Finite Group Databasebeta

← C127×#1824 #30634776

Subgroups — C127×#1824 #30634776

Order 16256.

344 conjugacy classes of subgroups; only the 136 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 136 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
1C22×C4⋊C4×C127C211yesmaximal, characteristic
2C2×C22⋊C8×C127C211yesmaximal, characteristic
3#380×C127C211yesmaximal, characteristic
4#340×C127C214yesmaximal, complemented
5C23×C4×C127—21no—
6C23×C4×C127C2211yescharacteristic
7C22×C8×C127C2212yes—
8C2×C4⋊C4×C127—21no—
9C2×C4⋊C4×C127—22no—
10C2×C4⋊C4×C127C414yescomplemented
11C2×C4⋊C4×C127C2212yes—
12C2×C4⋊C4×C127C2212yes—
13C2×C22⋊C4×C127—21no—
14C22⋊C8×C127—22no—
15#95×C127—21no—
16C24×C127D411yescharacteristic
17C22×C4×C127—24no—
18C22×C4×C127—24no—
19C22×C4×C127—22no—
20C22×C4×C127—22no—
21C22×C4×C127—44no—
22C22×C4×C127C2×C412yes—
23C22×C4×C127D411yescharacteristic
24C22×C4×C127D412yes—
25C22×C4×C127C2311yescharacteristic
26C2×C8×C127—22no—
27C2×C8×C127—24no—
28C4⋊C4×C127—24no—
29C4⋊C4×C127—22no—
30C4⋊C4×C127—24no—
31C4⋊C4×C127C2×C414yes—
32C22⋊C4×C127—42no—
33C23×C127—22no—
34C23×C127—22no—
35C23×C127C22⋊C412yes—
36C23×C127SD1612yes—
37C23×C127Q1612yes—
38C23×C127C2×D411yescharacteristic
39C2×C4×C127—22no—
40C2×C4×C127—24no—
41C2×C4×C127—24no—
42C2×C4×C127—24no—
43C2×C4×C127—48no—
44C2×C4×C127—44no—
45C2×C4×C127—42no—
46C2×C4×C127—42no—
47C2×C4×C127—42no—
48C2×C4×C127C22⋊C412yes—
49C2×C4×C127C22×C411yescharacteristic
50C2×C4×C127C2×D411yescharacteristic
51C2×C4×C127#4114yes—
52C8×C127—42no—
53C22×C127—22no—
54C22×C127—22no—
55C22×C127—24no—
56C22×C127—24no—
57C22×C127#10314yes—
58C22×C127C2×C22⋊C411yescharacteristic
59C22×C127#12312yes—
60C22×C127C2×SD1611yescharacteristic
61C22×C127C2×Q1611yescharacteristic
62C22×C127AGL(1,ℤ/8)12yes—
63C4×C127—22no—
64C4×C127—44no—
65C4×C127—82no—
66C4×C127#11712yes—
67C4×C127#12312yes—
68C2×C127—24no—
69C2×C127#38111yescharacteristic
70C2×C127C2×#10311yescharacteristic
71C2×C127#41811yescharacteristic
72C2×C127#48112yes—
73C2×C127#48412yes—
74#1824C12711yesmaximal, characteristic, direct product factor, Sylow
75C127#182411yescharacteristic, direct product factor, Sylow
76C22×C4⋊C4C2×C12711yescharacteristic
77C2×C22⋊C8C2×C12711yescharacteristic
78#380C2×C12711yescharacteristic
79#340C2×C12714yescomplemented
80C23×C4—21no—
81C23×C4C22×C12711yescharacteristic
82C22×C8C22×C12712yes—
83C2×C4⋊C4—21no—
84C2×C4⋊C4—22no—
85C2×C4⋊C4C4×C12714yescomplemented
86C2×C4⋊C4C22×C12712yes—
87C2×C4⋊C4C22×C12712yes—
88C2×C22⋊C4—21no—
89C22⋊C8—22no—
90#95—21no—
91C24D4×C12711yescharacteristic
92C22×C4—24no—
93C22×C4—24no—
94C22×C4—22no—
95C22×C4—22no—
96C22×C4—44no—
97C22×C4C2×C4×C12712yes—
98C22×C4D4×C12711yescharacteristic
99C22×C4D4×C12712yes—
100C22×C4C23×C12711yescharacteristic
101C2×C8—22no—
102C2×C8—24no—
103C4⋊C4—24no—
104C4⋊C4—22no—
105C4⋊C4—24no—
106C4⋊C4C2×C4×C12714yes—
107C22⋊C4—42no—
108C23—22no—
109C23—22no—
110C23C22⋊C4×C12712yes—
111C23SD16×C12712yes—
112C23Q16×C12712yes—
113C23C2×D4×C12711yescharacteristic
114C2×C4—22no—
115C2×C4—24no—
116C2×C4—24no—
117C2×C4—24no—
118C2×C4—48no—
119C2×C4—44no—
120C2×C4—42no—
121C2×C4—42no—
122C2×C4—42no—
123C2×C4C22⋊C4×C12712yes—
124C2×C4C22×C4×C12711yescharacteristic
125C2×C4C2×D4×C12711yescharacteristic
126C2×C4#41×C12714yes—
127C8—42no—
128C22—22no—
129C22—22no—
130C22—24no—
131C22—24no—
132C22#103×C12714yes—
133C22C2×C22⋊C4×C12711yescharacteristic
134C22#123×C12712yes—
135C22C2×SD16×C12711yescharacteristic
136C22C2×Q16×C12711yescharacteristic
137C22AGL(1,ℤ/8)×C12712yes—
138C4—22no—
139C4—44no—
140C4—82no—
141C4#117×C12712yes—
142C4#123×C12712yes—
143C2—24no—
144C2#381×C12711yescharacteristic
145C2C2×#103×C12711yescharacteristic
146C2#418×C12711yescharacteristic
147C2#481×C12712yes—
148C2#484×C12712yes—
subgroupG/H
center, socleC23×C127C2×D4
commutatorC2×C4C22×C4×C127
Frattini, cosocleC22×C4C23×C127
prime radicalC24×C127D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C127 ◁ C23×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
4. #340×C127C2semidirect
10. C2×C4⋊C4×C127C4semidirect
74. #1824C127direct (N × H)
75. C127#1824direct (N × H)
79. #340C2×C127semidirect
85. C2×C4⋊C4C4×C127semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊C4×C1272
C2×C22⋊C8×C1272
#380×C1272
#340×C1272
#1824127