
245C2×C22⋊C4—311no—
246C2×C22⋊C4—311no—
247C2×C22⋊C4—311no—
248C2×C22⋊C4—318no—
249C2×C22⋊C4—311no—
250C2×C22⋊C4—311no—
251C2×C22⋊C4—311no—
252C2×C22⋊C4—311no—
253C2×C22⋊C4—311no—
254C2×C22⋊C4—311no—
255C2×C22⋊C4—311no—
256C2×C22⋊C4—311no—
257C2×C22⋊C4—311no—
258C2×C22⋊C4—311no—
259C2×C22⋊C4C2×D3111yescharacteristic
260C2×C22⋊C4C2×D3111yescharacteristic
261C2×C22⋊C4C2×D3111yescharacteristic
262C2×C42—311no—
263C2×C42—311no—
264C2×C42—311no—
265C2×C42C2×D3111yescharacteristic, complemented
266#95—311no—
267#95—311no—
268#95—311no—
269#95—311no—
270#95—311no—
271#95—311no—
272#95C2×D3111yescharacteristic, complemented
273#95C2×D3111yescharacteristic, complemented
274C31#231211yescharacteristic, complemented, Sylow
275C24—311no—
276C24—311no—
277C24—314no—
278C24—622no—
279C24—622no—
280C24—1241no—
281C24—1241no—
282C24—1241no—
283C24—1241no—
284C24C22×D3111yescharacteristic
285C22×C4—311no—
286C22×C4—311no—
287C22×C4—314no—
288C22×C4—314no—
289C22×C4—311no—
290C22×C4—311no—
291C22×C4—311no—
292C22×C4—311no—
293C22×C4—1241no—
294C22×C4—1241no—
295C22×C4—1241no—
296C22×C4—1241no—
297C22×C4C22×D3111yescharacteristic
298C22×C4C22×D3111yescharacteristic
299C22×C4C22×D3111yescharacteristic
300C22×C4C22×D3111yescharacteristic
301C22×C4C22×D3111yescharacteristic
302C22×C4C22×D3111yescharacteristic
303C4⋊C4—41no—
304C4⋊C4—1241no—
305C4⋊C4—1241no—
306C4⋊C4—1241no—
307C22⋊C4—41no—
308C22⋊C4—41no—
309C22⋊C4—314no—
310C22⋊C4—314no—
311C22⋊C4—314no—
312C22⋊C4—622no—
313C22⋊C4—622no—
314C22⋊C4—622no—
315C22⋊C4—622no—
316C22⋊C4—1241no—
317C22⋊C4—1241no—
318C22⋊C4—1241no—
319C22⋊C4—1241no—
320C22⋊C4—1241no—
321C22⋊C4—1241no—
322C22⋊C4C4×D3114yes—
323C42—41no—
324C42—1241no—
325C42—1241no—
326C42—1241no—
327C23—21no—
328C23—21no—
329C23—21no—
330C23—21no—
331C23—21no—
332C23—21no—
333C23—312no—
334C23—312no—
335C23—312no—
336C23—312no—
337C23—628no—
338C23—621no—
339C23—621no—
340C23—621no—
341C23—621no—
342C23—621no—
343C23—621no—
344C23—621no—
345C23—621no—
346C23—621no—
347C23—621no—
348C23—1244no—
349C23—1244no—
350C23—1244no—
351C23—1244no—
352C23—1244no—
353C23—1244no—
354C23C2×C4×D3112yes—
355C23C23×D3111yescharacteristic
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—312no—
373C2×C4—312no—
374C2×C4—621no—
375C2×C4—621no—
376C2×C4—621no—
377C2×C4—621no—
378C2×C4—621no—
379C2×C4—621no—
380C2×C4—621no—
381C2×C4—621no—
382C2×C4—621no—
383C2×C4—621no—
384C2×C4—621no—
385C2×C4—621no—
386C2×C4—621no—
387C2×C4—621no—
388C2×C4—621no—
389C2×C4—621no—
390C2×C4—1244no—
391C2×C4—1244no—
392C2×C4C2×C4×D3112yes—
393C2×C4C2×C4×D3112yes—
394C22—22no—
395C22—22no—
396C22—22no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—314no—
402C22—622no—
403C22—622no—
404C22—622no—
405C22—622no—
406C22—622no—
407C22—622no—
408C22—622no—
409C22—622no—
410C22—622no—
411C22—12416no—
412C22—1241no—
413C22—1241no—
414C22—1241no—
415C22—1241no—
416C22C22×C4×D3111yescharacteristic
417C22#1175856111yescharacteristic
418C22#1175856111yescharacteristic
419C22#41×D3111yescharacteristic
420C22#41×D3111yescharacteristic
421C22#1175856611yescharacteristic
422C22#1175856611yescharacteristic
423C4—22no—
424C4—22no—
425C4—41no—
426C4—41no—
427C4—41no—
428C4—41no—
429C4—622no—
430C4—622no—
431C4—1241no—
432C4—1241no—
433C4—1241no—
434C4—1241no—
435C2—42no—
436C2—624no—
437C2—1242no—
438C2#117×D3111yescharacteristic
439C2#1452152111yescharacteristic
440C2#1452152111yescharacteristic
441C2#1452163111yescharacteristic
442C2#1452163311yescharacteristic
443C2#1452163511yescharacteristic
444C2#1452163811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D31
commutatorC22×C31C23×C4
FittingC31×#388C2
socle, cosocleC23×C31C24
prime radicalC24×D31C22
hypercenter#388D31
hypocenterC31#2312
LCSG ▷ C22×C31 ▷ C31
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
2. #14520943C2semidirect
3. #14520942C2semidirect
4. #14520941C2semidirect
5. #14520940C2semidirect
6. #14520939C2semidirect
7. #14520938C2semidirect
8. #14520937C2semidirect
9. #14520908C2semidirect
10. #14520906C2semidirect
13. C4×(C2×D31)⋊C4C2semidirect
14. #14520896C2semidirect
15. C31×#388C2semidirect
19. C2×C4⋊C4×C31C22semidirect
23. 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
43. C22⋊C4×D31C4semidirect
44. C31×#95C22semidirect
45. C31×#95C22semidirect
46. C31⋊#95C22semidirect
47. C31⋊#95C22semidirect
48. C31⋊#95C22semidirect
49. C31⋊#95C22semidirect
50. C31⋊#95C22semidirect
51. C31⋊#95C22semidirect
221. #388D31semidirect
244. C2×C4⋊C4C2×D31semidirect
265. C2×C42C2×D31semidirect
272. #95C2×D31semidirect
273. #95C2×D31semidirect
274. C31#2312semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊C4×D312
#145209432
#145209422
#145209412
#145209402
#145209392
#145209382
#145209372
#145209082
#145209062
#145209042
C4×(C2×D31)⋊C42
#145208962
C31×#3882
#231231