Finite Group Databasebeta

← C127×#11669 #44575342

Subgroups — C127×#11669 #44575342

Order 32512.

360 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 106 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×#2956C211yesmaximal, characteristic
2C127×#2165C211yesmaximal, characteristic, complemented
3C127×#1455C211yesmaximal, characteristic, complemented
4C127×#1336C212yesmaximal, complemented
5C127×#1335C212yesmaximal, complemented
6#575×C127C411yescharacteristic
7#568×C127—21no—
8#444×C127—21no—
9#444×C127C412yes—
10#443×C127—21no—
11#443×C127C2212yes—
12#430×C127C411yescharacteristic
13C2×#104×C127—21no—
14C4×M16×C127—21no—
15C4×M16×C127C2211yescharacteristic
16#364×C127C2212yescomplemented
17#349×C127—21no—
18#347×C127—21no—
19#322×C127—21no—
20#322×C127C2211yescharacteristic, complemented
21C82×C127C2211yescharacteristic, complemented
22C2×#41×C127—21no—
23#137×C127—22no—
24AGL(1,ℤ/8)×C127—22no—
25#135×C127—21no—
26#135×C127C2×C412yes—
27#131×C127—22no—
28#131×C127—22no—
29#131×C127—42no—
30C2×M16×C127—22no—
31C2×M16×C127—21no—
32C2×M16×C127—42no—
33C2×M16×C127C2×C411yescharacteristic
34C2×M16×C127D411yescharacteristic
35C2×C42×C127D411yescharacteristic
36M32×C127—22no—
37#108×C127—21no—
38#108×C127C2×C412yes—
39#104×C127—22no—
40#104×C127—22no—
41#97×C127—22no—
42#97×C127C2×C411yescharacteristic
43#97×C127D411yescharacteristic
44C4×C8×C127—21no—
45C4×C8×C127—21no—
46C4×C8×C127D411yescharacteristic
47C4×C8×C127C2311yescharacteristic
48#41×C127—22no—
49#41×C127—22no—
50#41×C127—41no—
51#41×C127—41no—
52C2×Q8×C127—21no—
53C2×D4×C127—21no—
54C2×D4×C127—41no—
55C22×C4×C127—21no—
56C22×C4×C127—41no—
57C22×C4×C127C22⋊C411yescharacteristic
58Q16×C127—21no—
59Q16×C127M1612yescomplemented
60SD16×C127—22no—
61SD16×C127—22no—
62D8×C127—21no—
63D8×C127M1612yescomplemented
64M16×C127—22no—
65M16×C127—22no—
66M16×C127—22no—
67M16×C127—44no—
68M16×C127—42no—
69M16×C127—41no—
70M16×C127—42no—
71C2×C8×C127—22no—
72C2×C8×C127—22no—
73C2×C8×C127—42no—
74C2×C8×C127—41no—
75C2×C8×C127—42no—
76C2×C8×C127C22⋊C411yescharacteristic
77C2×C8×C127C22⋊C411yescharacteristic
78C2×C8×C127C22×C411yescharacteristic
79C2×C8×C127C2×D411yescharacteristic
80C42×C127—21no—
81C42×C127C22⋊C411yescharacteristic
82C42×C127C2×D411yescharacteristic
83C16×C127—42no—
84C23×C127—41no—
85C23×C127#10411yescharacteristic
86Q8×C127—22no—
87Q8×C127—41no—
88D4×C127—22no—
89D4×C127—41no—
90D4×C127—42no—
91D4×C127—42no—
92C2×C4×C127—21no—
93C2×C4×C127—21no—
94C2×C4×C127—21no—
95C2×C4×C127—21no—
96C2×C4×C127—42no—
97C2×C4×C127—42no—
98C2×C4×C127—41no—
99C2×C4×C127—42no—
100C2×C4×C127#10411yescharacteristic
101C2×C4×C127C2×C22⋊C411yescharacteristic
102C8×C127—24no—
103C8×C127—21no—
104C8×C127—21no—
105C8×C127—42no—
106C8×C127—42no—
107C8×C127C2×M1612yes—
108C8×C127AGL(1,ℤ/8)12yes—
109C22×C127—21no—
110C22×C127—41no—
111C22×C127—42no—
112C22×C127—161no—
113C22×C127C2×#10411yescharacteristic
114C4×C127—22no—
115C4×C127—21no—
116C4×C127—41no—
117C4×C127—42no—
118C4×C127#40711yescharacteristic
119C4×C127#41811yescharacteristic
120#11669C12711yesmaximal, characteristic, direct product factor, Sylow
121C2×C127—21no—
122C2×C127—41no—
123C2×C127—82no—
124C2×C127#149011yescharacteristic
125#2956C2×C12711yescharacteristic
126#2165C2×C12711yescharacteristic, complemented
127#1455C2×C12711yescharacteristic, complemented
128#1336C2×C12712yescomplemented
