Finite Group Databasebeta

← C127×#1869 #30634821

Subgroups — C127×#1869 #30634821

Order 16256.

432 conjugacy classes of subgroups.

The subgroup lattice has 228 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C8×C127C211yesmaximal, characteristic, complemented
2C2×C4×D4×C127C211yesmaximal, characteristic
3C2×C22⋊C8×C127C211yesmaximal, characteristic, complemented
4C2×C22⋊C8×C127C212yesmaximal, complemented
5#336×C127C212yesmaximal, complemented
6C22×D4×C127C411yescharacteristic
7C23×C4×C127C2211yescharacteristic
8C23×C4×C127C2211yescharacteristic
9C22×C8×C127—22no—
10C22×C8×C127—24no—
11C22×C8×C127C2212yes—
12C22×C8×C127C2212yes—
13C4×D4×C127—22no—
14C4×D4×C127—22no—
15C2×C4⋊C4×C127C411yescharacteristic
16C2×C22⋊C4×C127C411yescharacteristic
17C2×C22⋊C4×C127C411yescharacteristic
18C2×C42×C127C2211yescharacteristic
19C22⋊C8×C127—22no—
20C22⋊C8×C127—24no—
21C24×C127C2×C411yescharacteristic
22C24×C127C2×C411yescharacteristic
23C2×D4×C127—22no—
24C2×D4×C127—22no—
25C2×D4×C127C814yescomplemented
26C22×C4×C127—22no—
27C22×C4×C127—22no—
28C22×C4×C127—22no—
29C22×C4×C127—21no—
30C22×C4×C127—21no—
31C22×C4×C127—22no—
32C22×C4×C127C2×C411yescharacteristic
33C22×C4×C127C2×C411yescharacteristic
34C22×C4×C127C2×C411yescharacteristic
35C22×C4×C127C2×C411yescharacteristic
36C22×C4×C127D412yes—
37C22×C4×C127D412yes—
38C22×C4×C127C2311yescharacteristic
39C2×C8×C127—28no—
40C2×C8×C127—22no—
41C2×C8×C127—22no—
42C2×C8×C127—22no—
43C2×C8×C127—22no—
44C2×C8×C127—22no—
45C2×C8×C127D414yescomplemented
46C4⋊C4×C127—22no—
47C22⋊C4×C127—22no—
48C22⋊C4×C127—22no—
49C42×C127—21no—
50C42×C127—21no—
51C23×C127—22no—
52C23×C127—22no—
53C23×C127—21no—
54C23×C127—22no—
55C23×C127—21no—
56C23×C127—22no—
57C23×C127C22⋊C412yes—
58C23×C127C2×C812yes—
59C23×C127C2×C812yescomplemented
60C23×C127M1612yes—
61C23×C127C22×C411yescharacteristic
62D4×C127—28no—
63C2×C4×C127—21no—
64C2×C4×C127—22no—
65C2×C4×C127—21no—
66C2×C4×C127—22no—
67C2×C4×C127—24no—
68C2×C4×C127—22no—
69C2×C4×C127—21no—
70C2×C4×C127—21no—
71C2×C4×C127—22no—
72C2×C4×C127—22no—
73C2×C4×C127—41no—
74C2×C4×C127—42no—
75C2×C4×C127—41no—
76C2×C4×C127C22⋊C412yes—
77C2×C4×C127C2×C812yescomplemented
78C2×C4×C127C2×D412yes—
79C2×C4×C127C2×D411yescharacteristic
80C2×C4×C127C2×D411yescharacteristic
81C2×C4×C127#4112yes—
82C8×C127—24no—
83C8×C127—42no—
84C22×C127—22no—
85C22×C127—22no—
86C22×C127—24no—
87C22×C127—24no—
88C22×C127—22no—
89C22×C127—24no—
90C22×C127—41no—
91C22×C127—41no—
92C22×C127—42no—
93C22×C127C22⋊C814yescomplemented
94C22×C127C2×C22⋊C411yescharacteristic
95C22×C127C4×D412yes—
96C22×C127C22×C811yescharacteristic
97C22×C127C2×M1611yescharacteristic
98C22×C127#13112yes—
99C4×C127—22no—
100C4×C127—22no—
101C4×C127—41no—
102C4×C127—41no—
103C4×C127#12011yescharacteristic
104C4×C127#12112yes—
105C4×C127#12311yescharacteristic
106C2×C127—24no—
107C2×C127—42no—
108C2×C127#38611yescharacteristic
109C2×C127C2×C22⋊C811yescharacteristic
110C2×C127#40811yescharacteristic
111C2×C127C8×D412yes—
112C2×C127#43512yes—
113#1869C12711yesmaximal, characteristic, direct product factor, Sylow
114C127#186911yescharacteristic, direct product factor, Sylow
115C23×C8C2×C12711yescharacteristic, complemented
116C2×C4×D4C2×C12711yescharacteristic
117C2×C22⋊C8C2×C12711yescharacteristic, complemented
