Finite Group Databasebeta

← C127×#12433 #44576106

Subgroups — C127×#12433 #44576106

Order 32512.

262 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 82 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
2C127×#2169C211yesmaximal, characteristic, complemented
3C127×#1667C212yesmaximal, complemented
4C127×#1372C211yesmaximal, characteristic, complemented
5C127×#1361C212yesmaximal, complemented
6C2×D16×C127—21no—
7C2×D16×C127—21no—
8C2×M32×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—
25M32×C127—42no—
26C2×C16×C127—21no—
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—22no—
58D4×C127—82no—
59D4×C127—82no—
60D4×C127—82no—
61D4×C127—82no—
62D4×C127—162no—
63C2×C4×C127—21no—
64C2×C4×C127—41no—
65C2×C4×C127—41no—
66C2×C4×C127#12111yescharacteristic
67C2×C4×C127C2×D811yescharacteristic
68C2×C4×C127#13511yescharacteristic
69C8×C127—21no—
70C8×C127—41no—
71C8×C127—82no—
72C8×C127C2×D811yescharacteristic
73C8×C127AGL(1,ℤ/8)11yescharacteristic
74C22×C127—41no—
75C22×C127—41no—
76C22×C127—41no—
77C22×C127—162no—
78C22×C127—162no—
79C22×C127—162no—
80C22×C127#46611yescharacteristic
81C4×C127—21no—
82C4×C127—41no—
83C4×C127#45911yescharacteristic
84C4×C127#47211yescharacteristic
85C4×C127#50912yes—
86#12433C12711yesmaximal, characteristic, direct product factor, Sylow
87C2×C127—81no—
88C2×C127—322no—
89C2×C127#166711yescharacteristic
90C2×C127#221811yescharacteristic
91C2×C127#222111yescharacteristic
92#2246C2×C12711yescharacteristic, complemented
93#2169C2×C12711yescharacteristic, complemented
94#1667C2×C12712yescomplemented
95#1372C2×C12711yescharacteristic, complemented
96#1361C2×C12712yescomplemented
97C127#1243311yescharacteristic, direct product factor, Sylow
98C2×D16—21no—
99C2×D16—21no—
100C2×M32—21no—
101#493C22×C12712yes—
102#459—22no—
103C8×D4C22×C12711yescharacteristic
104C4⋊C16C22×C12711yescharacteristic
105C22⋊C16—21no—
106C4×C16C22×C12711yescharacteristic
107#335C22×C12712yes—
108#331—22no—
109C2×D8—22no—
110C2×D8—22no—
111C2×D8—42no—
112C22×C8—21no—
113#127—22no—
114C4×D4D4×C12711yescharacteristic
115D16—42no—
116D16—42no—
117M32—42no—
118C2×C16—21no—
119C2×C16D4×C12711yescharacteristic
120C2×C16D4×C12711yescharacteristic
121C4⋊C8—22no—
122C4⋊C8D4×C12711yescharacteristic
123#102—42no—
124C22⋊C8—21no—
125C4×C8C23×C12711yescharacteristic
126C2×D4—42no—
127C2×D4—42no—
128C2×D4—42no—
129C2×D4D8×C12711yescharacteristic
130C22×C4—21no—
131D8—42no—
132D8—42no—
133D8—82no—
134D8—84no—
135C2×C8—21no—
136C2×C8—41no—
137C2×C8—41no—
138C2×C8—42no—
139C2×C8C2×D4×C12711yescharacteristic
140C2×C8#41×C12711yescharacteristic
141C4⋊C4D8×C12711yescharacteristic
142C22⋊C4—21no—
143C42C2×D4×C12711yescharacteristic
144C16—21no—
145C16—41no—
146C16D8×C12712yescomplemented
147C23—21no—
148C23—82no—
149D4—22no—
150D4—82no—
151D4—82no—
152D4—82no—
153D4—82no—
154D4—162no—
155C2×C4—21no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4#121×C12711yescharacteristic
159C2×C4C2×D8×C12711yescharacteristic
160C2×C4#135×C12711yescharacteristic
161C8—21no—
162C8—41no—
163C8—82no—
164C8C2×D8×C12711yescharacteristic
165C8AGL(1,ℤ/8)×C12711yescharacteristic
166C22—41no—
167C22—41no—
168C22—41no—
169C22—162no—
170C22—162no—
171C22—162no—
172C22#466×C12711yescharacteristic
173C4—21no—
174C4—41no—
175C4#459×C12711yescharacteristic
176C4#472×C12711yescharacteristic
177C4#509×C12712yes—
178C2—81no—
179C2—322no—
180C2C127×#166711yescharacteristic
181C2C127×#221811yescharacteristic
182C2C127×#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. C127×#2169C2semidirect
3. C127×#1667C2semidirect
4. C127×#1372C2semidirect
5. C127×#1361C2semidirect
54. C16×C127D8semidirect
86. #12433C127direct (N × H)
92. #2246C2×C127semidirect
93. #2169C2×C127semidirect
94. #1667C2×C127semidirect
95. #1372C2×C127semidirect
96. #1361C2×C127semidirect
97. C127#12433direct (N × H)
146. C16D8×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#22462
C127×#21692
C127×#16672
C127×#13722
C127×#13612
#12433127