Finite Group Databasebeta

← #16846116

Subgroups — #16846116

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×#11758530C211yesmaximal, characteristic
2#14521522C211yesmaximal, characteristic, complemented
3C2×#11758394C211yesmaximal, characteristic, complemented
4#14520905C211yesmaximal, characteristic, complemented
5#14520816C211yesmaximal, characteristic, complemented
6#14520815C211yesmaximal, characteristic, complemented
7C31×#379C211yesmaximal, characteristic, complemented
8C25×C31C2211yescharacteristic
9C22×C22⋊D31—21no—
10C22×C22⋊D31C2211yescharacteristic
11C2×C22⋊C4×C31—22no—
12C2×C22⋊C4×C31C2211yescharacteristic
13C2×C22⋊C4×C31C2211yescharacteristic
14#11758530—22no—
15#11758530C414yescomplemented
16C2×C22⋊Dic31—21no—
17C2×C22⋊Dic31—22no—
18C2×C22⋊Dic31C2211yescharacteristic
19C2×C22⋊Dic31C2211yescharacteristic
20C2×C22⋊Dic31C2211yescharacteristic
21C4×C22⋊D31—22no—
22(C22⋊D31)⋊C4—22no—
23C22⋊C4×D31—21no—
24#11758454—21no—
25#11758394—22no—
26C24×C31—21no—
27C24×C31—21no—
28C24×C31—21no—
29C24×C31—21no—
30C24×C31—21no—
31C24×C31—21no—
32C24×C31—44no—
33C24×C31C2×C412yescomplemented
34C24×C31C2311yescharacteristic
35C23×D31D411yescharacteristic
36C22×C4×C31—21no—
37C22×C4×C31D412yescomplemented
38C2×C22⋊D31—21no—
39C2×C22⋊D31—21no—
40C2×C22⋊D31—21no—
41C2×C22⋊D31—21no—
42C2×C22⋊D31—24no—
43C2×C22⋊D31—44no—
44C2×C22⋊D31C2×C412yes—
45C2×C22⋊D31D412yes—
46C22×Dic31—21no—
47C22×Dic31—21no—
48C22×Dic31D411yescharacteristic
49C22×Dic31D412yescomplemented
50C2×C4×D31—22no—
51C22⋊C4×C31—21no—
52C22⋊C4×C31—21no—
53C22⋊C4×C31—21no—
54C22⋊C4×C31—21no—
55C22⋊C4×C31—44no—
56C22⋊Dic31—21no—
57C22⋊Dic31—21no—
58C22⋊Dic31—21no—
59C22⋊Dic31—24no—
60C22⋊Dic31—21no—
61C22⋊Dic31—21no—
62C22⋊Dic31—44no—
63C22⋊Dic31C2×C412yescomplemented
64(C2×D31)⋊C4—22no—
65Dic31⋊C4—22no—
66C4×Dic31—22no—
67C23×C31—24no—
68C23×C31—24no—
69C23×C31—24no—
70C23×C31—22no—
71C23×C31—22no—
72C23×C31—22no—
73C23×C31—44no—
74C23×C31—42no—
75C23×C31—42no—
76C23×C31—42no—
77C23×C31—42no—
78C23×C31—44no—
79C23×C31—44no—
80C23×C31—44no—
81C23×C31—41no—
82C23×C31—41no—
83C23×C31—41no—
84C23×C31—41no—
85C23×C31C22×C411yescharacteristic
86C23×C31C2×D411yescharacteristic
87C23×C31C2×D411yescharacteristic
88C23×C31C2×D411yescharacteristic
89C23×C31C2×D411yescharacteristic
90C23×C31#4111yescharacteristic
91C23×C31#4111yescharacteristic
92C22×D31—21no—
93C22×D31—21no—
94C22×D31—42no—
95C22×D31C22⋊C412yescomplemented
96C2×C4×C31—22no—
97C2×C4×C31—42no—
98C2×C4×C31—42no—
99C2×C4×C31—41no—
100C22⋊D31—22no—
