Finite Group Databasebeta

← C127×#14683 #44578356

Subgroups — C127×#14683 #44578356

Order 32512.

2286 conjugacy classes of subgroups; only the 606 normal subgroups are shown.

normal subgroups only

This group has 2286 conjugacy classes of subgroups — too many to draw. Only its 606 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
1C23×C42×C127C211yesmaximal, characteristic
2C2×#383×C127C212yesmaximal, complemented
3C127×#1434C216yesmaximal, complemented
4C127×C22⋊#95C216yesmaximal
5C24×C4×C127C2213yes—
6C22×C22⋊C4×C127C2214yes—
7C22×C42×C127—28no—
8C22×C42×C127C418yescomplemented
9C22×C42×C127C2213yes—
10C22×C42×C127C2211yescharacteristic
11#383×C127—28no—
12C2×#95×C127C22112yes—
13C2×#95×C127C22112yes—
14C25×C127C2311yescharacteristic
15C23×C4×C127—212no—
16C23×C4×C127—212no—
17C23×C4×C127—212no—
18C23×C4×C127C2×C4112yes—
19C23×C4×C127C2318yes—
20C23×C4×C127C2313yes—
21C23×C4×C127C2313yes—
22C2×C22⋊C4×C127—224no—
23C2×C42×C127—212no—
24C2×C42×C127—232no—
25C2×C42×C127C2×C4112yes—
26C2×C42×C127C2×C414yes—
27C2×C42×C127D418yes—
28#95×C127—224no—
29#95×C127—224no—
30C24×C127—22no—
31C24×C127—26no—
32C24×C127C22×C412yes—
33C24×C127#41112yes—
34C24×C127C2411yescharacteristic
35C22×C4×C127—296no—
36C22×C4×C127—224no—
37C22×C4×C127—26no—
38C22×C4×C127—26no—
39C22×C4×C127—26no—
40C22×C4×C127—26no—
41C22×C4×C127—224no—
42C22×C4×C127—224no—
43C22×C4×C127—28no—
44C22×C4×C127—224no—
45C22×C4×C127—224no—
46C22×C4×C127C22×C416yes—
47C22×C4×C127C22×C416yes—
48C22×C4×C127C2×D4112yes—
49C22×C4×C127#41112yes—
50C22⋊C4×C127—416no—
51C42×C127—224no—
52C42×C127C22⋊C4116yescomplemented
53C23×C127—22no—
54C23×C127—26no—
55C23×C127—224no—
56C23×C127—224no—
57C23×C127#117112yes—
58C23×C127#126116yes—
59C23×C127C23×C411yescharacteristic
60C23×C127C22×D412yes—
61C23×C127C2×#4116yes—
62C23×C127C2×#4116yes—
63C2×C4×C127—296no—
64C2×C4×C127—26no—
65C2×C4×C127—26no—
66C2×C4×C127—26no—
67C2×C4×C127—26no—
68C2×C4×C127—224no—
69C2×C4×C127—224no—
70C2×C4×C127—424no—
71C2×C4×C127—48no—
72C2×C4×C127—424no—
73C2×C4×C127C2×C22⋊C4112yes—
74C2×C4×C127#117112yes—
75C22×C127—232no—
76C22×C127—212no—
77C22×C127—212no—
78C22×C127#38318yescomplemented
79C22×C127C22×C22⋊C411yescharacteristic
80C22×C127C2×#11713yes—
81C22×C127C2×#11713yes—
82C22×C127#525112yes—
83C22×C127C2×#12614yes—
84C22×C127#529112yes—
85C4×C127—212no—
86C4×C127—212no—
87C4×C127—88no—
88#14683C12711yesmaximal, characteristic, direct product factor, Sylow
89C2×C127—28no—
90C2×C127#228013yes—
91C2×C127C2×#38311yescharacteristic
92C2×C127#228313yes—
93C2×C127#285218yes—
94C23×C42C2×C12711yescharacteristic
95C2×#383C2×C12712yescomplemented
