Finite Group Databasebeta

← #16854102

Subgroups — #16854102

Order 3968.

418 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14520943C211yesmaximal, characteristic
2#14520943C211yesmaximal, characteristic
3#14520942C211yesmaximal, characteristic
4#14520942C211yesmaximal, characteristic
5#14520937C211yesmaximal, characteristic
6#14520937C211yesmaximal, characteristic
7#14520936C211yesmaximal, characteristic, complemented
8#14520935C211yesmaximal, characteristic, complemented
9#14520934C211yesmaximal, characteristic, complemented
10#14520933C211yesmaximal, characteristic, complemented
11#14520932C211yesmaximal, characteristic, complemented
12#14520931C211yesmaximal, characteristic, complemented
13#14520930C211yesmaximal, characteristic, complemented
14C42×Dic31C211yesmaximal, characteristic, complemented
15C31×#388C211yesmaximal, characteristic
16C2×C4⋊C4×C31C2211yescharacteristic
17C2×C22⋊C4×C31C2211yescharacteristic
18C2×C22⋊C4×C31C2211yescharacteristic
19C2×C22⋊C4×C31C2211yescharacteristic
20C2×C42×C31C2211yescharacteristic
21C2×C22⋊Dic31C2211yescharacteristic
22C2×C22⋊Dic31C2211yescharacteristic
23C2×C22⋊Dic31C2211yescharacteristic
24C2×C22⋊Dic31C2211yescharacteristic
25C2×C4⋊Dic31C2211yescharacteristic
26C2×C4⋊Dic31C2211yescharacteristic
27C2×Dic31⋊C4C2211yescharacteristic
28C2×Dic31⋊C4C2211yescharacteristic
29C2×Dic31⋊C4C2211yescharacteristic
30C2×Dic31⋊C4C2211yescharacteristic
31C2×C4×Dic31C2211yescharacteristic
32C2×C4×Dic31C2211yescharacteristic
33C2×C4×Dic31C2211yescharacteristic
34C2×C4×Dic31C2211yescharacteristic
35C2×C4×Dic31C2211yescharacteristic
36C2×C4×Dic31C2211yescharacteristic
37C31×#95C2211yescharacteristic
38C31×#95C2211yescharacteristic
39C31⋊#95C2211yescharacteristic
40C31⋊#95C2211yescharacteristic
41C31⋊#95C2211yescharacteristic
42C31⋊#95C2211yescharacteristic
43C31⋊#95C2211yescharacteristic
44C31⋊#95C2211yescharacteristic
45C31⋊#95C2211yescharacteristic
46C31⋊#95C2211yescharacteristic
47C31⋊#95C2211yescharacteristic
48C31⋊#95C2211yescharacteristic
49C31⋊#95C2211yescharacteristic
50C31⋊#95C2211yescharacteristic
51C24×C31C2311yescharacteristic
52C22×C4×C31C2311yescharacteristic
53C22×C4×C31C2311yescharacteristic
54C22×C4×C31C2311yescharacteristic
55C22×C4×C31C2311yescharacteristic
56C22×C4×C31C2311yescharacteristic
57C22×C4×C31C2311yescharacteristic
58C22×Dic31C2311yescharacteristic
59C22×Dic31C2311yescharacteristic
60C22×Dic31C2311yescharacteristic
61C22×Dic31C2311yescharacteristic
62C22×Dic31C2311yescharacteristic
63C22×Dic31C2311yescharacteristic
64C22×Dic31C2311yescharacteristic
65C22×Dic31C2311yescharacteristic
66C4⋊C4×C31—22no—
67C22⋊C4×C31—22no—
68C22⋊C4×C31—22no—
69C22⋊C4×C31—22no—
70C42×C31—22no—
71C22⋊Dic31—22no—
72C22⋊Dic31—22no—
73C22⋊Dic31—22no—
74C22⋊Dic31—22no—
75C4⋊Dic31—22no—
76C4⋊Dic31—22no—
77Dic31⋊C4—22no—
78Dic31⋊C4—22no—
79Dic31⋊C4—22no—
