Finite Group Databasebeta

← #16846118

Subgroups — #16846118

Order 3968.

578 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 578 conjugacy classes of subgroups — too many to draw. Only its 83 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
1C2×#11758459C211yesmaximal, characteristic
2#14521522C211yesmaximal, characteristic, complemented
3C2×#11758394C211yesmaximal, characteristic, complemented
4#14520904C211yesmaximal, characteristic, complemented
5#14520904C211yesmaximal, characteristic, complemented
6#14520815C211yesmaximal, characteristic, complemented
7C31×#342C211yesmaximal, characteristic, complemented
8C24×D31C2211yescharacteristic
9C22×C22⋊D31C2211yescharacteristic
10C22×D124—21no—
11C2×C22⋊C4×C31C2211yescharacteristic
12C2×C22⋊C4×C31C2211yescharacteristic
13C2×C22⋊C4×C31C2211yescharacteristic
14C2×C22⋊Dic31C2211yescharacteristic
15C2×C22⋊Dic31C2211yescharacteristic
16C4×C22⋊D31—22no—
17C2×(C2×D31)⋊C4—21no—
18C2×(C2×D31)⋊C4—22no—
19C2×(C2×D31)⋊C4—22no—
20#11758459—22no—
21#11758459C414yescomplemented
22(C22⋊D31)⋊C4—22no—
23C22⋊C4×D31—21no—
24#11758454—21no—
25#11758394—22no—
26C24×C31C2311yescharacteristic
27C23×D31—21no—
28C23×D31—21no—
29C23×D31—21no—
30C23×D31—21no—
31C23×D31—21no—
32C23×D31—21no—
33C23×D31—44no—
34C23×D31C2×C412yescomplemented
35C23×D31D411yescharacteristic
36C22×C4×C31—21no—
37C22×C4×C31—21no—
38C22×C4×C31D412yescomplemented
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×Dic31D411yescharacteristic
47C22×Dic31D412yescomplemented
48C2×D124—24no—
49C2×D124—44no—
50C2×C4×D31—22no—
51C22⋊C4×C31—21no—
52C22⋊C4×C31—21no—
53C22⋊C4×C31—21no—
54C22⋊C4×C31—21no—
55C22⋊C4×C31—21no—
56C22⋊C4×C31C2×C412yescomplemented
57C22⋊Dic31—21no—
58C22⋊Dic31—21no—
59C22⋊Dic31—21no—
60C22⋊Dic31—21no—
61(C2×D31)⋊C4—22no—
62(C2×D31)⋊C4—24no—
63(C2×D31)⋊C4—44no—
64(C2×D31)⋊C4—44no—
65Dic31⋊C4—22no—
66C4×Dic31—22no—
67C23×C31—42no—
68C23×C31C22×C411yescharacteristic
69C23×C31C2×D411yescharacteristic
70C23×C31C2×D411yescharacteristic
71C23×C31C2×D411yescharacteristic
72C23×C31C2×D411yescharacteristic
73C23×C31#4111yescharacteristic
74C23×C31#4111yescharacteristic
75C22×D31—24no—
76C22×D31—24no—
77C22×D31—24no—
78C22×D31—22no—
79C22×D31—22no—
80C22×D31—22no—
81C22×D31—21no—
82C22×D31—21no—
83C22×D31—44no—
84C22×D31—44no—
85C22×D31—44no—
86C22×D31—44no—
87C22×D31—42no—
88C22×D31—42no—
89C22×D31—42no—
90C22×D31—41no—
91C22×D31—41no—
92C22×D31—41no—
93C22×D31—41no—
94C22×D31—42no—
95C22×D31C22⋊C412yescomplemented
96C2×C4×C31—22no—
97C2×C4×C31—22no—
98C2×C4×C31—42no—
99C2×C4×C31—42no—
100C2×C4×C31—42no—
101C2×C4×C31—41no—
102C22⋊D31—22no—
103C22⋊D31—22no—
104C22⋊D31—22no—
105C22⋊D31—22no—
106C2×Dic31—21no—
107C2×Dic31—21no—
108C2×Dic31—22no—
109C2×Dic31—42no—
110C2×Dic31—42no—
111C2×Dic31—41no—
112C2×Dic31C22⋊C412yescomplemented
113D124—48no—
114C4×D31—82no—
115#1889—311nomaximal, Sylow
116C22×C31—22no—
117C22×C31—22no—
118C22×C31—22no—
119C22×C31—41no—
120C22×C31—41no—
121C22×C31—41no—
122C22×C31—41no—
123C22×C31C2×C22⋊C411yescharacteristic
124C22×C31C4×D411yescharacteristic
125C22×C31C4×D411yescharacteristic
126C22×C31#12011yescharacteristic
127C22×C31#12111yescharacteristic
128C22×C31#12111yescharacteristic
129C22×C31#12311yescharacteristic
130C2×D31—24no—
131C2×D31—24no—
132C2×D31—24no—
133C2×D31—22no—
134C2×D31—44no—
135C2×D31—42no—
136C2×D31—44no—
137C2×D31—42no—
138C2×D31—42no—
139C2×D31—44no—
140C2×D31—42no—
141C2×D31—42no—
142C2×D31—44no—
143C2×D31—42no—
144C2×D31—81no—
145C4×C31—42no—
146C4×C31—42no—
147C4×C31—81no—
148Dic31—22no—
149Dic31—42no—
150Dic31—81no—
151C2×#120—311no—
152#518—311no—
153C2×#99—311no—
154#379—311no—
155#379—311no—
156#342—311no—
157#342D3111yescharacteristic, complemented
158C2×C31—21no—
159C2×C31—21no—
160C2×C31—21no—
161C2×C31—21no—
