Finite Group Databasebeta

← #14570664

Subgroups — #14570664

Order 2432.

456 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 149 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×#10597334C212yesmaximal
2#11926474C211yesmaximal, characteristic
3#11926465C212yesmaximal
4#11926464C212yesmaximal
5#11926449C211yesmaximal, characteristic
6#11926439C212yesmaximal
7#11926431C212yesmaximal
8#11926426C212yesmaximal
9C19×#398C211yesmaximal, characteristic
10C22×Dic38C2212yes—
11C22×Dic38C2211yescharacteristic
12C2×C4⋊C4×C19C2212yes—
13C2×C4⋊C4×C19C2211yescharacteristic
14C2×C4⋊C4×C19C2211yescharacteristic
15C2×C4⋊Dic19C2212yes—
16C2×C4⋊Dic19C2211yescharacteristic
17C2×Dic19⋊C4C2212yes—
18C2×Dic19⋊C4C2212yes—
19C2×Dic19⋊C4C2212yes—
20C2×Dic19⋊C4C2212yes—
21C2×C4×Dic19C2212yes—
22C2×C4×Dic19C2211yescharacteristic
23#10597334—28no—
24C19×#95C2212yes—
25C19×#95C2211yescharacteristic
26C19⋊#95C2211yescharacteristic
27C19⋊#95C2212yes—
28C19⋊#95C2212yes—
29C19⋊#95C2212yes—
30C19⋊#95C2212yes—
31C19⋊#95C2212yes—
32C22×C4×C19C2312yes—
33C22×C4×C19C2311yescharacteristic
34C22×C4×C19C2311yescharacteristic
35C22×C4×C19C2311yescharacteristic
36C22×C4×C19C2312yes—
37C22×Dic19C2312yes—
38C22×Dic19C2312yes—
39C22×Dic19C2312yes—
40C22×Dic19C2312yes—
41C2×Dic38—24no—
42C2×Dic38—41no—
43C2×Dic38—41no—
44C2×Dic38—42no—
45C2×Dic38—42no—
46C2×Dic38D414yes—
47C4⋊C4×C19—24no—
48C4⋊C4×C19—41no—
49C4⋊C4×C19—41no—
50C4⋊Dic19—24no—
51C4⋊Dic19—41no—
52Dic19⋊C4—24no—
53Dic19⋊C4—24no—
54Dic19⋊C4—42no—
55Dic19⋊C4Q818yescomplemented
56C4×Dic19—24no—
57C4×Dic19—41no—
58C23×C19C2411yescharacteristic
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—21no—
66C2×C4×C19—21no—
67C2×C4×C19—22no—
68C2×C4×C19—22no—
69C2×C4×C19—22no—
70C2×C4×C19C2×D412yes—
71C2×C4×C19C2×Q814yes—
72C2×Dic19—22no—
73C2×Dic19—22no—
74C2×Dic19—22no—
75C2×Dic19—22no—
76C2×Dic19—22no—
77C2×Dic19—22no—
78C2×Dic19—22no—
79C2×Dic19—22no—
80C2×Dic19—22no—
81C2×Dic19C2×D414yes—
82C2×Dic19C2×Q814yes—
83C2×Dic19C2×Q814yes—
84Dic38—44no—
85Dic38—48no—
86#2734—191nomaximal, Sylow
87C22×C19C22×D411yescharacteristic
88C22×C19C22×Q812yes—
89C22×C19H(5,𝔽2)11yescharacteristic
90C22×C19H(5,𝔽2)11yescharacteristic
91C22×C192−1+412yes—
92C4×C19—22no—
93C4×C19—24no—
94C4×C19—42no—
95C4×C19—41no—
96C4×C19—41no—
97Dic19—24no—
98Dic19—24no—
99Dic19—24no—
100Dic19—42no—
101C2×C4⋊Q8—192no—
102#398—191no—
103#398D1911yescharacteristic
104#395—192no—
105#395—192no—
106#391—191no—
107#389—192no—
108#387—192no—
109#387—192no—
110C2×C19#53411yescharacteristic
111C2×C19#54412yes—
112C2×C19D4×Q812yes—
113C2×C19Q8211yescharacteristic
114C2×C19#56311yescharacteristic
115C22×Q8—191no—
116C22×Q8—192no—
117C4⋊Q8—388no—
118C2×C4⋊C4—192no—
119C2×C4⋊C4—192no—
120C2×C4⋊C4—192no—
121C2×C4⋊C4—192no—
122C2×C4⋊C4—192no—
123C2×C4⋊C4—191no—
124C2×C4⋊C4C2×D1912yes—
125C2×C4⋊C4C2×D1911yescharacteristic
126C2×C4⋊C4C2×D1911yescharacteristic
127C2×C42—192no—
128C2×C42—191no—
129#95—191no—
130#95—192no—
131#95—192no—
132#95—192no—
133#95—192no—
134#95—192no—
135#95C2×D1911yescharacteristic
136#95C2×D1912yes—
137C19#273411yescharacteristic, complemented, Sylow
138C2×Q8—194no—
139C2×Q8—384no—
140C2×Q8—761no—
141C2×Q8—761no—
142C2×Q8—762no—
143C2×Q8—762no—
144C22×C4—192no—
145C22×C4—192no—
146C22×C4—192no—
147C22×C4—192no—
148C22×C4C22×D1911yescharacteristic
149C22×C4C22×D1911yescharacteristic
150C22×C4C22×D1912yes—
151C22×C4C22×D1911yescharacteristic
152C22×C4C22×D1912yes—
153C4⋊C4—24no—
154C4⋊C4—41no—
155C4⋊C4—41no—
156C4⋊C4—198no—
157C4⋊C4—384no—
158C4⋊C4—384no—
159C4⋊C4—384no—
160C4⋊C4—762no—
161C4⋊C4—761no—
162C42—384no—
163C42—761no—
164C23C23×D1911yescharacteristic
165Q8—764no—
166Q8—768no—
167C2×C4—22no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—21no—
173C2×C4—21no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—194no—
179C2×C4—194no—
180C2×C4—194no—
181C2×C4—382no—
182C2×C4—382no—
183C2×C4—382no—
184C2×C4—382no—
185C2×C4—382no—
186C2×C4—382no—
187C2×C4—382no—
188C2×C4—382no—
189C2×C4—382no—
190C2×C4D4×D1912yes—
191C2×C4Q8×D1914yes—
192C22C2×D4×D1911yescharacteristic
193C22#1059743011yescharacteristic
194C22C2×Q8×D1912yes—
195C22#1059743511yescharacteristic
196C22#1059743612yes—
197C4—22no—
198C4—24no—
199C4—41no—
200C4—41no—
201C4—42no—
202C4—384no—
203C4—384no—
204C4—384no—
205C4—762no—
206C2#1192710211yescharacteristic
207C2#1192717412yes—
208C2#1192720712yes—
209C2#1192727411yescharacteristic
210C2#1192729711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, prime radical, cosocleC23×C19C24
FittingC19×#398C2
hypercenter#398D19
hypocenterC19#2734
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
55. Dic19⋊C4Q8semidirect
137. C19#2734semidirect

Maximal subgroups

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

subgroupindex
C2×#105973342
#119264742
#119264652
#119264642
#119264492
#119264392
#119264312
#119264262
C19×#3982
#273419