Finite Group Databasebeta

← C127×#11518 #44575191

Subgroups — C127×#11518 #44575191

Order 32512.

446 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 446 conjugacy classes of subgroups — too many to draw. Only its 110 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
1C127×#2296C211yesmaximal, characteristic
2C127×#1464C212yesmaximal
3C127×#1326C214yesmaximal
4C2×#117×C127C411yescharacteristic
5C2×#117×C127C2211yescharacteristic
6C22×C42×C127C411yescharacteristic
7#432×C127—22no—
8#389×C127—22no—
9#385×C127C412yes—
10#385×C127C2212yes—
11C4×C4⋊C4×C127—22no—
12#324×C127—22no—
13#323×C127C2214yes—
14C23×C4×C127C2×C411yescharacteristic
15C23×C4×C127C2×C412yes—
16#117×C127—24no—
17#117×C127—42no—
18C2×C4⋊C4×C127—21no—
19C2×C4⋊C4×C127—22no—
20C2×C4⋊C4×C127—22no—
21C2×C4⋊C4×C127D412yes—
22C2×C22⋊C4×C127C2×C412yes—
23C2×C22⋊C4×C127C2×C411yescharacteristic
24C2×C22⋊C4×C127C2311yescharacteristic
25C2×C42×C127—21no—
26C2×C42×C127—21no—
27C2×C42×C127—21no—
28C2×C42×C127—42no—
29C2×C42×C127D412yes—
30C4⋊C8×C127—42no—
31C22⋊C8×C127—24no—
32#97×C127—42no—
33#95×C127—22no—
34#95×C127—22no—
35C24×C127C22×C411yescharacteristic
36C22×C4×C127—22no—
37C22×C4×C127—22no—
38C22×C4×C127—22no—
39C22×C4×C127—22no—
40C22×C4×C127—22no—
41C22×C4×C127—44no—
42C22×C4×C127—42no—
43C22×C4×C127C22⋊C411yescharacteristic
44C22×C4×C127C22⋊C412yes—
45C22×C4×C127C22⋊C411yescharacteristic
46C22×C4×C127C2×D412yes—
47C2×C8×C127—44no—
48C4⋊C4×C127—24no—
49C4⋊C4×C127—42no—
50C4⋊C4×C127—44no—
51C4⋊C4×C127—44no—
52C22⋊C4×C127—22no—
53C22⋊C4×C127—41no—
54C22⋊C4×C127—41no—
55C22⋊C4×C127M1614yes—
56C42×C127—24no—
57C42×C127—22no—
58C42×C127—22no—
59C42×C127—42no—
60C42×C127—42no—
61C23×C127—21no—
62C23×C127—21no—
63C23×C127—42no—
64C23×C127C2×C22⋊C411yescharacteristic
65C23×C127C2×M1612yes—
66C2×C4×C127—28no—
67C2×C4×C127—21no—
68C2×C4×C127—21no—
69C2×C4×C127—21no—
70C2×C4×C127—21no—
71C2×C4×C127—24no—
72C2×C4×C127—24no—
73C2×C4×C127—22no—
74C2×C4×C127—22no—
75C2×C4×C127—42no—
76C2×C4×C127—42no—
77C2×C4×C127—42no—
78C2×C4×C127—44no—
79C2×C4×C127—42no—
80C2×C4×C127—42no—
81C2×C4×C127—42no—
82C2×C4×C127—44no—
83C2×C4×C127#9912yes—
84C2×C4×C127#10112yes—
85C8×C127—84no—
86C22×C127—22no—
87C22×C127—22no—
88C22×C127—42no—
89C22×C127—42no—
90C22×C127—42no—
91C22×C127#40711yescharacteristic
92C22×C127C2×#9911yescharacteristic
93C22×C127C2×#10111yescharacteristic
94C4×C127—22no—
95C4×C127—22no—
96C4×C127—44no—
97C4×C127—42no—
98C4×C127—42no—
99C4×C127—44no—
100#11518C12711yesmaximal, characteristic, direct product factor, Sylow
101C2×C127—21no—
102C2×C127—21no—
103C2×C127—42no—