101C22⋊D31—22no—
102C22⋊D31—22no—
103C22⋊D31—22no—
104C22⋊D31—48no—
105C2×Dic31—21no—
106C2×Dic31—21no—
107C2×Dic31—22no—
108C2×Dic31—22no—
109C2×Dic31—42no—
110C2×Dic31—42no—
111C2×Dic31—42no—
112C2×Dic31—41no—
113C2×Dic31C22⋊C412yescomplemented
114C4×D31—82no—
115#1889—311nomaximal, Sylow
116C22×C31—22no—
117C22×C31—22no—
118C22×C31—22no—
119C22×C31—24no—
120C22×C31—24no—
121C22×C31—24no—
122C22×C31—41no—
123C22×C31—41no—
124C22×C31—41no—
125C22×C31—41no—
126C22×C31—42no—
127C22×C31—44no—
128C22×C31—44no—
129C22×C31—44no—
130C22×C31—42no—
131C22×C31—42no—
132C22×C31—42no—
133C22×C31—44no—
134C22×C31C2×C22⋊C411yescharacteristic
135C22×C31C4×D411yescharacteristic
136C22×C31C4×D411yescharacteristic
137C22×C31#12011yescharacteristic
138C22×C31#12111yescharacteristic
139C22×C31#12111yescharacteristic
140C22×C31#12311yescharacteristic
141C2×D31—22no—
142C2×D31—42no—
143C2×D31—42no—
144C2×D31—81no—
145C4×C31—42no—
146C4×C31—81no—
147Dic31—22no—
148Dic31—42no—
149Dic31—42no—
150Dic31—81no—
151C2×#120—311no—
152#518—311no—
153C2×#99—311no—
154#379—311no—
155#379D3111yescharacteristic, complemented
156#342—311no—
157#342—311no—
158C2×C31—21no—
159C2×C31—21no—
160C2×C31—21no—
161C2×C31—21no—
162C2×C31—21no—
163C2×C31—21no—
164C2×C31—44no—
165C2×C31#38611yescharacteristic
166C2×C31B(4,𝔽2)12yes—
167D31—42no—
168C25C2×D3111yescharacteristic
169C22×D4—311no—
170C22×D4—621no—
171#120—314no—
172#120—622no—
173C4×D4—622no—
174C4×D4—622no—
175#117—621no—
176C2×C22⋊C4—22no—
177C2×C22⋊C4—311no—
178C2×C22⋊C4—311no—
179C2×C22⋊C4—311no—
180C2×C22⋊C4—621no—
181C2×C22⋊C4—621no—
182C2×C22⋊C4—622no—
183C2×C22⋊C4C2×D3111yescharacteristic
184C2×C22⋊C4C2×D3111yescharacteristic
185#99—622no—
186C31#188911yescharacteristic, complemented, Sylow
187C24—21no—
188C24—21no—
189C24—21no—
190C24—21no—
191C24—21no—
192C24—21no—
193C24—44no—
194C24—311no—
195C24C4×D3112yescomplemented
196C24C22×D3111yescharacteristic
197C2×D4—312no—
198C2×D4—312no—
199C2×D4—621no—
200C2×D4—621no—
201C2×D4—621no—
202C2×D4—621no—
203C2×D4—624no—
204C2×D4—1244no—
205C22×C4—21no—
206C22×C4—311no—
207C22×C4—312no—
208C22×C4—622no—
209C22×C4—621no—
210C22×C4—621no—
211C22×C4C22⋊D3112yescomplemented
212C4⋊C4—622no—
213C22⋊C4—21no—
214C22⋊C4—21no—
215C22⋊C4—21no—
216C22⋊C4—21no—
217C22⋊C4—44no—
218C22⋊C4—312no—
219C22⋊C4—622no—
220C22⋊C4—624no—
221C22⋊C4—621no—
222C22⋊C4—621no—
223C22⋊C4—621no—
224C22⋊C4—621no—
225C22⋊C4—621no—
226C22⋊C4—1244no—
227C42—622no—
228C23—24no—
229C23—24no—
230C23—24no—
231C23—22no—
232C23—22no—
