Finite Group Databasebeta

← #16846231

Subgroups — #16846231

Order 3968.

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

normal subgroups only

This group has 312 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
2#14521620C211yesmaximal, characteristic
3#14521057C212yesmaximal, complemented
4#14520805C212yesmaximal, complemented
5C31×#410C211yesmaximal, characteristic
6C2×#41×C31C2211yescharacteristic
7C22×Dic62C2211yescharacteristic
8C31×#117C2212yes—
9#11758525—24no—
10#11758521C412yescomplemented
11#11758513C412yescomplemented
12#11758512—22no—
13#11758503C2211yescharacteristic
14#11758501—22no—
15C2×#92474—22no—
16C2×#92474C2212yes—
17C31×#99—22no—
18#11758398—24no—
19#41×C31—22no—
20#41×C31—22no—
21C2×Q8×C31C2×C411yescharacteristic
22C2×D4×C31C2×C411yescharacteristic
23C2×D4×C31D412yes—
24C22×C4×C31D412yes—
25C22×C4×C31C2311yescharacteristic
26C22×Dic31—21no—
27C2×Dic62—22no—
28C2×Dic62—22no—
29C2×Dic62—21no—
30C2×Dic62C2×C412yes—
31C4⋊C4×C31—22no—
32C22⋊C4×C31—22no—
33C42×C31—22no—
34C22⋊Dic31—24no—
35C22⋊Dic31—21no—
36C4⋊Dic31—21no—
37Dic31⋊C4—24no—
38C4×Dic31C2×C412yes—
39#92474—24no—
40#92474—22no—
41#92474—22no—
42C2×C31⋊C8—24no—
43C2×C31⋊C8D414yes—
44C23×C31C22⋊C412yes—
45C23×C31C2×D411yescharacteristic
46Q8×C31—22no—
47D4×C31—24no—
48D4×C31—22no—
49C2×C4×C31—22no—
50C2×C4×C31—22no—
51C2×C4×C31—42no—
52C2×C4×C31C22⋊C412yes—
53C2×C4×C31C22×C411yescharacteristic
54C2×C4×C31C2×D411yescharacteristic
55C2×C4×C31C2×D412yes—
56C2×C4×C31#4112yes—
57C2×Dic31—22no—
58C2×Dic31—22no—
59C2×Dic31—42no—
60Dic62—24no—
61Dic62—41no—
62Dic62—41no—
63C31⋊C8—24no—
64#1909—311nomaximal, Sylow
65C22×C31—22no—
66C22×C31—41no—
67C22×C31—42no—
68C22×C31C2×C22⋊C411yescharacteristic
69C22×C31#12112yes—
70C4×C31—22no—
71C4×C31—82no—
72C4×C31C4×D412yes—
73C4×C31#12011yescharacteristic
74C4×C31#12311yescharacteristic
75Dic31—42no—
76Dic31—42no—
77#568—311no—
78#536—311no—
79#419—312no—
80#410D3111yescharacteristic
81H(3,ℤ/4)—312no—
82C2×C31—21no—
83C2×C31—22no—
84C2×C31—42no—
85C2×C31#38611yescharacteristic
86C2×#41C2×D3111yescharacteristic
87C22×Q8—311no—
88#131—624no—
89C2×M16—312no—
90C2×M16—622no—
91C4⋊Q8—312no—
92#124—312no—
93#123—622no—
94C22⋊Q8—622no—
95#117—311no—
96#117C2×D3112yes—
97#103—624no—
98#99—22no—
99C31#190911yescharacteristic, complemented, Sylow
100#41—22no—
101#41—22no—
102C2×Q8—312no—
103C2×Q8—621no—
104C2×Q8—622no—
105C2×Q8—622no—
106C2×Q8C4×D3111yescharacteristic
107C2×D4C4×D3111yescharacteristic
108C2×D4C22⋊D3112yes—
109C22×C4—621no—
110C22×C4D12412yes—
111C22×C4C22×D3111yescharacteristic
112M16—624no—
113M16—622no—
114M16—622no—
115C2×C8—314no—
116C2×C8—624no—
117C4⋊C4—22no—
118C4⋊C4—624no—
119C4⋊C4—621no—
120C22⋊C4—22no—
121C22⋊C4—624no—
122C22⋊C4—621no—
123C42—22no—
124C42—312no—
125C23(C2×D31)⋊C412yes—
126C23C2×C22⋊D3111yescharacteristic
127Q8—22no—
128Q8—624no—
129Q8—1241no—
130Q8—1241no—
131D4—24no—
132D4—22no—
133C2×C4—22no—
134C2×C4—22no—
135C2×C4—42no—
136C2×C4—622no—
137C2×C4—622no—
138C2×C4—1242no—
139C2×C4(C2×D31)⋊C412yes—
140C2×C4C2×C4×D3111yescharacteristic
141C2×C4C2×D12411yescharacteristic
142C2×C4D4×D3112yes—
143C2×C4#9249712yes—
144C8—624no—
145C22—22no—
146C22—41no—
147C22—42no—
148C22C2×(C2×D31)⋊C411yescharacteristic
149C22#1175851612yes—
150C4—22no—
151C4—82no—
152C4—1242no—
153C4—1242no—
154C4(C22⋊D31)⋊C412yes—
155C4#1175845911yescharacteristic
156C4#1175846311yescharacteristic
157C2—22no—
158C2—21no—
159C2—42no—
160C2#1452092611yescharacteristic
subgroupG/H
centerC2#14520926
commutatorC2×C4×C31C22×C4
FrattiniC22×C4C22×D31
FittingC31×#410C2
socleC2×C31#386
prime radicalC2×#41×C31C22
cosocleC22×C4×C31C23
hypercenter#410D31
hypocenterC31#1909
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
3. #14521057C2semidirect
4. #14520805C2semidirect
10. #11758521C4semidirect
11. #11758513C4semidirect
99. C31#1909semidirect

Maximal subgroups

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

subgroupindex
#145218162
#145216202
#145210572
#145208052
C31×#4102
#190931