Finite Group Databasebeta

← #16848261

Subgroups — #16848261

Order 3968.

516 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11758475C211yesmaximal, characteristic
2#14520941C211yesmaximal, characteristic
3#14520940C211yesmaximal, characteristic
4#14520939C211yesmaximal, characteristic
5#14520936C211yesmaximal, characteristic, complemented
6#14520934C211yesmaximal, characteristic, complemented
7#14520916C211yesmaximal, characteristic, complemented
8C4⋊C4×Dic31C211yesmaximal, characteristic, complemented
9C4⋊C4×Dic31C211yesmaximal, characteristic, complemented
10#14520900C211yesmaximal, characteristic, complemented
11#14520896C211yesmaximal, characteristic
12#14520896C211yesmaximal, characteristic
13#14520896C211yesmaximal, characteristic
14C42×Dic31C211yesmaximal, characteristic, complemented
15C31×#387C211yesmaximal, characteristic, complemented
16C22×C4×D31C2211yescharacteristic
17C2×C4⋊C4×C31C2211yescharacteristic
18C2×C4⋊C4×C31C2211yescharacteristic
19C2×C42×C31C2211yescharacteristic
20C2×(C2×D31)⋊C4C2211yescharacteristic
21C2×(C2×D31)⋊C4C2211yescharacteristic
22C2×(C2×D31)⋊C4C2211yescharacteristic
23C2×(C2×D31)⋊C4C2211yescharacteristic
24C2×(C2×D31)⋊C4C2211yescharacteristic
25C2×(C2×D31)⋊C4C2211yescharacteristic
26C2×C4⋊Dic31C2211yescharacteristic
27C2×C4⋊Dic31C2211yescharacteristic
28C2×Dic31⋊C4C2211yescharacteristic
29C2×Dic31⋊C4C2211yescharacteristic
30C2×C4×Dic31C2211yescharacteristic
31C2×C4×Dic31C2211yescharacteristic
32C2×C4×Dic31C2211yescharacteristic
33C2×C4×Dic31C2211yescharacteristic
34C2×C4×Dic31C2211yescharacteristic
35C2×C4×Dic31C2211yescharacteristic
36C2×C4×Dic31C2211yescharacteristic
37C2×C4×Dic31C2211yescharacteristic
38C2×C4×Dic31C2211yescharacteristic
39#11758475C418yescomplemented
40C31×#95C2211yescharacteristic
41C31×#95C2211yescharacteristic
42C31×#95C2211yescharacteristic
43C31×#95C2211yescharacteristic
44C31⋊#95C2211yescharacteristic
45C31⋊#95C2211yescharacteristic
46C31⋊#95C2211yescharacteristic
47C31⋊#95C2211yescharacteristic
48C31⋊#95C2211yescharacteristic
49C31⋊#95C2211yescharacteristic
50C31⋊#95C2211yescharacteristic
51C31⋊#95C2211yescharacteristic
52C23×D31C2311yescharacteristic
53C22×C4×C31C2311yescharacteristic
54C22×C4×C31C2311yescharacteristic
55C22×C4×C31C2311yescharacteristic
56C22×C4×C31C2311yescharacteristic
57C22×C4×C31C2311yescharacteristic
58C22×C4×C31C2311yescharacteristic
59C22×C4×C31C2311yescharacteristic
60C22×Dic31C2311yescharacteristic
61C22×Dic31C2311yescharacteristic
62C22×Dic31C2311yescharacteristic
63C22×Dic31C2311yescharacteristic
64C22×Dic31C2311yescharacteristic
65C22×Dic31C2311yescharacteristic
66C22×Dic31C2311yescharacteristic
67C2×C4×D31—22no—
68C2×C4×D31—22no—
69C2×C4×D31—22no—
70C4⋊C4×C31—22no—
71C4⋊C4×C31C2×C414yescomplemented
72C42×C31—22no—
73(C2×D31)⋊C4—22no—
74(C2×D31)⋊C4—22no—
75(C2×D31)⋊C4—22no—
76(C2×D31)⋊C4C2×C414yes—
77(C2×D31)⋊C4C2×C414yes—
78(C2×D31)⋊C4C2×C414yes—
79C4⋊Dic31—22no—
80C4⋊Dic31C2×C414yescomplemented
81Dic31⋊C4—22no—
