Finite Group Databasebeta

← #14568566

Subgroups — #14568566

Order 2432.

900 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 900 conjugacy classes of subgroups — too many to draw. Only its 173 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×#10597375C212yesmaximal, complemented
2C2×#10597376C211yesmaximal, characteristic, complemented
3C2×#10597399C212yesmaximal, complemented
4#11926480C212yesmaximal, complemented
5#11926453C212yesmaximal, complemented
6#11926444C214yesmaximal, complemented
7C4×C22⋊Dic19C211yesmaximal, characteristic, complemented
8C22×C22⋊C4×C19C211yesmaximal, characteristic, complemented
9C25×C19C2211yescharacteristic
10C23×C4×C19C2211yescharacteristic
11C23×C4×C19C2211yescharacteristic
12C22×C22⋊D19C2212yes—
13C22×C22⋊D19C2214yes—
14C22×D76C2211yescharacteristic, complemented
15C2×C22⋊C4×C19—24no—
16C2×C22⋊C4×C19C2212yes—
17C2×C22⋊C4×C19C2212yes—
18#10597399—28no—
19C2×C22⋊Dic19C2214yes—
20C2×C22⋊Dic19C2212yes—
21#10597376—24no—
22#10597375—28no—
23C2×(C2×D19)⋊C4C2214yescomplemented
24C2×(C2×D19)⋊C4C2212yescomplemented
25C2×C4⋊Dic19C2211yescharacteristic, complemented
26C2×Dic19⋊C4C2214yescomplemented
27C2×C4×Dic19C2212yescomplemented
28C19⋊#95C2212yescomplemented
29C24×C19—22no—
30C24×C19—24no—
31C24×C19—24no—
32C24×C19—42no—
33C24×C19C2312yes—
34C24×C19C2311yescharacteristic
35C23×D19C2312yes—
36C22×C4×C19—22no—
37C22×C4×C19—24no—
38C22×C4×C19—42no—
39C22×C4×C19D414yescomplemented
40C22×C4×C19C2312yes—
41C22×C4×C19C2311yescharacteristic
42C22×C4×C19C2311yescharacteristic
43C2×C22⋊D19—24no—
44C2×C22⋊D19—24no—
45C2×C22⋊D19—24no—
46C2×C22⋊D19—28no—
47C2×C22⋊D19—28no—
48C2×C22⋊D19—44no—
49C22×Dic19C2312yes—
50C22×Dic19C2314yes—
51C2×D76—22no—
52C2×D76—42no—
53C22⋊C4×C19—24no—
54C22⋊C4×C19—24no—
55C22⋊Dic19—28no—
56C22⋊Dic19D418yescomplemented
57(C2×D19)⋊C4—24no—
58(C2×D19)⋊C4—28no—
59C4⋊Dic19—22no—
60Dic19⋊C4—28no—
61C4×Dic19—42no—
62C23×C19—22no—
63C23×C19—22no—
64C23×C19—28no—
65C23×C19—24no—
66C23×C19—22no—
67C23×C19—22no—
68C23×C19—24no—
69C23×C19—416no—
70C23×C19—44no—
71C23×C19—44no—
72C23×C19C2×D414yes—
73C23×C19C2×D412yes—
74C23×C19#4114yes—
75C23×C19C2411yescharacteristic
76C22×D19—22no—
77C22×D19—22no—
78C22×D19—22no—
79C22×D19—24no—
80C22×D19—24no—
81C2×C4×C19—22no—
82C2×C4×C19—22no—
83C2×C4×C19—24no—
84C2×C4×C19—22no—
85C2×C4×C19—44no—
86C2×C4×C19—44no—
87C2×C4×C19C2×D412yes—
88C2×C4×C19C2×D412yes—
89C22⋊D19—416no—
90C22⋊D19—48no—
91C2×Dic19—24no—
92C2×Dic19—24no—
93C2×Dic19—22no—
94C2×Dic19—22no—
95C2×Dic19—22no—
96C2×Dic19C2×D418yes—
97D76—44no—
98#2539—191nomaximal, Sylow
99C22×C19—22no—
100C22×C19—22no—
101C22×C19—28no—
102C22×C19—24no—
103C22×C19—28no—
104C22×C19—416no—
105C22×C19—42no—
106C22×C19—42no—
107C22×C19—44no—
108C22×C19#12714yes—
109C22×C19C22×D412yes—
110C22×C19C22×D411yescharacteristic
111C22×C19C2×#4112yes—
112C22×C19H(5,𝔽2)12yes—
113C2×D19—42no—
114C2×D19—42no—
115C2×D19—42no—
116C2×D19—44no—
117C2×D19—44no—
118C4×C19—22no—
119C4×C19—22no—
120C4×C19—42no—
121Dic19—28no—
122Dic19—42no—
123C2×#123—192no—
124C2×#121—191no—
125C2×#120—192no—
126C22×C22⋊C4D1911yescharacteristic, complemented
127#399—192no—
128#392—192no—
129#390—194no—
130C4×C22⋊C4—191no—
131C2×C19—24no—
132C2×C19—44no—
133C2×C19#52511yescharacteristic
