Finite Group Databasebeta

← #16858778

Subgroups — #16858778

Order 3968.

368 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14521784C211yesmaximal, characteristic, complemented
2#14521771C211yesmaximal, characteristic, complemented
3#14521442C211yesmaximal, characteristic, complemented
4#14521438C211yesmaximal, characteristic
5#14521434C211yesmaximal, characteristic, complemented
6#14521274C211yesmaximal, characteristic, complemented
7#14521271C211yesmaximal, characteristic, complemented
8#14521267C211yesmaximal, characteristic, complemented
9#14521267C211yesmaximal, characteristic, complemented
10#14521253C211yesmaximal, characteristic, complemented
11#14521249C211yesmaximal, characteristic, complemented
12#14521177C211yesmaximal, characteristic, complemented
13#14521160C211yesmaximal, characteristic, complemented
14#14521136C211yesmaximal, characteristic, complemented
15C31×#441C211yesmaximal, characteristic, complemented
16C2×Q16×C31C2211yescharacteristic
17C4×Q8×C31C2211yescharacteristic
18C4×Q8×C31C2211yescharacteristic
19#11758524C2211yescharacteristic
20#11758524C2211yescharacteristic
21#11758524C2211yescharacteristic
22#11758521C2211yescharacteristic
23C2×#92482C2211yescharacteristic
24C2×#92481C2211yescharacteristic
25C2×#92481C2211yescharacteristic
26C2×#92481C2211yescharacteristic
27C2×D248C2211yescharacteristic
28C2×D248C2211yescharacteristic
29C2×#92470C2211yescharacteristic
30C2×#92470C2211yescharacteristic
31#11758475—21no—
32#11758473—21no—
33#11758471—21no—
34#11758471—21no—
35#11758470C2211yescharacteristic
36#11758470C2211yescharacteristic
37#11758470C2211yescharacteristic
38#11758464C2211yescharacteristic
39#11758453—21no—
40#11758452—21no—
41#11758452C2211yescharacteristic
42#11758451C2211yescharacteristic
43C4×D124—21no—
44#11758449—21no—
45C4×Dic62C2211yescharacteristic
46C31×#106C2211yescharacteristic
47C31×#103C2211yescharacteristic
48C31×#103C2211yescharacteristic
49C31×#97C2211yescharacteristic
50#11758403C2211yescharacteristic
51Dic31⋊C8C2211yescharacteristic
52Dic31⋊C8C2211yescharacteristic
53C8×Dic31C2211yescharacteristic
54#11758398C2211yescharacteristic
55#11758397C2211yescharacteristic
56#11758397C2211yescharacteristic
57#11758397C2211yescharacteristic
58C4⋊(C31⋊C8)C2211yescharacteristic
59C2×Q8×C31C2311yescharacteristic
60C2×Q8×C31C2311yescharacteristic
61C2×D124—21no—
62C2×D124—21no—
63C2×D124C2311yescharacteristic
64C2×D124C2311yescharacteristic
65C2×D124C2311yescharacteristic
66C2×C4×D31—21no—
67C2×C4×D31—21no—
68C2×C4×D31—21no—
69C2×Dic62D411yescharacteristic
70C2×Dic62C2311yescharacteristic
71Q16×C31—22no—
72C2×C8×C31C2311yescharacteristic
73C2×C8×C31C2311yescharacteristic
74C4⋊C4×C31—21no—
75C4⋊C4×C31—21no—
76C4⋊C4×C31C2311yescharacteristic
77C4⋊C4×C31C2311yescharacteristic
78C42×C31—21no—
79C42×C31—21no—
80C42×C31C2311yescharacteristic
81#92482—41no—
82#92481—41no—
83#92481—41no—
84#92481—41no—
85(C2×D31)⋊C4—21no—
86(C2×D31)⋊C4—21no—
