Finite Group Databasebeta

← C127×#1877 #30634829

Subgroups — C127×#1877 #30634829

Order 16256.

402 conjugacy classes of subgroups.

The subgroup lattice has 268 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×SD16×C127C211yesmaximal, characteristic
2C2×C4×D4×C127C211yesmaximal, characteristic
3C2×#103×C127C211yesmaximal, characteristic, complemented
4C2×#102×C127C211yesmaximal, characteristic
5#391×C127C211yesmaximal, characteristic, complemented
6#340×C127C211yesmaximal, characteristic, complemented
7#336×C127C211yesmaximal, characteristic, complemented
8C22×Q8×C127C2211yescharacteristic
9C22×D4×C127C2211yescharacteristic
10C23×C4×C127—21no—
11C2×SD16×C127—22no—
12C2×SD16×C127—22no—
13C2×SD16×C127C414yescomplemented
14C22×C8×C127C2211yescharacteristic
15C22×C8×C127C2211yescharacteristic
16C4×D4×C127—22no—
17C4×D4×C127—22no—
18C2×C4⋊C4×C127C2211yescharacteristic
19C2×C4⋊C4×C127C2211yescharacteristic
20C2×C22⋊C4×C127—21no—
21C2×C42×C127C2211yescharacteristic
22#103×C127—22no—
23#102×C127—22no—
24#95×C127—21no—
25#95×C127—21no—
26C24×C127—21no—
27C2×Q8×C127—21no—
28C2×Q8×C127—21no—
29C2×Q8×C127—21no—
30C2×Q8×C127—21no—
31C2×Q8×C127—21no—
32C2×Q8×C127C2×C412yescomplemented
33C2×D4×C127—21no—
34C2×D4×C127—21no—
35C2×D4×C127—21no—
36C2×D4×C127C2×C412yes—
37C2×D4×C127D412yes—
38C2×D4×C127D412yes—
39C22×C4×C127—24no—
40C22×C4×C127—21no—
41C22×C4×C127—21no—
42C22×C4×C127—21no—
43C22×C4×C127—42no—
44C22×C4×C127—42no—
45C22×C4×C127D411yescharacteristic
46C22×C4×C127D411yescharacteristic
47C22×C4×C127C2311yescharacteristic
48SD16×C127—28no—
49C2×C8×C127—21no—
50C2×C8×C127—21no—
51C2×C8×C127—21no—
52C2×C8×C127—21no—
53C2×C8×C127—21no—
54C2×C8×C127C2×C412yescomplemented
55C4⋊C4×C127—21no—
56C4⋊C4×C127—21no—
57C4⋊C4×C127—21no—
58C4⋊C4×C127D412yes—
59C22⋊C4×C127—24no—
60C42×C127—21no—
61C42×C127—21no—
62C23×C127—22no—
63C23×C127—22no—
64C23×C127—22no—
65C23×C127—41no—
66C23×C127—41no—
67C23×C127—41no—
68C23×C127—41no—
69C23×C127C2×D411yescharacteristic
70Q8×C127—22no—
71Q8×C127—22no—
72Q8×C127—41no—
73Q8×C127—41no—
74D4×C127—22no—
75D4×C127—22no—
76D4×C127—22no—
77D4×C127C22⋊C414yes—
78C2×C4×C127—21no—
79C2×C4×C127—21no—
80C2×C4×C127—22no—
81C2×C4×C127—21no—
82C2×C4×C127—22no—
83C2×C4×C127—21no—
84C2×C4×C127—21no—
85C2×C4×C127—48no—
86C2×C4×C127—41no—
87C2×C4×C127—41no—
88C2×C4×C127—41no—
89C2×C4×C127—41no—
90C2×C4×C127—41no—
91C2×C4×C127—41no—
92C2×C4×C127—41no—
93C2×C4×C127SD1612yescomplemented
94C2×C4×C127C22×C411yescharacteristic
95C2×C4×C127C2×D411yescharacteristic
96C2×C4×C127C2×D411yescharacteristic
97C2×C4×C127C2×D411yescharacteristic
98C2×C4×C127#4111yescharacteristic
99C2×C4×C127#4111yescharacteristic
100C8×C127—22no—
101C8×C127—41no—
102C22×C127—24no—
103C22×C127—42no—
104C22×C127—42no—
105C22×C127—42no—
106C22×C127—42no—
107C22×C127—42no—
108C22×C127—42no—
109C22×C127C4×D411yescharacteristic
110C22×C127#12011yescharacteristic
111C22×C127#12111yescharacteristic
112C22×C127C2×SD1611yescharacteristic
113C22×C127#13511yescharacteristic
114C22×C127AGL(1,ℤ/8)11yescharacteristic
115C22×C127#13711yescharacteristic
116C4×C127—22no—
117C4×C127—42no—
118C4×C127—42no—
119C4×C127—41no—
120C4×C127—81no—
121C4×C127C2×C22⋊C411yescharacteristic
122C4×C127C4×D411yescharacteristic
123C4×C127#12111yescharacteristic
124C4×C127#12311yescharacteristic
125C2×C127—44no—
126C2×C127#38611yescharacteristic
127C2×C127C4×SD1611yescharacteristic
128C2×C127#44011yescharacteristic
129C2×C127#45011yescharacteristic
130C2×C127#45211yescharacteristic
131C2×C127#46111yescharacteristic
132C2×C127#46311yescharacteristic
133#1877C12711yesmaximal, characteristic, direct product factor, Sylow
134C127#187711yescharacteristic, direct product factor, Sylow
135C22×SD16C2×C12711yescharacteristic
136C2×C4×D4C2×C12711yescharacteristic
