Finite Group Databasebeta

← #14566958

Subgroups — #14566958

Order 2432.

1116 conjugacy classes of subgroups; only the 197 normal subgroups are shown.

normal subgroups only

This group has 1116 conjugacy classes of subgroups — too many to draw. Only its 197 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×#10597381C212yesmaximal, complemented
2C22×C22⋊Dic19C211yesmaximal, characteristic, complemented
3#11926458C214yesmaximal, complemented
4#11926424C212yesmaximal, complemented
5#11926417C212yesmaximal, complemented
6#11926400C211yesmaximal, characteristic, complemented
7#11926400C212yesmaximal, complemented
8C23×D4×C19C211yesmaximal, characteristic
9C25×C19C2211yescharacteristic
10C25×C19C2211yescharacteristic
11C22×D4×C19—24no—
12C22×D4×C19—28no—
13C22×D4×C19C2212yes—
14C22×D4×C19C2212yes—
15C23×C4×C19C2211yescharacteristic
16C23×Dic19C2211yescharacteristic, complemented
17C23×Dic19C2211yescharacteristic, complemented
18C2×C22⋊Dic19—24no—
19C2×C22⋊Dic19C2212yes—
20C2×C22⋊Dic19C2212yes—
21C2×C22⋊Dic19C2212yescomplemented
22C2×C22⋊Dic19C2214yescomplemented
23C2×C22⋊Dic19C2212yescomplemented
24C2×C22⋊Dic19C2214yescomplemented
25C2×C22⋊Dic19C2212yescomplemented
26#10597381—28no—
27C2×Dic19⋊C4C2214yescomplemented
28C19⋊#95C2214yescomplemented
29C24×C19—24no—
30C24×C19—24no—
31C24×C19—22no—
32C24×C19—24no—
33C24×C19—24no—
34C24×C19—42no—
35C24×C19—42no—
36C24×C19D414yes—
37C24×C19C2311yescharacteristic
38C24×C19C2312yes—
39C24×C19C2311yescharacteristic
40C24×C19C2311yescharacteristic
41C2×D4×C19—232no—
42C2×D4×C19—24no—
43C2×D4×C19—24no—
44C2×D4×C19—24no—
45C2×D4×C19—24no—
46C2×D4×C19—24no—
47C2×D4×C19D418yes—
48C22×C4×C19—22no—
49C22×C4×C19—24no—
50C22×C4×C19C2312yes—
51C22×Dic19—24no—
52C22×Dic19—22no—
53C22×Dic19—22no—
54C22×Dic19—42no—
55C22×Dic19C2314yes—
56C22×Dic19C2312yes—
57C22×Dic19C2312yes—
58C22⋊Dic19—24no—
59C22⋊Dic19—28no—
60C22⋊Dic19—24no—
61C22⋊Dic19—24no—
62C22⋊Dic19—24no—
63C22⋊Dic19—42no—
64C22⋊Dic19—44no—
65Dic19⋊C4—28no—
66C23×C19—22no—
67C23×C19—22no—
68C23×C19—22no—
69C23×C19—22no—
70C23×C19—28no—
71C23×C19—28no—
72C23×C19—28no—
73C23×C19—22no—
74C23×C19—22no—
75C23×C19—22no—
76C23×C19—22no—
77C23×C19—24no—
78C23×C19—22no—
79C23×C19—24no—
80C23×C19—44no—
81C23×C19—416no—
82C23×C19—416no—
83C23×C19—44no—
84C23×C19—44no—
85C23×C19C2×D412yes—
86C23×C19C2×D414yes—
87C23×C19C2×D414yes—
88C23×C19C2×D412yes—
89C23×C19C2×D412yes—
90C23×C19#4114yes—
91C23×C19C2411yescharacteristic
92D4×C19—216no—
93D4×C19—216no—
94C2×C4×C19—28no—
95C2×C4×C19—22no—
96C2×C4×C19—22no—
97C2×C4×C19C2×D414yes—
98C2×Dic19—24no—
99C2×Dic19—24no—
100C2×Dic19—22no—
101C2×Dic19—22no—
102C2×Dic19—24no—
103C2×Dic19—24no—
104C2×Dic19—24no—
105C2×Dic19—44no—
106C2×Dic19—44no—
107#2405—191nomaximal, Sylow
108C22×C19—22no—
109C22×C19—22no—
110C22×C19—22no—
111C22×C19—22no—
112C22×C19—28no—
113C22×C19—28no—
114C22×C19—22no—
115C22×C19—24no—
116C22×C19—22no—
117C22×C19—22no—
118C22×C19—28no—
119C22×C19—416no—
120C22×C19—416no—
121C22×C19—42no—
122C22×C19—42no—
123C22×C19—44no—
124C22×C19—44no—
125C22×C19#12014yes—
126C22×C19#12314yescomplemented
127C22×C19C22×D411yescharacteristic
128C22×C19C22×D412yes—
129C22×C19C2×#4112yes—
130C22×C19H(5,𝔽2)12yes—
131C4×C19—24no—
132Dic19—42no—
133Dic19—42no—
134Dic19—44no—
135C23×D4D1911yescharacteristic
136C2×#123—192no—
137C22×C22⋊C4—191no—
138#394—194no—
139#386—192no—
140#385—192no—
141#379—192no—
142#379—191no—
143C2×C19—24no—
144C2×C19—24no—
145C2×C19—42no—
146C2×C19—44no—
