Finite Group Databasebeta

← C127×#1926 #30634878

Subgroups — C127×#1926 #30634878

Order 16256.

290 conjugacy classes of subgroups.

The subgroup lattice has 238 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#106×C127C211yesmaximal, characteristic, complemented
2C2×#102×C127C211yesmaximal, characteristic
3C2×#102×C127C211yesmaximal, characteristic
4#390×C127C211yesmaximal, characteristic
5C4×C4⋊C4×C127C211yesmaximal, characteristic, complemented
6#340×C127C211yesmaximal, characteristic, complemented
7#336×C127C211yesmaximal, characteristic, complemented
8C22×D4×C127C2211yescharacteristic
9C22×C8×C127C2211yescharacteristic
10C22×C8×C127C2211yescharacteristic
11C2×C4⋊C4×C127C2211yescharacteristic
12C2×C4⋊C4×C127C2211yescharacteristic
13C2×C4⋊C4×C127C2211yescharacteristic
14C2×C22⋊C4×C127—21no—
15C2×C22⋊C4×C127—21no—
16C2×C42×C127—21no—
17C2×C42×C127C2211yescharacteristic
18#106×C127—22no—
19#102×C127—22no—
20#102×C127C414yescomplemented
21#95×C127—21no—
22C24×C127—21no—
23C2×D4×C127—21no—
24C2×D4×C127—21no—
25C2×D4×C127—21no—
26C2×D4×C127—21no—
27C2×D4×C127—21no—
28C2×D4×C127C2×C412yes—
29C22×C4×C127—21no—
30C22×C4×C127—21no—
31C22×C4×C127—21no—
32C22×C4×C127D411yescharacteristic
33C22×C4×C127D411yescharacteristic
34C22×C4×C127C2311yescharacteristic
35C2×C8×C127—21no—
36C2×C8×C127—21no—
37C2×C8×C127—21no—
38C2×C8×C127—21no—
39C2×C8×C127—21no—
40C2×C8×C127C2×C412yes—
41C4⋊C4×C127—21no—
42C4⋊C4×C127—21no—
43C4⋊C4×C127—21no—
44C4⋊C4×C127—21no—
45C4⋊C4×C127C2×C412yes—
46C4⋊C4×C127D412yes—
47C22⋊C4×C127—42no—
48C22⋊C4×C127—42no—
49C42×C127—21no—
50C42×C127—21no—
51C42×C127—42no—
52C23×C127—22no—
53C23×C127—41no—
54C23×C127—41no—
55C23×C127—41no—
56C23×C127—41no—
57C23×C127—41no—
58C23×C127—41no—
59C23×C127C2×D411yescharacteristic
60D4×C127—22no—
61D4×C127—22no—
62D4×C127—41no—
63D4×C127—41no—
64C2×C4×C127—21no—
65C2×C4×C127—21no—
66C2×C4×C127—22no—
67C2×C4×C127—22no—
68C2×C4×C127—21no—
69C2×C4×C127—21no—
70C2×C4×C127—21no—
71C2×C4×C127—41no—
72C2×C4×C127—41no—
73C2×C4×C127—41no—
74C2×C4×C127—41no—
75C2×C4×C127—41no—
76C2×C4×C127—41no—
77C2×C4×C127—41no—
78C2×C4×C127SD1612yes—
79C2×C4×C127C22×C411yescharacteristic
80C2×C4×C127C2×D411yescharacteristic
81C2×C4×C127#4111yescharacteristic
82C2×C4×C127#4111yescharacteristic
83C2×C4×C127#4111yescharacteristic
84C2×C4×C127#4111yescharacteristic
85C8×C127—22no—
86C8×C127—41no—
87C22×C127—42no—
88C22×C127—42no—
89C22×C127—42no—
90C22×C127—81no—
91C22×C127—81no—
92C22×C127—81no—
93C22×C127—81no—
94C22×C127C4×D411yescharacteristic
95C22×C127#12111yescharacteristic
96C22×C127#12311yescharacteristic
97C22×C127C2×SD1611yescharacteristic
98C22×C127#13511yescharacteristic
99C22×C127AGL(1,ℤ/8)11yescharacteristic
100C22×C127AGL(1,ℤ/8)11yescharacteristic
101C4×C127—22no—
102C4×C127—42no—
103C4×C127—42no—
104C4×C127—41no—
105C4×C127—81no—
106C4×C127#11711yescharacteristic
107C4×C127C4×D411yescharacteristic
108C4×C127#12411yescharacteristic
109C4×C127#12611yescharacteristic
110C2×C127—82no—
111C2×C127#38811yescharacteristic
112C2×C127C4×SD1611yescharacteristic
113C2×C127#44211yescharacteristic
114C2×C127#46011yescharacteristic
115C2×C127#46311yescharacteristic
116C2×C127#48111yescharacteristic
117C2×C127#48211yescharacteristic