134C2×C19C2×#12711yescharacteristic
135C2×C19#53411yescharacteristic
136C2×C19#54614yes—
137D19—82no—
138C25C2×D1911yescharacteristic
139C22×D4—192no—
140C22×D4—194no—
141C22×D4—191no—
142C23×C4C2×D1911yescharacteristic
143C23×C4C2×D1911yescharacteristic
144#123—388no—
145#121—384no—
146#120—388no—
147C2×C4⋊C4—191no—
148C2×C4⋊C4—194no—
149C2×C22⋊C4—24no—
150C2×C22⋊C4—192no—
151C2×C22⋊C4—194no—
152C2×C22⋊C4—192no—
153C2×C22⋊C4—194no—
154C2×C22⋊C4C2×D1912yes—
155C2×C22⋊C4C2×D1912yes—
156C2×C42—192no—
157#95—192no—
158C19#253911yescharacteristic, complemented, Sylow
159C24—24no—
160C24—22no—
161C24—24no—
162C24—42no—
163C24—192no—
164C24C22×D1912yes—
165C24C22×D1911yescharacteristic
166C2×D4—388no—
167C2×D4—388no—
168C2×D4—384no—
169C2×D4—384no—
170C2×D4—384no—
171C2×D4—382no—
172C2×D4—762no—
173C2×D4—764no—
174C22×C4—24no—
175C22×C4—22no—
176C22×C4—42no—
177C22×C4—194no—
178C22×C4—192no—
179C22×C4C22⋊D1914yescomplemented
180C22×C4C22×D1912yes—
181C22×C4C22×D1911yescharacteristic
182C22×C4C22×D1911yescharacteristic
183C4⋊C4—388no—
184C4⋊C4—382no—
185C22⋊C4—24no—
186C22⋊C4—24no—
187C22⋊C4—198no—
188C22⋊C4—388no—
189C22⋊C4—388no—
190C22⋊C4—384no—
191C42—762no—
192C23—22no—
193C23—22no—
194C23—28no—
195C23—22no—
196C23—24no—
197C23—24no—
198C23—22no—
199C23—416no—
200C23—44no—
201C23—44no—
202C23—384no—
203C23—382no—
204C23—382no—
205C23—384no—
206C23—382no—
207C23#6454114yes—
208C23D4×D1914yes—
209C23C2×C22⋊D1912yes—
210C23C23×D1911yescharacteristic
211D4—764no—
212D4—7616no—
213D4—768no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—24no—
217C2×C4—22no—
218C2×C4—44no—
219C2×C4—44no—
220C2×C4—198no—
221C2×C4—384no—
222C2×C4—384no—
223C2×C4—382no—
224C2×C4—382no—
225C2×C4—382no—
226C2×C4C2×C22⋊D1912yes—
227C2×C4C2×C22⋊D1912yes—
228C22—22no—
229C22—22no—
230C22—28no—
231C22—24no—
232C22—28no—
233C22—416no—
234C22—42no—
235C22—42no—
236C22—44no—
237C22—762no—
238C22—762no—
239C22—762no—
240C22—764no—
241C22—764no—
242C22#1059738614yes—
243C22C2×#6454112yes—
244C22C2×D4×D1912yes—
245C22#1059743012yes—
246C22C22×C22⋊D1911yescharacteristic
247C4—22no—
248C4—22no—
249C4—42no—
250C4—388no—
251C4—762no—
252C2—24no—
253C2—44no—
254C2—1522no—
255C2#1192705511yescharacteristic
256C2C2×#1059738611yescharacteristic
257C2#1192710311yescharacteristic
258C2#1192718414yes—
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC22×C22⋊C4×C19C2
hypercenterC22×C22⋊C4D19
hypocenterC19#2539
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×#10597375C2semidirect
2. C2×#10597376C2semidirect
3. C2×#10597399C2semidirect
4. #11926480C2semidirect
5. #11926453C2semidirect
6. #11926444C2semidirect
7. C4×C22⋊Dic19C2semidirect
8. C22×C22⋊C4×C19C2semidirect
14. C22×D76C22semidirect
23. C2×(C2×D19)⋊C4C22semidirect
24. C2×(C2×D19)⋊C4C22semidirect
25. C2×C4⋊Dic19C22semidirect
26. C2×Dic19⋊C4C22semidirect
27. C2×C4×Dic19C22semidirect
28. C19⋊#95C22semidirect
39. C22×C4×C19D4semidirect
56. C22⋊Dic19D4semidirect
126. C22×C22⋊C4D19semidirect
158. C19#2539semidirect
179. C22×C4C22⋊D19semidirect

Maximal subgroups

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

subgroupindex
C2×#105973752
C2×#105973762
C2×#105973992
#119264802
#119264532
#119264442
C4×C22⋊Dic192
C22×C22⋊C4×C192
#253919