118C2×C22⋊C8C2×C12712yescomplemented
119#336C2×C12712yescomplemented
120C22×D4C4×C12711yescharacteristic
121C23×C4C22×C12711yescharacteristic
122C23×C4C22×C12711yescharacteristic
123C22×C8—22no—
124C22×C8—24no—
125C22×C8C22×C12712yes—
126C22×C8C22×C12712yes—
127C4×D4—22no—
128C4×D4—22no—
129C2×C4⋊C4C4×C12711yescharacteristic
130C2×C22⋊C4C4×C12711yescharacteristic
131C2×C22⋊C4C4×C12711yescharacteristic
132C2×C42C22×C12711yescharacteristic
133C22⋊C8—22no—
134C22⋊C8—24no—
135C24C2×C4×C12711yescharacteristic
136C24C2×C4×C12711yescharacteristic
137C2×D4—22no—
138C2×D4—22no—
139C2×D4C8×C12714yescomplemented
140C22×C4—22no—
141C22×C4—22no—
142C22×C4—22no—
143C22×C4—21no—
144C22×C4—21no—
145C22×C4—22no—
146C22×C4C2×C4×C12711yescharacteristic
147C22×C4C2×C4×C12711yescharacteristic
148C22×C4C2×C4×C12711yescharacteristic
149C22×C4C2×C4×C12711yescharacteristic
150C22×C4D4×C12712yes—
151C22×C4D4×C12712yes—
152C22×C4C23×C12711yescharacteristic
153C2×C8—28no—
154C2×C8—22no—
155C2×C8—22no—
156C2×C8—22no—
157C2×C8—22no—
158C2×C8—22no—
159C2×C8D4×C12714yescomplemented
160C4⋊C4—22no—
161C22⋊C4—22no—
162C22⋊C4—22no—
163C42—21no—
164C42—21no—
165C23—22no—
166C23—22no—
167C23—21no—
168C23—22no—
169C23—21no—
170C23—22no—
171C23C22⋊C4×C12712yes—
172C23C2×C8×C12712yes—
173C23C2×C8×C12712yescomplemented
174C23M16×C12712yes—
175C23C22×C4×C12711yescharacteristic
176D4—28no—
177C2×C4—21no—
178C2×C4—22no—
179C2×C4—21no—
180C2×C4—22no—
181C2×C4—24no—
182C2×C4—22no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—41no—
188C2×C4—42no—
189C2×C4—41no—
190C2×C4C22⋊C4×C12712yes—
191C2×C4C2×C8×C12712yescomplemented
192C2×C4C2×D4×C12712yes—
193C2×C4C2×D4×C12711yescharacteristic
194C2×C4C2×D4×C12711yescharacteristic
195C2×C4#41×C12712yes—
196C8—24no—
197C8—42no—
198C22—22no—
199C22—22no—
200C22—24no—
201C22—24no—
202C22—22no—
203C22—24no—
204C22—41no—
205C22—41no—
206C22—42no—
207C22C22⋊C8×C12714yescomplemented
208C22C2×C22⋊C4×C12711yescharacteristic
209C22C4×D4×C12712yes—
210C22C22×C8×C12711yescharacteristic
211C22C2×M16×C12711yescharacteristic
212C22#131×C12712yes—
213C4—22no—
214C4—22no—
215C4—41no—
216C4—41no—
217C4#120×C12711yescharacteristic
218C4#121×C12712yes—
219C4#123×C12711yescharacteristic
220C2—24no—
221C2—42no—
222C2#386×C12711yescharacteristic
223C2C2×C22⋊C8×C12711yescharacteristic
224C2#408×C12711yescharacteristic
225C2C8×D4×C12712yes—
226C2#435×C12712yes—
subgroupG/H
centerC22×C4×C127C23
commutatorC22C22×C8×C127
Frattini, cosocleC22×C4C23×C127
socleC23×C127C22×C4
prime radicalC22×D4×C127C4
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C23×C8×C127C2semidirect
3. C2×C22⋊C8×C127C2semidirect
4. C2×C22⋊C8×C127C2semidirect
5. #336×C127C2semidirect
25. C2×D4×C127C8semidirect
45. C2×C8×C127D4semidirect
59. C23×C127C2×C8semidirect
77. C2×C4×C127C2×C8semidirect
93. C22×C127C22⋊C8semidirect
113. #1869C127direct (N × H)
114. C127#1869direct (N × H)
115. C23×C8C2×C127semidirect
117. C2×C22⋊C8C2×C127semidirect
118. C2×C22⋊C8C2×C127semidirect
119. #336C2×C127semidirect
139. C2×D4C8×C127semidirect
159. C2×C8D4×C127semidirect
173. C23C2×C8×C127semidirect
191. C2×C4C2×C8×C127semidirect
207. C22C22⋊C8×C127semidirect

Maximal subgroups

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

subgroupindex
C23×C8×C1272
C2×C4×D4×C1272
C2×C22⋊C8×C1272
#336×C1272
#1869127