Finite Group Databasebeta

← C127×#11523 #44575196

Subgroups — C127×#11523 #44575196

Order 32512.

280 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 98 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×#2923C211yesmaximal, characteristic
2C127×#2165C212yesmaximal, complemented
3C127×#1328C212yesmaximal, complemented
4C127×#1321C212yesmaximal
5C4×#41×C127C411yescharacteristic
6#433×C127—22no—
7#432×C127—22no—
8#424×C127C411yescharacteristic
9#424×C127C2211yescharacteristic
10#408×C127C411yescharacteristic
11#408×C127C2211yescharacteristic
12C4×M16×C127C2211yescharacteristic
13C2×#97×C127C411yescharacteristic
14#364×C127—22no—
15#349×C127C2214yes—
16#347×C127—22no—
17C2×#41×C127C2×C411yescharacteristic
18C2×M16×C127C2×C411yescharacteristic
19C2×M16×C127C2311yescharacteristic
20C22×C8×C127C2×C411yescharacteristic
21C22×C8×C127C2×C411yescharacteristic
22C4×Q8×C127—21no—
23C4×D4×C127—21no—
24C4×D4×C127—22no—
25#117×C127—21no—
26#117×C127C2×C411yescharacteristic
27C2×C42×C127—21no—
28C2×C42×C127C2×C411yescharacteristic
29M32×C127—24no—
30C4⋊C8×C127—22no—
31C4⋊C8×C127—22no—
32C22⋊C8×C127—22no—
33C22⋊C8×C127—22no—
34#97×C127—21no—
35#97×C127—21no—
36#97×C127D412yes—
37C4×C8×C127D412yes—
38#41×C127—41no—
39#41×C127—41no—
40C2×Q8×C127M1611yescharacteristic
41C2×D4×C127—21no—
42C2×D4×C127M1611yescharacteristic
43C22×C4×C127—22no—
44C22×C4×C127—21no—
45C22×C4×C127—21no—
46C22×C4×C127C22×C411yescharacteristic
47M16×C127—41no—
48M16×C127—41no—
49C2×C8×C127—21no—
50C2×C8×C127—21no—
51C2×C8×C127—41no—
52C2×C8×C127—41no—
53C2×C8×C127C22⋊C412yes—
54C2×C8×C127C2×D412yes—
55C4⋊C4×C127—22no—
56C4⋊C4×C127—21no—
57C22⋊C4×C127—22no—
58C22⋊C4×C127M1612yes—
59C42×C127—22no—
60C42×C127—21no—
61C42×C127—21no—
62C42×C127C22⋊C411yescharacteristic
63C42×C127C22⋊C411yescharacteristic
64C16×C127—44no—
65C23×C127—21no—
66C23×C127C2×M1611yescharacteristic
67Q8×C127—41no—
68D4×C127—41no—
69D4×C127—42no—
70C2×C4×C127—21no—
71C2×C4×C127—21no—
72C2×C4×C127—21no—
73C2×C4×C127—22no—
74C2×C4×C127—21no—
75C2×C4×C127—21no—
76C2×C4×C127—41no—
77C2×C4×C127—41no—
78C2×C4×C127—81no—
79C2×C4×C127—82no—
80C2×C4×C127C2×C22⋊C411yescharacteristic
81C2×C4×C127C2×M1611yescharacteristic
82C8×C127—22no—
83C8×C127—22no—
84C8×C127—41no—
85C8×C127—41no—
86C22×C127—21no—
87C22×C127—41no—
88C22×C127—42no—
89C22×C127—41no—
90C22×C127#40711yescharacteristic
91C4×C127—21no—
92C4×C127—42no—
93C4×C127—41no—
94C4×C127—41no—
95C4×C127—41no—
96C4×C127#41011yescharacteristic
97C4×C127#41311yescharacteristic
98#11523C12711yesmaximal, characteristic, direct product factor, Sylow
99C2×C127—21no—
100C2×C127—41no—
101C2×C127—81no—
102C2×C127#146411yescharacteristic
103#2923C2×C12711yescharacteristic
