Finite Group Databasebeta

← #16857729

Subgroups — #16857729

Order 3968.

450 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14521737C211yesmaximal, characteristic, complemented
2D4×D124C211yesmaximal, characteristic
3#14521415C211yesmaximal, characteristic, complemented
4#14521375C211yesmaximal, characteristic, complemented
5#14521364C211yesmaximal, characteristic, complemented
6#14521296C211yesmaximal, characteristic, complemented
7#14521279C211yesmaximal, characteristic, complemented
8#14521250C211yesmaximal, characteristic, complemented
9#14521201C211yesmaximal, characteristic, complemented
10#14521201C211yesmaximal, characteristic, complemented
11#14521149C211yesmaximal, characteristic, complemented
12#14521119C211yesmaximal, characteristic, complemented
13#14521052C211yesmaximal, characteristic, complemented
14#102×D31C211yesmaximal, characteristic, complemented
15C31×#478C211yesmaximal, characteristic, complemented
16C2×D4×D31C2211yescharacteristic
17C2×D4×D31C2211yescharacteristic
18C22×D124—21no—
19C31×#125C2211yescharacteristic, complemented
20C4×D4×C31C2211yescharacteristic
21C2×#92480C2211yescharacteristic
22#11758507—21no—
23C2×#92470C2211yescharacteristic, complemented
24C2×#92470C2211yescharacteristic, complemented
25C2×#92469C2211yescharacteristic, complemented
26C2×C8×D31C2211yescharacteristic, complemented
27#11758475—21no—
28#11758474C2211yescharacteristic, complemented
29#11758474C2211yescharacteristic, complemented
30#11758472C2211yescharacteristic
31#11758472C2211yescharacteristic
32#11758471—21no—
33#11758469—21no—
34#11758469C2211yescharacteristic, complemented
35C4⋊C4×D31C2211yescharacteristic, complemented
36#11758467—21no—
37#11758459—21no—
38#11758459—21no—
39#11758451C2211yescharacteristic
40C4×D124C2211yescharacteristic
41C4×Dic62C2211yescharacteristic, complemented
42C31×#107C2211yescharacteristic, complemented
43C31×#106C2211yescharacteristic, complemented
44C31×C4⋊C8C2211yescharacteristic, complemented
45C31×#102C2211yescharacteristic
46C31×#102C2211yescharacteristic
47#11758420C2211yescharacteristic
48#11758409C2211yescharacteristic, complemented
49#11758409C2211yescharacteristic, complemented
50(C2×D31)⋊C8C2211yescharacteristic, complemented
51(C2×D31)⋊C8C2211yescharacteristic, complemented
52#11758398C2211yescharacteristic, complemented
53#11758397C2211yescharacteristic, complemented
54#11758397C2211yescharacteristic, complemented
55#11758397C2211yescharacteristic, complemented
56#11758397C2211yescharacteristic, complemented
57#11758395C2211yescharacteristic, complemented
58#11758391C2211yescharacteristic, complemented
59C23×D31—21no—
60C23×D31—21no—
61C2×D4×C31C2311yescharacteristic
62C22×C4×C31—21no—
63C2×C22⋊D31—21no—
64C2×C22⋊D31—21no—
65D4×D31—22no—
66D4×D31—22no—
67D4×D31—41no—
68D4×D31—41no—
69C2×D124—21no—
70C2×D124—21no—
71C2×D124—21no—
72C2×D124—21no—
73C2×D124—44no—
74C2×D124D411yescharacteristic
75C2×D124C2311yescharacteristic
76C2×D124C2311yescharacteristic
77C2×C4×D31—21no—
78C2×C4×D31C2311yescharacteristic
79C2×C4×D31C2311yescharacteristic
80C2×Dic62C2311yescharacteristic
81C2×C8×C31C2311yescharacteristic
82C2×C8×C31C2311yescharacteristic
83C4⋊C4×C31—21no—
84C4⋊C4×C31—21no—
85C4⋊C4×C31C2311yescharacteristic
86C4⋊C4×C31C2311yescharacteristic
87C4⋊C4×C31C2311yescharacteristic
88C22⋊C4×C31—21no—
89C42×C31C2311yescharacteristic
90#92480—22no—
91(C2×D31)⋊C4—21no—
92(C2×D31)⋊C4—21no—
93(C2×D31)⋊C4—21no—
94(C2×D31)⋊C4—21no—
95(C2×D31)⋊C4—21no—
96(C2×D31)⋊C4D411yescharacteristic
97(C2×D31)⋊C4D411yescharacteristic
