Finite Group Databasebeta

← #14562644

Subgroups — #14562644

Order 2432.

210 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 51 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#11927173C211yesmaximal, characteristic
2#11926875C211yesmaximal, characteristic
3#11926872C211yesmaximal, characteristic
4#11926476C211yesmaximal, characteristic
5#11926280C211yesmaximal, characteristic
6#11926269C211yesmaximal, characteristic
7C19×#328C211yesmaximal, characteristic
8C19×C22⋊Q8C2211yescharacteristic
9#10597390—21no—
10C2×C4⋊Dic19—21no—
11C2×C4⋊Dic19C2211yescharacteristic
12#10597370C2211yescharacteristic
13C2×Dic19⋊C4C2211yescharacteristic
14#10597335—21no—
15#10597335—21no—
16#10597334—21no—
17#10597324—21no—
18#10597323—21no—
19C19×C22⋊C8C2211yescharacteristic
20C19×#95C2211yescharacteristic
21#10597292—21no—
22C19⋊#95—21no—
23C22⋊(C19⋊C8)C2211yescharacteristic
24#10597274—21no—
25#10597273—21no—
26#10597265—21no—
27C2×Q8×C19D411yescharacteristic
28C22×C4×C19—21no—
29C22×C4×C19C2311yescharacteristic
30C22×Dic19—21no—
31C22×Dic19D411yescharacteristic
32C22×Dic19D411yescharacteristic
33C2×Dic38—21no—
34C2×Dic38D411yescharacteristic
35C2×C8×C19—21no—
36C4⋊C4×C19—21no—
37C4⋊C4×C19D411yescharacteristic
38C22⋊C4×C19—21no—
39C22⋊Dic19—21no—
40C4⋊Dic19—21no—
41C4⋊Dic19—21no—
42C4⋊Dic19—21no—
43C4⋊Dic19—42no—
44C4⋊Dic19D411yescharacteristic
45Dic19⋊C4—21no—
46Dic19⋊C4—21no—
47Dic19⋊C4—21no—
48Dic19⋊C4—21no—
49Dic19⋊C4—21no—
50Dic19⋊C4—21no—
51Dic19⋊C4—21no—
52C4×Dic19—21no—
53C4×Dic19—21no—
54C2×C19⋊C8—21no—
55C23×C19C2×D411yescharacteristic
56Q8×C19—41no—
57C2×C4×C19—22no—
58C2×C4×C19—21no—
59C2×C4×C19—21no—
60C2×C4×C19—41no—
61C2×C4×C19—41no—
62C2×C4×C19—41no—
63C2×C4×C19C2×D411yescharacteristic
64C2×C4×C19C2×D411yescharacteristic
65C2×Dic19—21no—
66C2×Dic19—21no—
67C2×Dic19—21no—
68C2×Dic19—21no—
69C2×Dic19—21no—
70C2×Dic19—41no—
71C2×Dic19—41no—
72C2×Dic19—41no—
73C2×Dic19—41no—
74C2×Dic19SD1612yes—
75Dic38—41no—
76Dic38—81no—
77C8×C19—41no—
78C19⋊C8—41no—
79#1611—191nomaximal, Sylow
80C22×C19—21no—
81C22×C19—21no—
82C22×C19#12011yescharacteristic
83C22×C19C2×SD1611yescharacteristic
84C22×C19#13711yescharacteristic
85C4×C19—21no—
86C4×C19—21no—
87C4×C19—42no—
88C4×C19—41no—
89C4×C19—41no—
90Dic19—22no—
91Dic19—41no—
92Dic19—41no—
93Dic19—41no—
94Dic19—81no—
95#544—191no—
96#483—191no—
97#483—191no—
98#398—191no—
99#328—191no—
100#328D1911yescharacteristic
101#324—191no—
102C2×C19—21no—
103C2×C19—21no—
104C2×C19#44811yescharacteristic
105C2×C19#45611yescharacteristic
106C2×C19#45811yescharacteristic
107C4⋊Q8—381no—
108C4⋊Q8—381no—
109#125—381no—
110#125—381no—
111C22⋊Q8—191no—
112C22⋊Q8—381no—
113C22⋊Q8C2×D1911yescharacteristic
114#117—381no—
115C2×C4⋊C4—191no—
116C2×C4⋊C4—191no—
117C2×C4⋊C4—381no—
118#106—381no—
119#106—381no—
120#103—381no—
121#103—381no—
122C22⋊C8—191no—
123C22⋊C8C2×D1911yescharacteristic
124#95—381no—
125#95C2×D1911yescharacteristic
126C19#161111yescharacteristic, complemented, Sylow
127C2×Q8—191no—
128C2×Q8—381no—
129C2×Q8D7611yescharacteristic
130C22×C4—21no—
131C22×C4—191no—
132C22×C4—191no—
133C22×C4—381no—
134C22×C4C22×D1911yescharacteristic
135C2×C8—21no—
136C2×C8—381no—
137C4⋊C4—21no—
138C4⋊C4—191no—
139C4⋊C4—381no—
140C4⋊C4—381no—
141C4⋊C4—381no—
142C4⋊C4—381no—
143C4⋊C4—381no—
144C4⋊C4—381no—
145C4⋊C4—381no—
146C4⋊C4—381no—
147C4⋊C4—381no—
148C4⋊C4—381no—
149C4⋊C4—762no—
150C4⋊C4D7611yescharacteristic
151C22⋊C4—21no—
152C22⋊C4—381no—
153C42—381no—
154C42—381no—
155C23D4×D1911yescharacteristic
156Q8—41no—
157Q8—761no—
158Q8—1521no—
159C2×C4—22no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—192no—
166C2×C4—381no—
167C2×C4—381no—
168C2×C4—381no—
169C2×C4—381no—
170C2×C4—381no—
171C2×C4—761no—
172C2×C4—761no—
173C2×C4—761no—
174C2×C4—761no—
175C2×C4C2×D7611yescharacteristic
176C2×C4D4×D1911yescharacteristic
177C8—41no—
178C8—761no—
179C22—21no—
180C22—21no—
181C22#1059732811yescharacteristic
182C22SD16×D1911yescharacteristic
183C22#1059736411yescharacteristic
184C4—21no—
185C4—21no—
186C4—42no—
187C4—41no—
188C4—41no—
189C4—382no—
190C4—761no—
191C4—761no—
192C4—761no—
193C4—1521no—
194C2—21no—
195C2—21no—
196C2#1192668411yescharacteristic
197C2#1192672811yescharacteristic
198C2#1192673511yescharacteristic
subgroupG/H
centerC22#10597328
commutator, cosocleC22×C4×C19C23
FrattiniC22×C4C22×D19
FittingC19×#328C2
socleC22×C19#120
prime radicalC23×C19C2×D4
hypercenter#328D19
hypocenterC19#1611
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
126. C19#1611semidirect

Maximal subgroups

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

subgroupindex
#119271732
#119268752
#119268722
#119264762
#119262802
#119262692
C19×#3282
#161119