Finite Group Databasebeta

← C127×#19710 #44583383

Subgroups — C127×#19710 #44583383

Order 32512.

772 conjugacy classes of subgroups; only the 230 normal subgroups are shown.

normal subgroups only

This group has 772 conjugacy classes of subgroups — too many to draw. Only its 230 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×#3207C214yesmaximal, complemented
2C127×#3169C212yesmaximal, complemented
3C127×#1721C214yesmaximal, complemented
4C127×#1719C214yesmaximal, complemented
5C127×#1452C211yesmaximal, characteristic, complemented
6#532×C127C2214yes—
7#500×C127C2212yes—
8#493×C127C2212yes—
9#493×C127C2214yes—
10#492×C127C2214yes—
11#487×C127C2214yes—
12#486×C127C2214yes—
13#486×C127C2214yes—
14#466×C127—24no—
15#463×C127—28no—
16#449×C127—28no—
17C4×D8×C127—24no—
18#431×C127C2212yes—
19C2×C4×C8×C127C2211yescharacteristic
20#322×C127C2214yes—
21C2×#41×C127—24no—
22C2×SD16×C127—28no—
23C2×D8×C127—24no—
24C2×D8×C127—28no—
25C22×C8×C127D412yes—
26C4⋊Q8×C127C2314yes—
27#127×C127C2314yes—
28#124×C127—24no—
29#121×C127—24no—
30#121×C127—24no—
31C4×D4×C127—24no—
32C4×D4×C127—24no—
33C2×C42×C127C2311yescharacteristic
34#107×C127—24no—
35C4⋊C8×C127D414yes—
36#103×C127—28no—
37#102×C127—28no—
38#102×C127—28no—
39C22⋊C8×C127D414yes—
40C4×C8×C127D412yes—
41C4×C8×C127C2312yes—
42C4×C8×C127C2314yes—
43#41×C127—88no—
44C2×Q8×C127—24no—
45C2×D4×C127—24no—
46C2×D4×C127—24no—
47C2×D4×C127—24no—
48C2×D4×C127—44no—
49C22×C4×C127—44no—
50C22×C4×C127C2×D412yes—
51C22×C4×C127C2×D411yescharacteristic
52SD16×C127—88no—
53D8×C127—48no—
54D8×C127—88no—
55C2×C8×C127—42no—
56C2×C8×C127C2×D414yes—
57C2×C8×C127C2×D418yes—
58C4⋊C4×C127—24no—
59C4⋊C4×C127—24no—
60C22⋊C4×C127—44no—
61C22⋊C4×C127—44no—
62C42×C127C2×D411yescharacteristic
63C42×C127C2×D412yes—
64C42×C127C2411yescharacteristic
65C23×C127—44no—
66C23×C127#12711yescharacteristic
67Q8×C127—48no—
68D4×C127—48no—
69D4×C127—48no—
70D4×C127—48no—
71D4×C127—88no—
72C2×C4×C127—22no—
73C2×C4×C127—24no—
74C2×C4×C127—44no—
75C2×C4×C127—88no—
76C2×C4×C127#12711yescharacteristic
77C2×C4×C127#12712yes—
78C2×C4×C127C22×D411yescharacteristic
79C2×C4×C127C22×D412yes—
80C8×C127—24no—
81C8×C127—28no—
82C22×C127—21no—
83C22×C127—22no—
84C22×C127—84no—
85C22×C127—84no—
86C22×C127—84no—
87C22×C127C2×#12711yescharacteristic
88C4×C127—21no—
89C4×C127—22no—
90C4×C127—84no—
91C4×C127#57512yes—
92C4×C127#57614yes—
93#19710C12711yesmaximal, characteristic, direct product factor, Sylow
94C2×C127—41no—
95C2×C127—164no—
96C2×C127#315011yescharacteristic
97C2×C127#315512yes—
98#3207C2×C12714yescomplemented
99#3169C2×C12712yescomplemented
100#1721C2×C12714yescomplemented
101#1719C2×C12714yescomplemented
102#1452C2×C12711yescharacteristic, complemented
103C127#1971011yescharacteristic, direct product factor, Sylow
104#532C22×C12714yes—
105#500C22×C12712yes—
106#493C22×C12712yes—
107#493C22×C12714yes—
108#492C22×C12714yes—
109#487C22×C12714yes—
110#486C22×C12714yes—
111#486C22×C12714yes—
112#466—24no—
113#463—28no—
114#449—28no—
115C4×D8—24no—
116#431C22×C12712yes—
117C2×C4×C8C22×C12711yescharacteristic
118#322C22×C12714yes—
119C2×#41—24no—
120C2×SD16—28no—
121C2×D8—24no—
122C2×D8—28no—
123C22×C8D4×C12712yes—
124C4⋊Q8C23×C12714yes—
125#127C23×C12714yes—
126#124—24no—
127#121—24no—
128#121—24no—
129C4×D4—24no—
130C4×D4—24no—
131C2×C42C23×C12711yescharacteristic
132#107—24no—
133C4⋊C8D4×C12714yes—
134#103—28no—
135#102—28no—
136#102—28no—
137C22⋊C8D4×C12714yes—
138C4×C8D4×C12712yes—
139C4×C8C23×C12712yes—
140C4×C8C23×C12714yes—
141#41—88no—
142C2×Q8—24no—
143C2×D4—24no—
144C2×D4—24no—
145C2×D4—24no—
146C2×D4—44no—
147C22×C4—44no—
148C22×C4C2×D4×C12712yes—
149C22×C4C2×D4×C12711yescharacteristic
150SD16—88no—
151D8—48no—
152D8—88no—
153C2×C8—42no—
154C2×C8C2×D4×C12714yes—
155C2×C8C2×D4×C12718yes—
156C4⋊C4—24no—
157C4⋊C4—24no—
158C22⋊C4—44no—
159C22⋊C4—44no—
160C42C2×D4×C12711yescharacteristic
161C42C2×D4×C12712yes—
162C42C24×C12711yescharacteristic
163C23—44no—
164C23#127×C12711yescharacteristic
165Q8—48no—
166D4—48no—
167D4—48no—
168D4—48no—
169D4—88no—
170C2×C4—22no—
171C2×C4—24no—
172C2×C4—44no—
173C2×C4—88no—
174C2×C4#127×C12711yescharacteristic
175C2×C4#127×C12712yes—
176C2×C4C22×D4×C12711yescharacteristic
177C2×C4C22×D4×C12712yes—
178C8—24no—
179C8—28no—
180C22—21no—
181C22—22no—
182C22—84no—
183C22—84no—
184C22—84no—
185C22C2×#127×C12711yescharacteristic
186C4—21no—
187C4—22no—
188C4—84no—
189C4#575×C12712yes—
190C4#576×C12714yes—
191C2—41no—
192C2—164no—
193C2C127×#315011yescharacteristic
194C2C127×#315512yes—
subgroupG/H
center, socleC22×C127C2×#127
commutator, Frattini, cosocleC42C24×C127
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C127×#3207C2semidirect
2. C127×#3169C2semidirect
3. C127×#1721C2semidirect
4. C127×#1719C2semidirect
5. C127×#1452C2semidirect
93. #19710C127direct (N × H)
98. #3207C2×C127semidirect
99. #3169C2×C127semidirect
100. #1721C2×C127semidirect
101. #1719C2×C127semidirect
102. #1452C2×C127semidirect
103. C127#19710direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#32072
C127×#31692
C127×#17212
C127×#17192
C127×#14522
#19710127