Finite Group Databasebeta

← C127×#20579 #44584252

Subgroups — C127×#20579 #44584252

Order 32512.

5990 conjugacy classes of subgroups; only the 750 normal subgroups are shown.

normal subgroups only

This group has 5990 conjugacy classes of subgroups — too many to draw. Only its 750 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
1C25×C4×C127C211yesmaximal, characteristic
2C2×#407×C127C216yesmaximal, complemented
3C127×#1779C218yesmaximal, complemented
4C26×C127C411yescharacteristic
5C24×C4×C127—224no—
6C24×C4×C127C413yes—
7C24×C4×C127C414yes—
8C24×C4×C127C2214yes—
9C24×C4×C127C2213yes—
10C22×M16×C127C2214yescomplemented
11#407×C127—224no—
12C2×C22⋊C8×C127C22124yescomplemented
13C25×C127—212no—
14C25×C127—216no—
15C25×C127C2×C413yes—
16C25×C127C2×C414yes—
17C23×C4×C127—2128no—
18C23×C4×C127—212no—
19C23×C4×C127—224no—
20C23×C4×C127—248no—
21C23×C4×C127—248no—
22C23×C4×C127—224no—
23C23×C4×C127C2×C4112yes—
24C23×C4×C127C2×C413yes—
25C23×C4×C127C2×C416yes—
26C23×C4×C127D4124yes—
27C23×C4×C127C2316yes—
28C23×C4×C127C2311yescharacteristic
29C2×M16×C127—224no—
30C22×C8×C127C2318yescomplemented
31C22⋊C8×C127—248no—
32C24×C127—232no—
33C24×C127—2192no—
34C24×C127—224no—
35C24×C127—212no—
36C24×C127—224no—
37C24×C127—224no—
38C24×C127C22⋊C4112yes—
39C24×C127M16116yescomplemented
40C24×C127C22×C411yescharacteristic
41C24×C127C22×C416yes—
42C22×C4×C127—296no—
43C22×C4×C127—2128no—
44C22×C4×C127—2128no—
45C22×C4×C127—224no—
46C22×C4×C127—212no—
47C22×C4×C127—248no—
48C22×C4×C127—224no—
49C22×C4×C127—296no—
50C22×C4×C127—224no—
51C22×C4×C127C22⋊C4112yes—
52C22×C4×C127C22⋊C4124yes—
53C22×C4×C127C22×C416yes—
54C22×C4×C127C22×C411yescharacteristic
55C22×C4×C127C2×D4124yes—
56C22×C4×C127C2×D4112yes—
57C22×C4×C127C2411yescharacteristic
58M16×C127—416no—
59C2×C8×C127—224no—
60C23×C127—232no—
61C23×C127—2256no—
62C23×C127—296no—
63C23×C127—296no—
64C23×C127—212no—
65C23×C127—24no—
66C23×C127—212no—
67C23×C127—224no—
68C23×C127—248no—
69C23×C127—296no—
70C23×C127C2×C22⋊C416yes—
71C23×C127C2×C22⋊C4112yes—
72C23×C127C2×M16124yes—
73C23×C127C23×C411yescharacteristic
74C2×C4×C127—296no—
75C2×C4×C127—212no—
76C2×C4×C127—224no—
77C2×C4×C127—248no—
78C2×C4×C127—248no—
79C2×C4×C127C2×C22⋊C4112yes—
80C2×C4×C127C2×C22⋊C416yes—
81C2×C4×C127#120116yes—
82C2×C4×C127C22×D416yes—
83C8×C127—48no—
84C22×C127—296no—
85C22×C127—2128no—
86C22×C127—212no—
87C22×C127—212no—
88C22×C127—248no—
89C22×C127—212no—
90C22×C127#37914yes—
91C22×C127#407124yescomplemented
92C22×C127C22×C22⋊C413yes—
93C22×C127C22×M1614yes—
94C4×C127—212no—
95C4×C127#37914yes—
96C4×C127C2×#12014yes—
97#20579C12711yesmaximal, characteristic, direct product factor, Sylow
98C2×C127—24no—
99C2×C127—224no—
100C2×C127C2×#37911yescharacteristic
101C2×C127C2×#40716yes—
102C25×C4C2×C12711yescharacteristic
103C2×#407C2×C12716yescomplemented
104#1779C2×C12718yescomplemented