82Dic31⋊C4C2×C414yescomplemented
83C4×Dic31—22no—
84C4×Dic31—22no—
85C4×Dic31—22no—
86C4×Dic31—22no—
87C4×Dic31—22no—
88C4×Dic31—22no—
89C4×Dic31—22no—
90C4×Dic31—22no—
91C4×Dic31C2×C414yescomplemented
92C23×C31C2411yescharacteristic
93C22×D31—21no—
94C22×D31—21no—
95C22×D31—21no—
96C22×D31—21no—
97C22×D31—21no—
98C22×D31—21no—
99C22×D31C22×C412yes—
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—21no—
111C2×C4×C31—21no—
112C2×C4×C31—21no—
113C2×C4×C31—21no—
114C2×C4×C31—21no—
115C2×C4×C31—21no—
116C2×C4×C31C22×C412yes—
117C2×C4×C31C22×C412yes—
118C2×C4×C31C22×C412yes—
119C2×C4×C31#4112yes—
120C2×C4×C31#4112yes—
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—21no—
134C2×Dic31—21no—
135C2×Dic31C22×C412yes—
136C2×Dic31C22×C412yes—
137C2×Dic31C22×C412yes—
138C2×Dic31#4112yes—
139C2×Dic31#4112yes—
140C2×Dic31#4112yes—
141C2×Dic31#4112yes—
142C4×D31—44no—
143C4×#126—311nomaximal, Sylow
144C22×C31C23×C411yescharacteristic
145C22×C31C2×#4111yescharacteristic
146C22×C31C2×#4111yescharacteristic
147C22×C31C2×#4111yescharacteristic
148C22×C31C2×#4111yescharacteristic
149C22×C31C2×#4111yescharacteristic
150C22×C31C2×#4111yescharacteristic
151C2×D31—22no—
152C2×D31—22no—
153C2×D31—22no—
154C2×D31—41no—
155C2×D31—41no—
156C2×D31—41no—
157C2×D31—41no—
158C4×C31—22no—
159C4×C31—22no—
160C4×C31—22no—
161C4×C31—22no—
162C4×C31—22no—
163C4×C31—41no—
164C4×C31—41no—
165Dic31—22no—
166Dic31—22no—
167Dic31—22no—
168Dic31—22no—
169Dic31—41no—
170Dic31—41no—
171Dic31#12614yescomplemented
172C2×#126—311no—
173#388—311no—
174#388—311no—
175#388—311no—
176#387—311no—
177#387—311no—
178#387D3111yescharacteristic, complemented
179#383—311no—
180C4×C4⋊C4—311no—
181C4×C4⋊C4—311no—
182C4×C4⋊C4—311no—
183C4×C22⋊C4—311no—
184C4×C22⋊C4—311no—
185C4×C22⋊C4—311no—
186C43—311no—
187C2×C31C4×#4111yescharacteristic
188C2×C31C4×#4111yescharacteristic
189C2×C31C4×#4111yescharacteristic
190C2×C31C2×#12611yescharacteristic
191C2×C31#52911yescharacteristic
192C2×C31#52911yescharacteristic
193C2×C31#52911yescharacteristic
194D31—42no—
195C23×C4—311no—
196#126—318no—
197C2×C4⋊C4—311no—
198C2×C4⋊C4—311no—
199C2×C4⋊C4—311no—
200C2×C4⋊C4—311no—
201C2×C4⋊C4C2×D3111yescharacteristic
202C2×C4⋊C4C2×D3111yescharacteristic
203C2×C22⋊C4—311no—
204C2×C22⋊C4—311no—
205C2×C22⋊C4—311no—
206C2×C22⋊C4—311no—
207C2×C22⋊C4—311no—
208C2×C22⋊C4—311no—
209C2×C42—311no—
210C2×C42—311no—
211C2×C42—311no—
212C2×C42—311no—
213C2×C42—311no—
214C2×C42—311no—
215C2×C42—311no—
216C2×C42—311no—
217C2×C42—311no—
218C2×C42C2×D3111yescharacteristic
219#95—311no—
220#95—311no—
221#95—311no—
222#95—311no—
223#95—311no—
224#95—311no—
225#95—311no—
226#95—311no—
227#95C2×D3111yescharacteristic
228#95C2×D3111yescharacteristic
229#95C2×D3111yescharacteristic
230#95C2×D3111yescharacteristic
231C31C4×#12611yescharacteristic, complemented, Sylow
232C24—311no—
233C22×C4—311no—
234C22×C4—311no—
235C22×C4—311no—
236C22×C4—311no—
237C22×C4—311no—
238C22×C4—311no—
239C22×C4—311no—
240C22×C4—622no—
