Finite Group Databasebeta

← C127×#2396 #30635348

Subgroups — C127×#2396 #30635348

Order 16256.

528 conjugacy classes of subgroups.

The subgroup lattice has 258 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×Q8×C127C211yesmaximal, characteristic, complemented
2C2×#117×C127C211yesmaximal, characteristic
3#400×C127C211yesmaximal, characteristic, complemented
4#399×C127C211yesmaximal, characteristic
5#398×C127C212yesmaximal, complemented
6#396×C127C212yesmaximal
7#395×C127C211yesmaximal, characteristic, complemented
8#393×C127C211yesmaximal, characteristic
9C4×C4⋊C4×C127C212yesmaximal, complemented
10C4×C4⋊C4×C127C211yesmaximal, characteristic, complemented
11C4×C22⋊C4×C127C212yesmaximal
12C22×Q8×C127C2211yescharacteristic
13C23×C4×C127C2211yescharacteristic
14C4×Q8×C127—24no—
15#117×C127—24no—
16C2×C4⋊C4×C127C2211yescharacteristic
17C2×C4⋊C4×C127C2211yescharacteristic
18C2×C4⋊C4×C127C2212yes—
19C2×C4⋊C4×C127C2211yescharacteristic
20C2×C4⋊C4×C127C2212yes—
21C2×C4⋊C4×C127C2212yes—
22C2×C4⋊C4×C127C2212yes—
23C2×C22⋊C4×C127C2211yescharacteristic
24C2×C22⋊C4×C127C2211yescharacteristic
25C2×C22⋊C4×C127C2212yes—
26C2×C22⋊C4×C127C2212yes—
27C2×C42×C127C2211yescharacteristic
28C2×C42×C127C2212yes—
29C2×C42×C127C2212yes—
30C2×C42×C127C2211yescharacteristic
31#95×C127C2212yes—
32#95×C127C2212yes—
33#95×C127C2212yes—
34#95×C127C2211yescharacteristic
35#95×C127C2211yescharacteristic
36#95×C127C2212yes—
37C24×C127C2311yescharacteristic
38C2×Q8×C127—22no—
39C2×Q8×C127—24no—
40C22×C4×C127—22no—
41C22×C4×C127—22no—
42C22×C4×C127Q814yescomplemented
43C22×C4×C127C2312yes—
44C22×C4×C127C2311yescharacteristic
45C22×C4×C127C2311yescharacteristic
46C22×C4×C127C2312yes—
47C22×C4×C127C2311yescharacteristic
48C22×C4×C127C2311yescharacteristic
49C22×C4×C127C2311yescharacteristic
50C22×C4×C127C2312yes—
51C22×C4×C127C2312yes—
52C22×C4×C127C2311yescharacteristic
53C4⋊C4×C127—22no—
54C4⋊C4×C127—22no—
55C4⋊C4×C127—24no—
56C4⋊C4×C127—22no—
57C4⋊C4×C127—24no—
58C4⋊C4×C127—24no—
59C4⋊C4×C127—24no—
60C22⋊C4×C127—22no—
61C22⋊C4×C127—22no—
62C22⋊C4×C127—24no—
63C22⋊C4×C127—24no—
64C42×C127—22no—
65C42×C127—24no—
66C42×C127—24no—
67C42×C127D414yes—
68C23×C127—21no—
69C23×C127—22no—
70C23×C127—22no—
71C23×C127—21no—
72C23×C127C2×Q812yes—
73C23×C127C2411yescharacteristic
74Q8×C127—28no—
75C2×C4×C127—22no—
76C2×C4×C127—21no—
77C2×C4×C127—22no—
78C2×C4×C127—22no—
79C2×C4×C127—22no—
80C2×C4×C127—21no—
81C2×C4×C127—22no—
82C2×C4×C127—22no—
83C2×C4×C127—28no—
84C2×C4×C127—21no—
85C2×C4×C127—21no—
86C2×C4×C127—22no—
87C2×C4×C127—22no—
88C2×C4×C127—22no—
89C2×C4×C127—22no—
90C2×C4×C127—22no—
91C2×C4×C127—22no—
92C2×C4×C127—22no—
93C2×C4×C127—22no—
94C2×C4×C127C2×D412yes—
95C2×C4×C127C2×D412yes—
96C2×C4×C127C2×D412yes—
97C2×C4×C127C2×Q812yes—
98C2×C4×C127C2×Q812yes—
99C2×C4×C127#4114yes—
100C2×C4×C127#4114yes—
101C2×C4×C127#4112yes—
102C22×C127—22no—
103C22×C127—24no—
104C22×C127—41no—
105C22×C127—42no—
106C22×C127—41no—
107C22×C127C22×D411yescharacteristic
108C22×C127C22×Q811yescharacteristic
109C22×C127C2×#4111yescharacteristic
110C22×C127C2×#4112yes—
111C22×C127C2×#4112yes—
112C4×C127—22no—
113C4×C127—22no—
114C4×C127—24no—
115C4×C127—24no—
116C4×C127—22no—
117C4×C127—41no—
118C4×C127—42no—
119C4×C127—41no—
120C4×C127—42no—
121C4×C127C22⋊Q814yes—
122C2×C127—42no—
123C2×C127C2×C22⋊Q811yescharacteristic
124C2×C127#52511yescharacteristic
125C2×C127#52912yes—
126C2×C127#53211yescharacteristic
127C2×C127#53312yes—
128#2396C12711yesmaximal, characteristic, direct product factor, Sylow
129C127#239611yescharacteristic, direct product factor, Sylow
130C2×C4×Q8C2×C12711yescharacteristic, complemented
