Finite Group Databasebeta

← C127×#11994 #44575667

Subgroups — C127×#11994 #44575667

Order 32512.

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

normal subgroups only

This group has 258 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×#3166C211yesmaximal, characteristic
2C127×#2165C212yesmaximal
3C127×#1366C214yesmaximal, complemented
4#533×C127C411yescharacteristic
5C2×#125×C127C411yescharacteristic
6#501×C127—22no—
7#499×C127C412yes—
8#499×C127C2212yes—
9#428×C127—22no—
10C4×M16×C127C2211yescharacteristic
11#364×C127C2214yes—
12#349×C127—22no—
13#347×C127—22no—
14C2×M16×C127D412yes—
15C4⋊Q8×C127—21no—
16#125×C127—21no—
17#125×C127—41no—
18#125×C127C2×C412yes—
19#125×C127C2×C412yes—
20C22⋊Q8×C127—41no—
21C4×Q8×C127—41no—
22#117×C127—21no—
23C2×C4⋊C4×C127—21no—
24C2×C4⋊C4×C127—41no—
25C2×C42×C127C2×C411yescharacteristic
26M32×C127—24no—
27#107×C127—22no—
28#107×C127—22no—
29#106×C127—22no—
30#106×C127—22no—
31#97×C127D412yes—
32C4×C8×C127C2×C411yescharacteristic
33C4×C8×C127C2311yescharacteristic
34C2×Q8×C127—41no—
35C22×C4×C127—21no—
36C22×C4×C127—41no—
37C22×C4×C127C22⋊C411yescharacteristic
38M16×C127—24no—
39C2×C8×C127C22⋊C412yes—
40C2×C8×C127C2×D412yes—
41C4⋊C4×C127—22no—
42C4⋊C4×C127—22no—
43C4⋊C4×C127—42no—
44C4⋊C4×C127—42no—
45C4⋊C4×C127—42no—
46C4⋊C4×C127—41no—
47C4⋊C4×C127—41no—
48C22⋊C4×C127—41no—
49C42×C127—21no—
50C42×C127—41no—
51C42×C127C22⋊C411yescharacteristic
52C42×C127C22×C411yescharacteristic
53C16×C127—44no—
54C23×C127#10011yescharacteristic
55Q8×C127—82no—
56C2×C4×C127—22no—
57C2×C4×C127—21no—
58C2×C4×C127—21no—
59C2×C4×C127—42no—
60C2×C4×C127—42no—
61C2×C4×C127—81no—
62C2×C4×C127—82no—
63C2×C4×C127#10011yescharacteristic
64C2×C4×C127C2×C22⋊C411yescharacteristic
65C8×C127—22no—
66C8×C127#13714yes—
67C22×C127—21no—
68C22×C127—41no—
69C22×C127C2×#10011yescharacteristic
70C4×C127—21no—
71C4×C127—41no—
72C4×C127—41no—
73C4×C127—82no—
74C4×C127—82no—
75C4×C127#41912yes—
76#11994C12711yesmaximal, characteristic, direct product factor, Sylow
77C2×C127—21no—
78C2×C127—41no—
79C2×C127#155811yescharacteristic
80#3166C2×C12711yescharacteristic
81#2165C2×C12712yes—
82#1366C2×C12714yescomplemented
83C127#1199411yescharacteristic, direct product factor, Sylow
84#533C4×C12711yescharacteristic
85C2×#125C4×C12711yescharacteristic
86#501—22no—
87#499C4×C12712yes—
88#499C22×C12712yes—
89#428—22no—
90C4×M16C22×C12711yescharacteristic
91#364C22×C12714yes—
92#349—22no—
93#347—22no—
94C2×M16D4×C12712yes—
95C4⋊Q8—21no—
96#125—21no—
97#125—41no—
98#125C2×C4×C12712yes—
99#125C2×C4×C12712yes—
100C22⋊Q8—41no—
101C4×Q8—41no—
102#117—21no—
103C2×C4⋊C4—21no—
104C2×C4⋊C4—41no—
105C2×C42C2×C4×C12711yescharacteristic
106M32—24no—
107#107—22no—
108#107—22no—
109#106—22no—
110#106—22no—
111#97D4×C12712yes—
112C4×C8C2×C4×C12711yescharacteristic
113C4×C8C23×C12711yescharacteristic
114C2×Q8—41no—
115C22×C4—21no—
116C22×C4—41no—
117C22×C4C22⋊C4×C12711yescharacteristic
118M16—24no—
119C2×C8C22⋊C4×C12712yes—
120C2×C8C2×D4×C12712yes—
121C4⋊C4—22no—
122C4⋊C4—22no—
123C4⋊C4—42no—
124C4⋊C4—42no—
125C4⋊C4—42no—
126C4⋊C4—41no—
127C4⋊C4—41no—
128C22⋊C4—41no—
129C42—21no—
130C42—41no—
131C42C22⋊C4×C12711yescharacteristic
132C42C22×C4×C12711yescharacteristic
133C16—44no—
134C23#100×C12711yescharacteristic
135Q8—82no—
136C2×C4—22no—
137C2×C4—21no—
138C2×C4—21no—
139C2×C4—42no—
140C2×C4—42no—
141C2×C4—81no—
142C2×C4—82no—
143C2×C4#100×C12711yescharacteristic
144C2×C4C2×C22⋊C4×C12711yescharacteristic
145C8—22no—
146C8#137×C12714yes—
147C22—21no—
148C22—41no—
149C22C2×#100×C12711yescharacteristic
150C4—21no—
151C4—41no—
152C4—41no—
153C4—82no—
154C4—82no—
155C4#419×C12712yes—
156C2—21no—
157C2—41no—
158C2C127×#155811yescharacteristic
subgroupG/H
center, socleC2×C127#1558
commutatorC42C22×C4×C127
Frattini, cosocleC4×C8C23×C127
prime radicalC23×C127#100
LCSG ▷ C42 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C127 ◁ C2×C4×C127 ◁ C4×M16×C127 ◁ G

Complements

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

NH ≅ G/Ntype
3. C127×#1366C2semidirect
76. #11994C127direct (N × H)
82. #1366C2×C127semidirect
83. C127#11994direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#31662
C127×#21652
C127×#13662
#11994127