Finite Group Databasebeta

← #14569739

Subgroups — #14569739

Order 2432.

804 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 804 conjugacy classes of subgroups — too many to draw. Only its 165 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×#10597376C211yesmaximal, characteristic, complemented
2C2×#10597385C214yesmaximal, complemented
3#11926480C212yesmaximal, complemented
4#11926479C212yesmaximal, complemented
5#11926453C212yesmaximal, complemented
6#11926452C212yesmaximal, complemented
7C2×C19⋊#95C211yesmaximal, characteristic, complemented
8C2×C19×#121C211yesmaximal, characteristic, complemented
9C22×D4×C19C2212yes—
10C22×D4×C19C2211yescharacteristic
11C23×C4×C19C2211yescharacteristic
12C22×C22⋊D19C2212yes—
13C22×C22⋊D19C2214yes—
14C23×Dic19C2212yes—
15C22×D76C2211yescharacteristic
16C19×#121—24no—
17C2×C4⋊C4×C19C2211yescharacteristic
18C2×C22⋊C4×C19C2212yes—
19C2×C22⋊Dic19C2214yes—
20#10597385—216no—
21#10597376—24no—
22C2×(C2×D19)⋊C4C2212yes—
23C2×(C2×D19)⋊C4C2214yes—
24C2×C4⋊Dic19C2211yescharacteristic
25C2×Dic19⋊C4C2214yes—
26C19⋊#95C2212yes—
27C19⋊#95C2212yes—
28C24×C19C2312yes—
29C24×C19C2311yescharacteristic
30C23×D19C2312yes—
31C2×D4×C19—28no—
32C2×D4×C19—24no—
33C2×D4×C19—22no—
34C2×D4×C19—42no—
35C22×C4×C19—42no—
36C22×C4×C19D414yescomplemented
37C22×C4×C19C2312yes—
38C22×C4×C19C2311yescharacteristic
39C22×C4×C19C2311yescharacteristic
40C2×C22⋊D19—24no—
41C2×C22⋊D19—28no—
42C2×C22⋊D19—28no—
43C2×C22⋊D19—44no—
44C2×C22⋊D19—44no—
45C22×Dic19—42no—
46C22×Dic19—42no—
47C22×Dic19D418yescomplemented
48C22×Dic19C2312yes—
49C22×Dic19C2314yes—
50C2×D76—22no—
51C2×D76—42no—
52C4⋊C4×C19—22no—
53C22⋊C4×C19—24no—
54C22⋊Dic19—28no—
55(C2×D19)⋊C4—24no—
56(C2×D19)⋊C4—28no—
57C4⋊Dic19—22no—
58Dic19⋊C4—28no—
59C23×C19—21no—
60C23×C19—22no—
61C23×C19—21no—
62C23×C19—24no—
63C23×C19—22no—
64C23×C19—22no—
65C23×C19—24no—
66C23×C19—22no—
67C23×C19C2×D414yes—
68C23×C19C2×D412yes—
69C23×C19C2411yescharacteristic
70C22×D19—22no—
71C22×D19—24no—
72C22×D19—24no—
73C22×D19—22no—
74C22×D19—22no—
75D4×C19—44no—
76D4×C19—48no—
77C2×C4×C19—22no—
78C2×C4×C19—22no—
79C2×C4×C19—24no—
80C2×C4×C19—22no—
81C2×C4×C19—44no—
82C2×C4×C19C2×D412yes—
83C2×C4×C19C2×D412yes—
84C22⋊D19—416no—
85C22⋊D19—48no—
86C2×Dic19—24no—
87C2×Dic19—24no—
88C2×Dic19—24no—
89C2×Dic19—22no—
90C2×Dic19—48no—
91C2×Dic19C2×D418yes—
92D76—44no—
93#2656—191nomaximal, Sylow
94C22×C19—24no—
95C22×C19—22no—
96C22×C19—24no—
97C22×C19—22no—
98C22×C19—42no—
99C22×C19—44no—
100C22×C19—42no—
101C22×C19—44no—
102C22×C19—42no—
103C22×C19#12714yes—
104C22×C19C22×D412yes—
105C22×C19C22×D411yescharacteristic
106C22×C19H(5,𝔽2)12yes—
107C22×C19H(5,𝔽2)11yescharacteristic
108C22×C192−1+411yescharacteristic
109C2×D19—42no—
110C2×D19—42no—
111C2×D19—44no—
112C2×D19—44no—
113C2×D19—42no—
114C4×C19—22no—
115C4×C19—22no—
116C4×C19—42no—
117Dic19—28no—
118Dic19—42no—
119C2×#121—194no—
120C2×#121—191no—
121C2×#121D1911yescharacteristic, complemented
122#399—192no—
123#399—192no—
124#392—192no—
125#392—192no—
126C2×#95—191no—
127C2×C19—24no—
