Finite Group Databasebeta

← C2×C127×#1323 #44575115

Subgroups — C2×C127×#1323 #44575115

Order 32512.

394 conjugacy classes of subgroups; only the 158 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 158 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×#424×C127C211yesmaximal, characteristic
2C2×C22⋊C16×C127C212yesmaximal
3C127×#1323C214yesmaximal, direct product factor
4C22×M16×C127C411yescharacteristic
5C23×C8×C127C2211yescharacteristic
6C2×#117×C127C411yescharacteristic
7C22×C16×C127—22no—
8#424×C127—22no—
9#424×C127C412yes—
10#424×C127C2212yes—
11C2×C4⋊C8×C127—22no—
12C22⋊C16×C127—22no—
13C22⋊C16×C127C2214yes—
14C23×C4×C127C2×C411yescharacteristic
15C2×M16×C127—21no—
16C2×M16×C127—42no—
17C2×M16×C127C2×C412yes—
18C22×C8×C127—21no—
19C22×C8×C127—42no—
20C22×C8×C127C2×C411yescharacteristic
21C22×C8×C127D412yes—
22C22×C8×C127D412yes—
23C22×C8×C127C2311yescharacteristic
24#117×C127—21no—
25#117×C127—21no—
26#117×C127C812yes—
27#117×C127C2×C412yes—
28C2×C4⋊C4×C127C812yes—
29C2×C22⋊C4×C127—21no—
30C2×C42×C127—21no—
31C2×C16×C127—24no—
32C2×C16×C127—44no—
33C4⋊C8×C127—24no—
34C4⋊C8×C127—24no—
35C24×C127M1611yescharacteristic
36C22×C4×C127—22no—
37C22×C4×C127—22no—
38C22×C4×C127—22no—
39C22×C4×C127C22⋊C411yescharacteristic
40C22×C4×C127C22⋊C411yescharacteristic
41C22×C4×C127C2×C811yescharacteristic
42C22×C4×C127C2×C811yescharacteristic
43C22×C4×C127M1611yescharacteristic
44C22×C4×C127C22×C411yescharacteristic
45M16×C127—42no—
46M16×C127—42no—
47C2×C8×C127—24no—
48C2×C8×C127—22no—
49C2×C8×C127—41no—
50C2×C8×C127—42no—
51C2×C8×C127—41no—
52C2×C8×C127—42no—
53C2×C8×C127C22⋊C412yes—
54C2×C8×C127C2×D412yes—
55C4⋊C4×C127—22no—
56C4⋊C4×C127C2×C814yes—
57C22⋊C4×C127—22no—
58C22⋊C4×C127—22no—
59C42×C127—22no—
60C42×C127—22no—
61C16×C127—44no—
62C23×C127—22no—
63C23×C127—24no—
64C23×C127C22⋊C811yescharacteristic
65C23×C127C22⋊C811yescharacteristic
66C23×C127C2×M1611yescharacteristic
67C2×C4×C127—22no—
68C2×C4×C127—22no—
69C2×C4×C127—22no—
70C2×C4×C127—21no—
71C2×C4×C127—21no—
72C2×C4×C127—21no—
73C2×C4×C127—21no—
74C2×C4×C127—24no—
75C2×C4×C127—44no—
76C2×C4×C127C22⋊C811yescharacteristic
77C2×C4×C127C22⋊C811yescharacteristic
78C2×C4×C127#9912yes—
79C2×C4×C127#10112yes—
80C2×C4×C127C2×C22⋊C411yescharacteristic
81C2×C4×C127C22×C811yescharacteristic
82C8×C127—22no—
83C8×C127—22no—
84C8×C127—42no—
85C22×C127—22no—
86C22×C127—22no—
87C22×C127—21no—
88C22×C127—21no—
89C22×C127—44no—
90C22×C127#32412yes—
91C22×C127#35014yes—
92C22×C127C2×C22⋊C811yescharacteristic
93C4×C127—21no—
94C4×C127—21no—
95C4×C127—44no—
96C4×C127#32412yes—
97C4×C127C2×#9911yescharacteristic
98C4×C127C2×#10111yescharacteristic
99C2×#1323C12711yesmaximal, characteristic, direct product factor, Sylow
100C2×C127—41no—
101C2×C127—41no—
102C2×C127#132314yesdirect product factor
103C2×C127C2×#32411yescharacteristic
104C2×C127C2×#35012yes—
