Finite Group Databasebeta

← #16848328

Subgroups — #16848328

Order 3968.

600 conjugacy classes of subgroups; only the 229 normal subgroups are shown.

normal subgroups only

This group has 600 conjugacy classes of subgroups — too many to draw. Only its 229 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×Dic31⋊C4C211yesmaximal, characteristic
3#14520946C214yesmaximal, complemented
4#14520944C214yesmaximal, complemented
5#14520909C211yesmaximal, characteristic
6#14520907C212yesmaximal
7C31×#380C211yesmaximal, characteristic
8C23×C4×C31C2211yescharacteristic
9C23×Dic31C2211yescharacteristic
10C23×Dic31C2211yescharacteristic
11C2×C4⋊C4×C31C2212yes—
12C2×C22⋊C4×C31C2212yes—
13C2×C22⋊Dic31C2212yes—
14C2×C4⋊Dic31C2212yes—
15C2×Dic31⋊C4C418yescomplemented
16C2×Dic31⋊C4C2214yes—
17C2×Dic31⋊C4C2214yes—
18C2×Dic31⋊C4C2212yes—
19C2×Dic31⋊C4C2212yes—
20C2×C4×Dic31C2214yes—
21#11758454—28no—
22C31×#95C2212yes—
23C31⋊#95C2214yes—
24C31⋊#95C2212yes—
25C24×C31C2311yescharacteristic
26C22×C4×C31—42no—
27C22×C4×C31C2×C414yes—
28C22×C4×C31C2314yes—
29C22×C4×C31C2311yescharacteristic
30C22×C4×C31C2311yescharacteristic
31C22×Dic31—42no—
32C22×Dic31C2×C414yes—
33C22×Dic31C2×C414yes—
34C22×Dic31D414yes—
35C22×Dic31Q814yes—
36C22×Dic31C2314yes—
37C22×Dic31C2312yes—
38C22×Dic31C2312yes—
39C4⋊C4×C31—42no—
40C22⋊C4×C31—24no—
41C22⋊Dic31—24no—
42C4⋊Dic31—42no—
43Dic31⋊C4—28no—
44Dic31⋊C4—44no—
45Dic31⋊C4C2×C418yes—
46Dic31⋊C4C2×C418yes—
47C4×Dic31—28no—
48C23×C31—22no—
49C23×C31—22no—
50C23×C31C22×C412yes—
51C23×C31C2×D412yes—
52C23×C31C2×Q812yes—
53C23×C31C2411yescharacteristic
54C2×C4×C31—22no—
55C2×C4×C31—22no—
56C2×C4×C31—24no—
57C2×C4×C31—24no—
58C2×C4×C31—24no—
59C2×C4×C31—44no—
60C2×C4×C31C22×C412yes—
61C2×C4×C31C22×C412yes—
62C2×Dic31—24no—
63C2×Dic31—24no—
64C2×Dic31—24no—
65C2×Dic31—24no—
66C2×Dic31—44no—
67C2×Dic31C4⋊C4116yescomplemented
68C2×Dic31C22×C414yes—
69C2×Dic31C22×C414yes—
70C2×Dic31C2×D414yes—
71C2×Dic31C2×Q814yes—
72#2316—311nomaximal, Sylow
73C22×C31—22no—
74C22×C31—22no—
75C22×C31—24no—
76C22×C31—24no—
77C22×C31C2×C4⋊C414yes—
78C22×C31C23×C411yescharacteristic
79C22×C31C22×D411yescharacteristic
80C22×C31C22×Q811yescharacteristic
81C22×C31H(5,𝔽2)12yes—
82C22×C312−1+412yes—
83C4×C31—22no—
84C4×C31—22no—
85C4×C31—44no—
86Dic31—24no—
87Dic31—44no—
88Dic31C2×C4⋊C418yes—
89C2×#117—312no—
90C22×C4⋊C4—311no—
91#389—314no—
92#389—314no—
93#380—311no—
94#380—312no—
95#380D3111yescharacteristic
96C2×C31—24no—
