Finite Group Databasebeta

← #16846115

Subgroups — #16846115

Order 3968.

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

normal subgroups only

This group has 344 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#14521527C211yesmaximal, characteristic, complemented
2#14521054C212yesmaximal
3C2×#11758424C211yesmaximal, characteristic, complemented
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
12Q8×Dic31—24no—
13#11758503—22no—
14#11758503C2212yes—
15C2×#92474C2212yes—
16#11758424—22no—
17#11758420—24no—
18C24×C31—21no—
19C2×Q8×C31—22no—
20C2×Q8×C31—22no—
21C2×Q8×C31C2×C412yes—
22C2×Q8×C31D412yes—
23C2×D4×C31—22no—
24C2×D4×C31—21no—
25C2×D4×C31—22no—
26C2×D4×C31C2×C412yes—
27C22×C4×C31—21no—
28C22×C4×C31D412yes—
29C22×C4×C31C2311yescharacteristic
30C22⋊C4×C31—28no—
31C42×C31—21no—
32C42×C31C2×C412yes—
33C22⋊Dic31—22no—
34C4⋊Dic31—24no—
35C4⋊Dic31D414yes—
36C4×Dic31—24no—
37C4×Dic31—22no—
38#92474—22no—
39#92474—22no—
40C2×C31⋊C8—22no—
41C23×C31—22no—
42C23×C31—44no—
43C23×C31—41no—
44C23×C31—41no—
45C23×C31C2×D411yescharacteristic
46Q8×C31—24no—
47Q8×C31—24no—
48D4×C31—24no—
49D4×C31—42no—
50C2×C4×C31—22no—
51C2×C4×C31—22no—
52C2×C4×C31—22no—
53C2×C4×C31—42no—
54C2×C4×C31C22⋊C414yes—
55C2×C4×C31C22×C411yescharacteristic
56C2×C4×C31C2×D412yes—
57C2×C4×C31C2×D411yescharacteristic
58C2×C4×C31#4112yes—
59C2×Dic31—24no—
60C31⋊C8—42no—
61#1888—311nomaximal, Sylow
62C22×C31—22no—
63C22×C31—44no—
64C22×C31—42no—
65C22×C31—82no—
66C22×C31—82no—
67C22×C31C2×C22⋊C411yescharacteristic
68C22×C31#12011yescharacteristic
69C22×C31#12311yescharacteristic
70C4×C31—24no—
71C4×C31—42no—
72C4×C31C4×D412yes—
73C4×C31#12112yes—
74Dic31—44no—
75C2×#124D3111yescharacteristic
76#519—311no—
77#418—312no—
78C2×#101—311no—
79#339—312no—
80C2×C31—21no—
81C2×C31—21no—
82C2×C31—82no—
83C2×C31#38611yescharacteristic
84C2×C31#45412yes—
85C22×Q8C2×D3111yescharacteristic
86C22×D4C2×D3111yescharacteristic
87C2×M16—312no—
88#124—22no—
89#124Dic3114yescomplemented
90C4×Q8—624no—
91#117—312no—
92#117—622no—
93C2×C22⋊C4—22no—
94C2×C42C2×D3111yescharacteristic
95#102—624no—
96#101—622no—
97C31#188811yescharacteristic, complemented, Sylow
98C24—21no—
99C2×Q8—22no—
100C2×Q8—22no—
101C2×Q8C2×Dic3112yes—
102C2×Q8C22⋊D3112yes—
103C2×D4—22no—
104C2×D4—22no—
105C2×D4—21no—
106C2×D4C2×Dic3112yes—
107C22×C4—21no—
108C22×C4C22⋊D3112yes—
109C22×C4C22×D3111yescharacteristic
110M16—622no—
111M16—622no—
112C2×C8—622no—
113C4⋊C4—314no—
114C4⋊C4—624no—
115C22⋊C4—28no—
116C22⋊C4—622no—
117C42—21no—
118C42—624no—
119C42—622no—
120C42C2×Dic3112yes—
121C23—22no—
122C23—44no—
123C23—41no—
124C23—41no—
125C23C2×C22⋊D3111yescharacteristic
126Q8—24no—
127Q8—24no—
128D4—24no—
129D4—42no—
130C2×C4—22no—
131C2×C4—22no—
132C2×C4—22no—
133C2×C4—42no—
134C2×C4—624no—
135C2×C4C22⋊Dic3114yes—
136C2×C4D4×D3112yes—
137C2×C4#9249712yes—
138C2×C4C22×Dic3111yescharacteristic
139C2×C4C2×C22⋊D3111yescharacteristic
140C8—1242no—
141C22—22no—
142C22—44no—
143C22—42no—
144C22—82no—
145C22—82no—
146C22#1175851211yescharacteristic
147C22#1175851411yescharacteristic
148C22C2×C22⋊Dic3111yescharacteristic
149C4—24no—
150C4—42no—
151C4—1244no—
152C4D4×Dic3112yes—
153C4#1175851612yes—
154C2—21no—
155C2—21no—
156C2—82no—
157C2#1452092911yescharacteristic
158C2#1452122112yes—
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#1888
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
1. #14521527C2semidirect
3. C2×#11758424C2semidirect
4. #14520809C2semidirect
9. C31×#124C4semidirect
89. #124Dic31semidirect
97. C31#1888semidirect

Maximal subgroups

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

subgroupindex
#145215272
#145210542
C2×#117584242
#145208092
C2×C31×#1242
#188831