Finite Group Databasebeta

← C127×#3214 #30636166

Subgroups — C127×#3214 #30636166

Order 16256.

434 conjugacy classes of subgroups.

The subgroup lattice has 236 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#532×C127C211yesmaximal, characteristic, complemented
2#532×C127C211yesmaximal, characteristic, complemented
3#496×C127C212yesmaximal, complemented
4#489×C127C212yesmaximal, complemented
5#461×C127C212yesmaximal, complemented
6#459×C127C212yesmaximal, complemented
7#449×C127C214yesmaximal, complemented
8#432×C127C211yesmaximal, characteristic, complemented
9C2×#41×C127—21no—
10C2×#41×C127C2212yes—
11C2×SD16×C127C2214yes—
12C2×D8×C127C2214yes—
13C4⋊Q8×C127C2211yescharacteristic
14C4⋊Q8×C127C2211yescharacteristic
15#127×C127C2211yescharacteristic
16#127×C127C2211yescharacteristic
17#124×C127—21no—
18#124×C127C2212yes—
19#121×C127—21no—
20#121×C127—21no—
21#121×C127—21no—
22#121×C127C2212yes—
23C4×D4×C127—21no—
24C4×D4×C127—21no—
25C4×D4×C127—21no—
26C4×D4×C127C2212yes—
27C2×C42×C127C2211yescharacteristic
28C4⋊C8×C127C2212yes—
29#103×C127C2214yes—
30#102×C127C2214yes—
31C22⋊C8×C127C2212yes—
32#97×C127C2212yes—
33#41×C127—44no—
34#41×C127—44no—
35C2×Q8×C127—21no—
36C2×Q8×C127C2312yes—
37C2×D4×C127—22no—
38C2×D4×C127—22no—
39C2×D4×C127—21no—
40C2×D4×C127—21no—
41C2×D4×C127—21no—
42C2×D4×C127—21no—
43C2×D4×C127C2312yes—
44C2×D4×C127C2312yes—
45C22×C4×C127—22no—
46C22×C4×C127—22no—
47C22×C4×C127D411yescharacteristic
48C22×C4×C127D411yescharacteristic
49C22×C4×C127C2311yescharacteristic
50SD16×C127—44no—
51D8×C127—44no—
52C2×C8×C127C2314yes—
53C4⋊C4×C127—21no—
54C4⋊C4×C127—21no—
55C4⋊C4×C127—21no—
56C4⋊C4×C127C2312yes—
57C22⋊C4×C127—22no—
58C22⋊C4×C127—22no—
59C22⋊C4×C127—22no—
60C22⋊C4×C127—22no—
61C42×C127D411yescharacteristic
62C42×C127D411yescharacteristic
63C42×C127C2311yescharacteristic
64C42×C127C2311yescharacteristic
65C23×C127—22no—
66C23×C127—22no—
67C23×C127C2×D411yescharacteristic
68Q8×C127—24no—
69Q8×C127—42no—
70D4×C127—22no—
71D4×C127—24no—
72D4×C127—22no—
73D4×C127—42no—
74D4×C127—42no—
75D4×C127—42no—
76D4×C127—44no—
77D4×C127—44no—
78D4×C127—42no—
79C2×C4×C127—22no—
80C2×C4×C127—22no—
81C2×C4×C127—22no—
82C2×C4×C127—22no—
83C2×C4×C127—41no—
84C2×C4×C127—44no—
85C2×C4×C127—44no—
86C2×C4×C127C2×D411yescharacteristic
87C2×C4×C127C2×D411yescharacteristic
88C2×C4×C127C2×D411yescharacteristic
89C2×C4×C127C2×D411yescharacteristic
90C2×C4×C127C2×D411yescharacteristic
91C2×C4×C127C2411yescharacteristic
92C8×C127—24no—
93C22×C127—21no—
94C22×C127—21no—
95C22×C127—21no—
96C22×C127—42no—
97C22×C127—42no—
98C22×C127—42no—
99C22×C127—42no—
100C22×C127—42no—
101C22×C127—42no—
102C22×C127C22×D411yescharacteristic
103C4×C127—21no—
104C4×C127—21no—
105C4×C127—21no—
106C4×C127—21no—
107C4×C127—42no—
108C4×C127—42no—
109C4×C127AGL(1,ℤ/8)12yes—
110C4×C127H(5,𝔽2)12yes—
111C2×C127—41no—
112C2×C127—82no—
113C2×C127—82no—
114C2×C127#53511yescharacteristic
115C2×C127C2×AGL(1,ℤ/8)11yescharacteristic
116C2×C127#57511yescharacteristic
117#3214C12711yesmaximal, characteristic, direct product factor, Sylow
118C127#321411yescharacteristic, direct product factor, Sylow
119#532C2×C12711yescharacteristic, complemented
