Finite Group Databasebeta

← #14562678

Subgroups — #14562678

Order 2432.

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

normal subgroups only

This group has 202 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#11926880C211yesmaximal, characteristic
3#11926877C211yesmaximal, characteristic
4#11926484C211yesmaximal, characteristic
5#11926280C211yesmaximal, characteristic
6#11926269C211yesmaximal, characteristic
7C19×#328C211yesmaximal, characteristic
8C19×C22⋊Q8C2211yescharacteristic
9#10597390—21no—
10C2×C4⋊Dic19C2211yescharacteristic
11#10597370C2211yescharacteristic
12C2×Dic19⋊C4C2211yescharacteristic
13#10597335—21no—
14#10597335—21no—
15#10597334—21no—
16#10597324—21no—
17#10597323—21no—
18C19×C22⋊C8C2211yescharacteristic
19C19×#95C2211yescharacteristic
20#10597292—21no—
21C19⋊#95—21no—
22C19⋊#95—21no—
23C22⋊(C19⋊C8)C2211yescharacteristic
24#10597275—21no—
25#10597273—21no—
26#10597264—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⋊Dic19D411yescharacteristic
44Dic19⋊C4—21no—
45Dic19⋊C4—21no—
46Dic19⋊C4—21no—
47Dic19⋊C4—21no—
48Dic19⋊C4—21no—
49Dic19⋊C4—21no—
50Dic19⋊C4—21no—
51C4×Dic19—21no—
52C4×Dic19—21no—
53C2×C19⋊C8—21no—
54C23×C19C2×D411yescharacteristic
55Q8×C19—41no—
56C2×C4×C19—21no—
57C2×C4×C19—21no—
58C2×C4×C19—41no—
59C2×C4×C19—41no—
60C2×C4×C19—41no—
61C2×C4×C19—41no—
62C2×C4×C19C2×D411yescharacteristic
63C2×C4×C19C2×D411yescharacteristic
64C2×Dic19—21no—
65C2×Dic19—21no—
66C2×Dic19—21no—
67C2×Dic19—21no—
68C2×Dic19—21no—
69C2×Dic19—41no—
70C2×Dic19—42no—
71C2×Dic19—41no—
72C2×Dic19Q1612yes—
73Dic38—41no—
74Dic38—81no—
75C8×C19—41no—
76C19⋊C8—41no—
77#1617—191nomaximal, Sylow
78C22×C19—21no—
79C22×C19—21no—
80C22×C19#12011yescharacteristic
81C22×C19C2×Q1611yescharacteristic
82C22×C19#13711yescharacteristic
83C4×C19—21no—
84C4×C19—21no—
85C4×C19—41no—
86C4×C19—41no—
87C4×C19—81no—
88Dic19—22no—
89Dic19—41no—
90Dic19—41no—
91Dic19—41no—
92Dic19—81no—
93#544—191no—
94#484—191no—
95#484—191no—
96#400—191no—
97#328—191no—
98#328D1911yescharacteristic
99#324—191no—
100C2×C19—21no—
101C2×C19—21no—
102C2×C19#45111yescharacteristic
103C2×C19#45411yescharacteristic
104C2×C19#45811yescharacteristic
105C4⋊Q8—381no—
106C4⋊Q8—381no—
107#125—381no—
108#125—381no—
109C22⋊Q8—191no—
110C22⋊Q8—381no—
111C22⋊Q8C2×D1911yescharacteristic
112#117—381no—
113C2×C4⋊C4—191no—
114C2×C4⋊C4—191no—
115#107—381no—
116#107—381no—
117#103—381no—
118#103—381no—
119C22⋊C8—191no—
120C22⋊C8C2×D1911yescharacteristic
121#95—381no—
122#95—381no—
123#95C2×D1911yescharacteristic
124C19#161711yescharacteristic, complemented, Sylow
125C2×Q8—191no—
126C2×Q8—381no—
127C2×Q8D7611yescharacteristic
128C22×C4—21no—
129C22×C4—191no—
130C22×C4—191no—
131C22×C4—381no—
132C22×C4C22×D1911yescharacteristic
133C2×C8—21no—
134C2×C8—381no—
135C4⋊C4—21no—
136C4⋊C4—191no—
137C4⋊C4—381no—
138C4⋊C4—381no—
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⋊C4D7611yescharacteristic
148C22⋊C4—21no—
149C22⋊C4—381no—
150C42—381no—
151C42—381no—
152C23D4×D1911yescharacteristic
153Q8—41no—
154Q8—761no—
155Q8—1521no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—192no—
163C2×C4—381no—
164C2×C4—381no—
165C2×C4—381no—
166C2×C4—381no—
167C2×C4—381no—
168C2×C4—761no—
169C2×C4—762no—
170C2×C4—761no—
171C2×C4C2×D7611yescharacteristic
172C2×C4D4×D1911yescharacteristic
173C8—41no—
174C8—761no—
175C22—21no—
176C22—21no—
177C22#1059732811yescharacteristic
178C22#1059736111yescharacteristic
179C22Q16×D1911yescharacteristic
180C4—21no—
181C4—21no—
182C4—41no—
183C4—41no—
184C4—81no—
185C4—382no—
186C4—761no—
187C4—761no—
188C4—761no—
189C4—1521no—
190C2—21no—
191C2—21no—
192C2#1192670111yescharacteristic
193C2#1192671811yescharacteristic
194C2#1192673511yescharacteristic
subgroupG/H
centerC22#10597328
commutator, cosocleC22×C4×C19C23
FrattiniC22×C4C22×D19
FittingC19×#328C2
socleC22×C19#120
prime radicalC23×C19C2×D4
hypercenter#328D19
hypocenterC19#1617
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
124. C19#1617semidirect

Maximal subgroups

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

subgroupindex
#119271732
#119268802
#119268772
#119264842
#119262802
#119262692
C19×#3282
#161719