Finite Group Databasebeta

← C127×#13499 #44577172

Subgroups — C127×#13499 #44577172

Order 32512.

276 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 98 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×#2161C211yesmaximal, characteristic, complemented
2C127×#2113C211yesmaximal, characteristic
3C127×#1814C212yesmaximal
4C127×#1384C211yesmaximal, characteristic, complemented
5C127×#1382C212yesmaximal, complemented
6C2×#131×C127C2211yescharacteristic
7C2×M32×C127C2211yescharacteristic
8C22×C16×C127C2211yescharacteristic
9C2×#108×C127C2212yes—
10#427×C127C2212yes—
11#421×C127—22no—
12#368×C127—22no—
13C22⋊C16×C127—22no—
14#344×C127—22no—
15C2×#41×C127D411yescharacteristic
16#131×C127—22no—
17#131×C127—22no—
18C2×M16×C127—21no—
19C2×M16×C127—22no—
20C2×M16×C127D411yescharacteristic
21C22×C8×C127—21no—
22C22×C8×C127C2311yescharacteristic
23#117×C127—22no—
24M32×C127—22no—
25C2×C16×C127—21no—
26C2×C16×C127—22no—
27C2×C16×C127D412yes—
28#108×C127—22no—
29#108×C127—22no—
30#107×C127—22no—
31#106×C127—22no—
32#104×C127—44no—
33#41×C127—22no—
34#41×C127—22no—
35C2×Q8×C127Q1611yescharacteristic
36C2×D4×C127—21no—
37C2×D4×C127Q1611yescharacteristic
38C22×C4×C127—21no—
39C22×C4×C127C2×D411yescharacteristic
40M16×C127—22no—
41M16×C127—42no—
42M16×C127—42no—
43M16×C127—42no—
44C2×C8×C127—21no—
45C2×C8×C127—41no—
46C2×C8×C127—41no—
47C2×C8×C127—42no—
48C2×C8×C127C2×D411yescharacteristic
49C2×C8×C127#4112yes—
50C2×C8×C127#4112yes—
51C2×C8×C127#4111yescharacteristic
52C4⋊C4×C127—42no—
53C22⋊C4×C127—42no—
54C42×C127—42no—
55C16×C127—22no—
56C16×C127—41no—
57C23×C127—21no—
58C23×C127#13511yescharacteristic
59Q8×C127—22no—
60D4×C127—22no—
61D4×C127—42no—
62C2×C4×C127—21no—
63C2×C4×C127—41no—
64C2×C4×C127—41no—
65C2×C4×C127—82no—
66C2×C4×C127#12111yescharacteristic
67C2×C4×C127#12312yes—
68C2×C4×C127C2×Q1611yescharacteristic
69C2×C4×C127AGL(1,ℤ/8)12yes—
70C8×C127—41no—
71C8×C127—82no—
72C8×C127#12311yescharacteristic
73C8×C127#12411yescharacteristic
74C8×C127#12612yes—
75C22×C127—41no—
76C22×C127—42no—
77C22×C127—41no—
78C22×C127#46711yescharacteristic
79C22×C127#48212yes—
80C4×C127—41no—
81C4×C127—162no—
82C4×C127#39711yescharacteristic
83C4×C127#46911yescharacteristic
84C4×C127#48412yes—
85#13499C12711yesmaximal, characteristic, direct product factor, Sylow
86C2×C127—22no—
87C2×C127—21no—
88C2×C127—81no—
89C2×C127#207611yescharacteristic
90#2161C2×C12711yescharacteristic, complemented
91#2113C2×C12711yescharacteristic
92#1814C2×C12712yes—
93#1384C2×C12711yescharacteristic, complemented
94#1382C2×C12712yescomplemented
95C127#1349911yescharacteristic, direct product factor, Sylow
96C2×#131C22×C12711yescharacteristic
97C2×M32C22×C12711yescharacteristic
98C22×C16C22×C12711yescharacteristic
99C2×#108C22×C12712yes—
100#427C22×C12712yes—
101#421—22no—
102#368—22no—
103C22⋊C16—22no—
104#344—22no—
105C2×#41D4×C12711yescharacteristic
106#131—22no—
107#131—22no—
108C2×M16—21no—
109C2×M16—22no—
110C2×M16D4×C12711yescharacteristic
111C22×C8—21no—
112C22×C8C23×C12711yescharacteristic
113#117—22no—
114M32—22no—
115C2×C16—21no—
116C2×C16—22no—
117C2×C16D4×C12712yes—
118#108—22no—
119#108—22no—
120#107—22no—
121#106—22no—
122#104—44no—
123#41—22no—
124#41—22no—
125C2×Q8Q16×C12711yescharacteristic
126C2×D4—21no—
127C2×D4Q16×C12711yescharacteristic
128C22×C4—21no—
129C22×C4C2×D4×C12711yescharacteristic
130M16—22no—
131M16—42no—
132M16—42no—
133M16—42no—
134C2×C8—21no—
135C2×C8—41no—
136C2×C8—41no—
137C2×C8—42no—
138C2×C8C2×D4×C12711yescharacteristic
139C2×C8#41×C12712yes—
140C2×C8#41×C12712yes—
141C2×C8#41×C12711yescharacteristic
142C4⋊C4—42no—
143C22⋊C4—42no—
144C42—42no—
145C16—22no—
146C16—41no—
147C23—21no—
148C23#135×C12711yescharacteristic
149Q8—22no—
150D4—22no—
151D4—42no—
152C2×C4—21no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—82no—
156C2×C4#121×C12711yescharacteristic
157C2×C4#123×C12712yes—
158C2×C4C2×Q16×C12711yescharacteristic
159C2×C4AGL(1,ℤ/8)×C12712yes—
160C8—41no—
161C8—82no—
162C8#123×C12711yescharacteristic
163C8#124×C12711yescharacteristic
164C8#126×C12712yes—
165C22—41no—
166C22—42no—
167C22—41no—
168C22#467×C12711yescharacteristic
169C22#482×C12712yes—
170C4—41no—
171C4—162no—
172C4#397×C12711yescharacteristic
173C4#469×C12711yescharacteristic
174C4#484×C12712yes—
175C2—22no—
176C2—21no—
177C2—81no—
178C2C127×#207611yescharacteristic
subgroupG/H
centerC4×C127#469
commutator, Frattini, cosocleC22×C8C23×C127
socleC2×C127#2076
prime radicalC2×#41×C127D4
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C127 ◁ C22×C4×C127 ◁ C2×#131×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C127×#2161C2semidirect
4. C127×#1384C2semidirect
5. C127×#1382C2semidirect
85. #13499C127direct (N × H)
90. #2161C2×C127semidirect
93. #1384C2×C127semidirect
94. #1382C2×C127semidirect
95. C127#13499direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#21612
C127×#21132
C127×#18142
C127×#13842
C127×#13822
#13499127