Finite Group Databasebeta

← C127×#2852 #30635804

Subgroups — C127×#2852 #30635804

Order 16256.

582 conjugacy classes of subgroups; only the 216 normal subgroups are shown.

normal subgroups only

This group has 582 conjugacy classes of subgroups — too many to draw. Only its 216 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×#126×C127C211yesmaximal, characteristic, complemented
2C22×C42×C127C211yesmaximal, characteristic, complemented
3#388×C127C213yesmaximal, complemented
4#387×C127C213yesmaximal, complemented
5#386×C127C213yesmaximal
6#385×C127C213yesmaximal, complemented
7#383×C127C211yesmaximal, characteristic, complemented
8C22×D4×C127C2211yescharacteristic
9C23×C4×C127C2213yes—
10#126×C127—24no—
11C2×C4⋊C4×C127C2213yes—
12C2×C4⋊C4×C127C2213yes—
13C2×C22⋊C4×C127C2213yes—
14C2×C22⋊C4×C127C2213yes—
15C2×C22⋊C4×C127C2213yes—
16C2×C42×C127—24no—
17C2×C42×C127C2213yes—
18C2×C42×C127C2211yescharacteristic
19#95×C127C2213yes—
20#95×C127C2213yes—
21#95×C127C2213yes—
22#95×C127C2213yes—
23C24×C127C2311yescharacteristic
24C24×C127C2311yescharacteristic
25C2×D4×C127—26no—
26C22×C4×C127—26no—
27C22×C4×C127—26no—
28C22×C4×C127—26no—
29C22×C4×C127C2311yescharacteristic
30C22×C4×C127C2313yes—
31C22×C4×C127C2313yes—
32C22×C4×C127C2313yes—
33C22×C4×C127C2313yes—
34C4⋊C4×C127—26no—
35C4⋊C4×C127—26no—
36C22⋊C4×C127—26no—
37C22⋊C4×C127—26no—
38C22⋊C4×C127—26no—
39C42×C127—26no—
40C42×C127D414yescomplemented
41C23×C127—21no—
42C23×C127—23no—
43C23×C127—21no—
44C23×C127—23no—
45C23×C127—23no—
46C23×C127#4116yes—
47C23×C127C2411yescharacteristic
48D4×C127—44no—
49C2×C4×C127—224no—
50C2×C4×C127—23no—
51C2×C4×C127—23no—
52C2×C4×C127—23no—
53C2×C4×C127—23no—
54C2×C4×C127—23no—
55C2×C4×C127—23no—
56C2×C4×C127—23no—
57C2×C4×C127—23no—
58C2×C4×C127—23no—
59C2×C4×C127—23no—
60C2×C4×C127—23no—
61C2×C4×C127C2×D416yes—
62C2×C4×C127#4116yes—
63C22×C127—26no—
64C22×C127—26no—
65C22×C127—43no—
66C22×C127—41no—
67C22×C127—43no—
68C22×C127#12614yescomplemented
69C22×C127C22×D411yescharacteristic
70C22×C127C2×#4113yes—
71C22×C127C2×#4113yes—
72C4×C127—26no—
73C4×C127—26no—
74C4×C127—43no—
75C4×C127—41no—
76C4×C127—43no—
77C2×C127—24no—
78C2×C127—81no—
79C2×C127#52513yes—
80C2×C127C2×#12611yescharacteristic
81C2×C127#52913yes—
82#2852C12711yesmaximal, characteristic, direct product factor, Sylow
83C127#285211yescharacteristic, direct product factor, Sylow
84C2×#126C2×C12711yescharacteristic, complemented
85C22×C42C2×C12711yescharacteristic, complemented
86#388C2×C12713yescomplemented
87#387C2×C12713yescomplemented
88#386C2×C12713yes—
89#385C2×C12713yescomplemented
90#383C2×C12711yescharacteristic, complemented
91C22×D4C22×C12711yescharacteristic
92C23×C4C22×C12713yes—
93#126—24no—
94C2×C4⋊C4C22×C12713yes—
95C2×C4⋊C4C22×C12713yes—
96C2×C22⋊C4C22×C12713yes—
97C2×C22⋊C4C22×C12713yes—
98C2×C22⋊C4C22×C12713yes—
99C2×C42—24no—
100C2×C42C22×C12713yes—
101C2×C42C22×C12711yescharacteristic
102#95C22×C12713yes—
103#95C22×C12713yes—
104#95C22×C12713yes—
105#95C22×C12713yes—
106C24C23×C12711yescharacteristic
107C24C23×C12711yescharacteristic
108C2×D4—26no—
109C22×C4—26no—
110C22×C4—26no—
111C22×C4—26no—
112C22×C4C23×C12711yescharacteristic
113C22×C4C23×C12713yes—
114C22×C4C23×C12713yes—
115C22×C4C23×C12713yes—
116C22×C4C23×C12713yes—
117C4⋊C4—26no—
118C4⋊C4—26no—
119C22⋊C4—26no—
120C22⋊C4—26no—
121C22⋊C4—26no—
122C42—26no—
123C42D4×C12714yescomplemented
124C23—21no—
125C23—23no—
126C23—21no—
127C23—23no—
128C23—23no—
129C23#41×C12716yes—
130C23C24×C12711yescharacteristic
131D4—44no—
132C2×C4—224no—
133C2×C4—23no—
134C2×C4—23no—
135C2×C4—23no—
136C2×C4—23no—
137C2×C4—23no—
138C2×C4—23no—
139C2×C4—23no—
140C2×C4—23no—
141C2×C4—23no—
142C2×C4—23no—
143C2×C4—23no—
144C2×C4C2×D4×C12716yes—
145C2×C4#41×C12716yes—
146C22—26no—
147C22—26no—
148C22—43no—
149C22—41no—
150C22—43no—
151C22#126×C12714yescomplemented
152C22C22×D4×C12711yescharacteristic
153C22C2×#41×C12713yes—
154C22C2×#41×C12713yes—
155C4—26no—
156C4—26no—
157C4—43no—
158C4—41no—
159C4—43no—
160C2—24no—
161C2—81no—
162C2#525×C12713yes—
163C2C2×#126×C12711yescharacteristic
164C2#529×C12713yes—
subgroupG/H
center, socleC23×C127C24
commutator, Frattini, cosocleC23C24×C127
prime radicalC22×D4×C127C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#126×C127C2semidirect
2. C22×C42×C127C2semidirect
3. #388×C127C2semidirect
4. #387×C127C2semidirect
6. #385×C127C2semidirect
7. #383×C127C2semidirect
40. C42×C127D4semidirect
68. C22×C127#126semidirect
82. #2852C127direct (N × H)
83. C127#2852direct (N × H)
84. C2×#126C2×C127semidirect
85. C22×C42C2×C127semidirect
86. #388C2×C127semidirect
87. #387C2×C127semidirect
89. #385C2×C127semidirect
90. #383C2×C127semidirect
123. C42D4×C127semidirect
151. C22#126×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#126×C1272
C22×C42×C1272
#388×C1272
#387×C1272
#386×C1272
#385×C1272
#383×C1272
#2852127