Finite Group Databasebeta

← C127×#11521 #44575194

Subgroups — C127×#11521 #44575194

Order 32512.

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

normal subgroups only

This group has 330 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×#2920C211yesmaximal, characteristic
2C127×#2165C212yesmaximal, complemented
3C127×#1327C212yesmaximal, complemented
4C127×#1320C212yesmaximal
5C22×C42×C127C411yescharacteristic
6#432×C127—22no—
7#431×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×C127—21no—
18C23×C4×C127C2×C411yescharacteristic
19C2×M16×C127C2×C411yescharacteristic
20C2×M16×C127C2×C411yescharacteristic
21C2×M16×C127C2×C411yescharacteristic
22C2×M16×C127C2311yescharacteristic
23C2×C42×C127—21no—
24C2×C42×C127—21no—
25C2×C42×C127—21no—
26C2×C42×C127—21no—
27C2×C42×C127—21no—
28C2×C42×C127C2×C411yescharacteristic
29C2×C42×C127C2×C411yescharacteristic
30M32×C127—24no—
31C4⋊C8×C127—22no—
32C4⋊C8×C127—22no—
33C22⋊C8×C127—22no—
34C22⋊C8×C127—22no—
35#97×C127—21no—
36#97×C127D412yes—
37C4×C8×C127—21no—
38C4×C8×C127D412yes—
39C24×C127M1611yescharacteristic
40C22×C4×C127—21no—
41C22×C4×C127—21no—
42C22×C4×C127—21no—
43C22×C4×C127—21no—
44C22×C4×C127—21no—
45C22×C4×C127—21no—
46C22×C4×C127—21no—
47C22×C4×C127—21no—
48C22×C4×C127—44no—
49C22×C4×C127—41no—
50C22×C4×C127—41no—
51C22×C4×C127M1611yescharacteristic
52C22×C4×C127C22×C411yescharacteristic
53M16×C127—41no—
54M16×C127—41no—
55M16×C127—41no—
56M16×C127—41no—
57C2×C8×C127—21no—
58C2×C8×C127—21no—
59C2×C8×C127C22⋊C412yes—
60C2×C8×C127C2×D412yes—
61C42×C127—21no—
62C42×C127—21no—
63C42×C127—21no—
64C42×C127—21no—
65C42×C127—21no—
66C42×C127—21no—
67C42×C127C22⋊C411yescharacteristic
68C42×C127C22⋊C411yescharacteristic
69C42×C127M1611yescharacteristic
70C42×C127M1611yescharacteristic
71C16×C127—44no—
72C23×C127—21no—
73C23×C127—42no—
74C23×C127—41no—
75C23×C127C2×M1611yescharacteristic
76C2×C4×C127—24no—
77C2×C4×C127—21no—
78C2×C4×C127—21no—
79C2×C4×C127—21no—
80C2×C4×C127—21no—
81C2×C4×C127—21no—
82C2×C4×C127—21no—
83C2×C4×C127—21no—
84C2×C4×C127—42no—
85C2×C4×C127—42no—
86C2×C4×C127—42no—
87C2×C4×C127—42no—
88C2×C4×C127—42no—
89C2×C4×C127—42no—
90C2×C4×C127—41no—
91C2×C4×C127—41no—
92C2×C4×C127—41no—
93C2×C4×C127C2×C22⋊C411yescharacteristic
94C2×C4×C127C2×M1611yescharacteristic
95C8×C127—22no—
96C8×C127—22no—
97C8×C127—41no—
98C8×C127—41no—
99C22×C127—22no—
100C22×C127—21no—
101C22×C127—41no—
102C22×C127—41no—
103C22×C127—42no—
104C22×C127—42no—
105C22×C127—41no—
106C22×C127#40711yescharacteristic
107C4×C127—22no—
108C4×C127—22no—
109C4×C127—21no—
110C4×C127—41no—
111C4×C127—41no—
112C4×C127—41no—
113C4×C127#41011yescharacteristic
114C4×C127#41311yescharacteristic
115#11521C12711yesmaximal, characteristic, direct product factor, Sylow
