Finite Group Databasebeta

← C127×#7183 #44570856

Subgroups — C127×#7183 #44570856

Order 32512.

386 conjugacy classes of subgroups.

The subgroup lattice has 256 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊C16×C127C212yesmaximal
2C2×#336×C127C211yesmaximal, characteristic
3C23×C8×C127C411yescharacteristic
4C23×C8×C127C2211yescharacteristic
5C22×C42×C127C411yescharacteristic
6C22×C16×C127—22no—
7C22⋊C16×C127—22no—
8C22⋊C16×C127C414yescomplemented
9#336×C127—22no—
10C23×C4×C127C812yes—
11C23×C4×C127C2×C411yescharacteristic
12C22×C8×C127—21no—
13C22×C8×C127—21no—
14C22×C8×C127—41no—
15C22×C8×C127—41no—
16C22×C8×C127—41no—
17C22×C8×C127—41no—
18C22×C8×C127C812yes—
19C22×C8×C127C2×C412yes—
20C22×C8×C127D412yes—
21C22×C8×C127D411yescharacteristic
22C22×C8×C127Q811yescharacteristic
23C2×C42×C127—21no—
24C2×C42×C127—21no—
25C2×C42×C127—41no—
26C2×C42×C127—41no—
27C2×C16×C127—24no—
28C2×C16×C127—42no—
29C2×C16×C127—42no—
30C24×C127C2×C811yescharacteristic
31C22×C4×C127—21no—
32C22×C4×C127—21no—
33C22×C4×C127—21no—
34C22×C4×C127—21no—
35C22×C4×C127—22no—
36C22×C4×C127—22no—
37C22×C4×C127—42no—
38C22×C4×C127—42no—
39C22×C4×C127C1614yescomplemented
40C22×C4×C127C4211yescharacteristic
41C22×C4×C127C22⋊C411yescharacteristic
42C22×C4×C127C4⋊C411yescharacteristic
43C22×C4×C127C2×C811yescharacteristic
44C22×C4×C127M1611yescharacteristic
45C22×C4×C127M1611yescharacteristic
46C2×C8×C127—22no—
47C2×C8×C127—22no—
48C2×C8×C127—22no—
49C2×C8×C127—42no—
50C2×C8×C127—41no—
51C2×C8×C127—41no—
52C2×C8×C127—42no—
53C2×C8×C127—41no—
54C2×C8×C127—41no—
55C2×C8×C127—42no—
56C2×C8×C127C22⋊C412yes—
57C2×C8×C127C4⋊C412yes—
58C42×C127—42no—
59C42×C127—41no—
60C42×C127—41no—
61C16×C127—44no—
62C23×C127—21no—
63C23×C127—21no—
64C23×C127—22no—
65C23×C127C4×C811yescharacteristic
66C23×C127C22⋊C811yescharacteristic
67C23×C127C4⋊C811yescharacteristic
68C23×C127C2×C1612yes—
69C23×C127M3212yes—
70C2×C4×C127—21no—
71C2×C4×C127—21no—
72C2×C4×C127—21no—
73C2×C4×C127—21no—
74C2×C4×C127—21no—
75C2×C4×C127—21no—
76C2×C4×C127—21no—
77C2×C4×C127—21no—
78C2×C4×C127—21no—
79C2×C4×C127—21no—
80C2×C4×C127—24no—
81C2×C4×C127—44no—
82C2×C4×C127—42no—
83C2×C4×C127—42no—
84C2×C4×C127—44no—
85C2×C4×C127#9511yescharacteristic
86C2×C4×C127#9711yescharacteristic
87C2×C4×C127C22⋊C811yescharacteristic
88C2×C4×C127#9911yescharacteristic
89C2×C4×C127#9911yescharacteristic
90C2×C4×C127#10011yescharacteristic
91C2×C4×C127#10111yescharacteristic
92C2×C4×C127C4⋊C811yescharacteristic
93C8×C127—22no—
94C8×C127—22no—
95C8×C127—42no—
96C22×C127—21no—
97C22×C127—21no—
98C22×C127—22no—
99C22×C127—22no—
100C22×C127—22no—
101C22×C127—22no—
102C22×C127—21no—
103C22×C127—21no—
104C22×C127#32311yescharacteristic
105C22×C127#32411yescharacteristic
106C22×C127#33611yescharacteristic
107C22×C127C4×C1611yescharacteristic
108C22×C127#34611yescharacteristic
109C22×C127C22⋊C1612yes—
110C22×C127#34912yes—
111C22×C127C4⋊C1612yes—
112C4×C127—21no—
113C4×C127—21no—
114C4×C127—44no—
115C4×C127#32311yescharacteristic
116C4×C127#32411yescharacteristic
117C4×C127#34211yescharacteristic
118C4×C127#34311yescharacteristic
119#7183C12711yesmaximal, characteristic, direct product factor, Sylow
120C2×C127—21no—
121C2×C127—21no—
122C2×C127—22no—
123C2×C127#128011yescharacteristic
124C2×C127#131412yes—
125C2×C127#132212yes—
126C2×C127#137411yescharacteristic
