Finite Group Databasebeta

← C127×#2379 #30635331

Subgroups — C127×#2379 #30635331

Order 16256.

520 conjugacy classes of subgroups; only the 264 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 264 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#391×C127C212yesmaximal, complemented
3#388×C127C214yesmaximal, complemented
4#386×C127C212yesmaximal
5#385×C127C214yesmaximal, complemented
6#382×C127C212yesmaximal, complemented
7C22×Q8×C127C2211yescharacteristic
8C22×D4×C127C2211yescharacteristic
9C23×C4×C127C2212yes—
10#124×C127C418yescomplemented
11C2×C4⋊C4×C127C2212yes—
12C2×C4⋊C4×C127C2212yes—
13C2×C4⋊C4×C127C2212yes—
14C2×C22⋊C4×C127C2214yes—
15C2×C22⋊C4×C127C2212yes—
16C2×C22⋊C4×C127C2214yes—
17C2×C42×C127C2212yes—
18C2×C42×C127C2211yescharacteristic
19#95×C127C2214yes—
20#95×C127C2214yes—
21#95×C127C2214yes—
22C24×C127C2312yes—
23C2×Q8×C127—41no—
24C2×Q8×C127—41no—
25C2×Q8×C127C2×C414yescomplemented
26C2×D4×C127—41no—
27C2×D4×C127—41no—
28C2×D4×C127C2×C414yes—
29C22×C4×C127—44no—
30C22×C4×C127—42no—
31C22×C4×C127C2314yes—
32C22×C4×C127C2314yes—
33C22×C4×C127C2311yescharacteristic
34C22×C4×C127C2312yes—
35C22×C4×C127C2312yes—
36C4⋊C4×C127—42no—
37C4⋊C4×C127—42no—
38C4⋊C4×C127—42no—
39C22⋊C4×C127—42no—
40C22⋊C4×C127—44no—
41C22⋊C4×C127C2×C4116yescomplemented
42C42×C127—42no—
43C42×C127C2×C414yescomplemented
44C23×C127—24no—
45C23×C127—22no—
46C23×C127—22no—
47C23×C127—24no—
48C23×C127C22×C414yes—
49C23×C127C2411yescharacteristic
50Q8×C127—44no—
51D4×C127—44no—
52C2×C4×C127—22no—
53C2×C4×C127—22no—
54C2×C4×C127—22no—
55C2×C4×C127—21no—
56C2×C4×C127—21no—
57C2×C4×C127—22no—
58C2×C4×C127—24no—
59C2×C4×C127—24no—
60C2×C4×C127—24no—
61C2×C4×C127—24no—
62C2×C4×C127—24no—
63C2×C4×C127—24no—
64C2×C4×C127—48no—
65C2×C4×C127C22×C414yes—
66C2×C4×C127C22×C412yes—
67C2×C4×C127C22×C414yes—
68C22×C127—24no—
69C22×C127—28no—
70C22×C127—42no—
71C22×C127—44no—
72C22×C127—42no—
73C22×C127C23×C411yescharacteristic
74C22×C127H(5,𝔽2)11yescharacteristic
75C22×C127H(5,𝔽2)11yescharacteristic
76C22×C127H(5,𝔽2)12yes—
77C22×C1272−1+412yes—
78C4×C127—22no—
79C4×C127—24no—
80C4×C127—24no—
81C4×C127—44no—
82C4×C127—44no—
83C2×C127—44no—
84C2×C127#51811yescharacteristic
85C2×C127#52012yes—
86C2×C127H(3,𝔽4)11yescharacteristic
87C2×C127#56212yes—
88C2×C127#56311yescharacteristic
89#2379C12711yesmaximal, characteristic, direct product factor, Sylow
90C127#237911yescharacteristic, direct product factor, Sylow
91C2×#124C2×C12711yescharacteristic
92#391C2×C12712yescomplemented
93#388C2×C12714yescomplemented
94#386C2×C12712yes—
95#385C2×C12714yescomplemented