104C2×C127#146311yescharacteristic
105C2×C127#212012yes—
106#2296C2×C12711yescharacteristic
107#1464C2×C12712yes—
108#1326C2×C12714yes—
109C127#1151811yescharacteristic, direct product factor, Sylow
110C2×#117C4×C12711yescharacteristic
111C2×#117C22×C12711yescharacteristic
112C22×C42C4×C12711yescharacteristic
113#432—22no—
114#389—22no—
115#385C4×C12712yes—
116#385C22×C12712yes—
117C4×C4⋊C4—22no—
118#324—22no—
119#323C22×C12714yes—
120C23×C4C2×C4×C12711yescharacteristic
121C23×C4C2×C4×C12712yes—
122#117—24no—
123#117—42no—
124C2×C4⋊C4—21no—
125C2×C4⋊C4—22no—
126C2×C4⋊C4—22no—
127C2×C4⋊C4D4×C12712yes—
128C2×C22⋊C4C2×C4×C12712yes—
129C2×C22⋊C4C2×C4×C12711yescharacteristic
130C2×C22⋊C4C23×C12711yescharacteristic
131C2×C42—21no—
132C2×C42—21no—
133C2×C42—21no—
134C2×C42—42no—
135C2×C42D4×C12712yes—
136C4⋊C8—42no—
137C22⋊C8—24no—
138#97—42no—
139#95—22no—
140#95—22no—
141C24C22×C4×C12711yescharacteristic
142C22×C4—22no—
143C22×C4—22no—
144C22×C4—22no—
145C22×C4—22no—
146C22×C4—22no—
147C22×C4—44no—
148C22×C4—42no—
149C22×C4C22⋊C4×C12711yescharacteristic
150C22×C4C22⋊C4×C12711yescharacteristic
151C22×C4C22⋊C4×C12712yes—
152C22×C4C2×D4×C12712yes—
153C2×C8—44no—
154C4⋊C4—24no—
155C4⋊C4—42no—
156C4⋊C4—44no—
157C4⋊C4—44no—
158C22⋊C4—22no—
159C22⋊C4—41no—
160C22⋊C4—41no—
161C22⋊C4M16×C12714yes—
162C42—24no—
163C42—22no—
164C42—22no—
165C42—42no—
166C42—42no—
167C23—21no—
168C23—21no—
169C23—42no—
170C23C2×C22⋊C4×C12711yescharacteristic
171C23C2×M16×C12712yes—
172C2×C4—28no—
173C2×C4—21no—
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—24no—
178C2×C4—24no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—42no—
182C2×C4—42no—
183C2×C4—42no—
184C2×C4—44no—
185C2×C4—42no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—44no—
189C2×C4#99×C12712yes—
190C2×C4#101×C12712yes—
191C8—84no—
192C22—22no—
193C22—22no—
194C22—42no—
195C22—42no—
196C22—42no—
197C22#407×C12711yescharacteristic
198C22C2×#99×C12711yescharacteristic
199C22C2×#101×C12711yescharacteristic
200C4—22no—
201C4—22no—
202C4—44no—
203C4—42no—
204C4—44no—
205C4—42no—
206C2—21no—
207C2—21no—
208C2—42no—
209C2C127×#146311yescharacteristic
210C2C127×#212012yes—
subgroupG/H
center, socleC22×C127C2×#99
commutatorC24C22×C4×C127
Frattini, cosocleC2×C22⋊C4C23×C127
prime radicalC24×C127C22×C4
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C22×C4×C127 ◁ C2×#117×C127 ◁ G

Complements

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

NH ≅ G/Ntype
100. #11518C127direct (N × H)
109. C127#11518direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#22962
C127×#14642
C127×#13262
#11518127