Finite Group Databasebeta

← #14571701

Subgroups — #14571701

Order 2432.

380 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 125 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×#10597335C212yesmaximal
2#11926486C212yesmaximal
3#11926485C212yesmaximal
4#11926478C212yesmaximal
5#11926477C212yesmaximal
6#11926477C212yesmaximal
7#11926474C211yesmaximal, characteristic
8#11926409C211yesmaximal, characteristic
9C19×#398C211yesmaximal, characteristic
10C2×C4⋊C4×C19C2212yes—
11C2×C4⋊C4×C19C2211yescharacteristic
12C2×C4⋊C4×C19C2211yescharacteristic
13C2×C4⋊Dic19C2212yes—
14C2×C4⋊Dic19C2211yescharacteristic
15C2×C4⋊Dic19C2211yescharacteristic
16C2×Dic19⋊C4C2212yes—
17C2×Dic19⋊C4C2212yes—
18C2×Dic19⋊C4C2212yes—
19C2×Dic19⋊C4C2212yes—
20C2×Dic19⋊C4C2212yes—
21C2×C4×Dic19C2211yescharacteristic
22#10597335—28no—
23C19×#95C2212yes—
24C19×#95C2211yescharacteristic
25C19⋊#95C2212yes—
26C19⋊#95C2212yes—
27C19⋊#95C2212yes—
28C19⋊#95C2211yescharacteristic
29C19⋊#95C2212yes—
30C19⋊#95C2212yes—
31C19⋊#95C2212yes—
32C22×C4×C19C2311yescharacteristic
33C22×C4×C19C2312yes—
34C22×C4×C19C2311yescharacteristic
35C22×C4×C19C2312yes—
36C22×C4×C19C2311yescharacteristic
37C22×Dic19C2312yes—
38C22×Dic19C2312yes—
39C22×Dic19C2312yes—
40C22×Dic19C2312yes—
41C4⋊C4×C19—24no—
42C4⋊C4×C19—41no—
43C4⋊C4×C19—41no—
44C4⋊Dic19—24no—
45C4⋊Dic19—41no—
46C4⋊Dic19—41no—
47Dic19⋊C4—24no—
48Dic19⋊C4—24no—
49Dic19⋊C4—24no—
50Dic19⋊C4—24no—
51Dic19⋊C4—42no—
52C4×Dic19D414yes—
53C23×C19C2411yescharacteristic
54C2×C4×C19—21no—
55C2×C4×C19—21no—
56C2×C4×C19—22no—
57C2×C4×C19—22no—
58C2×C4×C19—22no—
59C2×C4×C19—21no—
60C2×C4×C19—21no—
61C2×C4×C19—22no—
62C2×C4×C19—22no—
63C2×C4×C19—22no—
64C2×C4×C19—22no—
65C2×C4×C19—22no—
66C2×C4×C19C2×D412yes—
67C2×Dic19—22no—
68C2×Dic19—22no—
69C2×Dic19—22no—
70C2×Dic19—22no—
71C2×Dic19—22no—
72C2×Dic19—22no—
73C2×Dic19—22no—
74C2×Dic19—24no—
75C2×Dic19—22no—
76C2×Dic19—22no—
77C2×Dic19C2×D414yes—
78#2822—191nomaximal, Sylow
79C22×C19C22×D411yescharacteristic
80C22×C19H(5,𝔽2)11yescharacteristic
81C22×C192−1+412yes—
82C22×C192−1+412yes—
83C22×C192−1+411yescharacteristic
84C4×C19—22no—
85C4×C19—42no—
86C4×C19—42no—
87C4×C19—41no—
88C4×C19—41no—
89Dic19—24no—
90Dic19—42no—
91Dic19—42no—
92Dic19—42no—
93C2×#125—192no—
94#400—192no—
95#400—192no—
96#398—191no—
97#398—192no—
98#398—192no—
99#398—192no—
100#398D1911yescharacteristic
101#382—191no—
102C2×C19#53612yes—
103C2×C19#53711yescharacteristic
104C2×C19#56311yescharacteristic
105C2×C19#56311yescharacteristic
106C2×C19#56412yes—
107#125—388no—
108C2×C4⋊C4—192no—
109C2×C4⋊C4—192no—
110C2×C4⋊C4—192no—
111C2×C4⋊C4—192no—
112C2×C4⋊C4—192no—
113C2×C4⋊C4—191no—
114C2×C4⋊C4—192no—
115C2×C4⋊C4—191no—
116C2×C4⋊C4C2×D1912yes—
117C2×C4⋊C4C2×D1911yescharacteristic
118C2×C4⋊C4C2×D1911yescharacteristic
119C2×C42—191no—
120#95—192no—
121#95—192no—
122#95—192no—
123#95—192no—
124#95—192no—
125#95—192no—
126#95—191no—
127#95C2×D1912yes—
128#95C2×D1911yescharacteristic
129C19#282211yescharacteristic, complemented, Sylow
130C22×C4—192no—
131C22×C4—192no—
132C22×C4—192no—
133C22×C4—192no—
134C22×C4C22×D1911yescharacteristic
135C22×C4C22×D1911yescharacteristic
136C22×C4C22×D1912yes—
137C22×C4C22×D1912yes—
138C22×C4C22×D1911yescharacteristic
139C4⋊C4—24no—
140C4⋊C4—41no—
141C4⋊C4—41no—
142C4⋊C4—384no—
143C4⋊C4—384no—
144C4⋊C4—384no—
145C4⋊C4—384no—
146C4⋊C4—384no—
147C4⋊C4—762no—
148C4⋊C4—761no—
149C4⋊C4—761no—
150C42—194no—
151C23C23×D1911yescharacteristic
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—22no—
155C2×C4—22no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—22no—
164C2×C4—194no—
165C2×C4—382no—
166C2×C4—382no—
167C2×C4—382no—
168C2×C4—382no—
169C2×C4—382no—
170C2×C4—382no—
171C2×C4—382no—
172C2×C4—384no—
173C2×C4—382no—
174C2×C4—382no—
175C2×C4D4×D1912yes—
176C22C2×D4×D1911yescharacteristic
177C22#1059743011yescharacteristic
178C22#1059743312yes—
179C22#1059743612yes—
180C22#1059743611yescharacteristic
181C4—22no—
182C4—41no—
183C4—41no—
184C4—42no—
185C4—42no—
186C4—384no—
187C4—762no—
188C4—762no—
189C4—762no—
190C2#1192711712yes—
191C2#1192712111yescharacteristic
192C2#1192729311yescharacteristic
193C2#1192729711yescharacteristic
194C2C19⋊#56412yes—
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, prime radical, cosocleC23×C19C24
FittingC19×#398C2
hypercenter#398D19
hypocenterC19#2822
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
129. C19#2822semidirect

Maximal subgroups

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

subgroupindex
C2×#105973352
#119264862
#119264852
#119264782
#119264772
#119264742
#119264092
C19×#3982
#282219