96#1434C2×C12716yescomplemented
97C22⋊#95C2×C12716yes—
98C127#1468311yescharacteristic, direct product factor, Sylow
99C24×C4C22×C12713yes—
100C22×C22⋊C4C22×C12714yes—
101C22×C42—28no—
102C22×C42C4×C12718yescomplemented
103C22×C42C22×C12713yes—
104C22×C42C22×C12711yescharacteristic
105#383—28no—
106C2×#95C22×C127112yes—
107C2×#95C22×C127112yes—
108C25C23×C12711yescharacteristic
109C23×C4—212no—
110C23×C4—212no—
111C23×C4—212no—
112C23×C4C2×C4×C127112yes—
113C23×C4C23×C12718yes—
114C23×C4C23×C12713yes—
115C23×C4C23×C12713yes—
116C2×C22⋊C4—224no—
117C2×C42—212no—
118C2×C42—232no—
119C2×C42C2×C4×C127112yes—
120C2×C42C2×C4×C12714yes—
121C2×C42D4×C12718yes—
122#95—224no—
123#95—224no—
124C24—22no—
125C24—26no—
126C24C22×C4×C12712yes—
127C24#41×C127112yes—
128C24C24×C12711yescharacteristic
129C22×C4—296no—
130C22×C4—224no—
131C22×C4—26no—
132C22×C4—26no—
133C22×C4—26no—
134C22×C4—26no—
135C22×C4—224no—
136C22×C4—224no—
137C22×C4—28no—
138C22×C4—224no—
139C22×C4—224no—
140C22×C4C22×C4×C12716yes—
141C22×C4C22×C4×C12716yes—
142C22×C4C2×D4×C127112yes—
143C22×C4#41×C127112yes—
144C22⋊C4—416no—
145C42—224no—
146C42C22⋊C4×C127116yescomplemented
147C23—22no—
148C23—26no—
149C23—224no—
150C23—224no—
151C23#117×C127112yes—
152C23#126×C127116yes—
153C23C23×C4×C12711yescharacteristic
154C23C22×D4×C12712yes—
155C23C2×#41×C12716yes—
156C23C2×#41×C12716yes—
157C2×C4—296no—
158C2×C4—26no—
159C2×C4—26no—
160C2×C4—26no—
161C2×C4—26no—
162C2×C4—224no—
163C2×C4—224no—
164C2×C4—424no—
165C2×C4—48no—
166C2×C4—424no—
167C2×C4C2×C22⋊C4×C127112yes—
168C2×C4#117×C127112yes—
169C22—232no—
170C22—212no—
171C22—212no—
172C22#383×C12718yescomplemented
173C22C22×C22⋊C4×C12711yescharacteristic
174C22C2×#117×C12713yes—
175C22C2×#117×C12713yes—
176C22#525×C127112yes—
177C22C2×#126×C12714yes—
178C22#529×C127112yes—
179C4—212no—
180C4—212no—
181C4—88no—
182C2—28no—
183C2C127×#228013yes—
184C2C2×#383×C12711yescharacteristic
185C2C127×#228313yes—
186C2C127×#285218yes—
subgroupG/H
center, socleC24×C127C24
commutatorC23C23×C4×C127
Frattini, cosocleC24C24×C127
prime radicalC25×C127C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#383×C127C2semidirect
3. C127×#1434C2semidirect
8. C22×C42×C127C4semidirect
52. C42×C127C22⋊C4semidirect
78. C22×C127#383semidirect
88. #14683C127direct (N × H)
95. C2×#383C2×C127semidirect
96. #1434C2×C127semidirect
98. C127#14683direct (N × H)
102. C22×C42C4×C127semidirect
146. C42C22⋊C4×C127semidirect
172. C22#383×C127semidirect

Maximal subgroups

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

subgroupindex
C23×C42×C1272
C2×#383×C1272
C127×#14342
C127×C22⋊#952
#14683127