Finite Group Databasebeta

← #14562967

Subgroups — #14562967

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#11927298C211yesmaximal, characteristic
2#11926912C211yesmaximal, characteristic, complemented
3#11926906C211yesmaximal, characteristic
4#11926286C211yesmaximal, characteristic, complemented
5#11926285C211yesmaximal, characteristic, complemented
6#11926283C211yesmaximal, characteristic
7C19×#501C211yesmaximal, characteristic, complemented
8C19×C4⋊Q8C2211yescharacteristic
9C19×#125C2211yescharacteristic
10#10597344—21no—
11#10597344—21no—
12#10597343—21no—
13#10597342—21no—
14#10597340—21no—
15#10597334—21no—
16#10597321C2211yescharacteristic
17#10597316C2211yescharacteristic
18C19×#107—21no—
19C19×#106—21no—
20C19×#97C2211yescharacteristic
21#10597292—21no—
22#10597292—21no—
23#10597267—21no—
24#10597266—21no—
25#10597260C2211yescharacteristic
26#10597260C2211yescharacteristic
27C2×Q8×C19—21no—
28C2×D76D411yescharacteristic
29C2×C4×D19—21no—
30C2×Dic38—21no—
31C2×Dic38D411yescharacteristic
32C2×C8×C19—21no—
33C4⋊C4×C19—21no—
34C4⋊C4×C19—21no—
35C4⋊C4×C19—21no—
36C4⋊C4×C19—21no—
37C4⋊C4×C19D411yescharacteristic
38C4⋊C4×C19D411yescharacteristic
39C42×C19C2311yescharacteristic
40(C2×D19)⋊C4—21no—
41(C2×D19)⋊C4—21no—
42(C2×D19)⋊C4—21no—
43(C2×D19)⋊C4—21no—
44(C2×D19)⋊C4—21no—
45C4⋊Dic19—21no—
46C4⋊Dic19D411yescharacteristic
47C4⋊Dic19D411yescharacteristic
48Dic19⋊C4—21no—
49Dic19⋊C4—21no—
50Dic19⋊C4—21no—
51C4×Dic19—21no—
52C2×C19⋊C8—21no—
53C2×C19⋊C8—21no—
54C22×D19—21no—
55Q8×C19—42no—
56C2×C4×C19—21no—
57C2×C4×C19—21no—
58C2×C4×C19—41no—
59C2×C4×C19C2×D411yescharacteristic
60C2×C4×C19C2×D411yescharacteristic
61C2×C4×C19C2×D411yescharacteristic
62C2×Dic19—21no—
63C2×Dic19—21no—
64C2×Dic19—21no—
65D76—41no—
66C4×D19—81no—
67Dic38—41no—
68Dic38—81no—
69C8×C19—22no—
70C19⋊C8—41no—
71C19⋊C8—41no—
72#1664—191nomaximal, Sylow
73C22×C19#12011yescharacteristic
74C2×D19—41no—
75C2×D19—41no—
76C2×D19—41no—
77C4×C19—21no—
78C4×C19—21no—
79C4×C19—21no—
80C4×C19—41no—
81C4×C19—41no—
82C4×C19—81no—
83Dic19—41no—
84Dic19—41no—
85Dic19—41no—
86#563—191no—
87#501D1911yescharacteristic, complemented
88#491—191no—
89#489—191no—
90#330—191no—
91#330—191no—
92#329—191no—
93C2×C19#45411yescharacteristic
94C2×C19#45511yescharacteristic
95C2×C19#45611yescharacteristic
96D19—81no—
97C4⋊Q8—381no—
98C4⋊Q8C2×D1911yescharacteristic
99#126—381no—
100#126—381no—
101#125—191no—
102#125C2×D1911yescharacteristic
103#124—191no—
104#123—381no—
105C22⋊Q8—381no—
106C22⋊Q8—381no—
107#107—21no—
108#106—21no—
109#103—381no—
110#103—381no—
111#103—381no—
112#102—381no—
113#97—191no—
114#97—191no—
115#97C2×D1911yescharacteristic
116C19#166411yescharacteristic, complemented, Sylow
117C2×Q8—21no—
118C2×Q8—191no—
119C2×Q8—381no—
120C2×D4—191no—
121C22×C4—381no—
122C2×C8—21no—
123C2×C8—381no—
124C2×C8—381no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—21no—
128C4⋊C4—21no—
129C4⋊C4—191no—
130C4⋊C4—191no—
131C4⋊C4—381no—
132C4⋊C4—381no—
133C4⋊C4—381no—
134C4⋊C4—381no—
135C4⋊C4C22⋊D1911yescharacteristic
136C4⋊C4C22⋊D1911yescharacteristic
137C22⋊C4—381no—
138C22⋊C4—381no—
139C22⋊C4—381no—
140C22⋊C4—381no—
141C22⋊C4—381no—
142C42—381no—
143C42C22×D1911yescharacteristic
144C23—381no—
145Q8—42no—
146Q8—761no—
147Q8—1521no—
148D4—761no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—41no—
152C2×C4—381no—
153C2×C4—381no—
154C2×C4—381no—
155C2×C4—1521no—
156C2×C4D4×D1911yescharacteristic
157C2×C4D4×D1911yescharacteristic
158C2×C4C2×C22⋊D1911yescharacteristic
159C8—22no—
160C8—761no—
161C8—761no—
162C22—761no—
163C22—761no—
164C22—761no—
165C22#1059738311yescharacteristic
166C4—21no—
167C4—21no—
168C4—21no—
169C4—41no—
170C4—41no—
171C4—81no—
172C4—761no—
173C4—761no—
174C4—761no—
175C2—1521no—
176C2#1192671511yescharacteristic
177C2#1192672011yescharacteristic
178C2#1192672611yescharacteristic
subgroupG/H
centerC22#10597383
commutator, cosocleC42×C19C23
FrattiniC42C22×D19
FittingC19×#501C2
socleC22×C19#120
prime radicalC2×D76D4
hypercenter#501D19
hypocenterC19#1664
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
2. #11926912C2semidirect
4. #11926286C2semidirect
5. #11926285C2semidirect
7. C19×#501C2semidirect
87. #501D19semidirect
116. C19#1664semidirect

Maximal subgroups

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

subgroupindex
#119272982
#119269122
#119269062
#119262862
#119262852
#119262832
C19×#5012
#166419