Finite Group Databasebeta

← #23752140

Subgroups — #23752140

Order 9664.

170 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 170 conjugacy classes of subgroups — too many to draw. Only its 57 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×Dic151⋊C4C211yesmaximal, characteristic, complemented
2C2×C22⋊Dic151C211yesmaximal, characteristic
3C2×C22⋊Dic151C211yesmaximal, characteristic
4C151⋊#95C211yesmaximal, characteristic, complemented
5C151⋊#95C211yesmaximal, characteristic, complemented
6C151⋊#95C211yesmaximal, characteristic, complemented
7C2×C22⋊C4×C151C211yesmaximal, characteristic
8C22×Dic151C2211yescharacteristic
9C22×Dic151C2211yescharacteristic
10C22×Dic151C2211yescharacteristic
11C22×Dic151C2211yescharacteristic
12Dic151⋊C4—22no—
13C22⋊Dic151—22no—
14C22⋊Dic151—22no—
15C24×C151C2211yescharacteristic
16C22×C4×C151C2211yescharacteristic
17C22×C4×C151C2211yescharacteristic
18C22⋊C4×C151—22no—
19C2×Dic151—21no—
20C2×Dic151—21no—
21C2×Dic151—21no—
22C2×Dic151—21no—
23C2×Dic151—21no—
24C2×Dic151—21no—
25C2×Dic151—21no—
26C2×Dic151—21no—
27C2×Dic151—21no—
28C2×Dic151—21no—
29C2×Dic151—21no—
30C2×Dic151D412yes—
31C23×C151—21no—
32C23×C151—21no—
33C23×C151—21no—
34C23×C151—21no—
35C23×C151—21no—
36C23×C151—21no—
37C23×C151D412yes—
38C23×C151C2311yescharacteristic
39C2×C4×C151—21no—
40C2×C4×C151—21no—
41C2×C4×C151—21no—
42C2×C4×C151—21no—
43C2×C4×C151—21no—
44C2×C4×C151—21no—
45C22×C151—22no—
46C22×C151—22no—
47C22×C151—22no—
48C22×C151—41no—
49C22×C151—41no—
50C22×C151—41no—
51C22×C151—41no—
52C22×C151C2×D411yescharacteristic
53C22×C151C2×D411yescharacteristic
54C22×C151#4111yescharacteristic
55C22×C151#4111yescharacteristic
56C22×C151#4111yescharacteristic
57C22×C151#4111yescharacteristic
58C22×C151#4111yescharacteristic
59C4×C151—41no—
60C4×C151—41no—
61Dic151—22no—
62Dic151—41no—
63Dic151—41no—
64Dic151—41no—
65C2×C151—42no—
66C2×C151#12111yescharacteristic
67C2×C151#12311yescharacteristic
68C2×C151#12311yescharacteristic
69C2×C151#12311yescharacteristic
70C2×C151#12411yescharacteristic
71C2×C151#12611yescharacteristic
72C2×C151#12611yescharacteristic
73C151#39711yescharacteristic, complemented, Sylow
74#397—1511nomaximal, Sylow
75C2×C4⋊C4—1511no—
76C2×C22⋊C4—1511no—
77C2×C22⋊C4—1511no—
78C2×C22⋊C4D15111yescharacteristic
79#95—1511no—
80#95—1511no—
81#95—1511no—
82C24C2×D15111yescharacteristic
83C22×C4—1511no—
84C22×C4—1511no—
85C22×C4—1511no—
86C22×C4—1511no—
87C22×C4C2×D15111yescharacteristic
88C22×C4C2×D15111yescharacteristic
89C4⋊C4—3022no—
90C22⋊C4—22no—
91C22⋊C4—3022no—
92C22⋊C4—3022no—
93C23—21no—
94C23—21no—
95C23—21no—
96C23—21no—
97C23—21no—
98C23—21no—
99C23C22⋊D15112yes—
100C23C22×D15111yescharacteristic
101C2×C4—21no—
102C2×C4—21no—
103C2×C4—21no—
104C2×C4—21no—
105C2×C4—21no—
106C2×C4—21no—
107C2×C4—3021no—
108C2×C4—3021no—
109C2×C4—3021no—
110C2×C4—3021no—
111C2×C4—3021no—
112C2×C4—3021no—
113C2×C4—3021no—
114C2×C4—3021no—
115C2×C4—3021no—
116C2×C4—3021no—
117C2×C4—3021no—
118C2×C4—1512no—
119C22—22no—
120C22—22no—
121C22—22no—
122C22—41no—
123C22—41no—
124C22—41no—
125C22—41no—
126C22D4×D15111yescharacteristic
127C22C2×C22⋊D15111yescharacteristic
128C22#1455900311yescharacteristic
129C22#1455900311yescharacteristic
130C22#1455900311yescharacteristic
131C22#1455900411yescharacteristic
132C22#1455900411yescharacteristic
133C4—41no—
134C4—41no—
135C4—3022no—
136C4—6041no—
137C4—6041no—
138C4—6041no—
139C2—42no—
140C2#1801271111yescharacteristic
141C2#1801272011yescharacteristic
142C2#1801272111yescharacteristic
143C2#1801272211yescharacteristic
144C2#1801272511yescharacteristic
145C2#1801273211yescharacteristic
146C2#1801273211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D151
commutator, socle, cosocleC23×C151C23
FittingC2×C22⋊C4×C151C2
prime radicalC24×C151C22
hypercenterC2×C22⋊C4D151
hypocenterC151#397
LCSG ▷ C23×C151 ▷ C151
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×Dic151⋊C4C2semidirect
4. C151⋊#95C2semidirect
5. C151⋊#95C2semidirect
6. C151⋊#95C2semidirect
73. C151#397semidirect