80Dic31⋊C4—22no—
81C4×Dic31—22no—
82C4×Dic31—22no—
83C4×Dic31—22no—
84C4×Dic31—22no—
85C4×Dic31—22no—
86C4×Dic31—22no—
87C23×C31—21no—
88C23×C31—21no—
89C23×C31—21no—
90C23×C31—21no—
91C23×C31—21no—
92C23×C31—21no—
93C23×C31—21no—
94C23×C31C2411yescharacteristic
95C2×C4×C31—21no—
96C2×C4×C31—21no—
97C2×C4×C31—21no—
98C2×C4×C31—21no—
99C2×C4×C31—21no—
100C2×C4×C31—21no—
101C2×C4×C31—21no—
102C2×C4×C31—21no—
103C2×C4×C31—21no—
104C2×C4×C31—21no—
105C2×C4×C31—21no—
106C2×C4×C31—21no—
107C2×C4×C31—21no—
108C2×C4×C31—21no—
109C2×C4×C31—21no—
110C2×C4×C31#4112yes—
111C2×C4×C31#4112yes—
112C2×C4×C31#4112yes—
113C2×Dic31—21no—
114C2×Dic31—21no—
115C2×Dic31—21no—
116C2×Dic31—21no—
117C2×Dic31—21no—
118C2×Dic31—21no—
119C2×Dic31—21no—
120C2×Dic31—21no—
121C2×Dic31—21no—
122C2×Dic31—21no—
123C2×Dic31—21no—
124C2×Dic31—21no—
125C2×Dic31—21no—
126C2×Dic31—21no—
127C2×Dic31—21no—
128C2×Dic31—21no—
129C2×Dic31—21no—
130C2×Dic31—21no—
131C2×Dic31—21no—
132C2×Dic31—21no—
133C2×Dic31#4112yes—
134C2×Dic31#4112yes—
135C2×Dic31#4112yes—
136C2×Dic31#4112yes—
137#2866—311nomaximal, Sylow
138C22×C31—41no—
139C22×C31—41no—
140C22×C31—41no—
141C22×C31—41no—
142C22×C31—41no—
143C22×C31—41no—
144C22×C31—41no—
145C22×C31C2×#4111yescharacteristic
146C22×C31C2×#4111yescharacteristic
147C22×C31C2×#4111yescharacteristic
148C22×C31C2×#4111yescharacteristic
149C22×C31C2×#4111yescharacteristic
150C22×C31C2×#4111yescharacteristic
151C22×C31C2×#4111yescharacteristic
152C4×C31—22no—
153C4×C31—22no—
154C4×C31—22no—
155C4×C31—41no—
156C4×C31—41no—
157C4×C31—41no—
158Dic31—22no—
159Dic31—22no—
160Dic31—22no—
161Dic31—22no—
162Dic31—41no—
163Dic31—41no—
164Dic31—41no—
165Dic31—41no—
166#388—311no—
167#388—311no—
168#388—311no—
169#388—311no—
170#388—311no—
171#388—311no—
172#388D3111yescharacteristic
173#387—311no—
174#387—311no—
175#387—311no—
176#387—311no—
177#387—311no—
178#387—311no—
179#387—311no—
180C43—311no—
181C2×C31—81no—
182C2×C31#52911yescharacteristic
183C2×C31#52911yescharacteristic
184C2×C31#52911yescharacteristic
185C2×C31#52911yescharacteristic
186C2×C31#52911yescharacteristic
187C2×C31#52911yescharacteristic
188C2×C31#52911yescharacteristic
189C2×C4⋊C4—311no—
190C2×C4⋊C4—311no—
191C2×C4⋊C4—311no—
192C2×C4⋊C4—311no—
193C2×C4⋊C4—311no—
194C2×C4⋊C4—311no—
195C2×C4⋊C4C2×D3111yescharacteristic
196C2×C22⋊C4—311no—
197C2×C22⋊C4—311no—
198C2×C22⋊C4—311no—
199C2×C22⋊C4—311no—
200C2×C22⋊C4C2×D3111yescharacteristic
201C2×C22⋊C4C2×D3111yescharacteristic
202C2×C22⋊C4C2×D3111yescharacteristic
203C2×C42—311no—
204C2×C42—311no—
205C2×C42—311no—
206C2×C42—311no—
207C2×C42—311no—
208C2×C42—311no—
209C2×C42C2×D3111yescharacteristic
210#95—311no—
211#95—311no—
212#95—311no—
213#95—311no—
214#95—311no—
215#95—311no—
216#95—311no—
217#95—311no—
218#95—311no—
219#95—311no—
220#95—311no—
221#95—311no—
222#95C2×D3111yescharacteristic
223#95C2×D3111yescharacteristic
