Finite Group Databasebeta

← C127×#7046 #44570719

Subgroups — C127×#7046 #44570719

Order 32512.

364 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 98 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
1C127×#1817C211yesmaximal, characteristic
2C127×#1749C212yesmaximal
3C22×C42×C127C2211yescharacteristic
4C2×C22⋊C8×C127—22no—
5C2×C22⋊C8×C127C412yes—
6C2×#97×C127—22no—
7#336×C127—22no—
8#336×C127C414yes—
9C23×C4×C127C2×C411yescharacteristic
10C23×C4×C127D411yescharacteristic
11C23×C4×C127Q811yescharacteristic
12C22×C8×C127—24no—
13C22×C8×C127—22no—
14C2×C42×C127—42no—
15C2×C42×C127C2×C412yes—
16C2×C42×C127D412yes—
17C22⋊C8×C127—28no—
18C22⋊C8×C127—42no—
19#97×C127—44no—
20C24×C127C4⋊C411yescharacteristic
21C22×C4×C127—22no—
22C22×C4×C127—22no—
23C22×C4×C127—24no—
24C22×C4×C127—41no—
25C22×C4×C127—41no—
26C22×C4×C127—42no—
27C22×C4×C127—41no—
28C22×C4×C127C4211yescharacteristic
29C22×C4×C127C22⋊C411yescharacteristic
30C22×C4×C127C22⋊C412yes—
31C22×C4×C127C4⋊C412yes—
32C2×C8×C127—28no—
33C2×C8×C127—44no—
34C2×C8×C127—44no—
35C2×C8×C127—44no—
36C2×C8×C127—42no—
37C42×C127—24no—
38C42×C127—42no—
39C23×C127—21no—
40C23×C127—22no—
41C23×C127—21no—
42C23×C127—22no—
43C23×C127#9511yescharacteristic
44C23×C127#10812yes—
45C2×C4×C127—22no—
46C2×C4×C127—22no—
47C2×C4×C127—22no—
48C2×C4×C127—22no—
49C2×C4×C127—22no—
50C2×C4×C127—22no—
51C2×C4×C127—21no—
52C2×C4×C127—22no—
53C2×C4×C127—44no—
54C2×C4×C127—44no—
55C2×C4×C127—44no—
56C2×C4×C127#9912yes—
57C2×C4×C127#10414yes—
58C8×C127—48no—
59C8×C127—82no—
60C22×C127—22no—
61C22×C127—24no—
62C22×C127—42no—
63C22×C127—41no—
64C22×C127—41no—
65C22×C127#33811yescharacteristic
66C22×C127#33912yes—
67C22×C127#34111yescharacteristic
68C22×C127#34211yescharacteristic
69C22×C127#34412yes—
70C4×C127—24no—
71C4×C127—22no—
72C4×C127—42no—
73C4×C127—41no—
74#7046C12711yesmaximal, characteristic, direct product factor, Sylow
75C2×C127—42no—
76C2×C127#129112yes—
77C2×C127#129311yescharacteristic
78C2×C127#129711yescharacteristic
79C2×C127#130212yes—
80C2×C127#130611yescharacteristic
81#1817C2×C12711yescharacteristic
82#1749C2×C12712yes—
83C127#704611yescharacteristic, direct product factor, Sylow
84C22×C42C22×C12711yescharacteristic
85C2×C22⋊C8—22no—
86C2×C22⋊C8C4×C12712yes—
87C2×#97—22no—
88#336—22no—
89#336C4×C12714yes—
90C23×C4C2×C4×C12711yescharacteristic
91C23×C4D4×C12711yescharacteristic
92C23×C4Q8×C12711yescharacteristic
93C22×C8—24no—
94C22×C8—22no—
95C2×C42—42no—
96C2×C42C2×C4×C12712yes—
97C2×C42D4×C12712yes—
98C22⋊C8—28no—
99C22⋊C8—42no—
100#97—44no—
101C24C4⋊C4×C12711yescharacteristic
102C22×C4—22no—
103C22×C4—22no—
104C22×C4—24no—
105C22×C4—41no—
106C22×C4—41no—
107C22×C4—42no—
108C22×C4—41no—
109C22×C4C42×C12711yescharacteristic
110C22×C4C22⋊C4×C12711yescharacteristic
111C22×C4C22⋊C4×C12712yes—
112C22×C4C4⋊C4×C12712yes—
113C2×C8—28no—
114C2×C8—44no—
115C2×C8—44no—
116C2×C8—44no—
117C2×C8—42no—
118C42—24no—
119C42—42no—
120C23—21no—
121C23—22no—
122C23—21no—
123C23—22no—
124C23#95×C12711yescharacteristic
125C23#108×C12712yes—
126C2×C4—22no—
127C2×C4—22no—
128C2×C4—22no—
129C2×C4—22no—
130C2×C4—22no—
131C2×C4—22no—
132C2×C4—21no—
133C2×C4—22no—
134C2×C4—44no—
135C2×C4—44no—
136C2×C4—44no—
137C2×C4#99×C12712yes—
138C2×C4#104×C12714yes—
139C8—48no—
140C8—82no—
141C22—22no—
142C22—24no—
143C22—42no—
144C22—41no—
145C22—41no—
146C22#338×C12711yescharacteristic
147C22#339×C12712yes—
148C22#341×C12711yescharacteristic
149C22#342×C12711yescharacteristic
150C22#344×C12712yes—
151C4—24no—
152C4—22no—
153C4—42no—
154C4—41no—
155C2—42no—
156C2C127×#129112yes—
157C2C127×#129311yescharacteristic
158C2C127×#129711yescharacteristic
159C2C127×#130212yes—
160C2C127×#130611yescharacteristic
subgroupG/H
center, socleC23×C127#95
commutatorC22×C4C42×C127
Frattini, cosocleC22×C42C22×C127
prime radicalC24×C127C4⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C127 ◁ C22×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
74. #7046C127direct (N × H)
83. C127#7046direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#18172
C127×#17492
#7046127