Finite Group Databasebeta

← #16846694

Subgroups — #16846694

Order 3968.

324 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 85 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×#11758455C211yesmaximal, characteristic
2#14520907C211yesmaximal, characteristic
3C22⋊C4×Dic31C211yesmaximal, characteristic
4#14520816C211yesmaximal, characteristic
5#14520815C211yesmaximal, characteristic
6#14520815C211yesmaximal, characteristic
7C31×#342C211yesmaximal, characteristic
8C23×Dic31C2211yescharacteristic
9C22×Dic62C411yescharacteristic, complemented
10C2×C22⋊C4×C31C2211yescharacteristic
11C2×C22⋊C4×C31C2211yescharacteristic
12C2×C22⋊C4×C31C2211yescharacteristic
13C2×C22⋊Dic31C2211yescharacteristic
14C2×C22⋊Dic31C2211yescharacteristic
15C2×C22⋊Dic31C2211yescharacteristic
16C2×C4⋊Dic31C411yescharacteristic, complemented
17C2×Dic31⋊C4—21no—
18C2×Dic31⋊C4C411yescharacteristic, complemented
19C2×Dic31⋊C4C411yescharacteristic, complemented
20C2×C4×Dic31—21no—
21#11758455—21no—
22#11758455—21no—
23#11758455—21no—
24#11758455—21no—
25C31⋊#95—21no—
26C31⋊#95—21no—
27C24×C31C2311yescharacteristic
28C22×C4×C31—21no—
29C22×C4×C31—21no—
30C22×C4×C31C2×C411yescharacteristic
31C22×C4×C31C2×C411yescharacteristic
32C22×Dic31—21no—
33C22×Dic31—21no—
34C22×Dic31—42no—
35C22×Dic31C2×C411yescharacteristic
36C22×Dic31C2×C411yescharacteristic
37C22×Dic31C2×C411yescharacteristic
38C22×Dic31C2×C411yescharacteristic
39C22×Dic31D411yescharacteristic
40C22×Dic31D411yescharacteristic
41C22×Dic31D411yescharacteristic
42C22×Dic31D411yescharacteristic
43C2×Dic62—21no—
44C2×Dic62—21no—
45C2×Dic62—42no—
46C22⋊C4×C31—21no—
47C22⋊C4×C31—21no—
48C22⋊C4×C31—21no—
49C22⋊C4×C31—21no—
50C22⋊C4×C31—21no—
51C22⋊C4×C31Q812yescomplemented
52C22⋊Dic31—21no—
53C22⋊Dic31—21no—
54C22⋊Dic31—21no—
55C22⋊Dic31—21no—
56C22⋊Dic31—21no—
57C22⋊Dic31Q812yescomplemented
58C4⋊Dic31—21no—
59C4⋊Dic31—21no—
60Dic31⋊C4—21no—
61Dic31⋊C4—21no—
62Dic31⋊C4—21no—
63Dic31⋊C4—21no—
64Dic31⋊C4—42no—
65C4×Dic31—42no—
66C23×C31—41no—
67C23×C31—41no—
68C23×C31C22×C411yescharacteristic
69C23×C31C2×D411yescharacteristic
70C23×C31C2×D411yescharacteristic
71C23×C31C2×Q811yescharacteristic
72C23×C31C2×Q811yescharacteristic
73C23×C31#4111yescharacteristic
74C23×C31#4111yescharacteristic
75C2×C4×C31—21no—
76C2×C4×C31—21no—
77C2×C4×C31—22no—
78C2×C4×C31—41no—
79C2×C4×C31—41no—
80C2×C4×C31—41no—
81C2×C4×C31—41no—
82C2×C4×C31—41no—
83C2×C4×C31—41no—
84C2×C4×C31—41no—
85C2×Dic31—22no—
86C2×Dic31—22no—
87C2×Dic31—22no—
88C2×Dic31—21no—
89C2×Dic31—21no—
90C2×Dic31—22no—
91C2×Dic31—41no—
92C2×Dic31—41no—
93C2×Dic31—41no—
94C2×Dic31—41no—
95C2×Dic31—41no—
96C2×Dic31—41no—
97C2×Dic31—41no—
98C2×Dic31—41no—
99C2×Dic31—41no—
100C2×Dic31—41no—
101C2×Dic31C22⋊C411yescharacteristic
102C2×Dic31C22⋊C411yescharacteristic
103C2×Dic31C22⋊C411yescharacteristic
104C2×Dic31C22⋊C411yescharacteristic
105Dic62—42no—
106Dic62—42no—
107#1996—311nomaximal, Sylow
108C22×C31—21no—
109C22×C31—21no—
110C22×C31—21no—
111C22×C31—21no—
112C22×C31—21no—
113C22×C31—21no—
114C22×C31—41no—
115C22×C31—41no—
116C22×C31—41no—
117C22×C31—41no—
118C22×C31C2×C22⋊C411yescharacteristic
119C22×C31C4×Q811yescharacteristic
120C22×C31C4×Q811yescharacteristic
121C22×C31C22⋊Q811yescharacteristic
122C22×C31C22⋊Q811yescharacteristic
123C22×C31#12411yescharacteristic
124C22×C31C4⋊Q811yescharacteristic
125C4×C31—42no—
126C4×C31—41no—
127C4×C31—41no—
128C4×C31—81no—
129Dic31—21no—
130Dic31—21no—
131Dic31—21no—
132Dic31—42no—
133Dic31—41no—
134Dic31—41no—
135Dic31—81no—
136Dic31#9912yes—
