Finite Group Databasebeta

← #14569302

Subgroups — #14569302

Order 2432.

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

normal subgroups only

This group has 428 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
1#11926467C212yesmaximal
2#11926467C212yesmaximal
3#11926442C212yesmaximal, complemented
4#11926441C212yesmaximal, complemented
5#11926431C212yesmaximal, complemented
6#11926428C212yesmaximal, complemented
7#11926407C211yesmaximal, characteristic
8C4×C22⋊Dic19C211yesmaximal, characteristic
9C4×C22⋊C4×C19C211yesmaximal, characteristic
10C23×C4×C19C2211yescharacteristic
11C2×C22⋊C4×C19C2212yes—
12C2×C42×C19C2211yescharacteristic
13C2×C42×C19C2211yescharacteristic
14C2×C22⋊Dic19C2212yes—
15C2×C22⋊Dic19C2211yescharacteristic
16C2×C22⋊Dic19C2211yescharacteristic
17C2×C4⋊Dic19C2212yes—
18C2×C4⋊Dic19C2212yes—
19C2×Dic19⋊C4C2212yes—
20C2×Dic19⋊C4C2212yes—
21C2×Dic19⋊C4C2212yes—
22C2×Dic19⋊C4C2212yes—
23C2×C4×Dic19C2211yescharacteristic
24C2×C4×Dic19C2211yescharacteristic
25C19×#95C2212yes—
26C19⋊#95C2212yes—
27C19⋊#95C2212yes—
28C19⋊#95C2212yes—
29C19⋊#95C2212yes—
30C19⋊#95C2212yes—
31C24×C19C2311yescharacteristic
32C22×C4×C19—41no—
33C22×C4×C19—41no—
34C22×C4×C19Q814yes—
35C22×C4×C19C2312yes—
36C22×C4×C19C2311yescharacteristic
37C22×C4×C19C2311yescharacteristic
38C22×C4×C19C2312yes—
39C22×Dic19C2312yes—
40C22×Dic19C2312yes—
41C22×Dic19C2312yes—
42C22×Dic19C2312yes—
43C22⋊C4×C19—24no—
44C42×C19—41no—
45C42×C19—41no—
46C22⋊Dic19—24no—
47C22⋊Dic19—41no—
48C22⋊Dic19—41no—
49C4⋊Dic19—24no—
50C4⋊Dic19—42no—
51Dic19⋊C4—24no—
52Dic19⋊C4—24no—
53Dic19⋊C4—24no—
54Dic19⋊C4—42no—
55C4×Dic19—41no—
56C4×Dic19—41no—
57C23×C19—22no—
58C23×C19—22no—
59C23×C19—21no—
60C23×C19—21no—
61C23×C19C2×Q812yes—
62C23×C19C2411yescharacteristic
63C2×C4×C19—22no—
64C2×C4×C19—21no—
65C2×C4×C19—21no—
66C2×C4×C19—22no—
67C2×C4×C19—21no—
68C2×C4×C19—21no—
69C2×C4×C19—22no—
70C2×C4×C19—22no—
71C2×C4×C19—22no—
72C2×C4×C19—44no—
73C2×C4×C19C2×Q812yes—
74C2×C4×C19C2×Q812yes—
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#2608—191nomaximal, Sylow
89C22×C19—22no—
90C22×C19—22no—
91C22×C19—22no—
92C22×C19—42no—
93C22×C19—42no—
94C22×C19C22×Q811yescharacteristic
95C22×C19C2×#4112yes—
96C22×C19C2×#4112yes—
97C22×C19H(5,𝔽2)11yescharacteristic
98C22×C19H(5,𝔽2)11yescharacteristic
99C4×C19—22no—
100C4×C19—22no—
101C4×C19—24no—
102C4×C19—42no—
103Dic19—24no—
104Dic19—42no—
105Dic19—42no—
106Dic19—42no—
107#396—192no—
108#396—192no—
109#389—192no—
110#389—192no—
111#387—192no—
112#387—192no—
113#381—191no—
114C4×C22⋊C4—191no—
115C4×C22⋊C4D1911yescharacteristic
116C2×C19—42no—
117C2×C19#53311yescharacteristic
118C2×C19#53311yescharacteristic
119C2×C19#54311yescharacteristic
120C2×C19#55312yes—
121C2×C19#55312yes—
122C23×C4C2×D1911yescharacteristic
123C2×C4⋊C4—192no—
124C2×C4⋊C4—192no—
125C2×C4⋊C4—192no—
126C2×C4⋊C4—192no—
127C2×C4⋊C4—192no—
128C2×C4⋊C4—192no—
129C2×C22⋊C4—192no—
130C2×C22⋊C4—191no—
131C2×C22⋊C4—191no—
132C2×C22⋊C4C2×D1912yes—
133C2×C42—191no—
134C2×C42—191no—
135C2×C42C2×D1911yescharacteristic
136C2×C42C2×D1911yescharacteristic
137#95—192no—
138#95—192no—
139#95—192no—
140#95—192no—
141#95—192no—
142#95C2×D1912yes—
143C19#260811yescharacteristic, complemented, Sylow
144C24C22×D1911yescharacteristic
145C22×C4—41no—
146C22×C4—41no—
147C22×C4—192no—
148C22×C4—192no—
149C22×C4—192no—
150C22×C4—192no—
151C22×C4Dic3814yes—
152C22×C4C22×D1912yes—
153C22×C4C22×D1911yescharacteristic
154C22×C4C22×D1911yescharacteristic
155C22×C4C22×D1912yes—
156C4⋊C4—384no—
157C4⋊C4—384no—
158C4⋊C4—384no—
159C4⋊C4—384no—
160C4⋊C4—762no—
161C4⋊C4—762no—
162C22⋊C4—24no—
163C22⋊C4—384no—
164C22⋊C4—761no—
165C22⋊C4—761no—
166C42—41no—
167C42—41no—
168C42—761no—
169C42—761no—
170C23—22no—
171C23—21no—
172C23—21no—
173C23—22no—
174C23C2×Dic3812yes—
175C23C23×D1911yescharacteristic
176C2×C4—22no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—44no—
186C2×C4—194no—
187C2×C4—382no—
188C2×C4—382no—
189C2×C4—382no—
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×C4C2×Dic3812yes—
199C2×C4C2×Dic3812yes—
200C2×C4#6454114yes—
201C22—22no—
202C22—22no—
203C22—22no—
204C22—42no—
205C22—42no—
206C22C22×Dic3811yescharacteristic
207C22C2×#6454112yes—
208C22#1059743011yescharacteristic
209C22#1059743011yescharacteristic
210C22#41×D1912yes—
211C4—22no—
212C4—22no—
213C4—24no—
214C4—42no—
215C4—384no—
216C4—762no—
217C4—762no—
218C4—762no—
219C2—42no—
220C2#1192709711yescharacteristic
221C2#1192710111yescharacteristic
222C2#1192717011yescharacteristic
223C2#1192724312yes—
224C2#1192724412yes—
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC4×C22⋊C4×C19C2
prime radicalC24×C19C23
hypercenterC4×C22⋊C4D19
hypocenterC19#2608
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. #11926442C2semidirect
4. #11926441C2semidirect
5. #11926431C2semidirect
6. #11926428C2semidirect
143. C19#2608semidirect

Maximal subgroups

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

subgroupindex
#119264672
#119264422
#119264412
#119264312
#119264282
#119264072
C4×C22⋊Dic192
C4×C22⋊C4×C192
#260819