Finite Group Databasebeta

← #14562971

Subgroups — #14562971

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#11926954C211yesmaximal, characteristic, complemented
3#11926913C211yesmaximal, characteristic, complemented
4#11926904C211yesmaximal, characteristic
5#11926285C211yesmaximal, characteristic, complemented
6#11926283C211yesmaximal, characteristic
7C19×#330C211yesmaximal, characteristic, complemented
8C19×#125C2211yescharacteristic
9#10597344—21no—
10#10597344—21no—
11#10597343—21no—
12#10597342—21no—
13#10597340—21no—
14#10597334—21no—
15#10597321C2211yescharacteristic
16#10597316C2211yescharacteristic
17#10597315C2211yescharacteristic
18C19×#97C2211yescharacteristic
19C19×#97C2211yescharacteristic
20#10597278—21no—
21#10597273—21no—
22#10597273—21no—
23#10597273—21no—
24#10597265—21no—
25#10597264—21no—
26#10597260C2211yescharacteristic
27C2×D76D411yescharacteristic
28C2×C4×D19—21no—
29C2×Dic38—21no—
30C2×Dic38—21no—
31C2×Dic38D411yescharacteristic
32C2×C8×C19—21no—
33C2×C8×C19—21no—
34C4⋊C4×C19—21no—
35C4⋊C4×C19—21no—
36C4⋊C4×C19D411yescharacteristic
37C4⋊C4×C19D411yescharacteristic
38C42×C19C2311yescharacteristic
39(C2×D19)⋊C4—21no—
40(C2×D19)⋊C4—21no—
41(C2×D19)⋊C4—21no—
42(C2×D19)⋊C4—21no—
43(C2×D19)⋊C4—21no—
44C4⋊Dic19—21no—
45C4⋊Dic19—21no—
46C4⋊Dic19—21no—
47C4⋊Dic19D411yescharacteristic
48C4⋊Dic19D411yescharacteristic
49Dic19⋊C4—21no—
50Dic19⋊C4—21no—
51Dic19⋊C4—21no—
52C4×Dic19—21no—
53C2×C19⋊C8—21no—
54C22×D19—21no—
55C2×C4×C19—21no—
56C2×C4×C19—21no—
57C2×C4×C19C2×D411yescharacteristic
58C2×C4×C19C2×D411yescharacteristic
59C2×C4×C19C2×D411yescharacteristic
60C2×Dic19—21no—
61C2×Dic19—21no—
62C2×Dic19—21no—
63C2×Dic19—41no—
64D76—41no—
65C4×D19—81no—
66Dic38—41no—
67Dic38—42no—
68Dic38—81no—
69C8×C19—41no—
70C8×C19—41no—
71C19⋊C8—22no—
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—
82Dic19—41no—
83Dic19—41no—
84Dic19—41no—
85Dic19—81no—
86#563—191no—
87#501—191no—
88#491—191no—
89#489—191no—
90#330—191no—
91#330D1911yescharacteristic, complemented
92#329—191no—
93C2×C19#45411yescharacteristic
94C2×C19#45511yescharacteristic
95C2×C19#45611yescharacteristic
96D19—81no—
97C4⋊Q8—191no—
98C4⋊Q8—381no—
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—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—191no—
118C2×Q8—381no—
119C2×Q8—381no—
120C2×D4—191no—
121C22×C4—381no—
122C2×C8—21no—
123C2×C8—21no—
124C2×C8—381no—
125C4⋊C4—21no—
126C4⋊C4—21no—
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⋊C4D7611yescharacteristic
136C4⋊C4D7611yescharacteristic
137C22⋊C4—381no—
138C22⋊C4—381no—
139C22⋊C4—381no—
140C22⋊C4—381no—
141C22⋊C4—381no—
142C42—381no—
143C42C22×D1911yescharacteristic
144C23—381no—
145Q8—761no—
146Q8—762no—
147Q8—1521no—
148D4—761no—
149C2×C4—21no—
150C2×C4—21no—
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—41no—
160C8—41no—
161C8—382no—
162C22—761no—
163C22—761no—
164C22—761no—
165C22#1059732811yescharacteristic
166C4—21no—
167C4—21no—
168C4—21no—
169C4—41no—
170C4—41no—
171C4—761no—
172C4—761no—
173C4—761no—
174C4—1521no—
175C2—1521no—
176C2#1192671811yescharacteristic
177C2#1192672311yescharacteristic
178C2#1192672911yescharacteristic
subgroupG/H
centerC22#10597328
commutator, cosocleC42×C19C23
FrattiniC42C22×D19
FittingC19×#330C2
socleC22×C19#120
prime radicalC2×D76D4
hypercenter#330D19
hypocenterC19#1664
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
2. #11926954C2semidirect
3. #11926913C2semidirect
5. #11926285C2semidirect
7. C19×#330C2semidirect
91. #330D19semidirect
116. C19#1664semidirect

Maximal subgroups

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

subgroupindex
#119272982
#119269542
#119269132
#119269042
#119262852
#119262832
C19×#3302
#166419