Finite Group Databasebeta

← C2×C127×#1328 #44575130

Subgroups — C2×C127×#1328 #44575130

Order 32512.

378 conjugacy classes of subgroups.

The subgroup lattice has 244 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#424×C127C211yesmaximal, characteristic
2C2×#349×C127C212yesmaximal
3C127×#1328C214yesmaximal, direct product factor
4C22×M16×C127C2211yescharacteristic
5C23×C8×C127C411yescharacteristic
6C2×#117×C127C411yescharacteristic
7C2×M32×C127—22no—
8#424×C127—22no—
9#424×C127C412yes—
10#424×C127C2212yes—
11C2×C4⋊C8×C127—22no—
12#349×C127—22no—
13#349×C127C2214yes—
14C23×C4×C127C2×C411yescharacteristic
15C2×M16×C127—41no—
16C2×M16×C127—41no—
17C2×M16×C127C2×C411yescharacteristic
18C2×M16×C127D412yes—
19C2×M16×C127C2311yescharacteristic
20C22×C8×C127—21no—
21C22×C8×C127—21no—
22C22×C8×C127—41no—
23C22×C8×C127—41no—
24C22×C8×C127C2×C412yes—
25C22×C8×C127D412yes—
26#117×C127—21no—
27#117×C127—21no—
28#117×C127C812yes—
29#117×C127C2×C412yes—
30C2×C4⋊C4×C127—21no—
31C2×C22⋊C4×C127C812yes—
32C2×C42×C127—21no—
33M32×C127—24no—
34M32×C127—42no—
35C2×C16×C127—42no—
36C4⋊C8×C127—24no—
37C4⋊C8×C127—24no—
38C24×C127C2×C811yescharacteristic
39C22×C4×C127—21no—
40C22×C4×C127—21no—
41C22×C4×C127—21no—
42C22×C4×C127—21no—
43C22×C4×C127—22no—
44C22×C4×C127C22⋊C411yescharacteristic
45C22×C4×C127C22⋊C411yescharacteristic
46C22×C4×C127C2×C811yescharacteristic
47C22×C4×C127M1611yescharacteristic
48C22×C4×C127M1611yescharacteristic
49C22×C4×C127C22×C411yescharacteristic
50M16×C127—41no—
51M16×C127—42no—
52M16×C127—41no—
53C2×C8×C127—22no—
54C2×C8×C127—22no—
55C2×C8×C127—22no—
56C2×C8×C127—42no—
57C2×C8×C127—41no—
58C2×C8×C127—41no—
59C2×C8×C127—42no—
60C2×C8×C127C22⋊C412yes—
61C2×C8×C127C2×D412yes—
62C4⋊C4×C127—22no—
63C4⋊C4×C127—22no—
64C22⋊C4×C127—22no—
65C22⋊C4×C127C2×C814yes—
66C42×C127—22no—
67C42×C127—22no—
68C16×C127—44no—
69C23×C127—21no—
70C23×C127—21no—
71C23×C127—42no—
72C23×C127C22⋊C811yescharacteristic
73C23×C127C22⋊C811yescharacteristic
74C23×C127C22×C811yescharacteristic
75C2×C4×C127—21no—
76C2×C4×C127—21no—
77C2×C4×C127—21no—
78C2×C4×C127—21no—
79C2×C4×C127—21no—
80C2×C4×C127—21no—
81C2×C4×C127—21no—
82C2×C4×C127—21no—
83C2×C4×C127—21no—
84C2×C4×C127—21no—
85C2×C4×C127—24no—
86C2×C4×C127—44no—
87C2×C4×C127C22⋊C811yescharacteristic
88C2×C4×C127C22⋊C811yescharacteristic
89C2×C4×C127#9911yescharacteristic
90C2×C4×C127#9911yescharacteristic
91C2×C4×C127#10111yescharacteristic
92C2×C4×C127#10111yescharacteristic
93C2×C4×C127C2×C22⋊C411yescharacteristic
94C2×C4×C127C2×M1611yescharacteristic
95C8×C127—22no—
96C8×C127—22no—
97C8×C127—42no—
98C22×C127—22no—
99C22×C127—21no—
100C22×C127—21no—
101C22×C127—41no—
102C22×C127—41no—
103C22×C127—42no—
104C22×C127—42no—
105C22×C127#32411yescharacteristic
106C22×C127#32411yescharacteristic
107C22×C127C2×C22⋊C811yescharacteristic
108C4×C127—21no—
109C4×C127—21no—
110C4×C127—44no—
111C4×C127#32411yescharacteristic
112C4×C127#32411yescharacteristic
113C4×C127C2×#9911yescharacteristic
114C4×C127C2×#10111yescharacteristic
115C2×#1328C12711yesmaximal, characteristic, direct product factor, Sylow
116C2×C127—21no—
117C2×C127—21no—
118C2×C127—41no—
119C2×C127—41no—
