Finite Group Databasebeta

← #34067735

Subgroups — #34067735

Order 19328.

196 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 59 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#125×D151C211yesmaximal, characteristic
2#23752267C212yesmaximal
3#23751954C211yesmaximal, characteristic, complemented
4#23751953C212yesmaximal, complemented
5#330×C151C211yesmaximal, characteristic, complemented
6#18012731C2211yescharacteristic
7#18012730C412yes—
8#18012729—22no—
9C4⋊C4×D151—22no—
10C4⋊C4×D151C412yes—
11C42×D151C2211yescharacteristic
12Dic151⋊C8—22no—
13(C2×D151)⋊C8—22no—
14#18012650C2212yes—
15#125×C151C2211yescharacteristic
16#97×C151C2212yes—
17C2×C4×D151—22no—
18C2×C4×D151C2×C411yescharacteristic
19C2×C4×D151D412yes—
20C2×C151⋊C8—22no—
21C4⋊Dic151—22no—
22C4⋊Dic151C2×C412yes—
23Dic151⋊C4—22no—
24Dic151⋊C4—22no—
25Dic151⋊C4—22no—
26C4×Dic151C2×C411yescharacteristic
27C4×Dic151D412yes—
28C2×C8×C151—22no—
29C4⋊C4×C151—22no—
30C4⋊C4×C151C2×C412yes—
31C42×C151C2311yescharacteristic
32C22×D151C22⋊C411yescharacteristic
33C2×Dic151—22no—
34C2×Dic151C22⋊C412yes—
35C2×Dic151C22⋊C411yescharacteristic
36C4×D151—22no—
37C4×D151—42no—
38C4×D151—44no—
39C151⋊C8—42no—
40C2×C4×C151—22no—
41C2×C4×C151C22×C411yescharacteristic
42C2×C4×C151C2×D412yes—
43C8×C151—42no—
44C22×C151C2×C22⋊C411yescharacteristic
45C2×D151—22no—
46C2×D151#10112yes—
47C4×C151—21no—
48C4×C151—22no—
49C4×C151—42no—
50Dic151—21no—
51Dic151—22no—
52Dic151—42no—
53C2×C151C2×#10111yescharacteristic
54C2×C151#42112yes—
55D151—22no—
56C151#153411yescharacteristic, complemented, Sylow
57#1534—1511nomaximal, Sylow
58C2×#125—1511no—
59#432—1512no—
60#330—1511no—
61#330—1512no—
62#330D15111yescharacteristic, complemented
63#125—3022no—
64#125—1512no—
65#125—1511no—
66#125C2×D15111yescharacteristic
67C2×C4⋊C4—3022no—
68C2×C4⋊C4—1512no—
69C2×C42—1511no—
70C4⋊C8—3022no—
71C22⋊C8—3022no—
72#97—1512no—
73#97C2×D15112yes—
74C22×C4—3022no—
75C22×C4—1511no—
76C22×C4—1512no—
77C2×C8—22no—
78C2×C8—3022no—
79C4⋊C4—22no—
80C4⋊C4—3022no—
81C4⋊C4—3022no—
82C4⋊C4—3022no—
83C4⋊C4—3022no—
84C4⋊C4—1512no—
85C4⋊C4C4×D15112yes—
86C42—1511no—
87C42—1512no—
88C42C22×D15111yescharacteristic
89C23—1511no—
90C2×C4—22no—
91C2×C4—3022no—
92C2×C4—3022no—
93C2×C4—6042no—
94C2×C4—6044no—
95C2×C4—1512no—
96C2×C4—1511no—
97C2×C4C2×C4×D15111yescharacteristic
98C2×C4D4×D15112yes—
99C8—42no—
100C8—6042no—
101C22—3022no—
102C22—1512no—
103C22C22⋊C4×D15111yescharacteristic
104C4—22no—
105C4—21no—
106C4—42no—
107C4—3022no—
108C4—3021no—
109C4—6042no—
110C2—3022no—
111C2#101×D15111yescharacteristic
112C2#2375222712yes—
subgroupG/H
centerC22C22⋊C4×D151
commutatorC2×C4×C151C22×C4
FrattiniC42C22×D151
Fitting#330×C151C2
socleC22×C151C2×C22⋊C4
prime radicalC22×D151C22⋊C4
cosocleC42×C151C23
hypercenter#330D151
hypocenterC151#1534
LCSG ▷ C2×C4×C151 ▷ C22×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
3. #23751954C2semidirect
4. #23751953C2semidirect
5. #330×C151C2semidirect
56. C151#1534semidirect
62. #330D151semidirect

Maximal subgroups

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

subgroupindex
#125×D1512
#237522672
#237519542
#237519532
#330×C1512
#1534151