Finite Group Databasebeta

← C127×#13464 #44577137

Subgroups — C127×#13464 #44577137

Order 32512.

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

normal subgroups only

This group has 416 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×#2811C211yesmaximal, characteristic
2C127×#1857C213yesmaximal
3C127×#1394C213yesmaximal
4#519×C127C2211yescharacteristic
5#428×C127—23no—
6C2×#101×C127C2213yes—
7#395×C127—23no—
8#391×C127—23no—
9#391×C127C2213yes—
10#339×C127—23no—
11C22×Q8×C127—21no—
12C22×Q8×C127—21no—
13C22×Q8×C127C2311yescharacteristic
14C2×M16×C127—23no—
15C4×Q8×C127—41no—
16C4×Q8×C127—41no—
17#117×C127—23no—
18C2×C4⋊C4×C127—23no—
19C2×C4⋊C4×C127D413yes—
20C2×C42×C127D413yes—
21#107×C127—43no—
22#106×C127—43no—
23#101×C127—23no—
24#101×C127Q816yescomplemented
25#95×C127—23no—
26#95×C127—26no—
27C2×Q8×C127—24no—
28C2×Q8×C127—41no—
29C2×Q8×C127—41no—
30C2×Q8×C127—81no—
31C2×Q8×C127—81no—
32C2×Q8×C127—82no—
33C2×Q8×C127—81no—
34C2×Q8×C127C2×Q813yes—
35C2×Q8×C127#4111yescharacteristic
36C22×C4×C127—23no—
37C22×C4×C127—23no—
38C22×C4×C127C2×D413yes—
39M16×C127—26no—
40M16×C127—43no—
41C2×C8×C127—43no—
42C4⋊C4×C127—23no—
43C4⋊C4×C127—23no—
44C4⋊C4×C127—43no—
45C4⋊C4×C127—83no—
46C22⋊C4×C127—41no—
47C42×C127—43no—
48C42×C127—43no—
49C23×C127#12011yescharacteristic
50Q8×C127—43no—
51Q8×C127—41no—
52Q8×C127—84no—
53Q8×C127—84no—
54C2×C4×C127—23no—
55C2×C4×C127—23no—
56C2×C4×C127—26no—
57C2×C4×C127—43no—
58C2×C4×C127—43no—
59C2×C4×C127—46no—
60C2×C4×C127—41no—
61C2×C4×C127—41no—
62C2×C4×C127—43no—
63C2×C4×C127C22⋊Q813yes—
64C2×C4×C127C4⋊Q813yes—
65C8×C127—46no—
66C22×C127—21no—
67C22×C127—21no—
68C22×C127#39511yescharacteristic
69C22×C127B(4,𝔽2)11yescharacteristic
70C22×C127#45811yescharacteristic
71C4×C127—23no—
72C4×C127—23no—
73C4×C127—46no—
74C4×C127—81no—
75C4×C127—83no—
76C4×C127—81no—
77#13464C12711yesmaximal, characteristic, direct product factor, Sylow
78C2×C127—21no—
79C2×C127—21no—
80C2×C127#206211yescharacteristic
81C2×C127#220211yescharacteristic
82C2×C127#220511yescharacteristic
83#2811C2×C12711yescharacteristic
84#1857C2×C12713yes—
85#1394C2×C12713yes—
86C127#1346411yescharacteristic, direct product factor, Sylow
87#519C22×C12711yescharacteristic
88#428—23no—
89C2×#101C22×C12713yes—
90#395—23no—
91#391—23no—
92#391C22×C12713yes—
93#339—23no—
94C22×Q8—21no—
95C22×Q8—21no—
96C22×Q8C23×C12711yescharacteristic
97C2×M16—23no—
98C4×Q8—41no—
99C4×Q8—41no—
100#117—23no—
101C2×C4⋊C4—23no—
102C2×C4⋊C4D4×C12713yes—
103C2×C42D4×C12713yes—
104#107—43no—
105#106—43no—
106#101—23no—
107#101Q8×C12716yescomplemented
108#95—23no—
109#95—26no—
110C2×Q8—24no—
111C2×Q8—41no—
112C2×Q8—41no—
113C2×Q8—81no—
114C2×Q8—81no—
115C2×Q8—82no—
116C2×Q8—81no—
117C2×Q8C2×Q8×C12713yes—
118C2×Q8#41×C12711yescharacteristic
119C22×C4—23no—
120C22×C4—23no—
121C22×C4C2×D4×C12713yes—
122M16—26no—
123M16—43no—
124C2×C8—43no—
125C4⋊C4—23no—
126C4⋊C4—23no—
127C4⋊C4—43no—
128C4⋊C4—83no—
129C22⋊C4—41no—
130C42—43no—
131C42—43no—
132C23#120×C12711yescharacteristic
133Q8—43no—
134Q8—41no—
135Q8—84no—
136Q8—84no—
137C2×C4—23no—
138C2×C4—23no—
139C2×C4—26no—
140C2×C4—43no—
141C2×C4—43no—
142C2×C4—46no—
143C2×C4—41no—
144C2×C4—41no—
145C2×C4—43no—
146C2×C4C22⋊Q8×C12713yes—
147C2×C4C4⋊Q8×C12713yes—
148C8—46no—
149C22—21no—
150C22—21no—
151C22#395×C12711yescharacteristic
152C22B(4,𝔽2)×C12711yescharacteristic
153C22#458×C12711yescharacteristic
154C4—23no—
155C4—23no—
156C4—46no—
157C4—83no—
158C4—81no—
159C4—81no—
160C2—21no—
161C2—21no—
162C2C127×#206211yescharacteristic
163C2C127×#220211yescharacteristic
164C2C127×#220511yescharacteristic
subgroupG/H
center, socleC22×C127B(4,𝔽2)
commutator, Frattini, cosocleC22×Q8C23×C127
prime radicalC23×C127#120
LCSG ▷ C22×Q8 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C23×C127 ◁ C22×Q8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
24. #101×C127Q8semidirect
77. #13464C127direct (N × H)
86. C127#13464direct (N × H)
107. #101Q8×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#28112
C127×#18572
C127×#13942
#13464127