Finite Group Databasebeta

← #14574087

Subgroups — #14574087

Order 2432.

656 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 656 conjugacy classes of subgroups — too many to draw. Only its 173 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×#10597354C214yesmaximal, complemented
2#11927094C211yesmaximal, characteristic, complemented
3C2×#10597320C211yesmaximal, characteristic, complemented
4#11926933C214yesmaximal, complemented
5#11926921C212yesmaximal, complemented
6#11926917C212yesmaximal, complemented
7C4×M16×C19C211yesmaximal, characteristic, complemented
8C2×#64541C2212yes—
9C22×D76—22no—
10C22×D76C2212yes—
11C2×M16×C19C2212yes—
12C2×C42×C19C2211yescharacteristic
13#10597376—22no—
14#10597354—216no—
15C2×D152C2218yescomplemented
16C2×#64516C2218yescomplemented
17#10597321C2212yescomplemented
18#10597320—22no—
19#10597320C2212yes—
20#10597320C2212yes—
21#10597320C2211yescharacteristic, complemented
22C4×D76—22no—
23#10597315C2211yescharacteristic, complemented
24C19×#97C2212yescomplemented
25C4×C8×C19C2212yescomplemented
26C23×D19—22no—
27C22×C4×C19D412yes—
28C22×C4×C19C2311yescharacteristic
29C2×C22⋊D19—22no—
30#64541—28no—
31C2×D76—28no—
32C2×D76—22no—
33C2×D76—24no—
34C2×D76—24no—
35C2×D76—22no—
36C2×D76—48no—
37C2×D76C2314yes—
38C2×D76C2312yes—
39C2×C4×D19—22no—
40C2×Dic38C2312yes—
41M16×C19D418yescomplemented
42C2×C8×C19C2314yes—
43C42×C19D412yes—
44C42×C19C2311yescharacteristic
45C42×C19C2311yescharacteristic
46(C2×D19)⋊C4—24no—
47C4⋊Dic19—22no—
48D152—216no—
49#64516—216no—
50C23×C19C2×D411yescharacteristic
51C22×D19—22no—
52C22×D19—24no—
53C22×D19—48no—
54C22×D19—44no—
55C2×C4×C19—24no—
56C2×C4×C19C2×D412yes—
57C2×C4×C19C2×D411yescharacteristic
58C2×C4×C19C2×D414yes—
59C2×C4×C19C2×D412yes—
60C2×C4×C19C2411yescharacteristic
61C22⋊D19—44no—
62C2×Dic19—22no—
63D76—28no—
64D76—24no—
65D76—48no—
66D76—44no—
67D76—44no—
68D76—48no—
69C4×D19—44no—
70Dic38—24no—
71C8×C19C2×D418yescomplemented
72#3151—191nomaximal, Sylow
73C22×C19—22no—
74C22×C19#12712yes—
75C22×C19C22×D411yescharacteristic
76C2×D19—42no—
77C2×D19—44no—
78C2×D19—48no—
79C2×D19—44no—
80C2×D19—88no—
81C4×C19—22no—
82C4×C19#12712yes—
83C4×C19AGL(1,ℤ/8)14yescomplemented
84C4×C19C22×D412yes—
85Dic19—42no—
86C2×AGL(1,ℤ/8)—194no—
87#532—191no—
88C2×#127—191no—
89#496—194no—
90#493—192no—
91#492—192no—
92C4×M16D1911yescharacteristic, complemented
93C2×C19—22no—
94C2×C19C2×#12711yescharacteristic
95C2×C19C2×AGL(1,ℤ/8)12yes—
96D19—82no—
97D19—84no—
98C2×#41—192no—
99C22×D4—192no—
100C22×D4—382no—
101AGL(1,ℤ/8)—3816no—
102C2×SD16—198no—
103C2×D8—198no—
104C2×M16C2×D1912yes—
105C4⋊Q8—191no—
106#127—192no—
107#127—192no—
108#127—191no—
109#127—382no—
110#124—192no—
111#121—382no—
112C4×D4—382no—
113C2×C42C2×D1911yescharacteristic
114#97C2×D1912yescomplemented
115C4×C8C2×D1912yescomplemented
116C19#315111yescharacteristic, complemented, Sylow
117C24—382no—
118#41—388no—
119C2×Q8—192no—
120C2×D4—192no—
121C2×D4—194no—
122C2×D4—382no—
123C2×D4—388no—
124C2×D4—382no—
125C2×D4—384no—
126C2×D4—384no—
127C2×D4—382no—
128C2×D4—768no—
129C22×C4—382no—
130C22×C4D7612yes—
131C22×C4C22×D1911yescharacteristic
132SD16—3816no—
133D8—3816no—
134M16D7618yescomplemented
135C2×C8C22×D1914yes—
136C4⋊C4—382no—
137C22⋊C4—384no—
138C42D7612yes—
139C42C22×D1911yescharacteristic
140C42C22×D1911yescharacteristic
141C23—382no—
142C23—384no—
143C23—768no—
144C23—764no—
145C23C2×D7611yescharacteristic
146Q8—384no—
147D4—384no—
148D4—388no—
149D4—768no—
150D4—764no—
151D4—764no—
152D4—768no—
153D4—764no—
154C2×C4—24no—
155C2×C4—382no—
156C2×C4—764no—
157C2×C4C2×D7612yes—
158C2×C4C2×D7614yes—
159C2×C4C2×D7611yescharacteristic
160C2×C4C2×D7612yes—
161C2×C4C23×D1911yescharacteristic
162C8C2×D7618yescomplemented
163C22—22no—
164C22—768no—
165C22—764no—
166C22—762no—
167C22—764no—
168C22—1528no—
169C22#1059732012yes—
170C22C22×D7611yescharacteristic
171C4—22no—
172C4—762no—
173C4#1059732012yes—
174C4#1059735414yescomplemented
175C4C22×D7612yes—
176C2—22no—
177C2—1524no—
178C2—1522no—
179C2C2×#1059732011yescharacteristic
180C2C2×#1059735412yes—
subgroupG/H
centerC22C22×D76
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC4×M16×C19C2
socleC22×C19C22×D4
hypercenterC4×M16D19
hypocenterC19#3151
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×M16

Complements

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

NH ≅ G/Ntype
1. C2×#10597354C2semidirect
2. #11927094C2semidirect
3. C2×#10597320C2semidirect
4. #11926933C2semidirect
5. #11926921C2semidirect
6. #11926917C2semidirect
7. C4×M16×C19C2semidirect
15. C2×D152C22semidirect
16. C2×#64516C22semidirect
17. #10597321C22semidirect
21. #10597320C22semidirect
23. #10597315C22semidirect
24. C19×#97C22semidirect
25. C4×C8×C19C22semidirect
41. M16×C19D4semidirect
71. C8×C19C2×D4semidirect
83. C4×C19AGL(1,ℤ/8)semidirect
92. C4×M16D19semidirect
114. #97C2×D19semidirect
115. C4×C8C2×D19semidirect
116. C19#3151semidirect
134. M16D76semidirect
162. C8C2×D76semidirect
174. C4#10597354semidirect

Maximal subgroups

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

subgroupindex
C2×#105973542
#119270942
C2×#105973202
#119269332
#119269212
#119269172
C4×M16×C192
#315119