Finite Group Databasebeta

← #14567909

Subgroups — #14567909

Order 2432.

672 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 672 conjugacy classes of subgroups — too many to draw. Only its 157 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×#10597372C211yesmaximal, characteristic, complemented
2#11926480C212yesmaximal, complemented
3#11926469C212yesmaximal, complemented
4#11926432C214yesmaximal, complemented
5#11926417C212yesmaximal, complemented
6#11926407C211yesmaximal, characteristic, complemented
7#11926400C212yesmaximal
8C22×C22⋊C4×C19C211yesmaximal, characteristic
9C25×C19C2211yescharacteristic
10C23×C4×C19C2211yescharacteristic
11C23×C4×C19C2211yescharacteristic
12C2×C22⋊C4×C19—24no—
13C2×C22⋊C4×C19C2212yes—
14C2×C22⋊C4×C19C2212yes—
15C2×C22⋊Dic19C2212yes—
16C2×C22⋊Dic19C2212yes—
17C2×C22⋊Dic19C2214yes—
18C2×C22⋊Dic19C2214yes—
19#10597372—24no—
20C2×C4⋊Dic19C2211yescharacteristic, complemented
21C2×C4⋊Dic19C2211yescharacteristic, complemented
22C2×Dic19⋊C4C2214yescomplemented
23C2×C4×Dic19C2212yescomplemented
24C19⋊#95C2212yescomplemented
25C19⋊#95C2212yescomplemented
26C19⋊#95C2214yescomplemented
27C24×C19—22no—
28C24×C19—24no—
29C24×C19—24no—
30C24×C19—42no—
31C24×C19C2312yes—
32C24×C19C2311yescharacteristic
33C22×C4×C19—24no—
34C22×C4×C19—22no—
35C22×C4×C19—42no—
36C22×C4×C19D414yes—
37C22×C4×C19C2312yes—
38C22×C4×C19C2311yescharacteristic
39C22×C4×C19C2311yescharacteristic
40C22×Dic19C2314yes—
41C22×Dic19C2312yes—
42C22×Dic19C2312yes—
43C22⋊C4×C19—24no—
44C22⋊C4×C19—24no—
45C22⋊Dic19—24no—
46C22⋊Dic19—28no—
47C22⋊Dic19—24no—
48C22⋊Dic19—44no—
49C4⋊Dic19—22no—
50C4⋊Dic19—22no—
51Dic19⋊C4—44no—
52C4×Dic19—24no—
53C23×C19—22no—
54C23×C19—22no—
55C23×C19—28no—
56C23×C19—22no—
57C23×C19—22no—
58C23×C19—24no—
59C23×C19—24no—
60C23×C19—416no—
61C23×C19—44no—
62C23×C19—44no—
63C23×C19C2×D412yes—
64C23×C19#4114yes—
65C23×C19#4114yes—
66C23×C19C2411yescharacteristic
67C2×C4×C19—28no—
68C2×C4×C19—22no—
69C2×C4×C19—22no—
70C2×C4×C19—22no—
71C2×C4×C19—24no—
72C2×C4×C19—44no—
73C2×C4×C19C2×D412yes—
74C2×C4×C19C2×D412yes—
75C2×Dic19—22no—
76C2×Dic19—22no—
77C2×Dic19—24no—
78C2×Dic19—24no—
79C2×Dic19—24no—
80C2×Dic19—24no—
81C2×Dic19—24no—
82#2482—191nomaximal, Sylow
83C22×C19—22no—
84C22×C19—22no—
85C22×C19—28no—
86C22×C19—24no—
87C22×C19—28no—
88C22×C19—416no—
89C22×C19—42no—
90C22×C19—42no—
91C22×C19—44no—
92C22×C19#12314yes—
93C22×C19C22×D411yescharacteristic
94C22×C19C2×#4112yes—
95C22×C19C2×#4112yes—
96C22×C19H(5,𝔽2)12yes—
97C4×C19—22no—
98C4×C19—22no—
99C4×C19—42no—
100Dic19—42no—
101Dic19—42no—
102Dic19—44no—
103C2×#117—191no—
104C22×C22⋊C4D1911yescharacteristic
105#399—192no—
106#397—192no—
107#388—194no—
108#385—192no—
109#381—191no—
110#379—192no—
111C2×C19—24no—
112C2×C19—44no—