233C23—22no—
234C23—44no—
235C23—42no—
236C23—42no—
237C23—42no—
238C23—42no—
239C23—44no—
240C23—44no—
241C23—44no—
242C23—41no—
243C23—41no—
244C23—41no—
245C23—41no—
246C23—312no—
247C23—621no—
248C23—621no—
249C23—1242no—
250C23C2×C4×D3111yescharacteristic
251C23#9249511yescharacteristic
252C23D4×D3111yescharacteristic
253C23D4×D3111yescharacteristic
254C23D4×D3111yescharacteristic
255C23#9249711yescharacteristic
256C23C2×C22⋊D3111yescharacteristic
257D4—622no—
258D4—622no—
259D4—622no—
260D4—622no—
261D4—1248no—
262C2×C4—22no—
263C2×C4—42no—
264C2×C4—42no—
265C2×C4—41no—
266C2×C4—312no—
267C2×C4—621no—
268C2×C4—621no—
269C2×C4—622no—
270C2×C4—622no—
271C2×C4—1242no—
272C2×C4—1242no—
273C2×C4—1242no—
274C2×C4—1241no—
275C2×C4—2482no—
276C22—22no—
277C22—22no—
278C22—22no—
279C22—24no—
280C22—24no—
281C22—24no—
282C22—41no—
283C22—41no—
284C22—41no—
285C22—41no—
286C22—44no—
287C22—42no—
288C22—44no—
289C22—42no—
290C22—42no—
291C22—44no—
292C22—42no—
293C22—44no—
294C22—622no—
295C22—1242no—
296C22—1242no—
297C22—2481no—
298C22C22⋊C4×D3111yescharacteristic
299C22(C22⋊D31)⋊C411yescharacteristic
300C22#1175846011yescharacteristic
301C22#1175846111yescharacteristic
302C22C4×C22⋊D3111yescharacteristic
303C22#1175851411yescharacteristic
304C22#1175851511yescharacteristic
305C4—42no—
306C4—81no—
307C4—622no—
308C4—1242no—
309C4—1242no—
310C4—2481no—
311C2—21no—
312C2—21no—
313C2—21no—
314C2—21no—
315C2—21no—
316C2—21no—
317C2—44no—
318C2—1242no—
319C2#1452092511yescharacteristic
320C2#1452123512yes—
subgroupG/H
centerC22#11758514
commutatorC23×C31C22×C4
FrattiniC24C22×D31
FittingC31×#379C2
socleC22×C31#120
prime radicalC2×#11758530C2
cosocleC24×C31C23
hypercenter#379D31
hypocenterC31#1889
LCSG ▷ C23×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C24 ◁ #379

Complements

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

NH ≅ G/Ntype
2. #14521522C2semidirect
3. C2×#11758394C2semidirect
4. #14520905C2semidirect
5. #14520816C2semidirect
6. #14520815C2semidirect
7. C31×#379C2semidirect
15. #11758530C4semidirect
33. C24×C31C2×C4semidirect
37. C22×C4×C31D4semidirect
49. C22×Dic31D4semidirect
63. C22⋊Dic31C2×C4semidirect
95. C22×D31C22⋊C4semidirect
113. C2×Dic31C22⋊C4semidirect
155. #379D31semidirect
186. C31#1889semidirect
195. C24C4×D31semidirect
211. C22×C4C22⋊D31semidirect

Maximal subgroups

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

subgroupindex
C2×#117585302
#145215222
C2×#117583942
#145209052
#145208162
#145208152
C31×#3792
#188931