Finite Group Databasebeta

← #16846653

Subgroups — #16846653

Order 3968.

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

normal subgroups only

This group has 260 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
1#14521602C211yesmaximal, characteristic
2M16×Dic31C211yesmaximal, characteristic
3C4×Dic31⋊C4C211yesmaximal, characteristic
4#14520810C211yesmaximal, characteristic
5#14520809C211yesmaximal, characteristic
6#14520808C211yesmaximal, characteristic
7C31×#339C211yesmaximal, characteristic
8C2×M16×C31C2211yescharacteristic
9C31×#117C2211yescharacteristic
10C2×C42×C31C2211yescharacteristic
11#11758503C2211yescharacteristic
12C2×Dic31⋊C4—21no—
13C2×C4×Dic31C2211yescharacteristic
14C2×C4×Dic31C2211yescharacteristic
15C2×#92474C2211yescharacteristic
16#11758467C411yescharacteristic, complemented
17#11758467C411yescharacteristic, complemented
18#11758465C411yescharacteristic, complemented
19#11758465C411yescharacteristic, complemented
20#11758455—21no—
21#11758455—21no—
22C4×Dic62—21no—
23C4×Dic62—21no—
24C31⋊#95—21no—
25#11758403—21no—
26C8×Dic31—21no—
27C22×C4×C31—21no—
28C22×C4×C31C2311yescharacteristic
29C22×Dic31—21no—
30C22×Dic31D411yescharacteristic
31C22×Dic31D411yescharacteristic
32C2×Dic62—21no—
33C2×Dic62—21no—
34M16×C31—21no—
35M16×C31Q812yescomplemented
36C2×C8×C31—21no—
37C4⋊C4×C31C2×C411yescharacteristic
38C4⋊C4×C31C2×C411yescharacteristic
39C22⋊C4×C31—21no—
40C42×C31—21no—
41C42×C31—21no—
42C42×C31—21no—
43C22⋊Dic31—21no—
44C4⋊Dic31—21no—
45C4⋊Dic31—21no—
46C4⋊Dic31C2×C411yescharacteristic
47C4⋊Dic31C2×C411yescharacteristic
48Dic31⋊C4—24no—
49Dic31⋊C4—21no—
50Dic31⋊C4—21no—
51Dic31⋊C4—21no—
52Dic31⋊C4—21no—
53C4×Dic31—21no—
54C4×Dic31—21no—
55C4×Dic31—21no—
56C4×Dic31C2×C411yescharacteristic
57C4×Dic31C2×C411yescharacteristic
58C4×Dic31D411yescharacteristic
59C4×Dic31D411yescharacteristic
60#92474—21no—
61#92474Q812yescomplemented
62C2×C31⋊C8—21no—
63C23×C31C2×D411yescharacteristic
64C2×C4×C31—22no—
65C2×C4×C31—21no—
66C2×C4×C31—21no—
67C2×C4×C31—41no—
68C2×C4×C31—41no—
69C2×C4×C31C22×C411yescharacteristic
70C2×C4×C31C2×D411yescharacteristic
71C2×C4×C31C2×Q811yescharacteristic
72C2×C4×C31C2×Q811yescharacteristic
73C2×C4×C31#4111yescharacteristic
74C2×C4×C31#4111yescharacteristic
75C2×Dic31—22no—
76C2×Dic31—22no—
77C2×Dic31—21no—
78C2×Dic31—21no—
79C2×Dic31—41no—
80C2×Dic31—41no—
81C2×Dic31—41no—
82C2×Dic31C22⋊C411yescharacteristic
83C2×Dic31C22⋊C411yescharacteristic
84C2×Dic31C22⋊C411yescharacteristic
85C2×Dic31C22⋊C411yescharacteristic
86Dic62—42no—
87Dic62—42no—
88C8×C31—22no—
89C31⋊C8—22no—
90#1986—311nomaximal, Sylow
91C22×C31—21no—
92C22×C31—21no—
93C22×C31C2×C22⋊C411yescharacteristic
94C22×C31#12411yescharacteristic
95C22×C31C4⋊Q811yescharacteristic
96C4×C31—42no—
97C4×C31—41no—
98C4×C31—41no—
99C4×C31C4×Q811yescharacteristic
100C4×C31C4×Q811yescharacteristic
101C4×C31C22⋊Q811yescharacteristic
102C4×C31C22⋊Q811yescharacteristic
103Dic31—21no—
104Dic31—21no—
105Dic31—21no—
106Dic31—42no—
107Dic31—41no—
