Finite Group Databasebeta

← C127×#11916 #44575589

Subgroups — C127×#11916 #44575589

Order 32512.

274 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 90 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×#3139C211yesmaximal, characteristic
2C127×#2165C212yesmaximal
3C127×#1356C214yesmaximal, complemented
4#533×C127C411yescharacteristic
5C2×C4⋊Q8×C127C411yescharacteristic
6#491×C127C412yes—
7#491×C127C2212yes—
8#487×C127—22no—
9#419×C127—22no—
10C4×M16×C127C2211yescharacteristic
11#364×C127—22no—
12#349×C127—22no—
13#347×C127C2214yes—
14C22×Q8×C127—21no—
15C2×M16×C127D412yes—
16C4⋊Q8×C127—21no—
17C4⋊Q8×C127—21no—
18C4⋊Q8×C127—41no—
19C4⋊Q8×C127C2×C412yes—
20#125×C127C2×C412yes—
21C22⋊Q8×C127—41no—
22C4×Q8×C127—41no—
23#117×C127—21no—
24C2×C4⋊C4×C127—41no—
25C2×C42×C127C2×C411yescharacteristic
26M32×C127—24no—
27#103×C127—24no—
28#103×C127—24no—
29#97×C127C2×C411yescharacteristic
30#97×C127C2311yescharacteristic
31C4×C8×C127D412yes—
32C2×Q8×C127—22no—
33C2×Q8×C127—41no—
34C2×Q8×C127—44no—
35C2×Q8×C127—41no—
36C22×C4×C127—21no—
37C22×C4×C127—41no—
38C22×C4×C127C22⋊C411yescharacteristic
39M16×C127—42no—
40C2×C8×C127C22⋊C412yes—
41C2×C8×C127C2×D412yes—
42C4⋊C4×C127—22no—
43C4⋊C4×C127—42no—
44C4⋊C4×C127—42no—
45C4⋊C4×C127—42no—
46C4⋊C4×C127—41no—
47C22⋊C4×C127—41no—
48C42×C127—21no—
49C42×C127—41no—
50C42×C127C22⋊C411yescharacteristic
51C42×C127C22×C411yescharacteristic
52C16×C127—44no—
53C23×C127#10011yescharacteristic
54Q8×C127—44no—
55Q8×C127—82no—
56Q8×C127—82no—
57C2×C4×C127—21no—
58C2×C4×C127—22no—
59C2×C4×C127—21no—
60C2×C4×C127—42no—
61C2×C4×C127—42no—
62C2×C4×C127—42no—
63C2×C4×C127—82no—
64C2×C4×C127#10011yescharacteristic
65C2×C4×C127C2×C22⋊C411yescharacteristic
66C8×C127—22no—
67C8×C127—22no—
68C22×C127—21no—
69C22×C127—41no—
70C22×C127C2×#10011yescharacteristic
71C4×C127—22no—
72C4×C127—21no—
73C4×C127—41no—
74C4×C127—82no—
75C4×C127—82no—
76C4×C127#42112yes—
77#11916C12711yesmaximal, characteristic, direct product factor, Sylow
78C2×C127—21no—
79C2×C127—41no—
80C2×C127#153311yescharacteristic
81#3139C2×C12711yescharacteristic
82#2165C2×C12712yes—
83#1356C2×C12714yescomplemented
84C127#1191611yescharacteristic, direct product factor, Sylow
85#533C4×C12711yescharacteristic
86C2×C4⋊Q8C4×C12711yescharacteristic
87#491C4×C12712yes—
88#491C22×C12712yes—
89#487—22no—
90#419—22no—
91C4×M16C22×C12711yescharacteristic
92#364—22no—
93#349—22no—
94#347C22×C12714yes—
95C22×Q8—21no—
96C2×M16D4×C12712yes—
97C4⋊Q8—21no—
98C4⋊Q8—21no—
99C4⋊Q8—41no—
100C4⋊Q8C2×C4×C12712yes—
101#125C2×C4×C12712yes—
102C22⋊Q8—41no—
103C4×Q8—41no—
104#117—21no—
105C2×C4⋊C4—41no—
106C2×C42C2×C4×C12711yescharacteristic
107M32—24no—
108#103—24no—
109#103—24no—
110#97C2×C4×C12711yescharacteristic
111#97C23×C12711yescharacteristic
112C4×C8D4×C12712yes—
113C2×Q8—22no—
114C2×Q8—41no—
115C2×Q8—44no—
116C2×Q8—41no—
117C22×C4—21no—
118C22×C4—41no—
119C22×C4C22⋊C4×C12711yescharacteristic
120M16—42no—
121C2×C8C22⋊C4×C12712yes—
122C2×C8C2×D4×C12712yes—
123C4⋊C4—22no—
124C4⋊C4—42no—
125C4⋊C4—42no—
126C4⋊C4—42no—
127C4⋊C4—41no—
128C22⋊C4—41no—
129C42—21no—
130C42—41no—
131C42C22⋊C4×C12711yescharacteristic
132C42C22×C4×C12711yescharacteristic
133C16—44no—
134C23#100×C12711yescharacteristic
135Q8—44no—
136Q8—82no—
137Q8—82no—
138C2×C4—21no—
139C2×C4—22no—
140C2×C4—21no—
141C2×C4—42no—
142C2×C4—42no—
143C2×C4—42no—
144C2×C4—82no—
145C2×C4#100×C12711yescharacteristic
146C2×C4C2×C22⋊C4×C12711yescharacteristic
147C8—22no—
148C8—22no—
149C22—21no—
150C22—41no—
151C22C2×#100×C12711yescharacteristic
152C4—22no—
153C4—21no—
154C4—41no—
155C4—82no—
156C4—82no—
157C4#421×C12712yes—
158C2—21no—
159C2—41no—
160C2C127×#153311yescharacteristic
subgroupG/H
center, socleC2×C127#1533
commutatorC42C22×C4×C127
Frattini, cosocle#97C23×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×#1356C2semidirect
77. #11916C127direct (N × H)
83. #1356C2×C127semidirect
84. C127#11916direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#31392
C127×#21652
C127×#13562
#11916127