224C31#286611yescharacteristic, complemented, Sylow
225C24C22×D3111yescharacteristic
226C22×C4—311no—
227C22×C4—311no—
228C22×C4—311no—
229C22×C4—311no—
230C22×C4—311no—
231C22×C4—311no—
232C22×C4—311no—
233C22×C4—311no—
234C22×C4C22×D3111yescharacteristic
235C22×C4C22×D3111yescharacteristic
236C22×C4C22×D3111yescharacteristic
237C22×C4C22×D3111yescharacteristic
238C22×C4C22×D3111yescharacteristic
239C22×C4C22×D3111yescharacteristic
240C4⋊C4—22no—
241C4⋊C4—622no—
242C4⋊C4—622no—
243C4⋊C4—622no—
244C4⋊C4—622no—
245C4⋊C4—622no—
246C4⋊C4—622no—
247C22⋊C4—22no—
248C22⋊C4—22no—
249C22⋊C4—22no—
250C22⋊C4—622no—
251C22⋊C4—622no—
252C22⋊C4—622no—
253C22⋊C4—622no—
254C42—22no—
255C42—622no—
256C42—622no—
257C42—622no—
258C42—622no—
259C42—622no—
260C42—622no—
261C23—21no—
262C23—21no—
263C23—21no—
264C23—21no—
265C23—21no—
266C23—21no—
267C23—21no—
268C23C23×D3111yescharacteristic
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—312no—
285C2×C4—312no—
286C2×C4—312no—
287C2×C4—312no—
288C2×C4—621no—
289C2×C4—621no—
290C2×C4—621no—
291C2×C4—621no—
292C2×C4—621no—
293C2×C4—621no—
294C2×C4—621no—
295C2×C4—621no—
296C2×C4—621no—
297C2×C4—621no—
298C2×C4—621no—
299C2×C4—621no—
300C2×C4—621no—
301C2×C4—621no—
302C2×C4—621no—
303C2×C4—621no—
304C2×C4—621no—
305C2×C4—621no—
306C2×C4—621no—
307C2×C4—621no—
308C2×C4#9249512yes—
309C2×C4#9249712yes—
310C2×C4#9249712yes—
311C22—41no—
312C22—41no—
313C22—41no—
314C22—41no—
315C22—41no—
316C22—41no—
317C22—41no—
318C22C2×#9249511yescharacteristic
319C22C2×#9249711yescharacteristic
320C22C2×#9249711yescharacteristic
321C22#41×D3111yescharacteristic
322C22#41×D3111yescharacteristic
323C22#41×D3111yescharacteristic
324C22#41×D3111yescharacteristic
325C4—22no—
326C4—22no—
327C4—22no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—622no—
332C4—622no—
333C4—622no—
334C4—622no—
335C4—1241no—
336C4—1241no—
337C4—1241no—
338C4—1241no—
339C2—81no—
340C2#1452157611yescharacteristic
341C2#1452157711yescharacteristic
342C2#1452157811yescharacteristic
343C2#1452157911yescharacteristic
344C2#1452158011yescharacteristic
345C2#1452158111yescharacteristic
346C2#1452158211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D31
commutator, socle, cosocleC23×C31C24
FittingC31×#388C2
prime radicalC24×C31C23
hypercenter#388D31
hypocenterC31#2866
LCSG ▷ C23×C31 ▷ C31
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
7. #14520936C2semidirect
8. #14520935C2semidirect
9. #14520934C2semidirect
10. #14520933C2semidirect
11. #14520932C2semidirect
12. #14520931C2semidirect
13. #14520930C2semidirect
14. C42×Dic31C2semidirect
224. C31#2866semidirect

Maximal subgroups

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

subgroupindex
#145209432
#145209422
#145209372
#145209362
#145209352
#145209342
#145209332
#145209322
#145209312
#145209302
C42×Dic312
C31×#3882
#286631