Finite Group Databasebeta

← #14564702

Subgroups — #14564702

Order 2432.

394 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 69 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#11927344C211yesmaximal, characteristic, complemented
2#11927055C212yesmaximal, complemented
3#11926560C212yesmaximal, complemented
4#11926301C211yesmaximal, characteristic, complemented
5C19×#407C211yesmaximal, characteristic, complemented
6C23×C4×C19C2211yescharacteristic
7C2×#64541C2212yes—
8C2×M16×C19C2211yescharacteristic
9C2×M16×C19C2211yescharacteristic
10#10597399—22no—
11#10597376—22no—
12#10597375—22no—
13C4×C22⋊D19—24no—
14#10597372C2212yes—
15#10597370—22no—
16#10597355—22no—
17#10597354—22no—
18#10597350—22no—
19C19×C22⋊C8—22no—
20#10597282—24no—
21C24×C19D411yescharacteristic
22C22×C4×C19—22no—
23C22×C4×C19—21no—
24C22×C4×C19—22no—
25C22×C4×C19—21no—
26C22×C4×C19D411yescharacteristic
27C22×C4×C19C2311yescharacteristic
28C2×C22⋊D19—24no—
29C2×C22⋊D19—22no—
30#64541—22no—
31#64541—22no—
32#64541—22no—
33#64541—22no—
34C2×D76D412yescomplemented
35C2×C4×D19—22no—
36C2×Dic38D412yescomplemented
37M16×C19—22no—
38M16×C19—22no—
39C2×C8×C19—21no—
40C2×C8×C19D412yescomplemented
41C22⋊Dic19—24no—
42C22⋊Dic19—22no—
43(C2×D19)⋊C4—24no—
44C4⋊Dic19—22no—
45Dic19⋊C4—24no—
46C4×Dic19D414yescomplemented
47Dic76—22no—
48D152—22no—
49#64516—24no—
50C23×C19—22no—
51C23×C19—21no—
52C23×C19—42no—
53C23×C19C2×D411yescharacteristic
54C22×D19—22no—
55C2×C4×C19—22no—
56C2×C4×C19—21no—
57C2×C4×C19—41no—
58C2×C4×C19—42no—
59C2×C4×C19—41no—
60C2×C4×C19C2×D412yes—
61C2×C4×C19C2×D412yes—
62C2×C4×C19C2×D411yescharacteristic
63C2×C4×C19#4111yescharacteristic
64C22⋊D19—48no—
65C22⋊D19—42no—
66C22⋊D19—42no—
67C2×Dic19—24no—
68C2×Dic19—22no—
69D76—22no—
70D76—22no—
71C4×D19—42no—
72C4×D19—42no—
73Dic38—22no—
74Dic38—22no—
75C8×C19—22no—
76C8×C19—41no—
77#2010—191nomaximal, Sylow
78C22×C19—24no—
79C22×C19—22no—
80C22×C19—41no—
81C22×C19—42no—
82C22×C19—41no—
83C22×C19—41no—
84C22×C19#12012yes—
85C22×C19#12111yescharacteristic
86C2×D19—44no—
87C2×D19—42no—
88C4×C19—41no—
89C4×C19#12011yescharacteristic
90C4×C19#12112yes—
91C4×C19#12711yescharacteristic
92Dic19—44no—
93Dic19—42no—
94#575—191no—
95#525—192no—
96#421—192no—
97#407D1911yescharacteristic, complemented
98H(3,ℤ/4)—191no—
99C2×C19—22no—
100C2×C19—21no—
101C2×C19—42no—
102C2×C19#39211yescharacteristic
103D19—82no—
104C2×#41—192no—
105C23×C4C2×D1911yescharacteristic
106#137—382no—
107AGL(1,ℤ/8)—382no—
108#135—382no—
109C2×M16C2×D1911yescharacteristic
110C2×M16C2×D1911yescharacteristic
111#123—382no—
112C22⋊Q8—382no—
113#121—382no—
114#120—382no—
115C4×D4—384no—
116#117—192no—
117#104—384no—
118C22⋊C8—22no—
119C19#201011yescharacteristic, complemented, Sylow
120C24D7611yescharacteristic
121#41—382no—
122#41—382no—
123#41—382no—
124#41—382no—
125C2×Q8—192no—
126C2×D4—192no—
127C2×D4—384no—
128C2×D4—382no—
129C22×C4—21no—
130C22×C4—22no—
131C22×C4—22no—
132C22×C4—21no—
133C22×C4—382no—
134C22×C4D7611yescharacteristic
135C22×C4C22×D1911yescharacteristic
136Q16—382no—
137SD16—384no—
138D8—382no—
139M16—22no—
140M16—22no—
141C2×C8—21no—
142C2×C8C22⋊D1912yescomplemented
143C4⋊C4—384no—
144C4⋊C4—382no—
145C22⋊C4—384no—
146C22⋊C4—384no—
147C22⋊C4—382no—
148C42—194no—
149C23—21no—
150C23—22no—
151C23—42no—
152C23—382no—
153C23C2×D7611yescharacteristic
154Q8—382no—
155Q8—382no—
156D4—382no—
157D4—382no—
158D4—768no—
159D4—762no—
160D4—762no—
161C2×C4—21no—
162C2×C4—22no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—42no—
166C2×C4—384no—
167C2×C4—382no—
168C2×C4—762no—
169C2×C4—762no—
170C2×C4#6454111yescharacteristic
171C2×C4D4×D1912yes—
172C2×C4D4×D1912yes—
173C2×C4C2×C22⋊D1911yescharacteristic
174C8—22no—
175C8—41no—
176C22—24no—
177C22—22no—
178C22—41no—
179C22—42no—
180C22—41no—
181C22—41no—
182C22—764no—
183C22—762no—
184C22#1059732812yes—
185C22#1059737611yescharacteristic
186C4—41no—
187C4—764no—
188C4—762no—
189C4#1059733012yes—
190C4#1059738311yescharacteristic
191C4#1059738611yescharacteristic
192C2—22no—
193C2—21no—
194C2—42no—
195C2—1522no—
196C2#1192645311yescharacteristic
subgroupG/H
centerC4#10597386
commutator, cosocleC22×C4×C19C23
FrattiniC22×C4C22×D19
FittingC19×#407C2
socleC2×C19#392
hypercenter#407D19
hypocenterC19#2010
LCSG ▷ C22×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C4 ◁ C22×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
1. #11927344C2semidirect
2. #11927055C2semidirect
3. #11926560C2semidirect
4. #11926301C2semidirect
5. C19×#407C2semidirect
34. C2×D76D4semidirect
36. C2×Dic38D4semidirect
40. C2×C8×C19D4semidirect
46. C4×Dic19D4semidirect
97. #407D19semidirect
119. C19#2010semidirect
142. C2×C8C22⋊D19semidirect

Maximal subgroups

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

subgroupindex
#119273442
#119270552
#119265602
#119263012
C19×#4072
#201019