Finite Group Databasebeta

← #16848578

Subgroups — #16848578

Order 3968.

604 conjugacy classes of subgroups; only the 221 normal subgroups are shown.

normal subgroups only

This group has 604 conjugacy classes of subgroups — too many to draw. Only its 221 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×#11758454C212yesmaximal
2C22×C4⋊Dic31C211yesmaximal, characteristic
3#14520947C212yesmaximal, complemented
4#14520934C214yesmaximal, complemented
5#14520910C212yesmaximal
6#14520909C211yesmaximal, characteristic
7C4×C4⋊Dic31C212yesmaximal, complemented
8C4×C22⋊C4×C31C211yesmaximal, characteristic
9C23×C4×C31C2211yescharacteristic
10C23×Dic31C2212yes—
11C2×C22⋊C4×C31C2211yescharacteristic
12C2×C22⋊C4×C31C2211yescharacteristic
13C2×C42×C31C2212yes—
14C2×C22⋊Dic31C2212yes—
15C2×C4⋊Dic31C418yescomplemented
16C2×C4⋊Dic31C2212yes—
17C2×C4⋊Dic31C2211yescharacteristic
18C2×C4⋊Dic31C2212yes—
19C2×C4⋊Dic31C2211yescharacteristic
20C2×Dic31⋊C4C2214yes—
21C2×C4×Dic31C2214yes—
22#11758454—28no—
23C31×#95C2212yes—
24C31⋊#95C2214yes—
25C31⋊#95C2212yes—
26C31⋊#95C2214yes—
27C24×C31C2311yescharacteristic
28C22×C4×C31—24no—
29C22×C4×C31C2×C414yes—
30C22×C4×C31C2312yes—
31C22×C4×C31C2311yescharacteristic
32C22×C4×C31C2312yes—
33C22×C4×C31C2311yescharacteristic
34C22×Dic31—24no—
35C22×Dic31—24no—
36C22×Dic31C2×C418yes—
37C22×Dic31C2314yes—
38C22×Dic31C2312yes—
39C22×Dic31C2312yes—
40C22⋊C4×C31—22no—
41C22⋊C4×C31D414yes—
42C42×C31—24no—
43C22⋊Dic31—24no—
44C4⋊Dic31—24no—
45C4⋊Dic31C2×C418yes—
46C4⋊Dic31C2×C414yes—
47C4⋊Dic31C2×C414yes—
48Dic31⋊C4—28no—
49C4×Dic31—28no—
50C23×C31—22no—
51C23×C31—22no—
52C23×C31C22×C412yes—
53C23×C31C2×D412yes—
54C23×C31#4112yes—
55C23×C31C2411yescharacteristic
56C2×C4×C31—22no—
57C2×C4×C31—22no—
58C2×C4×C31—22no—
59C2×C4×C31—28no—
60C2×C4×C31—22no—
61C2×C4×C31—22no—
62C2×C4×C31—22no—
63C2×C4×C31C22×C412yes—
64C2×C4×C31C22×C412yes—
65C2×C4×C31C2×D414yes—
66C2×C4×C31#4114yes—
67C2×Dic31—216no—
68C2×Dic31—22no—
69C2×Dic31—22no—
70C2×Dic31—22no—
71C2×Dic31—22no—
72C2×Dic31—24no—
73C2×Dic31—24no—
74C2×Dic31—24no—
75C2×Dic31C22×C414yes—
76C2×Dic31C22×C414yes—
77#2344—311nomaximal, Sylow
78C22×C31—22no—
79C22×C31—22no—
80C22×C31—24no—
81C22×C31—24no—
82C22×C31C4×D414yes—
83C22×C31C23×C411yescharacteristic
84C22×C31C22×D411yescharacteristic
85C22×C31C2×#4111yescharacteristic
86C22×C31C2×#4112yes—
87C22×C312−1+412yes—
88C4×C31—22no—
89C4×C31—24no—
90C4×C31—42no—
91C4×C31#11714yescomplemented
92Dic31—24no—
93Dic31—24no—
94Dic31—44no—
95C2×#117—312no—
96C22×C4⋊C4—311no—
97#389—312no—
98#387—314no—
99#381—312no—
100#380—311no—
101C4×C4⋊C4—312no—
102C4×C22⋊C4D3111yescharacteristic
103C2×C31—24no—