137C2×#103C2×C12711yescharacteristic, complemented
138C2×#102C2×C12711yescharacteristic
139#391C2×C12711yescharacteristic, complemented
140#340C2×C12711yescharacteristic, complemented
141#336C2×C12711yescharacteristic, complemented
142C22×Q8C22×C12711yescharacteristic
143C22×D4C22×C12711yescharacteristic
144C23×C4—21no—
145C2×SD16—22no—
146C2×SD16—22no—
147C2×SD16C4×C12714yescomplemented
148C22×C8C22×C12711yescharacteristic
149C22×C8C22×C12711yescharacteristic
150C4×D4—22no—
151C4×D4—22no—
152C2×C4⋊C4C22×C12711yescharacteristic
153C2×C4⋊C4C22×C12711yescharacteristic
154C2×C22⋊C4—21no—
155C2×C42C22×C12711yescharacteristic
156#103—22no—
157#102—22no—
158#95—21no—
159#95—21no—
160C24—21no—
161C2×Q8—21no—
162C2×Q8—21no—
163C2×Q8—21no—
164C2×Q8—21no—
165C2×Q8—21no—
166C2×Q8C2×C4×C12712yescomplemented
167C2×D4—21no—
168C2×D4—21no—
169C2×D4—21no—
170C2×D4C2×C4×C12712yes—
171C2×D4D4×C12712yes—
172C2×D4D4×C12712yes—
173C22×C4—24no—
174C22×C4—21no—
175C22×C4—21no—
176C22×C4—21no—
177C22×C4—42no—
178C22×C4—42no—
179C22×C4D4×C12711yescharacteristic
180C22×C4D4×C12711yescharacteristic
181C22×C4C23×C12711yescharacteristic
182SD16—28no—
183C2×C8—21no—
184C2×C8—21no—
185C2×C8—21no—
186C2×C8—21no—
187C2×C8—21no—
188C2×C8C2×C4×C12712yescomplemented
189C4⋊C4—21no—
190C4⋊C4—21no—
191C4⋊C4—21no—
192C4⋊C4D4×C12712yes—
193C22⋊C4—24no—
194C42—21no—
195C42—21no—
196C23—22no—
197C23—22no—
198C23—22no—
199C23—41no—
200C23—41no—
201C23—41no—
202C23—41no—
203C23C2×D4×C12711yescharacteristic
204Q8—22no—
205Q8—22no—
206Q8—41no—
207Q8—41no—
208D4—22no—
209D4—22no—
210D4—22no—
211D4C22⋊C4×C12714yes—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—22no—
215C2×C4—21no—
216C2×C4—22no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—48no—
220C2×C4—41no—
221C2×C4—41no—
222C2×C4—41no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4SD16×C12712yescomplemented
228C2×C4C22×C4×C12711yescharacteristic
229C2×C4C2×D4×C12711yescharacteristic
230C2×C4C2×D4×C12711yescharacteristic
231C2×C4C2×D4×C12711yescharacteristic
232C2×C4#41×C12711yescharacteristic
233C2×C4#41×C12711yescharacteristic
234C8—22no—
235C8—41no—
236C22—24no—
237C22—42no—
238C22—42no—
239C22—42no—
240C22—42no—
241C22—42no—
242C22—42no—
243C22C4×D4×C12711yescharacteristic
244C22#120×C12711yescharacteristic
245C22#121×C12711yescharacteristic
246C22C2×SD16×C12711yescharacteristic
247C22#135×C12711yescharacteristic
248C22AGL(1,ℤ/8)×C12711yescharacteristic
249C22#137×C12711yescharacteristic
250C4—22no—
251C4—42no—
252C4—42no—
253C4—41no—
254C4—81no—
255C4C2×C22⋊C4×C12711yescharacteristic
256C4C4×D4×C12711yescharacteristic
257C4#121×C12711yescharacteristic
258C4#123×C12711yescharacteristic
259C2—44no—
260C2#386×C12711yescharacteristic
261C2C4×SD16×C12711yescharacteristic
262C2#440×C12711yescharacteristic
263C2#450×C12711yescharacteristic
264C2#452×C12711yescharacteristic
265C2#461×C12711yescharacteristic
266C2#463×C12711yescharacteristic
subgroupG/H
center, socleC23×C127C2×D4
commutatorC2×C4C22×C4×C127
Frattini, cosocleC22×C4C23×C127
prime radicalC22×D4×C127C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×#103×C127C2semidirect
5. #391×C127C2semidirect
6. #340×C127C2semidirect
7. #336×C127C2semidirect
13. C2×SD16×C127C4semidirect
32. C2×Q8×C127C2×C4semidirect
54. C2×C8×C127C2×C4semidirect
93. C2×C4×C127SD16semidirect
133. #1877C127direct (N × H)
134. C127#1877direct (N × H)
137. C2×#103C2×C127semidirect
139. #391C2×C127semidirect
140. #340C2×C127semidirect
141. #336C2×C127semidirect
147. C2×SD16C4×C127semidirect
166. C2×Q8C2×C4×C127semidirect
188. C2×C8C2×C4×C127semidirect
227. C2×C4SD16×C127semidirect

Maximal subgroups

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

subgroupindex
C22×SD16×C1272
C2×C4×D4×C1272
C2×#103×C1272
C2×#102×C1272
#391×C1272
#340×C1272
#336×C1272
#1877127