Finite Group Databasebeta

← #14568793

Subgroups — #14568793

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×#10597370C211yesmaximal, characteristic, complemented
2#11926469C212yesmaximal, complemented
3#11926456C212yesmaximal, complemented
4#11926438C214yesmaximal, complemented
5#11926407C212yesmaximal, complemented
6#11926400C212yesmaximal
7C4×C22⋊Dic19C211yesmaximal, characteristic, complemented
8C22×C22⋊C4×C19C211yesmaximal, characteristic
9C25×C19C2211yescharacteristic
10C23×C4×C19C2211yescharacteristic
11C23×C4×C19C2211yescharacteristic
12C22×Dic38C2211yescharacteristic, complemented
13C2×C22⋊C4×C19—24no—
14C2×C22⋊C4×C19C2212yes—
15C2×C22⋊C4×C19C2212yes—
16C2×C22⋊Dic19C2212yes—
17C2×C22⋊Dic19C2212yes—
18C2×C22⋊Dic19C2214yes—
19C2×C22⋊Dic19C2214yes—
20C2×C4⋊Dic19C2211yescharacteristic, complemented
21#10597370—24no—
22C2×Dic19⋊C4C2212yescomplemented
23C2×C4×Dic19C2212yescomplemented
24C19⋊#95C2212yescomplemented
25C19⋊#95C2214yescomplemented
26C19⋊#95C2214yescomplemented
27C24×C19—22no—
28C24×C19—24no—
29C24×C19—24no—
30C24×C19—42no—
31C24×C19C2312yes—
32C24×C19C2311yescharacteristic
33C22×C4×C19—22no—
34C22×C4×C19—24no—
35C22×C4×C19—42no—
36C22×C4×C19D414yes—
37C22×C4×C19C2312yes—
38C22×C4×C19C2311yescharacteristic
39C22×C4×C19C2311yescharacteristic
40C22×Dic19C2312yes—
41C22×Dic19C2314yes—
42C22×Dic19C2312yes—
43C2×Dic38—22no—
44C2×Dic38—42no—
45C22⋊C4×C19—24no—
46C22⋊C4×C19—24no—
47C22⋊Dic19—24no—
48C22⋊Dic19—28no—
49C22⋊Dic19—24no—
50C22⋊Dic19—44no—
51C4⋊Dic19—22no—
52Dic19⋊C4—24no—
53C4×Dic19—42no—
54C23×C19—22no—
55C23×C19—22no—
56C23×C19—28no—
57C23×C19—22no—
58C23×C19—22no—
59C23×C19—24no—
60C23×C19—24no—
61C23×C19—416no—
62C23×C19—44no—
63C23×C19—44no—
64C23×C19C2×D412yes—
65C23×C19#4114yes—
66C23×C19#4114yes—
67C23×C19C2411yescharacteristic
68C2×C4×C19—22no—
69C2×C4×C19—22no—
70C2×C4×C19—22no—
71C2×C4×C19—24no—
72C2×C4×C19—44no—
73C2×C4×C19—44no—
74C2×C4×C19C2×D412yes—
75C2×C4×C19C2×D412yes—
76C2×Dic19—22no—
77C2×Dic19—22no—
78C2×Dic19—24no—
79C2×Dic19—24no—
80C2×Dic19—24no—
81C2×Dic19—24no—
82C2×Dic19—24no—
83Dic38—44no—
84#2561—191nomaximal, Sylow
85C22×C19—22no—
86C22×C19—22no—
87C22×C19—28no—
88C22×C19—24no—
89C22×C19—28no—
90C22×C19—416no—
91C22×C19—42no—
92C22×C19—42no—
93C22×C19—44no—
94C22×C19#12414yes—
95C22×C19C22×D411yescharacteristic
96C22×C19C2×#4112yes—
97C22×C19C2×#4112yes—
98C22×C19H(5,𝔽2)12yes—
99C4×C19—22no—
100C4×C19—22no—
101C4×C19—42no—
102Dic19—42no—
103Dic19—42no—
104Dic19—44no—
105C2×C22⋊Q8—191no—
106C22×C22⋊C4D1911yescharacteristic
107#397—192no—
108#393—192no—
109#388—194no—
110#381—192no—
111#379—192no—
112C4×C22⋊C4—191no—
113C2×C19—24no—
114C2×C19—44no—
115C2×C19#52511yescharacteristic
116C2×C19C2×#12411yescharacteristic