113C2×C19C2×#12311yescharacteristic
114C2×C19#52511yescharacteristic
115C2×C19#53511yescharacteristic
116C2×C19#55114yes—
117C25C2×D1911yescharacteristic
118C23×C4C2×D1911yescharacteristic
119C23×C4C2×D1911yescharacteristic
120#117—384no—
121C2×C4⋊C4—191no—
122C2×C4⋊C4—191no—
123C2×C4⋊C4—194no—
124C2×C22⋊C4—24no—
125C2×C22⋊C4—192no—
126C2×C22⋊C4—192no—
127C2×C22⋊C4—194no—
128C2×C22⋊C4—194no—
129C2×C22⋊C4C2×D1912yes—
130C2×C22⋊C4C2×D1912yes—
131C2×C42—192no—
132#95—192no—
133#95—192no—
134#95—194no—
135C19#248211yescharacteristic, complemented, Sylow
136C24—24no—
137C24—22no—
138C24—24no—
139C24—42no—
140C24C22×D1912yes—
141C24C22×D1911yescharacteristic
142C22×C4—24no—
143C22×C4—22no—
144C22×C4—42no—
145C22×C4—194no—
146C22×C4—192no—
147C22×C4—192no—
148C22×C4C22⋊D1914yes—
149C22×C4C22×D1912yes—
150C22×C4C22×D1911yescharacteristic
151C22×C4C22×D1911yescharacteristic
152C4⋊C4—382no—
153C4⋊C4—382no—
154C4⋊C4—764no—
155C22⋊C4—24no—
156C22⋊C4—24no—
157C22⋊C4—388no—
158C22⋊C4—384no—
159C22⋊C4—384no—
160C22⋊C4—764no—
161C42—384no—
162C23—22no—
163C23—22no—
164C23—28no—
165C23—22no—
166C23—24no—
167C23—24no—
168C23—22no—
169C23—416no—
170C23—44no—
171C23—44no—
172C23#6454114yes—
173C23#6454314yes—
174C23C2×C22⋊D1912yes—
175C23C23×D1911yescharacteristic
176C2×C4—28no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—24no—
180C2×C4—22no—
181C2×C4—44no—
182C2×C4—384no—
183C2×C4—384no—
184C2×C4—384no—
185C2×C4—384no—
186C2×C4—384no—
187C2×C4—382no—
188C2×C4—382no—
189C2×C4C2×C22⋊D1912yes—
190C2×C4C2×C22⋊D1912yes—
191C22—22no—
192C22—22no—
193C22—28no—
194C22—24no—
195C22—28no—
196C22—416no—
197C22—42no—
198C22—42no—
199C22—44no—
200C22#1059738114yes—
201C22C2×#6454112yes—
202C22C2×#6454312yes—
203C22#1059743012yes—
204C22C22×C22⋊D1911yescharacteristic
205C4—22no—
206C4—22no—
207C4—42no—
208C4—762no—
209C4—762no—
210C4—764no—
211C2—24no—
212C2—44no—
213C2C2×#1059738111yescharacteristic
214C2#1192705511yescharacteristic
215C2#1192711111yescharacteristic
216C2#1192722014yes—
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC22×C22⋊C4×C19C2
prime radicalC25×C19C22
hypercenterC22×C22⋊C4D19
hypocenterC19#2482
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#10597372C2semidirect
2. #11926480C2semidirect
3. #11926469C2semidirect
4. #11926432C2semidirect
5. #11926417C2semidirect
6. #11926407C2semidirect
20. C2×C4⋊Dic19C22semidirect
21. C2×C4⋊Dic19C22semidirect
22. C2×Dic19⋊C4C22semidirect
23. C2×C4×Dic19C22semidirect
24. C19⋊#95C22semidirect
25. C19⋊#95C22semidirect
26. C19⋊#95C22semidirect
135. C19#2482semidirect

Maximal subgroups

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

subgroupindex
C2×#105973722
#119264802
#119264692
#119264322
#119264172
#119264072
#119264002
C22×C22⋊C4×C192
#248219