Finite Group Databasebeta

← C127×#14673 #44578346

Subgroups — C127×#14673 #44578346

Order 32512.

2734 conjugacy classes of subgroups; only the 462 normal subgroups are shown.

normal subgroups only

This group has 2734 conjugacy classes of subgroups — too many to draw. Only its 462 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×#379×C127C212yesmaximal
2C2×#379×C127C211yesmaximal, characteristic
3C127×#1439C2112yesmaximal, complemented
4C26×C127C2211yescharacteristic
5C22×C4⋊C4×C127C2214yescomplemented
6C22×C22⋊C4×C127C22112yes—
7C22×C22⋊C4×C127C2216yes—
8#379×C127—28no—
9#379×C127C418yescomplemented
10C2×#95×C127C22112yescomplemented
11C25×C127—46no—
12C25×C127—46no—
13C25×C127C2×C414yes—
14C25×C127D414yes—
15C25×C127Q814yes—
16C25×C127C2313yes—
17C23×C4×C127C2318yes—
18C23×C4×C127C2314yes—
19C2×C4⋊C4×C127—412no—
20C2×C22⋊C4×C127—224no—
21C2×C22⋊C4×C127—46no—
22C2×C22⋊C4×C127—46no—
23C2×C22⋊C4×C127—412no—
24C2×C22⋊C4×C127—412no—
25C2×C22⋊C4×C127C2×C4124yes—
26#95×C127—412no—
27C24×C127—26no—
28C24×C127—26no—
29C24×C127—212no—
30C24×C127—212no—
31C24×C127—424no—
32C24×C127—424no—
33C24×C127—412no—
34C24×C127—412no—
35C24×C127—448no—
36C24×C127—416no—
37C24×C127C4⋊C4116yescomplemented
38C24×C127C22×C416yes—
39C24×C127C2×D416yes—
40C24×C127C2×Q816yes—
41C24×C127C2411yescharacteristic
42C22×C4×C127—212no—
43C22×C4×C127—212no—
44C22×C4×C127—28no—
45C22×C4×C127—224no—
46C22×C4×C127—224no—
47C22×C4×C127C22×C418yes—
48C4⋊C4×C127—416no—
49C22⋊C4×C127—424no—
50C22⋊C4×C127—448no—
51C23×C127—212no—
52C23×C127—224no—
53C23×C127—224no—
54C23×C127—212no—
55C23×C127—26no—
56C23×C127—212no—
57C23×C127—26no—
58C23×C127—212no—
59C23×C127—448no—
60C23×C127—416no—
61C23×C127—448no—
62C23×C127—464no—
63C23×C127—464no—
64C23×C127—424no—
65C23×C127—412no—
66C23×C127—412no—
67C23×C127C2×C4⋊C4112yes—
68C23×C127C23×C411yescharacteristic
69C23×C127C22×D411yescharacteristic
70C23×C127C22×Q811yescharacteristic
71C23×C127H(5,𝔽2)16yes—
72C23×C127H(5,𝔽2)16yes—
73C2×C4×C127—224no—
74C2×C4×C127—412no—
75C2×C4×C127—44no—
76C2×C4×C127—424no—
77C2×C4×C127—424no—
78C2×C4×C127—48no—
79C22×C127—212no—
80C22×C127—224no—
81C22×C127—464no—
82C22×C127—46no—
83C22×C127—46no—
84C22×C127—412no—
85C22×C127—424no—
86C22×C127—424no—
87C22×C127C22×C4⋊C411yescharacteristic
88C22×C127#51816yes—
89C22×C127#53416yes—
90C22×C127#54313yes—
91C22×C127#54313yes—
92C22×C127#560112yes—
93C22×C127H(3,𝔽4)14yes—
94C4×C127—48no—
95C4×C127—88no—
96#14673C12711yesmaximal, characteristic, direct product factor, Sylow
97C2×C127—412no—
98C2×C127#231513yes—
99C2×C127#237514yes—
100C2×C127#281214yes—
101C2×C127#284011yescharacteristic
102C2×C127#284213yes—
