Finite Group Databasebeta

← #16845755

Subgroups — #16845755

Order 3968.

260 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 89 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
1C2×#11758525C211yesmaximal, characteristic
2#14521085C212yesmaximal, complemented
3#14521023C211yesmaximal, characteristic
4#14520805C212yesmaximal, complemented
5C31×#410C211yesmaximal, characteristic
6C2×#41×C31C2211yescharacteristic
7C31×#117C2212yes—
8#11758525—22no—
9#11758525—22no—
10#11758503C2212yes—
11C2×#92474C412yescomplemented
12C2×#92474C2211yescharacteristic
13C22×C31⋊C8C412yescomplemented
14C22×C31⋊C8C2211yescharacteristic
15C31×#99—22no—
16#11758422—22no—
17#11758396—22no—
18#11758395—22no—
19#41×C31—22no—
20#41×C31—22no—
21C2×Q8×C31Q811yescharacteristic
22C2×D4×C31D412yes—
23C2×D4×C31Q811yescharacteristic
24C22×C4×C31C2×C412yes—
25C22×C4×C31C2311yescharacteristic
26C4⋊C4×C31—22no—
27C22⋊C4×C31—22no—
28C42×C31—22no—
29C22⋊Dic31—22no—
30C4⋊Dic31—22no—
31C4×Dic31—22no—
32#92474—22no—
33#92474—24no—
34C2×C31⋊C8—22no—
35C2×C31⋊C8—22no—
36C2×C31⋊C8C2×C412yes—
37C2×C31⋊C8C2×C411yescharacteristic
38C2×C31⋊C8C2×C411yescharacteristic
39C2×C31⋊C8D412yes—
40C2×C31⋊C8D412yes—
41C23×C31C4⋊C412yes—
42C23×C31C2×D411yescharacteristic
43Q8×C31—22no—
44D4×C31—24no—
45D4×C31—22no—
46C2×C4×C31—22no—
47C2×C4×C31—22no—
48C2×C4×C31—42no—
49C2×C4×C31C4⋊C412yes—
50C2×C4×C31C22×C411yescharacteristic
51C2×C4×C31C2×D412yes—
52C2×C4×C31C2×Q811yescharacteristic
53C2×C4×C31#4112yes—
54C2×Dic31—42no—
55C31⋊C8—22no—
56C31⋊C8C22⋊C411yescharacteristic
57C31⋊C8C22⋊C411yescharacteristic
58C31⋊C8C22⋊C412yes—
59#1812—311nomaximal, Sylow
60C22×C31—22no—
61C22×C31—41no—
62C22×C31—42no—
63C22×C31C2×C4⋊C411yescharacteristic
64C22×C31#12112yes—
65C4×C31—22no—
66C4×C31—82no—
67C4×C31C2×C22⋊C411yescharacteristic
68C4×C31#11711yescharacteristic
69C4×C31C22⋊Q812yes—
70Dic31—82no—
71C2×#131—311no—
72#427—312no—
73#410—311no—
74#410D3111yescharacteristic
75H(3,ℤ/4)—312no—
76C2×C31—22no—
77C2×C31—21no—
78C2×C31—42no—
79C2×C31#38011yescharacteristic
80C2×#41C2×D3111yescharacteristic
81#131—622no—
82#131—622no—
83C2×M16—312no—
84C2×M16—311no—
85C22×C8—311no—
86C22×C8—312no—
87#117—312no—
88#117C2×D3112yes—
89#107—622no—
90#106—622no—
91#99—22no—
92#99—622no—
93C31#181211yescharacteristic, complemented, Sylow
94#41—22no—
95#41—22no—
96C2×Q8Dic6211yescharacteristic
97C2×D4Dic6211yescharacteristic
98C2×D4C22⋊D3112yes—
99C22×C4C4×D3112yes—
100C22×C4C22×D3111yescharacteristic
101M16—624no—
102M16—622no—
103C2×C8—311no—
104C2×C8—311no—
105C2×C8—312no—
106C2×C8—312no—
107C2×C8—312no—
108C2×C8—622no—
109C2×C8—622no—
110C4⋊C4—22no—
111C4⋊C4—622no—
112C22⋊C4—22no—
113C22⋊C4—622no—
114C42—22no—
115C42—622no—
116C23Dic31⋊C412yes—
117C23C2×C22⋊D3111yescharacteristic
118Q8—22no—
119D4—24no—
120D4—22no—
121C2×C4—22no—
122C2×C4—22no—
123C2×C4—42no—
124C2×C4—1242no—
125C2×C4Dic31⋊C412yes—
126C2×C4C2×Dic6211yescharacteristic
127C2×C4C2×C4×D3111yescharacteristic
128C2×C4D4×D3112yes—
129C2×C4#9249712yes—
130C8—311no—
131C8—311no—
132C8—312no—
133C8—622no—
134C22—22no—
135C22—41no—
136C22—42no—
137C22C2×Dic31⋊C411yescharacteristic
138C22#1175851612yes—
139C4—22no—
140C4—82no—
141C4—2482no—
142C4#1175845411yescharacteristic
143C4#1175845512yes—
144C4C22⋊C4×D3111yescharacteristic
145C2—22no—
146C2—21no—
147C2—42no—
148C2#1452090711yescharacteristic
subgroupG/H
centerC4#11758454
commutatorC2×C4×C31C22×C4
FrattiniC22×C4C22×D31
FittingC31×#410C2
socleC2×C31#380
prime radicalC2×#41×C31C22
cosocleC22×C4×C31C23
hypercenter#410D31
hypocenterC31#1812
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C4 ◁ C22×C4 ◁ #410

Complements

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

NH ≅ G/Ntype
2. #14521085C2semidirect
4. #14520805C2semidirect
11. C2×#92474C4semidirect
13. C22×C31⋊C8C4semidirect
93. C31#1812semidirect

Maximal subgroups

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

subgroupindex
C2×#117585252
#145210852
#145210232
#145208052
C31×#4102
#181231