Finite Group Databasebeta

← C127×#12848 #44576521

Subgroups — C127×#12848 #44576521

Order 32512.

440 conjugacy classes of subgroups.

The subgroup lattice has 274 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#405×C127C211yesmaximal, characteristic
2C127×#2112C211yesmaximal, characteristic
3C2×C22⋊C16×C127C211yesmaximal, characteristic
4C127×#1379C214yesmaximal, complemented
5C22×M16×C127C411yescharacteristic
6C23×C8×C127C2211yescharacteristic
7C2×#117×C127C411yescharacteristic
8C2×M32×C127C2212yes—
9C22×C16×C127C2212yes—
10#405×C127—21no—
11#405×C127—21no—
12#405×C127C412yes—
13#405×C127C2212yes—
14C2×#97×C127—21no—
15C2×C4×C8×C127—21no—
16C22⋊C16×C127—21no—
17C22⋊C16×C127—21no—
18C22⋊C16×C127—21no—
19C22⋊C16×C127—21no—
20C23×C4×C127C2×C411yescharacteristic
21C2×M16×C127—21no—
22C2×M16×C127—24no—
23C2×M16×C127C2×C412yes—
24C22×C8×C127—21no—
25C22×C8×C127—24no—
26C22×C8×C127C2×C411yescharacteristic
27C22×C8×C127D411yescharacteristic
28C22×C8×C127D411yescharacteristic
29C22×C8×C127D411yescharacteristic
30C22×C8×C127D411yescharacteristic
31C22×C8×C127C2311yescharacteristic
32#117×C127—21no—
33#117×C127—21no—
34#117×C127C812yes—
35#117×C127C2×C412yes—
36C2×C4⋊C4×C127C811yescharacteristic
37C2×C4⋊C4×C127C811yescharacteristic
38C2×C22⋊C4×C127—21no—
39C2×C42×C127—21no—
40M32×C127—24no—
41C2×C16×C127—22no—
42C2×C16×C127—22no—
43C2×C16×C127—24no—
44#97×C127—22no—
45#97×C127—22no—
46C4×C8×C127—22no—
47C4×C8×C127—22no—
48C24×C127M1611yescharacteristic
49C22×C4×C127—22no—
50C22×C4×C127—22no—
51C22×C4×C127—21no—
52C22×C4×C127—21no—
53C22×C4×C127C22⋊C411yescharacteristic
54C22×C4×C127C22⋊C411yescharacteristic
55C22×C4×C127C2×C811yescharacteristic
56C22×C4×C127C2×C811yescharacteristic
57C22×C4×C127M1611yescharacteristic
58C22×C4×C127C22×C411yescharacteristic
59M16×C127—24no—
60M16×C127—22no—
61M16×C127M1614yes—
62C2×C8×C127—24no—
63C2×C8×C127—22no—
64C2×C8×C127—22no—
65C2×C8×C127—22no—
66C2×C8×C127—22no—
67C2×C8×C127—22no—
68C2×C8×C127—22no—
69C2×C8×C127C22⋊C411yescharacteristic
70C2×C8×C127C22⋊C411yescharacteristic
71C2×C8×C127C2×D411yescharacteristic
72C2×C8×C127C2×D411yescharacteristic
73C2×C8×C127#4114yes—
74C4⋊C4×C127—21no—
75C4⋊C4×C127—21no—
76C4⋊C4×C127C2×C812yes—
77C4⋊C4×C127C2×C812yes—
78C22⋊C4×C127—22no—
79C22⋊C4×C127—22no—
80C42×C127—22no—
81C42×C127—22no—
82C16×C127—42no—
83C16×C127—42no—
84C23×C127—22no—
85C23×C127—22no—
86C23×C127—41no—
87C23×C127C22⋊C811yescharacteristic
88C23×C127C22⋊C811yescharacteristic
89C23×C127C2×M1611yescharacteristic
90C2×C4×C127—22no—
91C2×C4×C127—21no—
92C2×C4×C127—21no—
93C2×C4×C127—21no—
94C2×C4×C127—21no—
95C2×C4×C127—22no—
96C2×C4×C127—22no—
97C2×C4×C127—22no—
98C2×C4×C127—22no—
99C2×C4×C127—42no—
100C2×C4×C127—42no—
101C2×C4×C127C22⋊C811yescharacteristic
102C2×C4×C127C22⋊C811yescharacteristic
103C2×C4×C127C2×C22⋊C411yescharacteristic
104C2×C4×C127#11712yes—
105C2×C4×C127C22×C811yescharacteristic
106C2×C4×C127C2×M1612yes—
107C8×C127—21no—
108C8×C127—21no—
109C8×C127—24no—
110C8×C127#12312yes—
111C8×C127#12312yes—
112C22×C127—21no—
113C22×C127—21no—
114C22×C127—21no—
115C22×C127—21no—
116C22×C127—21no—
117C22×C127—21no—
118C22×C127—21no—
119C22×C127—44no—
120C22×C127#35012yes—
121C22×C127C2×C22⋊C811yescharacteristic
122C22×C127#43212yes—
123C4×C127—21no—
124C4×C127—21no—
125C4×C127—42no—
126C4×C127—42no—
127C4×C127#38111yescharacteristic
128C4×C127#40711yescharacteristic
129C4×C127#43112yes—
130#12848C12711yesmaximal, characteristic, direct product factor, Sylow
131C2×C127—22no—
132C2×C127—22no—
133C2×C127—41no—
134C2×C127#181711yescharacteristic
