Finite Group Databasebeta

← C127×#11667 #44575340

Subgroups — C127×#11667 #44575340

Order 32512.

418 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 126 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
1C2×C4×D8×C127C211yesmaximal, characteristic
2C127×#2163C211yesmaximal, characteristic, complemented
3C127×#1568C211yesmaximal, characteristic, complemented
4C127×#1333C214yesmaximal, complemented
5C22×D8×C127C411yescharacteristic
6C2×C4×D4×C127—21no—
7C4×D8×C127—21no—
8C4×D8×C127—21no—
9C4×D8×C127C412yes—
10C4×D8×C127C2212yes—
11#432×C127—21no—
12C2×#107×C127C411yescharacteristic
13C2×#102×C127—21no—
14C2×C4×C8×C127C2211yescharacteristic
15C4⋊C16×C127—21no—
16C22⋊C16×C127—21no—
17#346×C127C2212yescomplemented
18#335×C127—21no—
19#334×C127C2212yescomplemented
20C22×D4×C127—21no—
21C23×C4×C127—41no—
22C2×D8×C127—24no—
23C2×D8×C127—21no—
24C2×D8×C127C2×C412yes—
25C22×C8×C127C2×C411yescharacteristic
26C22×C8×C127D411yescharacteristic
27C4×D4×C127—22no—
28C4×D4×C127—22no—
29C4×D4×C127—41no—
30C4×D4×C127—41no—
31C2×C4⋊C4×C127—21no—
32C2×C22⋊C4×C127—41no—
33C2×C42×C127D411yescharacteristic
34C2×C16×C127—22no—
35#107×C127—21no—
36#107×C127C2×C412yes—
37C4⋊C8×C127—22no—
38#102×C127—22no—
39#102×C127—22no—
40C22⋊C8×C127—41no—
41#97×C127—41no—
42C4×C8×C127C2×C411yescharacteristic
43C4×C8×C127D411yescharacteristic
44C4×C8×C127D411yescharacteristic
45C4×C8×C127C2311yescharacteristic
46C24×C127—41no—
47C2×D4×C127—24no—
48C2×D4×C127—22no—
49C2×D4×C127—42no—
50C2×D4×C127—41no—
51C22×C4×C127—41no—
52C22×C4×C127—42no—
53C22×C4×C127—42no—
54C22×C4×C127—84no—
55C22×C4×C127C22⋊C411yescharacteristic
56C22×C4×C127D811yescharacteristic
57C22×C4×C127SD1611yescharacteristic
58D8×C127—24no—
59D8×C127—22no—
60D8×C127M1614yes—
61C2×C8×C127—22no—
62C2×C8×C127—41no—
63C2×C8×C127—42no—
64C2×C8×C127C22⋊C411yescharacteristic
65C2×C8×C127C22⋊C411yescharacteristic
66C2×C8×C127C22×C411yescharacteristic
67C2×C8×C127C2×D411yescharacteristic
68C4⋊C4×C127—22no—
69C4⋊C4×C127—41no—
70C22⋊C4×C127—42no—
71C22⋊C4×C127—42no—
72C42×C127C22⋊C411yescharacteristic
73C42×C127D811yescharacteristic
74C42×C127SD1611yescharacteristic
75C42×C127C2×D411yescharacteristic
76C16×C127—42no—
77C23×C127—44no—
78C23×C127—42no—
79C23×C127—82no—
80C23×C127—82no—
81C23×C127#10211yescharacteristic
82D4×C127—24no—
83D4×C127—44no—
84D4×C127—42no—
85C2×C4×C127—22no—
86C2×C4×C127—21no—
87C2×C4×C127—21no—
88C2×C4×C127—41no—
89C2×C4×C127—42no—
90C2×C4×C127—84no—
91C2×C4×C127—84no—
92C2×C4×C127—82no—
93C2×C4×C127#10211yescharacteristic
94C2×C4×C127#10211yescharacteristic
95C2×C4×C127#10211yescharacteristic
96C2×C4×C127C2×C22⋊C411yescharacteristic
97C2×C4×C127C2×D811yescharacteristic
98C2×C4×C127C2×SD1611yescharacteristic
99C8×C127—21no—
100C8×C127—21no—
101C8×C127—21no—
102C8×C127—82no—
103C8×C127C2×M1612yes—
104C22×C127—21no—
105C22×C127—21no—
106C22×C127—44no—
107C22×C127—88no—
108C22×C127—82no—
109C22×C127—82no—
110C22×C127#36112yes—
111C22×C127C2×#10211yescharacteristic
112C4×C127—21no—
113C4×C127—21no—
114C4×C127—21no—
115C4×C127—21no—
116C4×C127—21no—
117C4×C127—82no—
118C4×C127#40711yescharacteristic
119C4×C127#42111yescharacteristic
120#11667C12711yesmaximal, characteristic, direct product factor, Sylow
121C2×C127—22no—
122C2×C127—84no—
123C2×C127#148611yescharacteristic
124C2×C127#214511yescharacteristic
125C2×C127C2×#36111yescharacteristic
126C2×C4×D8C2×C12711yescharacteristic
127#2163C2×C12711yescharacteristic, complemented
