Finite Group Databasebeta

← #14568660

Subgroups — #14568660

Order 2432.

556 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 556 conjugacy classes of subgroups — too many to draw. Only its 181 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×#10597334C212yesmaximal
2C2×#10597390C212yesmaximal
3#11926465C212yesmaximal
4#11926464C211yesmaximal, characteristic
5#11926441C212yesmaximal
6#11926439C212yesmaximal
7#11926413C211yesmaximal, characteristic
8#11926395C212yesmaximal
9C19×#395C211yesmaximal, characteristic
10C22×Q8×C19C2211yescharacteristic
11C22×Dic38C2212yes—
12C22×Dic38C2211yescharacteristic
13C2×C4⋊C4×C19C2212yes—
14C2×C4⋊C4×C19C2211yescharacteristic
15#10597390—28no—
16C2×C4⋊Dic19C2212yes—
17C2×C4⋊Dic19C2211yescharacteristic
18C2×Dic19⋊C4C2212yes—
19C2×Dic19⋊C4C2212yes—
20C2×Dic19⋊C4C2212yes—
21C2×Dic19⋊C4C2212yes—
22C2×Dic19⋊C4C2212yes—
23C2×Dic19⋊C4C2212yes—
24C2×C4×Dic19C2212yes—
25C2×C4×Dic19C2212yes—
26C2×C4×Dic19C2211yescharacteristic
27#10597334—28no—
28C19×#95C2212yes—
29C19×#95C2211yescharacteristic
30C19⋊#95C2212yes—
31C19⋊#95C2211yescharacteristic
32C19⋊#95C2212yes—
33C2×Q8×C19—24no—
34C2×Q8×C19—41no—
35C22×C4×C19C2311yescharacteristic
36C22×C4×C19C2311yescharacteristic
37C22×C4×C19C2312yes—
38C22×C4×C19C2311yescharacteristic
39C22×C4×C19C2312yes—
40C22×Dic19C2312yes—
41C22×Dic19C2312yes—
42C22×Dic19C2312yes—
43C22×Dic19C2312yes—
44C2×Dic38—24no—
45C2×Dic38—24no—
46C2×Dic38—24no—
47C2×Dic38—41no—
48C2×Dic38—42no—
49C4⋊C4×C19—24no—
50C4⋊C4×C19—41no—
51C4⋊Dic19—24no—
52C4⋊Dic19—41no—
53Dic19⋊C4—24no—
54Dic19⋊C4—24no—
55Dic19⋊C4—24no—
56Dic19⋊C4—24no—
57Dic19⋊C4D418yes—
58Dic19⋊C4Q818yescomplemented
59C4×Dic19—24no—
60C4×Dic19—24no—
61C4×Dic19Q814yescomplemented
62C23×C19C2411yescharacteristic
63Q8×C19—44no—
64C2×C4×C19—22no—
65C2×C4×C19—22no—
66C2×C4×C19—21no—
67C2×C4×C19—22no—
68C2×C4×C19—21no—
69C2×C4×C19—22no—
70C2×C4×C19—22no—
71C2×C4×C19—22no—
72C2×C4×C19—21no—
73C2×C4×C19—21no—
74C2×C4×C19C2×D414yes—
75C2×C4×C19C2×Q812yes—
76C2×C4×C19C2×Q814yes—
77C2×Dic19—22no—
78C2×Dic19—22no—
79C2×Dic19—22no—
80C2×Dic19—22no—
81C2×Dic19—22no—
82C2×Dic19—22no—
83C2×Dic19—22no—
84C2×Dic19C2×D414yes—
85C2×Dic19C2×D414yes—
86C2×Dic19C2×Q814yes—
87C2×Dic19C2×Q814yes—
88C2×Dic19C2×Q814yes—
89Dic38—44no—
90Dic38—48no—
91#2551—191nomaximal, Sylow
92C22×C19C22×D412yes—
93C22×C19C22×Q811yescharacteristic
94C22×C19C22×Q812yes—
95C22×C19H(5,𝔽2)11yescharacteristic
96C22×C192−1+411yescharacteristic
97C4×C19—22no—
98C4×C19—24no—
99C4×C19—24no—
100C4×C19—41no—
101C4×C19—41no—
102Dic19—24no—
103Dic19—24no—
104Dic19—42no—
105Dic19C4⋊Q818yescomplemented
106C2×C4⋊Q8—192no—
107C2×C4⋊Q8—192no—
