Finite Group Databasebeta

← C2×C127×#1355 #44575582

Subgroups — C2×C127×#1355 #44575582

Order 32512.

366 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 366 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×#490×C127C211yesmaximal, characteristic
2C2×#347×C127C212yesmaximal, complemented
3C127×#1355C214yesmaximal, direct product factor
4C2×#127×C127C411yescharacteristic
5C2×#125×C127C411yescharacteristic
6C2×M32×C127—22no—
7#490×C127—22no—
8#490×C127C412yes—
9#490×C127C2212yes—
10C2×#102×C127—22no—
11C2×#97×C127C2211yescharacteristic
12#347×C127—22no—
13#347×C127C2214yescomplemented
14C22×D4×C127—21no—
15C22×D4×C127—41no—
16C22×C8×C127D412yes—
17#127×C127—21no—
18#127×C127—41no—
19#127×C127C2×C412yes—
20#125×C127—21no—
21#125×C127—41no—
22#125×C127C2×C412yes—
23C2×C4⋊C4×C127—21no—
24C2×C4⋊C4×C127—41no—
25C2×C42×C127C2×C411yescharacteristic
26M32×C127—24no—
27M32×C127—24no—
28C2×C16×C127—24no—
29#102×C127—24no—
30#102×C127—24no—
31#97×C127C2×C411yescharacteristic
32#97×C127D412yes—
33#97×C127C2311yescharacteristic
34C24×C127—41no—
35C2×D4×C127—22no—
36C2×D4×C127—42no—
37C2×D4×C127—42no—
38C2×D4×C127—41no—
39C2×D4×C127—42no—
40C2×D4×C127—42no—
41C2×D4×C127—84no—
42C22×C4×C127—21no—
43C22×C4×C127—41no—
44C22×C4×C127C22⋊C411yescharacteristic
45C2×C8×C127—22no—
46C2×C8×C127—22no—
47C2×C8×C127C22⋊C412yes—
48C2×C8×C127C2×D412yes—
49C4⋊C4×C127—22no—
50C4⋊C4×C127—42no—
51C4⋊C4×C127—42no—
52C4⋊C4×C127—41no—
53C42×C127—21no—
54C42×C127C22⋊C411yescharacteristic
55C42×C127C22×C411yescharacteristic
56C16×C127—28no—
57C23×C127—42no—
58C23×C127—84no—
59C23×C127—81no—
60C23×C127—81no—
61C23×C127#10011yescharacteristic
62D4×C127—44no—
63D4×C127—84no—
64D4×C127—84no—
65D4×C127—82no—
66C2×C4×C127—21no—
67C2×C4×C127—21no—
68C2×C4×C127—42no—
69C2×C4×C127—42no—
70C2×C4×C127—82no—
71C2×C4×C127#10011yescharacteristic
72C2×C4×C127#10412yes—
73C2×C4×C127#10412yes—
74C2×C4×C127C2×C22⋊C411yescharacteristic
75C8×C127—22no—
76C8×C127—22no—
77C22×C127—22no—
78C22×C127—84no—
79C22×C127—82no—
80C22×C127—162no—
81C22×C127—162no—
82C22×C127#32911yescharacteristic
83C22×C127#32911yescharacteristic
84C22×C127C2×#10011yescharacteristic
85C4×C127—41no—
86C4×C127—41no—
87C4×C127—82no—
88C4×C127#32912yes—
89C4×C127C2×#10412yes—
90C2×#1355C12711yesmaximal, characteristic, direct product factor, Sylow
91C2×C127—21no—
92C2×C127—21no—
93C2×C127—162no—
94C2×C127#135512yesdirect product factor
95C2×C127C2×#32911yescharacteristic
96C2×#490C2×C12711yescharacteristic
97C2×#347C2×C12712yescomplemented
98#1355C2×C12714yesdirect product factor
99C127C2×#135511yescharacteristic, direct product factor, Sylow
100C2×#127C4×C12711yescharacteristic
101C2×#125C4×C12711yescharacteristic
102C2×M32—22no—
103#490—22no—
104#490C4×C12712yes—
105#490C22×C12712yes—
106C2×#102—22no—
107C2×#97C22×C12711yescharacteristic
108#347—22no—
109#347C22×C12714yescomplemented
110C22×D4—21no—
111C22×D4—41no—
112C22×C8D4×C12712yes—
113#127—21no—
114#127—41no—
115#127C2×C4×C12712yes—
116#125—21no—
117#125—41no—
118#125C2×C4×C12712yes—
119C2×C4⋊C4—21no—
120C2×C4⋊C4—41no—
121C2×C42C2×C4×C12711yescharacteristic
122M32—24no—
123M32—24no—
124C2×C16—24no—
125#102—24no—
126#102—24no—
127#97C2×C4×C12711yescharacteristic
128#97D4×C12712yes—
129#97C23×C12711yescharacteristic
130C24—41no—
131C2×D4—22no—
132C2×D4—42no—
133C2×D4—42no—
134C2×D4—41no—
135C2×D4—42no—
136C2×D4—42no—
137C2×D4—84no—
138C22×C4—21no—
139C22×C4—41no—
140C22×C4C22⋊C4×C12711yescharacteristic
141C2×C8—22no—
142C2×C8—22no—
143C2×C8C22⋊C4×C12712yes—
144C2×C8C2×D4×C12712yes—
145C4⋊C4—22no—
146C4⋊C4—42no—
147C4⋊C4—42no—
148C4⋊C4—41no—
149C42—21no—
150C42C22⋊C4×C12711yescharacteristic
151C42C22×C4×C12711yescharacteristic
152C16—28no—
153C23—42no—
154C23—84no—
155C23—81no—
156C23—81no—
157C23#100×C12711yescharacteristic
158D4—44no—
159D4—84no—
160D4—84no—
161D4—82no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—42no—
165C2×C4—42no—
166C2×C4—82no—
167C2×C4#100×C12711yescharacteristic
168C2×C4#104×C12712yes—
169C2×C4#104×C12712yes—
170C2×C4C2×C22⋊C4×C12711yescharacteristic
171C8—22no—
172C8—22no—
173C22—22no—
174C22—84no—
175C22—82no—
176C22—162no—
177C22—162no—
178C22#329×C12711yescharacteristic
179C22#329×C12711yescharacteristic
180C22C2×#100×C12711yescharacteristic
181C4—41no—
182C4—41no—
183C4—82no—
184C4#329×C12712yes—
185C4C2×#104×C12712yes—
186C2—21no—
187C2—21no—
188C2—162no—
189C2C127×#135512yesdirect product factor
190C2C2×#329×C12711yescharacteristic
subgroupG/H
center, socleC22×C127#329
commutatorC42C22×C4×C127
Frattini, cosocle#97C23×C127
prime radicalC2×#127×C127C4
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
2. C2×#347×C127C2semidirect
3. C127×#1355C2direct (N × H)
13. #347×C127C22semidirect
90. C2×#1355C127direct (N × H)
94. C2×C127#1355direct (N × H)
97. C2×#347C2×C127semidirect
98. #1355C2×C127direct (N × H)
99. C127C2×#1355direct (N × H)
109. #347C22×C127semidirect
189. C2C127×#1355direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#490×C1272
C2×#347×C1272
C127×#13552
C2×#1355127