Finite Group Databasebeta

← C127×#14168 #44577841

Subgroups — C127×#14168 #44577841

Order 32512.

1342 conjugacy classes of subgroups.

The subgroup lattice has 220 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#382×C127C211yesmaximal, characteristic
2C2×#376×C127C212yesmaximal
3C127×#1441C214yesmaximal
4C127×#1436C218yesmaximal
5C22×C4⋊C4×C127C2214yes—
6C22×C4⋊C4×C127C2212yes—
7C22×C42×C127C2214yes—
8C22×C42×C127C2211yescharacteristic
9#382×C127C418yescomplemented
10#376×C127—28no—
11C2×#95×C127C2218yes—
12C2×#95×C127C2214yes—
13C2×#95×C127C2214yes—
14C2×#95×C127C2214yes—
15C2×#95×C127C2214yes—
16C23×C4×C127C2314yes—
17C23×C4×C127C2318yes—
18C23×C4×C127C2312yes—
19C23×C4×C127C2311yescharacteristic
20C2×C4⋊C4×C127—216no—
21C2×C4⋊C4×C127—42no—
22C2×C4⋊C4×C127—42no—
23C2×C4⋊C4×C127—44no—
24C2×C4⋊C4×C127C2×C418yes—
25C2×C42×C127—28no—
26C2×C42×C127—216no—
27C2×C42×C127C2×C414yes—
28C2×C42×C127D414yes—
29C2×C42×C127Q814yes—
30#95×C127—28no—
31#95×C127—28no—
32#95×C127—216no—
33#95×C127—44no—
34#95×C127C2×C4116yes—
35C24×C127C2411yescharacteristic
36C22×C4×C127—28no—
37C22×C4×C127—22no—
38C22×C4×C127—22no—
39C22×C4×C127—28no—
40C22×C4×C127—28no—
41C22×C4×C127—28no—
42C22×C4×C127—28no—
43C22×C4×C127—28no—
44C22×C4×C127—28no—
45C22×C4×C127—24no—
46C22×C4×C127—28no—
47C22×C4×C127—24no—
48C22×C4×C127—28no—
49C22×C4×C127C22×C418yes—
50C22×C4×C127C22×C414yes—
51C22×C4×C127C22×C412yes—
52C22×C4×C127C2×D412yes—
53C22×C4×C127C2×D414yes—
54C22×C4×C127C2×Q814yes—
55C22×C4×C127C2×Q812yes—
56C22×C4×C127#41116yes—
57C4⋊C4×C127—48no—
58C4⋊C4×C127—416no—
59C42×C127—232no—
60C42×C127C4⋊C4116yescomplemented
61C23×C127C23×C411yescharacteristic
62C23×C127C22×D411yescharacteristic
63C23×C127C22×Q811yescharacteristic
64C23×C127C2×#4118yes—
65C23×C127H(5,𝔽2)12yes—
66C23×C1272−1+412yes—
67C2×C4×C127—28no—
68C2×C4×C127—22no—
69C2×C4×C127—22no—
70C2×C4×C127—28no—
71C2×C4×C127—28no—
72C2×C4×C127—24no—
73C2×C4×C127—24no—
74C2×C4×C127—216no—
75C2×C4×C127—28no—
76C2×C4×C127—216no—
77C2×C4×C127—216no—
78C2×C4×C127—216no—
79C2×C4×C127—48no—
80C2×C4×C127—48no—
81C2×C4×C127—44no—
82C2×C4×C127—44no—
83C2×C4×C127—48no—
84C2×C4×C127—48no—
85C2×C4×C127—48no—
86C2×C4×C127C2×C4⋊C414yes—
87C2×C4×C127C2×C4⋊C418yes—
88C22×C127C22×C4⋊C411yescharacteristic
89C22×C127C4×#4114yes—
90C22×C127#51811yescharacteristic
91C22×C127#51911yescharacteristic
92C22×C127#52514yes—
93C22×C127#53314yes—
94C22×C127#53712yes—
95C22×C127#54412yes—
96C22×C127#55114yes—
97C22×C127#55218yes—
98C22×C127#55514yes—
99C4×C127—24no—
100C4×C127—28no—
101C4×C127—416no—
102C4×C127—48no—
103#14168C12711yesmaximal, characteristic, direct product factor, Sylow
104C2×C127#229612yes—
105C2×C127#231611yescharacteristic
106C2×C127#237112yes—
107C2×C127#237212yes—
108C2×C127#260914yes—
