Finite Group Databasebeta

← #16856060

Subgroups — #16856060

Order 3968.

404 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14521676C211yesmaximal, characteristic, complemented
2#14521612C211yesmaximal, characteristic
3#14521413C211yesmaximal, characteristic, complemented
4#14521412C211yesmaximal, characteristic, complemented
5#14521411C211yesmaximal, characteristic, complemented
6#14521407C211yesmaximal, characteristic, complemented
7#14521404C211yesmaximal, characteristic, complemented
8#14521402C211yesmaximal, characteristic, complemented
9#14521394C211yesmaximal, characteristic, complemented
10#14521052C211yesmaximal, characteristic, complemented
11#14521047C211yesmaximal, characteristic, complemented
12#14521042C211yesmaximal, characteristic, complemented
13#102×D31C211yesmaximal, characteristic, complemented
14#14521003C211yesmaximal, characteristic, complemented
15C31×#486C211yesmaximal, characteristic, complemented
16C2×#92497C2211yescharacteristic
17C2×D4×D31C2211yescharacteristic
18C31×C4⋊Q8C2211yescharacteristic, complemented
19C31×#127C2211yescharacteristic
20#11758523—21no—
21#11758521—21no—
22#11758517C2211yescharacteristic
23#11758516—21no—
24#11758516—21no—
25#11758514—21no—
26#11758514—21no—
27#11758513C2211yescharacteristic
28C2×#92469C2211yescharacteristic
29C2×C8×D31C2211yescharacteristic
30#11758473—21no—
31#11758469C2211yescharacteristic
32C4⋊C4×D31C2211yescharacteristic
33#11758467C2211yescharacteristic, complemented
34#11758466—21no—
35#11758465C2211yescharacteristic, complemented
36#11758452C2211yescharacteristic
37#11758449C2211yescharacteristic
38#11758447C2211yescharacteristic, complemented
39C31×#102C2211yescharacteristic
40C31×#102C2211yescharacteristic
41C31×#102C2211yescharacteristic, complemented
42C31×#102C2211yescharacteristic, complemented
43C4×C8×C31C2211yescharacteristic, complemented
44#11758420C2211yescharacteristic
45#11758420C2211yescharacteristic
46#11758420C2211yescharacteristic, complemented
47#11758420C2211yescharacteristic, complemented
48#11758409C2211yescharacteristic
49#11758409C2211yescharacteristic
50#11758404C2211yescharacteristic, complemented
51#11758404C2211yescharacteristic, complemented
52#11758403C2211yescharacteristic, complemented
53C8×Dic31C2211yescharacteristic, complemented
54#11758398C2211yescharacteristic, complemented
55#11758398C2211yescharacteristic, complemented
56#11758397C2211yescharacteristic
57#11758397C2211yescharacteristic
58#11758391C2211yescharacteristic, complemented
59C23×D31—21no—
60C2×Q8×C31—21no—
61C2×D4×C31—21no—
62C2×D4×C31—21no—
63C2×D4×C31C2311yescharacteristic
64C2×D4×C31C2311yescharacteristic
65C2×C22⋊D31—21no—
66C2×C22⋊D31—21no—
67C2×C22⋊D31—21no—
68C2×C22⋊D31—21no—
69C22×Dic31—21no—
70#92497—22no—
71#92497—22no—
72D4×D31—22no—
73D4×D31—22no—
74C2×D124C2311yescharacteristic
75C2×C4×D31—21no—
76C2×C4×D31C2311yescharacteristic
77C2×Dic62—21no—
78C2×Dic62C2311yescharacteristic
79C2×C8×C31C2311yescharacteristic
80C2×C8×C31C2311yescharacteristic
81C4⋊C4×C31—21no—
82C4⋊C4×C31C2311yescharacteristic
83C4⋊C4×C31C2311yescharacteristic
84C42×C31C2311yescharacteristic
85C22⋊Dic31—21no—
86C22⋊Dic31—21no—
87(C2×D31)⋊C4—21no—
88(C2×D31)⋊C4—21no—
89(C2×D31)⋊C4—21no—
90(C2×D31)⋊C4D411yescharacteristic
91(C2×D31)⋊C4D411yescharacteristic
