Finite Group Databasebeta

← #16846252

Subgroups — #16846252

Order 3968.

380 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 79 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14521611C211yesmaximal, characteristic
2#14521522C211yesmaximal, characteristic, complemented
3C2×#11758394C211yesmaximal, characteristic, complemented
4C2×#11758394C211yesmaximal, characteristic, complemented
5C2×#11758394C211yesmaximal, characteristic, complemented
6#14520815C211yesmaximal, characteristic, complemented
7C31×#342C211yesmaximal, characteristic, complemented
8C22×C22⋊D31C2211yescharacteristic
9C22×C22⋊D31C2211yescharacteristic
10C2×C22⋊C4×C31C2211yescharacteristic
11C2×C22⋊C4×C31C2211yescharacteristic
12C2×C22⋊C4×C31C2211yescharacteristic
13C2×C22⋊Dic31C2211yescharacteristic
14C2×C22⋊Dic31C2211yescharacteristic
15#11758507—22no—
16C4×C22⋊D31—22no—
17#11758463—21no—
18#11758463C412yescomplemented
19#11758459—21no—
20#11758459C412yescomplemented
21(C22⋊D31)⋊C4—22no—
22C22⋊C4×D31—21no—
23#11758454—21no—
24#11758394—22no—
25#11758394—22no—
26#11758394—22no—
27C24×C31C2311yescharacteristic
28C23×D31C2×C411yescharacteristic, complemented
29C23×D31D411yescharacteristic
30C22×C4×C31—21no—
31C22×C4×C31—21no—
32C22×C4×C31—21no—
33C2×C22⋊D31—21no—
34C2×C22⋊D31—21no—
35C2×C22⋊D31—21no—
36C2×C22⋊D31—21no—
37C2×C22⋊D31—21no—
38C2×C22⋊D31—21no—
39C2×C22⋊D31—21no—
40C2×C22⋊D31—21no—
41C2×C22⋊D31—21no—
42C2×C22⋊D31—21no—
43C2×C22⋊D31C2×C412yes—
44C2×C22⋊D31D412yes—
45C22×Dic31—21no—
46C22×Dic31—21no—
47C22×Dic31C2×C411yescharacteristic, complemented
48C22×Dic31D411yescharacteristic
49C2×D124—22no—
50C2×C4×D31—22no—
51C22⋊C4×C31—21no—
52C22⋊C4×C31—21no—
53C22⋊C4×C31—21no—
54C22⋊C4×C31—21no—
55C22⋊C4×C31C2×C412yescomplemented
56C22⋊C4×C31D412yescomplemented
57C22⋊Dic31—21no—
58C22⋊Dic31—21no—
59C22⋊Dic31—21no—
60C22⋊Dic31D412yescomplemented
61(C2×D31)⋊C4—22no—
62(C2×D31)⋊C4—22no—
63(C2×D31)⋊C4—22no—
64C4⋊Dic31—22no—
65Dic31⋊C4—22no—
66C4×Dic31—22no—
67C23×C31—81no—
68C23×C31C22×C411yescharacteristic
69C23×C31C2×D411yescharacteristic
70C23×C31C2×D411yescharacteristic
71C23×C31C2×D411yescharacteristic
72C23×C31C2×D411yescharacteristic
73C23×C31#4111yescharacteristic
74C23×C31#4111yescharacteristic
75C22×D31—21no—
76C22×D31—21no—
77C22×D31—21no—
78C22×D31—21no—
79C22×D31—21no—
80C22×D31—81no—
81C22×D31—81no—
82C22×D31C22⋊C412yes—
83C2×C4×C31—22no—
84C2×C4×C31—22no—
85C2×C4×C31—41no—
86C2×C4×C31—81no—
87C2×C4×C31—81no—
88C2×C4×C31—81no—
89C22⋊D31—22no—
90C22⋊D31—22no—
91C22⋊D31—22no—
92C22⋊D31—22no—
93C22⋊D31—41no—
94C22⋊D31—41no—
95C22⋊D31—41no—
96C22⋊D31—41no—
97C2×Dic31—21no—
98C2×Dic31—21no—
99C2×Dic31—21no—
100C2×Dic31—21no—
101C2×Dic31—21no—
102C2×Dic31—22no—
103C2×Dic31—41no—
104C2×Dic31—81no—
105C2×Dic31—81no—
106C2×Dic31C22⋊C412yes—
107D124—82no—
108C4×D31—82no—
109#1913—311nomaximal, Sylow
110C22×C31—41no—
111C22×C31—41no—
112C22×C31—41no—
113C22×C31—41no—
114C22×C31—41no—
115C22×C31—41no—
116C22×C31—41no—
117C22×C31C2×C22⋊C411yescharacteristic
118C22×C31C4×D411yescharacteristic
119C22×C31C4×D411yescharacteristic
120C22×C31#12011yescharacteristic
121C22×C31#12111yescharacteristic
122C22×C31#12111yescharacteristic
123C22×C31#12311yescharacteristic
124C2×D31—22no—
125C2×D31—42no—
126C2×D31—42no—
127C2×D31—42no—
128C2×D31—41no—
129C2×D31—81no—
130C2×D31—81no—
131C2×D31—81no—
132C4×C31—42no—
133C4×C31—42no—
134C4×C31—81no—
135Dic31—22no—
136Dic31—42no—
137Dic31—41no—
138Dic31—81no—
139#534—311no—
140#518—311no—
141C2×#99—311no—
142C2×#99—311no—
143C2×#99—311no—
144#342—311no—
145#342D3111yescharacteristic, complemented
146C2×C31—21no—
