Finite Group Databasebeta

← C127×#1787 #30634739

Subgroups — C127×#1787 #30634739

Order 16256.

592 conjugacy classes of subgroups; only the 168 normal subgroups are shown.

normal subgroups only

This group has 592 conjugacy classes of subgroups — too many to draw. Only its 168 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×Q8×C127C211yesmaximal, characteristic
2C2×#103×C127C214yesmaximal, complemented
3C2×C22⋊C8×C127C211yesmaximal, characteristic
4#380×C127C211yesmaximal, characteristic
5C22×Q8×C127—28no—
6C22×Q8×C127—22no—
7C22×Q8×C127—21no—
8C22×Q8×C127C414yescomplemented
9C22×Q8×C127C2212yes—
10C23×C4×C127—21no—
11C23×C4×C127C2211yescharacteristic
12C22×C8×C127C2212yes—
13C2×C4⋊C4×C127C2212yes—
14C2×C22⋊C4×C127—21no—
15#103×C127—28no—
16C22⋊C8×C127—22no—
17#95×C127—21no—
18C24×C127D411yescharacteristic
19C2×Q8×C127—216no—
20C2×Q8×C127—28no—
21C2×Q8×C127—216no—
22C2×Q8×C127—24no—
23C2×Q8×C127—22no—
24C2×Q8×C127—24no—
25C2×Q8×C127C2×C414yes—
26C2×Q8×C127D418yes—
27C22×C4×C127—28no—
28C22×C4×C127—24no—
29C22×C4×C127—22no—
30C22×C4×C127—24no—
31C22×C4×C127—22no—
32C22×C4×C127C2×C412yes—
33C22×C4×C127D411yescharacteristic
34C22×C4×C127D412yes—
35C22×C4×C127C2311yescharacteristic
36C2×C8×C127—22no—
37C2×C8×C127—24no—
38C4⋊C4×C127—24no—
39C22⋊C4×C127—42no—
40C23×C127—22no—
41C23×C127—22no—
42C23×C127C22⋊C412yes—
43C23×C127SD1612yes—
44C23×C127Q1612yes—
45C23×C127C2×D411yescharacteristic
46Q8×C127—216no—
47Q8×C127—24no—
48Q8×C127—28no—
49Q8×C127C22⋊C418yescomplemented
50C2×C4×C127—216no—
51C2×C4×C127—24no—
52C2×C4×C127—28no—
53C2×C4×C127—22no—
54C2×C4×C127—24no—
55C2×C4×C127—24no—
56C2×C4×C127—42no—
57C2×C4×C127—42no—
58C2×C4×C127—42no—
59C2×C4×C127C22⋊C412yes—
60C2×C4×C127C22×C411yescharacteristic
61C2×C4×C127C2×D414yes—
62C2×C4×C127C2×D411yescharacteristic
63C8×C127—42no—
64C22×C127—22no—
65C22×C127—22no—
66C22×C127—24no—
67C22×C127—24no—
68C22×C127#10314yescomplemented
69C22×C127C2×C22⋊C411yescharacteristic
70C22×C127#12012yes—
71C22×C127C2×SD1611yescharacteristic
72C22×C127C2×Q1611yescharacteristic
73C22×C127#13712yes—
74C4×C127—28no—
75C4×C127—22no—
76C4×C127—82no—
77C4×C127C2×C22⋊C412yes—
78C4×C127#12012yes—
79C2×C127—24no—
80C2×C127#37911yescharacteristic
81C2×C127C2×#10311yescharacteristic
82C2×C127#41911yescharacteristic
83C2×C127#44812yes—
84C2×C127#45112yes—
85#1787C12711yesmaximal, characteristic, direct product factor, Sylow
86C127#178711yescharacteristic, direct product factor, Sylow
87C23×Q8C2×C12711yescharacteristic
88C2×#103C2×C12714yescomplemented
89C2×C22⋊C8C2×C12711yescharacteristic
90#380C2×C12711yescharacteristic
91C22×Q8—28no—
92C22×Q8—22no—
93C22×Q8—21no—
94C22×Q8C4×C12714yescomplemented
95C22×Q8C22×C12712yes—
96C23×C4—21no—
97C23×C4C22×C12711yescharacteristic
98C22×C8C22×C12712yes—
99C2×C4⋊C4C22×C12712yes—
100C2×C22⋊C4—21no—
101#103—28no—
102C22⋊C8—22no—
103#95—21no—
104C24D4×C12711yescharacteristic
105C2×Q8—216no—
106C2×Q8—28no—
107C2×Q8—216no—
108C2×Q8—24no—
109C2×Q8—22no—
110C2×Q8—24no—
111C2×Q8C2×C4×C12714yes—
112C2×Q8D4×C12718yes—
113C22×C4—28no—
114C22×C4—24no—
115C22×C4—22no—
116C22×C4—24no—
117C22×C4—22no—
118C22×C4C2×C4×C12712yes—
119C22×C4D4×C12711yescharacteristic
120C22×C4D4×C12712yes—
121C22×C4C23×C12711yescharacteristic
122C2×C8—22no—
123C2×C8—24no—
124C4⋊C4—24no—
125C22⋊C4—42no—
126C23—22no—
127C23—22no—
128C23C22⋊C4×C12712yes—
129C23SD16×C12712yes—
130C23Q16×C12712yes—
131C23C2×D4×C12711yescharacteristic
132Q8—216no—
133Q8—24no—
134Q8—28no—
135Q8C22⋊C4×C12718yescomplemented
136C2×C4—216no—
137C2×C4—24no—
138C2×C4—28no—
139C2×C4—22no—
140C2×C4—24no—
141C2×C4—24no—
142C2×C4—42no—
143C2×C4—42no—
144C2×C4—42no—
145C2×C4C22⋊C4×C12712yes—
146C2×C4C22×C4×C12711yescharacteristic
147C2×C4C2×D4×C12714yes—
148C2×C4C2×D4×C12711yescharacteristic
149C8—42no—
150C22—22no—
151C22—22no—
152C22—24no—
153C22—24no—
154C22#103×C12714yescomplemented
155C22C2×C22⋊C4×C12711yescharacteristic
156C22#120×C12712yes—
157C22C2×SD16×C12711yescharacteristic
158C22C2×Q16×C12711yescharacteristic
159C22#137×C12712yes—
160C4—28no—
161C4—22no—
162C4—82no—
163C4C2×C22⋊C4×C12712yes—
164C4#120×C12712yes—
165C2—24no—
166C2#379×C12711yescharacteristic
167C2C2×#103×C12711yescharacteristic
168C2#419×C12711yescharacteristic
169C2#448×C12712yes—
170C2#451×C12712yes—
subgroupG/H
center, socleC23×C127C2×D4
commutatorC2×C4C22×C4×C127
Frattini, cosocleC22×C4C23×C127
prime radicalC24×C127D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C127 ◁ C23×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#103×C127C2semidirect
8. C22×Q8×C127C4semidirect
49. Q8×C127C22⋊C4semidirect
68. C22×C127#103semidirect
85. #1787C127direct (N × H)
86. C127#1787direct (N × H)
88. C2×#103C2×C127semidirect
94. C22×Q8C4×C127semidirect
135. Q8C22⋊C4×C127semidirect
154. C22#103×C127semidirect

Maximal subgroups

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

subgroupindex
C23×Q8×C1272
C2×#103×C1272
C2×C22⋊C8×C1272
#380×C1272
#1787127