Finite Group Databasebeta

← #16858800

Subgroups — #16858800

Order 3968.

380 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#14521784C211yesmaximal, characteristic, complemented
2#14521782C211yesmaximal, characteristic, complemented
3#14521438C211yesmaximal, characteristic, complemented
4#14521435C211yesmaximal, characteristic, complemented
5#14521430C211yesmaximal, characteristic, complemented
6#14521274C211yesmaximal, characteristic, complemented
7#14521271C211yesmaximal, characteristic, complemented
8#14521267C211yesmaximal, characteristic, complemented
9#14521263C211yesmaximal, characteristic, complemented
10#14521244C211yesmaximal, characteristic, complemented
11#14521243C211yesmaximal, characteristic, complemented
12#14521177C211yesmaximal, characteristic, complemented
13#14521148C211yesmaximal, characteristic, complemented
14#14521131C211yesmaximal, characteristic, complemented
15C31×#440C211yesmaximal, characteristic, complemented
16C2×SD16×C31C2211yescharacteristic
17C4×Q8×C31C2211yescharacteristic
18C4×D4×C31C2211yescharacteristic
19#11758524C2211yescharacteristic
20#11758524C2211yescharacteristic
21C2×#92482C2211yescharacteristic
22C2×#92481C2211yescharacteristic
23#11758517C2211yescharacteristic
24#11758513C2211yescharacteristic
25C2×#92479C2211yescharacteristic
26C2×#92479C2211yescharacteristic
27#11758506—21no—
28C4×C22⋊D31—21no—
29C2×D248C2211yescharacteristic
30C2×D248C2211yescharacteristic
31C2×#92470C2211yescharacteristic
32C2×#92470C2211yescharacteristic
33#11758471—21no—
34#11758471—21no—
35#11758470C2211yescharacteristic
36#11758470C2211yescharacteristic
37#11758470C2211yescharacteristic
38#11758464C2211yescharacteristic
39#11758462—21no—
40#11758460—21no—
41#11758452—21no—
42#11758452C2211yescharacteristic
43#11758451C2211yescharacteristic
44C4×D124—21no—
45C4×Dic62C2211yescharacteristic
46C31×#107C2211yescharacteristic
47C31×#103C2211yescharacteristic
48C31×#102C2211yescharacteristic
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×D4×C31C2311yescharacteristic
61C22×C4×C31—21no—
62C2×C22⋊D31—21no—
63C2×C22⋊D31—21no—
64C2×D124—21no—
65C2×D124—21no—
66C2×D124C2311yescharacteristic
67C2×D124C2311yescharacteristic
68C2×D124C2311yescharacteristic
69C2×C4×D31—21no—
70C2×C4×D31—21no—
71C2×C4×D31—21no—
72C2×Dic62D411yescharacteristic
73C2×Dic62C2311yescharacteristic
74SD16×C31—22no—
75C2×C8×C31C2311yescharacteristic
76C2×C8×C31C2311yescharacteristic
77C4⋊C4×C31—21no—
78C4⋊C4×C31C2311yescharacteristic
79C4⋊C4×C31C2311yescharacteristic
80C22⋊C4×C31—21no—
81C42×C31—21no—
82C42×C31C2311yescharacteristic
83C22⋊Dic31—21no—
84C22⋊Dic31—21no—
85#92482—41no—
86#92481—41no—
87#92479—41no—
88#92479—41no—
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—
96(C2×D31)⋊C4—21no—
97(C2×D31)⋊C4—21no—
98C4⋊Dic31D411yescharacteristic
