Finite Group Databasebeta

← #16855896

Subgroups — #16855896

Order 3968.

406 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14521672C211yesmaximal, characteristic, complemented
2#14521524C211yesmaximal, characteristic, complemented
3#14521387C211yesmaximal, characteristic, complemented
4#14521374C211yesmaximal, characteristic, complemented
5#14521337C211yesmaximal, characteristic, complemented
6#14521327C211yesmaximal, characteristic, complemented
7#14521266C211yesmaximal, characteristic, complemented
8#14521266C211yesmaximal, characteristic, complemented
9#14521183C211yesmaximal, characteristic
10#14521158C211yesmaximal, characteristic, complemented
11#14521150C211yesmaximal, characteristic, complemented
12SD16×Dic31C211yesmaximal, characteristic, complemented
13#14521129C211yesmaximal, characteristic, complemented
14#14521107C211yesmaximal, characteristic, complemented
15C31×#450C211yesmaximal, characteristic, complemented
16C22×D4×C31C2211yescharacteristic
17C2×SD16×C31C2211yescharacteristic
18C2×SD16×C31C2211yescharacteristic
19C31×C22⋊Q8C2211yescharacteristic
20C2×C22⋊Dic31—21no—
21C2×C22⋊Dic31—21no—
22#11758524C2211yescharacteristic, complemented
23Q8×Dic31C2211yescharacteristic, complemented
24D4×Dic31—21no—
25D4×Dic31—21no—
26D4×Dic31C2211yescharacteristic
27D4×Dic31C2211yescharacteristic
28D4×Dic31C2211yescharacteristic
29D4×Dic31C2211yescharacteristic
30C2×#92479C2211yescharacteristic
31C2×#92479C2211yescharacteristic
32#11758507C2211yescharacteristic
33#11758503C2211yescharacteristic
34#11758503C2211yescharacteristic
35#11758475—21no—
36#11758474—21no—
37#11758470C2211yescharacteristic, complemented
38#11758465C2211yescharacteristic, complemented
39#11758462—21no—
40#11758460—21no—
41C31×#102C2211yescharacteristic
42C31×#102C2211yescharacteristic
43C31×C22⋊C8C2211yescharacteristic
44#11758423C2211yescharacteristic, complemented
45#11758423C2211yescharacteristic, complemented
46#11758420C2211yescharacteristic
47#11758420C2211yescharacteristic
48C22⋊(C31⋊C8)C2211yescharacteristic
49#11758409C2211yescharacteristic, complemented
50#11758409C2211yescharacteristic, complemented
51#11758406C2211yescharacteristic, complemented
52#11758405C2211yescharacteristic, complemented
53#11758403C2211yescharacteristic, complemented
54Dic31⋊C8C2211yescharacteristic, complemented
55Dic31⋊C8C2211yescharacteristic, complemented
56C8×Dic31C2211yescharacteristic, complemented
57#11758396C2211yescharacteristic, complemented
58#11758395C2211yescharacteristic, complemented
59C24×C31—21no—
60C2×Q8×C31C2311yescharacteristic
61C2×D4×C31—22no—
62C2×D4×C31—22no—
63C2×D4×C31—21no—
64C2×D4×C31C2311yescharacteristic
65C2×D4×C31C2311yescharacteristic
66C22×C4×C31C2311yescharacteristic
67C2×C22⋊D31—21no—
68C22×Dic31—21no—
69C22×Dic31—21no—
70C22×Dic31—21no—
71C22×Dic31—21no—
72C2×D124C2311yescharacteristic
73C2×C4×D31—21no—
74C2×Dic62—21no—
75SD16×C31—22no—
76SD16×C31—22no—
77C2×C8×C31C2311yescharacteristic
78C2×C8×C31C2311yescharacteristic
79C4⋊C4×C31—21no—
80C4⋊C4×C31C2311yescharacteristic
81C22⋊C4×C31—21no—
82C22⋊Dic31—21no—
83C22⋊Dic31—21no—
84C22⋊Dic31—21no—
85C22⋊Dic31—21no—
86C22⋊Dic31—21no—
87C22⋊Dic31D411yescharacteristic
88C22⋊Dic31D411yescharacteristic
89#92479—22no—