109C2×C127#261214yes—
110C2×#382C2×C12711yescharacteristic
111C2×#376C2×C12712yes—
112#1441C2×C12714yes—
113#1436C2×C12718yes—
114C127#1416811yescharacteristic, direct product factor, Sylow
115C22×C4⋊C4C22×C12714yes—
116C22×C4⋊C4C22×C12712yes—
117C22×C42C22×C12714yes—
118C22×C42C22×C12711yescharacteristic
119#382C4×C12718yescomplemented
120#376—28no—
121C2×#95C22×C12718yes—
122C2×#95C22×C12714yes—
123C2×#95C22×C12714yes—
124C2×#95C22×C12714yes—
125C2×#95C22×C12714yes—
126C23×C4C23×C12714yes—
127C23×C4C23×C12718yes—
128C23×C4C23×C12711yescharacteristic
129C23×C4C23×C12712yes—
130C2×C4⋊C4—216no—
131C2×C4⋊C4—42no—
132C2×C4⋊C4—42no—
133C2×C4⋊C4—44no—
134C2×C4⋊C4C2×C4×C12718yes—
135C2×C42—28no—
136C2×C42—216no—
137C2×C42C2×C4×C12714yes—
138C2×C42D4×C12714yes—
139C2×C42Q8×C12714yes—
140#95—28no—
141#95—28no—
142#95—216no—
143#95—44no—
144#95C2×C4×C127116yes—
145C24C24×C12711yescharacteristic
146C22×C4—28no—
147C22×C4—22no—
148C22×C4—22no—
149C22×C4—28no—
150C22×C4—28no—
151C22×C4—28no—
152C22×C4—28no—
153C22×C4—28no—
154C22×C4—28no—
155C22×C4—24no—
156C22×C4—28no—
157C22×C4—24no—
158C22×C4—28no—
159C22×C4C22×C4×C12718yes—
160C22×C4C22×C4×C12714yes—
161C22×C4C22×C4×C12712yes—
162C22×C4C2×D4×C12712yes—
163C22×C4C2×D4×C12714yes—
164C22×C4C2×Q8×C12714yes—
165C22×C4C2×Q8×C12712yes—
166C22×C4#41×C127116yes—
167C4⋊C4—48no—
168C4⋊C4—416no—
169C42—232no—
170C42C4⋊C4×C127116yescomplemented
171C23C23×C4×C12711yescharacteristic
172C23C22×D4×C12711yescharacteristic
173C23C22×Q8×C12711yescharacteristic
174C23C2×#41×C12718yes—
175C23H(5,𝔽2)×C12712yes—
176C232−1+4×C12712yes—
177C2×C4—28no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—28no—
181C2×C4—28no—
182C2×C4—24no—
183C2×C4—24no—
184C2×C4—216no—
185C2×C4—28no—
186C2×C4—216no—
187C2×C4—216no—
188C2×C4—216no—
189C2×C4—48no—
190C2×C4—48no—
191C2×C4—44no—
192C2×C4—44no—
193C2×C4—48no—
194C2×C4—48no—
195C2×C4—48no—
196C2×C4C2×C4⋊C4×C12714yes—
197C2×C4C2×C4⋊C4×C12718yes—
198C22C22×C4⋊C4×C12711yescharacteristic
199C22C4×#41×C12714yes—
200C22#518×C12711yescharacteristic
201C22#519×C12711yescharacteristic
202C22#525×C12714yes—
203C22#533×C12714yes—
204C22#537×C12712yes—
205C22#544×C12712yes—
206C22#551×C12714yes—
207C22#552×C12718yes—
208C22#555×C12714yes—
209C4—24no—
210C4—28no—
211C4—416no—
212C4—48no—
213C2C127×#229612yes—
214C2C127×#231611yescharacteristic
215C2C127×#237112yes—
216C2C127×#237212yes—
217C2C127×#260914yes—
218C2C127×#261214yes—
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
9. #382×C127C4semidirect
60. C42×C127C4⋊C4semidirect
103. #14168C127direct (N × H)
114. C127#14168direct (N × H)
119. #382C4×C127semidirect
170. C42C4⋊C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#382×C1272
C2×#376×C1272
C127×#14412
C127×#14362
#14168127