Finite Group Databasebeta

← #14569004

Subgroups — #14569004

Order 2432.

484 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 161 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×#10597333C212yesmaximal
2#11926477C212yesmaximal
3#11926474C211yesmaximal, characteristic
4#11926448C212yesmaximal
5#11926448C212yesmaximal
6#11926441C212yesmaximal
7#11926439C212yesmaximal
8#11926413C211yesmaximal, characteristic
9C19×#398C211yesmaximal, characteristic
10C22×Dic38C2212yes—
11C2×C4⋊C4×C19C2212yes—
12C2×C4⋊C4×C19C2211yescharacteristic
13C2×C4⋊C4×C19C2211yescharacteristic
14C2×C4⋊Dic19C2211yescharacteristic
15C2×C4⋊Dic19C2211yescharacteristic
16C2×Dic19⋊C4C2212yes—
17C2×Dic19⋊C4C2212yes—
18C2×Dic19⋊C4C2212yes—
19C2×Dic19⋊C4C2212yes—
20C2×Dic19⋊C4C2212yes—
21C2×C4×Dic19C2212yes—
22C2×C4×Dic19C2212yes—
23C2×C4×Dic19C2211yescharacteristic
24#10597333—28no—
25C19×#95C2212yes—
26C19×#95C2211yescharacteristic
27C19⋊#95C2212yes—
28C19⋊#95C2212yes—
29C19⋊#95C2212yes—
30C19⋊#95C2211yescharacteristic
31C19⋊#95C2212yes—
32C22×C4×C19C2311yescharacteristic
33C22×C4×C19C2312yes—
34C22×C4×C19C2311yescharacteristic
35C22×C4×C19C2311yescharacteristic
36C22×C4×C19C2312yes—
37C22×Dic19C2312yes—
38C22×Dic19C2312yes—
39C22×Dic19C2312yes—
40C22×Dic19C2312yes—
41C2×Dic38—24no—
42C2×Dic38—24no—
43C2×Dic38Q818yescomplemented
44C4⋊C4×C19—24no—
45C4⋊C4×C19—41no—
46C4⋊C4×C19—41no—
47C4⋊Dic19—41no—
48C4⋊Dic19—41no—
49Dic19⋊C4—24no—
50Dic19⋊C4—24no—
51Dic19⋊C4—24no—
52Dic19⋊C4—24no—
53Dic19⋊C4—42no—
54C4×Dic19—24no—
55C4×Dic19—24no—
56C4×Dic19D414yes—
57C23×C19C2411yescharacteristic
58C2×C4×C19—22no—
59C2×C4×C19—22no—
60C2×C4×C19—21no—
61C2×C4×C19—21no—
62C2×C4×C19—22no—
63C2×C4×C19—22no—
64C2×C4×C19—22no—
65C2×C4×C19—22no—
66C2×C4×C19—21no—
67C2×C4×C19—21no—
68C2×C4×C19—22no—
69C2×C4×C19C2×D412yes—
70C2×C4×C19C2×Q814yes—
71C2×Dic19—22no—
72C2×Dic19—22no—
73C2×Dic19—22no—
74C2×Dic19—22no—
75C2×Dic19—22no—
76C2×Dic19—22no—
77C2×Dic19—22no—
78C2×Dic19—22no—
79C2×Dic19C2×D414yes—
80C2×Dic19C2×Q814yes—
81C2×Dic19C2×Q814yes—
82C2×Dic19#4114yes—
83Dic38—216no—
84#2582—191nomaximal, Sylow
85C22×C19C22×D411yescharacteristic
86C22×C19C22×Q812yes—
87C22×C19C2×#4112yes—
88C22×C19H(5,𝔽2)11yescharacteristic
89C22×C192−1+411yescharacteristic
90C4×C19—24no—
91C4×C19—22no—
92C4×C19—42no—
93C4×C19—41no—
94C4×C19—41no—
95Dic19—24no—
96Dic19—42no—
97Dic19—42no—
98Dic19C22⋊Q818yes—
99C2×C4×Q8—192no—
100#398—191no—
101#398—192no—
102#398D1911yescharacteristic
103#391—192no—
104#391—192no—
105#389—192no—
106#389—192no—
107#384—191no—
108C2×C19C2×C22⋊Q812yes—
109C2×C19#53711yescharacteristic
110C2×C19#55712yes—
111C2×C19Q8211yescharacteristic
112C2×C19#55911yescharacteristic
113C22×Q8—192no—
114C4×Q8—388no—
115C2×C4⋊C4—192no—
116C2×C4⋊C4—192no—
117C2×C4⋊C4—192no—
118C2×C4⋊C4—192no—
119C2×C4⋊C4—191no—
120C2×C4⋊C4—192no—
121C2×C4⋊C4—191no—
122C2×C4⋊C4C2×D1912yes—
123C2×C4⋊C4C2×D1911yescharacteristic
124C2×C4⋊C4C2×D1911yescharacteristic
125C2×C42—191no—
126C2×C42—192no—
127C2×C42—192no—
128#95—192no—
129#95—192no—
130#95—192no—
131#95—191no—
132#95—192no—
133#95C2×D1912yes—
134#95C2×D1911yescharacteristic
135C19#258211yescharacteristic, complemented, Sylow
136C2×Q8—198no—
137C2×Q8—384no—
138C2×Q8—384no—
139C22×C4—192no—
140C22×C4—192no—
141C22×C4—192no—
142C22×C4—192no—
143C22×C4C22×D1911yescharacteristic
144C22×C4C22×D1911yescharacteristic
145C22×C4C22×D1912yes—
146C22×C4C22×D1911yescharacteristic
147C22×C4C22×D1912yes—
148C4⋊C4—24no—
149C4⋊C4—41no—
150C4⋊C4—41no—
151C4⋊C4—384no—
152C4⋊C4—384no—
153C4⋊C4—384no—
154C4⋊C4—384no—
155C4⋊C4—762no—
156C4⋊C4—761no—
157C4⋊C4—761no—
158C42—194no—
159C42—384no—
160C42—384no—
161C23C23×D1911yescharacteristic
162Q8—3816no—
163C2×C4—22no—
164C2×C4—21no—
165C2×C4—22no—
166C2×C4—21no—
167C2×C4—22no—
168C2×C4—21no—
169C2×C4—22no—
170C2×C4—21no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—194no—
175C2×C4—194no—
176C2×C4—194no—
177C2×C4—194no—
178C2×C4—382no—
179C2×C4—382no—
180C2×C4—382no—
181C2×C4—382no—
182C2×C4—382no—
183C2×C4—382no—
184C2×C4—382no—
185C2×C4—382no—
186C2×C4D4×D1912yes—
187C2×C4Q8×D1914yes—
188C22C2×D4×D1911yescharacteristic
189C22#1059743011yescharacteristic
190C22C2×Q8×D1912yes—
191C22#41×D1912yes—
192C22#1059743611yescharacteristic
193C4—22no—
194C4—24no—
195C4—42no—
196C4—41no—
197C4—41no—
198C4—198no—
199C4—384no—
200C4—762no—
201C4—762no—
202C2C22⋊Q8×D1912yes—
203C2#1192712111yescharacteristic
204C2#1192727112yes—
205C2#1192727411yescharacteristic
206C2#1192727811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, prime radical, cosocleC23×C19C24
FittingC19×#398C2
hypercenter#398D19
hypocenterC19#2582
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
43. C2×Dic38Q8semidirect
135. C19#2582semidirect

Maximal subgroups

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

subgroupindex
C2×#105973332
#119264772
#119264742
#119264482
#119264412
#119264392
#119264132
C19×#3982
#258219