Finite Group Databasebeta

← C2×C127×#1327 #44575128

Subgroups — C2×C127×#1327 #44575128

Order 32512.

410 conjugacy classes of subgroups.

The subgroup lattice has 264 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#423×C127C211yesmaximal, characteristic
2C2×#349×C127C212yesmaximal
3C127×#1327C214yesmaximal, direct product factor
4C22×M16×C127C411yescharacteristic
5C22×M16×C127C2211yescharacteristic
6C22×C42×C127C411yescharacteristic
7C2×M32×C127—22no—
8#423×C127—22no—
9#423×C127C412yes—
10#423×C127C2212yes—
11C2×C4⋊C8×C127—22no—
12#349×C127—22no—
13#349×C127C2214yes—
14C23×C4×C127—21no—
15C23×C4×C127C2×C411yescharacteristic
16C2×M16×C127—21no—
17C2×M16×C127—41no—
18C2×M16×C127—41no—
19C2×M16×C127—41no—
20C2×M16×C127—41no—
21C2×M16×C127C2×C412yes—
22C2×M16×C127C2×C411yescharacteristic
23C2×M16×C127D412yes—
24C2×M16×C127C2311yescharacteristic
25C22×C8×C127—21no—
26C22×C8×C127D412yes—
27C2×C42×C127—21no—
28C2×C42×C127—21no—
29C2×C42×C127—21no—
30C2×C42×C127C811yescharacteristic
31C2×C42×C127C812yes—
32C2×C42×C127C811yescharacteristic
33C2×C42×C127C2×C412yes—
34M32×C127—24no—
35M32×C127—42no—
36C2×C16×C127—42no—
37C4⋊C8×C127—24no—
38C4⋊C8×C127—24no—
39C24×C127M1611yescharacteristic
40C22×C4×C127—21no—
41C22×C4×C127—21no—
42C22×C4×C127—21no—
43C22×C4×C127—21no—
44C22×C4×C127—21no—
45C22×C4×C127—22no—
46C22×C4×C127—21no—
47C22×C4×C127—22no—
48C22×C4×C127—44no—
49C22×C4×C127C22⋊C411yescharacteristic
50C22×C4×C127C22⋊C411yescharacteristic
51C22×C4×C127C2×C811yescharacteristic
52C22×C4×C127C2×C811yescharacteristic
53C22×C4×C127M1611yescharacteristic
54C22×C4×C127C22×C411yescharacteristic
55M16×C127—41no—
56M16×C127—42no—
57M16×C127—41no—
58M16×C127—42no—
59M16×C127—42no—
60C2×C8×C127—22no—
61C2×C8×C127—22no—
62C2×C8×C127—22no—
63C2×C8×C127—41no—
64C2×C8×C127—41no—
65C2×C8×C127C22⋊C412yes—
66C2×C8×C127C2×D412yes—
67C42×C127—21no—
68C42×C127—22no—
69C42×C127—21no—
70C42×C127—22no—
71C42×C127C2×C812yes—
72C42×C127C2×C812yes—
73C16×C127—44no—
74C23×C127—21no—
75C23×C127—21no—
76C23×C127—42no—
77C23×C127C22⋊C811yescharacteristic
78C23×C127C22⋊C811yescharacteristic
79C23×C127C2×M1611yescharacteristic
80C2×C4×C127—24no—
81C2×C4×C127—21no—
82C2×C4×C127—21no—
83C2×C4×C127—22no—
84C2×C4×C127—21no—
85C2×C4×C127—21no—
86C2×C4×C127—21no—
87C2×C4×C127—21no—
88C2×C4×C127—21no—
89C2×C4×C127—21no—
90C2×C4×C127—21no—
91C2×C4×C127—21no—
92C2×C4×C127—22no—
93C2×C4×C127—44no—
94C2×C4×C127—44no—
95C2×C4×C127—42no—
96C2×C4×C127C22⋊C811yescharacteristic
97C2×C4×C127C22⋊C811yescharacteristic
98C2×C4×C127#9911yescharacteristic
99C2×C4×C127#9911yescharacteristic
100C2×C4×C127#10111yescharacteristic
101C2×C4×C127#10111yescharacteristic
102C2×C4×C127C2×C22⋊C411yescharacteristic
103C2×C4×C127C22×C811yescharacteristic
104C8×C127—22no—
105C8×C127—22no—
106C8×C127—42no—
107C22×C127—22no—
108C22×C127—21no—
109C22×C127—21no—
110C22×C127—41no—
111C22×C127—41no—
112C22×C127—42no—
113C22×C127—42no—
114C22×C127#32411yescharacteristic
115C22×C127#32411yescharacteristic
116C22×C127C2×C22⋊C811yescharacteristic
117C4×C127—24no—
118C4×C127—21no—
119C4×C127—21no—
120C4×C127—42no—
121C4×C127#32411yescharacteristic
122C4×C127#32411yescharacteristic
123C4×C127C2×#9911yescharacteristic
124C4×C127C2×#10111yescharacteristic
125C2×#1327C12711yesmaximal, characteristic, direct product factor, Sylow
126C2×C127—21no—
127C2×C127—21no—
128C2×C127—41no—
129C2×C127—41no—
130C2×C127#132712yesdirect product factor
131C2×C127C2×#32411yescharacteristic
