Finite Group Databasebeta

← #16848898

Subgroups — #16848898

Order 3968.

456 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×#11758456C211yesmaximal, characteristic
2#14520947C211yesmaximal, characteristic, complemented
3#14520946C211yesmaximal, characteristic, complemented
4#14520944C211yesmaximal, characteristic, complemented
5#14520943C211yesmaximal, characteristic
6#14520937C211yesmaximal, characteristic
7#14520936C211yesmaximal, characteristic, complemented
8#14520934C211yesmaximal, characteristic, complemented
9#14520933C211yesmaximal, characteristic, complemented
10#14520924C211yesmaximal, characteristic
11#14520921C211yesmaximal, characteristic
12#14520921C211yesmaximal, characteristic
13#14520918C211yesmaximal, characteristic, complemented
14#14520916C211yesmaximal, characteristic, complemented
15C31×#388C211yesmaximal, characteristic
16C23×Dic31C2211yescharacteristic
17C2×C4⋊C4×C31C2211yescharacteristic
18C2×C22⋊C4×C31C2211yescharacteristic
19C2×C22⋊C4×C31C2211yescharacteristic
20C2×C22⋊C4×C31C2211yescharacteristic
21C2×C42×C31C2211yescharacteristic
22C2×C22⋊Dic31C2211yescharacteristic
23C2×C22⋊Dic31C2211yescharacteristic
24C2×C22⋊Dic31C2211yescharacteristic
25C2×C4⋊Dic31C2211yescharacteristic
26C2×C4⋊Dic31C2211yescharacteristic
27C2×C4⋊Dic31C2211yescharacteristic
28C2×Dic31⋊C4C2211yescharacteristic
29C2×Dic31⋊C4C2211yescharacteristic
30C2×Dic31⋊C4C2211yescharacteristic
31C2×Dic31⋊C4C2211yescharacteristic
32C2×Dic31⋊C4C2211yescharacteristic
33C2×Dic31⋊C4C2211yescharacteristic
34C2×Dic31⋊C4C2211yescharacteristic
35C2×Dic31⋊C4C2211yescharacteristic
36C2×C4×Dic31C2211yescharacteristic
37C2×C4×Dic31C2211yescharacteristic
38C2×C4×Dic31C2211yescharacteristic
39#11758456C418yescomplemented
40C31×#95C2211yescharacteristic
41C31×#95C2211yescharacteristic
42C31⋊#95C2211yescharacteristic
43C31⋊#95C2211yescharacteristic
44C31⋊#95C2211yescharacteristic
45C31⋊#95C2211yescharacteristic
46C31⋊#95C2211yescharacteristic
47C31⋊#95C2211yescharacteristic
48C31⋊#95C2211yescharacteristic
49C31⋊#95C2211yescharacteristic
50C31⋊#95C2211yescharacteristic
51C31⋊#95C2211yescharacteristic
52C24×C31C2311yescharacteristic
53C22×C4×C31C2311yescharacteristic
54C22×C4×C31C2311yescharacteristic
55C22×C4×C31C2311yescharacteristic
56C22×C4×C31C2311yescharacteristic
57C22×C4×C31C2311yescharacteristic
58C22×C4×C31C2311yescharacteristic
59C22×Dic31—41no—
60C22×Dic31—41no—
61C22×Dic31—41no—
62C22×Dic31C2311yescharacteristic
63C22×Dic31C2311yescharacteristic
64C22×Dic31C2311yescharacteristic
65C22×Dic31C2311yescharacteristic
66C22×Dic31C2311yescharacteristic
67C22×Dic31C2311yescharacteristic
68C22×Dic31C2311yescharacteristic
69C22×Dic31C2311yescharacteristic
70C4⋊C4×C31—41no—
71C22⋊C4×C31—41no—
72C22⋊C4×C31—41no—
73C22⋊C4×C31C2×C414yes—
74C42×C31—41no—
75C22⋊Dic31—41no—
76C22⋊Dic31C2×C414yes—
77C22⋊Dic31C2×C414yes—
78C4⋊Dic31—41no—
79C4⋊Dic31—41no—
80C4⋊Dic31C2×C414yescomplemented
81Dic31⋊C4—41no—
82Dic31⋊C4—41no—
83Dic31⋊C4—41no—
84Dic31⋊C4—41no—
85Dic31⋊C4—41no—
86Dic31⋊C4—41no—
87Dic31⋊C4C2×C414yescomplemented
88Dic31⋊C4C2×C414yescomplemented
89C4×Dic31—41no—
90C4×Dic31—41no—
91C4×Dic31C2×C414yescomplemented
92C23×C31—21no—
93C23×C31—21no—
94C23×C31—21no—
95C23×C31—21no—
96C23×C31—21no—
97C23×C31—21no—
98C23×C31C22×C412yes—
99C23×C31C2411yescharacteristic
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×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—21no—
134C2×Dic31—21no—
135C2×Dic31—21no—
136C2×Dic31—21no—
137C2×Dic31—21no—
138C2×Dic31—44no—
139C2×Dic31C22×C412yes—
140C2×Dic31C22×C412yes—
141C2×Dic31C22×C412yes—
142C2×Dic31C22×C412yes—
143#2383—311nomaximal, Sylow
144C22×C31—22no—
145C22×C31—22no—
146C22×C31—22no—
147C22×C31—41no—
148C22×C31—41no—
149C22×C31—41no—
150C22×C31—41no—
151C22×C31C23×C411yescharacteristic
152C22×C31H(5,𝔽2)11yescharacteristic
153C22×C31H(5,𝔽2)11yescharacteristic
154C22×C31H(5,𝔽2)11yescharacteristic
155C22×C312−1+411yescharacteristic
156C22×C312−1+411yescharacteristic
157C22×C312−1+411yescharacteristic
158C4×C31—22no—
159C4×C31—22no—
160C4×C31—41no—