90#92479—22no—
91(C2×D31)⋊C4—21no—
92(C2×D31)⋊C4—21no—
93(C2×D31)⋊C4—21no—
94(C2×D31)⋊C4—21no—
95C4⋊Dic31—21no—
96C4⋊Dic31D411yescharacteristic
97C4⋊Dic31D411yescharacteristic
98C4⋊Dic31C2311yescharacteristic
99C4⋊Dic31C2311yescharacteristic
100C4⋊Dic31C2311yescharacteristic
101Dic31⋊C4—21no—
102C4×Dic31—21no—
103C4×Dic31—21no—
104C4×Dic31C2311yescharacteristic
105C4×Dic31C2311yescharacteristic
106C2×C31⋊C8C2311yescharacteristic
107C2×C31⋊C8C2311yescharacteristic
108C23×C31—24no—
109C23×C31—21no—
110C23×C31—21no—
111C23×C31—81no—
112C23×C31—81no—
113C23×C31C2×D411yescharacteristic
114C22×D31—21no—
115Q8×C31—21no—
116Q8×C31—21no—
117D4×C31—24no—
118D4×C31—21no—
119D4×C31—21no—
120D4×C31#4112yes—
121D4×C31#4112yes—
122C2×C4×C31—21no—
123C2×C4×C31—21no—
124C2×C4×C31—21no—
125C2×C4×C31—21no—
126C2×C4×C31C2×D411yescharacteristic
127C2×C4×C31C2411yescharacteristic
128C22⋊D31—81no—
129C2×Dic31—21no—
130C2×Dic31—21no—
131C2×Dic31—21no—
132C2×Dic31—81no—
133C2×Dic31—81no—
134C2×Dic31—81no—
135C2×Dic31—81no—
136C2×Dic31C2×D411yescharacteristic
137C2×Dic31C2×D411yescharacteristic
138C2×Dic31C2×D411yescharacteristic
139C2×Dic31C2×D411yescharacteristic
140D124—21no—
141D124—21no—
142C4×D31—81no—
143Dic62—81no—
144C8×C31—21no—
145C8×C31—21no—
146C31⋊C8—21no—
147C31⋊C8—21no—
148#3118—311nomaximal, Sylow
149C22×C31—21no—
150C22×C31—22no—
151C22×C31—22no—
152C22×C31—21no—
153C22×C31—21no—
154C22×C31—41no—
155C22×C31—41no—
156C22×C31—41no—
157C22×C31—41no—
158C22×C31—84no—
159C22×C31C22×D411yescharacteristic
160C2×D31—41no—
161C2×D31—41no—
162C2×D31—41no—
163C4×C31—21no—
164C4×C31—41no—
165C4×C31—41no—
166C4×C31C2×#4111yescharacteristic
167C4×C31C2×#4111yescharacteristic
168Dic31—21no—
169Dic31—21no—
170Dic31—21no—
171Dic31—21no—
172Dic31—41no—
173Dic31—41no—
174Dic31—41no—
175#542—311no—
176#518—311no—
177#485—311no—
178#482—311no—
179#476—311no—
180#474—311no—
181#463—311no—
182#463—311no—
183#450D3111yescharacteristic, complemented
184#447—311no—
185#442—311no—
186#440—311no—
187C4×SD16—311no—
188C4×D8—311no—
189#433—311no—
190C2×C31—41no—
191C2×C31—42no—
192C2×C31—42no—
193C2×C31#52511yescharacteristic
194C2×C31#57611yescharacteristic
195C2×C31#57711yescharacteristic
196D31—81no—
197C22×D4C2×D3111yescharacteristic
198C2×SD16C2×D3111yescharacteristic
199C2×SD16C2×D3111yescharacteristic
200C2×D8—311no—
201C2×D8—311no—
202C4⋊Q8—311no—
203#126—621no—
204#124—311no—
205#124—621no—
206#123—621no—
207C22⋊Q8—621no—
208C22⋊Q8C2×D3111yescharacteristic
209#121—311no—
210C4×Q8—311no—
211C4×D4—311no—
212C4×D4—311no—
213C4×D4—311no—
214C4×D4—311no—
215C4×D4—311no—
216C4×D4—621no—
217C4×D4—621no—
218#117—311no—
219#117—311no—
220C2×C22⋊C4—621no—
221C2×C22⋊C4—621no—
222#107—311no—
223#107—311no—
224#106—311no—
225#106—311no—
226C4⋊C8—311no—
227C4⋊C8—311no—
228#103—311no—
229#103—311no—
230#102—311no—
231#102—311no—
232#102—311no—
233#102—311no—
234#102C2×D3111yescharacteristic
235#102C2×D3111yescharacteristic
236C22⋊C8—311no—
237C22⋊C8C2×D3111yescharacteristic
238#97—311no—
239C4×C8—311no—
240C31#311811yescharacteristic, complemented, Sylow
241C24—21no—
242C2×Q8—621no—
243C2×Q8C22×D3111yescharacteristic
244C2×D4—22no—
245C2×D4—22no—
246C2×D4—21no—
247C2×D4—311no—
248C2×D4—621no—
