Finite Group Databasebeta

← #16854022

Subgroups — #16854022

Order 3968.

556 conjugacy classes of subgroups; only the 169 normal subgroups are shown.

normal subgroups only

This group has 556 conjugacy classes of subgroups — too many to draw. Only its 169 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×#11758447C211yesmaximal, characteristic, complemented
2C2×C42×D31C211yesmaximal, characteristic
3#14520948C212yesmaximal, complemented
4#14520934C214yesmaximal, complemented
5#14520923C214yesmaximal
6#14520906C212yesmaximal
7C31×#382C211yesmaximal, characteristic, complemented
8C22×C4×D31C2212yes—
9C22×C4×D31C2211yescharacteristic
10C2×C4⋊C4×C31C2212yes—
11C2×C42×C31C2211yescharacteristic
12C2×(C2×D31)⋊C4C2214yes—
13C2×C4⋊Dic31C2212yes—
14C2×C4⋊Dic31C2214yes—
15C2×Dic31⋊C4C2214yes—
16C2×C4×Dic31C2212yes—
17C2×C4×Dic31C2211yescharacteristic
18C42×D31—24no—
19#11758447—24no—
20C31×#95C2214yes—
21C31⋊#95C2214yes—
22C31⋊#95C2214yes—
23C23×D31C2311yescharacteristic
24C22×C4×C31C2314yes—
25C22×C4×C31C2312yes—
26C22×C4×C31C2311yescharacteristic
27C22×Dic31C2314yes—
28C22×Dic31C2311yescharacteristic
29C22×Dic31C2312yes—
30C2×C4×D31—24no—
31C2×C4×D31—24no—
32C2×C4×D31—22no—
33C2×C4×D31—22no—
34C2×C4×D31—24no—
35C2×C4×D31Q814yes—
36C4⋊C4×C31—24no—
37C42×C31D414yes—
38(C2×D31)⋊C4—28no—
39C4⋊Dic31—24no—
40C4⋊Dic31—28no—
41Dic31⋊C4—28no—
42C4×Dic31—24no—
43C4×Dic31—22no—
44C23×C31C2411yescharacteristic
45C22×D31—21no—
46C22×D31—21no—
47C22×D31—22no—
48C22×D31C2×Q812yes—
49C22×D31#4114yes—
50C2×C4×C31—22no—
51C2×C4×C31—22no—
52C2×C4×C31—24no—
53C2×C4×C31—24no—
54C2×C4×C31—24no—
55C2×C4×C31C2×D414yes—
56C2×C4×C31C2×D412yes—
57C2×C4×C31C2×Q812yes—
58C2×C4×C31#4112yes—
59C2×Dic31—21no—
60C2×Dic31—22no—
61C2×Dic31—21no—
62C2×Dic31—22no—
63C2×Dic31—24no—
64C2×Dic31—24no—
65C2×Dic31—24no—
66C2×Dic31C2×Q812yes—
67C2×Dic31#4114yes—
68C4×D31—216no—
69C4×D31—28no—
70#2851—311nomaximal, Sylow
71C22×C31C22×D411yescharacteristic
72C22×C31C22×Q811yescharacteristic
73C22×C31C2×#4111yescharacteristic
74C22×C31C2×#4112yes—
75C22×C31C2×#4112yes—
76C2×D31—22no—
77C2×D31—24no—
78C2×D31—24no—
79C2×D31—22no—
80C2×D31#12514yescomplemented
81C4×C31—24no—
82C4×C31—44no—
83C4×C31C22⋊Q814yes—
84Dic31—22no—
85Dic31—24no—
86Dic31—44no—
87C2×#125—311no—
88C22×C42—311no—
89#389—312no—
90#387—314no—
91#385—314no—
92#382D3111yescharacteristic, complemented
93#380—312no—
94C2×C31C2×C22⋊Q811yescharacteristic
95C2×C31#52512yes—
96C2×C31C2×#12511yescharacteristic
97C2×C31#52912yes—
98C2×C31#53311yescharacteristic
99D31—24no—
100C23×C4—311no—
101C23×C4—312no—
102#125—624no—
103C2×C4⋊C4—312no—
104C2×C4⋊C4—314no—
105C2×C4⋊C4—314no—
106C2×C4⋊C4C2×D3112yes—
107C2×C22⋊C4—314no—
108C2×C42—312no—
109C2×C42—311no—
110C2×C42—624no—
111C2×C42C2×D3111yescharacteristic
112#95—314no—
113#95—314no—
114#95C2×D3114yes—
115C31#285111yescharacteristic, complemented, Sylow
116C24—311no—
117C22×C4—311no—
118C22×C4—312no—
119C22×C4—314no—
120C22×C4—314no—
121C22×C4—624no—
122C22×C4—624no—
123C22×C4—624no—
124C22×C4—622no—
125C22×C4—622no—
126C22×C4C22×D3114yes—
127C22×C4C22×D3112yes—
128C22×C4C22×D3111yescharacteristic
129C4⋊C4—24no—
130C4⋊C4—628no—
131C4⋊C4—628no—
132C4⋊C4—624no—
133C22⋊C4—628no—
134C42—624no—
135C42—622no—
136C42D12414yes—
137C23—312no—
138C23—314no—
139C23—621no—
140C23—621no—
141C23—622no—
142C23C23×D3111yescharacteristic
143C2×C4—22no—
144C2×C4—22no—
145C2×C4—24no—
146C2×C4—24no—
147C2×C4—24no—
148C2×C4—312no—
149C2×C4—314no—
150C2×C4—6216no—
151C2×C4—621no—
152C2×C4—622no—
153C2×C4—621no—
154C2×C4—622no—
155C2×C4—628no—
156C2×C4—624no—
157C2×C4—624no—
158C2×C4—624no—
159C2×C4C2×D12414yes—
160C2×C4C2×D12412yes—
161C2×C4#9249712yes—
162C2×C4Q8×D3112yes—
163C22—314no—
164C22—622no—
165C22—622no—
166C22—624no—
167C22—624no—
168C22C22×D12411yescharacteristic
169C22C2×#9249711yescharacteristic
170C22C2×Q8×D3111yescharacteristic
171C22#41×D3112yes—
172C22#41×D3112yes—
173C4—24no—
174C4—44no—
175C4—622no—
176C4—624no—
177C4—1244no—
178C4#1175847414yes—
179C2—624no—
180C2C2×#1175847411yescharacteristic
181C2#1452156112yes—
182C2#125×D3111yescharacteristic
183C2#1452157812yes—
184C2#1452160511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D31
commutator, socle, cosocleC23×C31C24
FittingC31×#382C2
prime radicalC23×D31C23
hypercenter#382D31
hypocenterC31#2851
LCSG ▷ C23×C31 ▷ C31
UCSC1 ◁ C23 ◁ #382

Complements

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

NH ≅ G/Ntype
1. C2×#11758447C2semidirect
3. #14520948C2semidirect
4. #14520934C2semidirect
7. C31×#382C2semidirect
80. C2×D31#125semidirect
92. #382D31semidirect
115. C31#2851semidirect

Maximal subgroups

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

subgroupindex
C2×#117584472
C2×C42×D312
#145209482
#145209342
#145209232
#145209062
C31×#3822
#285131