Finite Group Databasebeta

← #14566954

Subgroups — #14566954

Order 2432.

1056 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 1056 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
1C22×#64541C211yesmaximal, characteristic, complemented
2C2×#10597399C212yesmaximal, complemented
3#11926456C212yesmaximal, complemented
4#11926453C212yesmaximal, complemented
5#11926423C212yesmaximal, complemented
6#11926420C214yesmaximal, complemented
7#11926407C211yesmaximal, characteristic, complemented
8C22×C22⋊C4×C19C211yesmaximal, characteristic, complemented
9C25×C19C2211yescharacteristic
10C23×C4×C19C2211yescharacteristic
11C23×C4×C19C2211yescharacteristic
12C22×C22⋊D19C2214yes—
13C22×C22⋊D19C2212yes—
14C2×#64541—24no—
15C2×#64541—28no—
16C22×D76C2211yescharacteristic, complemented
17C22×C4×D19C2212yescomplemented
18C22×Dic38C2211yescharacteristic, complemented
19C2×C22⋊C4×C19—24no—
20C2×C22⋊C4×C19C2212yes—
21C2×C22⋊C4×C19C2212yes—
22#10597399—28no—
23C2×C22⋊Dic19C2212yes—
24C2×C22⋊Dic19C2214yes—
25C2×(C2×D19)⋊C4C2214yescomplemented
26C19⋊#95C2212yescomplemented
27C19⋊#95C2212yescomplemented
28C19⋊#95C2214yescomplemented
29C24×C19—22no—
30C24×C19—24no—
31C24×C19—24no—
32C24×C19—42no—
33C24×C19C2312yes—
34C24×C19C2311yescharacteristic
35C23×D19C2312yes—
36C22×C4×C19—24no—
37C22×C4×C19—22no—
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—28no—
46C2×C22⋊D19—28no—
47C2×C22⋊D19—44no—
48C2×C22⋊D19D418yescomplemented
49C22×Dic19C2314yes—
50C22×Dic19C2312yes—
51#64541—232no—
52C2×D76—24no—
53C2×D76—22no—
54C2×C4×D19—24no—
55C2×C4×D19—24no—
56C2×C4×D19—24no—
57C2×Dic38—22no—
58C2×Dic38—24no—
59C22⋊C4×C19—24no—
60C22⋊C4×C19—24no—
61C22⋊Dic19—24no—
62C22⋊Dic19—28no—
63(C2×D19)⋊C4—44no—
64C23×C19—22no—
65C23×C19—22no—
66C23×C19—28no—
67C23×C19—24no—
68C23×C19—22no—
69C23×C19—22no—
70C23×C19—24no—
71C23×C19—416no—
72C23×C19—44no—
73C23×C19—44no—
74C23×C19C2×D414yes—
75C23×C19C2×D412yes—
76C23×C19#4114yescomplemented
77C23×C19C2411yescharacteristic
78C22×D19—22no—
79C22×D19—22no—
80C22×D19—24no—
81C22×D19—24no—
82C22×D19C2×D414yes—
83C2×C4×C19—28no—
84C2×C4×C19—22no—
85C2×C4×C19—22no—
86C2×C4×C19—22no—
87C2×C4×C19—24no—
88C2×C4×C19—44no—
89C2×C4×C19C2×D412yes—
90C2×C4×C19C2×D412yes—
91C22⋊D19—216no—
92C22⋊D19—416no—
93C2×Dic19—22no—
94C2×Dic19—22no—
95C2×Dic19—24no—
96C2×Dic19—24no—
97C2×Dic19—24no—
98C2×Dic19C2×D414yes—
99D76—28no—
100C4×D19—216no—
101Dic38—28no—
102#2404—191nomaximal, Sylow
103C22×C19—22no—
104C22×C19—22no—
105C22×C19—28no—
106C22×C19—24no—
107C22×C19—28no—
108C22×C19—416no—
109C22×C19—42no—
110C22×C19—42no—
111C22×C19—44no—
112C22×C19#12014yes—
113C22×C19C22×D412yes—
114C22×C19C22×D411yescharacteristic
115C22×C19C2×#4112yes—
116C22×C19H(5,𝔽2)12yes—
117C2×D19—24no—
118C2×D19—28no—
119C2×D19—42no—
120C2×D19—42no—
121C2×D19—44no—
122C4×C19—22no—
123C4×C19—22no—
124C4×C19—42no—
125Dic19—24no—
126Dic19—44no—
127C22×#41—191no—
128C2×#120—192no—
129C22×C22⋊C4D1911yescharacteristic, complemented
130#393—192no—
131#392—192no—
132#386—192no—
133#386—194no—
134#381—191no—
135C2×C19—24no—
136C2×C19—44no—
137C2×C19C2×#12011yescharacteristic
138C2×C19#52511yescharacteristic
139C2×C19#53511yescharacteristic
140C2×C19#54614yes—
141D19—44no—
