Finite Group Databasebeta

← C127×#2054 #30635006

Subgroups — C127×#2054 #30635006

Order 16256.

360 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 104 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D8×C127C211yesmaximal, characteristic
2C2×C4⋊C8×C127C211yesmaximal, characteristic, complemented
3C2×#102×C127C212yesmaximal, complemented
4#390×C127C212yesmaximal, complemented
5#340×C127C211yesmaximal, characteristic, complemented
6C22×D4×C127C2212yes—
7C2×D8×C127—24no—
8C2×D8×C127—22no—
9C22×C8×C127C2211yescharacteristic
10C22×C8×C127C2211yescharacteristic
11C2×C4⋊C4×C127C2212yes—
12C2×C22⋊C4×C127—22no—
13C2×C22⋊C4×C127—22no—
14C2×C42×C127C2211yescharacteristic
15C4⋊C8×C127—22no—
16#102×C127—24no—
17C24×C127—22no—
18C2×D4×C127—22no—
19C2×D4×C127—22no—
20C2×D4×C127—22no—
21C2×D4×C127—22no—
22C2×D4×C127—22no—
23C2×D4×C127D414yes—
24C22×C4×C127—22no—
25C22×C4×C127D411yescharacteristic
26C22×C4×C127D411yescharacteristic
27C22×C4×C127C2311yescharacteristic
28D8×C127—28no—
29C2×C8×C127—22no—
30C2×C8×C127—22no—
31C2×C8×C127—21no—
32C2×C8×C127D412yes—
33C4⋊C4×C127—22no—
34C4⋊C4×C127—22no—
35C22⋊C4×C127—44no—
36C22⋊C4×C127—44no—
37C42×C127—21no—
38C42×C127—21no—
39C23×C127—24no—
40C23×C127—42no—
41C23×C127—42no—
42C23×C127—42no—
43C23×C127—42no—
44C23×C127—42no—
45C23×C127—42no—
46C23×C127C2×D411yescharacteristic
47D4×C127—24no—
48D4×C127—24no—
49D4×C127—42no—
50D4×C127—42no—
51C2×C4×C127—21no—
52C2×C4×C127—21no—
53C2×C4×C127—21no—
54C2×C4×C127—22no—
55C2×C4×C127—42no—
56C2×C4×C127—42no—
57C2×C4×C127—42no—
58C2×C4×C127D812yescomplemented
59C2×C4×C127C2×D412yes—
60C2×C4×C127C2×D411yescharacteristic
61C2×C4×C127#4111yescharacteristic
62C2×C4×C127#4112yes—
63C8×C127—22no—
64C8×C127—41no—
65C22×C127—44no—
66C22×C127—44no—
67C22×C127—44no—
68C22×C127—82no—
69C22×C127—82no—
70C22×C127—82no—
71C22×C127—82no—
72C22×C127#12112yes—
73C22×C127#12111yescharacteristic
74C22×C127C2×D811yescharacteristic
75C22×C127#13511yescharacteristic
76C22×C127AGL(1,ℤ/8)12yes—
77C4×C127—22no—
78C4×C127—41no—
79C4×C127—82no—
80C4×C127#12011yescharacteristic
81C4×C127#12312yes—
82C4×C127#12411yescharacteristic
83C2×C127—84no—
84C2×C127#39411yescharacteristic
85C2×C127#45912yes—
86C2×C127#46312yes—
87C2×C127#46611yescharacteristic
88C2×C127#46911yescharacteristic
89#2054C12711yesmaximal, characteristic, direct product factor, Sylow
90C127#205411yescharacteristic, direct product factor, Sylow
91C22×D8C2×C12711yescharacteristic
92C2×C4⋊C8C2×C12711yescharacteristic, complemented
93C2×#102C2×C12712yescomplemented
94#390C2×C12712yescomplemented
95#340C2×C12711yescharacteristic, complemented
96C22×D4C22×C12712yes—
97C2×D8—24no—
98C2×D8—22no—
99C22×C8C22×C12711yescharacteristic
100C22×C8C22×C12711yescharacteristic
101C2×C4⋊C4C22×C12712yes—
102C2×C22⋊C4—22no—
103C2×C22⋊C4—22no—
104C2×C42C22×C12711yescharacteristic
105C4⋊C8—22no—
106#102—24no—
107C24—22no—
108C2×D4—22no—
109C2×D4—22no—
110C2×D4—22no—
111C2×D4—22no—
112C2×D4—22no—
113C2×D4D4×C12714yes—
114C22×C4—22no—
115C22×C4D4×C12711yescharacteristic
116C22×C4D4×C12711yescharacteristic
117C22×C4C23×C12711yescharacteristic
118D8—28no—
119C2×C8—22no—
120C2×C8—22no—
121C2×C8—21no—
122C2×C8D4×C12712yes—
123C4⋊C4—22no—
124C4⋊C4—22no—
125C22⋊C4—44no—
126C22⋊C4—44no—
127C42—21no—
128C42—21no—
129C23—24no—
130C23—42no—
131C23—42no—
132C23—42no—
133C23—42no—
134C23—42no—
135C23—42no—
136C23C2×D4×C12711yescharacteristic
137D4—24no—
138D4—24no—
139D4—42no—
140D4—42no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—21no—
144C2×C4—22no—
145C2×C4—42no—
146C2×C4—42no—
147C2×C4—42no—
148C2×C4D8×C12712yescomplemented
149C2×C4C2×D4×C12712yes—
150C2×C4C2×D4×C12711yescharacteristic
151C2×C4#41×C12711yescharacteristic
152C2×C4#41×C12712yes—
153C8—22no—
154C8—41no—
155C22—44no—
156C22—44no—
157C22—44no—
158C22—82no—
159C22—82no—
160C22—82no—
161C22—82no—
162C22#121×C12712yes—
163C22#121×C12711yescharacteristic
164C22C2×D8×C12711yescharacteristic
165C22#135×C12711yescharacteristic
166C22AGL(1,ℤ/8)×C12712yes—
167C4—22no—
168C4—41no—
169C4—82no—
170C4#120×C12711yescharacteristic
171C4#123×C12712yes—
172C4#124×C12711yescharacteristic
173C2—84no—
174C2#394×C12711yescharacteristic
175C2#459×C12712yes—
176C2#463×C12712yes—
177C2#466×C12711yescharacteristic
178C2#469×C12711yescharacteristic
subgroupG/H
center, socleC23×C127C2×D4
commutator, Frattini, cosocleC22×C4C23×C127
prime radicalC22×D8×C127C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C8×C127C2semidirect
3. C2×#102×C127C2semidirect
4. #390×C127C2semidirect
5. #340×C127C2semidirect
58. C2×C4×C127D8semidirect
89. #2054C127direct (N × H)
90. C127#2054direct (N × H)
92. C2×C4⋊C8C2×C127semidirect
93. C2×#102C2×C127semidirect
94. #390C2×C127semidirect
95. #340C2×C127semidirect
148. C2×C4D8×C127semidirect

Maximal subgroups

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

subgroupindex
C22×D8×C1272
C2×C4⋊C8×C1272
C2×#102×C1272
#390×C1272
#340×C1272
#2054127