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—
111C23×C31—21no—
112C22×D31—21no—
113C22×D31—21no—
114C22×D31—21no—
115Q8×C31—21no—
116Q8×C31—21no—
117D4×C31—21no—
118D4×C31—21no—
119C2×C4×C31—21no—
120C2×C4×C31—21no—
121C2×C4×C31—21no—
122C2×C4×C31—81no—
123C2×C4×C31C2×D411yescharacteristic
124C2×C4×C31C2×D411yescharacteristic
125C2×C4×C31C2411yescharacteristic
126C22⋊D31—42no—
127C22⋊D31—81no—
128C2×Dic31—21no—
129C2×Dic31C2×D411yescharacteristic
130C2×Dic31C2×D411yescharacteristic
131C2×Dic31C2×D411yescharacteristic
132C2×Dic31C2×D411yescharacteristic
133D124—21no—
134D124—21no—
135D124—21no—
136D124—21no—
137D124—21no—
138D124—21no—
139D124—42no—
140D124—81no—
141C4×D31—81no—
142C4×D31—81no—
143C4×D31—81no—
144Dic62—21no—
145Dic62—21no—
146Dic62—41no—
147C8×C31—21no—
148C8×C31#4112yes—
149C31⋊C8—21no—
150C31⋊C8—21no—
151#3403—311nomaximal, Sylow
152C22×C31—41no—
153C22×C31—41no—
154C22×C31—41no—
155C22×C31C22×D411yescharacteristic
156C2×D31—41no—
157C2×D31—41no—
158C2×D31—41no—
159C2×D31—41no—
160C2×D31—41no—
161C2×D31—41no—
162C2×D31—41no—
163C2×D31—41no—
164C2×D31—41no—
165C4×C31—21no—
166C4×C31—21no—
167C4×C31—41no—
168C4×C31—41no—
169C4×C31—41no—
170C4×C31C2×#4111yescharacteristic
171C4×C31H(5,𝔽2)11yescharacteristic
172Dic31—21no—
173Dic31—21no—
174Dic31—21no—
175Dic31—21no—
176Dic31—41no—
177#559—311no—
178#559—311no—
179#496—311no—
180#496—311no—
181#495—311no—
182#464—311no—
183#464—311no—
184#463—311no—
185#463—311no—
186#459—311no—
187#459—311no—
188#446—311no—
189#440—311no—
190#440D3111yescharacteristic, complemented
191C4×D8—311no—
192C2×C31—81no—
193C2×C31#55011yescharacteristic
194C2×C31#57511yescharacteristic
195C2×C31#57611yescharacteristic
196D31—81no—
197D31—81no—
198D31—81no—
199C2×Q16—311no—
200C2×SD16—311no—
201C2×SD16—311no—
202C2×SD16—311no—
203C2×SD16C2×D3111yescharacteristic
204C2×D8—311no—
205C2×D8—311no—
206C2×D8—311no—
207C2×D8—311no—
208#127—311no—
209#127—311no—
210#124—311no—
211#124—311no—
212#124—311no—
213#124—311no—
214#124—621no—
215#124—621no—
216#123—621no—
217#123—621no—
218#123—621no—
219#123—621no—
220C4×Q8—311no—
221C4×Q8—311no—
222C4×Q8C2×D3111yescharacteristic
223C4×D4—311no—
224C4×D4—311no—
225C4×D4—311no—
226C4×D4—621no—
227C4×D4—621no—
228C4×D4C2×D3111yescharacteristic
229#107C2×D3111yescharacteristic
230C4⋊C8—311no—
231C4⋊C8—311no—
232C4⋊C8—311no—
233#103—311no—
234#103C2×D3111yescharacteristic
235#102—311no—
236#102—311no—
237#102—311no—
238#102C2×D3111yescharacteristic
239#97—311no—
240#97C2×D3111yescharacteristic
241C4×C8—311no—
242C31#340311yescharacteristic, complemented, Sylow
243C2×Q8—311no—
244C2×Q8—311no—
245C2×Q8C22×D3111yescharacteristic
246C2×D4—311no—
247C2×D4—311no—
248C2×D4—311no—
249C2×D4—621no—
250C2×D4—621no—
251C2×D4—621no—
252C2×D4—621no—
