Finite Group Databasebeta

← C127×#12871 #44576544

Subgroups — C127×#12871 #44576544

Order 32512.

442 conjugacy classes of subgroups.

The subgroup lattice has 254 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#107×C127C211yesmaximal, characteristic
2C127×#2112C211yesmaximal, characteristic
3C127×#1810C211yesmaximal, characteristic
4C127×#1387C214yesmaximal, complemented
5C23×C8×C127C2211yescharacteristic
6C22×C4⋊C4×C127—21no—
7C2×M32×C127C2212yes—
8C2×#108×C127C2212yes—
9C2×#107×C127—21no—
10C2×#107×C127—21no—
11C2×#107×C127—21no—
12C2×#107×C127C412yes—
13C2×#107×C127C412yes—
14C2×#107×C127C2212yes—
15#407×C127—21no—
16C22⋊C16×C127—21no—
17C22⋊C16×C127—21no—
18#341×C127—21no—
19C23×C4×C127—41no—
20C23×C4×C127D411yescharacteristic
21C2×M16×C127—22no—
22C22×C8×C127—24no—
23C22×C8×C127C2×C411yescharacteristic
24C22×C8×C127C2×C411yescharacteristic
25C22×C8×C127D411yescharacteristic
26C22×C8×C127D411yescharacteristic
27C22×C8×C127D411yescharacteristic
28C22×C8×C127C2311yescharacteristic
29C2×C4⋊C4×C127—22no—
30C2×C4⋊C4×C127—22no—
31C2×C4⋊C4×C127—22no—
32C2×C4⋊C4×C127—41no—
33C2×C4⋊C4×C127—41no—
34C2×C4⋊C4×C127—41no—
35M32×C127—24no—
36C2×C16×C127—22no—
37#108×C127—24no—
38#107×C127—22no—
39#107×C127—22no—
40#107×C127—22no—
41#107×C127C2×C414yes—
42C22⋊C8×C127—41no—
43C22⋊C8×C127—41no—
44C24×C127SD1611yescharacteristic
45C22×C4×C127—22no—
46C22×C4×C127—22no—
47C22×C4×C127—42no—
48C22×C4×C127—42no—
49C22×C4×C127—42no—
50C22×C4×C127—84no—
51C22×C4×C127C22⋊C411yescharacteristic
52C22×C4×C127C22⋊C411yescharacteristic
53C22×C4×C127D811yescharacteristic
54C22×C4×C127D811yescharacteristic
55C22×C4×C127SD1611yescharacteristic
56C22×C4×C127C2×D411yescharacteristic
57M16×C127—42no—
58M16×C127—42no—
59C2×C8×C127—22no—
60C2×C8×C127—22no—
61C2×C8×C127—22no—
62C2×C8×C127—22no—
63C2×C8×C127—22no—
64C2×C8×C127—42no—
65C2×C8×C127C22⋊C411yescharacteristic
66C2×C8×C127C22⋊C411yescharacteristic
67C2×C8×C127C22×C411yescharacteristic
68C2×C8×C127C2×D411yescharacteristic
69C2×C8×C127#4114yes—
70C4⋊C4×C127—24no—
71C4⋊C4×C127—42no—
72C4⋊C4×C127—42no—
73C4⋊C4×C127—42no—
74C16×C127—42no—
75C23×C127—22no—
76C23×C127—22no—
77C23×C127—22no—
78C23×C127#10211yescharacteristic
79C23×C127#10211yescharacteristic
80C23×C127C2×SD1611yescharacteristic
81C2×C4×C127—22no—
82C2×C4×C127—21no—
83C2×C4×C127—21no—
84C2×C4×C127—21no—
85C2×C4×C127—21no—
86C2×C4×C127—22no—
87C2×C4×C127—22no—
88C2×C4×C127—44no—
89C2×C4×C127—84no—
90C2×C4×C127—84no—
91C2×C4×C127—84no—
92C2×C4×C127#10211yescharacteristic
93C2×C4×C127#10211yescharacteristic
94C2×C4×C127C2×C22⋊C411yescharacteristic
95C2×C4×C127#12312yes—
96C2×C4×C127C2×D811yescharacteristic
97C2×C4×C127#13712yes—
98C8×C127—21no—
99C8×C127—21no—
100C8×C127—82no—
101C8×C127#11712yes—
102C8×C127#12312yes—
103C22×C127—28no—
104C22×C127—21no—
105C22×C127—21no—
106C22×C127—21no—
107C22×C127—21no—
108C22×C127—21no—
109C22×C127—21no—
110C22×C127#36112yes—
111C22×C127#36212yes—
112C22×C127C2×#10211yescharacteristic
113C22×C127#48312yes—
114C4×C127—21no—
115C4×C127—21no—
116C4×C127—84no—
117C4×C127#38111yescharacteristic
118C4×C127#41911yescharacteristic
119C4×C127#48012yes—
120#12871C12711yesmaximal, characteristic, direct product factor, Sylow
121C2×C127—22no—
122C2×C127—22no—
123C2×C127—22no—
124C2×C127#182311yescharacteristic
125C2×C127C2×#36111yescharacteristic