118#1926C12711yesmaximal, characteristic, direct product factor, Sylow
119C127#192611yescharacteristic, direct product factor, Sylow
120C2×#106C2×C12711yescharacteristic, complemented
121C2×#102C2×C12711yescharacteristic
122C2×#102C2×C12711yescharacteristic
123#390C2×C12711yescharacteristic
124C4×C4⋊C4C2×C12711yescharacteristic, complemented
125#340C2×C12711yescharacteristic, complemented
126#336C2×C12711yescharacteristic, complemented
127C22×D4C22×C12711yescharacteristic
128C22×C8C22×C12711yescharacteristic
129C22×C8C22×C12711yescharacteristic
130C2×C4⋊C4C22×C12711yescharacteristic
131C2×C4⋊C4C22×C12711yescharacteristic
132C2×C4⋊C4C22×C12711yescharacteristic
133C2×C22⋊C4—21no—
134C2×C22⋊C4—21no—
135C2×C42—21no—
136C2×C42C22×C12711yescharacteristic
137#106—22no—
138#102—22no—
139#102C4×C12714yescomplemented
140#95—21no—
141C24—21no—
142C2×D4—21no—
143C2×D4—21no—
144C2×D4—21no—
145C2×D4—21no—
146C2×D4—21no—
147C2×D4C2×C4×C12712yes—
148C22×C4—21no—
149C22×C4—21no—
150C22×C4—21no—
151C22×C4D4×C12711yescharacteristic
152C22×C4D4×C12711yescharacteristic
153C22×C4C23×C12711yescharacteristic
154C2×C8—21no—
155C2×C8—21no—
156C2×C8—21no—
157C2×C8—21no—
158C2×C8—21no—
159C2×C8C2×C4×C12712yes—
160C4⋊C4—21no—
161C4⋊C4—21no—
162C4⋊C4—21no—
163C4⋊C4—21no—
164C4⋊C4C2×C4×C12712yes—
165C4⋊C4D4×C12712yes—
166C22⋊C4—42no—
167C22⋊C4—42no—
168C42—21no—
169C42—21no—
170C42—42no—
171C23—22no—
172C23—41no—
173C23—41no—
174C23—41no—
175C23—41no—
176C23—41no—
177C23—41no—
178C23C2×D4×C12711yescharacteristic
179D4—22no—
180D4—22no—
181D4—41no—
182D4—41no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—41no—
195C2×C4—41no—
196C2×C4—41no—
197C2×C4SD16×C12712yes—
198C2×C4C22×C4×C12711yescharacteristic
199C2×C4C2×D4×C12711yescharacteristic
200C2×C4#41×C12711yescharacteristic
201C2×C4#41×C12711yescharacteristic
202C2×C4#41×C12711yescharacteristic
203C2×C4#41×C12711yescharacteristic
204C8—22no—
205C8—41no—
206C22—42no—
207C22—42no—
208C22—42no—
209C22—81no—
210C22—81no—
211C22—81no—
212C22—81no—
213C22C4×D4×C12711yescharacteristic
214C22#121×C12711yescharacteristic
215C22#123×C12711yescharacteristic
216C22C2×SD16×C12711yescharacteristic
217C22#135×C12711yescharacteristic
218C22AGL(1,ℤ/8)×C12711yescharacteristic
219C22AGL(1,ℤ/8)×C12711yescharacteristic
220C4—22no—
221C4—42no—
222C4—42no—
223C4—41no—
224C4—81no—
225C4#117×C12711yescharacteristic
226C4C4×D4×C12711yescharacteristic
227C4#124×C12711yescharacteristic
228C4#126×C12711yescharacteristic
229C2—82no—
230C2#388×C12711yescharacteristic
231C2C4×SD16×C12711yescharacteristic
232C2#442×C12711yescharacteristic
233C2#460×C12711yescharacteristic
234C2#463×C12711yescharacteristic
235C2#481×C12711yescharacteristic
236C2#482×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
1. C2×#106×C127C2semidirect
5. C4×C4⋊C4×C127C2semidirect
6. #340×C127C2semidirect
7. #336×C127C2semidirect
20. #102×C127C4semidirect
118. #1926C127direct (N × H)
119. C127#1926direct (N × H)
120. C2×#106C2×C127semidirect
124. C4×C4⋊C4C2×C127semidirect
125. #340C2×C127semidirect
126. #336C2×C127semidirect
139. #102C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#106×C1272
C2×#102×C1272
#390×C1272
C4×C4⋊C4×C1272
#340×C1272
#336×C1272
#1926127