Finite Group Databasebeta

← #14567517

Subgroups — #14567517

Order 2432.

660 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 660 conjugacy classes of subgroups — too many to draw. Only its 145 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×#10597340C212yesmaximal, complemented
2C2×C4×C22⋊D19C212yesmaximal, complemented
3#11926480C211yesmaximal, characteristic, complemented
4#11926459C212yesmaximal, complemented
5#11926453C211yesmaximal, characteristic
6#11926439C212yesmaximal, complemented
7#11926433C212yesmaximal, complemented
8#11926418C212yesmaximal, complemented
9C19×#385C211yesmaximal, characteristic, complemented
10C23×C4×C19C2211yescharacteristic
11C22×C22⋊D19C2212yes—
12C22×D76C2211yescharacteristic
13C22×C4×D19C2212yes—
14C2×C4⋊C4×C19C2212yes—
15C2×C22⋊C4×C19C2211yescharacteristic
16C2×C22⋊C4×C19C2211yescharacteristic
17C2×C22⋊Dic19C2212yes—
18C4×C22⋊D19—28no—
19C2×(C2×D19)⋊C4C2212yes—
20C2×(C2×D19)⋊C4C2212yes—
21C2×(C2×D19)⋊C4C2212yes—
22C2×(C2×D19)⋊C4C2212yes—
23C2×C4⋊Dic19C2211yescharacteristic
24C2×Dic19⋊C4C2212yes—
25C2×Dic19⋊C4C2212yes—
26C2×Dic19⋊C4C2212yes—
27C2×C4×Dic19C2212yes—
28#10597340—28no—
29C19×#95C2212yes—
30C19⋊#95C2212yes—
31C19⋊#95C2211yescharacteristic
32C19⋊#95C2211yescharacteristic
33C24×C19C2311yescharacteristic
34C23×D19C2312yes—
35C22×C4×C19—24no—
36C22×C4×C19—41no—
37C22×C4×C19C2311yescharacteristic
38C22×C4×C19C2312yes—
39C22×C4×C19C2311yescharacteristic
40C22×C4×C19C2312yes—
41C2×C22⋊D19—24no—
42C2×C22⋊D19—24no—
43C2×C22⋊D19—24no—
44C22×Dic19C2312yes—
45C22×Dic19C2312yes—
46C22×Dic19C2312yes—
47C2×D76—24no—
48C2×D76—41no—
49C2×C4×D19—24no—
50C2×C4×D19—24no—
51C2×C4×D19—42no—
52C4⋊C4×C19—24no—
53C22⋊C4×C19—22no—
54C22⋊C4×C19—41no—
55C22⋊Dic19—24no—
56(C2×D19)⋊C4—24no—
57(C2×D19)⋊C4—24no—
58(C2×D19)⋊C4—24no—
59(C2×D19)⋊C4D418yescomplemented
60C4⋊Dic19—41no—
61Dic19⋊C4—24no—
62Dic19⋊C4—24no—
63Dic19⋊C4—24no—
64C4×Dic19—24no—
65C23×C19—22no—
66C23×C19—22no—
67C23×C19—21no—
68C23×C19—21no—
69C23×C19#4112yes—
70C23×C19C2411yescharacteristic
71C22×D19—22no—
72C22×D19—22no—
73C22×D19—22no—
74C22×D19—22no—
75C22×D19—22no—
76C22×D19—22no—
77C22×D19C2×D414yes—
78C2×C4×C19—22no—
79C2×C4×C19—22no—
80C2×C4×C19—22no—
81C2×C4×C19—22no—
82C2×C4×C19—22no—
83C2×C4×C19—22no—
84C2×C4×C19—22no—
85C2×C4×C19—21no—
86C2×C4×C19—21no—
87C2×C4×C19—44no—
88C2×C4×C19C2×D414yes—
89C22⋊D19—216no—
90C2×Dic19—22no—
91C2×Dic19—22no—
92C2×Dic19—22no—
93C2×Dic19—22no—
94C2×Dic19—22no—
95C2×Dic19—22no—
96C2×Dic19—22no—
97C2×Dic19C2×D414yes—
98C2×Dic19#4114yes—
99D76—44no—
100C4×D19—48no—
101#2455—191nomaximal, Sylow
102C22×C19—24no—
103C22×C19—22no—
104C22×C19—41no—
105C22×C19—42no—
106C22×C19—41no—
107C22×C19C22×D412yes—
108C22×C19C2×#4111yescharacteristic
109C22×C19C2×#4112yes—
110C22×C19H(5,𝔽2)11yescharacteristic
111C22×C192−1+411yescharacteristic
112C2×D19—24no—
113C2×D19—24no—
114C2×D19—24no—
115C2×D19—42no—
116C2×D19—42no—
117C2×D19—42no—
118C2×D19—42no—
119C4×C19—24no—
120C4×C19—42no—
121C4×C19—41no—
122C4×C19—41no—
123Dic19—24no—
124Dic19—24no—
125Dic19—42no—
126C2×#123—192no—
127C2×C4×D4—192no—
128#399—191no—