135C2×C127C2×#35011yescharacteristic
136C2×C127#211711yescharacteristic
137C2×#405C2×C12711yescharacteristic
138#2112C2×C12711yescharacteristic
139C2×C22⋊C16C2×C12711yescharacteristic
140#1379C2×C12714yescomplemented
141C127#1284811yescharacteristic, direct product factor, Sylow
142C22×M16C4×C12711yescharacteristic
143C23×C8C22×C12711yescharacteristic
144C2×#117C4×C12711yescharacteristic
145C2×M32C22×C12712yes—
146C22×C16C22×C12712yes—
147#405—21no—
148#405—21no—
149#405C4×C12712yes—
150#405C22×C12712yes—
151C2×#97—21no—
152C2×C4×C8—21no—
153C22⋊C16—21no—
154C22⋊C16—21no—
155C22⋊C16—21no—
156C22⋊C16—21no—
157C23×C4C2×C4×C12711yescharacteristic
158C2×M16—21no—
159C2×M16—24no—
160C2×M16C2×C4×C12712yes—
161C22×C8—21no—
162C22×C8—24no—
163C22×C8C2×C4×C12711yescharacteristic
164C22×C8D4×C12711yescharacteristic
165C22×C8D4×C12711yescharacteristic
166C22×C8D4×C12711yescharacteristic
167C22×C8D4×C12711yescharacteristic
168C22×C8C23×C12711yescharacteristic
169#117—21no—
170#117—21no—
171#117C8×C12712yes—
172#117C2×C4×C12712yes—
173C2×C4⋊C4C8×C12711yescharacteristic
174C2×C4⋊C4C8×C12711yescharacteristic
175C2×C22⋊C4—21no—
176C2×C42—21no—
177M32—24no—
178C2×C16—22no—
179C2×C16—22no—
180C2×C16—24no—
181#97—22no—
182#97—22no—
183C4×C8—22no—
184C4×C8—22no—
185C24M16×C12711yescharacteristic
186C22×C4—22no—
187C22×C4—22no—
188C22×C4—21no—
189C22×C4—21no—
190C22×C4C22⋊C4×C12711yescharacteristic
191C22×C4C22⋊C4×C12711yescharacteristic
192C22×C4C2×C8×C12711yescharacteristic
193C22×C4C2×C8×C12711yescharacteristic
194C22×C4M16×C12711yescharacteristic
195C22×C4C22×C4×C12711yescharacteristic
196M16—24no—
197M16—22no—
198M16M16×C12714yes—
199C2×C8—24no—
200C2×C8—22no—
201C2×C8—22no—
202C2×C8—22no—
203C2×C8—22no—
204C2×C8—22no—
205C2×C8—22no—
206C2×C8C22⋊C4×C12711yescharacteristic
207C2×C8C22⋊C4×C12711yescharacteristic
208C2×C8C2×D4×C12711yescharacteristic
209C2×C8C2×D4×C12711yescharacteristic
210C2×C8#41×C12714yes—
211C4⋊C4—21no—
212C4⋊C4—21no—
213C4⋊C4C2×C8×C12712yes—
214C4⋊C4C2×C8×C12712yes—
215C22⋊C4—22no—
216C22⋊C4—22no—
217C42—22no—
218C42—22no—
219C16—42no—
220C16—42no—
221C23—22no—
222C23—22no—
223C23—41no—
224C23C22⋊C8×C12711yescharacteristic
225C23C22⋊C8×C12711yescharacteristic
226C23C2×M16×C12711yescharacteristic
227C2×C4—22no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—42no—
237C2×C4—42no—
238C2×C4C22⋊C8×C12711yescharacteristic
239C2×C4C22⋊C8×C12711yescharacteristic
240C2×C4C2×C22⋊C4×C12711yescharacteristic
241C2×C4#117×C12712yes—
242C2×C4C22×C8×C12711yescharacteristic
243C2×C4C2×M16×C12712yes—
244C8—21no—
245C8—21no—
246C8—24no—
247C8#123×C12712yes—
248C8#123×C12712yes—
249C22—21no—
250C22—21no—
251C22—21no—
252C22—21no—
253C22—21no—
254C22—21no—
255C22—21no—
256C22—44no—
257C22#350×C12712yes—
258C22C2×C22⋊C8×C12711yescharacteristic
259C22#432×C12712yes—
260C4—21no—
261C4—21no—
262C4—42no—
263C4—42no—
264C4#381×C12711yescharacteristic
265C4#407×C12711yescharacteristic
266C4#431×C12712yes—
267C2—22no—
268C2—22no—
269C2—41no—
270C2C127×#181711yescharacteristic
271C2C2×#350×C12711yescharacteristic
272C2C127×#211711yescharacteristic
subgroupG/H
centerC2×C8×C127C2×D4
commutatorC2×C4C22×C8×C127
Frattini, cosocleC22×C8C23×C127
socleC22×C127C2×C22⋊C8
prime radicalC24×C127M16
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C8×C127 ◁ C23×C8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
4. C127×#1379C2semidirect
130. #12848C127direct (N × H)
140. #1379C2×C127semidirect
141. C127#12848direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#405×C1272
C127×#21122
C2×C22⋊C16×C1272
C127×#13792
#12848127