Finite Group Databasebeta

← C127×#12465 #44576138

Subgroups — C127×#12465 #44576138

Order 32512.

196 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 70 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×#2244C211yesmaximal, characteristic, complemented
2C127×#2231C211yesmaximal, characteristic, complemented
3C127×#2213C211yesmaximal, characteristic
4C127×#2171C211yesmaximal, characteristic, complemented
5C127×#1369C211yesmaximal, characteristic, complemented
6C127×#1366C211yesmaximal, characteristic, complemented
7C127×#1357C211yesmaximal, characteristic, complemented
8#509×C127—21no—
9#504×C127—21no—
10#499×C127C2211yescharacteristic
11#493×C127C2211yescharacteristic
12#443×C127C2211yescharacteristic
13#365×C127—21no—
14#364×C127C2211yescharacteristic
15#364×C127C2211yescharacteristic
16#364×C127C2211yescharacteristic
17#361×C127—21no—
18#360×C127—21no—
19#357×C127—21no—
20#357×C127—21no—
21#350×C127—21no—
22#346×C127C2211yescharacteristic
23#135×C127D411yescharacteristic
24C2×D8×C127—21no—
25C2×D8×C127—21no—
26#131×C127—21no—
27#127×C127—21no—
28#125×C127—21no—
29SD32×C127—41no—
30D16×C127—41no—
31M32×C127—21no—
32M32×C127—21no—
33M32×C127—21no—
34M32×C127—41no—
35C2×C16×C127—41no—
36C2×C16×C127D411yescharacteristic
37C2×C16×C127D411yescharacteristic
38#108×C127D411yescharacteristic
39#107×C127—21no—
40#106×C127—21no—
41#104×C127—21no—
42C4×C8×C127C2311yescharacteristic
43#41×C127—21no—
44C2×D4×C127—41no—
45C2×D4×C127—81no—
46Q16×C127SD1611yescharacteristic
47SD16×C127—21no—
48D8×C127—41no—
49D8×C127—41no—
50D8×C127—41no—
51D8×C127—41no—
52D8×C127SD1611yescharacteristic
53M16×C127—21no—
54M16×C127—41no—
55C2×C8×C127—41no—
56C2×C8×C127C2×D411yescharacteristic
57C2×C8×C127C2×D411yescharacteristic
58C4⋊C4×C127—41no—
59C4⋊C4×C127—81no—
60C42×C127#4111yescharacteristic
61C16×C127—21no—
62C16×C127—21no—
63C16×C127—41no—
64C16×C127—41no—
65C16×C127—41no—
66C23×C127—81no—
67Q8×C127—21no—
68D4×C127—21no—
69D4×C127—41no—
70D4×C127—81no—
71D4×C127—81no—
72D4×C127—162no—
73C2×C4×C127—21no—
74C2×C4×C127—41no—
75C2×C4×C127—81no—
76C2×C4×C127#12111yescharacteristic
77C8×C127—41no—
78C8×C127C2×SD1611yescharacteristic
79C8×C127#13511yescharacteristic
80C8×C127#13511yescharacteristic
81C8×C127AGL(1,ℤ/8)11yescharacteristic
82C22×C127—41no—
83C22×C127—162no—
84C22×C127—161no—
85C22×C127#47211yescharacteristic
86C4×C127—41no—
87C4×C127—41no—
88C4×C127—161no—
89C4×C127#46311yescharacteristic
90C4×C127#46511yescharacteristic
91#12465C12711yesmaximal, characteristic, direct product factor, Sylow
92C2×C127—21no—
93C2×C127—81no—
94C2×C127—321no—
95C2×C127#167711yescharacteristic
96#2244C2×C12711yescharacteristic, complemented
97#2231C2×C12711yescharacteristic, complemented
98#2213C2×C12711yescharacteristic
99#2171C2×C12711yescharacteristic, complemented
100#1369C2×C12711yescharacteristic, complemented
101#1366C2×C12711yescharacteristic, complemented
102#1357C2×C12711yescharacteristic, complemented
103C127#1246511yescharacteristic, direct product factor, Sylow
104#509—21no—
105#504—21no—
106#499C22×C12711yescharacteristic
107#493C22×C12711yescharacteristic
108#443C22×C12711yescharacteristic
109#365—21no—
110#364C22×C12711yescharacteristic
111#364C22×C12711yescharacteristic
112#364C22×C12711yescharacteristic
113#361—21no—
114#360—21no—
115#357—21no—
116#357—21no—
117#350—21no—
118#346C22×C12711yescharacteristic
119#135D4×C12711yescharacteristic
120C2×D8—21no—
121C2×D8—21no—
122#131—21no—
123#127—21no—
124#125—21no—
125SD32—41no—
126D16—41no—
127M32—21no—
128M32—21no—
129M32—21no—
130M32—41no—
131C2×C16—41no—
132C2×C16D4×C12711yescharacteristic
133C2×C16D4×C12711yescharacteristic
134#108D4×C12711yescharacteristic
135#107—21no—
136#106—21no—
137#104—21no—
138C4×C8C23×C12711yescharacteristic
139#41—21no—
140C2×D4—41no—
141C2×D4—81no—
142Q16SD16×C12711yescharacteristic
143SD16—21no—
144D8—41no—
145D8—41no—
146D8—41no—
147D8—41no—
148D8SD16×C12711yescharacteristic
149M16—21no—
150M16—41no—
151C2×C8—41no—
152C2×C8C2×D4×C12711yescharacteristic
153C2×C8C2×D4×C12711yescharacteristic
154C4⋊C4—41no—
155C4⋊C4—81no—
156C42#41×C12711yescharacteristic
157C16—21no—
158C16—21no—
159C16—41no—
160C16—41no—
161C16—41no—
162C23—81no—
163Q8—21no—
164D4—21no—
165D4—41no—
166D4—81no—
167D4—81no—
168D4—162no—
169C2×C4—21no—
170C2×C4—41no—
171C2×C4—81no—
172C2×C4#121×C12711yescharacteristic
173C8—41no—
174C8C2×SD16×C12711yescharacteristic
175C8#135×C12711yescharacteristic
176C8#135×C12711yescharacteristic
177C8AGL(1,ℤ/8)×C12711yescharacteristic
178C22—41no—
179C22—162no—
180C22—161no—
181C22#472×C12711yescharacteristic
182C4—41no—
183C4—41no—
184C4—161no—
185C4#463×C12711yescharacteristic
186C4#465×C12711yescharacteristic
187C2—21no—
188C2—81no—
189C2—321no—
190C2C127×#167711yescharacteristic
subgroupG/H
center, socleC2×C127#1677
commutator, Frattini, cosocleC4×C8C23×C127
prime radicalC127×#2213C2
LCSG ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C127 ◁ C2×C4×C127 ◁ C4×C8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C127×#2244C2semidirect
2. C127×#2231C2semidirect
4. C127×#2171C2semidirect
5. C127×#1369C2semidirect
6. C127×#1366C2semidirect
7. C127×#1357C2semidirect
91. #12465C127direct (N × H)
96. #2244C2×C127semidirect
97. #2231C2×C127semidirect
99. #2171C2×C127semidirect
100. #1369C2×C127semidirect
101. #1366C2×C127semidirect
102. #1357C2×C127semidirect
103. C127#12465direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#22442
C127×#22312
C127×#22132
C127×#21712
C127×#13692
C127×#13662
C127×#13572
#12465127