Finite Group Databasebeta

← #16855853

Subgroups — #16855853

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#14521586C211yesmaximal, characteristic, complemented
2C4×D4×D31C211yesmaximal, characteristic, complemented
3#14521378C211yesmaximal, characteristic, complemented
4#14521364C211yesmaximal, characteristic, complemented
5#14521352C211yesmaximal, characteristic, complemented
6#14521351C211yesmaximal, characteristic, complemented
7#14521267C211yesmaximal, characteristic, complemented
8#14521266C211yesmaximal, characteristic, complemented
9#14521198C211yesmaximal, characteristic, complemented
10#14521184C211yesmaximal, characteristic
11#14521162C211yesmaximal, characteristic, complemented
12#14521159C211yesmaximal, characteristic, complemented
13#14521147C211yesmaximal, characteristic, complemented
14#14521104C211yesmaximal, characteristic, complemented
15C31×#440C211yesmaximal, characteristic, complemented
16C2×D4×D31C2211yescharacteristic
17C22×C4×D31—21no—
18C2×SD16×C31C2211yescharacteristic
19C4×Q8×C31C2211yescharacteristic, complemented
20C4×D4×C31C2211yescharacteristic
21#11758524C2211yescharacteristic, complemented
22#11758523C2211yescharacteristic
23C2×#92481C2211yescharacteristic
24D4×Dic31C2211yescharacteristic
25C2×#92479C2211yescharacteristic
26C4×C22⋊D31—21no—
27C2×D248C2211yescharacteristic
28#11758475—21no—
29#11758472C2211yescharacteristic
30#11758471—21no—
31#11758470C2211yescharacteristic
32C4⋊C4×D31C2211yescharacteristic
33#11758467C2211yescharacteristic, complemented
34(C22⋊D31)⋊C4—21no—
35C22⋊C4×D31—21no—
36C4×D124—21no—
37C4×D124C2211yescharacteristic
38C4×D124C2211yescharacteristic, complemented
39#11758449—21no—
40C42×D31C2211yescharacteristic
41C31×#107C2211yescharacteristic, complemented
42C31×#103C2211yescharacteristic, complemented
43C31×#102C2211yescharacteristic
44C31×#97C2211yescharacteristic, complemented
45#11758423C2211yescharacteristic, complemented
46#11758420C2211yescharacteristic
47#11758409C2211yescharacteristic
48#11758409C2211yescharacteristic, complemented
49(C2×D31)⋊C8C2211yescharacteristic
50(C2×D31)⋊C8C2211yescharacteristic
51#11758405C2211yescharacteristic, complemented
52Dic31⋊C8C2211yescharacteristic, complemented
53Dic31⋊C8C2211yescharacteristic, complemented
54#11758397C2211yescharacteristic
55#11758397C2211yescharacteristic, complemented
56#11758396C2211yescharacteristic, complemented
57#11758395C2211yescharacteristic, complemented
58#11758391C2211yescharacteristic, complemented
59C23×D31—21no—
60C2×Q8×C31C2311yescharacteristic
61C2×D4×C31C2311yescharacteristic
62C22×C4×C31—21no—
63C2×C22⋊D31—21no—
64C22×Dic31—21no—
65D4×D31—22no—
66D4×D31—22no—
67C2×D124—21no—
68C2×D124C2311yescharacteristic
69C2×D124C2311yescharacteristic
70C2×C4×D31—21no—
71C2×C4×D31—21no—
72C2×C4×D31—21no—
73C2×C4×D31—21no—
74C2×C4×D31—44no—
75C2×C4×D31D411yescharacteristic
76C2×C4×D31D411yescharacteristic
77C2×C4×D31C2311yescharacteristic
78SD16×C31—22no—
79C2×C8×C31C2311yescharacteristic
80C2×C8×C31C2311yescharacteristic
81C4⋊C4×C31—21no—
