Finite Group Databasebeta

← #34070802

Subgroups — #34070802

Order 19328.

262 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 73 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#23752196C212yesmaximal, complemented
2#23752009C214yesmaximal, complemented
3#535×C151C211yesmaximal, characteristic
4C2×#14558988—22no—
5#18012658C2214yescomplemented
6#18012656—22no—
7C2×#41×C151C2211yescharacteristic
8C22×D4×C151C411yescharacteristic
9#127×C151C412yes—
10#124×C151C2212yes—
11#121×C151—22no—
12#120×C151—22no—
13#117×C151C411yescharacteristic
14#14558988—24no—
15#14558988—42no—
16C2×C151⋊C8—42no—
17C24×C151—21no—
18#41×C151—42no—
19C2×Q8×C151C2311yescharacteristic
20C2×D4×C151—24no—
21C2×D4×C151—21no—
22C2×D4×C151—42no—
23C2×D4×C151C2×C412yes—
24C2×D4×C151C2×C411yescharacteristic
25C2×D4×C151D412yes—
26C22×C4×C151C2×C411yescharacteristic
27C22×C4×C151D412yes—
28C4⋊C4×C151—21no—
29C22⋊C4×C151—21no—
30C22⋊C4×C151—24no—
31C42×C151C2×C412yes—
32C151⋊C8—44no—
33C23×C151—22no—
34C23×C151—42no—
35C23×C151—82no—
36C23×C151C22⋊C411yescharacteristic
37C23×C151C22⋊C412yes—
38Q8×C151—41no—
39D4×C151—41no—
40D4×C151—42no—
41D4×C151—42no—
42D4×C151—42no—
43D4×C151—84no—
44C2×C4×C151—22no—
45C2×C4×C151—22no—
46C2×C4×C151—22no—
47C2×C4×C151—22no—
48C2×C4×C151C22⋊C411yescharacteristic
49C2×C4×C151C22×C411yescharacteristic
50C2×C4×C151C2×D412yes—
51C22×C151—21no—
52C22×C151—22no—
53C22×C151—42no—
54C22×C151—41no—
55C22×C151—44no—
56C22×C151—42no—
57C22×C151—84no—
58C22×C151C2×C22⋊C411yescharacteristic
59C4×C151—21no—
60C4×C151—22no—
61C4×C151—42no—
62C4×C151#9912yes—
63C2×C151—21no—
64C2×C151—42no—
65C2×C151—41no—
66C2×C151—82no—
67C2×C151C2×#9911yescharacteristic
68C151#213411yescharacteristic, complemented, Sylow
69#2134—1511nomaximal, Sylow
70#535D15111yescharacteristic
71#413—1512no—
72#355—1514no—
73C2×#41C2×D15111yescharacteristic
74C22×D4Dic15111yescharacteristic
75C2×M16—3022no—
76#127Dic15112yes—
77#124C2×D15112yes—
78#121—22no—
79#120—22no—
80#117Dic15111yescharacteristic
81#101—1514no—
82#100—3022no—
83C24—21no—
84#41—42no—
85C2×Q8C22×D15111yescharacteristic
86C2×D4—24no—
87C2×D4—21no—
88C2×D4—42no—
89C2×D4C2×Dic15112yes—
90C2×D4C2×Dic15111yescharacteristic
91C2×D4C22⋊D15112yes—
92C22×C4C2×Dic15111yescharacteristic
93C22×C4C22⋊D15112yes—
94M16—3024no—
95M16—6042no—
96C2×C8—6042no—
97C4⋊C4—21no—
98C22⋊C4—21no—
99C22⋊C4—24no—
100C42C2×Dic15112yes—
101C23—22no—
102C23—42no—
103C23—82no—
104C23C22⋊Dic15111yescharacteristic
105C23C22⋊Dic15112yes—
106Q8—41no—
107D4—41no—
108D4—42no—
109D4—42no—
110D4—42no—
111D4—84no—
112C2×C4—22no—
113C2×C4—22no—
114C2×C4—22no—
115C2×C4—22no—
116C2×C4C22⋊Dic15111yescharacteristic
117C2×C4C22×Dic15111yescharacteristic
118C2×C4C2×C22⋊D15112yes—
119C8—6044no—
120C22—21no—
121C22—22no—
122C22—42no—
123C22—41no—
124C22—44no—
125C22—42no—
126C22—84no—
127C22C2×C22⋊Dic15111yescharacteristic
128C4—22no—
129C4—21no—
130C4—42no—
131C4#1801265412yes—
132C2—21no—
133C2—41no—
134C2—42no—
135C2—82no—
136C2C2×#1801265411yescharacteristic
subgroupG/H
centerC2C2×#18012654
commutatorC2×C4×C151C22×C4
FrattiniC2×Q8C22×D151
Fitting, prime radical#535×C151C2
socleC2×C151C2×#99
cosocleC2×Q8×C151C23
hypercenter#535D151
hypocenterC151#2134
LCSG ▷ C2×C4×C151 ▷ C22×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #535

Complements

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

NH ≅ G/Ntype
1. #23752196C2semidirect
2. #23752009C2semidirect
5. #18012658C22semidirect
68. C151#2134semidirect

Maximal subgroups

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

subgroupindex
#237521962
#237520092
#535×C1512
#2134151