Finite Group Databasebeta

← #14564989

Subgroups — #14564989

Order 2432.

314 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 75 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#11927170C211yesmaximal, characteristic
2#11926419C212yesmaximal
3#11926416C211yesmaximal, characteristic
4#11926310C212yesmaximal
5C19×#342C211yesmaximal, characteristic
6C23×Dic19C2211yescharacteristic
7C2×C22⋊C4×C19C2211yescharacteristic
8C2×C22⋊C4×C19C2212yes—
9C2×C22⋊Dic19C2212yes—
10C2×C22⋊Dic19C2211yescharacteristic
11C2×C4⋊Dic19—22no—
12#10597370—21no—
13#10597370—21no—
14C2×Dic19⋊C4—21no—
15#10597324—22no—
16#10597324—22no—
17C19⋊#95—21no—
18C19⋊#95—22no—
19C24×C19C2311yescharacteristic
20C22×C4×C19—22no—
21C22×C4×C19D411yescharacteristic
22C22×C4×C19D411yescharacteristic
23C22×Dic19—21no—
24C22×Dic19—21no—
25C22×Dic19—22no—
26C22×Dic19—42no—
27C22×Dic19D412yes—
28C22×Dic19D412yes—
29C2×Dic38—21no—
30C2×Dic38—21no—
31C22⋊C4×C19—22no—
32C22⋊C4×C19—22no—
33C22⋊C4×C19Q814yescomplemented
34C22⋊Dic19—22no—
35C22⋊Dic19—22no—
36C22⋊Dic19—21no—
37C22⋊Dic19Q812yescomplemented
38C4⋊Dic19—21no—
39C4⋊Dic19—21no—
40C4⋊Dic19—44no—
41Dic19⋊C4—22no—
42Dic19⋊C4—22no—
43Dic19⋊C4—42no—
44C23×C19—41no—
45C23×C19—41no—
46C23×C19C2×D411yescharacteristic
47C23×C19C2×D412yes—
48C23×C19C2×Q812yes—
49C23×C19C2×Q811yescharacteristic
50C23×C19#4111yescharacteristic
51C2×C4×C19—21no—
52C2×C4×C19—21no—
53C2×C4×C19—24no—
54C2×C4×C19—42no—
55C2×C4×C19—42no—
56C2×C4×C19—41no—
57C2×C4×C19—41no—
58C2×Dic19—22no—
59C2×Dic19—24no—
60C2×Dic19—22no—
61C2×Dic19—22no—
62C2×Dic19—22no—
63C2×Dic19—41no—
64C2×Dic19—41no—
65C2×Dic19—41no—
66C2×Dic19—42no—
67C2×Dic19—41no—
68C2×Dic19—42no—
69C2×Dic19—42no—
70Dic38—81no—
71Dic38—81no—
72#2062—191nomaximal, Sylow
73C22×C19—21no—
74C22×C19—22no—
75C22×C19—21no—
76C22×C19—22no—
77C22×C19—42no—
78C22×C19—41no—
79C22×C19—41no—
80C22×C19#12011yescharacteristic
81C22×C19C22⋊Q812yes—
82C22×C19C22⋊Q811yescharacteristic
83C22×C19C4⋊Q811yescharacteristic
84C22×C19C4⋊Q812yes—
85C4×C19—44no—
86C4×C19—41no—
87C4×C19—41no—
88Dic19—42no—
89Dic19—42no—
90Dic19—42no—
91Dic19—42no—
92#543—191no—
93#385—191no—
94#385—192no—
95#342—192no—
96#342D1911yescharacteristic
97C2×C19—21no—
98C2×C19—22no—
99C2×C19—21no—
100C2×C19—22no—
101C2×C19#39511yescharacteristic
102C2×C19B(4,𝔽2)11yescharacteristic
103C2×C19#45811yescharacteristic
104C23×C4—191no—
105C22⋊Q8—382no—
106C22⋊Q8—382no—
107C22⋊Q8—381no—
108C22⋊Q8—381no—
109C2×C4⋊C4—382no—
110C2×C4⋊C4—381no—
111C2×C22⋊C4—191no—
112C2×C22⋊C4—192no—
113C2×C22⋊C4C2×D1911yescharacteristic
114C2×C22⋊C4C2×D1912yes—
115#95—382no—
116#95—381no—
117C19#206211yescharacteristic, complemented, Sylow
118C24C22×D1911yescharacteristic
119C2×Q8—381no—
120C2×Q8—381no—
121C22×C4—22no—
122C22×C4—192no—
123C22×C4—192no—
124C22×C4—381no—
125C22×C4—381no—
126C22×C4—382no—
127C22×C4—762no—
128C22×C4D7611yescharacteristic
129C22×C4D7611yescharacteristic
130C4⋊C4—382no—
131C4⋊C4—382no—
132C4⋊C4—381no—
133C4⋊C4—381no—
134C4⋊C4—762no—
135C4⋊C4—764no—
136C22⋊C4—22no—
137C22⋊C4—22no—
138C22⋊C4—192no—
139C22⋊C4—382no—
140C22⋊C4—382no—
141C22⋊C4—381no—
142C22⋊C4Dic3814yescomplemented
143C23—41no—
144C23—41no—
145C23C2×Dic3812yes—
146C23C2×D7611yescharacteristic
147C23D4×D1912yes—
148C23#6454311yescharacteristic
149C23Q8×D1911yescharacteristic
150Q8—1521no—
151Q8—1521no—
152C2×C4—24no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—42no—
156C2×C4—42no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—382no—
160C2×C4—384no—
161C2×C4—382no—
162C2×C4—382no—
163C2×C4—382no—
164C2×C4—761no—
165C2×C4—761no—
166C2×C4—762no—
167C2×C4—761no—
168C2×C4—761no—
169C2×C4—762no—
170C2×C4—762no—
171C22—21no—
172C22—22no—
173C22—21no—
174C22—22no—
175C22—42no—
176C22—41no—
177C22—41no—
178C22#1059731511yescharacteristic
179C22#1059732412yes—
180C22#1059732811yescharacteristic
181C22#1059733412yes—
182C22#1059734311yescharacteristic
183C4—44no—
184C4—41no—
185C4—41no—
186C4—762no—
187C4—762no—
188C4—762no—
189C4—762no—
190C2—22no—
191C2—21no—
192C2—21no—
193C2—22no—
194C2#1192646511yescharacteristic
195C2#1192673211yescharacteristic
196C2#1192673511yescharacteristic
subgroupG/H
centerC22#10597328
commutator, prime radical, cosocleC24×C19C23
FrattiniC24C22×D19
FittingC19×#342C2
socleC22×C19#120
hypercenter#342D19
hypocenterC19#2062
LCSG ▷ C24×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
33. C22⋊C4×C19Q8semidirect
37. C22⋊Dic19Q8semidirect
117. C19#2062semidirect
142. C22⋊C4Dic38semidirect

Maximal subgroups

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

subgroupindex
#119271702
#119264192
#119264162
#119263102
C19×#3422
#206219