253C2×D4C22×D3111yescharacteristic
254C22×C4—21no—
255C22×C4—621no—
256C22×C4—621no—
257C22×C4—621no—
258Q16—1241no—
259SD16—22no—
260SD16—622no—
261SD16—1241no—
262SD16—1241no—
263D8—622no—
264D8—1241no—
265D8—1241no—
266D8—1241no—
267C2×C8—311no—
268C2×C8—311no—
269C2×C8C22×D3111yescharacteristic
270C2×C8C22×D3111yescharacteristic
271C4⋊C4—21no—
272C4⋊C4—311no—
273C4⋊C4—311no—
274C4⋊C4—311no—
275C4⋊C4—621no—
276C4⋊C4C22×D3111yescharacteristic
277C4⋊C4C22×D3111yescharacteristic
278C22⋊C4—21no—
279C22⋊C4—621no—
280C22⋊C4—621no—
281C22⋊C4—621no—
282C22⋊C4—621no—
283C22⋊C4—621no—
284C22⋊C4—621no—
285C22⋊C4—621no—
286C22⋊C4—621no—
287C22⋊C4—621no—
288C22⋊C4—621no—
289C22⋊C4—621no—
290C42—21no—
291C42—311no—
292C42—311no—
293C42—621no—
294C42C22×D3111yescharacteristic
295C23—21no—
296C23—621no—
297C23—621no—
298C23—621no—
299Q8—21no—
300Q8—21no—
301Q8—621no—
302Q8—621no—
303Q8—1241no—
304D4—21no—
305D4—21no—
306D4—621no—
307D4—621no—
308D4—621no—
309D4—621no—
310D4—621no—
311D4—621no—
312D4—1242no—
313D4—1242no—
314D4—2481no—
315D4—2481no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—81no—
320C2×C4—311no—
321C2×C4—311no—
322C2×C4—311no—
323C2×C4—311no—
324C2×C4—621no—
325C2×C4—2481no—
326C2×C4—2481no—
327C2×C4—2481no—
328C2×C4D4×D3111yescharacteristic
329C2×C4D4×D3111yescharacteristic
330C2×C4C23×D3111yescharacteristic
331C8—21no—
332C8—621no—
333C8—621no—
334C8#9249512yes—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—1241no—
339C22—1241no—
340C22—1241no—
341C22—1241no—
342C22—1241no—
343C22—1241no—
344C22—1241no—
345C22—1241no—
346C22—1241no—
347C22C2×D4×D3111yescharacteristic
348C4—21no—
349C4—21no—
350C4—41no—
351C4—41no—
352C4—41no—
353C4—621no—
354C4—621no—
355C4—621no—
356C4—621no—
357C4—1241no—
358C4C2×#9249511yescharacteristic
359C4#1175856611yescharacteristic
360C2—81no—
361C2—2481no—
362C2—2481no—
363C2—2481no—
364C2#1452172011yescharacteristic
365C2#1452184811yescharacteristic
366C2#1452185311yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#440C2
socleC22×C31C22×D4
hypercenter#440D31
hypocenterC31#3403
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. #14521784C2semidirect
2. #14521782C2semidirect
3. #14521438C2semidirect
4. #14521435C2semidirect
5. #14521430C2semidirect
6. #14521274C2semidirect
7. #14521271C2semidirect
8. #14521267C2semidirect
9. #14521263C2semidirect
10. #14521244C2semidirect
11. #14521243C2semidirect
12. #14521177C2semidirect
13. #14521148C2semidirect
14. #14521131C2semidirect
15. C31×#440C2semidirect
190. #440D31semidirect
242. C31#3403semidirect

Maximal subgroups

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

subgroupindex
#145217842
#145217822
#145214382
#145214352
#145214302
#145212742
#145212712
#145212672
#145212632
#145212442
#145212432
#145211772
#145211482
#145211312
C31×#4402
#340331