87(C2×D31)⋊C4—21no—
88(C2×D31)⋊C4—21no—
89(C2×D31)⋊C4—21no—
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—
96C4⋊Dic31D411yescharacteristic
97Dic31⋊C4—21no—
98Dic31⋊C4—21no—
99Dic31⋊C4—21no—
100Dic31⋊C4D411yescharacteristic
101Dic31⋊C4D411yescharacteristic
102C4×Dic31—21no—
103C4×Dic31C2311yescharacteristic
104C4×Dic31C2311yescharacteristic
105C2×C31⋊C8C2311yescharacteristic
106C2×C31⋊C8C2311yescharacteristic
107D248—22no—
108D248—41no—
109#92470—22no—
110#92470—41no—
111C22×D31—21no—
112C22×D31—21no—
113C22×D31—21no—
114Q8×C31—21no—
115Q8×C31—21no—
116Q8×C31—21no—
117Q8×C31—21no—
118C2×C4×C31—21no—
119C2×C4×C31—21no—
120C2×C4×C31—21no—
121C2×C4×C31—21no—
122C2×C4×C31C2×D411yescharacteristic
123C2×C4×C31C2×D411yescharacteristic
124C2×C4×C31C2411yescharacteristic
125C2×Dic31—21no—
126C2×Dic31C2×D411yescharacteristic
127C2×Dic31C2×D411yescharacteristic
128C2×Dic31C2×D411yescharacteristic
129C2×Dic31C2×D411yescharacteristic
130D124—21no—
131D124—21no—
132D124—21no—
133D124—21no—
134D124—21no—
135D124—21no—
136D124—42no—
137D124—81no—
138C4×D31—42no—
139C4×D31—81no—
140C4×D31—81no—
141Dic62—21no—
142Dic62—21no—
143Dic62—41no—
144C8×C31—21no—
145C8×C31#4112yes—
146C31⋊C8—21no—
147C31⋊C8—21no—
148#3401—311nomaximal, Sylow
149C22×C31C22×D411yescharacteristic
150C2×D31—41no—
151C2×D31—41no—
152C2×D31—41no—
153C2×D31—41no—
154C2×D31—41no—
155C2×D31—41no—
156C2×D31—41no—
157C2×D31—41no—
158C2×D31—41no—
159C4×C31—21no—
160C4×C31—21no—
161C4×C31—41no—
162C4×C31—41no—
163C4×C31—41no—
164C4×C31—41no—
165C4×C31C2×#4111yescharacteristic
166C4×C31H(5,𝔽2)11yescharacteristic
167Dic31—21no—
168Dic31—21no—
169Dic31—21no—
170Dic31—21no—
171Dic31—41no—
172#559—311no—
173#556—311no—
174#497—311no—
175#496—311no—
176#495—311no—
177#464—311no—
178#464—311no—
179#463—311no—
180#463—311no—
181#461—311no—
182#460—311no—
183#446—311no—
184#442—311no—
185#441D3111yescharacteristic, complemented
186C4×SD16—311no—
187C2×C31#55011yescharacteristic
188C2×C31#57511yescharacteristic
189C2×C31#57711yescharacteristic
190D31—81no—
191D31—81no—
192D31—81no—
193C2×Q16—311no—
194C2×Q16C2×D3111yescharacteristic
195C2×SD16—311no—
196C2×SD16—311no—
197C2×SD16—311no—
198C2×SD16—311no—
199C2×SD16—311no—
200C2×D8—311no—
201C2×D8—311no—
202C4⋊Q8—311no—
203#127—311no—
204#126—621no—
205#126—621no—
206#124—311no—
207#124—311no—
208#124—311no—
209#124—311no—
210#124—621no—
211#123—621no—
212#123—621no—
213C22⋊Q8—621no—
214C4×Q8—311no—
215C4×Q8—311no—
216C4×Q8C2×D3111yescharacteristic
217C4×Q8C2×D3111yescharacteristic
218C4×D4—311no—
219C4×D4—311no—
220C4×D4—311no—
221C4×D4—621no—
222#117—621no—
223#106C2×D3111yescharacteristic
224C4⋊C8—311no—
225C4⋊C8—311no—
226C4⋊C8—311no—
227#103—311no—
228#103C2×D3111yescharacteristic
229#103C2×D3111yescharacteristic
230#102—311no—
231#102—311no—
232#102—311no—
233#97—311no—
234#97C2×D3111yescharacteristic
235C4×C8—311no—
236C31#340111yescharacteristic, complemented, Sylow
237C2×Q8—311no—
238C2×Q8—311no—
