Finite Group Databasebeta

← C19⋊#7318 #18069841

Subgroups — C19⋊#7318 #18069841

Order 4864.

484 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 67 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#14563553C212yesmaximal
2C19×#1782C211yesmaximal, characteristic
3C2×#10597291—22no—
4C2×#10597291—22no—
5#11926407C414yescomplemented
6C22×#41×C19C2211yescharacteristic
7C2×C19×#99—22no—
8C19×#381C412yescomplemented
9C2×#41×C19—44no—
10C2×#41×C19—42no—
11C22×Q8×C19Q811yescharacteristic
12C22×D4×C19D411yescharacteristic
13C22×D4×C19D412yes—
14C23×C4×C19C2×C412yes—
15C23×C4×C19C2×C411yescharacteristic
16C2×C22⋊C4×C19—22no—
17C2×C22⋊Dic19—24no—
18C19×#99—44no—
19C19×#95—42no—
20#10597291—44no—
21#10597291—44no—
22C19⋊#95—44no—
23C24×C19C22⋊C412yes—
24C24×C19C22⋊C411yescharacteristic
25#41×C19—416no—
26C2×Q8×C19—42no—
27C2×Q8×C19—41no—
28C2×D4×C19—24no—
29C2×D4×C19—24no—
30C2×D4×C19—24no—
31C2×D4×C19—41no—
32C2×D4×C19—42no—
33C22×C4×C19—24no—
34C22×C4×C19—22no—
35C22×C4×C19—42no—
36C22×C4×C19—42no—
37C22×C4×C19—42no—
38C22×C4×C19—42no—
39C22×C4×C19C4211yescharacteristic
40C22×C4×C19C4⋊C412yes—
41C22×C4×C19C4⋊C411yescharacteristic
42C22×Dic19—44no—
43C22⋊C4×C19—44no—
44C22⋊Dic19—44no—
45C22⋊Dic19—44no—
46#7318—191nomaximal, Sylow
47C23×C19—22no—
48C23×C19—22no—
49C23×C19—22no—
50C23×C19—82no—
51C23×C19—81no—
52C23×C19#9511yescharacteristic
53C23×C19#9914yes—
54C23×C19#9912yes—
55Q8×C19—44no—
56D4×C19—44no—
57D4×C19—48no—
58C2×C4×C19—22no—
59C2×C4×C19—21no—
60C2×C4×C19—22no—
61C2×C4×C19—21no—
62C2×C4×C19—22no—
63C2×C4×C19—22no—
64C2×C4×C19—22no—
65C2×C4×C19—48no—
66C2×C4×C19—44no—
67C2×C4×C19—82no—
68C2×C4×C19—84no—
69C2×Dic19—84no—
70C2×Dic19—88no—
71#1782—192no—
72#1782D1911yescharacteristic
73C22×C19—24no—
74C22×C19—22no—
75C22×C19—41no—
76C22×C19—44no—
77C22×C19—42no—
78C22×C19—82no—
79C22×C19—82no—
80C22×C19—82no—
81C22×C19#34212yes—
82C22×C19#34211yescharacteristic
83C4×C19—41no—
84C4×C19—42no—
85C4×C19—41no—
86C4×C19—162no—
87Dic19—164no—
88C22×#41C2×D1911yescharacteristic
89C2×#99—22no—
90C2×#99—382no—
91C2×#99—382no—
92#381—194no—
93#381Dic1912yescomplemented
94C2×C19—22no—
95C2×C19—21no—
96C2×C19—44no—
97C2×C19—42no—
98C2×C19#130411yescharacteristic
99C2×#41—44no—
100C2×#41—42no—
101C22×Q8Dic3811yescharacteristic
102C22×D4D7611yescharacteristic
103C22×D4C22⋊D1912yes—
104C23×C4C4×D1912yes—
105C23×C4C2×Dic1911yescharacteristic
106C2×C22⋊C4—22no—
107C2×C22⋊C4—384no—
108#99—44no—
109#99—764no—
110#99—764no—
111#95—42no—
112#95—764no—
113C19#731811yescharacteristic, complemented, Sylow
114C24(C2×D19)⋊C412yes—
115C24C22⋊Dic1911yescharacteristic
116#41—416no—
117C2×Q8—42no—
118C2×Q8—41no—
119C2×D4—24no—
120C2×D4—24no—
121C2×D4—24no—
122C2×D4—41no—
123C2×D4—42no—
124C22×C4—24no—
125C22×C4—22no—
126C22×C4—42no—
127C22×C4—42no—
128C22×C4—42no—
129C22×C4—42no—
130C22×C4—764no—
131C22×C4C4×Dic1911yescharacteristic
132C22×C4Dic19⋊C412yes—
133C22×C4C4⋊Dic1911yescharacteristic
134C22⋊C4—44no—
135C22⋊C4—764no—
136C22⋊C4—764no—
137C23—22no—
138C23—22no—
139C23—22no—
140C23—82no—
141C23—81no—
142C23#1059726314yes—
143C23C19⋊#9511yescharacteristic
144C23#1059729112yes—
145Q8—44no—
146D4—48no—
147D4—44no—
148C2×C4—22no—
149C2×C4—22no—
150C2×C4—22no—
151C2×C4—22no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—22no—
155C2×C4—44no—
156C2×C4—48no—
157C2×C4—82no—
158C2×C4—84no—
159C2×C4—1524no—
160C2×C4—1528no—
161C22—22no—
162C22—24no—
163C22—41no—
164C22—42no—
165C22—44no—
166C22—82no—
167C22—82no—
168C22—82no—
169C22#1192631012yes—
170C22#1192631111yescharacteristic
171C4—41no—
172C4—42no—
173C4—41no—
174C4—162no—
175C4—3044no—
176C2—22no—
177C2—21no—
178C2—42no—
179C2—44no—
180C2C19⋊#130411yescharacteristic
subgroupG/H
centerC2C19⋊#1304
commutatorC22×C4×C19C42
FrattiniC22×#41C2×D19
FittingC19×#1782C2
socleC2×C19#1304
prime radical, cosocleC22×#41×C19C22
hypercenter#1782D19
hypocenterC19#7318
LCSG ▷ C22×C4×C19 ▷ C23×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C2 ◁ C23 ◁ C22×#41 ◁ #1782

Complements

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

NH ≅ G/Ntype
5. #11926407C4semidirect
8. C19×#381C4semidirect
93. #381Dic19semidirect
113. C19#7318semidirect

Maximal subgroups

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

subgroupindex
#145635532
C19×#17822
#731819