Finite Group Databasebeta

← #14571706

Subgroups — #14571706

Order 2432.

456 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 125 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×#10597325C212yesmaximal, complemented
2#11926478C212yesmaximal, complemented
3#11926474C211yesmaximal, characteristic, complemented
4#11926467C212yesmaximal, complemented
5#11926467C212yesmaximal, complemented
6#11926467C212yesmaximal, complemented
7#11926458C212yesmaximal
8#11926413C211yesmaximal, characteristic, complemented
9C19×#394C211yesmaximal, characteristic
10C22×D4×C19C2211yescharacteristic
11C2×C4⋊C4×C19C2211yescharacteristic
12C2×C22⋊C4×C19C2212yes—
13C2×C22⋊C4×C19C2212yes—
14C2×C22⋊Dic19C2212yes—
15C2×C22⋊Dic19C2212yes—
16C2×C22⋊Dic19C2212yes—
17C2×C22⋊Dic19C2212yes—
18C2×C4⋊Dic19C2212yes—
19C2×C4⋊Dic19C2211yescharacteristic
20C2×C4⋊Dic19C2211yescharacteristic
21C2×Dic19⋊C4C2212yes—
22C2×Dic19⋊C4C2212yes—
23C2×Dic19⋊C4C2212yes—
24C2×Dic19⋊C4C2212yes—
25C2×Dic19⋊C4C2212yes—
26C2×C4×Dic19C2211yescharacteristic
27#10597325—28no—
28C19×#95C2211yescharacteristic
29C19⋊#95C2212yes—
30C19⋊#95C2211yescharacteristic
31C19⋊#95C2212yes—
32C24×C19C2312yes—
33C2×D4×C19—42no—
34C2×D4×C19—41no—
35C22×C4×C19C2311yescharacteristic
36C22×C4×C19C2312yes—
37C22×C4×C19C2311yescharacteristic
38C22×C4×C19C2311yescharacteristic
39C22×Dic19C2312yes—
40C22×Dic19C2312yes—
41C22×Dic19C2312yes—
42C22×Dic19C2312yes—
43C4⋊C4×C19—41no—
44C22⋊C4×C19—24no—
45C22⋊C4×C19—42no—
46C22⋊Dic19—24no—
47C22⋊Dic19—24no—
48C22⋊Dic19—42no—
49C22⋊Dic19—42no—
50C4⋊Dic19—24no—
51C4⋊Dic19—41no—
52C4⋊Dic19—41no—
53Dic19⋊C4—24no—
54Dic19⋊C4—24no—
55Dic19⋊C4—42no—
56Dic19⋊C4—42no—
57Dic19⋊C4—42no—
58C4×Dic19D414yescomplemented
59C23×C19—22no—
60C23×C19—22no—
61C23×C19—22no—
62C23×C19—22no—
63C23×C19—22no—
64C23×C19—22no—
65C23×C19—22no—
66C23×C19C2411yescharacteristic
67D4×C19—44no—
68C2×C4×C19—21no—
69C2×C4×C19—21no—
70C2×C4×C19—22no—
71C2×C4×C19—22no—
72C2×C4×C19—22no—
73C2×C4×C19—22no—
74C2×C4×C19—21no—
75C2×C4×C19—21no—
76C2×C4×C19—22no—
77C2×C4×C19C2×D412yes—
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—22no—
88C2×Dic19—22no—
89C2×Dic19C2×D414yes—
90#2823—191nomaximal, Sylow
91C22×C19—42no—
92C22×C19—42no—
93C22×C19—42no—
94C22×C19—42no—
95C22×C19—42no—
96C22×C19—42no—
97C22×C19—42no—
98C22×C19C22×D411yescharacteristic
99C22×C19H(5,𝔽2)12yes—
100C22×C19H(5,𝔽2)11yescharacteristic
101C22×C192−1+411yescharacteristic
102C22×C192−1+412yes—
103C4×C19—22no—
104C4×C19—42no—
105C4×C19—41no—
106C4×C19—41no—
107Dic19—24no—
108Dic19—42no—
109Dic19—42no—
110Dic19—42no—
111C2×#126—192no—
112#398—191no—
113#398—192no—
114#396—192no—
115#396—192no—
116#396—192no—
117#394—192no—
