Finite Group Databasebeta

← #16846236

Subgroups — #16846236

Order 3968.

344 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 85 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#14521816C211yesmaximal, characteristic, complemented
2#14521613C211yesmaximal, characteristic
3#14521053C212yesmaximal, complemented
4#14520805C212yesmaximal, complemented
5C31×#410C211yesmaximal, characteristic, complemented
6C2×#41×C31C2211yescharacteristic
7C22×D124C2211yescharacteristic
8C31×#117C2212yes—
9#11758525—24no—
10#11758524C412yescomplemented
11#11758517C412yescomplemented
12#11758514—22no—
13#11758507—22no—
14#11758503C2211yescharacteristic
15C2×#92474—22no—
16C2×#92474C2212yes—
17C31×#99—22no—
18#11758397—24no—
19C23×D31—21no—
20#41×C31—22no—
21#41×C31—22no—
22C2×Q8×C31C2×C411yescharacteristic
23C2×D4×C31C2×C411yescharacteristic
24C2×D4×C31D412yes—
25C22×C4×C31D412yes—
26C22×C4×C31C2311yescharacteristic
27C2×C22⋊D31—24no—
28C2×D124—22no—
29C2×D124—22no—
30C2×D124—21no—
31C2×D124C2×C412yes—
32C4⋊C4×C31—22no—
33C22⋊C4×C31—22no—
34C42×C31—22no—
35C22⋊Dic31—21no—
36(C2×D31)⋊C4—24no—
37C4⋊Dic31—21no—
38C4×Dic31C2×C412yes—
39#92474—24no—
40#92474—22no—
41#92474—22no—
42C2×C31⋊C8—24no—
43C2×C31⋊C8D414yescomplemented
44C23×C31C22⋊C412yes—
45C23×C31C2×D411yescharacteristic
46C22×D31—22no—
47C22×D31—42no—
48C22×D31—82no—
49Q8×C31—22no—
50D4×C31—24no—
51D4×C31—22no—
52C2×C4×C31—22no—
53C2×C4×C31—22no—
54C2×C4×C31—42no—
55C2×C4×C31C22⋊C412yes—
56C2×C4×C31C22×C411yescharacteristic
57C2×C4×C31C2×D411yescharacteristic
58C2×C4×C31C2×D412yes—
59C2×C4×C31#4112yes—
60C22⋊D31—84no—
61C2×Dic31—22no—
62D124—24no—
63D124—41no—
64D124—41no—
65C31⋊C8—24no—
66#1910—311nomaximal, Sylow
67C22×C31—22no—
68C22×C31—41no—
69C22×C31—42no—
70C22×C31C2×C22⋊C411yescharacteristic
71C22×C31#12112yes—
72C2×D31—44no—
73C2×D31—42no—
74C2×D31—84no—
75C4×C31—22no—
76C4×C31—82no—
77C4×C31C4×D412yes—
78C4×C31#12011yescharacteristic
79C4×C31#12311yescharacteristic
80Dic31—42no—
81#568—311no—
82#535—311no—
83#418—312no—
84#410D3111yescharacteristic, complemented
85H(3,ℤ/4)—312no—
86C2×C31—21no—
87C2×C31—22no—
88C2×C31—42no—
89C2×C31#38611yescharacteristic
90D31—82no—
91C2×#41C2×D3111yescharacteristic
92C22×D4—311no—
93#131—624no—
94C2×M16—312no—
95C2×M16—622no—
96#127—312no—
97#124—312no—
98#121—622no—
99#120—622no—
100#117—311no—
101#117C2×D3112yes—
102#102—624no—
103#99—22no—
104C31#191011yescharacteristic, complemented, Sylow
105C24—621no—
106#41—22no—
107#41—22no—
108C2×Q8C4×D3111yescharacteristic
109C2×D4—312no—
110C2×D4—624no—
111C2×D4—621no—
112C2×D4—622no—
113C2×D4—622no—
114C2×D4C4×D3111yescharacteristic
115C2×D4C22⋊D3112yes—
116C22×C4D12412yes—
117C22×C4C22×D3111yescharacteristic
118M16—624no—
119M16—622no—
120M16—622no—
121C2×C8—314no—
122C2×C8—624no—
123C4⋊C4—22no—
124C4⋊C4—621no—
125C22⋊C4—22no—
126C22⋊C4—621no—
127C22⋊C4—624no—
128C42—22no—
129C42—312no—
130C23—622no—
131C23—1242no—
132C23—2482no—
133C23(C2×D31)⋊C412yes—
134C23C2×C22⋊D3111yescharacteristic
135Q8—22no—
136D4—24no—
137D4—22no—
138D4—624no—
139D4—1241no—
140D4—1241no—
141D4—2484no—
142C2×C4—22no—
143C2×C4—22no—
144C2×C4—42no—
145C2×C4—622no—
146C2×C4(C2×D31)⋊C412yes—
147C2×C4C2×C4×D3111yescharacteristic
148C2×C4C2×D12411yescharacteristic
149C2×C4D4×D3112yes—
150C2×C4#9249712yes—
151C8—624no—
152C22—22no—
153C22—41no—
154C22—42no—
155C22—1244no—
156C22—1242no—
157C22—2484no—
158C22C2×(C2×D31)⋊C411yescharacteristic
159C22#1175851612yes—
160C4—22no—
161C4—82no—
162C4—1242no—
163C4(C22⋊D31)⋊C412yes—
164C4#1175845911yescharacteristic
165C4#1175846311yescharacteristic
166C2—22no—
167C2—21no—
168C2—42no—
169C2—2482no—
170C2#1452092611yescharacteristic
subgroupG/H
centerC2#14520926
commutatorC2×C4×C31C22×C4
FrattiniC22×C4C22×D31
FittingC31×#410C2
socleC2×C31#386
prime radical#14521613C2
cosocleC22×C4×C31C23
hypercenter#410D31
hypocenterC31#1910
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2 ◁ C22×C4 ◁ #410

Complements

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

NH ≅ G/Ntype
1. #14521816C2semidirect
3. #14521053C2semidirect
4. #14520805C2semidirect
5. C31×#410C2semidirect
10. #11758524C4semidirect
11. #11758517C4semidirect
43. C2×C31⋊C8D4semidirect
84. #410D31semidirect
104. C31#1910semidirect

Maximal subgroups

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

subgroupindex
#145218162
#145216132
#145210532
#145208052
C31×#4102
#191031