Finite Group Databasebeta

← #16847785

Subgroups — #16847785

Order 3968.

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

normal subgroups only

This group has 170 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#14521484C211yesmaximal, characteristic, complemented
2#14521424C211yesmaximal, characteristic, complemented
3#14521166C211yesmaximal, characteristic, complemented
4#14520869C211yesmaximal, characteristic, complemented
5#14520863C211yesmaximal, characteristic, complemented
6#14520862C211yesmaximal, characteristic, complemented
7C31×#509C211yesmaximal, characteristic, complemented
8C31×#135C2211yescharacteristic
9C2×D8×C31C2211yescharacteristic
10#11758525—21no—
11#11758517—21no—
12C2×#92479—21no—
13C2×D248C2211yescharacteristic
14C31×SD32—21no—
15C31×D16—21no—
16C31×M32C2211yescharacteristic
17#11758425—21no—
18#11758416—21no—
19#11758414—21no—
20#11758407C2211yescharacteristic
21C8×Dic31C2211yescharacteristic
22#11758400C2211yescharacteristic
23#41×C31—21no—
24C2×D4×C31—21no—
25C2×C22⋊D31—42no—
26C2×D124—21no—
27Q16×C31D411yescharacteristic, complemented
28SD16×C31—21no—
29D8×C31—21no—
30D8×C31—21no—
31D8×C31D411yescharacteristic, complemented
32C2×C8×C31C2311yescharacteristic
33#92479—41no—
34#92479—41no—
35C4×Dic31D411yescharacteristic
36#92474—21no—
37#92474—41no—
38C2×C31⋊C8—41no—
39C2×C31⋊C8D411yescharacteristic
40D248—21no—
41D248—21no—
42C16×C31—21no—
43C31⋊C16—21no—
44C23×C31—41no—
45C22×D31—41no—
46Q8×C31—21no—
47D4×C31—21no—
48D4×C31—41no—
49D4×C31—41no—
50D4×C31—41no—
51C2×C4×C31—41no—
52C2×C4×C31C2×D411yescharacteristic
53C22⋊D31—84no—
54C2×Dic31—21no—
55D124—41no—
56D124—41no—
57C8×C31C2×D411yescharacteristic
58C8×C31#4111yescharacteristic
59C31⋊C8—41no—
60C31⋊C8D811yescharacteristic
61C31⋊C8D811yescharacteristic
62#2213—311nomaximal, Sylow
63C22×C31—41no—
64C22×C31—82no—
65C22×C31—81no—
66C22×C31AGL(1,ℤ/8)11yescharacteristic
67C2×D31—82no—
68C2×D31—81no—
69C4×C31—41no—
70C4×C31#12111yescharacteristic
71C4×C31C2×D811yescharacteristic
72Dic31—22no—
73#509—311no—
74#509D3111yescharacteristic, complemented
75#493—311no—
76#443—311no—
77#364—311no—
78#361—311no—
79#361—311no—
80C2×C31—21no—
81C2×C31—81no—
82C2×C31—161no—
83C2×C31#45911yescharacteristic
84D31—161no—
85#135C2×D3111yescharacteristic
86C2×D8—311no—
87C2×D8—621no—
88C2×D8C2×D3111yescharacteristic
89#131—621no—
90#127—621no—
91SD32—21no—
92SD32—621no—
93D16—21no—
94D16—621no—
95M32—311no—
96M32C2×D3111yescharacteristic
97#108—311no—
98#104—621no—
99C4×C8—311no—
100C31#221311yescharacteristic, complemented, Sylow
101#41—21no—
102C2×D4—21no—
103C2×D4—621no—
104C2×D4—1242no—
105Q16C22⋊D3111yescharacteristic, complemented
106SD16—21no—
107D8—21no—
108D8—21no—
109D8—621no—
110D8—621no—
111D8—1241no—
112D8—1241no—
113D8C22⋊D3111yescharacteristic, complemented
114M16—621no—
115M16—1241no—
116C2×C8—311no—
117C2×C8—1241no—
118C2×C8C22×D3111yescharacteristic
119C42—311no—
120C16—21no—
121C16—621no—
122C23—41no—
123C23—1241no—
124Q8—21no—
125D4—21no—
126D4—41no—
127D4—41no—
128D4—41no—
129D4—1241no—
130D4—1241no—
131D4—2484no—
132C2×C4—41no—
133C2×C4—621no—
134C2×C4D4×D3111yescharacteristic
135C8—311no—
136C8—311no—
137C8—1241no—
138C8#9249711yescharacteristic
139C8C2×C22⋊D3111yescharacteristic
140C22—41no—
141C22—82no—
142C22—81no—
143C22—2482no—
144C22—2481no—
145C22#1175848811yescharacteristic
146C4—41no—
147C4—622no—
148C4D8×D3111yescharacteristic
149C4#1175851611yescharacteristic
150C2—21no—
151C2—81no—
152C2—161no—
153C2—4961no—
154C2#1452124211yescharacteristic
subgroupG/H
centerC2#14521242
commutator, cosocleC2×C8×C31C23
FrattiniC2×C8C22×D31
FittingC31×#509C2
socleC2×C31#459
hypercenter#509D31
hypocenterC31#2213
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. #14521484C2semidirect
2. #14521424C2semidirect
3. #14521166C2semidirect
4. #14520869C2semidirect
5. #14520863C2semidirect
6. #14520862C2semidirect
7. C31×#509C2semidirect
27. Q16×C31D4semidirect
31. D8×C31D4semidirect
74. #509D31semidirect
100. C31#2213semidirect
105. Q16C22⋊D31semidirect
113. D8C22⋊D31semidirect

Maximal subgroups

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

subgroupindex
#145214842
#145214242
#145211662
#145208692
#145208632
#145208622
C31×#5092
#221331