Finite Group Databasebeta

← C127×#13448 #44577121

Subgroups — C127×#13448 #44577121

Order 32512.

482 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 482 conjugacy classes of subgroups — too many to draw. Only its 130 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
1C22×D16×C127C211yesmaximal, characteristic
2C2×C4⋊C16×C127C211yesmaximal, characteristic, complemented
3C2×#357×C127C212yesmaximal, complemented
4C127×#1970C212yesmaximal, complemented
5C127×#1380C211yesmaximal, characteristic, complemented
6C22×D8×C127C2212yes—
7C2×D16×C127—24no—
8C2×D16×C127—22no—
9C22×C16×C127C2211yescharacteristic
10C22×C16×C127C2211yescharacteristic
11C2×#107×C127C2212yes—
12C2×#102×C127—22no—
13C2×C4×C8×C127C2211yescharacteristic
14#390×C127—22no—
15C4⋊C16×C127—22no—
16#357×C127—24no—
17C22×D4×C127—22no—
18C2×D8×C127—22no—
19C2×D8×C127—22no—
20C2×D8×C127—22no—
21C2×D8×C127—22no—
22C2×D8×C127—22no—
23C2×D8×C127D414yes—
24C22×C8×C127D411yescharacteristic
25C22×C8×C127C2311yescharacteristic
26C2×C4⋊C4×C127—22no—
27C2×C22⋊C4×C127—42no—
28C2×C22⋊C4×C127—42no—
29C2×C42×C127D411yescharacteristic
30D16×C127—28no—
31C2×C16×C127—22no—
32C2×C16×C127—22no—
33C2×C16×C127—21no—
34C2×C16×C127D412yes—
35#107×C127—22no—
36#107×C127—22no—
37#102×C127—44no—
38C4×C8×C127—21no—
39C4×C8×C127—21no—
40C24×C127—42no—
41C2×D4×C127—24no—
42C2×D4×C127—42no—
43C2×D4×C127—42no—
44C2×D4×C127—42no—
45C2×D4×C127—42no—
46C2×D4×C127—42no—
47C22×C4×C127—42no—
48C22×C4×C127D811yescharacteristic
49C22×C4×C127D811yescharacteristic
50C22×C4×C127C2×D411yescharacteristic
51D8×C127—24no—
52D8×C127—24no—
53D8×C127—42no—
54D8×C127—42no—
55C2×C8×C127—21no—
56C2×C8×C127—22no—
57C2×C8×C127C2×D412yes—
58C2×C8×C127C2×D411yescharacteristic
59C2×C8×C127#4111yescharacteristic
60C2×C8×C127#4112yes—
61C4⋊C4×C127—42no—
62C4⋊C4×C127—42no—
63C22⋊C4×C127—84no—
64C22⋊C4×C127—84no—
65C42×C127—21no—
66C42×C127—21no—
67C16×C127—22no—
68C16×C127—41no—
69C23×C127—44no—
70C23×C127—82no—
71C23×C127—82no—
72C23×C127—82no—
73C23×C127—82no—
74C23×C127—82no—
75C23×C127—82no—
76C23×C127C2×D811yescharacteristic
77D4×C127—44no—
78D4×C127—44no—
79D4×C127—82no—
80D4×C127—82no—
81C2×C4×C127—21no—
82C2×C4×C127—21no—
83C2×C4×C127—21no—
84C2×C4×C127—22no—
85C2×C4×C127—82no—
86C2×C4×C127—82no—
87C2×C4×C127—82no—
88C2×C4×C127D1612yescomplemented
89C2×C4×C127#12112yes—
90C2×C4×C127#12111yescharacteristic
91C2×C4×C127#13511yescharacteristic
92C2×C4×C127AGL(1,ℤ/8)12yes—
93C8×C127—41no—
94C8×C127#12011yescharacteristic
95C8×C127#12312yes—
96C8×C127#12411yescharacteristic
97C22×C127—84no—
98C22×C127—84no—
99C22×C127—84no—
100C22×C127—162no—
101C22×C127—162no—
102C22×C127—162no—
103C22×C127—162no—
104C22×C127#45912yes—
105C22×C127#46611yescharacteristic
106C22×C127C2×D1611yescharacteristic
107C22×C127#50811yescharacteristic
108C22×C127#50912yes—
109C4×C127—22no—
110C4×C127—41no—
111C4×C127—162no—
112C4×C127#39411yescharacteristic
113C4×C127#46312yes—
114C4×C127#46911yescharacteristic
115#13448C12711yesmaximal, characteristic, direct product factor, Sylow
116C2×C127—164no—
117C2×C127#205411yescharacteristic
118C2×C127#220612yes—
119C2×C127#221012yes—
120C2×C127#221511yescharacteristic
121C2×C127#221811yescharacteristic
122C22×D16C2×C12711yescharacteristic
123C2×C4⋊C16C2×C12711yescharacteristic, complemented