142C25C2×D1911yescharacteristic
143C2×#41—388no—
144C2×#41—384no—
145C22×Q8—191no—
146C22×D4—192no—
147C22×D4—194no—
148C22×D4—191no—
149C23×C4—192no—
150C23×C4C2×D1911yescharacteristic
151C23×C4C2×D1911yescharacteristic
152#120—388no—
153C2×C22⋊C4—24no—
154C2×C22⋊C4—192no—
155C2×C22⋊C4—194no—
156C2×C22⋊C4—194no—
157C2×C22⋊C4C2×D1912yes—
158C2×C22⋊C4C2×D1912yes—
159#95—192no—
160#95—192no—
161#95—194no—
162C19#240411yescharacteristic, complemented, Sylow
163C24—24no—
164C24—22no—
165C24—24no—
166C24—42no—
167C24—192no—
168C24C22×D1912yes—
169C24C22×D1911yescharacteristic
170#41—3832no—
171C2×Q8—384no—
172C2×Q8—382no—
173C2×D4—198no—
174C2×D4—384no—
175C2×D4—384no—
176C2×D4—384no—
177C2×D4—388no—
178C2×D4—388no—
179C2×D4—382no—
180C2×D4—764no—
181C22×C4—24no—
182C22×C4—22no—
183C22×C4—42no—
184C22×C4—192no—
185C22×C4—194no—
186C22×C4—384no—
187C22×C4—384no—
188C22×C4—384no—
189C22×C4C22⋊D1914yescomplemented
190C22×C4C22×D1912yes—
191C22×C4C22×D1911yescharacteristic
192C22×C4C22×D1911yescharacteristic
193C22⋊C4—24no—
194C22⋊C4—24no—
195C22⋊C4—388no—
196C22⋊C4—384no—
197C22⋊C4—764no—
198C23—22no—
199C23—22no—
200C23—28no—
201C23—22no—
202C23—24no—
203C23—24no—
204C23—22no—
205C23—416no—
206C23—44no—
207C23—44no—
208C23—194no—
209C23—384no—
210C23—382no—
211C23—384no—
212C23—382no—
213C23#6454114yescomplemented
214C23D4×D1914yes—
215C23C2×C22⋊D1912yes—
216C23C23×D1911yescharacteristic
217Q8—388no—
218D4—388no—
219D4—3816no—
220D4—7616no—
221C2×C4—28no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—24no—
225C2×C4—22no—
226C2×C4—44no—
227C2×C4—194no—
228C2×C4—3816no—
229C2×C4—382no—
230C2×C4—382no—
231C2×C4—384no—
232C2×C4—384no—
233C2×C4—384no—
234C2×C4C2×C22⋊D1912yes—
235C2×C4C2×C22⋊D1912yes—
236C22—22no—
237C22—22no—
238C22—28no—
239C22—24no—
240C22—28no—
241C22—416no—
242C22—42no—
243C22—44no—
244C22—42no—
245C22—388no—
246C22—384no—
247C22—762no—
248C22—762no—
249C22—764no—
250C22#1059738314yes—
251C22C2×#6454112yes—
252C22C2×D4×D1912yes—
253C22#1059743012yes—
254C22C22×C22⋊D1911yescharacteristic
255C4—22no—
256C4—22no—
257C4—42no—
258C4—384no—
259C4—764no—
260C2—24no—
261C2—44no—
262C2—764no—
263C2C2×#1059738311yescharacteristic
264C2#1192705511yescharacteristic
265C2#1192711111yescharacteristic
266C2#1192718414yes—
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC22×C22⋊C4×C19C2
hypercenterC22×C22⋊C4D19
hypocenterC19#2404
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#64541C2semidirect
2. C2×#10597399C2semidirect
3. #11926456C2semidirect
4. #11926453C2semidirect
5. #11926423C2semidirect
6. #11926420C2semidirect
7. #11926407C2semidirect
8. C22×C22⋊C4×C19C2semidirect
16. C22×D76C22semidirect
17. C22×C4×D19C22semidirect
18. C22×Dic38C22semidirect
25. C2×(C2×D19)⋊C4C22semidirect
26. C19⋊#95C22semidirect
27. C19⋊#95C22semidirect
28. C19⋊#95C22semidirect
39. C22×C4×C19D4semidirect
48. C2×C22⋊D19D4semidirect
76. C23×C19#41semidirect
129. C22×C22⋊C4D19semidirect
162. C19#2404semidirect
189. C22×C4C22⋊D19semidirect
213. C23#64541semidirect

Maximal subgroups

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

subgroupindex
C22×#645412
C2×#105973992
#119264562
#119264532
#119264232
#119264202
#119264072
C22×C22⋊C4×C192
#240419