Finite Group Databasebeta

← #14574101

Subgroups — #14574101

Order 2432.

572 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 572 conjugacy classes of subgroups — too many to draw. Only its 165 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×#10597355C212yesmaximal, complemented
2C2×#10597354C212yesmaximal, complemented
3#11927094C211yesmaximal, characteristic, complemented
4C2×#10597321C211yesmaximal, characteristic, complemented
5#11926938C212yesmaximal, complemented
6#11926933C212yesmaximal, complemented
7#11926928C214yesmaximal, complemented
8C4×M16×C19C211yesmaximal, characteristic, complemented
9C2×#64541C2212yes—
10C22×D76C2211yescharacteristic
11C22×Dic38C2211yescharacteristic
12C2×M16×C19C2212yes—
13C2×C42×C19C2211yescharacteristic
14#10597376—22no—
15C2×(C2×D19)⋊C4—22no—
16#10597355—28no—
17#10597354—28no—
18C2×Dic76C2214yescomplemented
19C2×D152C2214yes—
20C2×#64516C2214yes—
21C2×#64516C2214yescomplemented
22#10597321—22no—
23#10597321C2212yes—
24#10597321C2212yes—
25#10597321C2212yescomplemented
26#10597320C2211yescharacteristic, complemented
27C4×D76—22no—
28#10597315C2211yescharacteristic, complemented
29C19×#97C2212yescomplemented
30C4×C8×C19C2212yescomplemented
31C23×D19—21no—
32C22×C4×C19D412yes—
33C22×C4×C19C2311yescharacteristic
34C2×C22⋊D19—22no—
35C22×Dic19—21no—
36#64541—24no—
37#64541—24no—
38C2×D76—24no—
39C2×D76—22no—
40C2×D76—21no—
41C2×D76C2312yes—
42C2×D76C2312yes—
43C2×C4×D19—22no—
44C2×Dic38—24no—
45C2×Dic38—21no—
46C2×Dic38C2312yes—
47C2×Dic38C2312yes—
48M16×C19D418yescomplemented
49C2×C8×C19C2314yes—
50C42×C19D412yes—
51C42×C19C2311yescharacteristic
52C42×C19C2311yescharacteristic
53(C2×D19)⋊C4—24no—
54(C2×D19)⋊C4—24no—
55(C2×D19)⋊C4—24no—
56C4⋊Dic19—22no—
57Dic76—28no—
58D152—28no—
59#64516—28no—
60#64516—28no—
61C23×C19C2×D411yescharacteristic
62C22×D19—22no—
63C22×D19—22no—
64C22×D19—44no—
65C22×D19—42no—
66C2×C4×C19—42no—
67C2×C4×C19C2×D412yes—
68C2×C4×C19C2×D412yes—
69C2×C4×C19C2×D411yescharacteristic
70C2×C4×C19C2×D414yes—
71C2×C4×C19C2411yescharacteristic
72C22⋊D19—44no—
73C2×Dic19—22no—
74C2×Dic19—22no—
75C2×Dic19—42no—
76D76—22no—
77D76—24no—
78D76—22no—
79D76—44no—
80D76—42no—
81C4×D19—44no—
82Dic38—22no—
83Dic38—24no—
84Dic38—22no—
85Dic38—42no—
86C8×C19C2×D418yes—
87#3153—191nomaximal, Sylow
88C22×C19—22no—
89C22×C19#12712yes—
90C22×C19C22×D411yescharacteristic
91C2×D19—42no—
92C2×D19—42no—
93C2×D19—44no—
94C2×D19—44no—
95C2×D19—84no—
96C4×C19—22no—
97C4×C19—22no—
98C4×C19#12712yes—
99C4×C19C22×D412yes—
100Dic19—42no—
101Dic19—42no—
102C2×#137—192no—
103C2×AGL(1,ℤ/8)—192no—
104#532—191no—
105C2×#124—191no—
106#497—192no—
107#496—192no—
108#495—194no—
109C4×M16D1911yescharacteristic, complemented
110C2×C19—22no—
111C2×C19C2×#12711yescharacteristic
112C2×C19#57512yes—
