Finite Group Databasebeta

← C127×#12869 #44576542

Subgroups — C127×#12869 #44576542

Order 32512.

404 conjugacy classes of subgroups.

The subgroup lattice has 268 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#427×C127C211yesmaximal, characteristic
2C2×C22⋊C16×C127C211yesmaximal, characteristic
3C127×#1810C211yesmaximal, characteristic
4C127×#1382C214yesmaximal, complemented
5C23×C8×C127C2211yescharacteristic
6C2×#117×C127—21no—
7C22×C16×C127C2212yes—
8C2×#108×C127C2212yes—
9#427×C127—21no—
10#427×C127—21no—
11#427×C127C412yes—
12#427×C127C2212yes—
13C2×#107×C127C411yescharacteristic
14C2×#107×C127C411yescharacteristic
15C2×#106×C127—21no—
16#407×C127—21no—
17C22⋊C16×C127—21no—
18C22⋊C16×C127—21no—
19#341×C127—21no—
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
29#117×C127—22no—
30#117×C127—22no—
31#117×C127—41no—
32#117×C127—41no—
33C2×C4⋊C4×C127—21no—
34C2×C4⋊C4×C127—21no—
35C2×C22⋊C4×C127—41no—
36C2×C42×C127—41no—
37C2×C16×C127—22no—
38C2×C16×C127—24no—
39#108×C127—24no—
40#107×C127—21no—
41#107×C127—21no—
42#107×C127C2×C412yes—
43#107×C127C2×C412yes—
44#106×C127—22no—
45#106×C127—22no—
46C22⋊C8×C127—41no—
47C22⋊C8×C127—41no—
48C24×C127SD1611yescharacteristic
49C22×C4×C127—22no—
50C22×C4×C127—22no—
51C22×C4×C127—41no—
52C22×C4×C127—41no—
53C22×C4×C127C22⋊C411yescharacteristic
54C22×C4×C127C22⋊C411yescharacteristic
55C22×C4×C127D811yescharacteristic
56C22×C4×C127D811yescharacteristic
57C22×C4×C127SD1611yescharacteristic
58C22×C4×C127C2×D411yescharacteristic
59M16×C127—42no—
60M16×C127—42no—
61C2×C8×C127—22no—
62C2×C8×C127—22no—
63C2×C8×C127—22no—
64C2×C8×C127—22no—
65C2×C8×C127—22no—
66C2×C8×C127—42no—
67C2×C8×C127C22⋊C411yescharacteristic
68C2×C8×C127C22⋊C411yescharacteristic
69C2×C8×C127C22×C411yescharacteristic
70C2×C8×C127C2×D411yescharacteristic
71C2×C8×C127#4114yes—
72C4⋊C4×C127—22no—
73C4⋊C4×C127—22no—
74C4⋊C4×C127—41no—
75C4⋊C4×C127—41no—
76C22⋊C4×C127—42no—
77C22⋊C4×C127—42no—
78C42×C127—42no—
79C42×C127—42no—
80C16×C127—42no—
81C23×C127—22no—
82C23×C127—22no—
83C23×C127—41no—
84C23×C127#10211yescharacteristic
85C23×C127#10211yescharacteristic
86C23×C127C2×SD1611yescharacteristic
87C2×C4×C127—22no—
88C2×C4×C127—21no—
89C2×C4×C127—21no—
90C2×C4×C127—21no—
91C2×C4×C127—21no—
92C2×C4×C127—22no—
93C2×C4×C127—22no—
94C2×C4×C127—42no—
95C2×C4×C127—42no—
96C2×C4×C127—82no—
97C2×C4×C127—82no—
98C2×C4×C127#10211yescharacteristic
99C2×C4×C127#10211yescharacteristic
100C2×C4×C127C2×C22⋊C411yescharacteristic
101C2×C4×C127#12312yes—
102C2×C4×C127C2×D811yescharacteristic
103C2×C4×C127#13712yes—
104C8×C127—21no—
105C8×C127—21no—
106C8×C127—82no—
107C8×C127#11712yes—
108C8×C127#12312yes—
109C22×C127—21no—
110C22×C127—21no—
111C22×C127—21no—
112C22×C127—21no—
113C22×C127—21no—
114C22×C127—21no—
115C22×C127—21no—
116C22×C127—44no—
117C22×C127#35912yes—
118C22×C127C2×#10211yescharacteristic
119C22×C127#48312yes—
120C4×C127—21no—
121C4×C127—21no—
122C4×C127—82no—
123C4×C127—82no—
124C4×C127#38111yescharacteristic
125C4×C127#41911yescharacteristic
126C4×C127#48012yes—
127#12869C12711yesmaximal, characteristic, direct product factor, Sylow
128C2×C127—22no—
129C2×C127—22no—
130C2×C127—41no—
131C2×C127#182311yescharacteristic
132C2×C127C2×#35911yescharacteristic
133C2×C127#214311yescharacteristic
134C2×#427C2×C12711yescharacteristic
