Finite Group Databasebeta

← C127×#12430 #44576103

Subgroups — C127×#12430 #44576103

Order 32512.

268 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 268 conjugacy classes of subgroups — too many to draw. Only its 86 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×#2246C211yesmaximal, characteristic, complemented
2D4×C16×C127C211yesmaximal, characteristic, complemented
3C127×#1667C212yesmaximal, complemented
4C127×#1371C211yesmaximal, characteristic, complemented
5C127×#1361C212yesmaximal, complemented
6C2×D16×C127—21no—
7C2×D16×C127—21no—
8C22×C16×C127—21no—
9#493×C127C2212yes—
10#459×C127—22no—
11C8×D4×C127C2211yescharacteristic
12C4⋊C16×C127C2211yescharacteristic
13C22⋊C16×C127—21no—
14C4×C16×C127C2211yescharacteristic
15#335×C127C2212yes—
16#331×C127—22no—
17C2×D8×C127—22no—
18C2×D8×C127—22no—
19C2×D8×C127—42no—
20C22×C8×C127—21no—
21#127×C127—22no—
22C4×D4×C127D411yescharacteristic
23D16×C127—42no—
24D16×C127—42no—
25C2×C16×C127—21no—
26C2×C16×C127—42no—
27C2×C16×C127D411yescharacteristic
28C2×C16×C127D411yescharacteristic
29C4⋊C8×C127—22no—
30C4⋊C8×C127D411yescharacteristic
31#102×C127—42no—
32C22⋊C8×C127—21no—
33C4×C8×C127C2311yescharacteristic
34C2×D4×C127—42no—
35C2×D4×C127—42no—
36C2×D4×C127—42no—
37C2×D4×C127D811yescharacteristic
38C22×C4×C127—21no—
39D8×C127—42no—
40D8×C127—42no—
41D8×C127—82no—
42D8×C127—84no—
43C2×C8×C127—21no—
44C2×C8×C127—41no—
45C2×C8×C127—41no—
46C2×C8×C127—42no—
47C2×C8×C127C2×D411yescharacteristic
48C2×C8×C127#4111yescharacteristic
49C4⋊C4×C127D811yescharacteristic
50C22⋊C4×C127—21no—
51C42×C127C2×D411yescharacteristic
52C16×C127—21no—
53C16×C127—41no—
54C16×C127D812yescomplemented
55C23×C127—21no—
56C23×C127—82no—
57D4×C127—21no—
58D4×C127—82no—
59D4×C127—82no—
60D4×C127—82no—
61D4×C127—82no—
62D4×C127—162no—
63D4×C127D1612yescomplemented
64C2×C4×C127—21no—
65C2×C4×C127—41no—
66C2×C4×C127—41no—
67C2×C4×C127#12111yescharacteristic
68C2×C4×C127C2×D811yescharacteristic
69C2×C4×C127#13511yescharacteristic
70C8×C127—21no—
71C8×C127—41no—
72C8×C127—82no—
73C8×C127C2×D811yescharacteristic
74C8×C127AGL(1,ℤ/8)11yescharacteristic
75C22×C127—22no—
76C22×C127—41no—
77C22×C127—41no—
78C22×C127—162no—
79C22×C127—162no—
80C22×C127—162no—
81C22×C127#46611yescharacteristic
82C4×C127—21no—
83C4×C127—41no—
84C4×C127#45911yescharacteristic
85C4×C127#47211yescharacteristic
86C4×C127C2×D1611yescharacteristic
87C4×C127#50811yescharacteristic
88#12430C12711yesmaximal, characteristic, direct product factor, Sylow
89C2×C127—42no—
90C2×C127—322no—
91C2×C127#166711yescharacteristic
92C2×C127#221511yescharacteristic
93C2×C127#222111yescharacteristic
94#2246C2×C12711yescharacteristic, complemented
95D4×C16C2×C12711yescharacteristic, complemented
96#1667C2×C12712yescomplemented
97#1371C2×C12711yescharacteristic, complemented
98#1361C2×C12712yescomplemented
99C127#1243011yescharacteristic, direct product factor, Sylow
100C2×D16—21no—
101C2×D16—21no—
102C22×C16—21no—
103#493C22×C12712yes—
104#459—22no—
105C8×D4C22×C12711yescharacteristic
106C4⋊C16C22×C12711yescharacteristic
107C22⋊C16—21no—
108C4×C16C22×C12711yescharacteristic
109#335C22×C12712yes—
110#331—22no—
111C2×D8—22no—
112C2×D8—22no—
113C2×D8—42no—
114C22×C8—21no—
115#127—22no—
116C4×D4D4×C12711yescharacteristic
117D16—42no—
118D16—42no—
119C2×C16—21no—
120C2×C16—42no—
121C2×C16D4×C12711yescharacteristic
122C2×C16D4×C12711yescharacteristic
123C4⋊C8—22no—
124C4⋊C8D4×C12711yescharacteristic
125#102—42no—
126C22⋊C8—21no—
127C4×C8C23×C12711yescharacteristic
128C2×D4—42no—
129C2×D4—42no—
130C2×D4—42no—
131C2×D4D8×C12711yescharacteristic
132C22×C4—21no—
133D8—42no—
134D8—42no—
135D8—82no—
136D8—84no—
137C2×C8—21no—
138C2×C8—41no—
139C2×C8—41no—
140C2×C8—42no—
141C2×C8C2×D4×C12711yescharacteristic
142C2×C8#41×C12711yescharacteristic
143C4⋊C4D8×C12711yescharacteristic
144C22⋊C4—21no—
145C42C2×D4×C12711yescharacteristic
146C16—21no—
147C16—41no—
148C16D8×C12712yescomplemented
149C23—21no—
150C23—82no—
151D4—21no—
152D4—82no—
153D4—82no—
154D4—82no—
155D4—82no—
156D4—162no—
157D4D16×C12712yescomplemented
158C2×C4—21no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4#121×C12711yescharacteristic
162C2×C4C2×D8×C12711yescharacteristic
163C2×C4#135×C12711yescharacteristic
164C8—21no—
165C8—41no—
166C8—82no—
167C8C2×D8×C12711yescharacteristic
168C8AGL(1,ℤ/8)×C12711yescharacteristic
169C22—22no—
170C22—41no—
171C22—41no—
172C22—162no—
173C22—162no—
174C22—162no—
175C22#466×C12711yescharacteristic
176C4—21no—
177C4—41no—
178C4#459×C12711yescharacteristic
179C4#472×C12711yescharacteristic
180C4C2×D16×C12711yescharacteristic
181C4#508×C12711yescharacteristic
182C2—42no—
183C2—322no—
184C2C127×#166711yescharacteristic
185C2C127×#221511yescharacteristic
186C2C127×#222111yescharacteristic
subgroupG/H
center, socleC22×C127#466
commutator, Frattini, cosocleC4×C8C23×C127
LCSG ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C42×C127 ◁ C8×D4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C127×#2246C2semidirect
2. D4×C16×C127C2semidirect
3. C127×#1667C2semidirect
4. C127×#1371C2semidirect
5. C127×#1361C2semidirect
54. C16×C127D8semidirect
63. D4×C127D16semidirect
88. #12430C127direct (N × H)
94. #2246C2×C127semidirect
95. D4×C16C2×C127semidirect
96. #1667C2×C127semidirect
97. #1371C2×C127semidirect
98. #1361C2×C127semidirect
99. C127#12430direct (N × H)
148. C16D8×C127semidirect
157. D4D16×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#22462
D4×C16×C1272
C127×#16672
C127×#13712
C127×#13612
#12430127