Finite Group Databasebeta

← C127×#7128 #44570801

Subgroups — C127×#7128 #44570801

Order 32512.

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

normal subgroups only

This group has 236 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×#1984C211yesmaximal, characteristic
2C127×#1374C212yesmaximal
3C2×C4×Q8×C127C411yescharacteristic
4C22×C16×C127—22no—
5C2×C4⋊C8×C127C411yescharacteristic
6C2×C4×C8×C127C2211yescharacteristic
7#336×C127—22no—
8C22×Q8×C127C811yescharacteristic
9C22×C8×C127—21no—
10C22×C8×C127D412yes—
11C4×Q8×C127—41no—
12C4×Q8×C127—41no—
13C2×C4⋊C4×C127—21no—
14C2×C4⋊C4×C127C811yescharacteristic
15C2×C42×C127—21no—
16C2×C42×C127C2×C411yescharacteristic
17C2×C16×C127—24no—
18C2×C16×C127—42no—
19C2×C16×C127—42no—
20C4⋊C8×C127—41no—
21C4×C8×C127—41no—
22C2×Q8×C127—21no—
23C2×Q8×C127—41no—
24C2×Q8×C127—41no—
25C2×Q8×C127C1612yescomplemented
26C22×C4×C127—21no—
27C22×C4×C127—21no—
28C22×C4×C127C22⋊C411yescharacteristic
29C22×C4×C127C2×C811yescharacteristic
30C22×C4×C127M1611yescharacteristic
31C2×C8×C127—22no—
32C2×C8×C127—22no—
33C2×C8×C127—41no—
34C2×C8×C127—42no—
35C2×C8×C127SD1612yes—
36C2×C8×C127Q1612yes—
37C4⋊C4×C127—41no—
38C4⋊C4×C127—42no—
39C42×C127—21no—
40C42×C127—21no—
41C42×C127—41no—
42C42×C127—41no—
43C16×C127—44no—
44C23×C127C22⋊C811yescharacteristic
45Q8×C127—42no—
46Q8×C127—42no—
47C2×C4×C127—21no—
48C2×C4×C127—21no—
49C2×C4×C127—21no—
50C2×C4×C127—22no—
51C2×C4×C127—22no—
52C2×C4×C127—41no—
53C2×C4×C127—41no—
54C2×C4×C127—41no—
55C2×C4×C127—42no—
56C2×C4×C127#9911yescharacteristic
57C2×C4×C127#10011yescharacteristic
58C2×C4×C127#10312yes—
59C2×C4×C127#10412yes—
60C2×C4×C127C2×C1611yescharacteristic
61C2×C4×C127M3211yescharacteristic
62C8×C127—22no—
63C8×C127—22no—
64C8×C127—81no—
65C22×C127#32311yescharacteristic
66C22×C127Q8⋊C812yes—
67C22×C127C22⋊C1611yescharacteristic
68C22×C127#34911yescharacteristic
69C22×C127#35012yes—
70C4×C127—21no—
71C4×C127—21no—
72C4×C127—42no—
73C4×C127—41no—
74C4×C127—81no—
75C4×C127#32812yes—
76C4×C127#32911yescharacteristic
77C4×C127#33311yescharacteristic
78#7128C12711yesmaximal, characteristic, direct product factor, Sylow
79C2×C127#127211yescharacteristic
80C2×C127#131411yescharacteristic
81C2×C127#131511yescharacteristic
82C2×C127Q8⋊C1612yes—
83C2×C127#133812yes—
84#1984C2×C12711yescharacteristic
85#1374C2×C12712yes—
86C127#712811yescharacteristic, direct product factor, Sylow
87C2×C4×Q8C4×C12711yescharacteristic
88C22×C16—22no—
89C2×C4⋊C8C4×C12711yescharacteristic
90C2×C4×C8C22×C12711yescharacteristic
91#336—22no—
92C22×Q8C8×C12711yescharacteristic
93C22×C8—21no—
94C22×C8D4×C12712yes—
95C4×Q8—41no—
96C4×Q8—41no—
97C2×C4⋊C4—21no—
98C2×C4⋊C4C8×C12711yescharacteristic
99C2×C42—21no—
100C2×C42C2×C4×C12711yescharacteristic
101C2×C16—24no—
102C2×C16—42no—
103C2×C16—42no—
104C4⋊C8—41no—
105C4×C8—41no—
106C2×Q8—21no—
107C2×Q8—41no—
108C2×Q8—41no—
109C2×Q8C16×C12712yescomplemented
110C22×C4—21no—
111C22×C4—21no—
112C22×C4C22⋊C4×C12711yescharacteristic
113C22×C4C2×C8×C12711yescharacteristic
114C22×C4M16×C12711yescharacteristic
115C2×C8—22no—
116C2×C8—22no—
117C2×C8—41no—
118C2×C8—42no—
119C2×C8SD16×C12712yes—
120C2×C8Q16×C12712yes—
121C4⋊C4—41no—
122C4⋊C4—42no—
123C42—21no—
124C42—21no—
125C42—41no—
126C42—41no—
127C16—44no—
128C23C22⋊C8×C12711yescharacteristic
129Q8—42no—
130Q8—42no—
131C2×C4—21no—
132C2×C4—21no—
133C2×C4—21no—
134C2×C4—22no—
135C2×C4—22no—
136C2×C4—41no—
137C2×C4—41no—
138C2×C4—41no—
139C2×C4—42no—
140C2×C4#99×C12711yescharacteristic
141C2×C4#100×C12711yescharacteristic
142C2×C4#103×C12712yes—
143C2×C4#104×C12712yes—
144C2×C4C2×C16×C12711yescharacteristic
145C2×C4M32×C12711yescharacteristic
146C8—22no—
147C8—22no—
148C8—81no—
149C22#323×C12711yescharacteristic
150C22Q8⋊C8×C12712yes—
151C22C22⋊C16×C12711yescharacteristic
152C22#349×C12711yescharacteristic
153C22#350×C12712yes—
154C4—21no—
155C4—21no—
156C4—42no—
157C4—41no—
158C4—81no—
159C4#328×C12712yes—
160C4#329×C12711yescharacteristic
161C4#333×C12711yescharacteristic
162C2C127×#127211yescharacteristic
163C2C127×#131411yescharacteristic
164C2C127×#131511yescharacteristic
165C2C127×Q8⋊C1612yes—
166C2C127×#133812yes—
subgroupG/H
centerC22×C4×C127C22⋊C4
commutatorC2×C4C2×C16×C127
Frattini, cosocleC2×C4×C8C22×C127
socle, prime radicalC23×C127C22⋊C8
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C4×C127 ◁ C2×C4×C8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
25. C2×Q8×C127C16semidirect
78. #7128C127direct (N × H)
86. C127#7128direct (N × H)
109. C2×Q8C16×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#19842
C127×#13742
#7128127