124C2×#357C2×C12712yescomplemented
125#1970C2×C12712yescomplemented
126#1380C2×C12711yescharacteristic, complemented
127C127#1344811yescharacteristic, direct product factor, Sylow
128C22×D8C22×C12712yes—
129C2×D16—24no—
130C2×D16—22no—
131C22×C16C22×C12711yescharacteristic
132C22×C16C22×C12711yescharacteristic
133C2×#107C22×C12712yes—
134C2×#102—22no—
135C2×C4×C8C22×C12711yescharacteristic
136#390—22no—
137C4⋊C16—22no—
138#357—24no—
139C22×D4—22no—
140C2×D8—22no—
141C2×D8—22no—
142C2×D8—22no—
143C2×D8—22no—
144C2×D8—22no—
145C2×D8D4×C12714yes—
146C22×C8D4×C12711yescharacteristic
147C22×C8C23×C12711yescharacteristic
148C2×C4⋊C4—22no—
149C2×C22⋊C4—42no—
150C2×C22⋊C4—42no—
151C2×C42D4×C12711yescharacteristic
152D16—28no—
153C2×C16—22no—
154C2×C16—22no—
155C2×C16—21no—
156C2×C16D4×C12712yes—
157#107—22no—
158#107—22no—
159#102—44no—
160C4×C8—21no—
161C4×C8—21no—
162C24—42no—
163C2×D4—24no—
164C2×D4—42no—
165C2×D4—42no—
166C2×D4—42no—
167C2×D4—42no—
168C2×D4—42no—
169C22×C4—42no—
170C22×C4D8×C12711yescharacteristic
171C22×C4D8×C12711yescharacteristic
172C22×C4C2×D4×C12711yescharacteristic
173D8—24no—
174D8—24no—
175D8—42no—
176D8—42no—
177C2×C8—21no—
178C2×C8—22no—
179C2×C8C2×D4×C12712yes—
180C2×C8C2×D4×C12711yescharacteristic
181C2×C8#41×C12711yescharacteristic
182C2×C8#41×C12712yes—
183C4⋊C4—42no—
184C4⋊C4—42no—
185C22⋊C4—84no—
186C22⋊C4—84no—
187C42—21no—
188C42—21no—
189C16—22no—
190C16—41no—
191C23—44no—
192C23—82no—
193C23—82no—
194C23—82no—
195C23—82no—
196C23—82no—
197C23—82no—
198C23C2×D8×C12711yescharacteristic
199D4—44no—
200D4—44no—
201D4—82no—
202D4—82no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—22no—
206C2×C4—21no—
207C2×C4—82no—
208C2×C4—82no—
209C2×C4—82no—
210C2×C4D16×C12712yescomplemented
211C2×C4#121×C12712yes—
212C2×C4#121×C12711yescharacteristic
213C2×C4#135×C12711yescharacteristic
214C2×C4AGL(1,ℤ/8)×C12712yes—
215C8—41no—
216C8#120×C12711yescharacteristic
217C8#123×C12712yes—
218C8#124×C12711yescharacteristic
219C22—84no—
220C22—84no—
221C22—84no—
222C22—162no—
223C22—162no—
224C22—162no—
225C22—162no—
226C22#459×C12712yes—
227C22#466×C12711yescharacteristic
228C22C2×D16×C12711yescharacteristic
229C22#508×C12711yescharacteristic
230C22#509×C12712yes—
231C4—22no—
232C4—41no—
233C4—162no—
234C4#394×C12711yescharacteristic
235C4#463×C12712yes—
236C4#469×C12711yescharacteristic
237C2—164no—
238C2C127×#205411yescharacteristic
239C2C127×#220612yes—
240C2C127×#221012yes—
241C2C127×#221511yescharacteristic
242C2C127×#221811yescharacteristic
subgroupG/H
center, socleC23×C127C2×D8
commutator, Frattini, cosocleC22×C8C23×C127
prime radicalC22×D16×C127C2
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C127 ◁ C2×C42×C127 ◁ C2×C4×C8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C16×C127C2semidirect
3. C2×#357×C127C2semidirect
4. C127×#1970C2semidirect
5. C127×#1380C2semidirect
88. C2×C4×C127D16semidirect
115. #13448C127direct (N × H)
123. C2×C4⋊C16C2×C127semidirect
124. C2×#357C2×C127semidirect
125. #1970C2×C127semidirect
126. #1380C2×C127semidirect
127. C127#13448direct (N × H)
210. C2×C4D16×C127semidirect

Maximal subgroups

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

subgroupindex
C22×D16×C1272
C2×C4⋊C16×C1272
C2×#357×C1272
C127×#19702
C127×#13802
#13448127