132C2×#423C2×C12711yescharacteristic
133C2×#349C2×C12712yes—
134#1327C2×C12714yesdirect product factor
135C127C2×#132711yescharacteristic, direct product factor, Sylow
136C22×M16C4×C12711yescharacteristic
137C22×M16C22×C12711yescharacteristic
138C22×C42C4×C12711yescharacteristic
139C2×M32—22no—
140#423—22no—
141#423C4×C12712yes—
142#423C22×C12712yes—
143C2×C4⋊C8—22no—
144#349—22no—
145#349C22×C12714yes—
146C23×C4—21no—
147C23×C4C2×C4×C12711yescharacteristic
148C2×M16—21no—
149C2×M16—41no—
150C2×M16—41no—
151C2×M16—41no—
152C2×M16—41no—
153C2×M16C2×C4×C12712yes—
154C2×M16C2×C4×C12711yescharacteristic
155C2×M16D4×C12712yes—
156C2×M16C23×C12711yescharacteristic
157C22×C8—21no—
158C22×C8D4×C12712yes—
159C2×C42—21no—
160C2×C42—21no—
161C2×C42—21no—
162C2×C42C8×C12711yescharacteristic
163C2×C42C8×C12712yes—
164C2×C42C8×C12711yescharacteristic
165C2×C42C2×C4×C12712yes—
166M32—24no—
167M32—42no—
168C2×C16—42no—
169C4⋊C8—24no—
170C4⋊C8—24no—
171C24M16×C12711yescharacteristic
172C22×C4—21no—
173C22×C4—21no—
174C22×C4—21no—
175C22×C4—21no—
176C22×C4—21no—
177C22×C4—22no—
178C22×C4—21no—
179C22×C4—22no—
180C22×C4—44no—
181C22×C4C22⋊C4×C12711yescharacteristic
182C22×C4C22⋊C4×C12711yescharacteristic
183C22×C4C2×C8×C12711yescharacteristic
184C22×C4C2×C8×C12711yescharacteristic
185C22×C4M16×C12711yescharacteristic
186C22×C4C22×C4×C12711yescharacteristic
187M16—41no—
188M16—42no—
189M16—41no—
190M16—42no—
191M16—42no—
192C2×C8—22no—
193C2×C8—22no—
194C2×C8—22no—
195C2×C8—41no—
196C2×C8—41no—
197C2×C8C22⋊C4×C12712yes—
198C2×C8C2×D4×C12712yes—
199C42—21no—
200C42—22no—
201C42—21no—
202C42—22no—
203C42C2×C8×C12712yes—
204C42C2×C8×C12712yes—
205C16—44no—
206C23—21no—
207C23—21no—
208C23—42no—
209C23C22⋊C8×C12711yescharacteristic
210C23C22⋊C8×C12711yescharacteristic
211C23C2×M16×C12711yescharacteristic
212C2×C4—24no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—22no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—22no—
225C2×C4—44no—
226C2×C4—44no—
227C2×C4—42no—
228C2×C4C22⋊C8×C12711yescharacteristic
229C2×C4C22⋊C8×C12711yescharacteristic
230C2×C4#99×C12711yescharacteristic
231C2×C4#99×C12711yescharacteristic
232C2×C4#101×C12711yescharacteristic
233C2×C4#101×C12711yescharacteristic
234C2×C4C2×C22⋊C4×C12711yescharacteristic
235C2×C4C22×C8×C12711yescharacteristic
236C8—22no—
237C8—22no—
238C8—42no—
239C22—22no—
240C22—21no—
241C22—21no—
242C22—41no—
243C22—41no—
244C22—42no—
245C22—42no—
246C22#324×C12711yescharacteristic
247C22#324×C12711yescharacteristic
248C22C2×C22⋊C8×C12711yescharacteristic
249C4—24no—
250C4—21no—
251C4—21no—
252C4—42no—
253C4#324×C12711yescharacteristic
254C4#324×C12711yescharacteristic
255C4C2×#99×C12711yescharacteristic
256C4C2×#101×C12711yescharacteristic
257C2—21no—
258C2—21no—
259C2—41no—
260C2—41no—
261C2C127×#132712yesdirect product factor
262C2C2×#324×C12711yescharacteristic
subgroupG/H
centerC2×C4×C127#99
commutatorC2×C4C22×C8×C127
Frattini, cosocleC2×M16C23×C127
socleC22×C127#324
prime radicalC24×C127M16
LCSG ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C127 ◁ C22×C4×C127 ◁ C22×M16×C127 ◁ G

Complements

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

NH ≅ G/Ntype
3. C127×#1327C2direct (N × H)
125. C2×#1327C127direct (N × H)
130. C2×C127#1327direct (N × H)
134. #1327C2×C127direct (N × H)
135. C127C2×#1327direct (N × H)
261. C2C127×#1327direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#423×C1272
C2×#349×C1272
C127×#13272
C2×#1327127