Finite Group Databasebeta

← C127×#13543 #44577216

Subgroups — C127×#13543 #44577216

Order 32512.

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

normal subgroups only

This group has 268 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×#1844C211yesmaximal, characteristic
3C127×#1386C212yesmaximal
4C127×#1383C212yesmaximal
5C127×#1376C211yesmaximal, characteristic
6C2×M32×C127C2212yes—
7C2×#108×C127C2211yescharacteristic
8#427×C127C2211yescharacteristic
9C2×#106×C127—21no—
10C2×#106×C127C2212yes—
11#424×C127—21no—
12C2×C4×C8×C127C2211yescharacteristic
13#384×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×C4⋊C4×C127—42no—
21C2×C42×C127D411yescharacteristic
22M32×C127—22no—
23M32×C127—22no—
24C2×C16×C127—22no—
25#108×C127—22no—
26#107×C127Q812yes—
27#106×C127—21no—
28#106×C127—24no—
29#106×C127—42no—
30C4⋊C8×C127—42no—
31C4×C8×C127—22no—
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—
48C4⋊C4×C127—84no—
49C22⋊C4×C127—41no—
50C42×C127—21no—
51C42×C127—41no—
52C42×C127Q1612yes—
53C16×C127—42no—
54C23×C127AGL(1,ℤ/8)11yescharacteristic
55C2×C4×C127—24no—
56C2×C4×C127—22no—
57C2×C4×C127—42no—
58C2×C4×C127—84no—
59C2×C4×C127—82no—
60C2×C4×C127C22⋊Q811yescharacteristic
61C2×C4×C127#12311yescharacteristic
62C2×C4×C127#12411yescharacteristic
63C2×C4×C127C2×SD1611yescharacteristic
64C2×C4×C127C2×Q1611yescharacteristic
65C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
66C8×C127—22no—
67C8×C127—81no—
68C8×C127#12512yes—
69C8×C127#12612yes—
70C22×C127—22no—
71C22×C127#47611yescharacteristic
72C22×C127#48411yescharacteristic
73C22×C127#49011yescharacteristic
74C4×C127—24no—
75C4×C127—82no—
76C4×C127—162no—
77C4×C127#40011yescharacteristic
78C4×C127#47711yescharacteristic
79C4×C127#48111yescharacteristic
80C4×C127#48711yescharacteristic
81#13543C12711yesmaximal, characteristic, direct product factor, Sylow
82C2×C127—21no—
83C2×C127—21no—
84C2×C127#210011yescharacteristic
85C2×C127#223012yes—
86#1945C2×C12711yescharacteristic
87#1844C2×C12711yescharacteristic
88#1386C2×C12712yes—
89#1383C2×C12712yes—
90#1376C2×C12711yescharacteristic
91C127#1354311yescharacteristic, direct product factor, Sylow
92C2×M32C22×C12712yes—
93C2×#108C22×C12711yescharacteristic
94#427C22×C12711yescharacteristic
95C2×#106—21no—
96C2×#106C22×C12712yes—
97#424—21no—
98C2×C4×C8C22×C12711yescharacteristic
99#384—21no—
100#339—21no—
101C2×M16—21no—
102C22×C8D4×C12711yescharacteristic
103C22×C8C23×C12711yescharacteristic
104#117—21no—
105C2×C4⋊C4—22no—
106C2×C4⋊C4—42no—
107C2×C42D4×C12711yescharacteristic
108M32—22no—
109M32—22no—
110C2×C16—22no—
111#108—22no—
112#107Q8×C12712yes—
113#106—21no—
114#106—24no—
115#106—42no—
116C4⋊C8—42no—
117C4×C8—22no—
118C22×C4—21no—
119C22×C4—42no—
120C22×C4C2×D4×C12711yescharacteristic
121M16—41no—
122M16—41no—
123C2×C8—21no—
124C2×C8—21no—
125C2×C8—41no—
126C2×C8SD16×C12712yes—
127C2×C8C2×Q8×C12711yescharacteristic
128C2×C8#41×C12712yes—
129C2×C8#41×C12712yes—
130C2×C8#41×C12711yescharacteristic
131C4⋊C4—22no—
132C4⋊C4—42no—
133C4⋊C4—42no—
134C4⋊C4—84no—
135C22⋊C4—41no—
136C42—21no—
137C42—41no—
138C42Q16×C12712yes—
139C16—42no—
140C23AGL(1,ℤ/8)×C12711yescharacteristic
141C2×C4—24no—
142C2×C4—22no—
143C2×C4—42no—
144C2×C4—84no—
145C2×C4—82no—
146C2×C4C22⋊Q8×C12711yescharacteristic
147C2×C4#123×C12711yescharacteristic
148C2×C4#124×C12711yescharacteristic
149C2×C4C2×SD16×C12711yescharacteristic
150C2×C4C2×Q16×C12711yescharacteristic
151C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
152C8—22no—
153C8—81no—
154C8#125×C12712yes—
155C8#126×C12712yes—
156C22—22no—
157C22#476×C12711yescharacteristic
158C22#484×C12711yescharacteristic
159C22#490×C12711yescharacteristic
160C4—24no—
161C4—82no—
162C4—162no—
163C4#400×C12711yescharacteristic
164C4#477×C12711yescharacteristic
165C4#481×C12711yescharacteristic
166C4#487×C12711yescharacteristic
167C2—21no—
168C2—21no—
169C2C127×#210011yescharacteristic
170C2C127×#223012yes—
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
81. #13543C127direct (N × H)
91. C127#13543direct (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×#18442
C127×#13862
C127×#13832
C127×#13762
#13543127