108Dic31—41no—
109Dic31#10412yes—
110#533—311no—
111C4×M16—311no—
112C4×C4⋊C4—311no—
113#339—311no—
114#339—311no—
115#339—311no—
116#339D3111yescharacteristic
117C2×C31—21no—
118C2×C31—21no—
119C2×C31#39111yescharacteristic
120C2×C31C2×#10411yescharacteristic
121C2×C31#42111yescharacteristic
122C2×M16—311no—
123C2×M16C2×D3111yescharacteristic
124C4⋊Q8—311no—
125C4⋊Q8—311no—
126#125—311no—
127#125—311no—
128C22⋊Q8—621no—
129C22⋊Q8—621no—
130C4×Q8—621no—
131C4×Q8—621no—
132#117—311no—
133#117C2×D3111yescharacteristic
134C2×C4⋊C4—621no—
135C2×C42—311no—
136C2×C42—311no—
137C2×C42C2×D3111yescharacteristic
138#97—621no—
139C4×C8—621no—
140#95—621no—
141C31#198611yescharacteristic, complemented, Sylow
142C2×Q8—621no—
143C2×Q8—621no—
144C22×C4—21no—
145C22×C4—311no—
146C22×C4—311no—
147C22×C4—621no—
148C22×C4C22×D3111yescharacteristic
149M16—21no—
150M16—312no—
151M16—621no—
152M16Dic6212yescomplemented
153C2×C8—21no—
154C2×C8—621no—
155C4⋊C4—311no—
156C4⋊C4—311no—
157C4⋊C4—621no—
158C4⋊C4—621no—
159C4⋊C4—621no—
160C4⋊C4—621no—
161C4⋊C4—621no—
162C4⋊C4—621no—
163C4⋊C4—624no—
164C4⋊C4C4×D3111yescharacteristic
165C4⋊C4C4×D3111yescharacteristic
166C22⋊C4—21no—
167C22⋊C4—621no—
168C42—21no—
169C42—21no—
170C42—21no—
171C42—311no—
172C42—311no—
173C42—311no—
174C42—311no—
175C42—621no—
176C42—621no—
177C42—621no—
178C23D4×D3111yescharacteristic
179Q8—1242no—
180Q8—1242no—
181C2×C4—22no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—311no—
187C2×C4—311no—
188C2×C4—311no—
189C2×C4—311no—
190C2×C4—622no—
191C2×C4—622no—
192C2×C4—621no—
193C2×C4—621no—
194C2×C4—1241no—
195C2×C4—1241no—
196C2×C4—1241no—
197C2×C4C2×Dic6211yescharacteristic
198C2×C4C2×C4×D3111yescharacteristic
199C2×C4#9249511yescharacteristic
200C2×C4D4×D3111yescharacteristic
201C2×C4#9249711yescharacteristic
202C2×C4Q8×D3111yescharacteristic
203C8—22no—
204C8—622no—
205C22—21no—
206C22—21no—
207C22C22⋊C4×D3111yescharacteristic
208C22#1175846211yescharacteristic
209C22#1175846511yescharacteristic
210C4—42no—
211C4—41no—
212C4—41no—
213C4—312no—
214C4—621no—
215C4—621no—
216C4—621no—
217C4—1242no—
218C4—1241no—
219C4—1241no—
220C4C4×Dic6211yescharacteristic
221C4#1175845511yescharacteristic
222C4#1175846411yescharacteristic
223C4#1175847311yescharacteristic
224C2—21no—
225C2—21no—
226C2#1452095311yescharacteristic
227C2#104×D3111yescharacteristic
228C2#1452106411yescharacteristic
subgroupG/H
centerC2×C4D4×D31
commutatorC2×C4×C31C22×C4
FrattiniC22×C4C22×D31
FittingC31×#339C2
socleC22×C31C2×C22⋊C4
prime radicalC23×C31C2×D4
cosocleC22×C4×C31C23
hypercenter#339D31
hypocenterC31#1986
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
16. #11758467C4semidirect
17. #11758467C4semidirect
18. #11758465C4semidirect
19. #11758465C4semidirect
35. M16×C31Q8semidirect
61. #92474Q8semidirect
141. C31#1986semidirect
152. M16Dic62semidirect

Maximal subgroups

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

subgroupindex
#145216022
M16×Dic312
C4×Dic31⋊C42
#145208102
#145208092
#145208082
C31×#3392
#198631