Finite Group Databasebeta

← #16853974

Subgroups — #16853974

Order 3968.

548 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 548 conjugacy classes of subgroups — too many to draw. Only its 125 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#14520986C211yesmaximal, characteristic, complemented
2#14520984C213yesmaximal, complemented
3#14520973C211yesmaximal, characteristic, complemented
4#14520972C213yesmaximal, complemented
5#14520971C213yesmaximal, complemented
6#14520904C213yesmaximal
7C31×#396C211yesmaximal, characteristic, complemented
8C24×D31C2211yescharacteristic
9C2×C4⋊C4×C31C2213yescomplemented
10C2×C22⋊C4×C31C2213yes—
11C2×C22⋊Dic31C2213yes—
12C2×(C2×D31)⋊C4C2213yes—
13C2×(C2×D31)⋊C4C2213yes—
14C2×(C2×D31)⋊C4C2213yes—
15C2×(C2×D31)⋊C4C2213yes—
16C2×C4⋊Dic31C2213yescomplemented
17C2×Dic31⋊C4C2213yescomplemented
18C2×Dic31⋊C4C2213yescomplemented
19C31×#95C2211yescharacteristic, complemented
20C31⋊#95C2213yescomplemented
21C24×C31C2311yescharacteristic
22C23×D31—43no—
23C23×D31—43no—
24C23×D31Q814yes—
25C23×D31C2311yescharacteristic
26C23×D31C2311yescharacteristic
27C22×C4×C31C2313yes—
28C22×C4×C31C2313yes—
29C22×Dic31C2313yes—
30C22×Dic31C2313yes—
31C4⋊C4×C31—43no—
32C22⋊C4×C31—43no—
33C22⋊Dic31—43no—
34(C2×D31)⋊C4—43no—
35(C2×D31)⋊C4—43no—
36(C2×D31)⋊C4—43no—
37(C2×D31)⋊C4—43no—
38C4⋊Dic31—43no—
39Dic31⋊C4—43no—
40Dic31⋊C4—43no—
41C23×C31—23no—
42C23×C31—23no—
43C23×C31C2×Q812yes—
44C23×C31C2411yescharacteristic
45C22×D31—23no—
46C22×D31—23no—
47C22×D31—23no—
48C22×D31—23no—
49C22×D31—412no—
50C22×D31—412no—
51C22×D31—44no—
52C22×D31C2×Q812yes—
53C22×D31C2×Q812yes—
54C2×C4×C31—23no—
55C2×C4×C31—23no—
56C2×C4×C31—23no—
57C2×C4×C31—23no—
58C2×C4×C31—23no—
59C2×C4×C31—23no—
60C2×Dic31—23no—
61C2×Dic31—23no—
62C2×Dic31—23no—
63C2×Dic31—23no—
64C2×Dic31—23no—
65C2×Dic31—23no—
66#2842—311nomaximal, Sylow
67C22×C31—26no—
68C22×C31—43no—
69C22×C31—41no—
70C22×C31C22×Q811yescharacteristic
71C22×C31H(5,𝔽2)13yes—
72C22×C31H(5,𝔽2)13yes—
73C2×D31—26no—
74C2×D31—26no—
75C2×D31—416no—
76C2×D31—43no—
77C2×D31—43no—
78C2×D31—41no—
79C2×D31—41no—
80C4×C31—43no—
81C4×C31—43no—
82Dic31—43no—
83Dic31—43no—
84#399—313no—
85#399—311no—
86#396—313no—
87#396—313no—
88#396—311no—
89#396D3111yescharacteristic, complemented
90#379—313no—
91C2×C31—42no—
92C2×C31#54313yes—
93C2×C31#56013yes—
94C2×C31#56011yescharacteristic
95D31—42no—
96D31—42no—
97C25—311no—
98C2×C4⋊C4—313no—
99C2×C4⋊C4—313no—
100C2×C4⋊C4—313no—
101C2×C4⋊C4C2×D3113yescomplemented
102C2×C22⋊C4—313no—
103C2×C22⋊C4—313no—
104C2×C22⋊C4—313no—
105C2×C22⋊C4—313no—
106C2×C22⋊C4—313no—
107C2×C22⋊C4C2×D3113yes—
108#95—313no—
109#95C2×D3111yescharacteristic, complemented
110C31#284211yescharacteristic, complemented, Sylow
111C24—311no—
112C24—311no—
113C24—314no—
114C24—1243no—
115C24—1243no—
116C24C22×D3111yescharacteristic
117C22×C4—313no—
118C22×C4—313no—
119C22×C4C22×D3113yes—
120C22×C4C22×D3113yes—
121C4⋊C4—43no—
122C4⋊C4—1243no—
123C4⋊C4—1243no—
124C4⋊C4—1243no—
125C22⋊C4—43no—
126C22⋊C4—1243no—
127C22⋊C4—1243no—
128C22⋊C4—1243no—
129C22⋊C4—1243no—
130C22⋊C4—1243no—
131C23—23no—
132C23—23no—
133C23—312no—
134C23—312no—
135C23—623no—
136C23—623no—
137C23—623no—
138C23—623no—
139C23—12412no—
140C23—12412no—
141C23—1244no—
142C23Q8×D3112yes—
143C23C23×D3111yescharacteristic
144C2×C4—23no—
145C2×C4—23no—
146C2×C4—23no—
147C2×C4—23no—
148C2×C4—23no—
149C2×C4—23no—
150C2×C4—623no—
151C2×C4—623no—
152C2×C4—623no—
153C2×C4—623no—
154C2×C4—623no—
155C2×C4—623no—
156C22—26no—
157C22—43no—
158C22—41no—
159C22—626no—
160C22—626no—
161C22—12416no—
162C22—1243no—
163C22—1243no—
164C22—1241no—
165C22—1241no—
166C22#1175856113yes—
167C22C2×Q8×D3111yescharacteristic
168C22#1175856613yes—
169C4—43no—
170C4—43no—
171C4—1243no—
172C4—1243no—
173C2—42no—
174C2—1242no—
175C2—1242no—
176C2#1452167413yes—
177C2#1452178713yes—
178C2#1452179011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D31
commutator, socle, cosocleC23×C31C24
FittingC31×#396C2
prime radicalC24×D31C22
hypercenter#396D31
hypocenterC31#2842
LCSG ▷ C23×C31 ▷ C31
UCSC1 ◁ C23 ◁ #396

Complements

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

NH ≅ G/Ntype
1. #14520986C2semidirect
2. #14520984C2semidirect
3. #14520973C2semidirect
4. #14520972C2semidirect
5. #14520971C2semidirect
7. C31×#396C2semidirect
9. C2×C4⋊C4×C31C22semidirect
16. C2×C4⋊Dic31C22semidirect
17. C2×Dic31⋊C4C22semidirect
18. C2×Dic31⋊C4C22semidirect
19. C31×#95C22semidirect
20. C31⋊#95C22semidirect
89. #396D31semidirect
101. C2×C4⋊C4C2×D31semidirect
109. #95C2×D31semidirect
110. C31#2842semidirect

Maximal subgroups

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

subgroupindex
#145209862
#145209842
#145209732
#145209722
#145209712
#145209042
C31×#3962
#284231