Finite Group Databasebeta

← #14562119

Subgroups — #14562119

Order 2432.

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

normal subgroups only

This group has 238 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
1#11927078C211yesmaximal, characteristic
2#11926597C211yesmaximal, characteristic, complemented
3#11926280C212yesmaximal, complemented
4#11926277C212yesmaximal
5C19×#376C211yesmaximal, characteristic, complemented
6C2×C42×C19—21no—
7C2×C42×C19C2211yescharacteristic
8#10597376C2211yescharacteristic
9#10597375—21no—
10C4×C22⋊D19—21no—
11#10597370C2211yescharacteristic
12#10597322—21no—
13#10597321C411yescharacteristic, complemented
14C4×D76C411yescharacteristic, complemented
15#10597318—21no—
16#10597316C411yescharacteristic, complemented
17C4×Dic38C411yescharacteristic, complemented
18C19×#95—21no—
19C19×#95C2212yes—
20C22⋊(C19⋊C8)C2212yes—
21C4⋊(C19⋊C8)—21no—
22C4×C19⋊C8—21no—
23C22×C4×C19—22no—
24C22×C4×C19D411yescharacteristic
25C22×C4×C19D411yescharacteristic
26C22×C4×C19C2311yescharacteristic
27C2×C22⋊D19—21no—
28C2×D76C2×C411yescharacteristic
29C2×C4×D19—21no—
30C2×Dic38C2×C411yescharacteristic
31C42×C19—24no—
32C42×C19C2×C411yescharacteristic
33C42×C19C2×C411yescharacteristic
34C42×C19D411yescharacteristic
35C42×C19D411yescharacteristic
36C22⋊Dic19—21no—
37(C2×D19)⋊C4—21no—
38(C2×D19)⋊C4—21no—
39(C2×D19)⋊C4—21no—
40(C2×D19)⋊C4—21no—
41C4⋊Dic19C2×C411yescharacteristic
42C4⋊Dic19C2×C411yescharacteristic
43Dic19⋊C4—21no—
44Dic19⋊C4—21no—
45Dic19⋊C4—21no—
46Dic19⋊C4—21no—
47C4×Dic19—21no—
48C2×C19⋊C8—22no—
49C23×C19C2×D411yescharacteristic
50C22×D19—21no—
51C2×C4×C19—22no—
52C2×C4×C19—22no—
53C2×C4×C19—24no—
54C2×C4×C19—41no—
55C2×C4×C19—42no—
56C2×C4×C19—42no—
57C2×C4×C19C22⋊C411yescharacteristic
58C2×C4×C19C22⋊C411yescharacteristic
59C2×C4×C19C22⋊C411yescharacteristic
60C2×C4×C19C22⋊C411yescharacteristic
61C2×C4×C19C22×C411yescharacteristic
62C2×C4×C19C2×D411yescharacteristic
63C22⋊D19—42no—
64C2×Dic19—21no—
65C2×Dic19—21no—
66C2×Dic19—21no—
67D76—41no—
68C4×D19—42no—
69Dic38—41no—
70C19⋊C8—42no—
71#1500—191nomaximal, Sylow
72C22×C19—21no—
73C22×C19—21no—
74C22×C19C2×C22⋊C411yescharacteristic
75C22×C19#13512yes—
76C2×D19—41no—
77C2×D19—41no—
78C2×D19—41no—
79C4×C19—21no—
80C4×C19—21no—
81C4×C19—21no—
82C4×C19—21no—
83C4×C19—21no—
84C4×C19—44no—
85C4×C19#10412yes—
86Dic19—41no—
87Dic19—41no—
88Dic19—41no—
89#529—191no—
90#431—191no—
91#376D1911yescharacteristic, complemented
92#328—192no—
93#327—192no—
94C2×C19—22no—
95C2×C19#41011yescharacteristic
96C2×C19#41611yescharacteristic
97C2×C19C2×#10411yescharacteristic
98D19—81no—
99#126—381no—
100#125—191no—
101#124—191no—
102#123—381no—
103C22⋊Q8—191no—
104#121—191no—
105C4×Q8—191no—
106C4×D4—191no—
107C4×D4—381no—
108#117—381no—
109C2×C42—21no—
110C2×C42C2×D1911yescharacteristic
111C4⋊C8—381no—
112C22⋊C8—192no—
113C4×C8—381no—
114#95—21no—
115#95C2×D1912yes—
116C19#150011yescharacteristic, complemented, Sylow
117C2×Q8—191no—
118C2×D4—191no—
119C2×D4—381no—
120C22×C4—22no—
121C22×C4—381no—
122C22×C4C22⋊D1911yescharacteristic
123C22×C4C22⋊D1911yescharacteristic
124C22×C4C22×D1911yescharacteristic
125C2×C8—382no—
126C4⋊C4—191no—
127C4⋊C4—191no—
128C4⋊C4—381no—
129C4⋊C4—381no—
130C4⋊C4—381no—
131C4⋊C4—381no—
132C22⋊C4—381no—
133C22⋊C4—381no—
134C22⋊C4—381no—
135C22⋊C4—381no—
136C22⋊C4—381no—
137C42—24no—
138C42—381no—
139C42C4×D1911yescharacteristic
140C42C4×D1911yescharacteristic
141C42D7611yescharacteristic
142C42D7611yescharacteristic
143C23—381no—
144C23C2×C22⋊D1911yescharacteristic
145Q8—761no—
146D4—761no—
147D4—762no—
148C2×C4—22no—
149C2×C4—22no—
150C2×C4—24no—
151C2×C4—41no—
152C2×C4—42no—
153C2×C4—42no—
154C2×C4—381no—
155C2×C4—381no—
156C2×C4—381no—
157C2×C4—762no—
158C2×C4(C2×D19)⋊C411yescharacteristic
159C2×C4(C2×D19)⋊C411yescharacteristic
160C2×C4(C2×D19)⋊C411yescharacteristic
161C2×C4(C2×D19)⋊C411yescharacteristic
162C2×C4C2×C4×D1911yescharacteristic
163C2×C4C2×D7611yescharacteristic
164C8—762no—
165C22—21no—
166C22—21no—
167C22—761no—
168C22—761no—
169C22—761no—
170C22C2×(C2×D19)⋊C411yescharacteristic
171C22#1059739612yes—
172C4—21no—
173C4—21no—
174C4—21no—
175C4—21no—
176C4—21no—
177C4—44no—
178C4—761no—
179C4—761no—
180C4—761no—
181C4#1059726212yes—
182C2—22no—
183C2—1521no—
184C2#1192651711yescharacteristic
185C2#1192653811yescharacteristic
186C2C2×#1059726211yescharacteristic
subgroupG/H
centerC2×C4(C2×D19)⋊C4
commutatorC2×C4×C19C22×C4
FrattiniC22×C4C22×D19
FittingC19×#376C2
socleC22×C19C2×C22⋊C4
prime radical#10597376C22
cosocleC22×C4×C19C23
hypercenter#376D19
hypocenterC19#1500
LCSG ▷ C2×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #376

Complements

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

NH ≅ G/Ntype
2. #11926597C2semidirect
3. #11926280C2semidirect
5. C19×#376C2semidirect
13. #10597321C4semidirect
14. C4×D76C4semidirect
16. #10597316C4semidirect
17. C4×Dic38C4semidirect
91. #376D19semidirect
116. C19#1500semidirect

Maximal subgroups

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

subgroupindex
#119270782
#119265972
#119262802
#119262772
C19×#3762
#150019