117C2×C19#53411yescharacteristic
118C2×C19#55114yes—
119C25C2×D1911yescharacteristic
120C22×Q8—191no—
121C23×C4C2×D1911yescharacteristic
122C23×C4C2×D1911yescharacteristic
123C22⋊Q8—384no—
124C2×C4⋊C4—192no—
125C2×C4⋊C4—191no—
126C2×C22⋊C4—24no—
127C2×C22⋊C4—192no—
128C2×C22⋊C4—192no—
129C2×C22⋊C4—194no—
130C2×C22⋊C4—194no—
131C2×C22⋊C4C2×D1912yes—
132C2×C22⋊C4C2×D1912yes—
133C2×C42—192no—
134#95—192no—
135#95—194no—
136#95—194no—
137C19#256111yescharacteristic, complemented, Sylow
138C24—24no—
139C24—22no—
140C24—24no—
141C24—42no—
142C24C22×D1912yes—
143C24C22×D1911yescharacteristic
144C2×Q8—382no—
145C2×Q8—762no—
146C22×C4—24no—
147C22×C4—22no—
148C22×C4—42no—
149C22×C4—194no—
150C22×C4—192no—
151C22×C4—192no—
152C22×C4C22⋊D1914yes—
153C22×C4C22×D1912yes—
154C22×C4C22×D1911yescharacteristic
155C22×C4C22×D1911yescharacteristic
156C4⋊C4—384no—
157C4⋊C4—382no—
158C22⋊C4—24no—
159C22⋊C4—24no—
160C22⋊C4—388no—
161C22⋊C4—384no—
162C22⋊C4—384no—
163C22⋊C4—764no—
164C42—762no—
165C23—22no—
166C23—22no—
167C23—28no—
168C23—22no—
169C23—24no—
170C23—24no—
171C23—22no—
172C23—416no—
173C23—44no—
174C23—44no—
175C23#6454114yes—
176C23#6454314yes—
177C23C2×C22⋊D1912yes—
178C23C23×D1911yescharacteristic
179Q8—764no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—24no—
183C2×C4—22no—
184C2×C4—44no—
185C2×C4—44no—
186C2×C4—384no—
187C2×C4—384no—
188C2×C4—384no—
189C2×C4—384no—
190C2×C4—384no—
191C2×C4—382no—
192C2×C4—382no—
193C2×C4C2×C22⋊D1912yes—
194C2×C4C2×C22⋊D1912yes—
195C22—22no—
196C22—22no—
197C22—28no—
198C22—24no—
199C22—28no—
200C22—416no—
201C22—42no—
202C22—42no—
203C22—44no—
204C22#1059738214yes—
205C22C2×#6454112yes—
206C22C2×#6454312yes—
207C22#1059743012yes—
208C22C22×C22⋊D1911yescharacteristic
209C4—22no—
210C4—22no—
211C4—42no—
212C4—762no—
213C4—762no—
214C4—764no—
215C2—24no—
216C2—44no—
217C2#1192705511yescharacteristic
218C2C2×#1059738211yescharacteristic
219C2#1192710311yescharacteristic
220C2#1192722014yes—
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC22×C22⋊C4×C19C2
prime radicalC25×C19C22
hypercenterC22×C22⋊C4D19
hypocenterC19#2561
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×#10597370C2semidirect
2. #11926469C2semidirect
3. #11926456C2semidirect
4. #11926438C2semidirect
5. #11926407C2semidirect
7. C4×C22⋊Dic19C2semidirect
12. C22×Dic38C22semidirect
20. C2×C4⋊Dic19C22semidirect
22. C2×Dic19⋊C4C22semidirect
23. C2×C4×Dic19C22semidirect
24. C19⋊#95C22semidirect
25. C19⋊#95C22semidirect
26. C19⋊#95C22semidirect
137. C19#2561semidirect

Maximal subgroups

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

subgroupindex
C2×#105973702
#119264692
#119264562
#119264382
#119264072
#119264002
C4×C22⋊Dic192
C22×C22⋊C4×C192
#256119