Finite Group Databasebeta

← #16855847

Subgroups — #16855847

Order 3968.

450 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14521581C211yesmaximal, characteristic, complemented
2C4×D4×D31C211yesmaximal, characteristic, complemented
3#14521381C211yesmaximal, characteristic, complemented
4#14521361C211yesmaximal, characteristic, complemented
5#14521348C211yesmaximal, characteristic, complemented
6#14521347C211yesmaximal, characteristic, complemented
7#14521263C211yesmaximal, characteristic, complemented
8#14521262C211yesmaximal, characteristic, complemented
9#14521201C211yesmaximal, characteristic, complemented
10#14521181C211yesmaximal, characteristic
11#14521159C211yesmaximal, characteristic, complemented
12#14521151C211yesmaximal, characteristic, complemented
13#14521149C211yesmaximal, characteristic, complemented
14#14521104C211yesmaximal, characteristic, complemented
15C31×#442C211yesmaximal, characteristic, complemented
16C2×D4×D31C2211yescharacteristic
17C22×C4×D31—21no—
18C2×D8×C31C2211yescharacteristic
19C4×D4×C31C2211yescharacteristic
20C4×D4×C31C2211yescharacteristic, complemented
21#11758515C2211yescharacteristic
22#11758513C2211yescharacteristic, complemented
23D4×Dic31C2211yescharacteristic
24C2×#92480C2211yescharacteristic
25C2×#92479C2211yescharacteristic
26C4×C22⋊D31—21no—
27C4×C22⋊D31—21no—
28#11758503—21no—
29C2×#92470C2211yescharacteristic
30#11758474C2211yescharacteristic
31#11758470C2211yescharacteristic
32C4⋊C4×D31C2211yescharacteristic
33#11758467C2211yescharacteristic, complemented
34#11758460—21no—
35(C22⋊D31)⋊C4—21no—
36C22⋊C4×D31—21no—
37#11758456—21no—
38C4×D124C2211yescharacteristic
39C42×D31C2211yescharacteristic
40C4×Dic62C2211yescharacteristic, complemented
41C31×#106C2211yescharacteristic, complemented
42C31×#102C2211yescharacteristic
43C31×#102C2211yescharacteristic, complemented
44C31×#97C2211yescharacteristic, complemented
45#11758420C2211yescharacteristic
46#11758420C2211yescharacteristic, complemented
47#11758409C2211yescharacteristic
48(C2×D31)⋊C8C2211yescharacteristic
49(C2×D31)⋊C8C2211yescharacteristic
50#11758406C2211yescharacteristic, complemented
51#11758404C2211yescharacteristic, complemented
52Dic31⋊C8C2211yescharacteristic, complemented
53Dic31⋊C8C2211yescharacteristic, complemented
54#11758398C2211yescharacteristic, complemented
55#11758397C2211yescharacteristic
56#11758396C2211yescharacteristic, complemented
57#11758395C2211yescharacteristic, complemented
58#11758391C2211yescharacteristic, complemented
59C23×D31—21no—
60C2×D4×C31C2311yescharacteristic
61C2×D4×C31C2311yescharacteristic
62C22×C4×C31—21no—
63C22×C4×C31—21no—
64C2×C22⋊D31—21no—
65C2×C22⋊D31—21no—
66C22×Dic31—21no—
67D4×D31—22no—
68D4×D31—22no—
69C2×D124C2311yescharacteristic
70C2×C4×D31—21no—
71C2×C4×D31—21no—
72C2×C4×D31—21no—
73C2×C4×D31—44no—
74C2×C4×D31D411yescharacteristic
75C2×C4×D31D411yescharacteristic
76C2×C4×D31C2311yescharacteristic
77C2×Dic62C2311yescharacteristic
78D8×C31—22no—
79C2×C8×C31C2311yescharacteristic
80C2×C8×C31C2311yescharacteristic
81C4⋊C4×C31C2311yescharacteristic
82C4⋊C4×C31C2311yescharacteristic
83C22⋊C4×C31—21no—
84C22⋊C4×C31—21no—
85C42×C31C2311yescharacteristic
86C22⋊Dic31—21no—
87C22⋊Dic31—21no—
88C22⋊Dic31—21no—
89C22⋊Dic31—21no—
90#92480—22no—
91#92479—22no—
92(C2×D31)⋊C4—21no—
