Finite Group Databasebeta

← #16846246

Subgroups — #16846246

Order 3968.

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

normal subgroups only

This group has 314 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#14521623C211yesmaximal, characteristic
2#14521527C211yesmaximal, characteristic, complemented
3#14521065C212yesmaximal
4#14520806C212yesmaximal, complemented
5C2×C31×#101C211yesmaximal, characteristic, complemented
6C22×Q8×C31C2211yescharacteristic
7C2×#92495C2211yescharacteristic
8C2×M16×C31C2212yes—
9#11758524C412yescomplemented
10#11758523—22no—
11Q8×Dic31—24no—
12#11758521C412yescomplemented
13#11758506—22no—
14#11758503—22no—
15#11758503C2211yescharacteristic
16#11758503C2212yes—
17C31×#101—22no—
18#11758413—24no—
19C2×Q8×C31—22no—
20C2×Q8×C31—22no—
21C2×Q8×C31C2×C412yes—
22C2×Q8×C31D412yes—
23C22×C4×C31D412yes—
24C22×C4×C31C2311yescharacteristic
25C2×C22⋊D31—21no—
26#92495—22no—
27#92495—22no—
28C2×D124C2×C411yescharacteristic
29C2×C4×D31—21no—
30C2×Dic62C2×C411yescharacteristic
31M16×C31—22no—
32M16×C31—22no—
33C2×C8×C31—22no—
34C22⋊Dic31—22no—
35C22⋊Dic31—21no—
36(C2×D31)⋊C4—24no—
37C4⋊Dic31—24no—
38C4⋊Dic31—22no—
39C4⋊Dic31—21no—
40Dic31⋊C4—24no—
41C4×Dic31—24no—
42C4×Dic31C2×C412yes—
43C4×Dic31D414yes—
44C23×C31C2×D411yescharacteristic
45C22×D31—21no—
46Q8×C31—24no—
47Q8×C31—24no—
48C2×C4×C31—22no—
49C2×C4×C31—22no—
50C2×C4×C31C22⋊C414yes—
51C2×C4×C31C22×C411yescharacteristic
52C2×C4×C31C2×D412yes—
53C2×C4×C31C2×D411yescharacteristic
54C2×C4×C31#4112yes—
55C22⋊D31—41no—
56C22⋊D31—41no—
57C2×Dic31—22no—
58C2×Dic31—21no—
59C2×Dic31—24no—
60D124—22no—
61C4×D31—42no—
62Dic62—22no—
63C8×C31—42no—
64#1912—311nomaximal, Sylow
65C22×C31—41no—
66C22×C31C2×C22⋊C411yescharacteristic
67C22×C31#12011yescharacteristic
68C22×C31#12311yescharacteristic
69C2×D31—42no—
70C2×D31—41no—
71C4×C31—24no—
72C4×C31C4×D412yes—
73C4×C31#12112yes—
74Dic31—44no—
75Dic31—42no—
76Dic31—41no—
77#536—311no—
78#519—311no—
79#421—312no—
80C2×#101D3111yescharacteristic, complemented
81H(3,ℤ/4)—312no—
82C2×C31—21no—
83C2×C31—21no—
84C2×C31—21no—
85C2×C31#38611yescharacteristic
86D31—81no—
87C2×#41—311no—
88C22×Q8C2×D3111yescharacteristic
89C2×M16C2×D3112yes—
90C4⋊Q8—312no—
91#124—312no—
92#123—622no—
93C22⋊Q8—622no—
94C4×Q8—624no—
95#117—312no—
96#117—311no—
97#117—622no—
98#104—624no—
99#101—22no—
100C31#191211yescharacteristic, complemented, Sylow
101#41—622no—
102#41—622no—
103C2×Q8—22no—
104C2×Q8—22no—
105C2×Q8—311no—
106C2×Q8C4×D3112yes—
107C2×Q8C22⋊D3112yes—
108C2×D4—311no—
109C2×D4—621no—
110C22×C4—621no—
111C22×C4D12412yes—
112C22×C4C22×D3111yescharacteristic
113M16—22no—
114M16—22no—
115C2×C8—22no—
116C4⋊C4—624no—
117C4⋊C4—624no—
118C4⋊C4—622no—
119C4⋊C4—621no—
120C22⋊C4—622no—
121C22⋊C4—621no—
122C22⋊C4—624no—
123C42—312no—
124C42—314no—
125C42—624no—
126C23—621no—
127C23C2×D12411yescharacteristic
128Q8—24no—
129Q8—24no—
130Q8—622no—
131D4—622no—
132D4—1241no—
133D4—1241no—
134C2×C4—22no—
135C2×C4—22no—
136C2×C4—624no—
137C2×C4—622no—
138C2×C4—621no—
139C2×C4—1242no—
140C2×C4(C2×D31)⋊C414yes—
141C2×C4C2×C4×D3111yescharacteristic
142C2×C4D4×D3112yes—
143C2×C4#9249712yes—
144C2×C4C2×C22⋊D3111yescharacteristic
145C8—42no—
146C22—41no—
147C22—1242no—
148C22—1241no—
149C22#1175845911yescharacteristic
150C22#1175846311yescharacteristic
151C22C2×(C2×D31)⋊C411yescharacteristic
152C4—24no—
153C4—1244no—
154C4—1242no—
155C4—1241no—
156C4(C22⋊D31)⋊C412yes—
157C4#1175851612yes—
158C2—21no—
159C2—21no—
160C2—21no—
161C2—2481no—
162C2#1452092611yescharacteristic
subgroupG/H
centerC2#14520926
commutatorC2×C4×C31C22×C4
FrattiniC22×C4C22×D31
FittingC2×C31×#101C2
socleC2×C31#386
prime radicalC2×#92495C22
cosocleC22×C4×C31C23
hypercenterC2×#101D31
hypocenterC31#1912
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
2. #14521527C2semidirect
4. #14520806C2semidirect
5. C2×C31×#101C2semidirect
9. #11758524C4semidirect
12. #11758521C4semidirect
80. C2×#101D31semidirect
100. C31#1912semidirect

Maximal subgroups

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

subgroupindex
#145216232
#145215272
#145210652
#145208062
C2×C31×#1012
#191231