82C4⋊C4×C31C2311yescharacteristic
83C4⋊C4×C31C2311yescharacteristic
84C22⋊C4×C31—21no—
85C42×C31—21no—
86C42×C31C2311yescharacteristic
87C22⋊Dic31—21no—
88#92481—22no—
89#92479—22no—
90(C2×D31)⋊C4—21no—
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)⋊C4—21no—
97C4⋊Dic31—21no—
98C4⋊Dic31C2311yescharacteristic
99C4⋊Dic31C2311yescharacteristic
100Dic31⋊C4—21no—
101Dic31⋊C4—21no—
102Dic31⋊C4—21no—
103C4×Dic31D411yescharacteristic
104C4×Dic31D411yescharacteristic
105C4×Dic31C2311yescharacteristic
106C2×C31⋊C8C2311yescharacteristic
107C2×C31⋊C8C2311yescharacteristic
108D248—22no—
109C23×C31—21no—
110C22×D31—24no—
111C22×D31—21no—
112C22×D31—21no—
113C22×D31—42no—
114C22×D31—42no—
115C22×D31C2×D411yescharacteristic
116Q8×C31—21no—
117Q8×C31—21no—
118D4×C31—21no—
119D4×C31#4112yes—
120C2×C4×C31—21no—
121C2×C4×C31—21no—
122C2×C4×C31—21no—
123C2×C4×C31—42no—
124C2×C4×C31C2×D411yescharacteristic
125C2×C4×C31C2×D411yescharacteristic
126C2×C4×C31C2411yescharacteristic
127C22⋊D31—24no—
128C2×Dic31—21no—
129C2×Dic31—21no—
130C2×Dic31—42no—
131C2×Dic31C2×D411yescharacteristic
132C2×Dic31C2×D411yescharacteristic
133C2×Dic31C2×D411yescharacteristic
134D124—21no—
135D124—21no—
136D124—21no—
137D124—42no—
138D124#4112yes—
139C4×D31—22no—
140C4×D31—21no—
141C4×D31—21no—
142C4×D31—41no—
143C4×D31—42no—
144C4×D31—42no—
145C4×D31—42no—
146C4×D31—42no—
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×C31C22×D411yescharacteristic
156C2×D31—21no—
157C2×D31—21no—
158C2×D31—22no—
159C2×D31—48no—
160C2×D31—41no—
161C2×D31—41no—
162C2×D31—41no—
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×C31—41no—
171C4×C31C2×#4111yescharacteristic
172C4×C31C2×#4111yescharacteristic
173Dic31—21no—
174Dic31—21no—
175Dic31—21no—
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#442—311no—
190#440—311no—
191#440D3111yescharacteristic, complemented
192#432—311no—
193C2×C31—42no—
194C2×C31#52511yescharacteristic
195C2×C31C2×AGL(1,ℤ/8)11yescharacteristic
196C2×C31#57511yescharacteristic
197D31—22no—
198D31—42no—
199D31—81no—
200C22×D4—311no—
201C23×C4—621no—
202C2×SD16—311no—
203C2×SD16C2×D3111yescharacteristic
204C2×D8—311no—
205C2×D8—311no—
206#126—621no—
207#125—311no—
208#124—311no—
209#123—621no—
210C22⋊Q8—311no—
211#121—311no—
212C4×Q8C2×D3111yescharacteristic, complemented
213C4×D4—311no—
214C4×D4—311no—
215C4×D4—311no—
216C4×D4—311no—
217C4×D4—621no—
218C4×D4—621no—
219C4×D4—621no—
220C4×D4C2×D3111yescharacteristic
221#117—621no—
222C2×C4⋊C4—311no—
223C2×C22⋊C4—621no—
224C2×C42—311no—
225#107—311no—
226#107C2×D3111yescharacteristic, complemented
227#106—311no—
228#106—311no—
229C4⋊C8—311no—
230C4⋊C8—311no—
231#103—311no—
232#103C2×D3111yescharacteristic, complemented
233#102—311no—
234#102—311no—
235#102—311no—
236#102—311no—
237#102—311no—
238#102C2×D3111yescharacteristic
239C22⋊C8—311no—
240C22⋊C8—311no—
241#97—311no—
242#97C2×D3111yescharacteristic, complemented
243C31#311411yescharacteristic, complemented, Sylow
244C24—621no—
245C2×Q8C22×D3111yescharacteristic
246C2×D4—311no—
247C2×D4—311no—
248C2×D4—621no—