120C2×C127#132812yesdirect product factor
121C2×C127C2×#32411yescharacteristic
122C2×#424C2×C12711yescharacteristic
123C2×#349C2×C12712yes—
124#1328C2×C12714yesdirect product factor
125C127C2×#132811yescharacteristic, direct product factor, Sylow
126C22×M16C22×C12711yescharacteristic
127C23×C8C4×C12711yescharacteristic
128C2×#117C4×C12711yescharacteristic
129C2×M32—22no—
130#424—22no—
131#424C4×C12712yes—
132#424C22×C12712yes—
133C2×C4⋊C8—22no—
134#349—22no—
135#349C22×C12714yes—
136C23×C4C2×C4×C12711yescharacteristic
137C2×M16—41no—
138C2×M16—41no—
139C2×M16C2×C4×C12711yescharacteristic
140C2×M16D4×C12712yes—
141C2×M16C23×C12711yescharacteristic
142C22×C8—21no—
143C22×C8—21no—
144C22×C8—41no—
145C22×C8—41no—
146C22×C8C2×C4×C12712yes—
147C22×C8D4×C12712yes—
148#117—21no—
149#117—21no—
150#117C8×C12712yes—
151#117C2×C4×C12712yes—
152C2×C4⋊C4—21no—
153C2×C22⋊C4C8×C12712yes—
154C2×C42—21no—
155M32—24no—
156M32—42no—
157C2×C16—42no—
158C4⋊C8—24no—
159C4⋊C8—24no—
160C24C2×C8×C12711yescharacteristic
161C22×C4—21no—
162C22×C4—21no—
163C22×C4—21no—
164C22×C4—21no—
165C22×C4—22no—
166C22×C4C22⋊C4×C12711yescharacteristic
167C22×C4C22⋊C4×C12711yescharacteristic
168C22×C4C2×C8×C12711yescharacteristic
169C22×C4M16×C12711yescharacteristic
170C22×C4M16×C12711yescharacteristic
171C22×C4C22×C4×C12711yescharacteristic
172M16—41no—
173M16—42no—
174M16—41no—
175C2×C8—22no—
176C2×C8—22no—
177C2×C8—22no—
178C2×C8—42no—
179C2×C8—41no—
180C2×C8—41no—
181C2×C8—42no—
182C2×C8C22⋊C4×C12712yes—
183C2×C8C2×D4×C12712yes—
184C4⋊C4—22no—
185C4⋊C4—22no—
186C22⋊C4—22no—
187C22⋊C4C2×C8×C12714yes—
188C42—22no—
189C42—22no—
190C16—44no—
191C23—21no—
192C23—21no—
193C23—42no—
194C23C22⋊C8×C12711yescharacteristic
195C23C22⋊C8×C12711yescharacteristic
196C23C22×C8×C12711yescharacteristic
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—24no—
208C2×C4—44no—
209C2×C4C22⋊C8×C12711yescharacteristic
210C2×C4C22⋊C8×C12711yescharacteristic
211C2×C4#99×C12711yescharacteristic
212C2×C4#99×C12711yescharacteristic
213C2×C4#101×C12711yescharacteristic
214C2×C4#101×C12711yescharacteristic
215C2×C4C2×C22⋊C4×C12711yescharacteristic
216C2×C4C2×M16×C12711yescharacteristic
217C8—22no—
218C8—22no—
219C8—42no—
220C22—22no—
221C22—21no—
222C22—21no—
223C22—41no—
224C22—41no—
225C22—42no—
226C22—42no—
227C22#324×C12711yescharacteristic
228C22#324×C12711yescharacteristic
229C22C2×C22⋊C8×C12711yescharacteristic
230C4—21no—
231C4—21no—
232C4—44no—
233C4#324×C12711yescharacteristic
234C4#324×C12711yescharacteristic
235C4C2×#99×C12711yescharacteristic
236C4C2×#101×C12711yescharacteristic
237C2—21no—
238C2—21no—
239C2—41no—
240C2—41no—
241C2C127×#132812yesdirect product factor
242C2C2×#324×C12711yescharacteristic
subgroupG/H
centerC2×C4×C127#99
commutatorC23C22×C8×C127
Frattini, cosocleC2×M16C23×C127
socleC22×C127#324
prime radicalC24×C127C2×C8
LCSG ▷ C23 ▷ 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×#1328C2direct (N × H)
115. C2×#1328C127direct (N × H)
120. C2×C127#1328direct (N × H)
124. #1328C2×C127direct (N × H)
125. C127C2×#1328direct (N × H)
241. C2C127×#1328direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#424×C1272
C2×#349×C1272
C127×#13282
C2×#1328127