Finite Group Databasebeta

← #16847778

Subgroups — #16847778

Order 3968.

154 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 154 conjugacy classes of subgroups — too many to draw. Only its 45 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#14521489C211yesmaximal, characteristic, complemented
2#14521432C211yesmaximal, characteristic, complemented
3#14521166C211yesmaximal, characteristic, complemented
4#14520869C211yesmaximal, characteristic, complemented
5#14520866C211yesmaximal, characteristic, complemented
6#14520862C211yesmaximal, characteristic, complemented
7C31×#509C211yesmaximal, characteristic
8C31×#135C2211yescharacteristic
9C2×D8×C31C2211yescharacteristic
10#11758525—21no—
11#11758513—21no—
12C2×#92480—21no—
13C2×Dic124C2211yescharacteristic
14C31×SD32—21no—
15C31×D16—21no—
16C31×M32C2211yescharacteristic
17#11758425—21no—
18#11758417—21no—
19#11758415—21no—
20#11758407C2211yescharacteristic
21C8×Dic31C2211yescharacteristic
22#11758400C2211yescharacteristic
23#41×C31—21no—
24C2×D4×C31—21no—
25C2×Dic62—21no—
26Q16×C31D411yescharacteristic
27SD16×C31—21no—
28D8×C31—21no—
29D8×C31—21no—
30D8×C31D411yescharacteristic
31C2×C8×C31C2311yescharacteristic
32C22⋊Dic31—42no—
33#92480—41no—
34#92480—41no—
35C4×Dic31D411yescharacteristic
36#92474—21no—
37#92474—41no—
38C2×C31⋊C8—41no—
39C2×C31⋊C8D411yescharacteristic
40Dic124—21no—
41Dic124—21no—
42C16×C31—21no—
43C31⋊C16—21no—
44C23×C31—41no—
45Q8×C31—21no—
46D4×C31—21no—
47D4×C31—41no—
48D4×C31—41no—
49D4×C31—41no—
50C2×C4×C31—41no—
51C2×C4×C31C2×D411yescharacteristic
52C2×Dic31—21no—
53C2×Dic31—41no—
54Dic62—41no—
55Dic62—41no—
56C8×C31C2×D411yescharacteristic
57C8×C31#4111yescharacteristic
58C31⋊C8—41no—
59C31⋊C8D811yescharacteristic
60C31⋊C8D811yescharacteristic
61#2212—311nomaximal, Sylow
62C22×C31—41no—
63C22×C31—82no—
64C22×C31—81no—
65C22×C31AGL(1,ℤ/8)11yescharacteristic
66C4×C31—41no—
67C4×C31#12111yescharacteristic
68C4×C31C2×D811yescharacteristic
69Dic31—41no—
70Dic31—81no—
71#510—311no—
72#509D3111yescharacteristic
73#495—311no—
74#443—311no—
75#364—311no—
76#362—311no—
77#361—311no—
78C2×C31—21no—
79C2×C31—81no—
80C2×C31—161no—
81C2×C31#45911yescharacteristic
82#135C2×D3111yescharacteristic
83C2×Q16—311no—
84C2×SD16—621no—
85C2×D8C2×D3111yescharacteristic
86#131—621no—
87#124—621no—
88Q32—621no—
89SD32—21no—
90SD32—621no—
91D16—21no—
92M32—311no—
93M32C2×D3111yescharacteristic
94#108—311no—
95#104—621no—
96C4×C8—311no—
97C31#221211yescharacteristic, complemented, Sylow
98#41—21no—
99C2×Q8—621no—
100C2×D4—21no—
101Q16—621no—
102Q16—621no—
103Q16C22⋊D3111yescharacteristic
104SD16—21no—
105SD16—1241no—
106SD16—1241no—
107D8—21no—
108D8—21no—
109D8C22⋊D3111yescharacteristic
110M16—621no—
111M16—1241no—
112C2×C8—311no—
113C2×C8—1241no—
114C2×C8C22×D3111yescharacteristic
115C22⋊C4—1242no—
116C42—311no—
117C16—21no—
118C16—621no—
119C23—41no—
120Q8—21no—
121Q8—1241no—
122Q8—1241no—
123D4—21no—
124D4—41no—
125D4—41no—
126D4—41no—
127C2×C4—41no—
128C2×C4—621no—
129C2×C4—1241no—
130C2×C4D4×D3111yescharacteristic
131C8—311no—
132C8—311no—
133C8—1241no—
134C8#9249711yescharacteristic
135C8C2×C22⋊D3111yescharacteristic
136C22—41no—
137C22—82no—
138C22—81no—
139C22#1175848811yescharacteristic
140C4—41no—
141C4—1241no—
142C4—2481no—
143C4D8×D3111yescharacteristic
144C4#1175851611yescharacteristic
145C2—21no—
146C2—81no—
147C2—161no—
148C2#1452124211yescharacteristic
subgroupG/H
centerC2#14521242
commutator, cosocleC2×C8×C31C23
FrattiniC2×C8C22×D31
Fitting, prime radicalC31×#509C2
socleC2×C31#459
hypercenter#509D31
hypocenterC31#2212
LCSG ▷ C2×C8×C31 ▷ C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #509

Complements

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

NH ≅ G/Ntype
1. #14521489C2semidirect
2. #14521432C2semidirect
3. #14521166C2semidirect
4. #14520869C2semidirect
5. #14520866C2semidirect
6. #14520862C2semidirect
97. C31#2212semidirect

Maximal subgroups

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

subgroupindex
#145214892
#145214322
#145211662
#145208692
#145208662
#145208622
C31×#5092
#221231