Finite Group Databasebeta

← C2×C127×#1356 #44575583

Subgroups — C2×C127×#1356 #44575583

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×#491×C127C211yesmaximal, characteristic
2C2×#347×C127C212yesmaximal
3C127×#1356C214yesmaximal, direct product factor
4C2×C4⋊Q8×C127C411yescharacteristic
5C2×#125×C127C411yescharacteristic
6C2×M32×C127—22no—
7#491×C127—22no—
8#491×C127C412yes—
9#491×C127C2212yes—
10C2×#103×C127—22no—
11C2×#97×C127C2211yescharacteristic
12#347×C127—22no—
13#347×C127C2214yes—
14C22×Q8×C127—21no—
15C22×C8×C127D412yes—
16C4⋊Q8×C127—21no—
17C4⋊Q8×C127—41no—
18C4⋊Q8×C127C2×C412yes—
19#125×C127—21no—
20#125×C127—41no—
21#125×C127C2×C412yes—
22C2×C4⋊C4×C127—21no—
23C2×C4⋊C4×C127—41no—
24C2×C4⋊C4×C127—41no—
25C2×C42×C127C2×C411yescharacteristic
26M32×C127—24no—
27M32×C127—24no—
28C2×C16×C127—24no—
29#103×C127—24no—
30#103×C127—24no—
31#97×C127C2×C411yescharacteristic
32#97×C127D412yes—
33#97×C127C2311yescharacteristic
34C2×Q8×C127—22no—
35C2×Q8×C127—41no—
36C2×Q8×C127—42no—
37C2×Q8×C127—42no—
38C22×C4×C127—21no—
39C22×C4×C127—41no—
40C22×C4×C127—41no—
41C22×C4×C127C22⋊C411yescharacteristic
42C2×C8×C127—22no—
43C2×C8×C127—22no—
44C2×C8×C127C22⋊C412yes—
45C2×C8×C127C2×D412yes—
46C4⋊C4×C127—22no—
47C4⋊C4×C127—42no—
48C4⋊C4×C127—42no—
49C4⋊C4×C127—42no—
50C4⋊C4×C127—42no—
51C4⋊C4×C127—41no—
52C42×C127—21no—
53C42×C127C22⋊C411yescharacteristic
54C42×C127C22×C411yescharacteristic
55C16×C127—28no—
56C23×C127#10011yescharacteristic
57Q8×C127—44no—
58Q8×C127—82no—
59C2×C4×C127—21no—
60C2×C4×C127—21no—
61C2×C4×C127—42no—
62C2×C4×C127—42no—
63C2×C4×C127—42no—
64C2×C4×C127—82no—
65C2×C4×C127—81no—
66C2×C4×C127—81no—
67C2×C4×C127#10011yescharacteristic
68C2×C4×C127#10412yes—
69C2×C4×C127#10412yes—
70C2×C4×C127C2×C22⋊C411yescharacteristic
71C8×C127—22no—
72C8×C127—22no—
73C22×C127—22no—
74C22×C127#32911yescharacteristic
75C22×C127#32911yescharacteristic
76C22×C127C2×#10011yescharacteristic
77C4×C127—41no—
78C4×C127—41no—
79C4×C127—82no—
80C4×C127—82no—
81C4×C127#32912yes—
82C4×C127C2×#10412yes—
83C2×#1356C12711yesmaximal, characteristic, direct product factor, Sylow
84C2×C127—21no—
85C2×C127—21no—
86C2×C127#135612yesdirect product factor
87C2×C127C2×#32911yescharacteristic
88C2×#491C2×C12711yescharacteristic
89C2×#347C2×C12712yes—
90#1356C2×C12714yesdirect product factor
91C127C2×#135611yescharacteristic, direct product factor, Sylow
92C2×C4⋊Q8C4×C12711yescharacteristic
93C2×#125C4×C12711yescharacteristic
94C2×M32—22no—
95#491—22no—
96#491C4×C12712yes—
97#491C22×C12712yes—
98C2×#103—22no—
99C2×#97C22×C12711yescharacteristic
100#347—22no—
101#347C22×C12714yes—
102C22×Q8—21no—
103C22×C8D4×C12712yes—
104C4⋊Q8—21no—
105C4⋊Q8—41no—
106C4⋊Q8C2×C4×C12712yes—
107#125—21no—
108#125—41no—
109#125C2×C4×C12712yes—
110C2×C4⋊C4—21no—
111C2×C4⋊C4—41no—
112C2×C4⋊C4—41no—
113C2×C42C2×C4×C12711yescharacteristic
114M32—24no—
115M32—24no—
116C2×C16—24no—
117#103—24no—
118#103—24no—
119#97C2×C4×C12711yescharacteristic
120#97D4×C12712yes—
121#97C23×C12711yescharacteristic
122C2×Q8—22no—
123C2×Q8—41no—
124C2×Q8—42no—
125C2×Q8—42no—
126C22×C4—21no—
127C22×C4—41no—
128C22×C4—41no—
129C22×C4C22⋊C4×C12711yescharacteristic
130C2×C8—22no—
131C2×C8—22no—
132C2×C8C22⋊C4×C12712yes—
133C2×C8C2×D4×C12712yes—
134C4⋊C4—22no—
135C4⋊C4—42no—
136C4⋊C4—42no—
137C4⋊C4—42no—
138C4⋊C4—42no—
139C4⋊C4—41no—
140C42—21no—
141C42C22⋊C4×C12711yescharacteristic
142C42C22×C4×C12711yescharacteristic
143C16—28no—
144C23#100×C12711yescharacteristic
145Q8—44no—
146Q8—82no—
147C2×C4—21no—
148C2×C4—21no—
149C2×C4—42no—
150C2×C4—42no—
151C2×C4—42no—
152C2×C4—82no—
153C2×C4—81no—
154C2×C4—81no—
155C2×C4#100×C12711yescharacteristic
156C2×C4#104×C12712yes—
157C2×C4#104×C12712yes—
158C2×C4C2×C22⋊C4×C12711yescharacteristic
159C8—22no—
160C8—22no—
161C22—22no—
162C22#329×C12711yescharacteristic
163C22#329×C12711yescharacteristic
164C22C2×#100×C12711yescharacteristic
165C4—41no—
166C4—41no—
167C4—82no—
168C4—82no—
169C4#329×C12712yes—
170C4C2×#104×C12712yes—
171C2—21no—
172C2—21no—
173C2C127×#135612yesdirect product factor
174C2C2×#329×C12711yescharacteristic
subgroupG/H
center, socleC22×C127#329
commutatorC42C22×C4×C127
Frattini, cosocle#97C23×C127
prime radicalC23×C127#100
LCSG ▷ C42 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C22×C4×C127 ◁ C2×#97×C127 ◁ G

Complements

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

NH ≅ G/Ntype
3. C127×#1356C2direct (N × H)
83. C2×#1356C127direct (N × H)
86. C2×C127#1356direct (N × H)
90. #1356C2×C127direct (N × H)
91. C127C2×#1356direct (N × H)
173. C2C127×#1356direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#491×C1272
C2×#347×C1272
C127×#13562
C2×#1356127