Finite Group Databasebeta

← #14574648

Subgroups — #14574648

Order 2432.

390 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 390 conjugacy classes of subgroups — too many to draw. Only its 121 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#11927101C211yesmaximal, characteristic, complemented
2#11927094C211yesmaximal, characteristic
3#11926938C212yesmaximal, complemented
4#11926904C212yesmaximal, complemented
5#11926755C212yesmaximal, complemented
6#11926745C212yesmaximal, complemented
7#11926708C214yesmaximal, complemented
8C19×#432C211yesmaximal, characteristic, complemented
9C2×#64541C2212yes—
10C2×C42×C19C2211yescharacteristic
11#10597376—21no—
12#10597376—21no—
13#10597372—21no—
14#10597370—21no—
15#10597370C2212yes—
16C2×Dic76C2214yes—
17C2×#64516C2214yes—
18#10597321C2212yes—
19#10597320C2211yescharacteristic
20C4×D76—21no—
21C4×D76—21no—
22#10597316—21no—
23#10597315C2211yescharacteristic
24#10597315C2211yescharacteristic
25#10597315C2211yescharacteristic
26C4×Dic38—21no—
27C4×Dic38C2212yes—
28C19×C4⋊C8C2212yes—
29C19×C22⋊C8C2212yes—
30C19×#97C2212yes—
31#10597278C2214yes—
32#10597273C2214yes—
33C22×C4×C19D411yescharacteristic
34C22×C4×C19D411yescharacteristic
35C22×C4×C19C2311yescharacteristic
36C2×C22⋊D19—22no—
37#64541—44no—
38C2×D76—21no—
39C2×D76—21no—
40C2×D76C2312yes—
41C2×C4×D19—22no—
42C2×Dic38—21no—
43C2×Dic38C2312yes—
44C2×Dic38C2312yes—
45C2×C8×C19C2314yes—
46C42×C19D411yescharacteristic
47C42×C19D411yescharacteristic
48C42×C19C2311yescharacteristic
49C42×C19C2311yescharacteristic
50C22⋊Dic19—22no—
51(C2×D19)⋊C4—22no—
52(C2×D19)⋊C4—22no—
53C4⋊Dic19—21no—
54C4⋊Dic19—21no—
55C4⋊Dic19—21no—
56C4⋊Dic19—21no—
57C4⋊Dic19—21no—
58C4⋊Dic19C2312yes—
59Dic19⋊C4—22no—
60Dic19⋊C4—22no—
61C4×Dic19—22no—
62Dic76—44no—
63#64516—44no—
64C23×C19C2×D411yescharacteristic
65C22×D19—22no—
66C2×C4×C19—22no—
67C2×C4×C19—22no—
68C2×C4×C19—41no—
69C2×C4×C19C2×D411yescharacteristic
70C2×C4×C19C2×D411yescharacteristic
71C2×C4×C19C2×D411yescharacteristic
72C2×C4×C19C2×D411yescharacteristic
73C2×C4×C19C2×D411yescharacteristic
74C2×C4×C19C2411yescharacteristic
75C22⋊D19—44no—
76C2×Dic19—22no—
77C2×Dic19—22no—
78C2×Dic19—22no—
79D76—24no—
80D76—42no—
81D76—42no—
82C4×D19—44no—
83Dic38—22no—
84Dic38—22no—
85Dic38—24no—
86Dic38—42no—
87C8×C19—24no—
88#3216—191nomaximal, Sylow
89C22×C19—21no—
90C22×C19—21no—
91C22×C19—21no—
92C22×C19C22×D411yescharacteristic
93C2×D19—42no—
94C2×D19—42no—
95C2×D19—42no—
96C4×C19—21no—
97C4×C19—21no—
98C4×C19—21no—
99C4×C19—21no—
100C4×C19#13712yes—
101C4×C19H(5,𝔽2)12yes—
102Dic19—42no—
103Dic19—42no—
104Dic19—42no—
105#533—191no—
106#532—191no—
107#497—192no—
108#489—192no—
109#462—192no—
110#460—192no—
111#452—194no—
112#432D1911yescharacteristic, complemented