105C2×#424C2×C12711yescharacteristic
106C2×C22⋊C16C2×C12712yes—
107#1323C2×C12714yesdirect product factor
108C127C2×#132311yescharacteristic, direct product factor, Sylow
109C22×M16C4×C12711yescharacteristic
110C23×C8C22×C12711yescharacteristic
111C2×#117C4×C12711yescharacteristic
112C22×C16—22no—
113#424—22no—
114#424C4×C12712yes—
115#424C22×C12712yes—
116C2×C4⋊C8—22no—
117C22⋊C16—22no—
118C22⋊C16C22×C12714yes—
119C23×C4C2×C4×C12711yescharacteristic
120C2×M16—21no—
121C2×M16—42no—
122C2×M16C2×C4×C12712yes—
123C22×C8—21no—
124C22×C8—42no—
125C22×C8C2×C4×C12711yescharacteristic
126C22×C8D4×C12712yes—
127C22×C8D4×C12712yes—
128C22×C8C23×C12711yescharacteristic
129#117—21no—
130#117—21no—
131#117C8×C12712yes—
132#117C2×C4×C12712yes—
133C2×C4⋊C4C8×C12712yes—
134C2×C22⋊C4—21no—
135C2×C42—21no—
136C2×C16—24no—
137C2×C16—44no—
138C4⋊C8—24no—
139C4⋊C8—24no—
140C24M16×C12711yescharacteristic
141C22×C4—22no—
142C22×C4—22no—
143C22×C4—22no—
144C22×C4C22⋊C4×C12711yescharacteristic
145C22×C4C22⋊C4×C12711yescharacteristic
146C22×C4C2×C8×C12711yescharacteristic
147C22×C4C2×C8×C12711yescharacteristic
148C22×C4M16×C12711yescharacteristic
149C22×C4C22×C4×C12711yescharacteristic
150M16—42no—
151M16—42no—
152C2×C8—24no—
153C2×C8—22no—
154C2×C8—41no—
155C2×C8—42no—
156C2×C8—41no—
157C2×C8—42no—
158C2×C8C22⋊C4×C12712yes—
159C2×C8C2×D4×C12712yes—
160C4⋊C4—22no—
161C4⋊C4C2×C8×C12714yes—
162C22⋊C4—22no—
163C22⋊C4—22no—
164C42—22no—
165C42—22no—
166C16—44no—
167C23—22no—
168C23—24no—
169C23C22⋊C8×C12711yescharacteristic
170C23C22⋊C8×C12711yescharacteristic
171C23C2×M16×C12711yescharacteristic
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—24no—
180C2×C4—44no—
181C2×C4C22⋊C8×C12711yescharacteristic
182C2×C4C22⋊C8×C12711yescharacteristic
183C2×C4#99×C12712yes—
184C2×C4#101×C12712yes—
185C2×C4C2×C22⋊C4×C12711yescharacteristic
186C2×C4C22×C8×C12711yescharacteristic
187C8—22no—
188C8—22no—
189C8—42no—
190C22—22no—
191C22—22no—
192C22—21no—
193C22—21no—
194C22—44no—
195C22#324×C12712yes—
196C22#350×C12714yes—
197C22C2×C22⋊C8×C12711yescharacteristic
198C4—21no—
199C4—21no—
200C4—44no—
201C4#324×C12712yes—
202C4C2×#99×C12711yescharacteristic
203C4C2×#101×C12711yescharacteristic
204C2—41no—
205C2—41no—
206C2C127×#132314yesdirect product factor
207C2C2×#324×C12711yescharacteristic
208C2C2×#350×C12712yes—
subgroupG/H
centerC22×C4×C127C22⋊C4
commutatorC2×C4C22×C8×C127
Frattini, cosocleC22×C8C23×C127
socleC23×C127C22⋊C8
prime radicalC24×C127M16
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C4×C127 ◁ C23×C8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
3. C127×#1323C2direct (N × H)
99. C2×#1323C127direct (N × H)
102. C2×C127#1323direct (N × H)
107. #1323C2×C127direct (N × H)
108. C127C2×#1323direct (N × H)
206. C2C127×#1323direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#424×C1272
C2×C22⋊C16×C1272
C127×#13232
C2×#1323127