249C2×D4C22×D3111yescharacteristic
250C2×D4C22×D3111yescharacteristic
251C22×C4—621no—
252C22×C4—621no—
253C22×C4—621no—
254C22×C4—621no—
255C22×C4—621no—
256C22×C4C22×D3111yescharacteristic
257SD16—22no—
258SD16—22no—
259D8—622no—
260D8—622no—
261C2×C8—311no—
262C2×C8—311no—
263C2×C8C22×D3111yescharacteristic
264C2×C8C22×D3111yescharacteristic
265C4⋊C4—21no—
266C4⋊C4—311no—
267C4⋊C4—311no—
268C4⋊C4—311no—
269C4⋊C4—311no—
270C4⋊C4—311no—
271C4⋊C4—621no—
272C4⋊C4—621no—
273C4⋊C4C22×D3111yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—311no—
276C22⋊C4—311no—
277C22⋊C4—621no—
278C22⋊C4—621no—
279C22⋊C4—621no—
280C22⋊C4—621no—
281C22⋊C4—621no—
282C22⋊C4—621no—
283C22⋊C4—621no—
284C22⋊C4—621no—
285C22⋊C4—621no—
286C42—311no—
287C42—311no—
288C42—621no—
289C42—621no—
290C23—24no—
291C23—21no—
292C23—21no—
293C23—81no—
294C23—81no—
295C23—621no—
296C23D4×D3111yescharacteristic
297Q8—21no—
298Q8—21no—
299Q8—2481no—
300D4—24no—
301D4—21no—
302D4—21no—
303D4—621no—
304D4—621no—
305D4—2481no—
306D4#9249712yes—
307D4#9249712yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—311no—
313C2×C4—311no—
314C2×C4—311no—
315C2×C4—311no—
316C2×C4—621no—
317C2×C4—621no—
318C2×C4—621no—
319C2×C4—2481no—
320C2×C4—2481no—
321C2×C4—2481no—
322C2×C4—2481no—
323C2×C4—2481no—
324C2×C4D4×D3111yescharacteristic
325C2×C4C23×D3111yescharacteristic
326C8—21no—
327C8—21no—
328C8—621no—
329C8—621no—
330C22—21no—
331C22—22no—
332C22—22no—
333C22—21no—
334C22—21no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—84no—
340C22—1241no—
341C22—1241no—
342C22—1241no—
343C22C2×D4×D3111yescharacteristic
344C4—21no—
345C4—41no—
346C4—41no—
347C4—621no—
348C4—621no—
349C4—621no—
350C4—621no—
351C4—1241no—
352C4—1241no—
353C4—1241no—
354C4C2×#9249711yescharacteristic
355C4C2×#9249711yescharacteristic
356C2—41no—
357C2—42no—
358C2—42no—
359C2—2481no—
360C2#1452155511yescharacteristic
361C2#1452185311yescharacteristic
362C2#1452185511yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#450C2
socleC22×C31C22×D4
prime radical#14521183C2
hypercenter#450D31
hypocenterC31#3118
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. #14521672C2semidirect
2. #14521524C2semidirect
3. #14521387C2semidirect
4. #14521374C2semidirect
5. #14521337C2semidirect
6. #14521327C2semidirect
7. #14521266C2semidirect
8. #14521266C2semidirect
10. #14521158C2semidirect
11. #14521150C2semidirect
12. SD16×Dic31C2semidirect
13. #14521129C2semidirect
14. #14521107C2semidirect
15. C31×#450C2semidirect
22. #11758524C22semidirect
23. Q8×Dic31C22semidirect
37. #11758470C22semidirect
38. #11758465C22semidirect
44. #11758423C22semidirect
45. #11758423C22semidirect
49. #11758409C22semidirect
50. #11758409C22semidirect
51. #11758406C22semidirect
52. #11758405C22semidirect
53. #11758403C22semidirect
54. Dic31⋊C8C22semidirect
55. Dic31⋊C8C22semidirect
56. C8×Dic31C22semidirect
57. #11758396C22semidirect
58. #11758395C22semidirect
183. #450D31semidirect
240. C31#3118semidirect

Maximal subgroups

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

subgroupindex
#145216722
#145215242
#145213872
#145213742
#145213372
#145213272
#145212662
#145211832
#145211582
#145211502
SD16×Dic312
#145211292
#145211072
C31×#4502
#311831