239C2×Q8C22×D3111yescharacteristic
240C2×Q8C22×D3111yescharacteristic
241C2×D4—311no—
242C2×D4—311no—
243C2×D4—311no—
244C2×D4—621no—
245C2×D4—621no—
246C22×C4—621no—
247C22×C4—621no—
248C22×C4—621no—
249Q16—22no—
250Q16—1241no—
251SD16—622no—
252SD16—1241no—
253SD16—1241no—
254SD16—1241no—
255SD16—1241no—
256D8—622no—
257D8—1241no—
258C2×C8—311no—
259C2×C8—311no—
260C2×C8C22×D3111yescharacteristic
261C2×C8C22×D3111yescharacteristic
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—311no—
265C4⋊C4—311no—
266C4⋊C4—311no—
267C4⋊C4—621no—
268C4⋊C4—621no—
269C4⋊C4—621no—
270C4⋊C4C22×D3111yescharacteristic
271C4⋊C4C22×D3111yescharacteristic
272C22⋊C4—621no—
273C22⋊C4—621no—
274C22⋊C4—621no—
275C22⋊C4—621no—
276C22⋊C4—621no—
277C22⋊C4—621no—
278C22⋊C4—621no—
279C22⋊C4—621no—
280C22⋊C4—621no—
281C22⋊C4—621no—
282C22⋊C4—621no—
283C42—21no—
284C42—21no—
285C42—311no—
286C42—311no—
287C42—621no—
288C42C22×D3111yescharacteristic
289C23—621no—
290C23—621no—
291C23—621no—
292Q8—21no—
293Q8—21no—
294Q8—21no—
295Q8—21no—
296Q8—621no—
297Q8—621no—
298Q8—1241no—
299D4—621no—
300D4—621no—
301D4—621no—
302D4—621no—
303D4—621no—
304D4—621no—
305D4—1242no—
306D4—2481no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—311no—
312C2×C4—311no—
313C2×C4—311no—
314C2×C4—311no—
315C2×C4—621no—
316C2×C4—1242no—
317C2×C4—2481no—
318C2×C4—2481no—
319C2×C4D4×D3111yescharacteristic
320C2×C4D4×D3111yescharacteristic
321C2×C4C23×D3111yescharacteristic
322C8—21no—
323C8—621no—
324C8—621no—
325C8#9249512yes—
326C22—1241no—
327C22—1241no—
328C22—1241no—
329C22—1241no—
330C22—1241no—
331C22—1241no—
332C22—1241no—
333C22—1241no—
334C22—1241no—
335C22C2×D4×D3111yescharacteristic
336C4—21no—
337C4—21no—
338C4—41no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—621no—
343C4—621no—
344C4—621no—
345C4—621no—
346C4—1241no—
347C4C2×#9249511yescharacteristic
348C4#1175856611yescharacteristic
349C2—2481no—
350C2—2481no—
351C2—2481no—
352C2#1452172011yescharacteristic
353C2#1452184811yescharacteristic
354C2#1452185811yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#441C2
socleC22×C31C22×D4
prime radical#14521438C2
hypercenter#441D31
hypocenterC31#3401
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ #441

Complements

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

NH ≅ G/Ntype
1. #14521784C2semidirect
2. #14521771C2semidirect
3. #14521442C2semidirect
5. #14521434C2semidirect
6. #14521274C2semidirect
7. #14521271C2semidirect
8. #14521267C2semidirect
9. #14521267C2semidirect
10. #14521253C2semidirect
11. #14521249C2semidirect
12. #14521177C2semidirect
13. #14521160C2semidirect
14. #14521136C2semidirect
15. C31×#441C2semidirect
185. #441D31semidirect
236. C31#3401semidirect

Maximal subgroups

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

subgroupindex
#145217842
#145217712
#145214422
#145214382
#145214342
#145212742
#145212712
#145212672
#145212532
#145212492
#145211772
#145211602
#145211362
C31×#4412
#340131