Finite Group Databasebeta

← #14571621

Subgroups — #14571621

Order 2432.

368 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 137 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#11926486C212yesmaximal
2#11926478C212yesmaximal
3#11926477C212yesmaximal
4#11926451C211yesmaximal, characteristic
5#11926451C211yesmaximal, characteristic
6#11926441C212yesmaximal
7#11926428C212yesmaximal
8#11926427C212yesmaximal
9C19×#391C211yesmaximal, characteristic
10C22×Q8×C19C2211yescharacteristic
11C2×C4⋊C4×C19C2211yescharacteristic
12C2×C42×C19C2211yescharacteristic
13C2×C4⋊Dic19C2212yes—
14C2×C4⋊Dic19C2211yescharacteristic
15C2×C4⋊Dic19C2211yescharacteristic
16C2×Dic19⋊C4C2212yes—
17C2×Dic19⋊C4C2212yes—
18C2×Dic19⋊C4C2212yes—
19C2×Dic19⋊C4C2212yes—
20C2×C4×Dic19C2211yescharacteristic
21C2×C4×Dic19C2211yescharacteristic
22C19×#95C2212yes—
23C19×#95C2212yes—
24C19⋊#95C2212yes—
25C19⋊#95C2212yes—
26C19⋊#95C2212yes—
27C19⋊#95C2212yes—
28C19⋊#95C2212yes—
29C19⋊#95C2212yes—
30C19⋊#95C2212yes—
31C2×Q8×C19—41no—
32C2×Q8×C19—41no—
33C2×Q8×C19Q814yes—
34C22×C4×C19C2312yes—
35C22×C4×C19C2312yes—
36C22×C4×C19C2311yescharacteristic
37C22×C4×C19C2311yescharacteristic
38C22×C4×C19C2311yescharacteristic
39C22×Dic19C2312yes—
40C22×Dic19C2312yes—
41C22×Dic19C2312yes—
42C22×Dic19C2312yes—
43C4⋊C4×C19—41no—
44C42×C19—41no—
45C4⋊Dic19—24no—
46C4⋊Dic19—41no—
47C4⋊Dic19—41no—
48Dic19⋊C4—24no—
49Dic19⋊C4—24no—
50Dic19⋊C4—42no—
51Dic19⋊C4—42no—
52C4×Dic19—41no—
53C4×Dic19—41no—
54C23×C19C2411yescharacteristic
55Q8×C19—44no—
56C2×C4×C19—21no—
57C2×C4×C19—21no—
58C2×C4×C19—21no—
59C2×C4×C19—21no—
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—22no—
67C2×C4×C19—22no—
68C2×C4×C19C2×Q812yes—
69C2×C4×C19C2×Q812yes—
70C2×C4×C19C2×Q812yes—
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×Dic19—22no—
80C2×Dic19—24no—
81C2×Dic19#4114yes—
82#2809—191nomaximal, Sylow
83C22×C19C22×Q811yescharacteristic
84C22×C19C2×#4112yes—
85C22×C19H(5,𝔽2)11yescharacteristic
86C22×C19H(5,𝔽2)11yescharacteristic
87C22×C192−1+412yes—
88C4×C19—22no—
89C4×C19—22no—
90C4×C19—22no—
91C4×C19—42no—
92C4×C19—42no—
93Dic19—24no—
94Dic19—42no—
95Dic19—42no—
96Dic19—42no—
97#400—192no—
98#398—192no—
99#398—192no—
100#391—191no—
101#391—191no—
102#391D1911yescharacteristic
103#389—192no—
104#387—192no—
105#387—192no—
106C2×C19#53912yes—
107C2×C19#54311yescharacteristic
108C2×C19#55511yescharacteristic
109C2×C19#55712yes—
110C2×C19#56311yescharacteristic
111C22×Q8C2×D1911yescharacteristic
112C2×C4⋊C4—192no—
113C2×C4⋊C4—192no—
114C2×C4⋊C4—192no—
115C2×C4⋊C4—192no—
116C2×C4⋊C4—191no—
117C2×C4⋊C4—191no—
118C2×C4⋊C4—192no—
119C2×C4⋊C4C2×D1911yescharacteristic
120C2×C42—191no—
121C2×C42—191no—
122C2×C42C2×D1911yescharacteristic
123#95—192no—
124#95—192no—
125#95—192no—
126#95—192no—
127#95—192no—
128#95—192no—
129#95—192no—
130#95C2×D1912yes—
131#95C2×D1912yes—
132C19#280911yescharacteristic, complemented, Sylow
133C2×Q8—41no—
134C2×Q8—41no—
135C2×Q8Dic3814yes—
136C22×C4—192no—
137C22×C4—192no—
138C22×C4—192no—
139C22×C4—192no—
140C22×C4C22×D1912yes—
141C22×C4C22×D1912yes—
142C22×C4C22×D1911yescharacteristic
143C22×C4C22×D1911yescharacteristic
144C22×C4C22×D1911yescharacteristic
145C4⋊C4—41no—
146C4⋊C4—384no—
147C4⋊C4—384no—
148C4⋊C4—384no—
149C4⋊C4—762no—
150C4⋊C4—762no—
151C4⋊C4—761no—
152C4⋊C4—761no—
153C42—41no—
154C42—761no—
155C42—761no—
156C23C23×D1911yescharacteristic
157Q8—44no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—22no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—22no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—194no—
171C2×C4—382no—
172C2×C4—382no—
173C2×C4—382no—
174C2×C4—382no—
175C2×C4—382no—
176C2×C4—382no—
177C2×C4—384no—
178C2×C4—382no—
179C2×C4—382no—
180C2×C4—382no—
181C2×C4C2×Dic3812yes—
182C2×C4C2×Dic3812yes—
183C2×C4C2×Dic3812yes—
184C22C22×Dic3811yescharacteristic
185C22#1059743011yescharacteristic
186C22#1059743011yescharacteristic
187C22#1059743312yes—
188C22#41×D1912yes—
189C4—22no—
190C4—22no—
191C4—22no—
192C4—42no—
193C4—42no—
194C4—384no—
195C4—762no—
196C4—762no—
197C4—762no—
198C2#1192714012yes—
199C2#1192717011yescharacteristic
200C2#1192725611yescharacteristic
201C2#1192727012yes—
202C2#1192729311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, prime radical, cosocleC23×C19C24
FittingC19×#391C2
hypercenter#391D19
hypocenterC19#2809
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
132. C19#2809semidirect

Maximal subgroups

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

subgroupindex
#119264862
#119264782
#119264772
#119264512
#119264412
#119264282
#119264272
C19×#3912
#280919