Finite Group Databasebeta

← C127×#2643 #30635595

Subgroups — C127×#2643 #30635595

Order 16256.

462 conjugacy classes of subgroups; only the 184 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 184 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#401×C127C211yesmaximal, characteristic, complemented
2#400×C127C213yesmaximal, complemented
3#397×C127C213yesmaximal, complemented
4#396×C127C211yesmaximal, characteristic, complemented
5#386×C127C213yesmaximal
6#385×C127C213yesmaximal, complemented
7C2×#95×C127C211yesmaximal, characteristic, complemented
8C22×D4×C127C2211yescharacteristic
9C23×C4×C127C2213yes—
10C2×C4⋊C4×C127C2213yes—
11C2×C4⋊C4×C127C2213yes—
12C2×C22⋊C4×C127C2213yes—
13C2×C22⋊C4×C127C2213yes—
14C2×C22⋊C4×C127C2213yes—
15#95×C127C2211yescharacteristic
16#95×C127C2213yes—
17#95×C127C2213yes—
18#95×C127C2213yes—
19#95×C127C2213yes—
20#95×C127C2213yes—
21C24×C127C2311yescharacteristic
22C24×C127C2311yescharacteristic
23C2×D4×C127—26no—
24C22×C4×C127—26no—
25C22×C4×C127—43no—
26C22×C4×C127—43no—
27C22×C4×C127C2311yescharacteristic
28C22×C4×C127C2313yes—
29C22×C4×C127C2313yes—
30C22×C4×C127C2313yes—
31C22×C4×C127C2313yes—
32C4⋊C4×C127—43no—
33C4⋊C4×C127—43no—
34C22⋊C4×C127—26no—
35C22⋊C4×C127—43no—
36C22⋊C4×C127—43no—
37C23×C127—23no—
38C23×C127—21no—
39C23×C127—23no—
40C23×C127—23no—
41C23×C127—21no—
42C23×C127#4116yes—
43C23×C127C2411yescharacteristic
44D4×C127—44no—
45C2×C4×C127—23no—
46C2×C4×C127—23no—
47C2×C4×C127—23no—
48C2×C4×C127—23no—
49C2×C4×C127—23no—
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—412no—
59C22×C127—26no—
60C22×C127—26no—
61C22×C127—41no—
62C22×C127—43no—
63C22×C127—43no—
64C22×C127#12614yes—
65C22×C127C2×#4113yes—
66C22×C127H(5,𝔽2)13yes—
67C22×C1272−1+411yescharacteristic
68C4×C127—41no—
69C4×C127—43no—
70C4×C127—43no—
71C4×C127—43no—
72C4×C127—43no—
73C2×C127—24no—
74C2×C127—81no—
75C2×C127C2×#12611yescharacteristic
76C2×C127#53813yes—
77C2×C127#53913yes—
78#2643C12711yesmaximal, characteristic, direct product factor, Sylow
79C127#264311yescharacteristic, direct product factor, Sylow
80#401C2×C12711yescharacteristic, complemented
81#400C2×C12713yescomplemented
82#397C2×C12713yescomplemented
83#396C2×C12711yescharacteristic, complemented
84#386C2×C12713yes—
85#385C2×C12713yescomplemented
86C2×#95C2×C12711yescharacteristic, complemented
87C22×D4C22×C12711yescharacteristic
88C23×C4C22×C12713yes—
89C2×C4⋊C4C22×C12713yes—
90C2×C4⋊C4C22×C12713yes—
91C2×C22⋊C4C22×C12713yes—
92C2×C22⋊C4C22×C12713yes—
93C2×C22⋊C4C22×C12713yes—
94#95C22×C12711yescharacteristic
95#95C22×C12713yes—
96#95C22×C12713yes—
97#95C22×C12713yes—
98#95C22×C12713yes—
99#95C22×C12713yes—
100C24C23×C12711yescharacteristic
101C24C23×C12711yescharacteristic
102C2×D4—26no—
103C22×C4—26no—
104C22×C4—43no—
105C22×C4—43no—
106C22×C4C23×C12711yescharacteristic
107C22×C4C23×C12713yes—
108C22×C4C23×C12713yes—
109C22×C4C23×C12713yes—
110C22×C4C23×C12713yes—
111C4⋊C4—43no—
112C4⋊C4—43no—
113C22⋊C4—26no—
114C22⋊C4—43no—
115C22⋊C4—43no—
116C23—23no—
117C23—21no—
118C23—23no—
119C23—23no—
120C23—21no—
121C23#41×C12716yes—
122C23C24×C12711yescharacteristic
123D4—44no—
124C2×C4—23no—
125C2×C4—23no—
126C2×C4—23no—
127C2×C4—23no—
128C2×C4—23no—
129C2×C4—23no—
130C2×C4—23no—
131C2×C4—23no—
132C2×C4—23no—
133C2×C4—23no—
134C2×C4—23no—
135C2×C4—23no—
136C2×C4—23no—
137C2×C4—412no—
138C22—26no—
139C22—26no—
140C22—41no—
141C22—43no—
142C22—43no—
143C22#126×C12714yes—
144C22C2×#41×C12713yes—
145C22H(5,𝔽2)×C12713yes—
146C222−1+4×C12711yescharacteristic
147C4—41no—
148C4—43no—
149C4—43no—
150C4—43no—
151C4—43no—
152C2—24no—
153C2—81no—
154C2C2×#126×C12711yescharacteristic
155C2#538×C12713yes—
156C2#539×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. #401×C127C2semidirect
2. #400×C127C2semidirect
3. #397×C127C2semidirect
4. #396×C127C2semidirect
6. #385×C127C2semidirect
7. C2×#95×C127C2semidirect
78. #2643C127direct (N × H)
79. C127#2643direct (N × H)
80. #401C2×C127semidirect
81. #400C2×C127semidirect
82. #397C2×C127semidirect
83. #396C2×C127semidirect
85. #385C2×C127semidirect
86. C2×#95C2×C127semidirect

Maximal subgroups

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

subgroupindex
#401×C1272
#400×C1272
#397×C1272
#396×C1272
#386×C1272
#385×C1272
C2×#95×C1272
#2643127