92C4⋊Dic31—21no—
93C4⋊Dic31C2311yescharacteristic
94C4⋊Dic31C2311yescharacteristic
95Dic31⋊C4—21no—
96Dic31⋊C4—21no—
97Dic31⋊C4—21no—
98Dic31⋊C4—21no—
99Dic31⋊C4—21no—
100Dic31⋊C4D411yescharacteristic
101Dic31⋊C4D411yescharacteristic
102C4×Dic31—21no—
103C4×Dic31C2311yescharacteristic
104C2×C31⋊C8C2311yescharacteristic
105C2×C31⋊C8C2311yescharacteristic
106#92469—22no—
107C8×D31—22no—
108C23×C31—21no—
109C23×C31—21no—
110C22×D31—21no—
111C22×D31—42no—
112C22×D31—81no—
113C22×D31—81no—
114C22×D31C2×D411yescharacteristic
115Q8×C31—81no—
116D4×C31—21no—
117D4×C31—21no—
118D4×C31—21no—
119D4×C31—21no—
120D4×C31—81no—
121D4×C31—81no—
122C2×C4×C31—21no—
123C2×C4×C31—21no—
124C2×C4×C31C2×D411yescharacteristic
125C2×C4×C31C2×D411yescharacteristic
126C2×C4×C31C2411yescharacteristic
127C22⋊D31—42no—
128C22⋊D31—42no—
129C22⋊D31—81no—
130C22⋊D31—81no—
131C2×Dic31—21no—
132C2×Dic31—21no—
133C2×Dic31—21no—
134C2×Dic31—42no—
135C2×Dic31C2×D411yescharacteristic
136C2×Dic31C2×D411yescharacteristic
137C2×Dic31C2×D411yescharacteristic
138D124—21no—
139D124—21no—
140C4×D31—81no—
141C4×D31#4112yes—
142C4×D31#4112yes—
143Dic62—21no—
144Dic62—21no—
145Dic62—81no—
146C8×C31—21no—
147C8×C31—21no—
148C31⋊C8—21no—
149C31⋊C8—21no—
150#3136—311nomaximal, Sylow
151C22×C31—41no—
152C22×C31—41no—
153C22×C31—41no—
154C22×C31—41no—
155C22×C31—41no—
156C22×C31—41no—
157C22×C31C22×D411yescharacteristic
158C2×D31—21no—
159C2×D31—21no—
160C2×D31—41no—
161C2×D31—41no—
162C2×D31—41no—
163C2×D31—84no—
164C2×D31#12412yes—
165C4×C31—21no—
166C4×C31—21no—
167C4×C31—41no—
168C4×C31—41no—
169C4×C31C2×#4111yescharacteristic
170C4×C31C2×#4111yescharacteristic
171Dic31—21no—
172Dic31—21no—
173Dic31—41no—
174Dic31—41no—
175Dic31—41no—
176Dic31#12412yes—
177#544—311no—
178#535—311no—
179#490—311no—
180#490—311no—
181#489—311no—
182#489—311no—
183#488—311no—
184#488—311no—
185#486—311no—
186#486D3111yescharacteristic, complemented
187#418—311no—
188#417—311no—
189#416—311no—
190C2×#102—311no—
191#405—311no—
192C2×C31—81no—
193C2×C31—81no—
194C2×C31C2×#12411yescharacteristic
195C2×C31#57611yescharacteristic
196C2×C31#57711yescharacteristic
197D31—22no—
198D31—81no—
199C2×#41—311no—
200C22×D4—311no—
201C2×M16—311no—
202C22×C8—311no—
203C4⋊Q8—311no—
204C4⋊Q8—621no—
205C4⋊Q8C2×D3111yescharacteristic, complemented
206#127—311no—
207#127C2×D3111yescharacteristic
208#125—311no—
209#125—311no—
210#125—621no—
211#124—311no—
212#124—311no—
213C22⋊Q8—621no—
214C22⋊Q8—621no—
215#121—621no—
216#121—621no—
217#120—621no—
218#120—621no—
219#117—311no—
220#117—311no—
221C2×C4⋊C4—311no—
222#103—311no—
223#103—311no—
224#103—311no—
225#103—311no—
226#102—311no—
227#102—311no—
228#102—311no—
229#102—311no—
230#102—311no—
231#102—311no—
232#102—311no—
233#102—311no—
234#102C2×D3111yescharacteristic
235#102C2×D3111yescharacteristic
236#102C2×D3111yescharacteristic, complemented
237#102C2×D3111yescharacteristic, complemented
238#97—311no—
239#97—311no—
240C4×C8—311no—
241C4×C8C2×D3111yescharacteristic, complemented
242C31#313611yescharacteristic, complemented, Sylow
243C24—621no—
244#41—622no—
245#41—622no—
246C2×Q8—21no—
247C2×Q8—311no—
248C2×Q8—621no—
249C2×D4—21no—
250C2×D4—21no—
251C2×D4—311no—
252C2×D4—622no—
253C2×D4—622no—
254C2×D4—621no—
255C2×D4—621no—
