Finite Group Databasebeta

← #16846234

Subgroups — #16846234

Order 3968.

312 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 93 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#14521058C212yesmaximal, complemented
3#14521023C211yesmaximal, characteristic
4#14520805C212yesmaximal, complemented
5C31×#536C211yesmaximal, characteristic
6C2×#41×C31C2211yescharacteristic
7C22×Q8×C31C2211yescharacteristic
8C31×C4⋊Q8C412yescomplemented
9C31×#124C412yescomplemented
10C31×#123—22no—
11C31×C22⋊Q8—22no—
12C31×#117C2211yescharacteristic
13#11758525—24no—
14#11758503C2212yes—
15C2×#92474—22no—
16C2×#92474C2212yes—
17#11758423—24no—
18#11758422—22no—
19#41×C31—22no—
20#41×C31—22no—
21C2×Q8×C31—21no—
22C2×Q8×C31—22no—
23C2×Q8×C31—22no—
24C2×Q8×C31C2×C412yes—
25C2×Q8×C31C2×C411yescharacteristic
26C2×D4×C31C2×C411yescharacteristic
27C2×D4×C31D412yes—
28C22×C4×C31—21no—
29C22×C4×C31D412yes—
30C22×C4×C31C2311yescharacteristic
31C4⋊C4×C31—24no—
32C4⋊C4×C31—21no—
33C22⋊C4×C31—24no—
34C22⋊C4×C31—21no—
35C42×C31C2×C412yes—
36C22⋊Dic31—22no—
37C4⋊Dic31—22no—
38C4×Dic31—22no—
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—
47Q8×C31—24no—
48Q8×C31—41no—
49Q8×C31—41no—
50D4×C31—24no—
51D4×C31—22no—
52C2×C4×C31—22no—
53C2×C4×C31—22no—
54C2×C4×C31—22no—
55C2×C4×C31—22no—
56C2×C4×C31—42no—
57C2×C4×C31C22⋊C412yes—
58C2×C4×C31C22×C411yescharacteristic
59C2×C4×C31C2×D412yes—
60C2×C4×C31C2×D411yescharacteristic
61C2×C4×C31#4112yes—
62C2×Dic31—42no—
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—42no—
72C4×C31—42no—
73C4×C31C4×D412yes—
74C4×C31#12011yescharacteristic
75C4×C31#12311yescharacteristic
76Dic31—82no—
77#568—311no—
78#536D3111yescharacteristic
79#419—312no—
80#410—311no—
81H(3,ℤ/4)—312no—
82C2×C31—22no—
83C2×C31—21no—
84C2×C31—42no—
85C2×C31#38611yescharacteristic
86C2×#41C2×D3111yescharacteristic
87C22×Q8C2×D3111yescharacteristic
88#131—624no—
89C2×M16—312no—
90C2×M16—622no—
91C4⋊Q8Dic3112yescomplemented
92#124Dic3112yescomplemented
93#123—22no—
94C22⋊Q8—22no—
95#117—312no—
96#117C2×D3111yescharacteristic
97#103—624no—
98#99—622no—
99C31#190911yescharacteristic, complemented, Sylow
100#41—22no—
101#41—22no—
102C2×Q8—21no—
103C2×Q8—22no—
104C2×Q8—22no—
105C2×Q8C2×Dic3112yes—
106C2×Q8C2×Dic3111yescharacteristic
107C2×D4C2×Dic3111yescharacteristic
108C2×D4C22⋊D3112yes—
109C22×C4—21no—
110C22×C4C22⋊D3112yes—
111C22×C4C22×D3111yescharacteristic
112M16—624no—
113M16—622no—
114M16—622no—
115C2×C8—314no—
116C2×C8—624no—
117C4⋊C4—24no—
118C4⋊C4—21no—
119C4⋊C4—622no—
120C22⋊C4—24no—
121C22⋊C4—21no—
122C22⋊C4—622no—
123C42—622no—
124C42C2×Dic3112yes—
125C23C22⋊Dic3112yes—
126C23C2×C22⋊D3111yescharacteristic
127Q8—22no—
128Q8—24no—
129Q8—41no—
130Q8—41no—
131D4—24no—
132D4—22no—
133C2×C4—22no—
134C2×C4—22no—
135C2×C4—22no—
136C2×C4—22no—
137C2×C4—42no—
138C2×C4—1242no—
139C2×C4C22⋊Dic3112yes—
140C2×C4D4×D3112yes—
141C2×C4#9249712yes—
142C2×C4C22×Dic3111yescharacteristic
143C2×C4C2×C22⋊D3111yescharacteristic
144C8—624no—
145C22—22no—
146C22—41no—
147C22—42no—
148C22#1175851612yes—
149C22C2×C22⋊Dic3111yescharacteristic
150C4—22no—
151C4—42no—
152C4—42no—
153C4—2482no—
154C4D4×Dic3112yes—
155C4#1175851211yescharacteristic
156C4#1175851411yescharacteristic
157C2—21no—
158C2—22no—
159C2—42no—
160C2#1452092911yescharacteristic
subgroupG/H
centerC2#14520929
commutatorC2×C4×C31C22×C4
FrattiniC22×C4C22×D31
FittingC31×#536C2
socleC2×C31#386
prime radicalC2×#41×C31C22
cosocleC22×C4×C31C23
hypercenter#536D31
hypocenterC31#1909
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2 ◁ C22×C4 ◁ #536

Complements

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

NH ≅ G/Ntype
2. #14521058C2semidirect
4. #14520805C2semidirect
8. C31×C4⋊Q8C4semidirect
9. C31×#124C4semidirect
91. C4⋊Q8Dic31semidirect
92. #124Dic31semidirect
99. C31#1909semidirect

Maximal subgroups

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

subgroupindex
#145218162
#145210582
#145210232
#145208052
C31×#5362
#190931