Finite Group Databasebeta

← #14569131

Subgroups — #14569131

Order 2432.

440 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 129 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
1#11926483C211yesmaximal, characteristic, complemented
2#11926474C211yesmaximal, characteristic, complemented
3#11926458C212yesmaximal
4#11926438C212yesmaximal, complemented
5#11926438C212yesmaximal, complemented
6#11926437C212yesmaximal, complemented
7#11926437C212yesmaximal, complemented
8C4×Dic19⋊C4C212yesmaximal, complemented
9C19×#390C211yesmaximal, characteristic
10C22×D4×C19C2211yescharacteristic
11C2×C4⋊C4×C19C2211yescharacteristic
12C2×C22⋊C4×C19C2212yes—
13C2×C22⋊C4×C19C2212yes—
14C2×C42×C19C2211yescharacteristic
15C2×C22⋊Dic19C2212yes—
16C2×C22⋊Dic19C2212yes—
17C2×C22⋊Dic19C2212yes—
18C2×C22⋊Dic19C2212yes—
19C2×C4⋊Dic19C2211yescharacteristic
20C2×C4⋊Dic19C2211yescharacteristic
21C2×Dic19⋊C4C2212yes—
22C2×Dic19⋊C4C2212yes—
23C2×C4×Dic19C2212yes—
24C2×C4×Dic19C2212yes—
25C19⋊#95C2212yes—
26C19⋊#95C2212yes—
27C19⋊#95C2212yes—
28C19⋊#95C2212yes—
29C19⋊#95C2211yescharacteristic
30C19⋊#95C2211yescharacteristic
31C24×C19C2312yes—
32C2×D4×C19—22no—
33C2×D4×C19—41no—
34C2×D4×C19—41no—
35C22×C4×C19C2311yescharacteristic
36C22×C4×C19C2311yescharacteristic
37C22×C4×C19C2312yes—
38C22×C4×C19C2311yescharacteristic
39C22×Dic19C2312yes—
40C22×Dic19C2312yes—
41C22×Dic19C2312yes—
42C22×Dic19C2312yes—
43C4⋊C4×C19—41no—
44C22⋊C4×C19—24no—
45C22⋊C4×C19—24no—
46C42×C19—41no—
47C22⋊Dic19—24no—
48C22⋊Dic19—24no—
49C22⋊Dic19—42no—
50C22⋊Dic19—42no—
51C4⋊Dic19—41no—
52C4⋊Dic19—41no—
53Dic19⋊C4—24no—
54Dic19⋊C4—24no—
55C4×Dic19—24no—
56C4×Dic19—42no—
57C23×C19—22no—
58C23×C19—22no—
59C23×C19—22no—
60C23×C19—22no—
61C23×C19—22no—
62C23×C19—22no—
63C23×C19—22no—
64C23×C19C2411yescharacteristic
65D4×C19—44no—
66C2×C4×C19—22no—
67C2×C4×C19—22no—
68C2×C4×C19—21no—
69C2×C4×C19—21no—
70C2×C4×C19—22no—
71C2×C4×C19—22no—
72C2×C4×C19—21no—
73C2×C4×C19—21no—
74C2×C4×C19#4112yes—
75C2×C4×C19#4114yes—
76C2×Dic19—22no—
77C2×Dic19—22no—
78C2×Dic19—22no—
79C2×Dic19—22no—
80C2×Dic19—22no—
81C2×Dic19—22no—
82C2×Dic19—22no—
83C2×Dic19—22no—
84C2×Dic19—22no—
85C2×Dic19—22no—
86C2×Dic19—22no—
87C2×Dic19#4114yes—
88#2593—191nomaximal, Sylow
89C22×C19—42no—
90C22×C19—42no—
91C22×C19—42no—
92C22×C19—42no—
93C22×C19—42no—
94C22×C19—42no—
95C22×C19—42no—
96C22×C19C2×#4111yescharacteristic
97C22×C19C2×#4112yes—
98C22×C19C2×#4112yes—
99C22×C19H(5,𝔽2)11yescharacteristic
100C22×C19H(5,𝔽2)11yescharacteristic
101C4×C19—22no—
102C4×C19—24no—
103C4×C19—41no—
104C4×C19—41no—
105Dic19—24no—
106Dic19—42no—
107Dic19—42no—
108Dic19—42no—
109#400—191no—
110#398—191no—
111#394—192no—