256C2×D4—621no—
257C2×D4—621no—
258C2×D4C22×D3111yescharacteristic
259C2×D4C22×D3111yescharacteristic
260C22×C4—311no—
261C22×C4—621no—
262C22×C4—621no—
263M16—622no—
264C2×C8—311no—
265C2×C8—311no—
266C2×C8—622no—
267C2×C8C22×D3111yescharacteristic
268C2×C8C22×D3111yescharacteristic
269C4⋊C4—21no—
270C4⋊C4—311no—
271C4⋊C4—311no—
272C4⋊C4—311no—
273C4⋊C4—311no—
274C4⋊C4—621no—
275C4⋊C4—621no—
276C4⋊C4—621no—
277C4⋊C4—621no—
278C4⋊C4—621no—
279C4⋊C4—621no—
280C4⋊C4C22×D3111yescharacteristic
281C4⋊C4C22×D3111yescharacteristic
282C22⋊C4—311no—
283C22⋊C4—311no—
284C22⋊C4—621no—
285C22⋊C4—621no—
286C22⋊C4—621no—
287C22⋊C4—621no—
288C22⋊C4—621no—
289C42—311no—
290C42—621no—
291C42C22×D3111yescharacteristic
292C23—21no—
293C23—21no—
294C23—311no—
295C23—621no—
296C23—1242no—
297C23—2481no—
298C23—2481no—
299Q8—81no—
300Q8—621no—
301Q8—621no—
302Q8—2481no—
303D4—21no—
304D4—21no—
305D4—21no—
306D4—21no—
307D4—81no—
308D4—81no—
309D4—621no—
310D4—621no—
311D4—1242no—
312D4—1242no—
313D4—2481no—
314D4—2481no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—311no—
318C2×C4—312no—
319C2×C4—312no—
320C2×C4—311no—
321C2×C4—311no—
322C2×C4—621no—
323C2×C4—621no—
324C2×C4—621no—
325C2×C4—1242no—
326C2×C4—2481no—
327C2×C4D4×D3111yescharacteristic
328C2×C4D4×D3111yescharacteristic
329C2×C4C23×D3111yescharacteristic
330C8—21no—
331C8—21no—
332C8—621no—
333C8—621no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—312no—
341C22—621no—
342C22—621no—
343C22—1241no—
344C22—1241no—
345C22—1241no—
346C22—2484no—
347C22C2×D4×D3111yescharacteristic
348C4—21no—
349C4—21no—
350C4—41no—
351C4—41no—
352C4—312no—
353C4—621no—
354C4—621no—
355C4—1241no—
356C4—1241no—
357C4—1241no—
358C4#41×D3111yescharacteristic
359C4#41×D3111yescharacteristic
360C2—81no—
361C2—81no—
362C2—622no—
363C2—2481no—
364C2#124×D3111yescharacteristic
365C2#1452185011yescharacteristic
366C2#1452185511yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#486C2
socleC22×C31C22×D4
prime radical#14521612C2
hypercenter#486D31
hypocenterC31#3136
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #14521676C2semidirect
3. #14521413C2semidirect
4. #14521412C2semidirect
5. #14521411C2semidirect
6. #14521407C2semidirect
7. #14521404C2semidirect
8. #14521402C2semidirect
9. #14521394C2semidirect
10. #14521052C2semidirect
11. #14521047C2semidirect
12. #14521042C2semidirect
13. #102×D31C2semidirect
14. #14521003C2semidirect
15. C31×#486C2semidirect
18. C31×C4⋊Q8C22semidirect
33. #11758467C22semidirect
35. #11758465C22semidirect
38. #11758447C22semidirect
41. C31×#102C22semidirect
42. C31×#102C22semidirect
43. C4×C8×C31C22semidirect
46. #11758420C22semidirect
47. #11758420C22semidirect
50. #11758404C22semidirect
51. #11758404C22semidirect
52. #11758403C22semidirect
53. C8×Dic31C22semidirect
54. #11758398C22semidirect
55. #11758398C22semidirect
58. #11758391C22semidirect
186. #486D31semidirect
205. C4⋊Q8C2×D31semidirect
236. #102C2×D31semidirect
237. #102C2×D31semidirect
241. C4×C8C2×D31semidirect
242. C31#3136semidirect

Maximal subgroups

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

subgroupindex
#145216762
#145216122
#145214132
#145214122
#145214112
#145214072
#145214042
#145214022
#145213942
#145210522
#145210472
#145210422
#102×D312
#145210032
C31×#4862
#313631