Finite Group Databasebeta

← C127×#13458 #44577131

Subgroups — C127×#13458 #44577131

Order 32512.

324 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 122 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
1C2×#499×C127C211yesmaximal, characteristic
2C2×#365×C127C212yesmaximal
3C127×#1945C211yesmaximal, characteristic
4C127×#1386C212yesmaximal
5C127×#1376C211yesmaximal, characteristic
6C2×#125×C127—21no—
7C2×M32×C127C2212yes—
8#499×C127—24no—
9C2×#108×C127C2211yescharacteristic
10#427×C127C2211yescharacteristic
11C2×#107×C127—21no—
12C2×#106×C127C2212yes—
13#424×C127—21no—
14C2×C4×C8×C127C2211yescharacteristic
15#365×C127—24no—
16#339×C127—21no—
17C2×M16×C127—21no—
18C22×C8×C127D411yescharacteristic
19C22×C8×C127C2311yescharacteristic
20#125×C127—24no—
21#125×C127—42no—
22#117×C127—21no—
23C2×C4⋊C4×C127—22no—
24C2×C4⋊C4×C127—42no—
25C2×C42×C127D411yescharacteristic
26M32×C127—22no—
27M32×C127Q814yes—
28C2×C16×C127—22no—
29#108×C127—22no—
30#107×C127—24no—
31#107×C127Q812yes—
32#106×C127—22no—
33#106×C127—21no—
34#106×C127D414yes—
35C4⋊C8×C127—42no—
36C4×C8×C127—22no—
37C22×C4×C127—21no—
38C22×C4×C127—42no—
39C22×C4×C127C2×D411yescharacteristic
40M16×C127—41no—
41M16×C127—41no—
42C2×C8×C127—21no—
43C2×C8×C127—21no—
44C2×C8×C127—41no—
45C2×C8×C127SD1612yes—
46C2×C8×C127C2×D412yes—
47C2×C8×C127C2×Q812yes—
48C2×C8×C127C2×Q811yescharacteristic
49C2×C8×C127#4111yescharacteristic
50C4⋊C4×C127—24no—
51C4⋊C4×C127—22no—
52C4⋊C4×C127—48no—
53C4⋊C4×C127—42no—
54C22⋊C4×C127—41no—
55C42×C127—21no—
56C42×C127—41no—
57C42×C127SD1612yes—
58C16×C127—24no—
59C23×C127AGL(1,ℤ/8)11yescharacteristic
60C2×C4×C127—22no—
61C2×C4×C127—42no—
62C2×C4×C127—44no—
63C2×C4×C127—42no—
64C2×C4×C127—84no—
65C2×C4×C127#12011yescharacteristic
66C2×C4×C127C22⋊Q811yescharacteristic
67C2×C4×C127C4⋊Q811yescharacteristic
68C2×C4×C127C2×SD1611yescharacteristic
69C2×C4×C127C2×SD1611yescharacteristic
70C2×C4×C127#13711yescharacteristic
71C8×C127—22no—
72C8×C127—81no—
73C8×C127C22⋊Q812yes—
74C8×C127C4⋊Q812yes—
75C22×C127—22no—
76C22×C127#45011yescharacteristic
77C22×C127#47611yescharacteristic
78C22×C127#50111yescharacteristic
79C4×C127—42no—
80C4×C127—84no—
81C4×C127—82no—
82C4×C127#39511yescharacteristic
83C4×C127#44811yescharacteristic
84C4×C127#47511yescharacteristic
85C4×C127#49811yescharacteristic
86#13458C12711yesmaximal, characteristic, direct product factor, Sylow
87C2×C127—21no—
88C2×C127—21no—
89C2×C127#205811yescharacteristic
90C2×C127#223112yes—
91C2×#499C2×C12711yescharacteristic
92C2×#365C2×C12712yes—
93#1945C2×C12711yescharacteristic
94#1386C2×C12712yes—
95#1376C2×C12711yescharacteristic
96C127#1345811yescharacteristic, direct product factor, Sylow
97C2×#125—21no—
98C2×M32C22×C12712yes—
99#499—24no—
100C2×#108C22×C12711yescharacteristic
101#427C22×C12711yescharacteristic
102C2×#107—21no—
103C2×#106C22×C12712yes—
104#424—21no—
105C2×C4×C8C22×C12711yescharacteristic
106#365—24no—
107#339—21no—
108C2×M16—21no—
109C22×C8D4×C12711yescharacteristic
110C22×C8C23×C12711yescharacteristic
111#125—24no—
112#125—42no—
113#117—21no—
114C2×C4⋊C4—22no—
115C2×C4⋊C4—42no—
116C2×C42D4×C12711yescharacteristic
117M32—22no—
118M32Q8×C12714yes—
119C2×C16—22no—
120#108—22no—
121#107—24no—
122#107Q8×C12712yes—
123#106—22no—
124#106—21no—
125#106D4×C12714yes—
126C4⋊C8—42no—
127C4×C8—22no—
128C22×C4—21no—
129C22×C4—42no—
130C22×C4C2×D4×C12711yescharacteristic
131M16—41no—
132M16—41no—
133C2×C8—21no—
134C2×C8—21no—
135C2×C8—41no—
136C2×C8SD16×C12712yes—
137C2×C8C2×D4×C12712yes—
138C2×C8C2×Q8×C12712yes—
139C2×C8C2×Q8×C12711yescharacteristic
140C2×C8#41×C12711yescharacteristic
141C4⋊C4—24no—
142C4⋊C4—22no—
143C4⋊C4—48no—
144C4⋊C4—42no—
145C22⋊C4—41no—
146C42—21no—
147C42—41no—
148C42SD16×C12712yes—
149C16—24no—
150C23AGL(1,ℤ/8)×C12711yescharacteristic
151C2×C4—22no—
152C2×C4—42no—
153C2×C4—44no—
154C2×C4—42no—
155C2×C4—84no—
156C2×C4#120×C12711yescharacteristic
157C2×C4C22⋊Q8×C12711yescharacteristic
158C2×C4C4⋊Q8×C12711yescharacteristic
159C2×C4C2×SD16×C12711yescharacteristic
160C2×C4C2×SD16×C12711yescharacteristic
161C2×C4#137×C12711yescharacteristic
162C8—22no—
163C8—81no—
164C8C22⋊Q8×C12712yes—
165C8C4⋊Q8×C12712yes—
166C22—22no—
167C22#450×C12711yescharacteristic
168C22#476×C12711yescharacteristic
169C22#501×C12711yescharacteristic
170C4—42no—
171C4—84no—
172C4—82no—
173C4#395×C12711yescharacteristic
174C4#448×C12711yescharacteristic
175C4#475×C12711yescharacteristic
176C4#498×C12711yescharacteristic
177C2—21no—
178C2—21no—
179C2C127×#205811yescharacteristic
180C2C127×#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
86. #13458C127direct (N × H)
96. C127#13458direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#499×C1272
C2×#365×C1272
C127×#19452
C127×#13862
C127×#13762
#13458127