Finite Group Databasebeta

← C127×#7334 #44571007

Subgroups — C127×#7334 #44571007

Order 32512.

182 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 182 conjugacy classes of subgroups — too many to draw. Only its 66 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×C22⋊C16×C127C211yesmaximal, characteristic
2C127×C22⋊C32C212yesmaximal, complemented
3C23×C8×C127C411yescharacteristic
4C22×C16×C127C411yescharacteristic
5C22×C16×C127C2211yescharacteristic
6C2×C32×C127—22no—
7C22⋊C16×C127—22no—
8C23×C4×C127C811yescharacteristic
9C22×C8×C127—21no—
10C22×C8×C127—21no—
11C22×C8×C127—41no—
12C22×C8×C127—41no—
13C22×C8×C127C811yescharacteristic
14C22×C8×C127C2×C411yescharacteristic
15C2×C16×C127—21no—
16C2×C16×C127—41no—
17C2×C16×C127—41no—
18C2×C16×C127D412yes—
19C32×C127—42no—
20C24×C127C1611yescharacteristic
21C22×C4×C127—21no—
22C22×C4×C127—21no—
23C22×C4×C127—41no—
24C22×C4×C127—41no—
25C22×C4×C127C1611yescharacteristic
26C22×C4×C127C2×C811yescharacteristic
27C2×C8×C127—21no—
28C2×C8×C127—21no—
29C2×C8×C127—21no—
30C2×C8×C127—42no—
31C2×C8×C127—41no—
32C2×C8×C127—41no—
33C2×C8×C127—41no—
34C2×C8×C127C22⋊C411yescharacteristic
35C2×C8×C127M1611yescharacteristic
36C16×C127—22no—
37C16×C127—41no—
38C23×C127—21no—
39C23×C127—21no—
40C23×C127—41no—
41C23×C127—41no—
42C23×C127C3212yescomplemented
43C23×C127C2×C1611yescharacteristic
44C2×C4×C127—21no—
45C2×C4×C127—21no—
46C2×C4×C127—21no—
47C2×C4×C127—42no—
48C2×C4×C127—41no—
49C2×C4×C127—41no—
50C2×C4×C127—41no—
51C2×C4×C127C22⋊C811yescharacteristic
52C2×C4×C127M3211yescharacteristic
53C8×C127—21no—
54C8×C127—41no—
55C8×C127#9911yescharacteristic
56C8×C127#10011yescharacteristic
57C22×C127—21no—
58C22×C127—21no—
59C22×C127—22no—
60C22×C127—42no—
61C22×C127—42no—
62C22×C127—41no—
63C22×C127—41no—
64C22×C127C22⋊C1611yescharacteristic
65C22×C127C2×C3211yescharacteristic
66C22×C127M6411yescharacteristic
67C4×C127—21no—
68C4×C127—41no—
69C4×C127#32311yescharacteristic
70C4×C127#34911yescharacteristic
71#7334C12711yesmaximal, characteristic, direct product factor, Sylow
72C2×C127—21no—
73C2×C127—21no—
74C2×C127—42no—
75C2×C127#131411yescharacteristic
76C2×C127C22⋊C3211yescharacteristic
77C2×C127#140011yescharacteristic
78C2×C22⋊C16C2×C12711yescharacteristic
79C22⋊C32C2×C12712yescomplemented
80C127#733411yescharacteristic, direct product factor, Sylow
81C23×C8C4×C12711yescharacteristic
82C22×C16C4×C12711yescharacteristic
83C22×C16C22×C12711yescharacteristic
84C2×C32—22no—
85C22⋊C16—22no—
86C23×C4C8×C12711yescharacteristic
87C22×C8—21no—
88C22×C8—21no—
89C22×C8—41no—
90C22×C8—41no—
91C22×C8C8×C12711yescharacteristic
92C22×C8C2×C4×C12711yescharacteristic
93C2×C16—21no—
94C2×C16—41no—
95C2×C16—41no—
96C2×C16D4×C12712yes—
97C32—42no—
98C24C16×C12711yescharacteristic
99C22×C4—21no—
100C22×C4—21no—
101C22×C4—41no—
102C22×C4—41no—
103C22×C4C16×C12711yescharacteristic
104C22×C4C2×C8×C12711yescharacteristic
105C2×C8—21no—
106C2×C8—21no—
107C2×C8—21no—
108C2×C8—42no—
109C2×C8—41no—
110C2×C8—41no—
111C2×C8—41no—
112C2×C8C22⋊C4×C12711yescharacteristic
113C2×C8M16×C12711yescharacteristic
114C16—22no—
115C16—41no—
116C23—21no—
117C23—21no—
118C23—41no—
119C23—41no—
120C23C32×C12712yescomplemented
121C23C2×C16×C12711yescharacteristic
122C2×C4—21no—
123C2×C4—21no—
124C2×C4—21no—
125C2×C4—42no—
126C2×C4—41no—
127C2×C4—41no—
128C2×C4—41no—
129C2×C4C22⋊C8×C12711yescharacteristic
130C2×C4M32×C12711yescharacteristic
131C8—21no—
132C8—41no—
133C8#99×C12711yescharacteristic
134C8#100×C12711yescharacteristic
135C22—21no—
136C22—21no—
137C22—22no—
138C22—42no—
139C22—42no—
140C22—41no—
141C22—41no—
142C22C22⋊C16×C12711yescharacteristic
143C22C2×C32×C12711yescharacteristic
144C22M64×C12711yescharacteristic
145C4—21no—
146C4—41no—
147C4#323×C12711yescharacteristic
148C4#349×C12711yescharacteristic
149C2—21no—
150C2—21no—
151C2—42no—
152C2C127×#131411yescharacteristic
153C2C127×C22⋊C3211yescharacteristic
154C2C127×#140011yescharacteristic
subgroupG/H
centerC2×C8×C127C22⋊C4
commutatorC22C2×C32×C127
Frattini, cosocleC22×C16C22×C127
socleC22×C127C22⋊C16
prime radicalC24×C127C16
LCSG ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C8×C127 ◁ C22×C16×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×C22⋊C32C2semidirect
42. C23×C127C32semidirect
71. #7334C127direct (N × H)
79. C22⋊C32C2×C127semidirect
80. C127#7334direct (N × H)
120. C23C32×C127semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊C16×C1272
C127×C22⋊C322
#7334127