112#390D1911yescharacteristic
113#388—192no—
114#388—192no—
115#388—192no—
116#388—192no—
117C4×C4⋊C4—192no—
118C2×C19—82no—
119C2×C19#52912yes—
120C2×C19#53811yescharacteristic
121C2×C19#55312yes—
122C2×C19#55511yescharacteristic
123C2×C19#55911yescharacteristic
124C22×D4C2×D1911yescharacteristic
125C2×C4⋊C4—192no—
126C2×C4⋊C4—192no—
127C2×C4⋊C4—191no—
128C2×C4⋊C4—191no—
129C2×C4⋊C4C2×D1911yescharacteristic
130C2×C22⋊C4—192no—
131C2×C22⋊C4—192no—
132C2×C22⋊C4—192no—
133C2×C22⋊C4—192no—
134C2×C22⋊C4C2×D1912yes—
135C2×C22⋊C4C2×D1912yes—
136C2×C42—192no—
137C2×C42—192no—
138C2×C42C2×D1911yescharacteristic
139#95—192no—
140#95—192no—
141#95—191no—
142#95—192no—
143#95—192no—
144#95—191no—
145C19#259311yescharacteristic, complemented, Sylow
146C24C22×D1912yes—
147C2×D4—22no—
148C2×D4—41no—
149C2×D4—41no—
150C22×C4—192no—
151C22×C4—192no—
152C22×C4—192no—
153C22×C4—192no—
154C22×C4C22×D1911yescharacteristic
155C22×C4C22×D1911yescharacteristic
156C22×C4C22×D1911yescharacteristic
157C22×C4C22×D1912yes—
158C4⋊C4—41no—
159C4⋊C4—384no—
160C4⋊C4—384no—
161C4⋊C4—761no—
162C4⋊C4—761no—
163C22⋊C4—24no—
164C22⋊C4—24no—
165C22⋊C4—384no—
166C22⋊C4—384no—
167C22⋊C4—762no—
168C22⋊C4—762no—
169C42—41no—
170C42—384no—
171C42—762no—
172C23—22no—
173C23—22no—
174C23—22no—
175C23—22no—
176C23—22no—
177C23—22no—
178C23—22no—
179C23C23×D1911yescharacteristic
180D4—44no—
181C2×C4—22no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—194no—
190C2×C4—382no—
191C2×C4—382no—
192C2×C4—382no—
193C2×C4—382no—
194C2×C4—382no—
195C2×C4—382no—
196C2×C4—382no—
197C2×C4—382no—
198C2×C4—382no—
199C2×C4—382no—
200C2×C4—382no—
201C2×C4#6454112yes—
202C2×C4#6454314yes—
203C22—42no—
204C22—42no—
205C22—42no—
206C22—42no—
207C22—42no—
208C22—42no—
209C22—42no—
210C22C2×#6454111yescharacteristic
211C22C2×#6454312yes—
212C22#1059743011yescharacteristic
213C22#1059743011yescharacteristic
214C22#41×D1912yes—
215C4—22no—
216C4—24no—
217C4—41no—
218C4—41no—
219C4—384no—
220C4—762no—
221C4—762no—
222C4—762no—
223C2—82no—
224C2#1192707612yes—
225C2#1192713211yescharacteristic
226C2#1192723712yes—
227C2#1192725611yescharacteristic
228C2#1192728011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC19×#390C2
prime radicalC22×D4×C19C22
hypercenter#390D19
hypocenterC19#2593
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
1. #11926483C2semidirect
2. #11926474C2semidirect
4. #11926438C2semidirect
5. #11926438C2semidirect
6. #11926437C2semidirect
7. #11926437C2semidirect
8. C4×Dic19⋊C4C2semidirect
145. C19#2593semidirect

Maximal subgroups

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

subgroupindex
#119264832
#119264742
#119264582
#119264382
#119264372
C4×Dic19⋊C42
C19×#3902
#259319