Finite Group Databasebeta

← C127×#1850 #30634802

Subgroups — C127×#1850 #30634802

Order 16256.

348 conjugacy classes of subgroups; only the 160 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 160 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
1C23×C8×C127C211yesmaximal, characteristic
2C2×C4⋊C8×C127C212yesmaximal, complemented
3C2×C22⋊C8×C127C211yesmaximal, characteristic
4C4×C22⋊C4×C127C211yesmaximal, characteristic
5#336×C127C212yesmaximal, complemented
6C23×C4×C127C2211yescharacteristic
7C22×C8×C127—22no—
8C22×C8×C127—24no—
9C22×C8×C127C2211yescharacteristic
10C22×C8×C127C2211yescharacteristic
11C22×C8×C127C2212yes—
12C2×C22⋊C4×C127C411yescharacteristic
13C2×C22⋊C4×C127C411yescharacteristic
14C2×C42×C127C2212yes—
15C4⋊C8×C127—24no—
16C22⋊C8×C127—22no—
17#95×C127C412yes—
18C24×C127C2×C411yescharacteristic
19C22×C4×C127—22no—
20C22×C4×C127—22no—
21C22×C4×C127C2×C412yes—
22C22×C4×C127C2×C411yescharacteristic
23C22×C4×C127C2×C412yes—
24C22×C4×C127D412yes—
25C22×C4×C127Q812yes—
26C22×C4×C127C2311yescharacteristic
27C2×C8×C127—28no—
28C2×C8×C127—22no—
29C2×C8×C127—22no—
30C2×C8×C127—21no—
31C2×C8×C127—21no—
32C2×C8×C127—22no—
33C2×C8×C127—22no—
34C2×C8×C127D414yes—
35C22⋊C4×C127—22no—
36C22⋊C4×C127C814yescomplemented
37C42×C127—22no—
38C42×C127—22no—
39C23×C127—22no—
40C23×C127—22no—
41C23×C127C4⋊C412yes—
42C23×C127C2×C812yes—
43C23×C127M1612yes—
44C23×C127C22×C411yescharacteristic
45C2×C4×C127—22no—
46C2×C4×C127—22no—
47C2×C4×C127—22no—
48C2×C4×C127—22no—
49C2×C4×C127—24no—
50C2×C4×C127—22no—
51C2×C4×C127—22no—
52C2×C4×C127—22no—
53C2×C4×C127—22no—
54C2×C4×C127C4⋊C412yes—
55C2×C4×C127C2×C814yescomplemented
56C2×C4×C127C2×D412yes—
57C2×C4×C127C2×D411yescharacteristic
58C2×C4×C127C2×Q811yescharacteristic
59C2×C4×C127#4112yes—
60C8×C127—24no—
61C8×C127—41no—
62C8×C127—41no—
63C22×C127—22no—
64C22×C127—22no—
65C22×C127—24no—
66C22×C127—24no—
67C22×C127C4⋊C814yescomplemented
68C22×C127C2×C4⋊C411yescharacteristic
69C22×C127C4×D412yes—
70C22×C127C22×C811yescharacteristic
71C22×C127C2×M1611yescharacteristic
72C22×C127#13112yes—
73C4×C127—22no—
74C4×C127—24no—
75C4×C127—42no—
76C4×C127#12011yescharacteristic
77C4×C127C22⋊Q812yes—
78C4×C127#12311yescharacteristic
79C2×C127—24no—
80C2×C127#38511yescharacteristic
81C2×C127C2×C4⋊C811yescharacteristic
82C2×C127#42411yescharacteristic
83C2×C127C8×D412yes—
84C2×C127#43512yes—
85#1850C12711yesmaximal, characteristic, direct product factor, Sylow
86C127#185011yescharacteristic, direct product factor, Sylow
87C23×C8C2×C12711yescharacteristic
88C2×C4⋊C8C2×C12712yescomplemented
