Finite Group Databasebeta

← C127×#7230 #44570903

Subgroups — C127×#7230 #44570903

Order 32512.

314 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 110 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×#1808C212yesmaximal
3C23×C8×C127C2211yescharacteristic
4C22×C16×C127C412yescomplemented
5C2×#107×C127—22no—
6#380×C127—22no—
7C22⋊C16×C127—22no—
8#340×C127C414yescomplemented
9C23×C4×C127D411yescharacteristic
10C22×C8×C127—42no—
11C22×C8×C127C2×C411yescharacteristic
12C22×C8×C127C2×C412yes—
13C22×C8×C127D412yes—
14C22×C8×C127Q811yescharacteristic
15C2×C4⋊C4×C127—24no—
16C2×C22⋊C4×C127—42no—
17C2×C16×C127—22no—
18C2×C16×C127—42no—
19#107×C127—44no—
20#95×C127—42no—
21C24×C127D811yescharacteristic
22C22×C4×C127—41no—
23C22×C4×C127—41no—
24C22×C4×C127—44no—
25C22×C4×C127C22⋊C412yes—
26C22×C4×C127C4⋊C411yescharacteristic
27C22×C4×C127SD1612yes—
28C22×C4×C127Q1611yescharacteristic
29C2×C8×C127—24no—
30C2×C8×C127—22no—
31C2×C8×C127—42no—
32C2×C8×C127—41no—
33C2×C8×C127C4211yescharacteristic
34C2×C8×C127C22⋊C411yescharacteristic
35C2×C8×C127C4⋊C412yes—
36C4⋊C4×C127—44no—
37C4⋊C4×C127—44no—
38C22⋊C4×C127—82no—
39C22⋊C4×C127—82no—
40C16×C127—42no—
41C23×C127—41no—
42C23×C127—41no—
43C23×C127#10212yes—
44C23×C127#10711yescharacteristic
45C23×C127D1611yescharacteristic
46C23×C127SD3212yes—
47C23×C127Q3211yescharacteristic
48C2×C4×C127—22no—
49C2×C4×C127—21no—
50C2×C4×C127—22no—
51C2×C4×C127—21no—
52C2×C4×C127—42no—
53C2×C4×C127—41no—
54C2×C4×C127—84no—
55C2×C4×C127—84no—
56C2×C4×C127—84no—
57C2×C4×C127#9511yescharacteristic
58C2×C4×C127#10312yes—
59C2×C4×C127#10611yescharacteristic
60C8×C127—21no—
61C8×C127—22no—
62C8×C127#9912yes—
63C22×C127—22no—
64C22×C127—21no—
65C22×C127—22no—
66C22×C127—21no—
67C22×C127—41no—
68C22×C127—42no—
69C22×C127—41no—
70C22×C127#34011yescharacteristic
71C22×C127#35712yes—
72C22×C127#35812yes—
73C22×C127#36611yescharacteristic
74C22×C127#36711yescharacteristic
75C4×C127—22no—
76C4×C127—21no—
77C4×C127—164no—
78C4×C127H(3,ℤ/4)11yescharacteristic
79C4×C127#34211yescharacteristic
80#7230C12711yesmaximal, characteristic, direct product factor, Sylow
81C2×C127—22no—
82C2×C127—22no—
83C2×C127—21no—
84C2×C127—21no—
85C2×C127#128911yescharacteristic
86C2×C127#138011yescharacteristic
87C2×C127#138411yescharacteristic
88C2×C22⋊C16C2×C12711yescharacteristic
89#1808C2×C12712yes—
90C127#723011yescharacteristic, direct product factor, Sylow
91C23×C8C22×C12711yescharacteristic
92C22×C16C4×C12712yescomplemented
93C2×#107—22no—
94#380—22no—
95C22⋊C16—22no—
96#340C4×C12714yescomplemented
97C23×C4D4×C12711yescharacteristic
98C22×C8—42no—
99C22×C8C2×C4×C12711yescharacteristic
100C22×C8C2×C4×C12712yes—
101C22×C8D4×C12712yes—
102C22×C8Q8×C12711yescharacteristic
103C2×C4⋊C4—24no—
104C2×C22⋊C4—42no—
105C2×C16—22no—
106C2×C16—42no—
107#107—44no—
108#95—42no—
109C24D8×C12711yescharacteristic
110C22×C4—41no—
111C22×C4—41no—
112C22×C4—44no—
113C22×C4C22⋊C4×C12712yes—
114C22×C4C4⋊C4×C12711yescharacteristic
115C22×C4SD16×C12712yes—
116C22×C4Q16×C12711yescharacteristic
117C2×C8—24no—
118C2×C8—22no—
119C2×C8—42no—
120C2×C8—41no—
121C2×C8C42×C12711yescharacteristic
122C2×C8C22⋊C4×C12711yescharacteristic
123C2×C8C4⋊C4×C12712yes—
124C4⋊C4—44no—
125C4⋊C4—44no—
126C22⋊C4—82no—
127C22⋊C4—82no—
128C16—42no—
129C23—41no—
130C23—41no—
131C23#102×C12712yes—
132C23#107×C12711yescharacteristic
133C23D16×C12711yescharacteristic
134C23SD32×C12712yes—
135C23Q32×C12711yescharacteristic
136C2×C4—22no—
137C2×C4—21no—
138C2×C4—22no—
139C2×C4—21no—
140C2×C4—42no—
141C2×C4—41no—
142C2×C4—84no—
143C2×C4—84no—
144C2×C4—84no—
145C2×C4#95×C12711yescharacteristic
146C2×C4#103×C12712yes—
147C2×C4#106×C12711yescharacteristic
148C8—21no—
149C8—22no—
150C8#99×C12712yes—
151C22—22no—
152C22—21no—
153C22—22no—
154C22—21no—
155C22—41no—
156C22—42no—
157C22—41no—
158C22#340×C12711yescharacteristic
159C22#357×C12712yes—
160C22#358×C12712yes—
161C22#366×C12711yescharacteristic
162C22#367×C12711yescharacteristic
163C4—22no—
164C4—21no—
165C4—164no—
166C4H(3,ℤ/4)×C12711yescharacteristic
167C4#342×C12711yescharacteristic
168C2—22no—
169C2—22no—
170C2—21no—
171C2—21no—
172C2C127×#128911yescharacteristic
173C2C127×#138011yescharacteristic
174C2C127×#138411yescharacteristic
subgroupG/H
center, socleC22×C127#340
commutatorC2×C8C42×C127
Frattini, cosocleC23×C8C22×C127
prime radicalC24×C127D8
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C23×C4×C127 ◁ C23×C8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
4. C22×C16×C127C4semidirect
8. #340×C127C4semidirect
80. #7230C127direct (N × H)
90. C127#7230direct (N × H)
92. C22×C16C4×C127semidirect
96. #340C4×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×#18082
#7230127