Finite Group Databasebeta

← #18070377

Subgroups — #18070377

Order 4864.

142 conjugacy classes of subgroups; only the 25 normal subgroups are shown.

normal subgroups only

This group has 142 conjugacy classes of subgroups — too many to draw. Only its 25 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#14562773C211yesmaximal, characteristic
2#14561804C211yesmaximal, characteristic
3C19×#1358C211yesmaximal, characteristic
4#11927274C411yescharacteristic
5#11926836—21no—
6#11926343—21no—
7#11926293C411yescharacteristic
8#11926276—21no—
9C19×#494C2211yescharacteristic
10C19×#364—21no—
11C2×Q16×C19—41no—
12C19×C4⋊Q8C2×C411yescharacteristic
13C19×C4⋊Q8D411yescharacteristic
14#10597390—41no—
15#10597334—41no—
16#10597333—41no—
17C4×Dic38—21no—
18C19×M32—41no—
19C4×C8×C19D411yescharacteristic
20#10597293—41no—
21#10597267—41no—
22#10597264—41no—
23C4⋊(C19⋊C8)—21no—
24C2×Q8×C19—21no—
25C2×Q8×C19—21no—
26C2×Dic38—21no—
27C2×Dic38—41no—
28Q16×C19—81no—
29Q16×C19—81no—
30C2×C8×C19—21no—
31C4⋊C4×C19—41no—
32C4⋊C4×C19—41no—
33C42×C19C22⋊C411yescharacteristic
34C4⋊Dic19—21no—
35Dic19⋊C4—42no—
36Dic19⋊C4—41no—
37C4×Dic19—41no—
38C4×Dic19—41no—
39#64520—81no—
40C2×C19⋊C8—41no—
41C16×C19—81no—
42#7522—191nomaximal, Sylow
43Q8×C19—81no—
44Q8×C19—81no—
45C2×C4×C19—21no—
46C2×C4×C19—41no—
47C2×C4×C19—41no—
48C2×C4×C19#9911yescharacteristic
49C2×Dic19—41no—
50C2×Dic19—41no—
51Dic38—22no—
52Dic38—41no—
53Dic38—161no—
54C8×C19—21no—
55C8×C19—21no—
56C19⋊C8—81no—
57C19⋊C8—161no—
58#1633—191no—
59#1411—191no—
60#1358D1911yescharacteristic
61C22×C19AΣL(1,𝔽16)11yescharacteristic
62C4×C19—21no—
63C4×C19—21no—
64C4×C19—21no—
65C4×C19—81no—
66C4×C19—81no—
67Dic19—42no—
68Dic19—81no—
69Q82—191no—
70#494C2×D1911yescharacteristic
71#477—381no—
72#364—21no—
73#356—381no—
74#333—191no—
75Q8⋊C8—381no—
76C2×C19—21no—
77C2×C19#140211yescharacteristic
78C2×Q16—41no—
79C4⋊Q8—761no—
80C4⋊Q8—761no—
81C4⋊Q8C4×D1911yescharacteristic
82C4⋊Q8D7611yescharacteristic
83C4×Q8—381no—
84C4×Q8—761no—
85M32—41no—
86#107—761no—
87C4⋊C8—381no—
88#103—761no—
89#101—761no—
90C4×C8C22⋊D1911yescharacteristic
91C19#752211yescharacteristic, complemented, Sylow
92C2×Q8—21no—
93C2×Q8—21no—
94C2×Q8—381no—
95C2×Q8—761no—
96Q16—81no—
97Q16—81no—
98M16—1521no—
99C2×C8—21no—
100C2×C8—761no—
101C4⋊C4—41no—
102C4⋊C4—41no—
103C4⋊C4—381no—
104C4⋊C4—762no—
105C4⋊C4—761no—
106C42—761no—
107C42—761no—
108C42(C2×D19)⋊C411yescharacteristic
109C16—81no—
110Q8—81no—
111Q8—81no—
112Q8—382no—
113Q8—3041no—
114Q8—761no—
115C2×C4—21no—
116C2×C4—41no—
117C2×C4—41no—
118C2×C4—761no—
119C2×C4—761no—
120C2×C4#1059726311yescharacteristic
121C8—21no—
122C8—21no—
123C8—3041no—
124C8—1521no—
125C22#1192633211yescharacteristic
126C4—21no—
127C4—21no—
128C4—21no—
129C4—81no—
130C4—81no—
131C4—762no—
132C4—1521no—
133C2—21no—
134C2#1456178111yescharacteristic
subgroupG/H
centerC2#14561781
commutatorC19×C4⋊Q8C2×C4
Frattini#494C2×D19
FittingC19×#1358C2
socleC2×C19#1402
prime radicalC22×C19AΣL(1,𝔽16)
cosocleC19×#494C22
hypercenter#1358D19
hypocenterC19#7522
LCSG ▷ C19×C4⋊Q8 ▷ C42×C19 ▷ C2×C4×C19 ▷ C22×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ #494 ◁ #1358

Complements

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

NH ≅ G/Ntype
91. C19#7522semidirect

Maximal subgroups

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

subgroupindex
#145627732
#145618042
C19×#13582
#752219