Finite Group Databasebeta

← C127×#12439 #44576112

Subgroups — C127×#12439 #44576112

Order 32512.

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

normal subgroups only

This group has 248 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
2Q8×C16×C127C211yesmaximal, characteristic, complemented
3C127×#1668C212yesmaximal, complemented
4C127×#1371C211yesmaximal, characteristic, complemented
5C127×#1361C212yesmaximal, complemented
6C2×D16×C127—21no—
7C2×D16×C127—21no—
8#493×C127C2212yes—
9#460×C127—22no—
10C8×Q8×C127C2211yescharacteristic
11C4⋊C16×C127—21no—
12C4⋊C16×C127C2211yescharacteristic
13C4×C16×C127—21no—
14C4×C16×C127C2211yescharacteristic
15#335×C127C2212yes—
16#331×C127—22no—
17C2×SD16×C127—42no—
18C2×D8×C127—22no—
19C2×D8×C127—22no—
20#127×C127—22no—
21C4×Q8×C127D411yescharacteristic
22D16×C127—42no—
23D16×C127—42no—
24C2×C16×C127—21no—
25C2×C16×C127D411yescharacteristic
26C2×C16×C127D411yescharacteristic
27C4⋊C8×C127—21no—
28C4⋊C8×C127—22no—
29C4⋊C8×C127D411yescharacteristic
30#102×C127—42no—
31C4×C8×C127—21no—
32C4×C8×C127C2311yescharacteristic
33C2×Q8×C127D811yescharacteristic
34C2×D4×C127—42no—
35C2×D4×C127—42no—
36C2×D4×C127—42no—
37SD16×C127—84no—
38D8×C127—42no—
39D8×C127—42no—
40D8×C127—82no—
41C2×C8×C127—21no—
42C2×C8×C127—42no—
43C2×C8×C127C2×D411yescharacteristic
44C2×C8×C127#4111yescharacteristic
45C4⋊C4×C127—21no—
46C4⋊C4×C127D811yescharacteristic
47C42×C127—21no—
48C42×C127C2×D411yescharacteristic
49C16×C127—21no—
50C16×C127—41no—
51C16×C127SD1612yescomplemented
52C23×C127—82no—
53Q8×C127—21no—
54Q8×C127D1612yescomplemented
55D4×C127—82no—
56D4×C127—82no—
57D4×C127—82no—
58D4×C127—82no—
59D4×C127—162no—
60C2×C4×C127—21no—
61C2×C4×C127—21no—
62C2×C4×C127#12111yescharacteristic
63C2×C4×C127C2×D811yescharacteristic
64C2×C4×C127#13511yescharacteristic
65C8×C127—21no—
66C8×C127—41no—
67C8×C127—82no—
68C8×C127C2×SD1611yescharacteristic
69C8×C127AGL(1,ℤ/8)11yescharacteristic
70C22×C127—162no—
71C22×C127—162no—
72C22×C127—162no—
73C22×C127#46611yescharacteristic
74C4×C127—22no—
75C4×C127—21no—
76C4×C127—41no—
77C4×C127#46011yescharacteristic
78C4×C127#47211yescharacteristic
79C4×C127C2×D1611yescharacteristic
80C4×C127#50811yescharacteristic
81#12439C12711yesmaximal, characteristic, direct product factor, Sylow
82C2×C127—322no—
83C2×C127#166811yescharacteristic
84C2×C127#221511yescharacteristic
85C2×C127#222111yescharacteristic
86#2246C2×C12711yescharacteristic
87Q8×C16C2×C12711yescharacteristic, complemented
88#1668C2×C12712yescomplemented
89#1371C2×C12711yescharacteristic, complemented
90#1361C2×C12712yescomplemented
91C127#1243911yescharacteristic, direct product factor, Sylow
92C2×D16—21no—
93C2×D16—21no—
94#493C22×C12712yes—
95#460—22no—
96C8×Q8C22×C12711yescharacteristic
97C4⋊C16—21no—
98C4⋊C16C22×C12711yescharacteristic
99C4×C16—21no—
100C4×C16C22×C12711yescharacteristic
101#335C22×C12712yes—
102#331—22no—
103C2×SD16—42no—
104C2×D8—22no—
105C2×D8—22no—
106#127—22no—
107C4×Q8D4×C12711yescharacteristic
108D16—42no—
109D16—42no—
110C2×C16—21no—
111C2×C16D4×C12711yescharacteristic
112C2×C16D4×C12711yescharacteristic
113C4⋊C8—21no—
114C4⋊C8—22no—
115C4⋊C8D4×C12711yescharacteristic
116#102—42no—
117C4×C8—21no—
118C4×C8C23×C12711yescharacteristic
119C2×Q8D8×C12711yescharacteristic
120C2×D4—42no—
121C2×D4—42no—
122C2×D4—42no—
123SD16—84no—
124D8—42no—
125D8—42no—
126D8—82no—
127C2×C8—21no—
128C2×C8—42no—
129C2×C8C2×D4×C12711yescharacteristic
130C2×C8#41×C12711yescharacteristic
131C4⋊C4—21no—
132C4⋊C4D8×C12711yescharacteristic
133C42—21no—
134C42C2×D4×C12711yescharacteristic
135C16—21no—
136C16—41no—
137C16SD16×C12712yescomplemented
138C23—82no—
139Q8—21no—
140Q8D16×C12712yescomplemented
141D4—82no—
142D4—82no—
143D4—82no—
144D4—82no—
145D4—162no—
146C2×C4—21no—
147C2×C4—21no—
148C2×C4#121×C12711yescharacteristic
149C2×C4C2×D8×C12711yescharacteristic
150C2×C4#135×C12711yescharacteristic
151C8—21no—
152C8—41no—
153C8—82no—
154C8C2×SD16×C12711yescharacteristic
155C8AGL(1,ℤ/8)×C12711yescharacteristic
156C22—162no—
157C22—162no—
158C22—162no—
159C22#466×C12711yescharacteristic
160C4—22no—
161C4—21no—
162C4—41no—
163C4#460×C12711yescharacteristic
164C4#472×C12711yescharacteristic
165C4C2×D16×C12711yescharacteristic
166C4#508×C12711yescharacteristic
167C2—322no—
168C2C127×#166811yescharacteristic
169C2C127×#221511yescharacteristic
170C2C127×#222111yescharacteristic
subgroupG/H
center, socleC22×C127#466
commutator, Frattini, cosocleC4×C8C23×C127
prime radicalC127×#2246C2
LCSG ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C42×C127 ◁ C8×Q8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. Q8×C16×C127C2semidirect
3. C127×#1668C2semidirect
4. C127×#1371C2semidirect
5. C127×#1361C2semidirect
51. C16×C127SD16semidirect
54. Q8×C127D16semidirect
81. #12439C127direct (N × H)
87. Q8×C16C2×C127semidirect
88. #1668C2×C127semidirect
89. #1371C2×C127semidirect
90. #1361C2×C127semidirect
91. C127#12439direct (N × H)
137. C16SD16×C127semidirect
140. Q8D16×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#22462
Q8×C16×C1272
C127×#16682
C127×#13712
C127×#13612
#12439127