135C2×C22⋊C16C2×C12711yescharacteristic
136#1810C2×C12711yescharacteristic
137#1382C2×C12714yescomplemented
138C127#1286911yescharacteristic, direct product factor, Sylow
139C23×C8C22×C12711yescharacteristic
140C2×#117—21no—
141C22×C16C22×C12712yes—
142C2×#108C22×C12712yes—
143#427—21no—
144#427—21no—
145#427C4×C12712yes—
146#427C22×C12712yes—
147C2×#107C4×C12711yescharacteristic
148C2×#107C4×C12711yescharacteristic
149C2×#106—21no—
150#407—21no—
151C22⋊C16—21no—
152C22⋊C16—21no—
153#341—21no—
154C23×C4D4×C12711yescharacteristic
155C2×M16—22no—
156C22×C8—24no—
157C22×C8C2×C4×C12711yescharacteristic
158C22×C8C2×C4×C12711yescharacteristic
159C22×C8D4×C12711yescharacteristic
160C22×C8D4×C12711yescharacteristic
161C22×C8D4×C12711yescharacteristic
162C22×C8C23×C12711yescharacteristic
163#117—22no—
164#117—22no—
165#117—41no—
166#117—41no—
167C2×C4⋊C4—21no—
168C2×C4⋊C4—21no—
169C2×C22⋊C4—41no—
170C2×C42—41no—
171C2×C16—22no—
172C2×C16—24no—
173#108—24no—
174#107—21no—
175#107—21no—
176#107C2×C4×C12712yes—
177#107C2×C4×C12712yes—
178#106—22no—
179#106—22no—
180C22⋊C8—41no—
181C22⋊C8—41no—
182C24SD16×C12711yescharacteristic
183C22×C4—22no—
184C22×C4—22no—
185C22×C4—41no—
186C22×C4—41no—
187C22×C4C22⋊C4×C12711yescharacteristic
188C22×C4C22⋊C4×C12711yescharacteristic
189C22×C4D8×C12711yescharacteristic
190C22×C4D8×C12711yescharacteristic
191C22×C4SD16×C12711yescharacteristic
192C22×C4C2×D4×C12711yescharacteristic
193M16—42no—
194M16—42no—
195C2×C8—22no—
196C2×C8—22no—
197C2×C8—22no—
198C2×C8—22no—
199C2×C8—22no—
200C2×C8—42no—
201C2×C8C22⋊C4×C12711yescharacteristic
202C2×C8C22⋊C4×C12711yescharacteristic
203C2×C8C22×C4×C12711yescharacteristic
204C2×C8C2×D4×C12711yescharacteristic
205C2×C8#41×C12714yes—
206C4⋊C4—22no—
207C4⋊C4—22no—
208C4⋊C4—41no—
209C4⋊C4—41no—
210C22⋊C4—42no—
211C22⋊C4—42no—
212C42—42no—
213C42—42no—
214C16—42no—
215C23—22no—
216C23—22no—
217C23—41no—
218C23#102×C12711yescharacteristic
219C23#102×C12711yescharacteristic
220C23C2×SD16×C12711yescharacteristic
221C2×C4—22no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4—82no—
231C2×C4—82no—
232C2×C4#102×C12711yescharacteristic
233C2×C4#102×C12711yescharacteristic
234C2×C4C2×C22⋊C4×C12711yescharacteristic
235C2×C4#123×C12712yes—
236C2×C4C2×D8×C12711yescharacteristic
237C2×C4#137×C12712yes—
238C8—21no—
239C8—21no—
240C8—82no—
241C8#117×C12712yes—
242C8#123×C12712yes—
243C22—21no—
244C22—21no—
245C22—21no—
246C22—21no—
247C22—21no—
248C22—21no—
249C22—21no—
250C22—44no—
251C22#359×C12712yes—
252C22C2×#102×C12711yescharacteristic
253C22#483×C12712yes—
254C4—21no—
255C4—21no—
256C4—82no—
257C4—82no—
258C4#381×C12711yescharacteristic
259C4#419×C12711yescharacteristic
260C4#480×C12712yes—
261C2—22no—
262C2—22no—
263C2—41no—
264C2C127×#182311yescharacteristic
265C2C2×#359×C12711yescharacteristic
266C2C127×#214311yescharacteristic
subgroupG/H
centerC2×C4×C127C2×D8
commutatorC2×C8C22×C4×C127
Frattini, cosocleC22×C8C23×C127
socleC22×C127C2×#102
prime radicalC24×C127SD16
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C127 ◁ C23×C4×C127 ◁ C23×C8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
4. C127×#1382C2semidirect
127. #12869C127direct (N × H)
137. #1382C2×C127semidirect
138. C127#12869direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#427×C1272
C2×C22⋊C16×C1272
C127×#18102
C127×#13822
#12869127