116C2×C127—21no—
117C2×C127—42no—
118C2×C127—41no—
119C2×C127#146411yescharacteristic
120#2920C2×C12711yescharacteristic
121#2165C2×C12712yescomplemented
122#1327C2×C12712yescomplemented
123#1320C2×C12712yes—
124C127#1152111yescharacteristic, direct product factor, Sylow
125C22×C42C4×C12711yescharacteristic
126#432—22no—
127#431—22no—
128#423C4×C12711yescharacteristic
129#423C22×C12711yescharacteristic
130#407C4×C12711yescharacteristic
131#407C22×C12711yescharacteristic
132C4×M16C4×C12711yescharacteristic
133C4×M16C22×C12711yescharacteristic
134#364—22no—
135#349C22×C12714yes—
136#347—22no—
137C23×C4—21no—
138C23×C4C2×C4×C12711yescharacteristic
139C2×M16C2×C4×C12711yescharacteristic
140C2×M16C2×C4×C12711yescharacteristic
141C2×M16C2×C4×C12711yescharacteristic
142C2×M16C23×C12711yescharacteristic
143C2×C42—21no—
144C2×C42—21no—
145C2×C42—21no—
146C2×C42—21no—
147C2×C42—21no—
148C2×C42C2×C4×C12711yescharacteristic
149C2×C42C2×C4×C12711yescharacteristic
150M32—24no—
151C4⋊C8—22no—
152C4⋊C8—22no—
153C22⋊C8—22no—
154C22⋊C8—22no—
155#97—21no—
156#97D4×C12712yes—
157C4×C8—21no—
158C4×C8D4×C12712yes—
159C24M16×C12711yescharacteristic
160C22×C4—21no—
161C22×C4—21no—
162C22×C4—21no—
163C22×C4—21no—
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—21no—
167C22×C4—21no—
168C22×C4—44no—
169C22×C4—41no—
170C22×C4—41no—
171C22×C4M16×C12711yescharacteristic
172C22×C4C22×C4×C12711yescharacteristic
173M16—41no—
174M16—41no—
175M16—41no—
176M16—41no—
177C2×C8—21no—
178C2×C8—21no—
179C2×C8C22⋊C4×C12712yes—
180C2×C8C2×D4×C12712yes—
181C42—21no—
182C42—21no—
183C42—21no—
184C42—21no—
185C42—21no—
186C42—21no—
187C42C22⋊C4×C12711yescharacteristic
188C42C22⋊C4×C12711yescharacteristic
189C42M16×C12711yescharacteristic
190C42M16×C12711yescharacteristic
191C16—44no—
192C23—21no—
193C23—42no—
194C23—41no—
195C23C2×M16×C12711yescharacteristic
196C2×C4—24no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—42no—
205C2×C4—42no—
206C2×C4—42no—
207C2×C4—42no—
208C2×C4—42no—
209C2×C4—42no—
210C2×C4—41no—
211C2×C4—41no—
212C2×C4—41no—
213C2×C4C2×C22⋊C4×C12711yescharacteristic
214C2×C4C2×M16×C12711yescharacteristic
215C8—22no—
216C8—22no—
217C8—41no—
218C8—41no—
219C22—22no—
220C22—21no—
221C22—41no—
222C22—41no—
223C22—42no—
224C22—42no—
225C22—41no—
226C22#407×C12711yescharacteristic
227C4—22no—
228C4—22no—
229C4—21no—
230C4—41no—
231C4—41no—
232C4—41no—
233C4#410×C12711yescharacteristic
234C4#413×C12711yescharacteristic
235C2—21no—
236C2—42no—
237C2—41no—
238C2C127×#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
115. #11521C127direct (N × H)
121. #2165C2×C127semidirect
122. #1327C2×C127semidirect
124. C127#11521direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#29202
C127×#21652
C127×#13272
C127×#13202
#11521127