129#394—192no—
130#392—191no—
131#389—192no—
132#388—192no—
133#385—192no—
134#385D1911yescharacteristic, complemented
135C2×C19—42no—
136C2×C19#52512yes—
137C2×C19#53911yescharacteristic
138C2×C19D4211yescharacteristic
139C2×C19#54712yes—
140C2×C19#55911yescharacteristic
141D19—44no—
142C22×D4—192no—
143C22×D4—191no—
144C23×C4—192no—
145C23×C4C2×D1911yescharacteristic
146#123—388no—
147C4×D4—388no—
148C2×C4⋊C4—192no—
149C2×C4⋊C4—192no—
150C2×C4⋊C4—192no—
151C2×C4⋊C4—191no—
152C2×C4⋊C4C2×D1912yes—
153C2×C22⋊C4—192no—
154C2×C22⋊C4—192no—
155C2×C22⋊C4—192no—
156C2×C22⋊C4—192no—
157C2×C22⋊C4—192no—
158C2×C22⋊C4C2×D1911yescharacteristic
159C2×C22⋊C4C2×D1911yescharacteristic
160C2×C42—192no—
161#95—192no—
162#95—191no—
163#95—191no—
164#95C2×D1912yes—
165C19#245511yescharacteristic, complemented, Sylow
166C24—192no—
167C24C22×D1911yescharacteristic
168C2×D4—384no—
169C2×D4—384no—
170C2×D4—384no—
171C2×D4—384no—
172C2×D4—761no—
173C22×C4—24no—
174C22×C4—41no—
175C22×C4—192no—
176C22×C4—192no—
177C22×C4—192no—
178C22×C4—384no—
179C22×C4—384no—
180C22×C4—762no—
181C22×C4C22×D1911yescharacteristic
182C22×C4C22×D1912yes—
183C22×C4C22×D1911yescharacteristic
184C22×C4C22×D1912yes—
185C4⋊C4—24no—
186C4⋊C4—384no—
187C4⋊C4—384no—
188C4⋊C4—384no—
189C4⋊C4—761no—
190C22⋊C4—22no—
191C22⋊C4—41no—
192C22⋊C4—198no—
193C22⋊C4—384no—
194C22⋊C4—384no—
195C22⋊C4—384no—
196C22⋊C4—384no—
197C42—384no—
198C23—22no—
199C23—21no—
200C23—21no—
201C23—22no—
202C23—194no—
203C23—382no—
204C23—382no—
205C23—382no—
206C23—382no—
207C23—382no—
208C23—382no—
209C23#6454112yes—
210C23C23×D1911yescharacteristic
211D4—3816no—
212D4—764no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—44no—
223C2×C4—194no—
224C2×C4—194no—
225C2×C4—382no—
226C2×C4—382no—
227C2×C4—382no—
228C2×C4—382no—
229C2×C4—382no—
230C2×C4—382no—
231C2×C4—382no—
232C2×C4—768no—
233C2×C4D4×D1914yes—
234C22—24no—
235C22—22no—
236C22—41no—
237C22—42no—
238C22—41no—
239C22—384no—
240C22—384no—
241C22—384no—
242C22—762no—
243C22—762no—
244C22—762no—
245C22—762no—
246C22C2×#6454111yescharacteristic
247C22C2×D4×D1912yes—
248C22#1059743011yescharacteristic
249C22#1059743311yescharacteristic
250C22#41×D1912yes—
251C4—24no—
252C4—42no—
253C4—41no—
254C4—41no—
255C4—384no—
256C4—384no—
257C4—762no—
258C2—42no—
259C2—764no—
260C2#1192705312yes—
261C2#1192714111yescharacteristic
262C2#1192717611yescharacteristic
263C2#1192719612yes—
264C2#1192727811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC19×#385C2
prime radical#11926453C2
hypercenter#385D19
hypocenterC19#2455
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
1. C2×#10597340C2semidirect
2. C2×C4×C22⋊D19C2semidirect
3. #11926480C2semidirect
4. #11926459C2semidirect
6. #11926439C2semidirect
7. #11926433C2semidirect
8. #11926418C2semidirect
9. C19×#385C2semidirect
59. (C2×D19)⋊C4D4semidirect
134. #385D19semidirect
165. C19#2455semidirect

Maximal subgroups

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

subgroupindex
C2×#105973402
C2×C4×C22⋊D192
#119264802
#119264592
#119264532
#119264392
#119264332
#119264182
C19×#3852
#245519