Finite Group Databasebeta

← #16846100

Subgroups — #16846100

Order 3968.

360 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 97 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#14521524C211yesmaximal, characteristic
2#14521058C212yesmaximal, complemented
3C2×#11758421C211yesmaximal, characteristic
4#14520809C212yesmaximal, complemented
5C2×C31×#124C211yesmaximal, characteristic
6C22×Q8×C31C2211yescharacteristic
7C22×D4×C31C2211yescharacteristic
8C31×#124—22no—
9C31×#124C414yescomplemented
10C2×C22⋊C4×C31—22no—
11C2×C42×C31C2211yescharacteristic
12C2×C22⋊Dic31—22no—
13D4×Dic31—24no—
14#11758503C2212yes—
15C2×#92474C2212yes—
16#11758423—24no—
17#11758421—22no—
18C24×C31D412yes—
19C2×Q8×C31—21no—
20C2×Q8×C31—22no—
21C2×Q8×C31—22no—
22C2×Q8×C31C2×C412yescomplemented
23C2×D4×C31—22no—
24C2×D4×C31—22no—
25C2×D4×C31C2×C412yes—
26C2×D4×C31D412yes—
27C22×C4×C31—21no—
28C22×C4×C31—21no—
29C22×C4×C31C2311yescharacteristic
30C22×Dic31—24no—
31C22⋊C4×C31—28no—
32C42×C31—21no—
33C42×C31C2×C412yescomplemented
34C22⋊Dic31—24no—
35C22⋊Dic31—22no—
36C4⋊Dic31D414yes—
37C4×Dic31—22no—
38#92474—22no—
39#92474—22no—
40C2×C31⋊C8—22no—
41C23×C31—22no—
42C23×C31—22no—
43C23×C31—44no—
44C23×C31C22⋊C414yes—
45C23×C31C2×D411yescharacteristic
46Q8×C31—24no—
47Q8×C31—42no—
48D4×C31—24no—
49D4×C31—24no—
50C2×C4×C31—22no—
51C2×C4×C31—22no—
52C2×C4×C31—42no—
53C2×C4×C31—41no—
54C2×C4×C31—41no—
55C2×C4×C31C22×C411yescharacteristic
56C2×C4×C31C2×D412yes—
57C2×C4×C31C2×D411yescharacteristic
58C2×C4×C31#4112yes—
59C2×Dic31—24no—
60C2×Dic31—84no—
61C31⋊C8—42no—
62#1885—311nomaximal, Sylow
63C22×C31—22no—
64C22×C31—24no—
65C22×C31—44no—
66C22×C31—44no—
67C22×C31—82no—
68C22×C31C2×C22⋊C411yescharacteristic
69C22×C31#12011yescharacteristic
70C22×C31#12311yescharacteristic
71C4×C31—42no—
72C4×C31—42no—
73C4×C31C4×D412yes—
74C4×C31#12112yes—
75Dic31—44no—
76C2×#124D3111yescharacteristic
77#518—311no—
78#419—312no—
79C2×#100—311no—
80#339—312no—
81C2×C31—21no—
82C2×C31—21no—
83C2×C31—44no—
84C2×C31#38611yescharacteristic
85C2×C31#45512yes—
86C22×Q8C2×D3111yescharacteristic
87C22×D4C2×D3111yescharacteristic
88C2×M16—312no—
89#124—22no—
90#124Dic3114yescomplemented
91C4×D4—624no—
92#117—312no—
93C2×C22⋊C4—22no—
94C2×C22⋊C4—622no—
95C2×C42C2×D3111yescharacteristic
96#103—624no—
97#100—622no—
98C31#188511yescharacteristic, complemented, Sylow
99C24C22⋊D3112yes—
100C2×Q8—21no—
101C2×Q8—22no—
102C2×Q8—22no—
103C2×Q8C2×Dic3112yescomplemented
104C2×D4—22no—
105C2×D4—22no—
106C2×D4C2×Dic3112yes—
107C2×D4C22⋊D3112yes—
108C22×C4—21no—
109C22×C4—21no—
110C22×C4—624no—
111C22×C4C22×D3111yescharacteristic
112M16—622no—
113M16—622no—
114C2×C8—622no—
115C4⋊C4—314no—
116C22⋊C4—28no—
117C22⋊C4—624no—
118C22⋊C4—622no—
119C42—21no—
120C42—622no—
121C42C2×Dic3112yescomplemented
122C23—22no—
123C23—22no—
124C23—44no—
125C23C22⋊Dic3114yes—
126C23C2×C22⋊D3111yescharacteristic
127Q8—24no—
128Q8—42no—
129D4—24no—
130D4—24no—
131C2×C4—22no—
132C2×C4—22no—
133C2×C4—42no—
134C2×C4—41no—
135C2×C4—41no—
136C2×C4—624no—
137C2×C4—2484no—
138C2×C4D4×D3112yes—
139C2×C4#9249712yes—
140C2×C4C22×Dic3111yescharacteristic
141C2×C4C2×C22⋊D3111yescharacteristic
142C8—1242no—
143C22—22no—
144C22—24no—
145C22—44no—
146C22—44no—
147C22—82no—
148C22#1175851211yescharacteristic
149C22#1175851411yescharacteristic
150C22C2×C22⋊Dic3111yescharacteristic
151C4—42no—
152C4—42no—
153C4—1244no—
154C4D4×Dic3112yes—
155C4#1175851612yes—
156C2—21no—
157C2—21no—
158C2—44no—
159C2#1452092911yescharacteristic
160C2#1452122612yes—
subgroupG/H
centerC22#11758514
commutatorC2×C4×C31C22×C4
FrattiniC22×C4C22×D31
FittingC2×C31×#124C2
socleC22×C31#120
prime radicalC22×D4×C31C22
cosocleC22×C4×C31C23
hypercenterC2×#124D31
hypocenterC31#1885
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
2. #14521058C2semidirect
4. #14520809C2semidirect
9. C31×#124C4semidirect
22. C2×Q8×C31C2×C4semidirect
33. C42×C31C2×C4semidirect
90. #124Dic31semidirect
98. C31#1885semidirect
103. C2×Q8C2×Dic31semidirect
121. C42C2×Dic31semidirect

Maximal subgroups

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

subgroupindex
#145215242
#145210582
C2×#117584212
#145208092
C2×C31×#1242
#188531