128#1568C2×C12711yescharacteristic, complemented
129#1333C2×C12714yescomplemented
130C127#1166711yescharacteristic, direct product factor, Sylow
131C22×D8C4×C12711yescharacteristic
132C2×C4×D4—21no—
133C4×D8—21no—
134C4×D8—21no—
135C4×D8C4×C12712yes—
136C4×D8C22×C12712yes—
137#432—21no—
138C2×#107C4×C12711yescharacteristic
139C2×#102—21no—
140C2×C4×C8C22×C12711yescharacteristic
141C4⋊C16—21no—
142C22⋊C16—21no—
143#346C22×C12712yescomplemented
144#335—21no—
145#334C22×C12712yescomplemented
146C22×D4—21no—
147C23×C4—41no—
148C2×D8—24no—
149C2×D8—21no—
150C2×D8C2×C4×C12712yes—
151C22×C8C2×C4×C12711yescharacteristic
152C22×C8D4×C12711yescharacteristic
153C4×D4—22no—
154C4×D4—22no—
155C4×D4—41no—
156C4×D4—41no—
157C2×C4⋊C4—21no—
158C2×C22⋊C4—41no—
159C2×C42D4×C12711yescharacteristic
160C2×C16—22no—
161#107—21no—
162#107C2×C4×C12712yes—
163C4⋊C8—22no—
164#102—22no—
165#102—22no—
166C22⋊C8—41no—
167#97—41no—
168C4×C8C2×C4×C12711yescharacteristic
169C4×C8D4×C12711yescharacteristic
170C4×C8D4×C12711yescharacteristic
171C4×C8C23×C12711yescharacteristic
172C24—41no—
173C2×D4—24no—
174C2×D4—22no—
175C2×D4—42no—
176C2×D4—41no—
177C22×C4—41no—
178C22×C4—42no—
179C22×C4—42no—
180C22×C4—84no—
181C22×C4C22⋊C4×C12711yescharacteristic
182C22×C4D8×C12711yescharacteristic
183C22×C4SD16×C12711yescharacteristic
184D8—24no—
185D8—22no—
186D8M16×C12714yes—
187C2×C8—22no—
188C2×C8—41no—
189C2×C8—42no—
190C2×C8C22⋊C4×C12711yescharacteristic
191C2×C8C22⋊C4×C12711yescharacteristic
192C2×C8C22×C4×C12711yescharacteristic
193C2×C8C2×D4×C12711yescharacteristic
194C4⋊C4—22no—
195C4⋊C4—41no—
196C22⋊C4—42no—
197C22⋊C4—42no—
198C42C22⋊C4×C12711yescharacteristic
199C42D8×C12711yescharacteristic
200C42SD16×C12711yescharacteristic
201C42C2×D4×C12711yescharacteristic
202C16—42no—
203C23—44no—
204C23—42no—
205C23—82no—
206C23—82no—
207C23#102×C12711yescharacteristic
208D4—24no—
209D4—44no—
210D4—42no—
211C2×C4—22no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—41no—
215C2×C4—42no—
216C2×C4—84no—
217C2×C4—84no—
218C2×C4—82no—
219C2×C4#102×C12711yescharacteristic
220C2×C4#102×C12711yescharacteristic
221C2×C4#102×C12711yescharacteristic
222C2×C4C2×C22⋊C4×C12711yescharacteristic
223C2×C4C2×D8×C12711yescharacteristic
224C2×C4C2×SD16×C12711yescharacteristic
225C8—21no—
226C8—21no—
227C8—21no—
228C8—82no—
229C8C2×M16×C12712yes—
230C22—21no—
231C22—21no—
232C22—44no—
233C22—88no—
234C22—82no—
235C22—82no—
236C22#361×C12712yes—
237C22C2×#102×C12711yescharacteristic
238C4—21no—
239C4—21no—
240C4—21no—
241C4—21no—
242C4—21no—
243C4—82no—
244C4#407×C12711yescharacteristic
245C4#421×C12711yescharacteristic
246C2—22no—
247C2—84no—
248C2C127×#148611yescharacteristic
249C2C127×#214511yescharacteristic
250C2C2×#361×C12711yescharacteristic
subgroupG/H
center, socleC22×C127C2×#102
commutatorC2×C8C22×C4×C127
Frattini, cosocleC4×C8C23×C127
prime radicalC22×D8×C127C4
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C2×C42×C127 ◁ C2×C4×C8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#2163C2semidirect
3. C127×#1568C2semidirect
4. C127×#1333C2semidirect
17. #346×C127C22semidirect
19. #334×C127C22semidirect
120. #11667C127direct (N × H)
127. #2163C2×C127semidirect
128. #1568C2×C127semidirect
129. #1333C2×C127semidirect
130. C127#11667direct (N × H)
143. #346C22×C127semidirect
145. #334C22×C127semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D8×C1272
C127×#21632
C127×#15682
C127×#13332
#11667127