105C127#2057911yescharacteristic, direct product factor, Sylow
106C26C4×C12711yescharacteristic
107C24×C4—224no—
108C24×C4C4×C12713yes—
109C24×C4C4×C12714yes—
110C24×C4C22×C12714yes—
111C24×C4C22×C12713yes—
112C22×M16C22×C12714yescomplemented
113#407—224no—
114C2×C22⋊C8C22×C127124yescomplemented
115C25—212no—
116C25—216no—
117C25C2×C4×C12713yes—
118C25C2×C4×C12714yes—
119C23×C4—2128no—
120C23×C4—212no—
121C23×C4—224no—
122C23×C4—248no—
123C23×C4—248no—
124C23×C4—224no—
125C23×C4C2×C4×C127112yes—
126C23×C4C2×C4×C12713yes—
127C23×C4C2×C4×C12716yes—
128C23×C4D4×C127124yes—
129C23×C4C23×C12716yes—
130C23×C4C23×C12711yescharacteristic
131C2×M16—224no—
132C22×C8C23×C12718yescomplemented
133C22⋊C8—248no—
134C24—232no—
135C24—2192no—
136C24—224no—
137C24—212no—
138C24—224no—
139C24—224no—
140C24C22⋊C4×C127112yes—
141C24M16×C127116yescomplemented
142C24C22×C4×C12711yescharacteristic
143C24C22×C4×C12716yes—
144C22×C4—296no—
145C22×C4—2128no—
146C22×C4—2128no—
147C22×C4—224no—
148C22×C4—212no—
149C22×C4—248no—
150C22×C4—224no—
151C22×C4—296no—
152C22×C4—224no—
153C22×C4C22⋊C4×C127112yes—
154C22×C4C22⋊C4×C127124yes—
155C22×C4C22×C4×C12716yes—
156C22×C4C22×C4×C12711yescharacteristic
157C22×C4C2×D4×C127124yes—
158C22×C4C2×D4×C127112yes—
159C22×C4C24×C12711yescharacteristic
160M16—416no—
161C2×C8—224no—
162C23—232no—
163C23—2256no—
164C23—296no—
165C23—296no—
166C23—212no—
167C23—24no—
168C23—212no—
169C23—224no—
170C23—248no—
171C23—296no—
172C23C2×C22⋊C4×C12716yes—
173C23C2×C22⋊C4×C127112yes—
174C23C2×M16×C127124yes—
175C23C23×C4×C12711yescharacteristic
176C2×C4—296no—
177C2×C4—212no—
178C2×C4—224no—
179C2×C4—248no—
180C2×C4—248no—
181C2×C4C2×C22⋊C4×C127112yes—
182C2×C4C2×C22⋊C4×C12716yes—
183C2×C4#120×C127116yes—
184C2×C4C22×D4×C12716yes—
185C8—48no—
186C22—296no—
187C22—2128no—
188C22—212no—
189C22—212no—
190C22—248no—
191C22—212no—
192C22#379×C12714yes—
193C22#407×C127124yescomplemented
194C22C22×C22⋊C4×C12713yes—
195C22C22×M16×C12714yes—
196C4—212no—
197C4#379×C12714yes—
198C4C2×#120×C12714yes—
199C2—24no—
200C2—224no—
201C2C2×#379×C12711yescharacteristic
202C2C2×#407×C12716yes—
subgroupG/H
centerC22×C4×C127C24
commutatorC23C23×C4×C127
Frattini, cosocleC22×C4C24×C127
socleC23×C127C23×C4
prime radicalC26×C127C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#407×C127C2semidirect
3. C127×#1779C2semidirect
10. C22×M16×C127C22semidirect
12. C2×C22⋊C8×C127C22semidirect
30. C22×C8×C127C23semidirect
39. C24×C127M16semidirect
91. C22×C127#407semidirect
97. #20579C127direct (N × H)
103. C2×#407C2×C127semidirect
104. #1779C2×C127semidirect
105. C127#20579direct (N × H)
112. C22×M16C22×C127semidirect
114. C2×C22⋊C8C22×C127semidirect
132. C22×C8C23×C127semidirect
141. C24M16×C127semidirect
193. C22#407×C127semidirect

Maximal subgroups

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

subgroupindex
C25×C4×C1272
C2×#407×C1272
C127×#17792
#20579127