98C4⋊Dic31—21no—
99C4⋊Dic31—21no—
100C4⋊Dic31D411yescharacteristic
101C4⋊Dic31C2311yescharacteristic
102Dic31⋊C4—21no—
103Dic31⋊C4—21no—
104C4×Dic31—21no—
105C4×Dic31—21no—
106C2×C31⋊C8C2311yescharacteristic
107C2×C31⋊C8C2311yescharacteristic
108#92470—41no—
109#92470—41no—
110#92469—41no—
111C8×D31—41no—
112C23×C31—21no—
113C22×D31—21no—
114C22×D31—21no—
115C22×D31—42no—
116C22×D31—42no—
117C22×D31—42no—
118C22×D31—42no—
119C22×D31—81no—
120C22×D31—81no—
121C22×D31C2×D411yescharacteristic
122C22×D31C2×D411yescharacteristic
123D4×C31—21no—
124D4×C31#4112yes—
125C2×C4×C31—21no—
126C2×C4×C31—21no—
127C2×C4×C31—21no—
128C2×C4×C31—42no—
129C2×C4×C31C2×D411yescharacteristic
130C2×C4×C31C2×D411yescharacteristic
131C2×C4×C31C2411yescharacteristic
132C22⋊D31—42no—
133C22⋊D31—42no—
134C2×Dic31—21no—
135C2×Dic31—21no—
136C2×Dic31C2×D411yescharacteristic
137C2×Dic31C2×D411yescharacteristic
138D124—22no—
139D124—21no—
140D124—21no—
141D124—21no—
142D124—21no—
143D124—42no—
144D124—42no—
145D124—42no—
146D124—81no—
147C4×D31—21no—
148C4×D31—21no—
149C4×D31—21no—
150C4×D31—21no—
151C4×D31—42no—
152Dic62—21no—
153Dic62—21no—
154C8×C31—21no—
155C8×C31—21no—
156C31⋊C8—21no—
157C31⋊C8—21no—
158#3310—311nomaximal, Sylow
159C22×C31—22no—
160C22×C31—41no—
161C22×C31—41no—
162C22×C31C22×D411yescharacteristic
163C2×D31—21no—
164C2×D31—21no—
165C2×D31—21no—
166C2×D31—21no—
167C2×D31—21no—
168C2×D31—41no—
169C2×D31—41no—
170C2×D31—41no—
171C2×D31—41no—
172C2×D31—41no—
173C2×D31—41no—
174C2×D31—84no—
175C2×D31—84no—
176C2×D31AGL(1,ℤ/8)12yes—
177C4×C31—21no—
178C4×C31—21no—
179C4×C31—41no—
180C4×C31—41no—
181C4×C31—41no—
182C4×C31C2×#4111yescharacteristic
183C4×C31H(5,𝔽2)11yescharacteristic
184Dic31—21no—
185Dic31—21no—
186Dic31—41no—
187Dic31—41no—
188#552—311no—
189D42—311no—
190#490—311no—
191#482—311no—
192#480—311no—
193#478D3111yescharacteristic, complemented
194#468—311no—
195#465—311no—
196#460—311no—
197#450—311no—
198#450—311no—
199#440—311no—
200#435—311no—
201#418—311no—
202C2×#102—311no—
203C2×C31—42no—
204C2×C31#54611yescharacteristic
205C2×C31C2×AGL(1,ℤ/8)11yescharacteristic
206C2×C31#57711yescharacteristic
207D31—22no—
208D31—41no—
209D31—81no—
210D31—81no—
211C22×D4—311no—
212C22×D4—311no—
213C22×D4—621no—
214C2×SD16—311no—
215C2×SD16—311no—
216C2×SD16—311no—
217C2×M16—311no—
218C22×C8—311no—
219#127—311no—
220#126—621no—
221#125—621no—
222#125C2×D3111yescharacteristic, complemented
223#123—621no—
224C22⋊Q8—311no—
225C22⋊Q8—311no—
226#121—311no—
227#121—311no—
228#121—621no—
229#120—621no—
230#120—621no—
231C4×Q8—311no—
232C4×D4—311no—
233C4×D4C2×D3111yescharacteristic
234#117—311no—
235#117—621no—
236C2×C4⋊C4—311no—
237#107—311no—
238#107C2×D3111yescharacteristic, complemented
239#106C2×D3111yescharacteristic, complemented
240C4⋊C8C2×D3111yescharacteristic, complemented
241#103—311no—
242#102—311no—
243#102—311no—
244#102—311no—
245#102—311no—
246#102—311no—
247#102—311no—
248#102—311no—
249#102C2×D3111yescharacteristic
250#102C2×D3111yescharacteristic
251C22⋊C8—311no—
252C22⋊C8—311no—
253#97—311no—
254C31#331011yescharacteristic, complemented, Sylow
255C24—621no—
256C24—621no—
257C2×Q8—311no—
258C2×D4—311no—
259C2×D4—311no—
260C2×D4—311no—
261C2×D4—621no—
262C2×D4—621no—
263C2×D4—621no—
264C2×D4—621no—
265C2×D4—622no—
266C2×D4—622no—
267C2×D4—621no—
268C2×D4—621no—
269C2×D4—1244no—
270C2×D4—1241no—
271C2×D4—1241no—
272C2×D4C22×D3111yescharacteristic
273C22×C4—21no—
274C22×C4—311no—
275C22×C4—311no—
276C22×C4—621no—
277SD16—622no—
278SD16—1241no—