120#532C2×C12711yescharacteristic, complemented
121#496C2×C12712yescomplemented
122#489C2×C12712yescomplemented
123#461C2×C12712yescomplemented
124#459C2×C12712yescomplemented
125#449C2×C12714yescomplemented
126#432C2×C12711yescharacteristic, complemented
127C2×#41—21no—
128C2×#41C22×C12712yes—
129C2×SD16C22×C12714yes—
130C2×D8C22×C12714yes—
131C4⋊Q8C22×C12711yescharacteristic
132C4⋊Q8C22×C12711yescharacteristic
133#127C22×C12711yescharacteristic
134#127C22×C12711yescharacteristic
135#124—21no—
136#124C22×C12712yes—
137#121—21no—
138#121—21no—
139#121—21no—
140#121C22×C12712yes—
141C4×D4—21no—
142C4×D4—21no—
143C4×D4—21no—
144C4×D4C22×C12712yes—
145C2×C42C22×C12711yescharacteristic
146C4⋊C8C22×C12712yes—
147#103C22×C12714yes—
148#102C22×C12714yes—
149C22⋊C8C22×C12712yes—
150#97C22×C12712yes—
151#41—44no—
152#41—44no—
153C2×Q8—21no—
154C2×Q8C23×C12712yes—
155C2×D4—22no—
156C2×D4—22no—
157C2×D4—21no—
158C2×D4—21no—
159C2×D4—21no—
160C2×D4—21no—
161C2×D4C23×C12712yes—
162C2×D4C23×C12712yes—
163C22×C4—22no—
164C22×C4—22no—
165C22×C4D4×C12711yescharacteristic
166C22×C4D4×C12711yescharacteristic
167C22×C4C23×C12711yescharacteristic
168SD16—44no—
169D8—44no—
170C2×C8C23×C12714yes—
171C4⋊C4—21no—
172C4⋊C4—21no—
173C4⋊C4—21no—
174C4⋊C4C23×C12712yes—
175C22⋊C4—22no—
176C22⋊C4—22no—
177C22⋊C4—22no—
178C22⋊C4—22no—
179C42D4×C12711yescharacteristic
180C42D4×C12711yescharacteristic
181C42C23×C12711yescharacteristic
182C42C23×C12711yescharacteristic
183C23—22no—
184C23—22no—
185C23C2×D4×C12711yescharacteristic
186Q8—24no—
187Q8—42no—
188D4—22no—
189D4—24no—
190D4—22no—
191D4—42no—
192D4—42no—
193D4—42no—
194D4—44no—
195D4—44no—
196D4—42no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—41no—
202C2×C4—44no—
203C2×C4—44no—
204C2×C4C2×D4×C12711yescharacteristic
205C2×C4C2×D4×C12711yescharacteristic
206C2×C4C2×D4×C12711yescharacteristic
207C2×C4C2×D4×C12711yescharacteristic
208C2×C4C2×D4×C12711yescharacteristic
209C2×C4C24×C12711yescharacteristic
210C8—24no—
211C22—21no—
212C22—21no—
213C22—21no—
214C22—42no—
215C22—42no—
216C22—42no—
217C22—42no—
218C22—42no—
219C22—42no—
220C22C22×D4×C12711yescharacteristic
221C4—21no—
222C4—21no—
223C4—21no—
224C4—21no—
225C4—42no—
226C4—42no—
227C4AGL(1,ℤ/8)×C12712yes—
228C4H(5,𝔽2)×C12712yes—
229C2—41no—
230C2—82no—
231C2—82no—
232C2#535×C12711yescharacteristic
233C2C2×AGL(1,ℤ/8)×C12711yescharacteristic
234C2#575×C12711yescharacteristic
subgroupG/H
center, socleC22×C127C22×D4
commutator, Frattini, cosocleC2×C4C24×C127
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. #532×C127C2semidirect
2. #532×C127C2semidirect
3. #496×C127C2semidirect
4. #489×C127C2semidirect
5. #461×C127C2semidirect
6. #459×C127C2semidirect
7. #449×C127C2semidirect
8. #432×C127C2semidirect
117. #3214C127direct (N × H)
118. C127#3214direct (N × H)
119. #532C2×C127semidirect
120. #532C2×C127semidirect
121. #496C2×C127semidirect
122. #489C2×C127semidirect
123. #461C2×C127semidirect
124. #459C2×C127semidirect
125. #449C2×C127semidirect
126. #432C2×C127semidirect

Maximal subgroups

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

subgroupindex
#532×C1272
#496×C1272
#489×C1272
#461×C1272
#459×C1272
#449×C1272
#432×C1272
#3214127