129#1335C2×C12712yescomplemented
130C127#1166911yescharacteristic, direct product factor, Sylow
131#575C4×C12711yescharacteristic
132#568—21no—
133#444—21no—
134#444C4×C12712yes—
135#443—21no—
136#443C22×C12712yes—
137#430C4×C12711yescharacteristic
138C2×#104—21no—
139C4×M16—21no—
140C4×M16C22×C12711yescharacteristic
141#364C22×C12712yescomplemented
142#349—21no—
143#347—21no—
144#322—21no—
145#322C22×C12711yescharacteristic, complemented
146C82C22×C12711yescharacteristic, complemented
147C2×#41—21no—
148#137—22no—
149AGL(1,ℤ/8)—22no—
150#135—21no—
151#135C2×C4×C12712yes—
152#131—22no—
153#131—22no—
154#131—42no—
155C2×M16—22no—
156C2×M16—21no—
157C2×M16—42no—
158C2×M16C2×C4×C12711yescharacteristic
159C2×M16D4×C12711yescharacteristic
160C2×C42D4×C12711yescharacteristic
161M32—22no—
162#108—21no—
163#108C2×C4×C12712yes—
164#104—22no—
165#104—22no—
166#97—22no—
167#97C2×C4×C12711yescharacteristic
168#97D4×C12711yescharacteristic
169C4×C8—21no—
170C4×C8—21no—
171C4×C8D4×C12711yescharacteristic
172C4×C8C23×C12711yescharacteristic
173#41—22no—
174#41—22no—
175#41—41no—
176#41—41no—
177C2×Q8—21no—
178C2×D4—21no—
179C2×D4—41no—
180C22×C4—21no—
181C22×C4—41no—
182C22×C4C22⋊C4×C12711yescharacteristic
183Q16—21no—
184Q16M16×C12712yescomplemented
185SD16—22no—
186SD16—22no—
187D8—21no—
188D8M16×C12712yescomplemented
189M16—22no—
190M16—22no—
191M16—22no—
192M16—44no—
193M16—42no—
194M16—41no—
195M16—42no—
196C2×C8—22no—
197C2×C8—22no—
198C2×C8—42no—
199C2×C8—41no—
200C2×C8—42no—
201C2×C8C22⋊C4×C12711yescharacteristic
202C2×C8C22⋊C4×C12711yescharacteristic
203C2×C8C22×C4×C12711yescharacteristic
204C2×C8C2×D4×C12711yescharacteristic
205C42—21no—
206C42C22⋊C4×C12711yescharacteristic
207C42C2×D4×C12711yescharacteristic
208C16—42no—
209C23—41no—
210C23#104×C12711yescharacteristic
211Q8—22no—
212Q8—41no—
213D4—22no—
214D4—41no—
215D4—42no—
216D4—42no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—42no—
222C2×C4—42no—
223C2×C4—41no—
224C2×C4—42no—
225C2×C4#104×C12711yescharacteristic
226C2×C4C2×C22⋊C4×C12711yescharacteristic
227C8—24no—
228C8—21no—
229C8—21no—
230C8—42no—
231C8—42no—
232C8C2×M16×C12712yes—
233C8AGL(1,ℤ/8)×C12712yes—
234C22—21no—
235C22—41no—
236C22—42no—
237C22—161no—
238C22C2×#104×C12711yescharacteristic
239C4—22no—
240C4—21no—
241C4—41no—
242C4—42no—
243C4#407×C12711yescharacteristic
244C4#418×C12711yescharacteristic
245C2—21no—
246C2—41no—
247C2—82no—
248C2C127×#149011yescharacteristic
subgroupG/H
centerC4×C127#418
commutatorC2×C8C22×C4×C127
Frattini, cosocleC4×C8C23×C127
socleC2×C127#1490
prime radical#575×C127C4
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C127 ◁ C2×C8×C127 ◁ C4×M16×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#2165C2semidirect
3. C127×#1455C2semidirect
4. C127×#1336C2semidirect
5. C127×#1335C2semidirect
16. #364×C127C22semidirect
20. #322×C127C22semidirect
21. C82×C127C22semidirect
59. Q16×C127M16semidirect
63. D8×C127M16semidirect
120. #11669C127direct (N × H)
126. #2165C2×C127semidirect
127. #1455C2×C127semidirect
128. #1336C2×C127semidirect
129. #1335C2×C127semidirect
130. C127#11669direct (N × H)
141. #364C22×C127semidirect
145. #322C22×C127semidirect
146. C82C22×C127semidirect
184. Q16M16×C127semidirect
188. D8M16×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#29562
C127×#21652
C127×#14552
C127×#13362
C127×#13352
#11669127