241C22×C4—622no—
242C22×C4—622no—
243C22×C4C22×D3111yescharacteristic
244C22×C4C22×D3111yescharacteristic
245C22×C4C22×D3111yescharacteristic
246C22×C4C22×D3111yescharacteristic
247C22×C4C22×D3111yescharacteristic
248C22×C4C22×D3111yescharacteristic
249C22×C4C22×D3111yescharacteristic
250C4⋊C4—22no—
251C4⋊C4—314no—
252C4⋊C4—314no—
253C4⋊C4—622no—
254C4⋊C4—622no—
255C4⋊C4C4×D3114yescomplemented
256C22⋊C4—314no—
257C22⋊C4—314no—
258C22⋊C4—314no—
259C22⋊C4—622no—
260C22⋊C4—622no—
261C22⋊C4—622no—
262C42—22no—
263C42—314no—
264C42—622no—
265C42—622no—
266C42—622no—
267C42—622no—
268C42—622no—
269C42—622no—
270C42—622no—
271C42—622no—
272C23—312no—
273C23—621no—
274C23—621no—
275C23—621no—
276C23—621no—
277C23—621no—
278C23—621no—
279C23C23×D3111yescharacteristic
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—312no—
297C2×C4—312no—
298C2×C4—312no—
299C2×C4—312no—
300C2×C4—312no—
301C2×C4—312no—
302C2×C4—312no—
303C2×C4—621no—
304C2×C4—621no—
305C2×C4—621no—
306C2×C4—621no—
307C2×C4—621no—
308C2×C4—621no—
309C2×C4—621no—
310C2×C4—621no—
311C2×C4—621no—
312C2×C4—621no—
313C2×C4—621no—
314C2×C4—621no—
315C2×C4—621no—
316C2×C4—621no—
317C2×C4—1244no—
318C2×C4C2×C4×D3112yes—
319C2×C4C2×C4×D3112yes—
320C2×C4C2×C4×D3112yes—
321C2×C4#9249712yes—
322C2×C4#9249912yes—
323C22—622no—
324C22—622no—
325C22—622no—
326C22—1241no—
327C22—1241no—
328C22—1241no—
329C22—1241no—
330C22C22×C4×D3111yescharacteristic
331C22C2×#9249711yescharacteristic
332C22C2×#9249911yescharacteristic
333C22#41×D3111yescharacteristic
334C22#41×D3111yescharacteristic
335C22#41×D3111yescharacteristic
336C22#41×D3111yescharacteristic
337C4—22no—
338C4—22no—
339C4—22no—
340C4—22no—
341C4—22no—
342C4—41no—
343C4—41no—
344C4—314no—
345C4—622no—
346C4—622no—
347C4—622no—
348C4—622no—
349C4—1241no—
350C4—1241no—
351C2—1242no—
352C2C4×#9249711yescharacteristic
353C2#1452151711yescharacteristic
354C2C4×#9249911yescharacteristic
355C2#126×D3111yescharacteristic
356C2#1452157611yescharacteristic
357C2#1452158411yescharacteristic
358C2#1452158511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D31
commutatorC22×C31C23×C4
FittingC31×#387C2
socle, cosocleC23×C31C24
prime radicalC23×D31C23
hypercenter#387D31
hypocenterC31C4×#126
LCSG ▷ C22×C31 ▷ C31
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
5. #14520936C2semidirect
6. #14520934C2semidirect
7. #14520916C2semidirect
8. C4⋊C4×Dic31C2semidirect
9. C4⋊C4×Dic31C2semidirect
10. #14520900C2semidirect
14. C42×Dic31C2semidirect
15. C31×#387C2semidirect
39. #11758475C4semidirect
71. C4⋊C4×C31C2×C4semidirect
80. C4⋊Dic31C2×C4semidirect
82. Dic31⋊C4C2×C4semidirect
91. C4×Dic31C2×C4semidirect
171. Dic31#126semidirect
178. #387D31semidirect
231. C31C4×#126semidirect
255. C4⋊C4C4×D31semidirect

Maximal subgroups

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

subgroupindex
C2×#117584752
#145209412
#145209402
#145209392
#145209362
#145209342
#145209162
C4⋊C4×Dic312
#145209002
#145208962
C42×Dic312
C31×#3872
C4×#12631