147C2×C19C2×#12011yescharacteristic
148C2×C19C2×#12311yescharacteristic
149C2×C19#53411yescharacteristic
150C2×C19#54614yes—
151C25C2×D1911yescharacteristic
152C25C2×D1911yescharacteristic
153C22×D4—24no—
154C22×D4—28no—
155C22×D4C2×D1912yes—
156C22×D4C2×D1912yes—
157C23×C4—191no—
158C23×C4—191no—
159C23×C4C2×D1911yescharacteristic
160#123—388no—
161C2×C4⋊C4—194no—
162C2×C22⋊C4—192no—
163C2×C22⋊C4—192no—
164C2×C22⋊C4—192no—
165C2×C22⋊C4—194no—
166C2×C22⋊C4—192no—
167C2×C22⋊C4—194no—
168C2×C22⋊C4—192no—
169C2×C22⋊C4—384no—
170#95—194no—
171C19#240511yescharacteristic, complemented, Sylow
172C24—24no—
173C24—24no—
174C24—24no—
175C24—22no—
176C24—24no—
177C24—42no—
178C24—42no—
179C24C22⋊D1914yes—
180C24C22×D1911yescharacteristic
181C24C22×D1912yes—
182C24C22×D1911yescharacteristic
183C24C22×D1911yescharacteristic
184C2×D4—232no—
185C2×D4—24no—
186C2×D4—24no—
187C2×D4—24no—
188C2×D4—24no—
189C2×D4—24no—
190C2×D4C22⋊D1918yes—
191C22×C4—22no—
192C22×C4—24no—
193C22×C4—192no—
194C22×C4—194no—
195C22×C4—192no—
196C22×C4—382no—
197C22×C4—382no—
198C22×C4—384no—
199C22×C4—762no—
200C22×C4C22×D1912yes—
201C4⋊C4—388no—
202C22⋊C4—384no—
203C22⋊C4—384no—
204C22⋊C4—384no—
205C22⋊C4—384no—
206C22⋊C4—388no—
207C22⋊C4—762no—
208C22⋊C4—764no—
209C23—22no—
210C23—22no—
211C23—22no—
212C23—22no—
213C23—28no—
214C23—28no—
215C23—28no—
216C23—22no—
217C23—24no—
218C23—22no—
219C23—24no—
220C23—22no—
221C23—22no—
222C23—22no—
223C23—44no—
224C23—416no—
225C23—416no—
226C23—44no—
227C23—44no—
228C23#6454314yes—
229C23C2×C22⋊D1912yes—
230C23C2×C22⋊D1914yes—
231C23C2×C22⋊D1912yes—
232C23C2×C22⋊D1914yes—
233C23C2×C22⋊D1912yes—
234C23C23×D1911yescharacteristic
235D4—216no—
236D4—216no—
237C2×C4—28no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—384no—
241C2×C4—384no—
242C2×C4—384no—
243C2×C4—384no—
244C2×C4—382no—
245C2×C4—382no—
246C2×C4—384no—
247C2×C4—764no—
248C2×C4—764no—
249C2×C4C2×C22⋊D1914yes—
250C22—22no—
251C22—22no—
252C22—22no—
253C22—28no—
254C22—28no—
255C22—22no—
256C22—22no—
257C22—22no—
258C22—28no—
259C22—22no—
260C22—24no—
261C22—416no—
262C22—416no—
263C22—42no—
264C22—42no—
265C22—44no—
266C22—44no—
267C22#1059738114yescomplemented
268C22#1059739914yes—
269C22C2×#6454312yes—
270C22#1059743012yes—
271C22C22×C22⋊D1911yescharacteristic
272C22C22×C22⋊D1912yes—
273C4—24no—
274C4—762no—
275C4—764no—
276C4—762no—
277C2—24no—
278C2—24no—
279C2—42no—
280C2—44no—
281C2C2×#1059739911yescharacteristic
282C2C2×#1059738111yescharacteristic
283C2#1192710311yescharacteristic
284C2#1192718814yes—
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
Fitting, prime radicalC23×D4×C19C2
hypercenterC23×D4D19
hypocenterC19#2405
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C23×D4

Complements

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

NH ≅ G/Ntype
1. C2×#10597381C2semidirect
2. C22×C22⋊Dic19C2semidirect
3. #11926458C2semidirect
4. #11926424C2semidirect
5. #11926417C2semidirect
6. #11926400C2semidirect
7. #11926400C2semidirect
16. C23×Dic19C22semidirect
17. C23×Dic19C22semidirect
21. C2×C22⋊Dic19C22semidirect
22. C2×C22⋊Dic19C22semidirect
23. C2×C22⋊Dic19C22semidirect
24. C2×C22⋊Dic19C22semidirect
25. C2×C22⋊Dic19C22semidirect
27. C2×Dic19⋊C4C22semidirect
28. C19⋊#95C22semidirect
126. C22×C19#123semidirect
171. C19#2405semidirect
267. C22#10597381semidirect

Maximal subgroups

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

subgroupindex
C2×#105973812
C22×C22⋊Dic192
#119264582
#119264242
#119264172
#119264002
C23×D4×C192
#240519