Finite Group Databasebeta

← #14573566

Subgroups — #14573566

Order 2432.

414 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 133 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#11927055C211yesmaximal, characteristic
2#11926885C214yesmaximal, complemented
3#11926868C214yesmaximal, complemented
4#11926584C212yesmaximal, complemented
5#11926543C212yesmaximal, complemented
6#11926508C211yesmaximal, characteristic, complemented
7C2×C19×#117C211yesmaximal, characteristic, complemented
8C23×C4×C19C2211yescharacteristic
9C2×#64541C2211yescharacteristic
10C19×#117—22no—
11C19×#117C2214yes—
12C2×C4⋊C4×C19C2212yes—
13C2×C22⋊C4×C19—21no—
14C2×C42×C19—21no—
15#10597399—21no—
16#10597376C2212yes—
17#10597375—21no—
18C4×C22⋊D19—22no—
19#10597372C2211yescharacteristic
20#10597370C2212yes—
21C2×#64520C2212yes—
22C22⋊(C19⋊C8)C2214yes—
23#10597267C2214yescomplemented
24#10597266C2214yescomplemented
25#10597265C2214yescomplemented
26#10597264C2214yescomplemented
27C24×C19D411yescharacteristic
28C22×C4×C19—24no—
29C22×C4×C19—22no—
30C22×C4×C19D411yescharacteristic
31C22×C4×C19D412yes—
32C22×C4×C19C2312yes—
33C22×C4×C19C2311yescharacteristic
34C2×C22⋊D19—22no—
35C2×C22⋊D19—21no—
36#64541—24no—
37C2×D76C2311yescharacteristic
38C2×C4×D19—21no—
39C2×Dic38C2311yescharacteristic
40C4⋊C4×C19—22no—
41C4⋊C4×C19C2314yes—
42C22⋊C4×C19—24no—
43C42×C19—24no—
44C22⋊Dic19—22no—
45C22⋊Dic19—21no—
46(C2×D19)⋊C4—22no—
47C4⋊Dic19C2312yes—
48Dic19⋊C4—22no—
49C4×Dic19—21no—
50#64520—24no—
51C2×C19⋊C8C2314yes—
52C23×C19—22no—
53C23×C19—42no—
54C23×C19C2×D412yes—
55C23×C19C2×D411yescharacteristic
56C22×D19—21no—
57C2×C4×C19—22no—
58C2×C4×C19—24no—
59C2×C4×C19—24no—
60C2×C4×C19—24no—
61C2×C4×C19—44no—
62C2×C4×C19C2×D412yes—
63C2×C4×C19C2×D411yescharacteristic
64C2×C4×C19#4114yes—
65C2×C4×C19C2411yescharacteristic
66C22⋊D19—44no—
67C22⋊D19—42no—
68C2×Dic19—22no—
69C2×Dic19—21no—
70D76—22no—
71C4×D19—42no—
72Dic38—22no—
73C19⋊C8—24no—
74#3093—191nomaximal, Sylow
75C22×C19—22no—
76C22×C19—22no—
77C22×C19—22no—
78C22×C19—22no—
79C22×C19—44no—
80C22×C19#12312yes—
81C22×C19C22×D411yescharacteristic
82C2×D19—41no—
83C2×D19—42no—
84C4×C19—22no—
85C4×C19—44no—
86C4×C19#12312yes—
87C4×C19C2×#4112yes—
88Dic19—41no—
89Dic19—42no—
90#525—191no—
91C2×#117D1911yescharacteristic, complemented
92#485—194no—
93#482—194no—
94#428—192no—
95#417—192no—
96#407—191no—
97C2×C19—22no—
98C2×C19—42no—
99C2×C19C2×#12311yescharacteristic
100C2×C19#57512yes—
101D19—81no—
102C2×#41—191no—
103C23×C4C2×D1911yescharacteristic
104C2×M16—192no—
105#123—381no—
106C22⋊Q8—192no—
107#121—192no—
108#120—381no—
109C4×D4—382no—
110#117—22no—
111#117—191no—
112#117C2×D1914yes—
113C2×C4⋊C4C2×D1912yes—
114C2×C22⋊C4—21no—
115C2×C42—21no—
116#107—194no—
117#106—194no—
118#103—194no—
119#102—194no—
120C22⋊C8—194no—
121C19#309311yescharacteristic, complemented, Sylow
122C24C22⋊D1911yescharacteristic
123#41—384no—
124C2×Q8—191no—
125C2×D4—191no—
126C2×D4—382no—
127C2×D4—381no—
128C22×C4—24no—
129C22×C4—22no—
130C22×C4—381no—
131C22×C4C22⋊D1911yescharacteristic
132C22×C4C22⋊D1912yes—
133C22×C4C22×D1912yes—
134C22×C4C22×D1911yescharacteristic
135M16—384no—
136C2×C8—194no—
137C4⋊C4—22no—
138C4⋊C4—192no—
139C4⋊C4—382no—
140C4⋊C4C22×D1914yes—
141C22⋊C4—24no—
142C22⋊C4—381no—
143C22⋊C4—382no—
144C22⋊C4—382no—
145C42—24no—
146C42—381no—
147C23—22no—
148C23—42no—
149C23—381no—
150C23C2×C22⋊D1912yes—
151C23C2×C22⋊D1911yescharacteristic
152Q8—382no—
153D4—382no—
154D4—764no—
155D4—762no—
156C2×C4—22no—
157C2×C4—24no—
158C2×C4—24no—
159C2×C4—24no—
160C2×C4—44no—
161C2×C4—382no—
162C2×C4—381no—
163C2×C4—762no—
164C2×C4#6454114yes—
165C2×C4C2×C22⋊D1912yes—
166C2×C4C2×C22⋊D1911yescharacteristic
167C2×C4C23×D1911yescharacteristic
168C8—384no—
169C22—22no—
170C22—22no—
171C22—22no—
172C22—22no—
173C22—44no—
174C22—761no—
175C22—762no—
176C22#1059737512yes—
177C22C22×C22⋊D1911yescharacteristic
178C4—22no—
179C4—44no—
180C4—761no—
181C4—762no—
182C4#1059737512yes—
183C4C2×#6454112yes—
184C2—22no—
185C2—42no—
186C2—1521no—
187C2C2×#1059737511yescharacteristic
188C2#1192734212yes—
subgroupG/H
centerC22C22×C22⋊D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC2×C19×#117C2
socleC22×C19C22×D4
prime radical#11927055C2
hypercenterC2×#117D19
hypocenterC19#3093
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. #11926885C2semidirect
3. #11926868C2semidirect
4. #11926584C2semidirect
5. #11926543C2semidirect
6. #11926508C2semidirect
7. C2×C19×#117C2semidirect
23. #10597267C22semidirect
24. #10597266C22semidirect
25. #10597265C22semidirect
26. #10597264C22semidirect
91. C2×#117D19semidirect
121. C19#3093semidirect

Maximal subgroups

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

subgroupindex
#119270552
#119268852
#119268682
#119265842
#119265432
#119265082
C2×C19×#1172
#309319