93(C2×D31)⋊C4—21no—
94(C2×D31)⋊C4—21no—
95C4⋊Dic31—21no—
96C4⋊Dic31—21no—
97C4⋊Dic31C2311yescharacteristic
98C4⋊Dic31C2311yescharacteristic
99Dic31⋊C4—21no—
100Dic31⋊C4—21no—
101Dic31⋊C4—21no—
102C4×Dic31—21no—
103C4×Dic31D411yescharacteristic
104C4×Dic31D411yescharacteristic
105C4×Dic31C2311yescharacteristic
106C2×C31⋊C8C2311yescharacteristic
107C2×C31⋊C8C2311yescharacteristic
108#92470—22no—
109C23×C31—21no—
110C23×C31—21no—
111C22×D31—24no—
112C22×D31—21no—
113C22×D31—42no—
114C22×D31—42no—
115C22×D31C2×D411yescharacteristic
116D4×C31—21no—
117D4×C31—21no—
118D4×C31—21no—
119D4×C31#4112yes—
120C2×C4×C31—21no—
121C2×C4×C31—21no—
122C2×C4×C31—42no—
123C2×C4×C31—42no—
124C2×C4×C31C2×D411yescharacteristic
125C2×C4×C31C2×D411yescharacteristic
126C2×C4×C31C2411yescharacteristic
127C22⋊D31—24no—
128C22⋊D31—42no—
129C2×Dic31—21no—
130C2×Dic31—21no—
131C2×Dic31—21no—
132C2×Dic31—42no—
133C2×Dic31C2×D411yescharacteristic
134C2×Dic31C2×D411yescharacteristic
135C2×Dic31C2×D411yescharacteristic
136D124—21no—
137D124#4112yes—
138C4×D31—22no—
139C4×D31—21no—
140C4×D31—21no—
141C4×D31—41no—
142C4×D31—42no—
143C4×D31—42no—
144C4×D31—42no—
145Dic62—21no—
146Dic62—21no—
147C8×C31—21no—
148C8×C31—21no—
149C31⋊C8—21no—
150C31⋊C8—21no—
151#3114—311nomaximal, Sylow
152C22×C31—22no—
153C22×C31—41no—
154C22×C31—41no—
155C22×C31—41no—
156C22×C31—41no—
157C22×C31—41no—
158C22×C31C22×D411yescharacteristic
159C2×D31—21no—
160C2×D31—21no—
161C2×D31—22no—
162C2×D31—48no—
163C2×D31—41no—
164C2×D31—41no—
165C2×D31AGL(1,ℤ/8)12yes—
166C4×C31—21no—
167C4×C31—21no—
168C4×C31—41no—
169C4×C31—41no—
170C4×C31C2×#4111yescharacteristic
171C4×C31C2×#4111yescharacteristic
172Dic31—21no—
173Dic31—21no—
174Dic31—21no—
175Dic31—41no—
176Dic31—41no—
177Dic31—41no—
178#529—311no—
179C2×C4×D4—311no—
180#483—311no—
181#480—311no—
182#478—311no—
183#478—311no—
184#463—311no—
185#463—311no—
186#450—311no—
187#447—311no—
188#442—311no—
189#442D3111yescharacteristic, complemented
190#440—311no—
191#440—311no—
192#432—311no—
193C2×C31—42no—
194C2×C31—81no—
195C2×C31#52511yescharacteristic
196C2×C31C2×AGL(1,ℤ/8)11yescharacteristic
197C2×C31#57511yescharacteristic
198D31—22no—
199D31—42no—
200C22×D4—311no—
201C23×C4—621no—
202C2×SD16—311no—
203C2×SD16—311no—
204C2×D8—311no—
205C2×D8C2×D3111yescharacteristic
206#126—621no—
207#125—311no—
208#124—311no—
209#123—621no—
210C22⋊Q8—311no—
211#121—311no—
212C4×Q8—311no—
213C4×D4—311no—
214C4×D4—311no—
215C4×D4—311no—
216C4×D4—621no—
217C4×D4—621no—
218C4×D4—621no—
219C4×D4C2×D3111yescharacteristic
220C4×D4C2×D3111yescharacteristic, complemented
221#117—621no—
222C2×C4⋊C4—311no—
223C2×C22⋊C4—621no—
224C2×C42—311no—
225#107—311no—
226#107—311no—
227#106—311no—
228#106C2×D3111yescharacteristic, complemented
229C4⋊C8—311no—
230C4⋊C8—311no—
231#103—311no—
232#103—311no—
233#102—311no—
234#102—311no—
235#102—311no—
236#102—311no—
237#102C2×D3111yescharacteristic
238#102C2×D3111yescharacteristic, complemented
239C22⋊C8—311no—
240C22⋊C8—311no—
241#97—311no—
242#97C2×D3111yescharacteristic, complemented
243C31#311411yescharacteristic, complemented, Sylow
244C24—621no—
245C2×Q8—311no—
246C2×D4—311no—
247C2×D4—621no—
248C2×D4—622no—
249C2×D4—622no—
250C2×D4—621no—
251C2×D4C22×D3111yescharacteristic
252C2×D4C22×D3111yescharacteristic
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—311no—