128C2×C19—82no—
129C2×C19C2×#12711yescharacteristic
130C2×C19#53412yes—
131C2×C19#53411yescharacteristic
132C2×C19#53712yes—
133C2×C19#53711yescharacteristic
134D19—82no—
135C22×D4—192no—
136C22×D4—194no—
137C22×D4—191no—
138C22×D4C2×D1912yes—
139C22×D4C2×D1911yescharacteristic
140C23×C4—192no—
141C23×C4C2×D1911yescharacteristic
142#121—24no—
143#121—3816no—
144#121—384no—
145C2×C4⋊C4—194no—
146C2×C4⋊C4—191no—
147C2×C4⋊C4C2×D1911yescharacteristic
148C2×C22⋊C4—194no—
149C2×C22⋊C4—194no—
150C2×C22⋊C4—192no—
151C2×C22⋊C4C2×D1912yes—
152#95—192no—
153#95—192no—
154C19#265611yescharacteristic, complemented, Sylow
155C24—192no—
156C24C22×D1912yes—
157C24C22×D1911yescharacteristic
158C2×D4—28no—
159C2×D4—24no—
160C2×D4—22no—
161C2×D4—42no—
162C2×D4—388no—
163C2×D4—388no—
164C2×D4—384no—
165C2×D4—382no—
166C2×D4—762no—
167C2×D4—764no—
168C2×D4—764no—
169C22×C4—42no—
170C22×C4—194no—
171C22×C4—198no—
172C22×C4—192no—
173C22×C4—762no—
174C22×C4—762no—
175C22×C4C22⋊D1914yescomplemented
176C22×C4C22×D1912yes—
177C22×C4C22×D1911yescharacteristic
178C22×C4C22×D1911yescharacteristic
179C4⋊C4—22no—
180C4⋊C4—388no—
181C4⋊C4—382no—
182C22⋊C4—24no—
183C22⋊C4—388no—
184C22⋊C4—388no—
185C22⋊C4—384no—
186C23—22no—
187C23—21no—
188C23—21no—
189C23—24no—
190C23—24no—
191C23—22no—
192C23—22no—
193C23—22no—
194C23—384no—
195C23—384no—
196C23—382no—
197C23—382no—
198C23—382no—
199C23D4×D1914yes—
200C23C2×C22⋊D1912yes—
201C23C23×D1911yescharacteristic
202D4—44no—
203D4—48no—
204D4—764no—
205D4—7616no—
206D4—768no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—24no—
210C2×C4—22no—
211C2×C4—44no—
212C2×C4—198no—
213C2×C4—384no—
214C2×C4—384no—
215C2×C4—384no—
216C2×C4—382no—
217C2×C4—768no—
218C2×C4C2×C22⋊D1912yes—
219C2×C4C2×C22⋊D1912yes—
220C22—24no—
221C22—22no—
222C22—24no—
223C22—22no—
224C22—42no—
225C22—44no—
226C22—42no—
227C22—44no—
228C22—42no—
229C22—762no—
230C22—764no—
231C22—762no—
232C22—764no—
233C22—762no—
234C22#1059738614yes—
235C22C2×D4×D1912yes—
236C22#1059743012yes—
237C22#1059743511yescharacteristic
238C22#1059743611yescharacteristic
239C22C22×C22⋊D1911yescharacteristic
240C4—22no—
241C4—22no—
242C4—42no—
243C4—388no—
244C4—762no—
245C2—24no—
246C2—82no—
247C2—1522no—
248C2C2×#1059738611yescharacteristic
249C2#1192710212yes—
250C2#1192710311yescharacteristic
251C2#1192712112yes—
252C2#1192712211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC2×C19×#121C2
hypercenterC2×#121D19
hypocenterC19#2656
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C2×#10597376C2semidirect
2. C2×#10597385C2semidirect
3. #11926480C2semidirect
4. #11926479C2semidirect
5. #11926453C2semidirect
6. #11926452C2semidirect
7. C2×C19⋊#95C2semidirect
8. C2×C19×#121C2semidirect
36. C22×C4×C19D4semidirect
47. C22×Dic19D4semidirect
121. C2×#121D19semidirect
154. C19#2656semidirect
175. C22×C4C22⋊D19semidirect

Maximal subgroups

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

subgroupindex
C2×#105973762
C2×#105973852
#119264802
#119264792
#119264532
#119264522
C2×C19⋊#952
C2×C19×#1212
#265619