Finite Group Databasebeta

← #16848991

Subgroups — #16848991

Order 3968.

840 conjugacy classes of subgroups; only the 163 normal subgroups are shown.

normal subgroups only

This group has 840 conjugacy classes of subgroups — too many to draw. Only its 163 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×#11758470C213yesmaximal, complemented
2C2×(C22⋊D31)⋊C4C213yesmaximal, complemented
3#14520984C213yesmaximal, complemented
4#14520959C211yesmaximal, characteristic, complemented
5#14520958C213yesmaximal, complemented
6#14520894C211yesmaximal, characteristic, complemented
7C31×#399C211yesmaximal, characteristic, complemented
8C22×C22⋊D31C2213yes—
9C23×Dic31C2211yescharacteristic
10C22×D124C2213yes—
11C22×C4×D31C2213yes—
12C2×C4⋊C4×C31C2213yes—
13C2×C22⋊C4×C31C2213yes—
14C2×(C2×D31)⋊C4C2216yes—
15C2×(C2×D31)⋊C4C2213yes—
16C2×Dic31⋊C4C2213yes—
17C2×C4×Dic31C2213yes—
18#11758470—212no—
19(C22⋊D31)⋊C4—212no—
20C31×#95C2211yescharacteristic
21C31⋊#95C2213yes—
22C24×C31C2311yescharacteristic
23C23×D31C2313yes—
24C22×C4×C31C2313yes—
25C22×C4×C31C2313yes—
26C2×C22⋊D31—26no—
27C2×C22⋊D31—26no—
28C2×C22⋊D31—26no—
29C22×Dic31—26no—
30C22×Dic31C2311yescharacteristic
31C22×Dic31C2313yes—
32C22×Dic31C2311yescharacteristic
33C2×D124—212no—
34C2×D124—26no—
35C2×C4×D31—26no—
36C2×C4×D31—212no—
37C4⋊C4×C31—26no—
38C22⋊C4×C31—26no—
39(C2×D31)⋊C4—26no—
40(C2×D31)⋊C4—212no—
41Dic31⋊C4—26no—
42C4×Dic31D4112yescomplemented
43C23×C31—23no—
44C23×C31—23no—
45C23×C31#4112yes—
46C23×C31C2411yescharacteristic
47C22×D31—26no—
48C22×D31—23no—
49C22×D31—26no—
50C22×D31—23no—
51C22×D31#4116yes—
52C2×C4×C31—26no—
53C2×C4×C31—23no—
54C2×C4×C31—26no—
55C2×C4×C31C2×D416yes—
56C22⋊D31—224no—
57C2×Dic31—23no—
58C2×Dic31—23no—
59C2×Dic31—23no—
60C2×Dic31—44no—
61C2×Dic31C2×D416yes—
62C2×Dic31C2×D416yes—
63D124—224no—
64C4×D31—412no—
65#2397—311nomaximal, Sylow
66C22×C31—26no—
67C22×C31—43no—
68C22×C31—41no—
69C22×C31C22×D413yes—
70C22×C31C2×#4111yescharacteristic
71C22×C31C2×#4113yes—
72C2×D31—212no—
73C2×D31—26no—
74C2×D31—43no—
75C2×D31—46no—
76C2×D31—43no—
77C4×C31—26no—
78C4×C31—43no—
79Dic31—26no—
80Dic31—41no—
81Dic31#12714yes—
82C2×C4×D4—313no—
83C2×C4×D4—313no—
84#399—313no—
85#399D3111yescharacteristic, complemented
86#392—313no—
87#392—311no—
88#376—311no—
89C2×C31—42no—
90C2×C31#52513yes—
91C2×C31#52513yes—
92C2×C31C2×#12711yescharacteristic
93D31—46no—
94C22×D4—313no—
95C22×D4—313no—
96C23×C4—311no—
97C23×C4—313no—
98C4×D4—6212no—
99C4×D4—6212no—
100C2×C4⋊C4—313no—
101C2×C4⋊C4C2×D3113yes—
102C2×C22⋊C4—316no—
103C2×C22⋊C4—313no—
104C2×C22⋊C4C2×D3113yes—
105C2×C42—313no—
106#95—313no—
107#95C2×D3111yescharacteristic
108C31#239711yescharacteristic, complemented, Sylow
109C24—313no—
110C24C22×D3111yescharacteristic
111C2×D4—6212no—
112C2×D4—626no—
113C2×D4—626no—
114C2×D4—626no—
115C2×D4—626no—
116C22×C4—311no—
117C22×C4—313no—
118C22×C4—311no—
119C22×C4—626no—
120C22×C4—6212no—
121C22×C4—626no—
122C22×C4C22×D3113yes—
123C22×C4C22×D3113yes—
124C4⋊C4—26no—
125C4⋊C4—626no—
126C22⋊C4—26no—
127C22⋊C4—6212no—
128C22⋊C4—626no—
129C42—3112no—
130C23—23no—
131C23—23no—
132C23—316no—
133C23—626no—
134C23—623no—
135C23—623no—
136C23—626no—
137C23#9249912yes—
138C23C23×D3111yescharacteristic
139D4—6224no—
140D4—6224no—
141C2×C4—26no—
142C2×C4—23no—
143C2×C4—26no—
144C2×C4—316no—
145C2×C4—316no—
146C2×C4—623no—
147C2×C4—623no—
148C2×C4—623no—
149C2×C4—12412no—
150C2×C4—1244no—
151C2×C4D4×D3116yes—
152C22—26no—
153C22—43no—
154C22—41no—
155C22—6212no—
156C22—626no—
157C22—1243no—
158C22—1246no—
159C22—1243no—
160C22C2×D4×D3113yes—
161C22C2×#9249911yescharacteristic
162C22#41×D3113yes—
163C4—26no—
164C4—43no—
165C4—314no—
166C4—626no—
167C4—1241no—
168C2—42no—
169C2—1246no—
170C2#1452155713yes—
171C2#1452156213yes—
172C2#127×D3111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D31
commutator, socle, cosocleC23×C31C24
FittingC31×#399C2
hypercenter#399D31
hypocenterC31#2397
LCSG ▷ C23×C31 ▷ C31
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
1. C2×#11758470C2semidirect
2. C2×(C22⋊D31)⋊C4C2semidirect
3. #14520984C2semidirect
4. #14520959C2semidirect
5. #14520958C2semidirect
6. #14520894C2semidirect
7. C31×#399C2semidirect
42. C4×Dic31D4semidirect
85. #399D31semidirect
108. C31#2397semidirect

Maximal subgroups

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

subgroupindex
C2×#117584702
C2×(C22⋊D31)⋊C42
#145209842
#145209592
#145209582
#145208942
C31×#3992
#239731