256C22×C4—311no—
257C22×C4—311no—
258C22×C4—621no—
259C22×C4—621no—
260C22×C4—621no—
261C22×C4—621no—
262C22×C4—1244no—
263SD16—622no—
264SD16—622no—
265D8—22no—
266D8—622no—
267C2×C8—311no—
268C2×C8—311no—
269C2×C8C22×D3111yescharacteristic
270C2×C8C22×D3111yescharacteristic
271C4⋊C4—311no—
272C4⋊C4—311no—
273C4⋊C4—621no—
274C4⋊C4—621no—
275C4⋊C4—621no—
276C4⋊C4—621no—
277C4⋊C4—621no—
278C4⋊C4C22×D3111yescharacteristic
279C4⋊C4C22×D3111yescharacteristic
280C22⋊C4—21no—
281C22⋊C4—21no—
282C22⋊C4—621no—
283C22⋊C4—621no—
284C22⋊C4—621no—
285C22⋊C4—621no—
286C22⋊C4—621no—
287C22⋊C4—621no—
288C22⋊C4—621no—
289C42—311no—
290C42—311no—
291C42—311no—
292C42—621no—
293C42C22×D3111yescharacteristic
294C23—21no—
295C23—21no—
296C23—311no—
297C23—624no—
298C23—621no—
299C23—1242no—
300C23—1242no—
301Q8—621no—
302Q8—621no—
303D4—21no—
304D4—21no—
305D4—21no—
306D4—312no—
307D4—624no—
308D4—621no—
309D4—1242no—
310D4#9249512yes—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—311no—
316C2×C4—311no—
317C2×C4—311no—
318C2×C4—622no—
319C2×C4—621no—
320C2×C4—621no—
321C2×C4—621no—
322C2×C4—621no—
323C2×C4—621no—
324C2×C4—1241no—
325C2×C4—1242no—
326C2×C4—1242no—
327C2×C4—1242no—
328C2×C4—1242no—
329C2×C4D4×D3111yescharacteristic
330C2×C4D4×D3111yescharacteristic
331C2×C4C23×D3111yescharacteristic
332C8—21no—
333C8—21no—
334C8—621no—
335C8—621no—
336C22—22no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—312no—
343C22—621no—
344C22—621no—
345C22—622no—
346C22—1248no—
347C22—1241no—
348C22—1241no—
349C22C2×D4×D3111yescharacteristic
350C4—21no—
351C4—21no—
352C4—41no—
353C4—41no—
354C4—621no—
355C4—621no—
356C4—621no—
357C4—1241no—
358C4—1241no—
359C4—1241no—
360C4C2×#9249511yescharacteristic
361C4#41×D3111yescharacteristic
362C2—42no—
363C2—81no—
364C2—622no—
365C2—1242no—
366C2#1452155811yescharacteristic
367C2AGL(1,ℤ/8)×D3111yescharacteristic
368C2#1452184511yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#442C2
socleC22×C31C22×D4
prime radical#14521181C2
hypercenter#442D31
hypocenterC31#3114
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #14521581C2semidirect
2. C4×D4×D31C2semidirect
3. #14521381C2semidirect
4. #14521361C2semidirect
5. #14521348C2semidirect
6. #14521347C2semidirect
7. #14521263C2semidirect
8. #14521262C2semidirect
9. #14521201C2semidirect
11. #14521159C2semidirect
12. #14521151C2semidirect
13. #14521149C2semidirect
14. #14521104C2semidirect
15. C31×#442C2semidirect
20. C4×D4×C31C22semidirect
22. #11758513C22semidirect
33. #11758467C22semidirect
40. C4×Dic62C22semidirect
41. C31×#106C22semidirect
43. C31×#102C22semidirect
44. C31×#97C22semidirect
46. #11758420C22semidirect
50. #11758406C22semidirect
51. #11758404C22semidirect
52. Dic31⋊C8C22semidirect
53. Dic31⋊C8C22semidirect
54. #11758398C22semidirect
56. #11758396C22semidirect
57. #11758395C22semidirect
58. #11758391C22semidirect
189. #442D31semidirect
220. C4×D4C2×D31semidirect
228. #106C2×D31semidirect
238. #102C2×D31semidirect
242. #97C2×D31semidirect
243. C31#3114semidirect

Maximal subgroups

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

subgroupindex
#145215812
C4×D4×D312
#145213812
#145213612
#145213482
#145213472
#145212632
#145212622
#145212012
#145211812
#145211592
#145211512
#145211492
#145211042
C31×#4422
#311431