Finite Group Databasebeta

← #14562972

Subgroups — #14562972

Order 2432.

184 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 45 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#11927294C211yesmaximal, characteristic
2#11926953C211yesmaximal, characteristic, complemented
3#11926913C211yesmaximal, characteristic, complemented
4#11926903C211yesmaximal, characteristic
5#11926285C211yesmaximal, characteristic, complemented
6#11926285C211yesmaximal, characteristic, complemented
7C19×#329C211yesmaximal, characteristic
8C19×#124C2211yescharacteristic
9#10597390—21no—
10#10597381—21no—
11#10597325—21no—
12#10597325—21no—
13#10597324—21no—
14#10597324—21no—
15#10597316C2211yescharacteristic
16#10597316C2211yescharacteristic
17#10597315C2211yescharacteristic
18C19×#97C2211yescharacteristic
19C19×#97C2211yescharacteristic
20#10597292—21no—
21#10597289—21no—
22#10597275—21no—
23#10597274—21no—
24#10597273—21no—
25#10597273—21no—
26#10597260C2211yescharacteristic
27C2×Q8×C19D411yescharacteristic
28C2×D4×C19D411yescharacteristic
29C22×Dic19—21no—
30C2×Dic38—21no—
31C2×Dic38—21no—
32C2×C8×C19—21no—
33C2×C8×C19—21no—
34C22⋊C4×C19—21no—
35C22⋊C4×C19—21no—
36C42×C19C2311yescharacteristic
37C22⋊Dic19—21no—
38C22⋊Dic19—21no—
39C22⋊Dic19—21no—
40C4⋊Dic19—21no—
41C4⋊Dic19—21no—
42C4⋊Dic19D411yescharacteristic
43C4⋊Dic19D411yescharacteristic
44C4⋊Dic19D411yescharacteristic
45C4⋊Dic19D411yescharacteristic
46Dic19⋊C4—21no—
47Dic19⋊C4—21no—
48Dic19⋊C4—21no—
49Dic19⋊C4—21no—
50Dic19⋊C4—21no—
51Dic19⋊C4—21no—
52C4×Dic19—21no—
53C2×C19⋊C8—21no—
54C23×C19—21no—
55Q8×C19—41no—
56D4×C19—41no—
57C2×C4×C19—21no—
58C2×C4×C19C2×D411yescharacteristic
59C2×C4×C19C2×D411yescharacteristic
60C2×C4×C19C2×D411yescharacteristic
61C2×Dic19—21no—
62C2×Dic19—21no—
63C2×Dic19—21no—
64C2×Dic19—21no—
65C2×Dic19—41no—
66C2×Dic19—81no—
67Dic38—42no—
68Dic38—81no—
69C8×C19—22no—
70C8×C19—41no—
71C19⋊C8—41no—
72#1664—191nomaximal, Sylow
73C22×C19—41no—
74C22×C19—41no—
75C22×C19—41no—
76C22×C19#12011yescharacteristic
77C4×C19—21no—
78C4×C19—21no—
79C4×C19—21no—
80C4×C19—41no—
81Dic19—41no—
82Dic19—41no—
83Dic19—41no—
84Dic19—41no—
85Dic19—81no—
86#563—191no—
87#501—191no—
88#491—191no—
89#489—191no—
90#330—191no—
91#330—191no—
92#329D1911yescharacteristic
93C2×C19—81no—
94C2×C19#45411yescharacteristic
95C2×C19#45511yescharacteristic
96C2×C19#45611yescharacteristic
97C4⋊Q8—191no—
98C4⋊Q8—381no—
99#126—381no—
100#126—381no—
101#125—191no—
102#125—191no—
103#124C2×D1911yescharacteristic
104#123—381no—
105C22⋊Q8—381no—
106C22⋊Q8—381no—
107#107—381no—
108#106—381no—
109#103—381no—
110#103—381no—
111#103—381no—
112#102—381no—
113#97—191no—
114#97C2×D1911yescharacteristic
115#97C2×D1911yescharacteristic
116C19#166411yescharacteristic, complemented, Sylow
117C2×Q8—381no—
118C2×Q8—381no—
119C2×Q8D7611yescharacteristic
120C2×D4D7611yescharacteristic
121C22×C4—381no—
122C2×C8—21no—
123C2×C8—21no—
124C2×C8—381no—
125C4⋊C4—191no—
126C4⋊C4—191no—
127C4⋊C4—191no—
128C4⋊C4—191no—
129C4⋊C4—381no—
130C4⋊C4—381no—
131C4⋊C4—381no—
132C4⋊C4—381no—
133C4⋊C4—381no—
134C4⋊C4—381no—
135C4⋊C4—381no—
136C4⋊C4—381no—
137C22⋊C4—21no—
138C22⋊C4—21no—
139C22⋊C4—381no—
140C22⋊C4—381no—
141C22⋊C4—381no—
142C42—381no—
143C42C22×D1911yescharacteristic
144C23—21no—
145Q8—41no—
146Q8—762no—
147Q8—1521no—
148D4—41no—
149C2×C4—21no—
150C2×C4—381no—
151C2×C4—381no—
152C2×C4—381no—
153C2×C4—381no—
154C2×C4—761no—
155C2×C4—1521no—
156C2×C4C2×D7611yescharacteristic
157C2×C4D4×D1911yescharacteristic
158C2×C4D4×D1911yescharacteristic
159C8—22no—
160C8—41no—
161C8—761no—
162C22—41no—
163C22—41no—
164C22—41no—
165C22#1059732811yescharacteristic
166C4—21no—
167C4—21no—
168C4—21no—
169C4—41no—
170C4—761no—
171C4—761no—
172C4—761no—
173C4—761no—
174C4—1521no—
175C2—81no—
176C2#1192671811yescharacteristic
177C2#1192672411yescharacteristic
178C2#1192672811yescharacteristic
subgroupG/H
centerC22#10597328
commutator, cosocleC42×C19C23
FrattiniC42C22×D19
FittingC19×#329C2
socleC22×C19#120
prime radicalC2×D4×C19D4
hypercenter#329D19
hypocenterC19#1664
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #11926953C2semidirect
3. #11926913C2semidirect
5. #11926285C2semidirect
6. #11926285C2semidirect
116. C19#1664semidirect

Maximal subgroups

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

subgroupindex
#119272942
#119269532
#119269132
#119269032
#119262852
C19×#3292
#166419