249C2×D4—621no—
250C2×D4—622no—
251C2×D4—622no—
252C2×D4C22×D3111yescharacteristic
253C22×C4—21no—
254C22×C4—311no—
255C22×C4—311no—
256C22×C4—311no—
257C22×C4—621no—
258C22×C4—621no—
259C22×C4—621no—
260C22×C4—621no—
261C22×C4—621no—
262C22×C4—1244no—
263SD16—22no—
264SD16—622no—
265D8—622no—
266D8—622no—
267C2×C8—311no—
268C2×C8—311no—
269C2×C8C22×D3111yescharacteristic
270C2×C8C22×D3111yescharacteristic
271C4⋊C4—21no—
272C4⋊C4—311no—
273C4⋊C4—311no—
274C4⋊C4—621no—
275C4⋊C4—621no—
276C4⋊C4—621no—
277C4⋊C4—621no—
278C4⋊C4C22×D3111yescharacteristic
279C4⋊C4C22×D3111yescharacteristic
280C22⋊C4—21no—
281C22⋊C4—621no—
282C22⋊C4—621no—
283C22⋊C4—621no—
284C22⋊C4—621no—
285C22⋊C4—621no—
286C22⋊C4—621no—
287C22⋊C4—621no—
288C22⋊C4—621no—
289C42—21no—
290C42—311no—
291C42—311no—
292C42—311no—
293C42C22×D3111yescharacteristic
294C23—21no—
295C23—311no—
296C23—624no—
297C23—621no—
298C23—621no—
299C23—1242no—
300C23—1242no—
301Q8—21no—
302Q8—21no—
303D4—21no—
304D4—312no—
305D4—624no—
306D4—621no—
307D4—621no—
308D4—621no—
309D4—1242no—
310D4#9249512yes—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
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—1241no—
324C2×C4—1242no—
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—312no—
340C22—621no—
341C22—621no—
342C22—622no—
343C22—1248no—
344C22—1241no—
345C22—1241no—
346C22—1241no—
347C22—1241no—
348C22—1241no—
349C22C2×D4×D3111yescharacteristic
350C4—21no—
351C4—21no—
352C4—41no—
353C4—41no—
354C4—41no—
355C4—621no—
356C4—621no—
357C4—621no—
358C4—1241no—
359C4—1241no—
360C4C2×#9249511yescharacteristic
361C4#41×D3111yescharacteristic
362C2—42no—
363C2—622no—
364C2—1242no—
365C2—2481no—
366C2#1452155811yescharacteristic
367C2AGL(1,ℤ/8)×D3111yescharacteristic
368C2#1452184811yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#440C2
socleC22×C31C22×D4
prime radical#14521184C2
hypercenter#440D31
hypocenterC31#3114
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #14521586C2semidirect
2. C4×D4×D31C2semidirect
3. #14521378C2semidirect
4. #14521364C2semidirect
5. #14521352C2semidirect
6. #14521351C2semidirect
7. #14521267C2semidirect
8. #14521266C2semidirect
9. #14521198C2semidirect
11. #14521162C2semidirect
12. #14521159C2semidirect
13. #14521147C2semidirect
14. #14521104C2semidirect
15. C31×#440C2semidirect
19. C4×Q8×C31C22semidirect
21. #11758524C22semidirect
33. #11758467C22semidirect
38. C4×D124C22semidirect
41. C31×#107C22semidirect
42. C31×#103C22semidirect
44. C31×#97C22semidirect
45. #11758423C22semidirect
48. #11758409C22semidirect
51. #11758405C22semidirect
52. Dic31⋊C8C22semidirect
53. Dic31⋊C8C22semidirect
55. #11758397C22semidirect
56. #11758396C22semidirect
57. #11758395C22semidirect
58. #11758391C22semidirect
191. #440D31semidirect
212. C4×Q8C2×D31semidirect
226. #107C2×D31semidirect
232. #103C2×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
#145215862
C4×D4×D312
#145213782
#145213642
#145213522
#145213512
#145212672
#145212662
#145211982
#145211842
#145211622
#145211592
#145211472
#145211042
C31×#4402
#311431