Finite Group Databasebeta

← C127×#2634 #30635586

Subgroups — C127×#2634 #30635586

Order 16256.

416 conjugacy classes of subgroups; only the 192 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 192 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×#125×C127C211yesmaximal, characteristic
2C2×C4×Q8×C127C211yesmaximal, characteristic
3#400×C127C212yesmaximal
4#400×C127C212yesmaximal
5#398×C127C212yesmaximal
6#395×C127C212yesmaximal
7#387×C127C214yesmaximal
8#383×C127C211yesmaximal, characteristic
9C22×Q8×C127C2211yescharacteristic
10#125×C127—24no—
11C4×Q8×C127—24no—
12C2×C4⋊C4×C127C2212yes—
13C2×C4⋊C4×C127C2211yescharacteristic
14C2×C4⋊C4×C127C2212yes—
15C2×C4⋊C4×C127C2212yes—
16C2×C4⋊C4×C127C2211yescharacteristic
17C2×C4⋊C4×C127C2211yescharacteristic
18C2×C4⋊C4×C127C2214yes—
19C2×C42×C127C2212yes—
20C2×C42×C127C2211yescharacteristic
21#95×C127C2212yes—
22#95×C127C2212yes—
23#95×C127C2212yes—
24#95×C127C2214yes—
25#95×C127C2214yes—
26#95×C127C2214yes—
27C2×Q8×C127—22no—
28C2×Q8×C127—24no—
29C22×C4×C127C2314yes—
30C22×C4×C127C2312yes—
31C22×C4×C127C2312yes—
32C22×C4×C127C2312yes—
33C22×C4×C127C2311yescharacteristic
34C22×C4×C127C2311yescharacteristic
35C22×C4×C127C2311yescharacteristic
36C22×C4×C127C2312yes—
37C4⋊C4×C127—24no—
38C4⋊C4×C127—22no—
39C4⋊C4×C127—24no—
40C4⋊C4×C127—22no—
41C4⋊C4×C127—22no—
42C4⋊C4×C127—24no—
43C4⋊C4×C127—28no—
44C42×C127—24no—
45C42×C127D414yes—
46C23×C127C2411yescharacteristic
47Q8×C127—28no—
48C2×C4×C127—22no—
49C2×C4×C127—22no—
50C2×C4×C127—22no—
51C2×C4×C127—22no—
52C2×C4×C127—22no—
53C2×C4×C127—22no—
54C2×C4×C127—22no—
55C2×C4×C127—22no—
56C2×C4×C127—24no—
57C2×C4×C127—24no—
58C2×C4×C127—24no—
59C2×C4×C127—24no—
60C2×C4×C127—24no—
61C2×C4×C127—24no—
62C2×C4×C127C2×D412yes—
63C2×C4×C127C2×D412yes—
64C2×C4×C127C2×D412yes—
65C2×C4×C127#4114yes—
66C22×C127C22×D411yescharacteristic
67C22×C127C2×#4112yes—
68C22×C1272−1+412yes—
69C22×C1272−1+412yes—
70C4×C127—22no—
71C4×C127—24no—
72C4×C127—22no—
73C4×C127—22no—
74C4×C127—42no—
75C4×C127—42no—
76C4×C127—42no—
77C4×C127—44no—
78C2×C127#52511yescharacteristic
79C2×C127#53611yescharacteristic
80C2×C127#53611yescharacteristic
81C2×C127#54114yes—
82#2634C12711yesmaximal, characteristic, direct product factor, Sylow
83C127#263411yescharacteristic, direct product factor, Sylow
84C2×#125C2×C12711yescharacteristic
85C2×C4×Q8C2×C12711yescharacteristic
86#400C2×C12712yes—
87#400C2×C12712yes—
88#398C2×C12712yes—
89#395C2×C12712yes—
90#387C2×C12714yes—
91#383C2×C12711yescharacteristic
92C22×Q8C22×C12711yescharacteristic
93#125—24no—
94C4×Q8—24no—
95C2×C4⋊C4C22×C12712yes—
96C2×C4⋊C4C22×C12711yescharacteristic
97C2×C4⋊C4C22×C12712yes—
98C2×C4⋊C4C22×C12712yes—
99C2×C4⋊C4C22×C12711yescharacteristic
100C2×C4⋊C4C22×C12711yescharacteristic
101C2×C4⋊C4C22×C12714yes—
102C2×C42C22×C12712yes—
103C2×C42C22×C12711yescharacteristic
104#95C22×C12712yes—
105#95C22×C12712yes—
106#95C22×C12712yes—
107#95C22×C12714yes—
108#95C22×C12714yes—
109#95C22×C12714yes—
110C2×Q8—22no—
111C2×Q8—24no—
112C22×C4C23×C12714yes—
113C22×C4C23×C12712yes—
114C22×C4C23×C12712yes—
115C22×C4C23×C12712yes—
116C22×C4C23×C12711yescharacteristic
117C22×C4C23×C12711yescharacteristic
118C22×C4C23×C12711yescharacteristic
119C22×C4C23×C12712yes—
120C4⋊C4—24no—
121C4⋊C4—22no—
122C4⋊C4—24no—
123C4⋊C4—22no—
124C4⋊C4—22no—
125C4⋊C4—24no—
126C4⋊C4—28no—
127C42—24no—
128C42D4×C12714yes—
129C23C24×C12711yescharacteristic
130Q8—28no—
131C2×C4—22no—
132C2×C4—22no—
133C2×C4—22no—
134C2×C4—22no—
135C2×C4—22no—
136C2×C4—22no—
137C2×C4—22no—
138C2×C4—22no—
139C2×C4—24no—
140C2×C4—24no—
141C2×C4—24no—
142C2×C4—24no—
143C2×C4—24no—
144C2×C4—24no—
145C2×C4C2×D4×C12712yes—
146C2×C4C2×D4×C12712yes—
147C2×C4C2×D4×C12712yes—
148C2×C4#41×C12714yes—
149C22C22×D4×C12711yescharacteristic
150C22C2×#41×C12712yes—
151C222−1+4×C12712yes—
152C222−1+4×C12712yes—
153C4—22no—
154C4—24no—
155C4—22no—
156C4—22no—
157C4—42no—
158C4—42no—
159C4—42no—
160C4—44no—
161C2#525×C12711yescharacteristic
162C2#536×C12711yescharacteristic
163C2#536×C12711yescharacteristic
164C2#541×C12714yes—
subgroupG/H
center, socle, prime radicalC23×C127C24
commutator, Frattini, cosocleC23C24×C127
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C127 ◁ G

Complements

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

NH ≅ G/Ntype
82. #2634C127direct (N × H)
83. C127#2634direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#125×C1272
C2×C4×Q8×C1272
#400×C1272
#398×C1272
#395×C1272
#387×C1272
#383×C1272
#2634127