Finite Group Databasebeta

← #14570666

Subgroups — #14570666

Order 2432.

456 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 157 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
2#11926477C212yesmaximal
3#11926465C212yesmaximal
4#11926464C212yesmaximal
5#11926450C211yesmaximal, characteristic
6#11926442C211yesmaximal, characteristic
7#11926430C212yesmaximal
8#11926427C212yesmaximal
9C19×#389C211yesmaximal, characteristic
10C22×Dic38C2212yes—
11C22×Dic38C2211yescharacteristic
12C2×C4⋊C4×C19C2212yes—
13C2×C4⋊C4×C19C2211yescharacteristic
14C2×C4⋊C4×C19C2211yescharacteristic
15C2×C42×C19C2211yescharacteristic
16C2×C4⋊Dic19C2212yes—
17C2×C4⋊Dic19C2211yescharacteristic
18C2×C4⋊Dic19C2211yescharacteristic
19C2×C4⋊Dic19C2211yescharacteristic
20C2×Dic19⋊C4C2212yes—
21C2×Dic19⋊C4C2212yes—
22C2×Dic19⋊C4C2212yes—
23C2×C4×Dic19C2212yes—
24#10597334—28no—
25C19×#95C2212yes—
26C19⋊#95C2212yes—
27C19⋊#95C2212yes—
28C19⋊#95C2212yes—
29C19⋊#95C2212yes—
30C19⋊#95C2212yes—
31C19⋊#95C2212yes—
32C22×C4×C19C2312yes—
33C22×C4×C19C2311yescharacteristic
34C22×C4×C19C2311yescharacteristic
35C22×C4×C19C2311yescharacteristic
36C22×C4×C19C2312yes—
37C22×Dic19C2312yes—
38C22×Dic19C2312yes—
39C22×Dic19C2312yes—
40C22×Dic19C2312yes—
41C2×Dic38—24no—
42C2×Dic38—41no—
43C2×Dic38—41no—
44C2×Dic38—42no—
45C2×Dic38—42no—
46C2×Dic38D414yes—
47C4⋊C4×C19—24no—
48C4⋊C4×C19—41no—
49C4⋊C4×C19Q814yescomplemented
50C42×C19—41no—
51C4⋊Dic19—24no—
52C4⋊Dic19—41no—
53C4⋊Dic19—41no—
54C4⋊Dic19Q814yescomplemented
55Dic19⋊C4—24no—
56Dic19⋊C4—24no—
57Dic19⋊C4—42no—
58C4×Dic19—24no—
59C23×C19C2411yescharacteristic
60C2×C4×C19—22no—
61C2×C4×C19—21no—
62C2×C4×C19—21no—
63C2×C4×C19—21no—
64C2×C4×C19—21no—
65C2×C4×C19—21no—
66C2×C4×C19—21no—
67C2×C4×C19—22no—
68C2×C4×C19—22no—
69C2×C4×C19—22no—
70C2×C4×C19—22no—
71C2×C4×C19C2×D412yes—
72C2×C4×C19C2×Q812yes—
73C2×C4×C19C2×Q814yes—
74C2×C4×C19C2×Q812yes—
75C2×Dic19—22no—
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×Dic19C2×D414yes—
86C2×Dic19C2×Q814yes—
87Dic38—44no—
88Dic38—48no—
89#2734—191nomaximal, Sylow
90C22×C19C22×D411yescharacteristic
91C22×C19C22×Q811yescharacteristic
92C22×C19C22×Q811yescharacteristic
93C22×C19H(5,𝔽2)11yescharacteristic
94C22×C19H(5,𝔽2)11yescharacteristic
95C22×C192−1+411yescharacteristic
96C22×C192−1+411yescharacteristic
97C4×C19—22no—
98C4×C19—22no—
99C4×C19—22no—
100C4×C19—24no—
101C4×C19—42no—
102Dic19—24no—
103Dic19—24no—
104Dic19—42no—
105Dic19—42no—
106C2×C4⋊Q8—192no—
107#398—192no—
108#395—192no—
109#395—192no—
110#391—191no—
111#389—191no—
112#389D1911yescharacteristic
113#387—192no—
