Finite Group Databasebeta

← C127×#14170 #44577843

Subgroups — C127×#14170 #44577843

Order 32512.

1494 conjugacy classes of subgroups; only the 494 normal subgroups are shown.

normal subgroups only

This group has 1494 conjugacy classes of subgroups — too many to draw. Only its 494 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
1C22×#125×C127C211yesmaximal, characteristic
2C2×#376×C127C212yesmaximal
3C127×#1445C214yesmaximal
4C127×#1436C218yesmaximal
5C2×#125×C127—28no—
6C2×#125×C127C418yescomplemented
7C22×C4⋊C4×C127C2214yes—
8C22×C4⋊C4×C127C2212yes—
9C22×C42×C127C2214yes—
10C22×C42×C127C2211yescharacteristic
11#376×C127—28no—
12C2×#95×C127C22116yes—
13C2×#95×C127C2214yes—
14C2×#95×C127C2214yes—
15C23×C4×C127C2314yes—
16C23×C4×C127C2318yes—
17C23×C4×C127C2312yes—
18C23×C4×C127C2311yescharacteristic
19#125×C127—232no—
20C2×C4⋊C4×C127—28no—
21C2×C4⋊C4×C127—24no—
22C2×C4⋊C4×C127—24no—
23C2×C4⋊C4×C127—28no—
24C2×C4⋊C4×C127C2×C4116yes—
25C2×C4⋊C4×C127C2×C418yes—
26C2×C42×C127—28no—
27C2×C42×C127—216no—
28C2×C42×C127C2×C414yes—
29C2×C42×C127D418yes—
30#95×C127—28no—
31#95×C127—28no—
32#95×C127—232no—
33C24×C127C2411yescharacteristic
34C22×C4×C127—28no—
35C22×C4×C127—24no—
36C22×C4×C127—28no—
37C22×C4×C127—24no—
38C22×C4×C127—24no—
39C22×C4×C127—216no—
40C22×C4×C127—216no—
41C22×C4×C127—28no—
42C22×C4×C127—216no—
43C22×C4×C127C22×C418yes—
44C22×C4×C127C22×C414yes—
45C22×C4×C127C22×C412yes—
46C22×C4×C127C2×D414yes—
47C22×C4×C127C2×D414yes—
48C22×C4×C127C2×D414yes—
49C22×C4×C127#41116yes—
50C4⋊C4×C127—216no—
51C4⋊C4×C127—232no—
52C42×C127—232no—
53C42×C127C22⋊C4116yes—
54C23×C127C23×C411yescharacteristic
55C23×C127C22×D412yes—
56C23×C127C2×#4118yes—
57C23×C1272−1+414yes—
58C2×C4×C127—28no—
59C2×C4×C127—24no—
60C2×C4×C127—28no—
61C2×C4×C127—28no—
62C2×C4×C127—28no—
63C2×C4×C127—28no—
64C2×C4×C127—216no—
65C2×C4×C127—216no—
66C2×C4×C127—232no—
67C2×C4×C127—48no—
68C2×C4×C127—48no—
69C2×C4×C127—48no—
70C2×C4×C127—48no—
71C2×C4×C127—416no—
72C2×C4×C127C2×C22⋊C414yes—
73C2×C4×C127C2×C22⋊C418yes—
74C22×C127C22×C22⋊C411yescharacteristic
75C22×C127C4×#4114yes—
76C22×C127#51912yes—
77C22×C127#52514yes—
78C22×C127#53214yes—
79C22×C127#53614yes—
80C22×C127#552116yes—
81C4×C127—24no—
82C4×C127—28no—
83C4×C127—416no—
84C4×C127—48no—
85#14170C12711yesmaximal, characteristic, direct product factor, Sylow
86C2×C127#229712yes—
87C2×C127#231011yescharacteristic
88C2×C127#237114yes—
89C2×C127#261118yes—
90C22×#125C2×C12711yescharacteristic
91C2×#376C2×C12712yes—
92#1445C2×C12714yes—
93#1436C2×C12718yes—
94C127#1417011yescharacteristic, direct product factor, Sylow
95C2×#125—28no—
96C2×#125C4×C12718yescomplemented
97C22×C4⋊C4C22×C12714yes—
98C22×C4⋊C4C22×C12712yes—
99C22×C42C22×C12714yes—
100C22×C42C22×C12711yescharacteristic
101#376—28no—
102C2×#95C22×C127116yes—
103C2×#95C22×C12714yes—
104C2×#95C22×C12714yes—
105C23×C4C23×C12714yes—
106C23×C4C23×C12718yes—
107C23×C4C23×C12711yescharacteristic
108C23×C4C23×C12712yes—
109#125—232no—
110C2×C4⋊C4—28no—
111C2×C4⋊C4—24no—
112C2×C4⋊C4—24no—
113C2×C4⋊C4—28no—
114C2×C4⋊C4C2×C4×C127116yes—
115C2×C4⋊C4C2×C4×C12718yes—
116C2×C42—28no—
117C2×C42—216no—
118C2×C42C2×C4×C12714yes—
119C2×C42D4×C12718yes—
120#95—28no—
121#95—28no—
122#95—232no—
123C24C24×C12711yescharacteristic
124C22×C4—28no—
125C22×C4—24no—
126C22×C4—28no—
127C22×C4—24no—
128C22×C4—24no—
129C22×C4—216no—
130C22×C4—216no—
131C22×C4—28no—
132C22×C4—216no—
133C22×C4C22×C4×C12718yes—
134C22×C4C22×C4×C12714yes—
135C22×C4C22×C4×C12712yes—
136C22×C4C2×D4×C12714yes—
137C22×C4C2×D4×C12714yes—
138C22×C4C2×D4×C12714yes—
139C22×C4#41×C127116yes—
140C4⋊C4—232no—
141C4⋊C4—216no—
142C42—232no—
143C42C22⋊C4×C127116yes—
144C23C23×C4×C12711yescharacteristic
145C23C22×D4×C12712yes—
146C23C2×#41×C12718yes—
147C232−1+4×C12714yes—
148C2×C4—28no—
149C2×C4—24no—
150C2×C4—28no—
151C2×C4—28no—
152C2×C4—28no—
153C2×C4—28no—
154C2×C4—216no—
155C2×C4—216no—
156C2×C4—232no—
157C2×C4—48no—
158C2×C4—48no—
159C2×C4—48no—
160C2×C4—48no—
161C2×C4—416no—
162C2×C4C2×C22⋊C4×C12718yes—
163C2×C4C2×C22⋊C4×C12714yes—
164C22C22×C22⋊C4×C12711yescharacteristic
165C22C4×#41×C12714yes—
166C22#519×C12712yes—
167C22#525×C12714yes—
168C22#532×C12714yes—
169C22#536×C12714yes—
170C22#552×C127116yes—
171C4—28no—
172C4—24no—
173C4—416no—
174C4—48no—
175C2C127×#229712yes—
176C2C127×#231011yescharacteristic
177C2C127×#237114yes—
178C2C127×#261118yes—
subgroupG/H
center, socle, prime radicalC24×C127C24
commutatorC23C23×C4×C127
Frattini, cosocleC24C24×C127
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
6. C2×#125×C127C4semidirect
85. #14170C127direct (N × H)
94. C127#14170direct (N × H)
96. C2×#125C4×C127semidirect

Maximal subgroups

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

subgroupindex
C22×#125×C1272
C2×#376×C1272
C127×#14452
C127×#14362
#14170127