113C2×C19—41no—
114C2×C19#53511yescharacteristic
115C2×C19C2×#13711yescharacteristic
116C2×C19#57511yescharacteristic
117D19—82no—
118C2×#41—192no—
119C2×Q16—194no—
120C2×SD16—194no—
121C4⋊Q8—191no—
122C4⋊Q8—191no—
123C4⋊Q8—191no—
124#127—191no—
125#125—381no—
126#124—192no—
127C22⋊Q8—192no—
128C22⋊Q8—381no—
129#121—381no—
130#121—381no—
131C4×Q8—192no—
132C4×Q8—381no—
133C4×D4—381no—
134C4×D4—381no—
135#117—381no—
136C2×C42C2×D1911yescharacteristic
137C4⋊C8C2×D1912yes—
138#103—194no—
139#102—194no—
140C22⋊C8C2×D1912yes—
141#97C2×D1912yes—
142C19#321611yescharacteristic, complemented, Sylow
143#41—764no—
144C2×Q8—192no—
145C2×Q8—192no—
146C2×Q8—381no—
147C2×D4—192no—
148C2×D4—382no—
149C2×D4—381no—
150C2×D4—381no—
151C22×C4—382no—
152C22×C4D7611yescharacteristic
153C22×C4D7611yescharacteristic
154C22×C4C22×D1911yescharacteristic
155Q16—764no—
156SD16—764no—
157C2×C8C22×D1914yes—
158C4⋊C4—192no—
159C4⋊C4—382no—
160C4⋊C4—382no—
161C4⋊C4—381no—
162C4⋊C4—381no—
163C4⋊C4—381no—
164C4⋊C4—381no—
165C4⋊C4—381no—
166C22⋊C4—382no—
167C22⋊C4—382no—
168C22⋊C4—382no—
169C42—382no—
170C42D7611yescharacteristic
171C42D7611yescharacteristic
172C42C22×D1911yescharacteristic
173C42C22×D1911yescharacteristic
174C23—382no—
175C23C2×D7611yescharacteristic
176Q8—382no—
177Q8—382no—
178Q8—384no—
179Q8—762no—
180D4—384no—
181D4—762no—
182D4—764no—
183D4—762no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—41no—
187C2×C4—382no—
188C2×C4—382no—
189C2×C4—382no—
190C2×C4—764no—
191C2×C4C2×D7611yescharacteristic
192C2×C4C2×D7611yescharacteristic
193C2×C4C2×D7611yescharacteristic
194C2×C4C2×D7611yescharacteristic
195C2×C4C2×D7611yescharacteristic
196C2×C4C23×D1911yescharacteristic
197C8—24no—
198C22—21no—
199C22—21no—
200C22—21no—
201C22—762no—
202C22—762no—
203C22—762no—
204C22C22×D7611yescharacteristic
205C4—21no—
206C4—21no—
207C4—21no—
208C4—21no—
209C4—762no—
210C4—762no—
211C4—762no—
212C4#1059735512yes—
213C4#1059743512yes—
214C2—41no—
215C2—1522no—
216C2#1192711311yescharacteristic
217C2C2×#1059735511yescharacteristic
218C2#1192734411yescharacteristic
subgroupG/H
centerC22C22×D76
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#432C2
socleC22×C19C22×D4
prime radical#11927094C2
hypercenter#432D19
hypocenterC19#3216
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
1. #11927101C2semidirect
3. #11926938C2semidirect
4. #11926904C2semidirect
5. #11926755C2semidirect
6. #11926745C2semidirect
7. #11926708C2semidirect
8. C19×#432C2semidirect
112. #432D19semidirect
142. C19#3216semidirect

Maximal subgroups

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

subgroupindex
#119271012
#119270942
#119269382
#119269042
#119267552
#119267452
#119267082
C19×#4322
#321619