Finite Group Databasebeta

← #30640796

Subgroups — #30640796

Order 16256.

154 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 154 conjugacy classes of subgroups — too many to draw. Only its 47 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#22550317C211yesmaximal, characteristic, complemented
2#22550312C211yesmaximal, characteristic
3#22549994C211yesmaximal, characteristic, complemented
4#22549697C211yesmaximal, characteristic, complemented
5#22549692C211yesmaximal, characteristic, complemented
6#22549689C211yesmaximal, characteristic, complemented
7#495×C127C211yesmaximal, characteristic, complemented
8#16861231C2211yescharacteristic
9#16861215—21no—
10#16861155—21no—
11#16861153—21no—
12#16861152—21no—
13#16861150—21no—
14#16861149C2211yescharacteristic
15#16861149C2211yescharacteristic
16#16861145C2211yescharacteristic
17#16861137—21no—
18C2×Q16×C127C2211yescharacteristic
19C2×SD16×C127—21no—
20C2×D8×C127C2211yescharacteristic
21#124×C127—21no—
22C4×C8×C127C2211yescharacteristic
23#14523248—21no—
24Dic508D411yescharacteristic
25#14523237—21no—
26D1016D411yescharacteristic
27#14523232—21no—
28#14523231—41no—
29C8×D127—41no—
30C127⋊C16—21no—
31C127⋊C16—21no—
32C2×Q8×C127—21no—
33C2×D4×C127—21no—
34Q16×C127—21no—
35Q16×C127—21no—
36SD16×C127—41no—
37SD16×C127—41no—
38D8×C127—21no—
39D8×C127—21no—
40C2×C8×C127D411yescharacteristic
41C2×C8×C127C2311yescharacteristic
42C22⋊C4×C127—42no—
43C42×C127D411yescharacteristic
44Dic254—21no—
45D508—21no—
46C22⋊D127—41no—
47C4×D127—41no—
48C127⋊C8—41no—
49C23×C127—41no—
50Q8×C127—41no—
51Q8×C127—41no—
52D4×C127—41no—
53D4×C127—41no—
54C2×C4×C127—21no—
55C2×C4×C127—41no—
56C2×C4×C127C2×D411yescharacteristic
57C8×C127D811yescharacteristic
58C8×C127D811yescharacteristic
59C8×C127C2×D411yescharacteristic
60C8×C127#4111yescharacteristic
61C22×C127—82no—
62C22×C127—81no—
63C22×C127AGL(1,ℤ/8)11yescharacteristic
64C2×D127—41no—
65C4×C127—41no—
66C4×C127—81no—
67C4×C127#12111yescharacteristic
68C4×C127C2×D811yescharacteristic
69Dic127—41no—
70C2×C127—21no—
71C2×C127—161no—
72C2×C127#45911yescharacteristic
73D127—81no—
74#2212—1271nomaximal, Sylow
75C127#221211yescharacteristic, complemented, Sylow
76#510—1271no—
77#509—1271no—
78#495D12711yescharacteristic, complemented
79#443—1271no—
80#364—1271no—
81#362—1271no—
82#361—1271no—
83#135—1271no—
84C2×Q16C2×D12711yescharacteristic
85C2×SD16—21no—
86C2×D8C2×D12711yescharacteristic
87#131—2541no—
88#124—21no—
89Q32—2541no—
90SD32—2541no—
91SD32—2541no—
92D16—2541no—
93M32—1271no—
94M32—1271no—
95#108—1271no—
96#104—2541no—
97C4×C8C2×D12711yescharacteristic
98#41—2541no—
99C2×Q8—21no—
100C2×D4—21no—
101Q16—21no—
102Q16—21no—
103Q16—1271no—
104SD16—41no—
105SD16—41no—
106SD16—2541no—
107D8—21no—
108D8—21no—
109D8—1271no—
110M16—5081no—
111M16—2541no—
112C2×C8—5081no—
113C2×C8C22⋊D12711yescharacteristic
114C2×C8C22×D12711yescharacteristic
115C22⋊C4—42no—
116C42C22⋊D12711yescharacteristic
117C16—2541no—
118C16—2541no—
119C23—41no—
120Q8—41no—
121Q8—41no—
122Q8—2541no—
123D4—41no—
124D4—41no—
125D4—5081no—
126D4—2541no—
127C2×C4—21no—
128C2×C4—41no—
129C2×C4—5081no—
130C2×C4C2×C22⋊D12711yescharacteristic
131C8—5081no—
132C8#1452323311yescharacteristic
133C8#1452323311yescharacteristic
134C8D4×D12711yescharacteristic
135C8#1452324711yescharacteristic
136C22—82no—
137C22—81no—
138C22—5081no—
139C22#1686123511yescharacteristic
140C4—41no—
141C4—81no—
142C4—5081no—
143C4#1686118011yescharacteristic
144C4C2×#1452323311yescharacteristic
145C2—21no—
146C2—161no—
147C2—10161no—
148C2#2255006811yescharacteristic
subgroupG/H
centerC2#22550068
commutator, cosocleC2×C8×C127C23
FrattiniC2×C8C22×D127
Fitting#495×C127C2
socleC2×C127#459
prime radical#22550312C2
hypercenter#495D127
hypocenterC127#2212
LCSG ▷ C2×C8×C127 ▷ C4×C127 ▷ C2×C127 ▷ C127
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #495

Complements

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

NH ≅ G/Ntype
1. #22550317C2semidirect
3. #22549994C2semidirect
4. #22549697C2semidirect
5. #22549692C2semidirect
6. #22549689C2semidirect
7. #495×C127C2semidirect
75. C127#2212semidirect
78. #495D127semidirect

Maximal subgroups

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

subgroupindex
#225503172
#225503122
#225499942
#225496972
#225496922
#225496892
#495×C1272
#2212127