Finite Group Databasebeta

← #30636616

Subgroups — #30636616

Order 16256.

246 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 65 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#22549840C211yesmaximal, characteristic
2C4×C22⋊Dic127C211yesmaximal, characteristic
3C4×C22⋊C4×C127C211yesmaximal, characteristic
4C2×#14523232C412yescomplemented
5C2×C22⋊Dic127—21no—
6C2×C4×Dic127—21no—
7C22⋊(C127⋊C8)—21no—
8C22⋊(C127⋊C8)—21no—
9C127⋊#95C412yescomplemented
10C23×C4×C127C2211yescharacteristic
11C2×C22⋊C4×C127—21no—
12C2×C42×C127—21no—
13#95×C127C412yescomplemented
14C22×Dic127—22no—
15#14523232—42no—
16C2×C127⋊C8—22no—
17C22⋊Dic127—24no—
18C4×Dic127—42no—
19C24×C127D411yescharacteristic
20C22×C4×C127—22no—
21C22×C4×C127—42no—
22C22×C4×C127C2×C411yescharacteristic
23C22×C4×C127C2×C411yescharacteristic
24C22×C4×C127C2×C411yescharacteristic
25C22×C4×C127D411yescharacteristic
26C22×C4×C127D411yescharacteristic
27C22×C4×C127Q811yescharacteristic
28C22⋊C4×C127—24no—
29C42×C127—42no—
30C2×Dic127—24no—
31C2×Dic127—42no—
32C2×Dic127—42no—
33C127⋊C8—42no—
34C23×C127—22no—
35C23×C127—22no—
36C23×C127—41no—
37C23×C127C22⋊C411yescharacteristic
38C23×C127C22⋊C411yescharacteristic
39C23×C127C4⋊C411yescharacteristic
40C2×C4×C127—22no—
41C2×C4×C127—22no—
42C2×C4×C127—22no—
43C2×C4×C127—24no—
44C2×C4×C127—41no—
45C2×C4×C127—41no—
46C2×C4×C127—41no—
47C2×C4×C127—42no—
48C2×C4×C127—42no—
49C2×C4×C127C4211yescharacteristic
50C2×C4×C127C22⋊C411yescharacteristic
51C2×C4×C127C4⋊C411yescharacteristic
52C2×C4×C127C4⋊C411yescharacteristic
53C22×C127—21no—
54C22×C127—21no—
55C22×C127—21no—
56C22×C127—21no—
57C22×C127—21no—
58C22×C127—21no—
59C22×C127—21no—
60C22×C127—44no—
61C22×C127#9511yescharacteristic
62C22×C127#10412yes—
63C22×C127#10412yes—
64C4×C127—21no—
65C4×C127—21no—
66C4×C127—21no—
67C4×C127—44no—
68C4×C127#9912yes—
69Dic127—44no—
70C2×C127—22no—
71C2×C127—22no—
72C2×C127—41no—
73C2×C127#33911yescharacteristic
74C2×C127#33911yescharacteristic
75C2×C127#34211yescharacteristic
76#1297—1271nomaximal, Sylow
77C127#129711yescharacteristic, complemented, Sylow
78#407—1271no—
79C4×C22⋊C4—1271no—
80C4×C22⋊C4D12711yescharacteristic
81C23×C4C2×D12711yescharacteristic
82C2×M16—1272no—
83C2×C22⋊C4—21no—
84C2×C22⋊C4—2541no—
85C2×C42—21no—
86C2×C42—2541no—
87C22⋊C8—2541no—
88C22⋊C8—2541no—
89#95—1272no—
90#95Dic12712yescomplemented
91C24C22⋊D12711yescharacteristic
92C22×C4—22no—
93C22×C4—42no—
94C22×C4—2542no—
95C22×C4C4×D12711yescharacteristic
96C22×C4C4×D12711yescharacteristic
97C22×C4C2×Dic12711yescharacteristic
98C22×C4C22⋊D12711yescharacteristic
99C22×C4D50811yescharacteristic
100C22×C4Dic25411yescharacteristic
101M16—5082no—
102C2×C8—2542no—
103C22⋊C4—24no—
104C22⋊C4—2544no—
105C42—42no—
106C42—5082no—
107C23—22no—
108C23—22no—
109C23—41no—
110C23(C2×D127)⋊C411yescharacteristic
111C23C22⋊Dic12711yescharacteristic
112C23Dic127⋊C411yescharacteristic
113C2×C4—22no—
114C2×C4—22no—
115C2×C4—22no—
116C2×C4—24no—
117C2×C4—41no—
118C2×C4—41no—
119C2×C4—41no—
120C2×C4—42no—
121C2×C4—42no—
122C2×C4—5082no—
123C2×C4—5082no—
124C2×C4—2544no—
125C2×C4C4×Dic12711yescharacteristic
126C2×C4(C2×D127)⋊C411yescharacteristic
127C2×C4Dic127⋊C411yescharacteristic
128C2×C4C4⋊Dic12711yescharacteristic
129C8—5082no—
130C22—21no—
131C22—21no—
132C22—21no—
133C22—21no—
134C22—21no—
135C22—21no—
136C22—21no—
137C22—44no—
138C22C127⋊#9511yescharacteristic
139C22#1686113612yes—
140C22#1686113712yes—
141C4—21no—
142C4—21no—
143C4—21no—
144C4—44no—
145C4—5084no—
146C4#1686112312yes—
147C2—22no—
148C2—22no—
149C2—41no—
150C2#2254963511yescharacteristic
151C2#2254963611yescharacteristic
152C2#2254964211yescharacteristic
subgroupG/H
centerC2×C4(C2×D127)⋊C4
commutatorC2×C4×C127C42
FrattiniC23×C4C2×D127
FittingC4×C22⋊C4×C127C2
socleC22×C127#95
prime radicalC24×C127D4
cosocleC23×C4×C127C22
hypercenterC4×C22⋊C4D127
hypocenterC127#1297
LCSG ▷ C2×C4×C127 ▷ C22×C127 ▷ C127
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
4. C2×#14523232C4semidirect
9. C127⋊#95C4semidirect
13. #95×C127C4semidirect
77. C127#1297semidirect
90. #95Dic127semidirect

Maximal subgroups

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

subgroupindex
#225498402
C4×C22⋊Dic1272
C4×C22⋊C4×C1272
#1297127