Finite Group Databasebeta

← C127×#11522 #44575195

Subgroups — C127×#11522 #44575195

Order 32512.

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

normal subgroups only

This group has 284 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×#2921C211yesmaximal, characteristic
2C127×#2165C212yesmaximal, complemented
3C127×#1327C212yesmaximal, complemented
4C127×#1320C212yesmaximal
5C2×#117×C127C411yescharacteristic
6#433×C127—22no—
7#433×C127—22no—
8#423×C127C411yescharacteristic
9#423×C127C2211yescharacteristic
10#407×C127C411yescharacteristic
11#407×C127C2211yescharacteristic
12C4×M16×C127C411yescharacteristic
13C4×M16×C127C2211yescharacteristic
14#364×C127—22no—
15#349×C127C2214yes—
16#347×C127—22no—
17C23×C4×C127C2×C411yescharacteristic
18C2×M16×C127C2×C411yescharacteristic
19C2×M16×C127C2×C411yescharacteristic
20C2×M16×C127C2×C411yescharacteristic
21C2×M16×C127C2311yescharacteristic
22#117×C127—21no—
23#117×C127—21no—
24#117×C127—22no—
25C2×C4⋊C4×C127—21no—
26C2×C22⋊C4×C127—21no—
27C2×C42×C127C2×C411yescharacteristic
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×C127D412yes—
36C4×C8×C127—21no—
37C4×C8×C127D412yes—
38C24×C127M1611yescharacteristic
39C22×C4×C127—21no—
40C22×C4×C127—21no—
41C22×C4×C127—21no—
42C22×C4×C127—21no—
43C22×C4×C127—41no—
44C22×C4×C127—41no—
45C22×C4×C127M1611yescharacteristic
46C22×C4×C127C22×C411yescharacteristic
47M16×C127—41no—
48M16×C127—41no—
49M16×C127—41no—
50M16×C127—41no—
51C2×C8×C127—21no—
52C2×C8×C127—21no—
53C2×C8×C127C22⋊C412yes—
54C2×C8×C127C2×D412yes—
55C4⋊C4×C127—22no—
56C4⋊C4×C127—22no—
57C22⋊C4×C127—22no—
58C22⋊C4×C127—22no—
59C42×C127—21no—
60C42×C127—21no—
61C42×C127C22⋊C411yescharacteristic
62C42×C127C22⋊C411yescharacteristic
63C42×C127M1612yes—
64C16×C127—44no—
65C23×C127—21no—
66C23×C127—41no—
67C23×C127—81no—
68C23×C127C2×M1611yescharacteristic
69C2×C4×C127—21no—
70C2×C4×C127—21no—
71C2×C4×C127—21no—
72C2×C4×C127—21no—
73C2×C4×C127—22no—
74C2×C4×C127—21no—
75C2×C4×C127—42no—
76C2×C4×C127—41no—
77C2×C4×C127—41no—
78C2×C4×C127—41no—
79C2×C4×C127—81no—
80C2×C4×C127—81no—
81C2×C4×C127C2×C22⋊C411yescharacteristic
82C2×C4×C127C2×M1611yescharacteristic
83C8×C127—22no—
84C8×C127—22no—
85C8×C127—41no—
86C8×C127—41no—
87C22×C127—21no—
88C22×C127—41no—
89C22×C127—42no—
90C22×C127—41no—
91C22×C127—82no—
92C22×C127#40711yescharacteristic
93C4×C127—21no—
94C4×C127—41no—
95C4×C127—41no—
96C4×C127—42no—
97C4×C127—41no—
98C4×C127#41011yescharacteristic
99C4×C127#41311yescharacteristic
100#11522C12711yesmaximal, characteristic, direct product factor, Sylow
101C2×C127—21no—
102C2×C127—41no—
103C2×C127—81no—
104C2×C127#146411yescharacteristic
105#2921C2×C12711yescharacteristic
106#2165C2×C12712yescomplemented
107#1327C2×C12712yescomplemented
108#1320C2×C12712yes—
109C127#1152211yescharacteristic, direct product factor, Sylow
110C2×#117C4×C12711yescharacteristic
111#433—22no—
112#433—22no—
113#423C4×C12711yescharacteristic
114#423C22×C12711yescharacteristic
115#407C4×C12711yescharacteristic
116#407C22×C12711yescharacteristic
117C4×M16C4×C12711yescharacteristic
118C4×M16C22×C12711yescharacteristic
119#364—22no—
120#349C22×C12714yes—
121#347—22no—
122C23×C4C2×C4×C12711yescharacteristic
123C2×M16C2×C4×C12711yescharacteristic
124C2×M16C2×C4×C12711yescharacteristic
125C2×M16C2×C4×C12711yescharacteristic
126C2×M16C23×C12711yescharacteristic
127#117—21no—
128#117—21no—
129#117—22no—
130C2×C4⋊C4—21no—
131C2×C22⋊C4—21no—
132C2×C42C2×C4×C12711yescharacteristic
133C2×C42C2×C4×C12711yescharacteristic
134M32—24no—
135C4⋊C8—22no—
136C4⋊C8—22no—
137C22⋊C8—22no—
138C22⋊C8—22no—
139#97—21no—
140#97D4×C12712yes—
141C4×C8—21no—
142C4×C8D4×C12712yes—
143C24M16×C12711yescharacteristic
144C22×C4—21no—
145C22×C4—21no—
146C22×C4—21no—
147C22×C4—21no—
148C22×C4—41no—
149C22×C4—41no—
150C22×C4M16×C12711yescharacteristic
151C22×C4C22×C4×C12711yescharacteristic
152M16—41no—
153M16—41no—
154M16—41no—
155M16—41no—
156C2×C8—21no—
157C2×C8—21no—
158C2×C8C22⋊C4×C12712yes—
159C2×C8C2×D4×C12712yes—
160C4⋊C4—22no—
161C4⋊C4—22no—
162C22⋊C4—22no—
163C22⋊C4—22no—
164C42—21no—
165C42—21no—
166C42C22⋊C4×C12711yescharacteristic
167C42C22⋊C4×C12711yescharacteristic
168C42M16×C12712yes—
169C16—44no—
170C23—21no—
171C23—41no—
172C23—81no—
173C23C2×M16×C12711yescharacteristic
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—22no—
179C2×C4—21no—
180C2×C4—42no—
181C2×C4—41no—
182C2×C4—41no—
183C2×C4—41no—
184C2×C4—81no—
185C2×C4—81no—
186C2×C4C2×C22⋊C4×C12711yescharacteristic
187C2×C4C2×M16×C12711yescharacteristic
188C8—22no—
189C8—22no—
190C8—41no—
191C8—41no—
192C22—21no—
193C22—41no—
194C22—42no—
195C22—41no—
196C22—82no—
197C22#407×C12711yescharacteristic
198C4—21no—
199C4—41no—
200C4—41no—
201C4—42no—
202C4—41no—
203C4#410×C12711yescharacteristic
204C4#413×C12711yescharacteristic
205C2—21no—
206C2—41no—
207C2—81no—
208C2C127×#146411yescharacteristic
subgroupG/H
centerC4×C127#410
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×M16C23×C127
socleC2×C127#1464
prime radicalC24×C127M16
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×#1327C2semidirect
100. #11522C127direct (N × H)
106. #2165C2×C127semidirect
107. #1327C2×C127semidirect
109. C127#11522direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#29212
C127×#21652
C127×#13272
C127×#13202
#11522127