103C2×#379C2×C12712yes—
104C2×#379C2×C12711yescharacteristic
105#1439C2×C127112yescomplemented
106C127#1467311yescharacteristic, direct product factor, Sylow
107C26C22×C12711yescharacteristic
108C22×C4⋊C4C22×C12714yescomplemented
109C22×C22⋊C4C22×C127112yes—
110C22×C22⋊C4C22×C12716yes—
111#379—28no—
112#379C4×C12718yescomplemented
113C2×#95C22×C127112yescomplemented
114C25—46no—
115C25—46no—
116C25C2×C4×C12714yes—
117C25D4×C12714yes—
118C25Q8×C12714yes—
119C25C23×C12713yes—
120C23×C4C23×C12718yes—
121C23×C4C23×C12714yes—
122C2×C4⋊C4—412no—
123C2×C22⋊C4—224no—
124C2×C22⋊C4—46no—
125C2×C22⋊C4—46no—
126C2×C22⋊C4—412no—
127C2×C22⋊C4—412no—
128C2×C22⋊C4C2×C4×C127124yes—
129#95—412no—
130C24—26no—
131C24—26no—
132C24—212no—
133C24—212no—
134C24—424no—
135C24—424no—
136C24—412no—
137C24—412no—
138C24—448no—
139C24—416no—
140C24C4⋊C4×C127116yescomplemented
141C24C22×C4×C12716yes—
142C24C2×D4×C12716yes—
143C24C2×Q8×C12716yes—
144C24C24×C12711yescharacteristic
145C22×C4—212no—
146C22×C4—212no—
147C22×C4—28no—
148C22×C4—224no—
149C22×C4—224no—
150C22×C4C22×C4×C12718yes—
151C4⋊C4—416no—
152C22⋊C4—424no—
153C22⋊C4—448no—
154C23—212no—
155C23—224no—
156C23—224no—
157C23—212no—
158C23—26no—
159C23—212no—
160C23—26no—
161C23—212no—
162C23—448no—
163C23—416no—
164C23—448no—
165C23—464no—
166C23—464no—
167C23—424no—
168C23—412no—
169C23—412no—
170C23C2×C4⋊C4×C127112yes—
171C23C23×C4×C12711yescharacteristic
172C23C22×D4×C12711yescharacteristic
173C23C22×Q8×C12711yescharacteristic
174C23H(5,𝔽2)×C12716yes—
175C23H(5,𝔽2)×C12716yes—
176C2×C4—224no—
177C2×C4—412no—
178C2×C4—44no—
179C2×C4—424no—
180C2×C4—424no—
181C2×C4—48no—
182C22—212no—
183C22—224no—
184C22—464no—
185C22—46no—
186C22—46no—
187C22—412no—
188C22—424no—
189C22—424no—
190C22C22×C4⋊C4×C12711yescharacteristic
191C22#518×C12716yes—
192C22#534×C12716yes—
193C22#543×C12713yes—
194C22#543×C12713yes—
195C22#560×C127112yes—
196C22H(3,𝔽4)×C12714yes—
197C4—48no—
198C4—88no—
199C2—412no—
200C2C127×#231513yes—
201C2C127×#237514yes—
202C2C127×#281214yes—
203C2C127×#284011yescharacteristic
204C2C127×#284213yes—
subgroupG/H
center, socleC24×C127C24
commutatorC23C23×C4×C127
Frattini, cosocleC24C24×C127
prime radicalC26×C127C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
3. C127×#1439C2semidirect
5. C22×C4⋊C4×C127C22semidirect
9. #379×C127C4semidirect
10. C2×#95×C127C22semidirect
37. C24×C127C4⋊C4semidirect
96. #14673C127direct (N × H)
105. #1439C2×C127semidirect
106. C127#14673direct (N × H)
108. C22×C4⋊C4C22×C127semidirect
112. #379C4×C127semidirect
113. C2×#95C22×C127semidirect
140. C24C4⋊C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#379×C1272
C127×#14392
#14673127