96#382C2×C12712yescomplemented
97C22×Q8C22×C12711yescharacteristic
98C22×D4C22×C12711yescharacteristic
99C23×C4C22×C12712yes—
100#124C4×C12718yescomplemented
101C2×C4⋊C4C22×C12712yes—
102C2×C4⋊C4C22×C12712yes—
103C2×C4⋊C4C22×C12712yes—
104C2×C22⋊C4C22×C12714yes—
105C2×C22⋊C4C22×C12712yes—
106C2×C22⋊C4C22×C12714yes—
107C2×C42C22×C12712yes—
108C2×C42C22×C12711yescharacteristic
109#95C22×C12714yes—
110#95C22×C12714yes—
111#95C22×C12714yes—
112C24C23×C12712yes—
113C2×Q8—41no—
114C2×Q8—41no—
115C2×Q8C2×C4×C12714yescomplemented
116C2×D4—41no—
117C2×D4—41no—
118C2×D4C2×C4×C12714yes—
119C22×C4—44no—
120C22×C4—42no—
121C22×C4C23×C12714yes—
122C22×C4C23×C12714yes—
123C22×C4C23×C12711yescharacteristic
124C22×C4C23×C12712yes—
125C22×C4C23×C12712yes—
126C4⋊C4—42no—
127C4⋊C4—42no—
128C4⋊C4—42no—
129C22⋊C4—42no—
130C22⋊C4—44no—
131C22⋊C4C2×C4×C127116yescomplemented
132C42—42no—
133C42C2×C4×C12714yescomplemented
134C23—24no—
135C23—22no—
136C23—22no—
137C23—24no—
138C23C22×C4×C12714yes—
139C23C24×C12711yescharacteristic
140Q8—44no—
141D4—44no—
142C2×C4—22no—
143C2×C4—22no—
144C2×C4—22no—
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—22no—
148C2×C4—24no—
149C2×C4—24no—
150C2×C4—24no—
151C2×C4—24no—
152C2×C4—24no—
153C2×C4—24no—
154C2×C4—48no—
155C2×C4C22×C4×C12714yes—
156C2×C4C22×C4×C12712yes—
157C2×C4C22×C4×C12714yes—
158C22—24no—
159C22—28no—
160C22—42no—
161C22—44no—
162C22—42no—
163C22C23×C4×C12711yescharacteristic
164C22H(5,𝔽2)×C12711yescharacteristic
165C22H(5,𝔽2)×C12711yescharacteristic
166C22H(5,𝔽2)×C12712yes—
167C222−1+4×C12712yes—
168C4—22no—
169C4—24no—
170C4—24no—
171C4—44no—
172C4—44no—
173C2—44no—
174C2#518×C12711yescharacteristic
175C2#520×C12712yes—
176C2H(3,𝔽4)×C12711yescharacteristic
177C2#562×C12712yes—
178C2#563×C12711yescharacteristic
subgroupG/H
center, socleC23×C127C24
commutatorC22C23×C4×C127
Frattini, cosocleC23C24×C127
prime radicalC22×D4×C127C22
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. #391×C127C2semidirect
3. #388×C127C2semidirect
5. #385×C127C2semidirect
6. #382×C127C2semidirect
10. #124×C127C4semidirect
25. C2×Q8×C127C2×C4semidirect
41. C22⋊C4×C127C2×C4semidirect
43. C42×C127C2×C4semidirect
89. #2379C127direct (N × H)
90. C127#2379direct (N × H)
92. #391C2×C127semidirect
93. #388C2×C127semidirect
95. #385C2×C127semidirect
96. #382C2×C127semidirect
100. #124C4×C127semidirect
115. C2×Q8C2×C4×C127semidirect
131. C22⋊C4C2×C4×C127semidirect
133. C42C2×C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#124×C1272
#391×C1272
#388×C1272
#386×C1272
#385×C1272
#382×C1272
#2379127