127C2×C127#137711yescharacteristic
128C2×C22⋊C16C2×C12712yes—
129C2×#336C2×C12711yescharacteristic
130C127#718311yescharacteristic, direct product factor, Sylow
131C23×C8C4×C12711yescharacteristic
132C23×C8C22×C12711yescharacteristic
133C22×C42C4×C12711yescharacteristic
134C22×C16—22no—
135C22⋊C16—22no—
136C22⋊C16C4×C12714yescomplemented
137#336—22no—
138C23×C4C8×C12712yes—
139C23×C4C2×C4×C12711yescharacteristic
140C22×C8—21no—
141C22×C8—21no—
142C22×C8—41no—
143C22×C8—41no—
144C22×C8—41no—
145C22×C8—41no—
146C22×C8C8×C12712yes—
147C22×C8C2×C4×C12712yes—
148C22×C8D4×C12712yes—
149C22×C8D4×C12711yescharacteristic
150C22×C8Q8×C12711yescharacteristic
151C2×C42—21no—
152C2×C42—21no—
153C2×C42—41no—
154C2×C42—41no—
155C2×C16—24no—
156C2×C16—42no—
157C2×C16—42no—
158C24C2×C8×C12711yescharacteristic
159C22×C4—21no—
160C22×C4—21no—
161C22×C4—21no—
162C22×C4—21no—
163C22×C4—22no—
164C22×C4—22no—
165C22×C4—42no—
166C22×C4—42no—
167C22×C4C16×C12714yescomplemented
168C22×C4C42×C12711yescharacteristic
169C22×C4C22⋊C4×C12711yescharacteristic
170C22×C4C4⋊C4×C12711yescharacteristic
171C22×C4C2×C8×C12711yescharacteristic
172C22×C4M16×C12711yescharacteristic
173C22×C4M16×C12711yescharacteristic
174C2×C8—22no—
175C2×C8—22no—
176C2×C8—22no—
177C2×C8—42no—
178C2×C8—41no—
179C2×C8—41no—
180C2×C8—42no—
181C2×C8—41no—
182C2×C8—41no—
183C2×C8—42no—
184C2×C8C22⋊C4×C12712yes—
185C2×C8C4⋊C4×C12712yes—
186C42—42no—
187C42—41no—
188C42—41no—
189C16—44no—
190C23—21no—
191C23—21no—
192C23—22no—
193C23C4×C8×C12711yescharacteristic
194C23C22⋊C8×C12711yescharacteristic
195C23C4⋊C8×C12711yescharacteristic
196C23C2×C16×C12712yes—
197C23M32×C12712yes—
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—21no—
208C2×C4—24no—
209C2×C4—44no—
210C2×C4—42no—
211C2×C4—42no—
212C2×C4—44no—
213C2×C4#95×C12711yescharacteristic
214C2×C4#97×C12711yescharacteristic
215C2×C4C22⋊C8×C12711yescharacteristic
216C2×C4#99×C12711yescharacteristic
217C2×C4#99×C12711yescharacteristic
218C2×C4#100×C12711yescharacteristic
219C2×C4#101×C12711yescharacteristic
220C2×C4C4⋊C8×C12711yescharacteristic
221C8—22no—
222C8—22no—
223C8—42no—
224C22—22no—
225C22—22no—
226C22—22no—
227C22—22no—
228C22—21no—
229C22—21no—
230C22—21no—
231C22—21no—
232C22#323×C12711yescharacteristic
233C22#324×C12711yescharacteristic
234C22#336×C12711yescharacteristic
235C22C4×C16×C12711yescharacteristic
236C22#346×C12711yescharacteristic
237C22C22⋊C16×C12712yes—
238C22#349×C12712yes—
239C22C4⋊C16×C12712yes—
240C4—21no—
241C4—21no—
242C4—44no—
243C4#323×C12711yescharacteristic
244C4#324×C12711yescharacteristic
245C4#342×C12711yescharacteristic
246C4#343×C12711yescharacteristic
247C2—21no—
248C2—21no—
249C2—22no—
250C2C127×#128011yescharacteristic
251C2C127×#131412yes—
252C2C127×#132212yes—
253C2C127×#137411yescharacteristic
254C2C127×#137711yescharacteristic
subgroupG/H
centerC22×C4×C127C22⋊C4
commutatorC22C4×C16×C127
Frattini, cosocleC23×C8C22×C127
socleC23×C127C22⋊C8
prime radicalC24×C127C2×C8
LCSG ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C127 ◁ C23×C8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
8. C22⋊C16×C127C4semidirect
39. C22×C4×C127C16semidirect
119. #7183C127direct (N × H)
130. C127#7183direct (N × H)
136. C22⋊C16C4×C127semidirect
167. C22×C4C16×C127semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊C16×C1272
C2×#336×C1272
#7183127