Finite Group Databasebeta

← C127×#1888 #30634840

Subgroups — C127×#1888 #30634840

Order 16256.

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

normal subgroups only

This group has 344 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
1C2×#124×C127C211yesmaximal, characteristic
2#519×C127C211yesmaximal, characteristic, complemented
3#418×C127C212yesmaximal
4C2×#101×C127C211yesmaximal, characteristic, complemented
5#339×C127C212yesmaximal, complemented
6C22×Q8×C127C2211yescharacteristic
7C22×D4×C127C2211yescharacteristic
8C2×M16×C127C2212yes—
9#124×C127—22no—
10#124×C127C414yescomplemented
11C4×Q8×C127—24no—
12#117×C127—22no—
13#117×C127C2212yes—
14C2×C22⋊C4×C127—22no—
15C2×C42×C127C2211yescharacteristic
16#102×C127—24no—
17#101×C127—22no—
18C24×C127—21no—
19C2×Q8×C127—22no—
20C2×Q8×C127—22no—
21C2×Q8×C127C2×C412yes—
22C2×Q8×C127D412yes—
23C2×D4×C127—22no—
24C2×D4×C127—21no—
25C2×D4×C127—22no—
26C2×D4×C127C2×C412yes—
27C22×C4×C127—21no—
28C22×C4×C127D412yes—
29C22×C4×C127C2311yescharacteristic
30M16×C127—22no—
31M16×C127—22no—
32C2×C8×C127—22no—
33C4⋊C4×C127—24no—
34C4⋊C4×C127D414yes—
35C22⋊C4×C127—22no—
36C22⋊C4×C127—28no—
37C42×C127—24no—
38C42×C127—21no—
39C42×C127—22no—
40C42×C127C2×C412yes—
41C23×C127—22no—
42C23×C127—44no—
43C23×C127—41no—
44C23×C127—41no—
45C23×C127C2×D411yescharacteristic
46Q8×C127—24no—
47Q8×C127—24no—
48D4×C127—24no—
49D4×C127—42no—
50C2×C4×C127—22no—
51C2×C4×C127—22no—
52C2×C4×C127—22no—
53C2×C4×C127—24no—
54C2×C4×C127—42no—
55C2×C4×C127C22⋊C414yes—
56C2×C4×C127C22×C411yescharacteristic
57C2×C4×C127C2×D412yes—
58C2×C4×C127C2×D411yescharacteristic
59C2×C4×C127#4112yes—
60C8×C127—42no—
61C22×C127—22no—
62C22×C127—44no—
63C22×C127—42no—
64C22×C127—82no—
65C22×C127—82no—
66C22×C127C2×C22⋊C411yescharacteristic
67C22×C127#12011yescharacteristic
68C22×C127#12311yescharacteristic
69C4×C127—24no—
70C4×C127—42no—
71C4×C127—44no—
72C4×C127C4×D412yes—
73C4×C127#12112yes—
74C2×C127—21no—
75C2×C127—21no—
76C2×C127—82no—
77C2×C127#38611yescharacteristic
78C2×C127#45412yes—
79#1888C12711yesmaximal, characteristic, direct product factor, Sylow
80C127#188811yescharacteristic, direct product factor, Sylow
81C2×#124C2×C12711yescharacteristic
82#519C2×C12711yescharacteristic, complemented
83#418C2×C12712yes—
84C2×#101C2×C12711yescharacteristic, complemented
85#339C2×C12712yescomplemented
86C22×Q8C22×C12711yescharacteristic
87C22×D4C22×C12711yescharacteristic
88C2×M16C22×C12712yes—
89#124—22no—
90#124C4×C12714yescomplemented
91C4×Q8—24no—
92#117—22no—
93#117C22×C12712yes—
94C2×C22⋊C4—22no—
95C2×C42C22×C12711yescharacteristic
96#102—24no—
97#101—22no—
98C24—21no—
99C2×Q8—22no—
100C2×Q8—22no—
101C2×Q8C2×C4×C12712yes—
102C2×Q8D4×C12712yes—
103C2×D4—22no—
104C2×D4—21no—
105C2×D4—22no—
106C2×D4C2×C4×C12712yes—
107C22×C4—21no—
108C22×C4D4×C12712yes—
109C22×C4C23×C12711yescharacteristic
110M16—22no—
111M16—22no—
112C2×C8—22no—
113C4⋊C4—24no—
114C4⋊C4D4×C12714yes—
115C22⋊C4—22no—
116C22⋊C4—28no—
117C42—24no—
118C42—21no—
119C42—22no—
120C42C2×C4×C12712yes—
121C23—22no—
122C23—44no—
123C23—41no—
124C23—41no—
125C23C2×D4×C12711yescharacteristic
126Q8—24no—
127Q8—24no—
128D4—24no—
129D4—42no—
130C2×C4—22no—
131C2×C4—22no—
132C2×C4—22no—
133C2×C4—24no—
134C2×C4—42no—
135C2×C4C22⋊C4×C12714yes—
136C2×C4C22×C4×C12711yescharacteristic
137C2×C4C2×D4×C12712yes—
138C2×C4C2×D4×C12711yescharacteristic
139C2×C4#41×C12712yes—
140C8—42no—
141C22—22no—
142C22—44no—
143C22—42no—
144C22—82no—
145C22—82no—
146C22C2×C22⋊C4×C12711yescharacteristic
147C22#120×C12711yescharacteristic
148C22#123×C12711yescharacteristic
149C4—24no—
150C4—42no—
151C4—44no—
152C4C4×D4×C12712yes—
153C4#121×C12712yes—
154C2—21no—
155C2—21no—
156C2—82no—
157C2#386×C12711yescharacteristic
158C2#454×C12712yes—
subgroupG/H
center, socleC22×C127#120
commutatorC2×C4C22×C4×C127
Frattini, cosocleC22×C4C23×C127
prime radicalC22×D4×C127C22
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
2. #519×C127C2semidirect
4. C2×#101×C127C2semidirect
5. #339×C127C2semidirect
10. #124×C127C4semidirect
79. #1888C127direct (N × H)
80. C127#1888direct (N × H)
82. #519C2×C127semidirect
84. C2×#101C2×C127semidirect
85. #339C2×C127semidirect
90. #124C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#124×C1272
#519×C1272
#418×C1272
C2×#101×C1272
#339×C1272
#1888127