108#395—191no—
109#395—192no—
110#395D1911yescharacteristic
111#389—192no—
112#389—192no—
113#384—191no—
114C4×C4⋊C4—192no—
115C2×C19C2×C4⋊Q812yes—
116C2×C19#54411yescharacteristic
117C2×C19D4211yescharacteristic
118C2×C19D4×Q812yes—
119C2×C19Q8211yescharacteristic
120C22×Q8—191no—
121C22×Q8—192no—
122C22×Q8C2×D1911yescharacteristic
123C4⋊Q8—388no—
124C4⋊Q8—388no—
125C2×C4⋊C4—192no—
126C2×C4⋊C4—192no—
127C2×C4⋊C4—192no—
128C2×C4⋊C4—192no—
129C2×C4⋊C4—192no—
130C2×C4⋊C4—192no—
131C2×C4⋊C4—192no—
132C2×C4⋊C4—191no—
133C2×C4⋊C4C2×D1912yes—
134C2×C4⋊C4C2×D1911yescharacteristic
135C2×C42—191no—
136C2×C42—192no—
137C2×C42—192no—
138#95—192no—
139#95—191no—
140#95—192no—
141#95C2×D1912yes—
142#95C2×D1911yescharacteristic
143C19#255111yescharacteristic, complemented, Sylow
144C2×Q8—24no—
145C2×Q8—41no—
146C2×Q8—384no—
147C2×Q8—384no—
148C2×Q8—384no—
149C2×Q8—762no—
150C2×Q8—761no—
151C22×C4—192no—
152C22×C4—192no—
153C22×C4—192no—
154C22×C4—192no—
155C22×C4C22×D1911yescharacteristic
156C22×C4C22×D1911yescharacteristic
157C22×C4C22×D1912yes—
158C22×C4C22×D1911yescharacteristic
159C22×C4C22×D1912yes—
160C4⋊C4—24no—
161C4⋊C4—41no—
162C4⋊C4—198no—
163C4⋊C4—198no—
164C4⋊C4—384no—
165C4⋊C4—384no—
166C4⋊C4—384no—
167C4⋊C4—384no—
168C4⋊C4—384no—
169C4⋊C4—761no—
170C42—194no—
171C42—384no—
172C42—384no—
173C23C23×D1911yescharacteristic
174Q8—44no—
175Q8—768no—
176Q8—764no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—21no—
180C2×C4—22no—
181C2×C4—21no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—194no—
188C2×C4—194no—
189C2×C4—194no—
190C2×C4—194no—
191C2×C4—194no—
192C2×C4—382no—
193C2×C4—382no—
194C2×C4—382no—
195C2×C4—382no—
196C2×C4—382no—
197C2×C4—382no—
198C2×C4—382no—
199C2×C4D4×D1914yes—
200C2×C4Q8×D1912yes—
201C2×C4Q8×D1914yes—
202C22C2×D4×D1912yes—
203C22#1059743011yescharacteristic
204C22C2×Q8×D1911yescharacteristic
205C22C2×Q8×D1912yes—
206C22#1059743611yescharacteristic
207C4—22no—
208C4—24no—
209C4—24no—
210C4—41no—
211C4—41no—
212C4—198no—
213C4—384no—
214C4—384no—
215C4—762no—
216C2C4⋊Q8×D1912yes—
217C2#1192717311yescharacteristic
218C2#1192717611yescharacteristic
219C2#1192720712yes—
220C2#1192727411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, prime radical, cosocleC23×C19C24
FittingC19×#395C2
hypercenter#395D19
hypocenterC19#2551
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
58. Dic19⋊C4Q8semidirect
61. C4×Dic19Q8semidirect
105. Dic19C4⋊Q8semidirect
143. C19#2551semidirect

Maximal subgroups

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

subgroupindex
C2×#105973342
C2×#105973902
#119264652
#119264642
#119264412
#119264392
#119264132
#119263952
C19×#3952
#255119