Finite Group Databasebeta

← #16846867

Subgroups — #16846867

Order 3968.

282 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 69 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#14521680C211yesmaximal, characteristic, complemented
2#14521054C212yesmaximal
3#14520818C211yesmaximal, characteristic, complemented
4#14520809C212yesmaximal, complemented
5C31×#390C211yesmaximal, characteristic
6C22×D4×C31C2211yescharacteristic
7C2×C4⋊C4×C31C2211yescharacteristic
8C2×C22⋊C4×C31—22no—
9C2×C42×C31C2211yescharacteristic
10#11758503C2212yes—
11#11758501—22no—
12C2×#92474C2212yes—
13#11758467—22no—
14#11758465—22no—
15#11758420—22no—
16#11758420—22no—
17C24×C31—21no—
18C2×D4×C31—22no—
19C2×D4×C31—22no—
20C2×D4×C31—21no—
21C2×D4×C31Q812yescomplemented
22C22×C4×C31—21no—
23C22×C4×C31D412yes—
24C22×C4×C31C2311yescharacteristic
25C2×Dic62—22no—
26C4⋊C4×C31—22no—
27C22⋊C4×C31—44no—
28C42×C31—22no—
29C22⋊Dic31—22no—
30C4⋊Dic31—22no—
31C4⋊Dic31D412yes—
32C4⋊Dic31D412yes—
33Dic31⋊C4—24no—
34C4×Dic31—22no—
35#92474—22no—
36#92474—22no—
37C2×C31⋊C8—22no—
38C23×C31—22no—
39C23×C31—42no—
40C23×C31—42no—
41C23×C31—41no—
42C23×C31—41no—
43C23×C31C2×D411yescharacteristic
44D4×C31—24no—
45D4×C31—42no—
46C2×C4×C31—22no—
47C2×C4×C31—22no—
48C2×C4×C31—41no—
49C2×C4×C31—41no—
50C2×C4×C31—42no—
51C2×C4×C31C2×D412yes—
52C2×C4×C31C2×Q811yescharacteristic
53C2×C4×C31#4111yescharacteristic
54C2×C4×C31#4112yes—
55C2×Dic31—22no—
56C2×Dic31—22no—
57Dic62—82no—
58C31⋊C8—42no—
59#2027—311nomaximal, Sylow
60C22×C31—21no—
61C22×C31—21no—
62C22×C31—44no—
63C22×C31—42no—
64C22×C31—82no—
65C22×C31—81no—
66C22×C31—81no—
67C22×C31#12011yescharacteristic
68C22×C31C22⋊Q811yescharacteristic
69C22×C31#12411yescharacteristic
70C4×C31—42no—
71C4×C31—42no—
72C4×C31C22⋊Q812yes—
73C4×C31#12412yes—
74Dic31—42no—
75Dic31—42no—
76#544—311no—
77#418—312no—
78#390D3111yescharacteristic
79#343—311no—
80#339—312no—
81C2×C31—21no—
82C2×C31—21no—
83C2×C31—82no—
84C2×C31#39311yescharacteristic
85C2×C31#45311yescharacteristic
86C2×C31#45411yescharacteristic
87C22×D4C2×D3111yescharacteristic
88C2×M16—312no—
89C4⋊Q8—622no—
90#125—622no—
91C22⋊Q8—622no—
92#117—312no—
93C2×C4⋊C4C2×D3111yescharacteristic
94C2×C22⋊C4—22no—
95C2×C42C2×D3111yescharacteristic
96#102—622no—
97#102—622no—
98C31#202711yescharacteristic, complemented, Sylow
99C24—21no—
100C2×Q8—622no—
101C2×D4—21no—
102C2×D4—22no—
103C2×D4—22no—
104C2×D4Dic6212yescomplemented
105C22×C4—21no—
106C22×C4C22⋊D3112yes—
107C22×C4C22×D3111yescharacteristic
108M16—622no—
109M16—622no—
110C2×C8—622no—
111C4⋊C4—22no—
112C4⋊C4—312no—
113C4⋊C4—312no—
114C4⋊C4—624no—
115C4⋊C4—622no—
116C22⋊C4—44no—
117C22⋊C4—622no—
118C42—22no—
119C42—622no—
120C23—22no—
121C23—42no—
122C23—42no—
123C23—41no—
124C23—41no—
125C23C2×C22⋊D3111yescharacteristic
126Q8—2482no—
127D4—24no—
128D4—42no—
129C2×C4—22no—
130C2×C4—22no—
131C2×C4—41no—
132C2×C4—41no—
133C2×C4—42no—
134C2×C4—622no—
135C2×C4—622no—
136C2×C4C2×Dic6211yescharacteristic
137C2×C4#9249511yescharacteristic
138C2×C4D4×D3112yes—
139C2×C4#9249712yes—
140C8—1242no—
141C22—21no—
142C22—21no—
143C22—44no—
144C22—42no—
145C22—82no—
146C22—81no—
147C22—81no—
148C22#1175850111yescharacteristic
149C22#1175851311yescharacteristic
150C22#1175851411yescharacteristic
151C4—42no—
152C4—42no—
153C4—1242no—
154C4—1242no—
155C4#1175845512yes—
156C4#1175846212yes—
157C2—21no—
158C2—21no—
159C2—82no—
160C2#1452096111yescharacteristic
161C2#1452121611yescharacteristic
162C2#1452122111yescharacteristic
subgroupG/H
centerC22#11758514
commutator, cosocleC22×C4×C31C23
FrattiniC22×C4C22×D31
FittingC31×#390C2
socleC22×C31#120
prime radicalC22×D4×C31C22
hypercenter#390D31
hypocenterC31#2027
LCSG ▷ C22×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ #390

Complements

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

NH ≅ G/Ntype
1. #14521680C2semidirect
3. #14520818C2semidirect
4. #14520809C2semidirect
21. C2×D4×C31Q8semidirect
98. C31#2027semidirect
104. C2×D4Dic62semidirect

Maximal subgroups

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

subgroupindex
#145216802
#145210542
#145208182
#145208092
C31×#3902
#202731