Finite Group Databasebeta

← C127×#13498 #44577171

Subgroups — C127×#13498 #44577171

Order 32512.

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

normal subgroups only

This group has 292 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×#2112C211yesmaximal, characteristic
3C127×#1810C212yesmaximal
4C127×#1388C212yesmaximal, complemented
5C127×#1385C211yesmaximal, characteristic, complemented
6C23×C8×C127C2211yescharacteristic
7C2×M32×C127C2211yescharacteristic
8C2×M32×C127C2211yescharacteristic
9C2×#108×C127C2212yes—
10C2×#108×C127C2212yes—
11#407×C127—22no—
12#368×C127—22no—
13C22⋊C16×C127—22no—
14#341×C127—22no—
15C23×C4×C127D411yescharacteristic
16C2×M16×C127—22no—
17C2×M16×C127—22no—
18C22×C8×C127—21no—
19C22×C8×C127—21no—
20C22×C8×C127—22no—
21C22×C8×C127—22no—
22C22×C8×C127D411yescharacteristic
23C22×C8×C127C2311yescharacteristic
24M32×C127—22no—
25M32×C127—22no—
26C2×C16×C127—21no—
27C2×C16×C127D412yes—
28#108×C127—22no—
29#108×C127—22no—
30#108×C127—22no—
31#108×C127—22no—
32C22⋊C8×C127—44no—
33C24×C127Q1611yescharacteristic
34C22×C4×C127—21no—
35C22×C4×C127—22no—
36C22×C4×C127—21no—
37C22×C4×C127—22no—
38C22×C4×C127Q1611yescharacteristic
39C22×C4×C127C2×D411yescharacteristic
40M16×C127—42no—
41M16×C127—42no—
42M16×C127—42no—
43M16×C127—42no—
44C2×C8×C127—21no—
45C2×C8×C127—22no—
46C2×C8×C127—41no—
47C2×C8×C127—41no—
48C2×C8×C127—42no—
49C2×C8×C127—42no—
50C2×C8×C127—42no—
51C2×C8×C127C2×D411yescharacteristic
52C2×C8×C127#4112yes—
53C2×C8×C127#4112yes—
54C2×C8×C127#4111yescharacteristic
55C16×C127—22no—
56C16×C127—41no—
57C23×C127—21no—
58C23×C127—22no—
59C23×C127—42no—
60C23×C127C2×Q1611yescharacteristic
61C2×C4×C127—21no—
62C2×C4×C127—22no—
63C2×C4×C127—41no—
64C2×C4×C127—41no—
65C2×C4×C127—42no—
66C2×C4×C127#12111yescharacteristic
67C2×C4×C127#12312yes—
68C2×C4×C127#13511yescharacteristic
69C2×C4×C127AGL(1,ℤ/8)12yes—
70C8×C127—41no—
71C8×C127—82no—
72C8×C127—82no—
73C8×C127#12311yescharacteristic
74C8×C127#12411yescharacteristic
75C8×C127#12612yes—
76C22×C127—22no—
77C22×C127—24no—
78C22×C127—41no—
79C22×C127—41no—
80C22×C127—42no—
81C22×C127—41no—
82C22×C127#46711yescharacteristic
83C22×C127#48412yes—
84C4×C127—41no—
85C4×C127#39711yescharacteristic
86C4×C127#46911yescharacteristic
87C4×C127#48212yes—
88#13498C12711yesmaximal, characteristic, direct product factor, Sylow
89C2×C127—21no—
90C2×C127—22no—
91C2×C127—42no—
92C2×C127#207611yescharacteristic
93#2161C2×C12711yescharacteristic, complemented
94#2112C2×C12711yescharacteristic
95#1810C2×C12712yes—
96#1388C2×C12712yescomplemented
97#1385C2×C12711yescharacteristic, complemented
98C127#1349811yescharacteristic, direct product factor, Sylow
99C23×C8C22×C12711yescharacteristic
100C2×M32C22×C12711yescharacteristic
101C2×M32C22×C12711yescharacteristic
102C2×#108C22×C12712yes—
103C2×#108C22×C12712yes—
104#407—22no—
105#368—22no—
106C22⋊C16—22no—
107#341—22no—
108C23×C4D4×C12711yescharacteristic
109C2×M16—22no—
110C2×M16—22no—
111C22×C8—21no—
112C22×C8—21no—
113C22×C8—22no—
114C22×C8—22no—
115C22×C8D4×C12711yescharacteristic
116C22×C8C23×C12711yescharacteristic
117M32—22no—
118M32—22no—
119C2×C16—21no—
120C2×C16D4×C12712yes—
121#108—22no—
122#108—22no—
123#108—22no—
124#108—22no—
125C22⋊C8—44no—
126C24Q16×C12711yescharacteristic
127C22×C4—21no—
128C22×C4—22no—
129C22×C4—21no—
130C22×C4—22no—
131C22×C4Q16×C12711yescharacteristic
132C22×C4C2×D4×C12711yescharacteristic
133M16—42no—
134M16—42no—
135M16—42no—
136M16—42no—
137C2×C8—21no—
138C2×C8—22no—
139C2×C8—41no—
140C2×C8—41no—
141C2×C8—42no—
142C2×C8—42no—
143C2×C8—42no—
144C2×C8C2×D4×C12711yescharacteristic
145C2×C8#41×C12712yes—
146C2×C8#41×C12712yes—
147C2×C8#41×C12711yescharacteristic
148C16—22no—
149C16—41no—
150C23—21no—
151C23—22no—
152C23—42no—
153C23C2×Q16×C12711yescharacteristic
154C2×C4—21no—
155C2×C4—22no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—42no—
159C2×C4#121×C12711yescharacteristic
160C2×C4#123×C12712yes—
161C2×C4#135×C12711yescharacteristic
162C2×C4AGL(1,ℤ/8)×C12712yes—
163C8—41no—
164C8—82no—
165C8—82no—
166C8#123×C12711yescharacteristic
167C8#124×C12711yescharacteristic
168C8#126×C12712yes—
169C22—22no—
170C22—24no—
171C22—41no—
172C22—41no—
173C22—42no—
174C22—41no—
175C22#467×C12711yescharacteristic
176C22#484×C12712yes—
177C4—41no—
178C4#397×C12711yescharacteristic
179C4#469×C12711yescharacteristic
180C4#482×C12712yes—
181C2—21no—
182C2—22no—
183C2—42no—
184C2C127×#207611yescharacteristic
subgroupG/H
centerC4×C127#469
commutator, Frattini, cosocleC22×C8C23×C127
socleC2×C127#2076
prime radicalC24×C127Q16
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C127 ◁ C22×C4×C127 ◁ C23×C8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C127×#2161C2semidirect
4. C127×#1388C2semidirect
5. C127×#1385C2semidirect
88. #13498C127direct (N × H)
93. #2161C2×C127semidirect
96. #1388C2×C127semidirect
97. #1385C2×C127semidirect
98. C127#13498direct (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×#21122
C127×#18102
C127×#13882
C127×#13852
#13498127