162C2×C31—21no—
163C2×C31—21no—
164C2×C31#38611yescharacteristic
165C2×C31B(4,𝔽2)12yes—
166D31—44no—
167D31—42no—
168C25—311no—
169C22×D4—311no—
170C22×D4—621no—
171#120—314no—
172#120—622no—
173C4×D4—622no—
174C4×D4—622no—
175#117—621no—
176C2×C22⋊C4—311no—
177C2×C22⋊C4—311no—
178C2×C22⋊C4—621no—
179C2×C22⋊C4—621no—
180C2×C22⋊C4—622no—
181C2×C22⋊C4—622no—
182C2×C22⋊C4C2×D3111yescharacteristic
183C2×C22⋊C4C2×D3111yescharacteristic
184C2×C22⋊C4C2×D3111yescharacteristic
185#99—622no—
186C31#188911yescharacteristic, complemented, Sylow
187C24—311no—
188C24—312no—
189C24—621no—
190C24—621no—
191C24—621no—
192C24—621no—
193C24—621no—
194C24—621no—
195C24—1244no—
196C24C22×D3111yescharacteristic
197C2×D4—312no—
198C2×D4—312no—
199C2×D4—624no—
200C2×D4—621no—
201C2×D4—621no—
202C2×D4—621no—
203C2×D4—621no—
204C2×D4—1244no—
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—311no—
208C22×C4—312no—
209C22×C4—622no—
210C22×C4—621no—
211C22×C4D12412yescomplemented
212C4⋊C4—622no—
213C22⋊C4—21no—
214C22⋊C4—21no—
215C22⋊C4—21no—
216C22⋊C4—21no—
217C22⋊C4—21no—
218C22⋊C4—624no—
219C22⋊C4—622no—
220C22⋊C4—621no—
221C22⋊C4—621no—
222C22⋊C4—621no—
223C22⋊C4—621no—
224C22⋊C4—1244no—
225C22⋊C4—1244no—
226C22⋊C4C4×D3112yescomplemented
227C42—622no—
228C23—42no—
229C23—312no—
230C23—624no—
231C23—624no—
232C23—624no—
233C23—622no—
234C23—622no—
235C23—621no—
236C23—622no—
237C23—621no—
238C23—1242no—
239C23—1242no—
240C23—1242no—
241C23—1242no—
242C23—1244no—
243C23—1244no—
244C23—1244no—
245C23—1244no—
246C23—1241no—
247C23—1241no—
248C23—1241no—
249C23—1241no—
250C23C2×C4×D3111yescharacteristic
251C23C2×D12411yescharacteristic
252C23#9249511yescharacteristic
253C23D4×D3111yescharacteristic
254C23D4×D3111yescharacteristic
255C23D4×D3111yescharacteristic
256C23#9249911yescharacteristic
257D4—622no—
258D4—622no—
259D4—622no—
260D4—622no—
261D4—1248no—
262C2×C4—22no—
263C2×C4—22no—
264C2×C4—42no—
265C2×C4—42no—
266C2×C4—42no—
267C2×C4—41no—
268C2×C4—312no—
269C2×C4—621no—
270C2×C4—621no—
271C2×C4—622no—
272C2×C4—1242no—
273C2×C4—1242no—
274C2×C4—1241no—
275C2×C4—2482no—
276C22—22no—
277C22—22no—
278C22—22no—
279C22—41no—
280C22—41no—
281C22—41no—
282C22—41no—
283C22—624no—
284C22—624no—
285C22—624no—
286C22—622no—
287C22—1242no—
288C22—1242no—
289C22—1244no—
290C22—1244no—
291C22—1242no—
292C22—1242no—
293C22—1244no—
294C22—1242no—
295C22—1242no—
296C22—1244no—
297C22—2481no—
298C22C4×D12411yescharacteristic
299C22C22⋊C4×D3111yescharacteristic
300C22#1175845911yescharacteristic
301C22#1175846111yescharacteristic
302C22#1175847011yescharacteristic
303C22#1175847111yescharacteristic
304C22#1175847211yescharacteristic
305C4—42no—
306C4—42no—
307C4—81no—
308C4—622no—
309C4—1242no—
310C4—2481no—
311C2—21no—
312C2—21no—
313C2—21no—
314C2—21no—
315C2—21no—
316C2—21no—
317C2—1244no—
318C2—1242no—
319C2#1452092711yescharacteristic
320C2#1452123712yes—
subgroupG/H
centerC22#11758459
commutatorC23×C31C22×C4
FrattiniC24C22×D31
FittingC31×#342C2
socleC22×C31#120
prime radicalC2×#11758459C2
cosocleC24×C31C23
hypercenter#342D31
hypocenterC31#1889
LCSG ▷ C23×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
2. #14521522C2semidirect
3. C2×#11758394C2semidirect
4. #14520904C2semidirect
5. #14520904C2semidirect
6. #14520815C2semidirect
7. C31×#342C2semidirect
21. #11758459C4semidirect
34. C23×D31C2×C4semidirect
38. C22×C4×C31D4semidirect
47. C22×Dic31D4semidirect
56. C22⋊C4×C31C2×C4semidirect
95. C22×D31C22⋊C4semidirect
112. C2×Dic31C22⋊C4semidirect
157. #342D31semidirect
186. C31#1889semidirect
211. C22×C4D124semidirect
226. C22⋊C4C4×D31semidirect

Maximal subgroups

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

subgroupindex
C2×#117584592
#145215222
C2×#117583942
#145209042
#145208152
C31×#3422
#188931