89C2×C22⋊C8C2×C12711yescharacteristic
90C4×C22⋊C4C2×C12711yescharacteristic
91#336C2×C12712yescomplemented
92C23×C4C22×C12711yescharacteristic
93C22×C8—22no—
94C22×C8—24no—
95C22×C8C22×C12711yescharacteristic
96C22×C8C22×C12711yescharacteristic
97C22×C8C22×C12712yes—
98C2×C22⋊C4C4×C12711yescharacteristic
99C2×C22⋊C4C4×C12711yescharacteristic
100C2×C42C22×C12712yes—
101C4⋊C8—24no—
102C22⋊C8—22no—
103#95C4×C12712yes—
104C24C2×C4×C12711yescharacteristic
105C22×C4—22no—
106C22×C4—22no—
107C22×C4C2×C4×C12712yes—
108C22×C4C2×C4×C12711yescharacteristic
109C22×C4C2×C4×C12712yes—
110C22×C4D4×C12712yes—
111C22×C4Q8×C12712yes—
112C22×C4C23×C12711yescharacteristic
113C2×C8—28no—
114C2×C8—22no—
115C2×C8—22no—
116C2×C8—21no—
117C2×C8—21no—
118C2×C8—22no—
119C2×C8—22no—
120C2×C8D4×C12714yes—
121C22⋊C4—22no—
122C22⋊C4C8×C12714yescomplemented
123C42—22no—
124C42—22no—
125C23—22no—
126C23—22no—
127C23C4⋊C4×C12712yes—
128C23C2×C8×C12712yes—
129C23M16×C12712yes—
130C23C22×C4×C12711yescharacteristic
131C2×C4—22no—
132C2×C4—22no—
133C2×C4—22no—
134C2×C4—22no—
135C2×C4—24no—
136C2×C4—22no—
137C2×C4—22no—
138C2×C4—22no—
139C2×C4—22no—
140C2×C4C4⋊C4×C12712yes—
141C2×C4C2×C8×C12714yescomplemented
142C2×C4C2×D4×C12712yes—
143C2×C4C2×D4×C12711yescharacteristic
144C2×C4C2×Q8×C12711yescharacteristic
145C2×C4#41×C12712yes—
146C8—24no—
147C8—41no—
148C8—41no—
149C22—22no—
150C22—22no—
151C22—24no—
152C22—24no—
153C22C4⋊C8×C12714yescomplemented
154C22C2×C4⋊C4×C12711yescharacteristic
155C22C4×D4×C12712yes—
156C22C22×C8×C12711yescharacteristic
157C22C2×M16×C12711yescharacteristic
158C22#131×C12712yes—
159C4—22no—
160C4—24no—
161C4—42no—
162C4#120×C12711yescharacteristic
163C4C22⋊Q8×C12712yes—
164C4#123×C12711yescharacteristic
165C2—24no—
166C2#385×C12711yescharacteristic
167C2C2×C4⋊C8×C12711yescharacteristic
168C2#424×C12711yescharacteristic
169C2C8×D4×C12712yes—
170C2#435×C12712yes—
subgroupG/H
centerC22×C4×C127C23
commutatorC22C22×C8×C127
Frattini, cosocleC22×C4C23×C127
socleC23×C127C22×C4
prime radicalC24×C127C2×C4
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C8×C127C2semidirect
5. #336×C127C2semidirect
36. C22⋊C4×C127C8semidirect
55. C2×C4×C127C2×C8semidirect
67. C22×C127C4⋊C8semidirect
85. #1850C127direct (N × H)
86. C127#1850direct (N × H)
88. C2×C4⋊C8C2×C127semidirect
91. #336C2×C127semidirect
122. C22⋊C4C8×C127semidirect
141. C2×C4C2×C8×C127semidirect
153. C22C4⋊C8×C127semidirect

Maximal subgroups

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

subgroupindex
C23×C8×C1272
C2×C4⋊C8×C1272
C2×C22⋊C8×C1272
C4×C22⋊C4×C1272
#336×C1272
#1850127