114#387—192no—
115C2×C19#53411yescharacteristic
116C2×C19#54411yescharacteristic
117C2×C19#54411yescharacteristic
118C2×C19D4×Q811yescharacteristic
119C2×C19D4×Q811yescharacteristic
120C2×C19Q8211yescharacteristic
121C2×C19#56311yescharacteristic
122C22×Q8—191no—
123C22×Q8—192no—
124C4⋊Q8—388no—
125C2×C4⋊C4—191no—
126C2×C4⋊C4—192no—
127C2×C4⋊C4—192no—
128C2×C4⋊C4—192no—
129C2×C4⋊C4—191no—
130C2×C4⋊C4—191no—
131C2×C4⋊C4—192no—
132C2×C4⋊C4C2×D1912yes—
133C2×C4⋊C4C2×D1911yescharacteristic
134C2×C4⋊C4C2×D1911yescharacteristic
135C2×C42—192no—
136C2×C42C2×D1911yescharacteristic
137#95—192no—
138#95—192no—
139#95—192no—
140#95—192no—
141#95—192no—
142#95—192no—
143#95C2×D1912yes—
144C19#273411yescharacteristic, complemented, Sylow
145C2×Q8—194no—
146C2×Q8—384no—
147C2×Q8—761no—
148C2×Q8—761no—
149C2×Q8—762no—
150C2×Q8—762no—
151C22×C4—192no—
152C22×C4—192no—
153C22×C4—192no—
154C22×C4—192no—
155C22×C4C22×D1912yes—
156C22×C4C22×D1911yescharacteristic
157C22×C4C22×D1912yes—
158C22×C4C22×D1911yescharacteristic
159C22×C4C22×D1911yescharacteristic
160C4⋊C4—24no—
161C4⋊C4—41no—
162C4⋊C4—194no—
163C4⋊C4—384no—
164C4⋊C4—384no—
165C4⋊C4—384no—
166C4⋊C4—762no—
167C4⋊C4—761no—
168C4⋊C4—761no—
169C4⋊C4Dic3814yescomplemented
170C42—41no—
171C42—384no—
172C23C23×D1911yescharacteristic
173Q8—764no—
174Q8—768no—
175C2×C4—22no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—194no—
187C2×C4—194no—
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×Dic3814yes—
200C2×C4D4×D1912yes—
201C2×C4Q8×D1912yes—
202C22C22×Dic3811yescharacteristic
203C22C2×D4×D1911yescharacteristic
204C22#1059743011yescharacteristic
205C22C2×Q8×D1911yescharacteristic
206C22#1059743311yescharacteristic
207C22#1059743511yescharacteristic
208C22#1059743611yescharacteristic
209C4—22no—
210C4—22no—
211C4—22no—
212C4—24no—
213C4—42no—
214C4—384no—
215C4—384no—
216C4—762no—
217C4—762no—
218C2#1192710211yescharacteristic
219C2#1192717311yescharacteristic
220C2#1192717511yescharacteristic
221C2#1192720911yescharacteristic
222C2D4×Dic3811yescharacteristic
223C2Q8×Dic3811yescharacteristic
224C2#1192729811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, prime radical, cosocleC23×C19C24
FittingC19×#389C2
hypercenter#389D19
hypocenterC19#2734
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
49. C4⋊C4×C19Q8semidirect
54. C4⋊Dic19Q8semidirect
144. C19#2734semidirect
169. C4⋊C4Dic38semidirect

Maximal subgroups

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

subgroupindex
C2×#105973342
#119264772
#119264652
#119264642
#119264502
#119264422
#119264302
#119264272
C19×#3892
#273419