Finite Group Databasebeta

← C127×#1857 #30634809

Subgroups — C127×#1857 #30634809

Order 16256.

272 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 112 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
1#519×C127C211yesmaximal, characteristic
2#428×C127C212yesmaximal
3C2×#101×C127C211yesmaximal, characteristic
4#391×C127C211yesmaximal, characteristic
5#339×C127C212yesmaximal
6C22×Q8×C127C2211yescharacteristic
7C2×M16×C127C2212yes—
8C4×Q8×C127—22no—
9C4×Q8×C127—22no—
10#117×C127—22no—
11#117×C127C2212yes—
12C2×C4⋊C4×C127C2211yescharacteristic
13C2×C42×C127C2211yescharacteristic
14#107×C127—22no—
15#106×C127—22no—
16#101×C127C414yescomplemented
17#95×C127—22no—
18C2×Q8×C127—22no—
19C2×Q8×C127—22no—
20C2×Q8×C127C2×C412yes—
21C2×Q8×C127Q812yes—
22C22×C4×C127—21no—
23C22×C4×C127—21no—
24C22×C4×C127D412yes—
25C22×C4×C127C2311yescharacteristic
26M16×C127—22no—
27M16×C127C2×C414yes—
28C2×C8×C127—22no—
29C4⋊C4×C127—22no—
30C4⋊C4×C127—22no—
31C4⋊C4×C127—22no—
32C4⋊C4×C127D412yes—
33C4⋊C4×C127D412yes—
34C22⋊C4×C127—22no—
35C42×C127—24no—
36C42×C127—22no—
37C42×C127—22no—
38C23×C127C2×D411yescharacteristic
39Q8×C127—24no—
40Q8×C127—24no—
41C2×C4×C127—22no—
42C2×C4×C127—22no—
43C2×C4×C127—22no—
44C2×C4×C127—22no—
45C2×C4×C127—22no—
46C2×C4×C127—41no—
47C2×C4×C127—41no—
48C2×C4×C127—42no—
49C2×C4×C127—41no—
50C2×C4×C127C4⋊C414yes—
51C2×C4×C127C22×C411yescharacteristic
52C2×C4×C127C2×D412yes—
53C2×C4×C127C2×Q811yescharacteristic
54C2×C4×C127#4112yes—
55C8×C127—24no—
56C22×C127—21no—
57C22×C127—21no—
58C22×C127C2×C4⋊C411yescharacteristic
59C22×C127#12011yescharacteristic
60C22×C127#12311yescharacteristic
61C4×C127—24no—
62C4×C127—42no—
63C4×C127—42no—
64C4×C127—42no—
65C4×C127—81no—
66C4×C127C4×D412yes—
67C4×C127C22⋊Q812yes—
68C2×C127—21no—
69C2×C127—21no—
70C2×C127#38511yescharacteristic
71C2×C127#45411yescharacteristic
72C2×C127#45611yescharacteristic
73#1857C12711yesmaximal, characteristic, direct product factor, Sylow
74C127#185711yescharacteristic, direct product factor, Sylow
75#519C2×C12711yescharacteristic
76#428C2×C12712yes—
77C2×#101C2×C12711yescharacteristic
78#391C2×C12711yescharacteristic
79#339C2×C12712yes—
80C22×Q8C22×C12711yescharacteristic
81C2×M16C22×C12712yes—
82C4×Q8—22no—
83C4×Q8—22no—
84#117—22no—
85#117C22×C12712yes—
86C2×C4⋊C4C22×C12711yescharacteristic
87C2×C42C22×C12711yescharacteristic
88#107—22no—
89#106—22no—
90#101C4×C12714yescomplemented
91#95—22no—
92C2×Q8—22no—
93C2×Q8—22no—
94C2×Q8C2×C4×C12712yes—
95C2×Q8Q8×C12712yes—
96C22×C4—21no—
97C22×C4—21no—
98C22×C4D4×C12712yes—
99C22×C4C23×C12711yescharacteristic
100M16—22no—
101M16C2×C4×C12714yes—
102C2×C8—22no—
103C4⋊C4—22no—
104C4⋊C4—22no—
105C4⋊C4—22no—
106C4⋊C4D4×C12712yes—
107C4⋊C4D4×C12712yes—
108C22⋊C4—22no—
109C42—24no—
110C42—22no—
111C42—22no—
112C23C2×D4×C12711yescharacteristic
113Q8—24no—
114Q8—24no—
115C2×C4—22no—
116C2×C4—22no—
117C2×C4—22no—
118C2×C4—22no—
119C2×C4—22no—
120C2×C4—41no—
121C2×C4—41no—
122C2×C4—42no—
123C2×C4—41no—
124C2×C4C4⋊C4×C12714yes—
125C2×C4C22×C4×C12711yescharacteristic
126C2×C4C2×D4×C12712yes—
127C2×C4C2×Q8×C12711yescharacteristic
128C2×C4#41×C12712yes—
129C8—24no—
130C22—21no—
131C22—21no—
132C22C2×C4⋊C4×C12711yescharacteristic
133C22#120×C12711yescharacteristic
134C22#123×C12711yescharacteristic
135C4—24no—
136C4—42no—
137C4—42no—
138C4—42no—
139C4—81no—
140C4C4×D4×C12712yes—
141C4C22⋊Q8×C12712yes—
142C2—21no—
143C2—21no—
144C2#385×C12711yescharacteristic
145C2#454×C12711yescharacteristic
146C2#456×C12711yescharacteristic
subgroupG/H
center, socleC22×C127#120
commutatorC2×C4C22×C4×C127
Frattini, cosocleC22×C4C23×C127
prime radicalC23×C127C2×D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C22×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
16. #101×C127C4semidirect
73. #1857C127direct (N × H)
74. C127#1857direct (N × H)
90. #101C4×C127semidirect

Maximal subgroups

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

subgroupindex
#519×C1272
#428×C1272
C2×#101×C1272
#391×C1272
#339×C1272
#1857127