118#394D1911yescharacteristic
119#384—191no—
120C2×C19—82no—
121C2×C19#53711yescharacteristic
122C2×C19#53712yes—
123C2×C19#56011yescharacteristic
124C2×C19#56312yes—
125C2×C19#56311yescharacteristic
126C22×D4C2×D1911yescharacteristic
127#126—388no—
128C2×C4⋊C4—192no—
129C2×C4⋊C4—192no—
130C2×C4⋊C4—192no—
131C2×C4⋊C4—192no—
132C2×C4⋊C4—192no—
133C2×C4⋊C4—191no—
134C2×C4⋊C4—192no—
135C2×C4⋊C4—191no—
136C2×C4⋊C4C2×D1911yescharacteristic
137C2×C22⋊C4—192no—
138C2×C22⋊C4—192no—
139C2×C22⋊C4—192no—
140C2×C22⋊C4—192no—
141C2×C22⋊C4C2×D1912yes—
142C2×C22⋊C4C2×D1912yes—
143C2×C42—191no—
144#95—192no—
145#95—191no—
146#95—192no—
147#95C2×D1911yescharacteristic
148C19#282311yescharacteristic, complemented, Sylow
149C24C22×D1912yes—
150C2×D4—41no—
151C2×D4—42no—
152C22×C4—192no—
153C22×C4—192no—
154C22×C4—192no—
155C22×C4—192no—
156C22×C4C22×D1911yescharacteristic
157C22×C4C22×D1912yes—
158C22×C4C22×D1911yescharacteristic
159C22×C4C22×D1911yescharacteristic
160C4⋊C4—41no—
161C4⋊C4—384no—
162C4⋊C4—384no—
163C4⋊C4—384no—
164C4⋊C4—762no—
165C4⋊C4—762no—
166C4⋊C4—762no—
167C4⋊C4—761no—
168C4⋊C4—761no—
169C22⋊C4—24no—
170C22⋊C4—42no—
171C22⋊C4—384no—
172C22⋊C4—384no—
173C22⋊C4—762no—
174C22⋊C4—762no—
175C42—194no—
176C23—22no—
177C23—22no—
178C23—22no—
179C23—22no—
180C23—22no—
181C23—22no—
182C23—22no—
183C23C23×D1911yescharacteristic
184D4—44no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—194no—
195C2×C4—382no—
196C2×C4—382no—
197C2×C4—382no—
198C2×C4—382no—
199C2×C4—382no—
200C2×C4—382no—
201C2×C4—382no—
202C2×C4—382no—
203C2×C4—382no—
204C2×C4—382no—
205C2×C4—382no—
206C2×C4D4×D1912yes—
207C22—42no—
208C22—42no—
209C22—42no—
210C22—42no—
211C22—42no—
212C22—42no—
213C22—42no—
214C22C2×D4×D1911yescharacteristic
215C22#1059743012yes—
216C22#1059743011yescharacteristic
217C22#1059743611yescharacteristic
218C22#1059743612yes—
219C4—22no—
220C4—42no—
221C4—41no—
222C4—41no—
223C4—384no—
224C4—762no—
225C4—762no—
226C4—762no—
227C2—82no—
228C2#1192712111yescharacteristic
229C2#1192712312yes—
230C2#1192728311yescharacteristic
231C2#1192729411yescharacteristic
232C2#1192729712yes—
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC19×#394C2
prime radicalC22×D4×C19C22
hypercenter#394D19
hypocenterC19#2823
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C2×#10597325C2semidirect
2. #11926478C2semidirect
3. #11926474C2semidirect
4. #11926467C2semidirect
5. #11926467C2semidirect
6. #11926467C2semidirect
8. #11926413C2semidirect
58. C4×Dic19D4semidirect
148. C19#2823semidirect

Maximal subgroups

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

subgroupindex
C2×#105973252
#119264782
#119264742
#119264672
#119264582
#119264132
C19×#3942
#282319