Finite Group Databasebeta

← #104×D31 #14521060

Subgroups — #104×D31 #14521060

Order 1984.

170 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 170 conjugacy classes of subgroups — too many to draw. Only its 53 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#41×D31C211yesmaximal, characteristic
2M16×D31C211yesmaximal, characteristic, complemented
3C42×D31C211yesmaximal, characteristic, complemented
4C31×#104C211yesmaximal, characteristic, complemented
5#11758425C211yesmaximal, characteristic, complemented
6#11758413C211yesmaximal, characteristic, complemented
7#11758393C211yesmaximal, characteristic, complemented
8#41×C31C2211yescharacteristic
9#92499C411yescharacteristic, complemented
10Q8×D31C411yescharacteristic, complemented
11#92497—21no—
12#92497C411yescharacteristic, complemented
13D4×D31—21no—
14D4×D31C411yescharacteristic, complemented
15#92495—21no—
16#92495C2211yescharacteristic
17C2×C4×D31—21no—
18C2×C4×D31—21no—
19C2×C4×D31C2211yescharacteristic
20M16×C31C2211yescharacteristic, complemented
21C42×C31C2211yescharacteristic, complemented
22C4×Dic31—21no—
23C4×Dic31C2211yescharacteristic, complemented
24#92474C2211yescharacteristic, complemented
25#92469—21no—
26C8×D31—21no—
27C22×D31—21no—
28C22×D31D411yescharacteristic
29Q8×C31C2×C411yescharacteristic, complemented
30D4×C31—21no—
31D4×C31C2×C411yescharacteristic, complemented
32C2×C4×C31—21no—
33C2×C4×C31—21no—
34C2×C4×C31C2311yescharacteristic
35C22⋊D31—21no—
36C22⋊D31—21no—
37C22⋊D31—21no—
38C2×Dic31—21no—
39C2×Dic31—21no—
40C2×Dic31D411yescharacteristic
41D124—21no—
42D124C2×C411yescharacteristic, complemented
43C4×D31—24no—
44C4×D31—21no—
45C4×D31—21no—
46C4×D31—21no—
47C4×D31C2×C411yescharacteristic
48C4×D31C2×C411yescharacteristic
49C4×D31D411yescharacteristic
50C4×D31D411yescharacteristic
51Dic62—21no—
52Dic62C2×C411yescharacteristic, complemented
53C8×C31—21no—
54C31⋊C8—21no—
55C22×C31—21no—
56C22×C31C2×D411yescharacteristic
57C2×D31—22no—
58C2×D31—21no—
59C2×D31—42no—
60C2×D31C22⋊C411yescharacteristic
61C2×D31C22⋊C411yescharacteristic
62C4×C31—22no—
63C4×C31—21no—
64C4×C31C22×C411yescharacteristic
65C4×C31C2×D411yescharacteristic
66Dic31—22no—
67Dic31—21no—
68Dic31C22⋊C411yescharacteristic
69Dic31C22⋊C411yescharacteristic
70C2×#104—311nomaximal, Sylow
71C2×C31—21no—
72C2×C31—41no—
73C2×C31C2×C22⋊C411yescharacteristic
74D31—21no—
75D31—41no—
76D31#10412yesdirect product factor
77C2×#41—311no—
78C2×M16—311no—
79C2×C42—311no—
80#104—311no—
81#104—311no—
82#104—311no—
83#104D3111yescharacteristic, direct product factor
84C31C2×#10411yescharacteristic, complemented, Sylow
85#41—311no—
86#41—311no—
87#41—311no—
88#41—621no—
89#41—621no—
90#41C2×D3111yescharacteristic
91C2×Q8—311no—
92C2×D4—311no—
93C2×D4—621no—
94C22×C4—311no—
95C22×C4—621no—
96C22×C4—621no—
97M16—311no—
98M16—621no—
99M16C2×D3111yescharacteristic, complemented
100C2×C8—621no—
101C42—311no—
102C42—621no—
103C42C2×D3111yescharacteristic, complemented
104C23—311no—
105C23—621no—
106Q8—311no—
107Q8—621no—
108Q8C4×D3111yescharacteristic, complemented
109D4—21no—
110D4—311no—
111D4—621no—
112D4—621no—
113D4—621no—
114D4—621no—
115D4C4×D3111yescharacteristic, complemented
116C2×C4—21no—
117C2×C4—21no—
118C2×C4—311no—
119C2×C4—311no—
120C2×C4—311no—
121C2×C4—311no—
122C2×C4—311no—
123C2×C4—621no—
124C2×C4—621no—
125C2×C4—624no—
126C2×C4—621no—
127C2×C4—621no—
128C2×C4—621no—
129C2×C4C22×D3111yescharacteristic
130C8—21no—
131C8—621no—
132C22—21no—
133C22—311no—
134C22—311no—
135C22—622no—
136C22—621no—
137C22—1242no—
138C22D4×D3111yescharacteristic
139C4—22no—
140C4—21no—
141C4—311no—
142C4—311no—
143C4—622no—
144C4—621no—
145C4C2×C4×D3111yescharacteristic
146C4D4×D3111yescharacteristic
147C2—21no—
148C2—41no—
149C2—312no—
150C2—621no—
151C2—1241no—
152C2C22⋊C4×D3111yescharacteristic
subgroupG/H
centerC4D4×D31
commutatorC4×C31C22×C4
FrattiniC2×C4C22×D31
FittingC31×#104C2
socleC2×C31C2×C22⋊C4
prime radical#41×D31C2
cosocleC2×C4×C31C23
hypercenter#104D31
hypocenterC31C2×#104
LCSG ▷ C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C4 ◁ C2×C4 ◁ #104

Complements

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

NH ≅ G/Ntype
2. M16×D31C2semidirect
3. C42×D31C2semidirect
4. C31×#104C2semidirect
5. #11758425C2semidirect
6. #11758413C2semidirect
7. #11758393C2semidirect
9. #92499C4semidirect
10. Q8×D31C4semidirect
12. #92497C4semidirect
14. D4×D31C4semidirect
20. M16×C31C22semidirect
21. C42×C31C22semidirect
23. C4×Dic31C22semidirect
24. #92474C22semidirect
29. Q8×C31C2×C4semidirect
31. D4×C31C2×C4semidirect
42. D124C2×C4semidirect
52. Dic62C2×C4semidirect
76. D31#104direct (N × H)
83. #104D31direct (N × H)
84. C31C2×#104semidirect
99. M16C2×D31semidirect
103. C42C2×D31semidirect
108. Q8C4×D31semidirect
115. D4C4×D31semidirect

Maximal subgroups

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

subgroupindex
#41×D312
M16×D312
C42×D312
C31×#1042
#117584252
#117584132
#117583932
C2×#10431