104#2165C2×C12712yescomplemented
105#1328C2×C12712yescomplemented
106#1321C2×C12712yes—
107C127#1152311yescharacteristic, direct product factor, Sylow
108C4×#41C4×C12711yescharacteristic
109#433—22no—
110#432—22no—
111#424C4×C12711yescharacteristic
112#424C22×C12711yescharacteristic
113#408C4×C12711yescharacteristic
114#408C22×C12711yescharacteristic
115C4×M16C22×C12711yescharacteristic
116C2×#97C4×C12711yescharacteristic
117#364—22no—
118#349C22×C12714yes—
119#347—22no—
120C2×#41C2×C4×C12711yescharacteristic
121C2×M16C2×C4×C12711yescharacteristic
122C2×M16C23×C12711yescharacteristic
123C22×C8C2×C4×C12711yescharacteristic
124C22×C8C2×C4×C12711yescharacteristic
125C4×Q8—21no—
126C4×D4—21no—
127C4×D4—22no—
128#117—21no—
129#117C2×C4×C12711yescharacteristic
130C2×C42—21no—
131C2×C42C2×C4×C12711yescharacteristic
132M32—24no—
133C4⋊C8—22no—
134C4⋊C8—22no—
135C22⋊C8—22no—
136C22⋊C8—22no—
137#97—21no—
138#97—21no—
139#97D4×C12712yes—
140C4×C8D4×C12712yes—
141#41—41no—
142#41—41no—
143C2×Q8M16×C12711yescharacteristic
144C2×D4—21no—
145C2×D4M16×C12711yescharacteristic
146C22×C4—22no—
147C22×C4—21no—
148C22×C4—21no—
149C22×C4C22×C4×C12711yescharacteristic
150M16—41no—
151M16—41no—
152C2×C8—21no—
153C2×C8—21no—
154C2×C8—41no—
155C2×C8—41no—
156C2×C8C22⋊C4×C12712yes—
157C2×C8C2×D4×C12712yes—
158C4⋊C4—22no—
159C4⋊C4—21no—
160C22⋊C4—22no—
161C22⋊C4M16×C12712yes—
162C42—22no—
163C42—21no—
164C42—21no—
165C42C22⋊C4×C12711yescharacteristic
166C42C22⋊C4×C12711yescharacteristic
167C16—44no—
168C23—21no—
169C23C2×M16×C12711yescharacteristic
170Q8—41no—
171D4—41no—
172D4—42no—
173C2×C4—21no—
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—22no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—41no—
180C2×C4—41no—
181C2×C4—81no—
182C2×C4—82no—
183C2×C4C2×C22⋊C4×C12711yescharacteristic
184C2×C4C2×M16×C12711yescharacteristic
185C8—22no—
186C8—22no—
187C8—41no—
188C8—41no—
189C22—21no—
190C22—41no—
191C22—42no—
192C22—41no—
193C22#407×C12711yescharacteristic
194C4—21no—
195C4—41no—
196C4—42no—
197C4—41no—
198C4—41no—
199C4#410×C12711yescharacteristic
200C4#413×C12711yescharacteristic
201C2—21no—
202C2—41no—
203C2—81no—
204C2C127×#146411yescharacteristic
subgroupG/H
centerC4×C127#410
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×M16C23×C127
socleC2×C127#1464
prime radicalC2×#41×C127C2×C4
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C4×C127 ◁ C42×C127 ◁ C4×M16×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#2165C2semidirect
3. C127×#1328C2semidirect
98. #11523C127direct (N × H)
104. #2165C2×C127semidirect
105. #1328C2×C127semidirect
107. C127#11523direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#29232
C127×#21652
C127×#13282
C127×#13212
#11523127