161C4×C31—41no—
162C4×C31—41no—
163C4×C31—41no—
164Dic31—22no—
165Dic31—22no—
166Dic31—22no—
167Dic31—22no—
168Dic31—41no—
169Dic31—41no—
170Dic31—41no—
171Dic31—41no—
172C2×#126—311no—
173#389—311no—
174#389—311no—
175#389—311no—
176#388—311no—
177#388—311no—
178#388D3111yescharacteristic
179#387—311no—
180#387—311no—
181#387—311no—
182#385—311no—
183#385—311no—
184#385—311no—
185#384—311no—
186#383—311no—
187C2×C31—42no—
188C2×C31#52011yescharacteristic
189C2×C31#52011yescharacteristic
190C2×C31#52011yescharacteristic
191C2×C31#56011yescharacteristic
192C2×C31#56311yescharacteristic
193C2×C31#56311yescharacteristic
194C2×C31#56311yescharacteristic
195C23×C4—311no—
196#126—318no—
197C2×C4⋊C4—311no—
198C2×C4⋊C4—311no—
199C2×C4⋊C4—311no—
200C2×C4⋊C4—311no—
201C2×C4⋊C4—311no—
202C2×C4⋊C4—311no—
203C2×C4⋊C4—311no—
204C2×C4⋊C4—311no—
205C2×C4⋊C4—311no—
206C2×C4⋊C4—311no—
207C2×C4⋊C4—311no—
208C2×C4⋊C4C2×D3111yescharacteristic
209C2×C22⋊C4—311no—
210C2×C22⋊C4—311no—
211C2×C22⋊C4—311no—
212C2×C22⋊C4C2×D3111yescharacteristic
213C2×C22⋊C4C2×D3111yescharacteristic
214C2×C22⋊C4C2×D3111yescharacteristic
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#95—311no—
228#95—311no—
229#95C2×D3111yescharacteristic
230#95C2×D3111yescharacteristic
231C31#238311yescharacteristic, complemented, Sylow
232C24C22×D3111yescharacteristic
233C22×C4—311no—
234C22×C4—311no—
235C22×C4—311no—
236C22×C4—311no—
237C22×C4—311no—
238C22×C4—311no—
239C22×C4—311no—
240C22×C4—311no—
241C22×C4—1241no—
242C22×C4—1241no—
243C22×C4—1241no—
244C22×C4C22×D3111yescharacteristic
245C22×C4C22×D3111yescharacteristic
246C22×C4C22×D3111yescharacteristic
247C22×C4C22×D3111yescharacteristic
248C22×C4C22×D3111yescharacteristic
249C22×C4C22×D3111yescharacteristic
250C4⋊C4—41no—
251C4⋊C4—314no—
252C4⋊C4—314no—
253C4⋊C4—314no—
254C4⋊C4—1241no—
255C4⋊C4—1241no—
256C4⋊C4—1241no—
257C4⋊C4—1241no—
258C4⋊C4—1241no—
259C4⋊C4—1241no—
260C4⋊C4—1241no—
261C4⋊C4—1241no—
262C22⋊C4—41no—
263C22⋊C4—41no—
264C22⋊C4—314no—
265C22⋊C4—314no—
266C22⋊C4—1241no—
267C22⋊C4C4×D3114yes—
268C42—41no—
269C42—314no—
270C42—1241no—
271C42—1241no—
272C23—21no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23C2×C4×D3112yes—
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—621no—
301C2×C4—621no—
302C2×C4—621no—
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—621no—
318C2×C4—621no—
319C2×C4—621no—
320C2×C4—1244no—
321C2×C4C2×C4×D3112yes—
322C2×C4C2×C4×D3112yes—
323C22—22no—
324C22—22no—
325C22—22no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22C22×C4×D3111yescharacteristic
331C22#1175856111yescharacteristic
332C22#1175856111yescharacteristic
333C22#1175856611yescharacteristic
334C22#1175856711yescharacteristic
335C22#1175856711yescharacteristic
336C22#1175856711yescharacteristic
337C4—22no—
338C4—22no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—622no—
344C4—622no—
345C4—622no—
346C4—622no—
347C4—1241no—
348C4—1241no—
349C4—1241no—
350C4—1241no—
351C2—42no—
352C2#1452152811yescharacteristic
353C2#1452152811yescharacteristic
354C2#1452152911yescharacteristic
355C2#1452178711yescharacteristic
356C2#1452179911yescharacteristic
357C2#1452180111yescharacteristic
358C2#1452180211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D31
commutatorC22×C31C23×C4
FittingC31×#388C2
socle, cosocleC23×C31C24
prime radicalC24×C31C23
hypercenter#388D31
hypocenterC31#2383
LCSG ▷ C22×C31 ▷ C31
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
2. #14520947C2semidirect
3. #14520946C2semidirect
4. #14520944C2semidirect
7. #14520936C2semidirect
8. #14520934C2semidirect
9. #14520933C2semidirect
13. #14520918C2semidirect
14. #14520916C2semidirect
39. #11758456C4semidirect
80. C4⋊Dic31C2×C4semidirect
87. Dic31⋊C4C2×C4semidirect
88. Dic31⋊C4C2×C4semidirect
91. C4×Dic31C2×C4semidirect
231. C31#2383semidirect

Maximal subgroups

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

subgroupindex
C2×#117584562
#145209472
#145209462
#145209442
#145209432
#145209372
#145209362
#145209342
#145209332
#145209242
#145209212
#145209182
#145209162
C31×#3882
#238331