104C2×C31C2×#11711yescharacteristic
105C2×C31C2×C4×D411yescharacteristic
106C2×C31#51911yescharacteristic
107C2×C31#54712yes—
108C2×C31#55212yes—
109C23×C4—312no—
110C23×C4C2×D3111yescharacteristic
111#117—628no—
112C2×C4⋊C4—318no—
113C2×C4⋊C4—311no—
114C2×C4⋊C4—312no—
115C2×C4⋊C4—311no—
116C2×C4⋊C4—314no—
117C2×C4⋊C4—312no—
118C2×C22⋊C4—312no—
119C2×C22⋊C4C2×D3111yescharacteristic
120C2×C22⋊C4C2×D3111yescharacteristic
121C2×C42—314no—
122C2×C42C2×D3112yes—
123#95—314no—
124#95—312no—
125#95—314no—
126#95C2×D3112yes—
127C31#234411yescharacteristic, complemented, Sylow
128C24C22×D3111yescharacteristic
129C22×C4—24no—
130C22×C4—318no—
131C22×C4—312no—
132C22×C4—312no—
133C22×C4—314no—
134C22×C4—624no—
135C22×C4—624no—
136C22×C4C4×D3114yes—
137C22×C4C22×D3112yes—
138C22×C4C22×D3111yescharacteristic
139C22×C4C22×D3112yes—
140C22×C4C22×D3111yescharacteristic
141C4⋊C4—318no—
142C4⋊C4—314no—
143C4⋊C4—314no—
144C4⋊C4—628no—
145C4⋊C4—624no—
146C22⋊C4—22no—
147C22⋊C4—624no—
148C22⋊C4D12414yes—
149C42—24no—
150C42—628no—
151C23—22no—
152C23—22no—
153C23C2×C4×D3112yes—
154C23C2×D12412yes—
155C23#9249512yes—
156C23C23×D3111yescharacteristic
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—28no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—22no—
164C2×C4—314no—
165C2×C4—314no—
166C2×C4—6216no—
167C2×C4—622no—
168C2×C4—622no—
169C2×C4—622no—
170C2×C4—622no—
171C2×C4—624no—
172C2×C4—624no—
173C2×C4—624no—
174C2×C4C2×C4×D3112yes—
175C2×C4C2×C4×D3112yes—
176C2×C4C2×D12414yes—
177C2×C4#9249714yes—
178C22—24no—
179C22—24no—
180C22—22no—
181C22—22no—
182C22C4×D12414yes—
183C22C22×C4×D3111yescharacteristic
184C22C22×D12411yescharacteristic
185C22C2×#9249511yescharacteristic
186C22C2×#9249712yes—
187C22#1175856712yes—
188C4—24no—
189C4—22no—
190C4—42no—
191C4—624no—
192C4—624no—
193C4—1244no—
194C4#1175845414yescomplemented
195C2—24no—
196C2C2×#1175845411yescharacteristic
197C2C2×C4×D12411yescharacteristic
198C2#1452152611yescharacteristic
199C2#1452170312yes—
200C2#1452173912yes—
subgroupG/H
center, FrattiniC23C23×D31
commutatorC22×C31C23×C4
FittingC4×C22⋊C4×C31C2
socle, cosocleC23×C31C24
prime radicalC24×C31C23
hypercenterC4×C22⋊C4D31
hypocenterC31#2344
LCSG ▷ C22×C31 ▷ C31
UCSC1 ◁ C23 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. #14520947C2semidirect
4. #14520934C2semidirect
7. C4×C4⋊Dic31C2semidirect
15. C2×C4⋊Dic31C4semidirect
91. C4×C31#117semidirect
127. C31#2344semidirect
194. C4#11758454semidirect

Maximal subgroups

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

subgroupindex
C2×#117584542
C22×C4⋊Dic312
#145209472
#145209342
#145209102
#145209092
C4×C4⋊Dic312
C4×C22⋊C4×C312
#234431