147C2×C31—21no—
148C2×C31—21no—
149C2×C31—21no—
150C2×C31—21no—
151C2×C31—21no—
152C2×C31—21no—
153C2×C31#38611yescharacteristic
154D31—42no—
155D31—81no—
156C22×D4—311no—
157C22×D4—311no—
158#123—312no—
159#123—621no—
160#121—622no—
161#120—312no—
162#120—621no—
163C4×D4—622no—
164C4×D4—622no—
165#117—621no—
166C2×C22⋊C4—311no—
167C2×C22⋊C4—311no—
168C2×C22⋊C4—621no—
169C2×C22⋊C4C2×D3111yescharacteristic
170C2×C22⋊C4C2×D3111yescharacteristic
171C2×C22⋊C4C2×D3111yescharacteristic
172#99—622no—
173#99—622no—
174#99—622no—
175C31#191311yescharacteristic, complemented, Sylow
176C24—311no—
177C24—311no—
178C24C22×D3111yescharacteristic
179C2×D4—312no—
180C2×D4—312no—
181C2×D4—622no—
182C2×D4—621no—
183C2×D4—621no—
184C2×D4—621no—
185C2×D4—621no—
186C2×D4—621no—
187C2×D4—621no—
188C2×D4—621no—
189C2×D4—621no—
190C2×D4—621no—
191C2×D4—621no—
192C22×C4—21no—
193C22×C4—21no—
194C22×C4—21no—
195C22×C4—311no—
196C22×C4—311no—
197C22×C4—622no—
198C22×C4—621no—
199C22×C4—621no—
200C4⋊C4—622no—
201C4⋊C4—622no—
202C22⋊C4—21no—
203C22⋊C4—21no—
204C22⋊C4—21no—
205C22⋊C4—21no—
206C22⋊C4—312no—
207C22⋊C4—622no—
208C22⋊C4—622no—
209C22⋊C4—622no—
210C22⋊C4—621no—
211C22⋊C4—621no—
212C22⋊C4—621no—
213C22⋊C4C4×D3112yescomplemented
214C22⋊C4D12412yescomplemented
215C42—622no—
216C23—81no—
217C23—312no—
218C23—621no—
219C23—621no—
220C23—621no—
221C23—621no—
222C23—621no—
223C23—2481no—
224C23—2481no—
225C23C2×C4×D3111yescharacteristic
226C23C2×D12411yescharacteristic
227C23#9249511yescharacteristic
228C23D4×D3111yescharacteristic
229C23D4×D3111yescharacteristic
230C23D4×D3111yescharacteristic
231C23#9249911yescharacteristic
232D4—622no—
233D4—622no—
234D4—622no—
235D4—622no—
236D4—1241no—
237D4—1241no—
238D4—1241no—
239D4—1241no—
240D4—2482no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—41no—
244C2×C4—81no—
245C2×C4—81no—
246C2×C4—81no—
247C2×C4—312no—
248C2×C4—621no—
249C2×C4—621no—
250C2×C4—621no—
251C2×C4—621no—
252C2×C4—622no—
253C2×C4—621no—
254C2×C4—1241no—
255C2×C4—2482no—
256C2×C4—2481no—
257C2×C4—2481no—
258C22—41no—
259C22—41no—
260C22—41no—
261C22—41no—
262C22—41no—
263C22—41no—
264C22—41no—
265C22—622no—
266C22—1242no—
267C22—1242no—
268C22—1242no—
269C22—1241no—
270C22—2481no—
271C22—2481no—
272C22—2481no—
273C22C4×D12411yescharacteristic
274C22C22⋊C4×D3111yescharacteristic
275C22#1175845911yescharacteristic
276C22#1175846111yescharacteristic
277C22#1175847011yescharacteristic
278C22#1175847111yescharacteristic
279C22#1175847211yescharacteristic
280C4—42no—
281C4—42no—
282C4—81no—
283C4—622no—
284C4—1242no—
285C4—1241no—
286C4—2481no—
287C2—21no—
288C2—21no—
289C2—21no—
290C2—21no—
291C2—21no—
292C2—21no—
293C2—21no—
294C2—1242no—
295C2—2481no—
296C2#1452092711yescharacteristic
subgroupG/H
centerC2#14520927
commutatorC23×C31C22×C4
FrattiniC24C22×D31
FittingC31×#342C2
socleC2×C31#386
prime radical#14521611C2
cosocleC24×C31C23
hypercenter#342D31
hypocenterC31#1913
LCSG ▷ C23×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
2. #14521522C2semidirect
3. C2×#11758394C2semidirect
4. C2×#11758394C2semidirect
5. C2×#11758394C2semidirect
6. #14520815C2semidirect
7. C31×#342C2semidirect
18. #11758463C4semidirect
20. #11758459C4semidirect
28. C23×D31C2×C4semidirect
47. C22×Dic31C2×C4semidirect
55. C22⋊C4×C31C2×C4semidirect
56. C22⋊C4×C31D4semidirect
60. C22⋊Dic31D4semidirect
145. #342D31semidirect
175. C31#1913semidirect
213. C22⋊C4C4×D31semidirect
214. C22⋊C4D124semidirect

Maximal subgroups

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

subgroupindex
#145216112
#145215222
C2×#117583942
#145208152
C31×#3422
#191331