Finite Group Databasebeta

← #30636852

Subgroups — #30636852

Order 16256.

158 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 53 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#22549860C211yesmaximal, characteristic
2#22549843C211yesmaximal, characteristic
3#413×C127C211yesmaximal, characteristic
4C2×#14523232—21no—
5C2×#14523232C411yescharacteristic
6C22×C127⋊C8C411yescharacteristic
7#16861128—21no—
8#16861126C412yes—
9C22⋊(C127⋊C8)—21no—
10C22⋊(C127⋊C8)—21no—
11C2×#41×C127C2211yescharacteristic
12C2×M16×C127—21no—
13#101×C127—21no—
14#100×C127C412yes—
15#14523232—22no—
16#14523232—41no—
17#14523232—41no—
18C2×C127⋊C8—21no—
19C2×C127⋊C8—21no—
20C2×C127⋊C8—41no—
21C2×C127⋊C8—41no—
22#41×C127—41no—
23#41×C127—41no—
24C2×Q8×C127D411yescharacteristic
25C2×D4×C127C2×C411yescharacteristic
26C2×D4×C127C2×C411yescharacteristic
27C2×D4×C127Q811yescharacteristic
28C22×C4×C127C2×C411yescharacteristic
29C22×C4×C127D411yescharacteristic
30C22×C4×C127D411yescharacteristic
31M16×C127—22no—
32M16×C127—41no—
33C2×C8×C127—41no—
34C127⋊C8—42no—
35C127⋊C8—41no—
36C127⋊C8—41no—
37C23×C127C4211yescharacteristic
38C23×C127C4⋊C411yescharacteristic
39C23×C127C4⋊C411yescharacteristic
40Q8×C127—41no—
41D4×C127—41no—
42D4×C127—41no—
43D4×C127—41no—
44C2×C4×C127—21no—
45C2×C4×C127—21no—
46C2×C4×C127—21no—
47C2×C4×C127—21no—
48C2×C4×C127—21no—
49C2×C4×C127—21no—
50C2×C4×C127C22⋊C411yescharacteristic
51C2×C4×C127C22⋊C411yescharacteristic
52C2×C4×C127C22⋊C411yescharacteristic
53C2×C4×C127C4⋊C411yescharacteristic
54C8×C127—42no—
55C22×C127—21no—
56C22×C127—21no—
57C22×C127—21no—
58C22×C127—41no—
59C22×C127—41no—
60C22×C127—41no—
61C22×C127#9511yescharacteristic
62C4×C127—21no—
63C4×C127—21no—
64C4×C127—21no—
65C4×C127#9911yescharacteristic
66C4×C127#9911yescharacteristic
67C2×C127—21no—
68C2×C127—41no—
69C2×C127—41no—
70C2×C127—41no—
71C2×C127#34211yescharacteristic
72#1392—1271nomaximal, Sylow
73C127#139211yescharacteristic, complemented, Sylow
74#413—1271no—
75#413D12711yescharacteristic
76#408—1271no—
77C2×#41C2×D12711yescharacteristic
78C2×M16—21no—
79C2×M16—1271no—
80C2×M16—2541no—
81C22×C8—1271no—
82#101—21no—
83#101—2541no—
84#100—1272no—
85#100Dic12712yes—
86C22⋊C8—2541no—
87C22⋊C8—2541no—
88#41—41no—
89#41—41no—
90C2×Q8C22⋊D12711yescharacteristic
91C2×D4C4×D12711yescharacteristic
92C2×D4C2×Dic12711yescharacteristic
93C2×D4Dic25411yescharacteristic
94C22×C4C4×D12711yescharacteristic
95C22×C4C22⋊D12711yescharacteristic
96C22×C4D50811yescharacteristic
97M16—22no—
98M16—41no—
99M16—5081no—
100M16—5081no—
101M16—2542no—
102C2×C8—41no—
103C2×C8—5081no—
104C2×C8—5081no—
105C2×C8—2541no—
106C2×C8—2541no—
107C23C4×Dic12711yescharacteristic
108C23Dic127⋊C411yescharacteristic
109C23C4⋊Dic12711yescharacteristic
110Q8—41no—
111D4—41no—
112D4—41no—
113D4—41no—
114C2×C4—21no—
115C2×C4—21no—
116C2×C4—21no—
117C2×C4—21no—
118C2×C4—21no—
119C2×C4—21no—
120C2×C4(C2×D127)⋊C411yescharacteristic
121C2×C4(C2×D127)⋊C411yescharacteristic
122C2×C4C22⋊Dic12711yescharacteristic
123C2×C4Dic127⋊C411yescharacteristic
124C8—42no—
125C8—5082no—
126C8—5081no—
127C8—5081no—
128C22—21no—
129C22—21no—
130C22—21no—
131C22—41no—
132C22—41no—
133C22—41no—
134C22C127⋊#9511yescharacteristic
135C4—21no—
136C4—21no—
137C4—21no—
138C4#1686112311yescharacteristic
139C4#1686112311yescharacteristic
140C2—21no—
141C2—41no—
142C2—41no—
143C2—41no—
144C2#2254964211yescharacteristic
subgroupG/H
centerC4#16861123
commutatorC23×C127C42
FrattiniC2×#41C2×D127
Fitting#413×C127C2
socleC2×C127#342
prime radical, cosocleC2×#41×C127C22
hypercenter#413D127
hypocenterC127#1392
LCSG ▷ C23×C127 ▷ C22×C127 ▷ C2×C127 ▷ C127
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #413

Complements

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

NH ≅ G/Ntype
73. C127#1392semidirect

Maximal subgroups

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

subgroupindex
#225498602
#225498432
#413×C1272
#1392127