Finite Group Databasebeta

← #16855842

Subgroups — #16855842

Order 3968.

380 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 129 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#14521606C211yesmaximal, characteristic
2C2×C4×Dic62C211yesmaximal, characteristic
3#14521380C212yesmaximal
4#14521335C212yesmaximal, complemented
5#14521260C212yesmaximal, complemented
6#14521207C212yesmaximal
7#14521157C214yesmaximal, complemented
8C31×#432C211yesmaximal, characteristic
9C22×Dic62C2211yescharacteristic
10C2×C42×C31C2211yescharacteristic
11#11758503—21no—
12C2×C4⋊Dic31C2211yescharacteristic
13#11758501—21no—
14#11758501C2212yes—
15C2×Dic31⋊C4—21no—
16C2×C4×Dic31—21no—
17C2×Dic124C2214yes—
18#11758447—21no—
19#11758446C2211yescharacteristic
20#11758446C2211yescharacteristic
21C4×Dic62—21no—
22C4×Dic62—21no—
23C4×Dic62—21no—
24C4×Dic62C2212yes—
25C4×Dic62C2212yes—
26C4×Dic62C2212yes—
27C31×C4⋊C8C2212yes—
28C31×C22⋊C8C2212yes—
29C31×#97C2212yes—
30#11758405C2214yes—
31#11758404C2214yes—
32#11758404C2214yes—
33C22×C4×C31D411yescharacteristic
34C22×C4×C31D411yescharacteristic
35C22×C4×C31C2311yescharacteristic
36C22×Dic31—21no—
37C22×Dic31—21no—
38C2×Dic62—21no—
39C2×Dic62—24no—
40C2×Dic62—21no—
41C2×Dic62C2312yes—
42C2×Dic62C2312yes—
43C2×C8×C31C2314yes—
44C42×C31D411yescharacteristic
45C42×C31D411yescharacteristic
46C42×C31C2311yescharacteristic
47C42×C31C2311yescharacteristic
48C22⋊Dic31—22no—
49C4⋊Dic31—21no—
50C4⋊Dic31—21no—
51C4⋊Dic31—21no—
52C4⋊Dic31—21no—
53C4⋊Dic31C2312yes—
54C4⋊Dic31C2312yes—
55Dic31⋊C4—22no—
56Dic31⋊C4—22no—
57Dic31⋊C4—22no—
58Dic31⋊C4—22no—
59C4×Dic31—22no—
60C4×Dic31—22no—
61C4×Dic31—22no—
62Dic124—28no—
63C23×C31C2×D411yescharacteristic
64C2×C4×C31—22no—
65C2×C4×C31—22no—
66C2×C4×C31—22no—
67C2×C4×C31C2×D411yescharacteristic
68C2×C4×C31C2×D411yescharacteristic
69C2×C4×C31C2×D411yescharacteristic
70C2×C4×C31C2×D411yescharacteristic
71C2×C4×C31C2×D411yescharacteristic
72C2×C4×C31C2411yescharacteristic
73C2×Dic31—24no—
74C2×Dic31—22no—
75C2×Dic31—22no—
76C2×Dic31—22no—
77C2×Dic31—22no—
78C2×Dic31—42no—
79Dic62—24no—
80Dic62—22no—
81Dic62—24no—
82Dic62—42no—
83Dic62#4114yes—
84C8×C31—24no—
85#3113—311nomaximal, Sylow
86C22×C31—21no—
87C22×C31—21no—
88C22×C31#13712yes—
89C22×C31C22×D411yescharacteristic
90C4×C31—21no—
91C4×C31—21no—
92C4×C31—21no—
93C4×C31—21no—
94C4×C31#13712yes—
95C4×C31C2×#4112yes—
96Dic31—24no—
97Dic31—42no—
98Dic31—42no—
99Dic31—42no—
100#533—311no—
101C2×C4×Q8—311no—
102#483—312no—
103#475—312no—
104#462—312no—
105#451—312no—
106#441—314no—
107#432D3111yescharacteristic
108C2×C31—22no—
109C2×C31#52511yescharacteristic
110C2×C31C2×#13711yescharacteristic
111C2×C31C2×#13711yescharacteristic
112C22×Q8—311no—
113C2×Q16—314no—
114C4⋊Q8—311no—
115C4⋊Q8—311no—
116#125—621no—
117C22⋊Q8—312no—
118C22⋊Q8—621no—
119C4×Q8—312no—
120C4×Q8—312no—
121C4×Q8—312no—
122C4×Q8—621no—
123C4×Q8—621no—
124C4×Q8—621no—
125#117—621no—
126C2×C4⋊C4—311no—
127C2×C4⋊C4—621no—
128C2×C42—621no—
129C2×C42C2×D3111yescharacteristic
130#106—314no—
131C4⋊C8C2×D3112yes—
132#103—314no—
133#103—314no—
134C22⋊C8C2×D3112yes—
135#97C2×D3112yes—
136C31#311311yescharacteristic, complemented, Sylow
137C2×Q8—312no—
138C2×Q8—312no—
139C2×Q8—624no—
140C2×Q8—621no—
141C2×Q8—621no—
142C22×C4—621no—
143C22×C4—621no—
144C22×C4D12411yescharacteristic
145C22×C4D12411yescharacteristic
146C22×C4C22×D3111yescharacteristic
147Q16—628no—
148C2×C8C22×D3114yes—
149C4⋊C4—312no—
150C4⋊C4—312no—
151C4⋊C4—622no—
152C4⋊C4—622no—
153C4⋊C4—622no—
154C4⋊C4—622no—
155C4⋊C4—621no—
156C4⋊C4—621no—
157C4⋊C4—621no—
158C4⋊C4—621no—
159C22⋊C4—622no—
160C42—622no—
161C42—622no—
162C42—622no—
163C42D12411yescharacteristic
164C42D12411yescharacteristic
165C42C22×D3111yescharacteristic
166C42C22×D3111yescharacteristic
167C23C2×D12411yescharacteristic
168Q8—314no—
169Q8—624no—
170Q8—622no—
171Q8—624no—
172Q8—1242no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—624no—
177C2×C4—622no—
178C2×C4—622no—
179C2×C4—622no—
180C2×C4—622no—
181C2×C4—1242no—
182C2×C4C2×D12411yescharacteristic
183C2×C4C2×D12411yescharacteristic
184C2×C4C2×D12411yescharacteristic
185C2×C4C2×D12411yescharacteristic
186C2×C4C2×D12411yescharacteristic
187C2×C4C23×D3111yescharacteristic
188C8—24no—
189C22—21no—
190C22—21no—
191C22#1175848612yes—
192C22C22×D12411yescharacteristic
193C4—21no—
194C4—21no—
195C4—21no—
196C4—21no—
197C4—624no—
198C4—1242no—
199C4—1242no—
200C4—1242no—
201C4#1175848612yes—
202C4#41×D3112yes—
203C2—22no—
204C2#1452156111yescharacteristic
205C2C2×#1175848611yescharacteristic
206C2C2×#1175848611yescharacteristic
subgroupG/H
centerC22C22×D124
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#432C2
socleC22×C31C22×D4
prime radicalC23×C31C2×D4
hypercenter#432D31
hypocenterC31#3113
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
4. #14521335C2semidirect
5. #14521260C2semidirect
7. #14521157C2semidirect
136. C31#3113semidirect

Maximal subgroups

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

subgroupindex
#145216062
C2×C4×Dic622
#145213802
#145213352
#145212602
#145212072
#145211572
C31×#4322
#311331