Finite Group Databasebeta

← #14562169

Subgroups — #14562169

Order 2432.

274 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 73 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
1C2×#10597370C211yesmaximal, characteristic
2#11926407C211yesmaximal, characteristic
3#11926282C214yesmaximal, complemented
4C19×#407C211yesmaximal, characteristic
5C23×C4×C19C2211yescharacteristic
6C22×Dic38C411yescharacteristic, complemented
7C2×M16×C19—21no—
8C2×C22⋊Dic19—21no—
9C2×C22⋊Dic19—21no—
10C2×C4⋊Dic19C411yescharacteristic, complemented
11#10597370—21no—
12#10597370—21no—
13#10597370C412yescomplemented
14#10597370C2212yes—
15C2×Dic19⋊C4—21no—
16C19×C22⋊C8—21no—
17C19×C22⋊C8C2212yes—
18C19⋊#95—21no—
19C19⋊#95C2212yes—
20C24×C19D411yescharacteristic
21C22×C4×C19—42no—
22C22×C4×C19C2×C411yescharacteristic
23C22×C4×C19C2×C411yescharacteristic
24C22×C4×C19D411yescharacteristic
25C22×C4×C19D411yescharacteristic
26C22×C4×C19D411yescharacteristic
27C22×C4×C19C2311yescharacteristic
28C22×Dic19—21no—
29C22×Dic19—21no—
30C22×Dic19—22no—
31C2×Dic38—21no—
32C2×Dic38—42no—
33C2×Dic38C2×C412yes—
34M16×C19—42no—
35C2×C8×C19—22no—
36C22⋊Dic19—22no—
37C22⋊Dic19—22no—
38C22⋊Dic19—42no—
39C4⋊Dic19—21no—
40C4⋊Dic19C2×C412yes—
41Dic19⋊C4—22no—
42Dic19⋊C4—22no—
43C23×C19—22no—
44C23×C19—22no—
45C23×C19—41no—
46C23×C19C22⋊C411yescharacteristic
47C23×C19C22⋊C411yescharacteristic
48C23×C19C2×D411yescharacteristic
49C2×C4×C19—22no—
50C2×C4×C19—22no—
51C2×C4×C19—41no—
52C2×C4×C19—41no—
53C2×C4×C19—41no—
54C2×C4×C19—41no—
55C2×C4×C19C22⋊C411yescharacteristic
56C2×C4×C19C22⋊C411yescharacteristic
57C2×C4×C19C22×C411yescharacteristic
58C2×C4×C19C2×D411yescharacteristic
59C2×Dic19—22no—
60C2×Dic19—22no—
61C2×Dic19—42no—
62C2×Dic19—42no—
63C2×Dic19—42no—
64C2×Dic19—42no—
65C2×Dic19—42no—
66Dic38—42no—
67Dic38—42no—
68C8×C19—42no—
69#1511—191nomaximal, Sylow
70C22×C19—21no—
71C22×C19—21no—
72C22×C19—21no—
73C22×C19—21no—
74C22×C19—21no—
75C22×C19—21no—
76C22×C19—21no—
77C22×C19—44no—
78C22×C19#9912yes—
79C22×C19C2×C22⋊C411yescharacteristic
80C22×C19#13712yes—
81C4×C19—21no—
82C4×C19—21no—
83C4×C19—21no—
84C4×C19—21no—
85Dic19—42no—
86Dic19—42no—
87Dic19—82no—
88C2×C22⋊Q8—191no—
89#407D1911yescharacteristic
90#381—191no—
91#328—194no—
92C2×C19—22no—
93C2×C19—22no—
94C2×C19—41no—
95C2×C19C2×#9911yescharacteristic
96C2×C19#41911yescharacteristic
97C2×C19#42111yescharacteristic
98C22×Q8—191no—
99C23×C4C2×D1911yescharacteristic
100C2×M16—21no—
101C22⋊Q8—192no—
102C22⋊Q8—192no—
103C22⋊Q8—381no—
104C22⋊Q8—381no—
105C2×C4⋊C4—191no—
106C2×C4⋊C4—381no—
107C2×C22⋊C4—381no—
108C2×C22⋊C4—381no—
109C22⋊C8—21no—
110C22⋊C8C2×D1912yes—
111#95—192no—
112#95—381no—
113C19#151111yescharacteristic, complemented, Sylow
114C24D7611yescharacteristic
115C2×Q8—192no—
116C2×Q8—381no—
117C2×Q8—762no—
118C22×C4—42no—
119C22×C4—381no—
120C22×C4—381no—
121C22×C4—382no—
122C22×C4C4×D1911yescharacteristic
123C22×C4C4×D1911yescharacteristic
124C22×C4D7611yescharacteristic
125C22×C4C22⋊D1911yescharacteristic
126C22×C4C22⋊D1911yescharacteristic
127C22×C4C22×D1911yescharacteristic
128M16—42no—
129C2×C8—22no—
130C4⋊C4—192no—
131C4⋊C4—382no—
132C4⋊C4—381no—
133C4⋊C4—382no—
134C22⋊C4—382no—
135C22⋊C4—382no—
136C22⋊C4—762no—
137C23—22no—
138C23—22no—
139C23—41no—
140C23(C2×D19)⋊C411yescharacteristic
141C23(C2×D19)⋊C411yescharacteristic
142C23C2×D7611yescharacteristic
143Q8—762no—
144Q8—762no—
145C2×C4—22no—
146C2×C4—22no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—382no—
152C2×C4—382no—
153C2×C4—762no—
154C2×C4—762no—
155C2×C4—762no—
156C2×C4—762no—
157C2×C4—762no—
158C2×C4(C2×D19)⋊C411yescharacteristic
159C2×C4(C2×D19)⋊C411yescharacteristic
160C2×C4C2×C4×D1911yescharacteristic
161C2×C4C2×C22⋊D1911yescharacteristic
162C8—42no—
163C22—21no—
164C22—21no—
165C22—21no—
166C22—21no—
167C22—21no—
168C22—21no—
169C22—21no—
170C22—44no—
171C22#1059726312yes—
172C22#1059735512yes—
173C22C2×(C2×D19)⋊C411yescharacteristic
174C4—21no—
175C4—21no—
176C4—21no—
177C4—21no—
178C4—762no—
179C4—762no—
180C4—1522no—
181C2—22no—
182C2—22no—
183C2—41no—
184C2C2×#1059726311yescharacteristic
185C2#1192655411yescharacteristic
186C2#1192656011yescharacteristic
subgroupG/H
centerC22C2×(C2×D19)⋊C4
commutatorC2×C4×C19C22×C4
FrattiniC22×C4C22×D19
FittingC19×#407C2
socleC22×C19C2×C22⋊C4
prime radicalC24×C19D4
cosocleC22×C4×C19C23
hypercenter#407D19
hypocenterC19#1511
LCSG ▷ C2×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
3. #11926282C2semidirect
6. C22×Dic38C4semidirect
10. C2×C4⋊Dic19C4semidirect
13. #10597370C4semidirect
113. C19#1511semidirect

Maximal subgroups

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

subgroupindex
C2×#105973702
#119264072
#119262822
C19×#4072
#151119