97C2×C31C22×C4⋊C411yescharacteristic
98C2×C31#51811yescharacteristic
99C2×C31#51911yescharacteristic
100C2×C31#53712yes—
101C2×C31#54412yes—
102C23×C4—311no—
103C23×C4—311no—
104C23×C4C2×D3111yescharacteristic
105#117—628no—
106C2×C4⋊C4—318no—
107C2×C4⋊C4—312no—
108C2×C4⋊C4—312no—
109C2×C4⋊C4—314no—
110C2×C4⋊C4—314no—
111C2×C4⋊C4—312no—
112C2×C4⋊C4C2×D3112yes—
113C2×C22⋊C4—312no—
114C2×C22⋊C4C2×D3112yes—
115C2×C42—314no—
116#95—314no—
117#95—312no—
118#95C2×D3112yes—
119C31#231611yescharacteristic, complemented, Sylow
120C24C22×D3111yescharacteristic
121C22×C4—42no—
122C22×C4—314no—
123C22×C4—314no—
124C22×C4—314no—
125C22×C4—312no—
126C22×C4—312no—
127C22×C4—314no—
128C22×C4—314no—
129C22×C4—1242no—
130C22×C4C4×D3114yes—
131C22×C4C22×D3114yes—
132C22×C4C22×D3111yescharacteristic
133C22×C4C22×D3111yescharacteristic
134C4⋊C4—42no—
135C4⋊C4—318no—
136C4⋊C4—318no—
137C4⋊C4—628no—
138C4⋊C4—1244no—
139C4⋊C4—1242no—
140C22⋊C4—24no—
141C22⋊C4—624no—
142C42—628no—
143C23—22no—
144C23—22no—
145C23C2×C4×D3112yes—
146C23D4×D3112yes—
147C23Q8×D3112yes—
148C23C23×D3111yescharacteristic
149C2×C4—22no—
150C2×C4—22no—
151C2×C4—24no—
152C2×C4—24no—
153C2×C4—24no—
154C2×C4—44no—
155C2×C4—3116no—
156C2×C4—314no—
157C2×C4—314no—
158C2×C4—314no—
159C2×C4—314no—
160C2×C4—624no—
161C2×C4—624no—
162C2×C4—624no—
163C2×C4—624no—
164C2×C4—1244no—
165C2×C4C2×C4×D3112yes—
166C2×C4C2×C4×D3112yes—
167C22—24no—
168C22—24no—
169C22—22no—
170C22—22no—
171C22C4⋊C4×D3114yes—
172C22C22×C4×D3111yescharacteristic
173C22C2×D4×D3111yescharacteristic
174C22#1175856112yes—
175C22C2×Q8×D3111yescharacteristic
176C22#1175856712yes—
177C4—22no—
178C4—22no—
179C4—44no—
180C4—318no—
181C4—624no—
182C4—1244no—
183C2—24no—
184C2C2×C4⋊C4×D3111yescharacteristic
185C2#1452152211yescharacteristic
186C2#1452152611yescharacteristic
187C2#1452162612yes—
188C2#1452167812yes—
subgroupG/H
center, FrattiniC23C23×D31
commutatorC22×C31C23×C4
FittingC31×#380C2
socle, cosocleC23×C31C24
prime radicalC24×C31C23
hypercenter#380D31
hypocenterC31#2316
LCSG ▷ C22×C31 ▷ C31
UCSC1 ◁ C23 ◁ #380

Complements

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

NH ≅ G/Ntype
3. #14520946C2semidirect
4. #14520944C2semidirect
15. C2×Dic31⋊C4C4semidirect
67. C2×Dic31C4⋊C4semidirect
119. C31#2316semidirect

Maximal subgroups

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

subgroupindex
C2×#117584542
C22×Dic31⋊C42
#145209462
#145209442
#145209092
#145209072
C31×#3802
#231631