Finite Group Databasebeta

← C127×#13542 #44577215

Subgroups — C127×#13542 #44577215

Order 32512.

252 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 106 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×#1945C211yesmaximal, characteristic
2C127×#1846C211yesmaximal, characteristic
3C127×#1386C212yesmaximal
4C127×#1383C212yesmaximal
5C127×#1376C211yesmaximal, characteristic
6C2×M32×C127C2212yes—
7C2×#108×C127C2211yescharacteristic
8#427×C127C2211yescharacteristic
9C2×#107×C127—21no—
10C2×#106×C127C2212yes—
11#424×C127—21no—
12C2×C4×C8×C127C2211yescharacteristic
13#382×C127—21no—
14#339×C127—21no—
15C2×M16×C127—21no—
16C22×C8×C127D411yescharacteristic
17C22×C8×C127C2311yescharacteristic
18#117×C127—21no—
19C2×C4⋊C4×C127—22no—
20C2×C42×C127D411yescharacteristic
21M32×C127—22no—
22M32×C127—22no—
23C2×C16×C127—22no—
24#108×C127—22no—
25#107×C127—42no—
26#107×C127Q812yes—
27#106×C127—21no—
28#106×C127—24no—
29C4⋊C8×C127—42no—
30C4×C8×C127—22no—
31#95×C127—42no—
32C22×C4×C127—21no—
33C22×C4×C127—42no—
34C22×C4×C127C2×D411yescharacteristic
35M16×C127—41no—
36M16×C127—41no—
37C2×C8×C127—21no—
38C2×C8×C127—21no—
39C2×C8×C127—41no—
40C2×C8×C127SD1612yes—
41C2×C8×C127C2×Q811yescharacteristic
42C2×C8×C127#4112yes—
43C2×C8×C127#4112yes—
44C2×C8×C127#4111yescharacteristic
45C4⋊C4×C127—22no—
46C4⋊C4×C127—42no—
47C4⋊C4×C127—42no—
48C22⋊C4×C127—41no—
49C42×C127—21no—
50C42×C127—41no—
51C42×C127Q1612yes—
52C16×C127—42no—
53C23×C127AGL(1,ℤ/8)11yescharacteristic
54C2×C4×C127—22no—
55C2×C4×C127—42no—
56C2×C4×C127—42no—
57C2×C4×C127—84no—
58C2×C4×C127—82no—
59C2×C4×C127C22⋊Q811yescharacteristic
60C2×C4×C127#12311yescharacteristic
61C2×C4×C127#12411yescharacteristic
62C2×C4×C127C2×SD1611yescharacteristic
63C2×C4×C127C2×Q1611yescharacteristic
64C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
65C8×C127—22no—
66C8×C127—81no—
67C8×C127#12512yes—
68C8×C127#12612yes—
69C22×C127—22no—
70C22×C127#47611yescharacteristic
71C22×C127#48411yescharacteristic
72C22×C127#49011yescharacteristic
73C4×C127—42no—
74C4×C127—82no—
75C4×C127—162no—
76C4×C127#40011yescharacteristic
77C4×C127#47711yescharacteristic
78C4×C127#48111yescharacteristic
79C4×C127#48711yescharacteristic
80#13542C12711yesmaximal, characteristic, direct product factor, Sylow
81C2×C127—21no—
82C2×C127—21no—
83C2×C127#210011yescharacteristic
84C2×C127#223112yes—
85#1945C2×C12711yescharacteristic
86#1846C2×C12711yescharacteristic
87#1386C2×C12712yes—
88#1383C2×C12712yes—
89#1376C2×C12711yescharacteristic
90C127#1354211yescharacteristic, direct product factor, Sylow
91C2×M32C22×C12712yes—
92C2×#108C22×C12711yescharacteristic
93#427C22×C12711yescharacteristic
94C2×#107—21no—
95C2×#106C22×C12712yes—
96#424—21no—
97C2×C4×C8C22×C12711yescharacteristic
98#382—21no—
99#339—21no—
100C2×M16—21no—
101C22×C8D4×C12711yescharacteristic
102C22×C8C23×C12711yescharacteristic
103#117—21no—
104C2×C4⋊C4—22no—
105C2×C42D4×C12711yescharacteristic
106M32—22no—
107M32—22no—
108C2×C16—22no—
109#108—22no—
110#107—42no—
111#107Q8×C12712yes—
112#106—21no—
113#106—24no—
114C4⋊C8—42no—
115C4×C8—22no—
116#95—42no—
117C22×C4—21no—
118C22×C4—42no—
119C22×C4C2×D4×C12711yescharacteristic
120M16—41no—
121M16—41no—
122C2×C8—21no—
123C2×C8—21no—
124C2×C8—41no—
125C2×C8SD16×C12712yes—
126C2×C8C2×Q8×C12711yescharacteristic
127C2×C8#41×C12712yes—
128C2×C8#41×C12712yes—
129C2×C8#41×C12711yescharacteristic
130C4⋊C4—22no—
131C4⋊C4—42no—
132C4⋊C4—42no—
133C22⋊C4—41no—
134C42—21no—
135C42—41no—
136C42Q16×C12712yes—
137C16—42no—
138C23AGL(1,ℤ/8)×C12711yescharacteristic
139C2×C4—22no—
140C2×C4—42no—
141C2×C4—42no—
142C2×C4—84no—
143C2×C4—82no—
144C2×C4C22⋊Q8×C12711yescharacteristic
145C2×C4#123×C12711yescharacteristic
146C2×C4#124×C12711yescharacteristic
147C2×C4C2×SD16×C12711yescharacteristic
148C2×C4C2×Q16×C12711yescharacteristic
149C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
150C8—22no—
151C8—81no—
152C8#125×C12712yes—
153C8#126×C12712yes—
154C22—22no—
155C22#476×C12711yescharacteristic
156C22#484×C12711yescharacteristic
157C22#490×C12711yescharacteristic
158C4—42no—
159C4—82no—
160C4—162no—
161C4#400×C12711yescharacteristic
162C4#477×C12711yescharacteristic
163C4#481×C12711yescharacteristic
164C4#487×C12711yescharacteristic
165C2—21no—
166C2—21no—
167C2C127×#210011yescharacteristic
168C2C127×#223112yes—
subgroupG/H
center, socleC22×C127#476
commutator, Frattini, cosocleC22×C8C23×C127
prime radicalC23×C127AGL(1,ℤ/8)
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C22×C4×C127 ◁ C2×C4×C8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
80. #13542C127direct (N × H)
90. C127#13542direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#19452
C127×#18462
C127×#13862
C127×#13832
C127×#13762
#13542127