126C2×C127C2×#36211yescharacteristic
127C22×#107C2×C12711yescharacteristic
128#2112C2×C12711yescharacteristic
129#1810C2×C12711yescharacteristic
130#1387C2×C12714yescomplemented
131C127#1287111yescharacteristic, direct product factor, Sylow
132C23×C8C22×C12711yescharacteristic
133C22×C4⋊C4—21no—
134C2×M32C22×C12712yes—
135C2×#108C22×C12712yes—
136C2×#107—21no—
137C2×#107—21no—
138C2×#107—21no—
139C2×#107C4×C12712yes—
140C2×#107C4×C12712yes—
141C2×#107C22×C12712yes—
142#407—21no—
143C22⋊C16—21no—
144C22⋊C16—21no—
145#341—21no—
146C23×C4—41no—
147C23×C4D4×C12711yescharacteristic
148C2×M16—22no—
149C22×C8—24no—
150C22×C8C2×C4×C12711yescharacteristic
151C22×C8C2×C4×C12711yescharacteristic
152C22×C8D4×C12711yescharacteristic
153C22×C8D4×C12711yescharacteristic
154C22×C8D4×C12711yescharacteristic
155C22×C8C23×C12711yescharacteristic
156C2×C4⋊C4—22no—
157C2×C4⋊C4—22no—
158C2×C4⋊C4—22no—
159C2×C4⋊C4—41no—
160C2×C4⋊C4—41no—
161C2×C4⋊C4—41no—
162M32—24no—
163C2×C16—22no—
164#108—24no—
165#107—22no—
166#107—22no—
167#107—22no—
168#107C2×C4×C12714yes—
169C22⋊C8—41no—
170C22⋊C8—41no—
171C24SD16×C12711yescharacteristic
172C22×C4—22no—
173C22×C4—22no—
174C22×C4—42no—
175C22×C4—42no—
176C22×C4—42no—
177C22×C4—84no—
178C22×C4C22⋊C4×C12711yescharacteristic
179C22×C4C22⋊C4×C12711yescharacteristic
180C22×C4D8×C12711yescharacteristic
181C22×C4D8×C12711yescharacteristic
182C22×C4SD16×C12711yescharacteristic
183C22×C4C2×D4×C12711yescharacteristic
184M16—42no—
185M16—42no—
186C2×C8—22no—
187C2×C8—22no—
188C2×C8—22no—
189C2×C8—22no—
190C2×C8—22no—
191C2×C8—42no—
192C2×C8C22⋊C4×C12711yescharacteristic
193C2×C8C22⋊C4×C12711yescharacteristic
194C2×C8C22×C4×C12711yescharacteristic
195C2×C8C2×D4×C12711yescharacteristic
196C2×C8#41×C12714yes—
197C4⋊C4—24no—
198C4⋊C4—42no—
199C4⋊C4—42no—
200C4⋊C4—42no—
201C16—42no—
202C23—22no—
203C23—22no—
204C23—22no—
205C23#102×C12711yescharacteristic
206C23#102×C12711yescharacteristic
207C23C2×SD16×C12711yescharacteristic
208C2×C4—22no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—44no—
216C2×C4—84no—
217C2×C4—84no—
218C2×C4—84no—
219C2×C4#102×C12711yescharacteristic
220C2×C4#102×C12711yescharacteristic
221C2×C4C2×C22⋊C4×C12711yescharacteristic
222C2×C4#123×C12712yes—
223C2×C4C2×D8×C12711yescharacteristic
224C2×C4#137×C12712yes—
225C8—21no—
226C8—21no—
227C8—82no—
228C8#117×C12712yes—
229C8#123×C12712yes—
230C22—28no—
231C22—21no—
232C22—21no—
233C22—21no—
234C22—21no—
235C22—21no—
236C22—21no—
237C22#361×C12712yes—
238C22#362×C12712yes—
239C22C2×#102×C12711yescharacteristic
240C22#483×C12712yes—
241C4—21no—
242C4—21no—
243C4—84no—
244C4#381×C12711yescharacteristic
245C4#419×C12711yescharacteristic
246C4#480×C12712yes—
247C2—22no—
248C2—22no—
249C2—22no—
250C2C127×#182311yescharacteristic
251C2C2×#361×C12711yescharacteristic
252C2C2×#362×C12711yescharacteristic
subgroupG/H
center, socleC22×C127C2×#102
commutatorC2×C8C22×C4×C127
Frattini, cosocleC22×C8C23×C127
prime radicalC24×C127SD16
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C23×C4×C127 ◁ C23×C8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
4. C127×#1387C2semidirect
120. #12871C127direct (N × H)
130. #1387C2×C127semidirect
131. C127#12871direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#107×C1272
C127×#21122
C127×#18102
C127×#13872
#12871127