131C2×#117C2×C12711yescharacteristic
132#400C2×C12711yescharacteristic, complemented
133#399C2×C12711yescharacteristic
134#398C2×C12712yescomplemented
135#396C2×C12712yes—
136#395C2×C12711yescharacteristic, complemented
137#393C2×C12711yescharacteristic
138C4×C4⋊C4C2×C12712yescomplemented
139C4×C4⋊C4C2×C12711yescharacteristic, complemented
140C4×C22⋊C4C2×C12712yes—
141C22×Q8C22×C12711yescharacteristic
142C23×C4C22×C12711yescharacteristic
143C4×Q8—24no—
144#117—24no—
145C2×C4⋊C4C22×C12711yescharacteristic
146C2×C4⋊C4C22×C12711yescharacteristic
147C2×C4⋊C4C22×C12712yes—
148C2×C4⋊C4C22×C12711yescharacteristic
149C2×C4⋊C4C22×C12712yes—
150C2×C4⋊C4C22×C12712yes—
151C2×C4⋊C4C22×C12712yes—
152C2×C22⋊C4C22×C12711yescharacteristic
153C2×C22⋊C4C22×C12711yescharacteristic
154C2×C22⋊C4C22×C12712yes—
155C2×C22⋊C4C22×C12712yes—
156C2×C42C22×C12711yescharacteristic
157C2×C42C22×C12712yes—
158C2×C42C22×C12712yes—
159C2×C42C22×C12711yescharacteristic
160#95C22×C12712yes—
161#95C22×C12712yes—
162#95C22×C12712yes—
163#95C22×C12711yescharacteristic
164#95C22×C12711yescharacteristic
165#95C22×C12712yes—
166C24C23×C12711yescharacteristic
167C2×Q8—22no—
168C2×Q8—24no—
169C22×C4—22no—
170C22×C4—22no—
171C22×C4Q8×C12714yescomplemented
172C22×C4C23×C12712yes—
173C22×C4C23×C12711yescharacteristic
174C22×C4C23×C12711yescharacteristic
175C22×C4C23×C12712yes—
176C22×C4C23×C12711yescharacteristic
177C22×C4C23×C12711yescharacteristic
178C22×C4C23×C12711yescharacteristic
179C22×C4C23×C12712yes—
180C22×C4C23×C12712yes—
181C22×C4C23×C12711yescharacteristic
182C4⋊C4—22no—
183C4⋊C4—22no—
184C4⋊C4—24no—
185C4⋊C4—22no—
186C4⋊C4—24no—
187C4⋊C4—24no—
188C4⋊C4—24no—
189C22⋊C4—22no—
190C22⋊C4—22no—
191C22⋊C4—24no—
192C22⋊C4—24no—
193C42—22no—
194C42—24no—
195C42—24no—
196C42D4×C12714yes—
197C23—21no—
198C23—22no—
199C23—22no—
200C23—21no—
201C23C2×Q8×C12712yes—
202C23C24×C12711yescharacteristic
203Q8—28no—
204C2×C4—22no—
205C2×C4—21no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—21no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—28no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4C2×D4×C12712yes—
224C2×C4C2×D4×C12712yes—
225C2×C4C2×D4×C12712yes—
226C2×C4C2×Q8×C12712yes—
227C2×C4C2×Q8×C12712yes—
228C2×C4#41×C12714yes—
229C2×C4#41×C12714yes—
230C2×C4#41×C12712yes—
231C22—22no—
232C22—24no—
233C22—41no—
234C22—42no—
235C22—41no—
236C22C22×D4×C12711yescharacteristic
237C22C22×Q8×C12711yescharacteristic
238C22C2×#41×C12711yescharacteristic
239C22C2×#41×C12712yes—
240C22C2×#41×C12712yes—
241C4—22no—
242C4—22no—
243C4—24no—
244C4—24no—
245C4—22no—
246C4—41no—
247C4—42no—
248C4—41no—
249C4—42no—
250C4C22⋊Q8×C12714yes—
251C2—42no—
252C2C2×C22⋊Q8×C12711yescharacteristic
253C2#525×C12711yescharacteristic
254C2#529×C12712yes—
255C2#532×C12711yescharacteristic
256C2#533×C12712yes—
subgroupG/H
centerC22×C4×C127C23
commutator, Frattini, cosocleC23C24×C127
socleC23×C127C24
prime radicalC24×C127C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C4×Q8×C127C2semidirect
3. #400×C127C2semidirect
5. #398×C127C2semidirect
7. #395×C127C2semidirect
9. C4×C4⋊C4×C127C2semidirect
10. C4×C4⋊C4×C127C2semidirect
42. C22×C4×C127Q8semidirect
128. #2396C127direct (N × H)
129. C127#2396direct (N × H)
130. C2×C4×Q8C2×C127semidirect
132. #400C2×C127semidirect
134. #398C2×C127semidirect
136. #395C2×C127semidirect
138. C4×C4⋊C4C2×C127semidirect
139. C4×C4⋊C4C2×C127semidirect
171. C22×C4Q8×C127semidirect

Maximal subgroups

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

subgroupindex
C2×C4×Q8×C1272
C2×#117×C1272
#400×C1272
#399×C1272
#398×C1272
#396×C1272
#395×C1272
#393×C1272
C4×C4⋊C4×C1272
C4×C22⋊C4×C1272
#2396127