279SD16—1241no—
280M16—1241no—
281C2×C8—311no—
282C2×C8—311no—
283C2×C8—1241no—
284C2×C8C22×D3111yescharacteristic
285C2×C8C22×D3111yescharacteristic
286C4⋊C4—21no—
287C4⋊C4—21no—
288C4⋊C4—311no—
289C4⋊C4—311no—
290C4⋊C4—621no—
291C4⋊C4—621no—
292C4⋊C4—621no—
293C4⋊C4—621no—
294C4⋊C4C22×D3111yescharacteristic
295C4⋊C4C22×D3111yescharacteristic
296C4⋊C4C22×D3111yescharacteristic
297C22⋊C4—21no—
298C22⋊C4—311no—
299C22⋊C4—311no—
300C22⋊C4—621no—
301C22⋊C4—621no—
302C22⋊C4—621no—
303C22⋊C4—621no—
304C22⋊C4—621no—
305C42—621no—
306C42—621no—
307C42C22×D3111yescharacteristic
308C23—21no—
309C23—311no—
310C23—311no—
311C23—621no—
312C23—621no—
313C23—1242no—
314C23—1242no—
315C23—1242no—
316C23—1242no—
317C23—2481no—
318C23—2481no—
319Q8—621no—
320Q8—621no—
321D4—21no—
322D4—622no—
323D4—621no—
324D4—621no—
325D4—621no—
326D4—621no—
327D4—1242no—
328D4—1242no—
329D4—1242no—
330D4—1242no—
331D4—1242no—
332D4—2481no—
333D4#9249912yes—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—42no—
338C2×C4—311no—
339C2×C4—311no—
340C2×C4—621no—
341C2×C4—621no—
342C2×C4—621no—
343C2×C4—621no—
344C2×C4—621no—
345C2×C4—621no—
346C2×C4—1242no—
347C2×C4D4×D3111yescharacteristic
348C2×C4D4×D3111yescharacteristic
349C2×C4C23×D3111yescharacteristic
350C8—21no—
351C8—21no—
352C8—621no—
353C8—621no—
354C22—22no—
355C22—41no—
356C22—41no—
357C22—312no—
358C22—621no—
359C22—621no—
360C22—621no—
361C22—621no—
362C22—621no—
363C22—1241no—
364C22—1241no—
365C22—1241no—
366C22—1241no—
367C22—1241no—
368C22—1241no—
369C22—2484no—
370C22—2484no—
371C22C2×D4×D3111yescharacteristic
372C4—21no—
373C4—21no—
374C4—41no—
375C4—41no—
376C4—41no—
377C4—621no—
378C4—621no—
379C4—1241no—
380C4—1241no—
381C4C2×#9249911yescharacteristic
382C4#1175856611yescharacteristic
383C2—42no—
384C2—622no—
385C2—1241no—
386C2—2481no—
387C2—2481no—
388C2#1452169011yescharacteristic
389C2AGL(1,ℤ/8)×D3111yescharacteristic
390C2#1452185611yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#478C2
socleC22×C31C22×D4
prime radicalD4×D124C2
hypercenter#478D31
hypocenterC31#3310
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #14521737C2semidirect
3. #14521415C2semidirect
4. #14521375C2semidirect
5. #14521364C2semidirect
6. #14521296C2semidirect
7. #14521279C2semidirect
8. #14521250C2semidirect
9. #14521201C2semidirect
10. #14521201C2semidirect
11. #14521149C2semidirect
12. #14521119C2semidirect
13. #14521052C2semidirect
14. #102×D31C2semidirect
15. C31×#478C2semidirect
19. C31×#125C22semidirect
23. C2×#92470C22semidirect
24. C2×#92470C22semidirect
25. C2×#92469C22semidirect
26. C2×C8×D31C22semidirect
28. #11758474C22semidirect
29. #11758474C22semidirect
34. #11758469C22semidirect
35. C4⋊C4×D31C22semidirect
41. C4×Dic62C22semidirect
42. C31×#107C22semidirect
43. C31×#106C22semidirect
44. C31×C4⋊C8C22semidirect
48. #11758409C22semidirect
49. #11758409C22semidirect
50. (C2×D31)⋊C8C22semidirect
51. (C2×D31)⋊C8C22semidirect
52. #11758398C22semidirect
53. #11758397C22semidirect
54. #11758397C22semidirect
55. #11758397C22semidirect
56. #11758397C22semidirect
57. #11758395C22semidirect
58. #11758391C22semidirect
193. #478D31semidirect
222. #125C2×D31semidirect
238. #107C2×D31semidirect
239. #106C2×D31semidirect
240. C4⋊C8C2×D31semidirect
254. C31#3310semidirect

Maximal subgroups

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

subgroupindex
#145217372
D4×D1242
#145214152
#145213752
#145213642
#145212962
#145212792
#145212502
#145212012
#145211492
#145211192
#145210522
#102×D312
C31×#4782
#331031