113D19—82no—
114D19—82no—
115C2×#41—192no—
116C22×Q8—191no—
117C22×D4—191no—
118#137—388no—
119AGL(1,ℤ/8)—388no—
120C2×Q16—194no—
121C2×SD16—194no—
122C2×SD16—194no—
123C2×D8—194no—
124C2×M16C2×D1912yes—
125C4⋊Q8—191no—
126#127—191no—
127#124—192no—
128#124—192no—
129#124—192no—
130#124—382no—
131#121—382no—
132C4×D4—382no—
133C2×C22⋊C4—382no—
134C2×C42C2×D1911yescharacteristic
135#97C2×D1912yescomplemented
136C4×C8C2×D1912yescomplemented
137C19#315311yescharacteristic, complemented, Sylow
138C24—381no—
139#41—384no—
140#41—384no—
141C2×Q8—192no—
142C2×Q8—192no—
143C2×Q8—381no—
144C2×Q8—384no—
145C2×D4—192no—
146C2×D4—192no—
147C2×D4—382no—
148C2×D4—384no—
149C2×D4—382no—
150C2×D4—381no—
151C22×C4—381no—
152C22×C4—382no—
153C22×C4D7612yes—
154C22×C4C22×D1911yescharacteristic
155Q16—388no—
156SD16—388no—
157SD16—388no—
158D8—388no—
159M16D7618yescomplemented
160C2×C8C22×D1914yes—
161C4⋊C4—382no—
162C22⋊C4—384no—
163C22⋊C4—384no—
164C22⋊C4—384no—
165C42D7612yes—
166C42C22×D1911yescharacteristic
167C42C22×D1911yescharacteristic
168C23—382no—
169C23—382no—
170C23—764no—
171C23—762no—
172C23C2×D7611yescharacteristic
173Q8—382no—
174Q8—384no—
175Q8—382no—
176Q8—762no—
177D4—382no—
178D4—384no—
179D4—382no—
180D4—764no—
181D4—764no—
182D4—762no—
183C2×C4—42no—
184C2×C4—382no—
185C2×C4—382no—
186C2×C4—762no—
187C2×C4—764no—
188C2×C4C2×D7612yes—
189C2×C4C2×D7612yes—
190C2×C4C2×D7614yes—
191C2×C4C2×D7611yescharacteristic
192C2×C4C23×D1911yescharacteristic
193C8C2×D7618yes—
194C22—22no—
195C22—762no—
196C22—762no—
197C22—764no—
198C22—764no—
199C22—1524no—
200C22#1059732012yes—
201C22C22×D7611yescharacteristic
202C4—22no—
203C4—22no—
204C4—762no—
205C4—762no—
206C4#1059732012yes—
207C4C22×D7612yes—
208C2—22no—
209C2—1522no—
210C2—1522no—
211C2C2×#1059732011yescharacteristic
212C2#1192734412yes—
subgroupG/H
centerC22C22×D76
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC4×M16×C19C2
socleC22×C19C22×D4
hypercenterC4×M16D19
hypocenterC19#3153
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×#10597355C2semidirect
2. C2×#10597354C2semidirect
3. #11927094C2semidirect
4. C2×#10597321C2semidirect
5. #11926938C2semidirect
6. #11926933C2semidirect
7. #11926928C2semidirect
8. C4×M16×C19C2semidirect
18. C2×Dic76C22semidirect
21. C2×#64516C22semidirect
25. #10597321C22semidirect
26. #10597320C22semidirect
28. #10597315C22semidirect
29. C19×#97C22semidirect
30. C4×C8×C19C22semidirect
48. M16×C19D4semidirect
109. C4×M16D19semidirect
135. #97C2×D19semidirect
136. C4×C8C2×D19semidirect
137. C19#3153semidirect
159. M16D76semidirect

Maximal subgroups

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

subgroupindex
C2×#105973552
C2×#105973542
#119270942
C2×#105973212
#119269382
#119269332
#119269282
C4×M16×C192
#315319