137C2×C22⋊Q8—311no—
138#380—311no—
139C4×C22⋊C4—311no—
140#342—311no—
141#342—311no—
142#342—311no—
143#342D3111yescharacteristic
144C2×C31—21no—
145C2×C31—21no—
146C2×C31—21no—
147C2×C31—21no—
148C2×C31—21no—
149C2×C31—21no—
150C2×C31#39111yescharacteristic
151C2×C31C2×#9911yescharacteristic
152C2×C31#41011yescharacteristic
153C22×Q8—311no—
154C23×C4—311no—
155C22⋊Q8—621no—
156C22⋊Q8—621no—
157C22⋊Q8—621no—
158C22⋊Q8—621no—
159C2×C4⋊C4—311no—
160C2×C4⋊C4—311no—
161C2×C4⋊C4—311no—
162C2×C4⋊C4—621no—
163C2×C22⋊C4—311no—
164C2×C22⋊C4—311no—
165C2×C22⋊C4—311no—
166C2×C22⋊C4C2×D3111yescharacteristic
167C2×C22⋊C4C2×D3111yescharacteristic
168C2×C22⋊C4C2×D3111yescharacteristic
169C2×C42—621no—
170#95—621no—
171#95—621no—
172C31#199611yescharacteristic, complemented, Sylow
173C24C22×D3111yescharacteristic
174C2×Q8—621no—
175C2×Q8—621no—
176C2×Q8—1242no—
177C22×C4—21no—
178C22×C4—21no—
179C22×C4—311no—
180C22×C4—311no—
181C22×C4—311no—
182C22×C4—311no—
183C22×C4—311no—
184C22×C4—311no—
185C22×C4—311no—
186C22×C4—311no—
187C22×C4—621no—
188C22×C4—621no—
189C22×C4—1242no—
190C22×C4C4×D3111yescharacteristic
191C22×C4C4×D3111yescharacteristic
192C4⋊C4—621no—
193C4⋊C4—621no—
194C4⋊C4—621no—
195C4⋊C4—621no—
196C4⋊C4—621no—
197C4⋊C4—621no—
198C4⋊C4—1242no—
199C22⋊C4—21no—
200C22⋊C4—21no—
201C22⋊C4—21no—
202C22⋊C4—21no—
203C22⋊C4—21no—
204C22⋊C4—312no—
205C22⋊C4—621no—
206C22⋊C4—621no—
207C22⋊C4—621no—
208C22⋊C4—621no—
209C22⋊C4—621no—
210C22⋊C4Dic6212yescomplemented
211C42—1242no—
212C23—41no—
213C23—41no—
214C23C2×Dic6211yescharacteristic
215C23C2×C4×D3111yescharacteristic
216C23#9249511yescharacteristic
217C23D4×D3111yescharacteristic
218C23D4×D3111yescharacteristic
219C23#9249711yescharacteristic
220C23Q8×D3111yescharacteristic
221Q8—1242no—
222Q8—1242no—
223C2×C4—22no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—41no—
232C2×C4—41no—
233C2×C4—311no—
234C2×C4—311no—
235C2×C4—311no—
236C2×C4—311no—
237C2×C4—622no—
238C2×C4—622no—
239C2×C4—622no—
240C2×C4—621no—
241C2×C4—621no—
242C2×C4—622no—
243C2×C4—1241no—
244C2×C4—1241no—
245C2×C4—1241no—
246C2×C4—1241no—
247C2×C4—1241no—
248C2×C4—1241no—
249C2×C4—1241no—
250C2×C4—1241no—
251C2×C4—1241no—
252C2×C4—1241no—
253C22—21no—
254C22—21no—
255C22—21no—
256C22—21no—
257C22—21no—
258C22—21no—
259C22—41no—
260C22—41no—
261C22—41no—
262C22—41no—
263C22C4×Dic6211yescharacteristic
264C22#1175845511yescharacteristic
265C22C22⋊C4×D3111yescharacteristic
266C22#1175846211yescharacteristic
267C22#1175846411yescharacteristic
268C22#1175846511yescharacteristic
269C22#1175847311yescharacteristic
270C4—42no—
271C4—41no—
272C4—41no—
273C4—81no—
274C4—312no—
275C4—621no—
276C4—621no—
277C4—621no—
278C4—1242no—
279C4—1241no—
280C4—1241no—
281C4—2481no—
282C2—21no—
283C2—21no—
284C2—21no—
285C2—21no—
286C2—21no—
287C2—21no—
288C2#1452095311yescharacteristic
289C2#99×D3111yescharacteristic
290C2#1452102111yescharacteristic
subgroupG/H
centerC22C22⋊C4×D31
commutatorC23×C31C22×C4
FrattiniC24C22×D31
FittingC31×#342C2
socleC22×C31C2×C22⋊C4
prime radical, cosocleC24×C31C23
hypercenter#342D31
hypocenterC31#1996
LCSG ▷ C23×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
9. C22×Dic62C4semidirect
16. C2×C4⋊Dic31C4semidirect
18. C2×Dic31⋊C4C4semidirect
19. C2×Dic31⋊C4C4semidirect
51. C22⋊C4×C31Q8semidirect
57. C22⋊Dic31Q8semidirect
172. C31#1996semidirect
210. C22⋊C4Dic62semidirect

Maximal subgroups

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

subgroupindex
C2×#117584552
#145209072
C22⋊C4×Dic312
#145208162
#145208152
C31×#3422
#199631