Finite Group Databasebeta

← #14571710

Subgroups — #14571710

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×#10597344C212yesmaximal, complemented
2#11926478C212yesmaximal, complemented
3#11926468C212yesmaximal, complemented
4#11926466C212yesmaximal, complemented
5#11926466C212yesmaximal, complemented
6#11926462C212yesmaximal
7#11926461C211yesmaximal, characteristic
8#11926413C211yesmaximal, characteristic, complemented
9C19×#398C211yesmaximal, characteristic, complemented
10C22×D76C2211yescharacteristic
11C2×C4⋊C4×C19C2212yes—
12C2×C4⋊C4×C19C2211yescharacteristic
13C2×C4⋊C4×C19C2211yescharacteristic
14C2×(C2×D19)⋊C4C2212yes—
15C2×(C2×D19)⋊C4C2212yes—
16C2×(C2×D19)⋊C4C2212yes—
17C2×(C2×D19)⋊C4C2212yes—
18C2×(C2×D19)⋊C4C2212yes—
19C2×(C2×D19)⋊C4C2212yes—
20C2×C4⋊Dic19C2212yes—
21C2×C4⋊Dic19C2211yescharacteristic
22C2×Dic19⋊C4C2212yes—
23C2×Dic19⋊C4C2212yes—
24C2×Dic19⋊C4C2212yes—
25C2×Dic19⋊C4C2212yes—
26C2×C4×Dic19C2211yescharacteristic
27#10597344—28no—
28C19×#95C2212yes—
29C19×#95C2211yescharacteristic
30C19⋊#95C2211yescharacteristic
31C19⋊#95C2212yes—
32C23×D19C2312yes—
33C22×C4×C19C2312yes—
34C22×C4×C19C2311yescharacteristic
35C22×C4×C19C2311yescharacteristic
36C22×C4×C19C2312yes—
37C22×C4×C19C2311yescharacteristic
38C22×Dic19C2312yes—
39C22×Dic19C2312yes—
40C22×Dic19C2312yes—
41C2×D76—42no—
42C2×D76—41no—
43C4⋊C4×C19—24no—
44C4⋊C4×C19—41no—
45C4⋊C4×C19—41no—
46(C2×D19)⋊C4—24no—
47(C2×D19)⋊C4—24no—
48(C2×D19)⋊C4—24no—
49(C2×D19)⋊C4—42no—
50(C2×D19)⋊C4—42no—
51(C2×D19)⋊C4—42no—
52C4⋊Dic19—24no—
53C4⋊Dic19—41no—
54Dic19⋊C4—24no—
55Dic19⋊C4—42no—
56Dic19⋊C4—42no—
57Dic19⋊C4—42no—
58C4×Dic19D414yescomplemented
59C23×C19C2411yescharacteristic
60C22×D19—22no—
61C22×D19—22no—
62C22×D19—22no—
63C22×D19—22no—
64C22×D19—22no—
65C22×D19—22no—
66C22×D19—22no—
67C2×C4×C19—21no—
68C2×C4×C19—21no—
69C2×C4×C19—22no—
70C2×C4×C19—22no—
71C2×C4×C19—22no—
72C2×C4×C19—22no—
73C2×C4×C19—22no—
74C2×C4×C19—22no—
75C2×C4×C19—21no—
76C2×C4×C19—21no—
77C2×C4×C19—22no—
78C2×C4×C19—22no—
79C2×C4×C19C2×D412yes—
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×Dic19C2×D414yes—
89D76—44no—
90#2823—191nomaximal, Sylow
91C22×C19C22×D411yescharacteristic
92C22×C19H(5,𝔽2)11yescharacteristic
93C22×C19H(5,𝔽2)12yes—
94C22×C192−1+412yes—
95C22×C192−1+411yescharacteristic
96C2×D19—42no—
97C2×D19—42no—
98C2×D19—42no—
99C2×D19—42no—
100C2×D19—42no—
101C2×D19—42no—
102C2×D19—42no—
103C4×C19—22no—
104C4×C19—42no—
105C4×C19—42no—
106C4×C19—41no—
107C4×C19—41no—
108Dic19—24no—
109Dic19—42no—
110Dic19—42no—
111C2×#126—192no—
112#398—192no—
113#398D1911yescharacteristic, complemented
114#396—192no—
115#396—192no—
116#396—192no—
117#394—191no—
118#394—192no—
119#384—191no—
120C2×C19#53711yescharacteristic
121C2×C19#53712yes—
122C2×C19#56011yescharacteristic
123C2×C19#56312yes—
124C2×C19#56311yescharacteristic
125D19—82no—
126C22×D4—191no—
127#126—388no—
128C2×C4⋊C4—192no—
129C2×C4⋊C4—192no—
130C2×C4⋊C4—192no—
131C2×C4⋊C4—192no—
132C2×C4⋊C4—191no—
133C2×C4⋊C4—192no—
134C2×C4⋊C4C2×D1912yes—
135C2×C4⋊C4C2×D1911yescharacteristic
136C2×C4⋊C4C2×D1911yescharacteristic
137C2×C22⋊C4—192no—
138C2×C22⋊C4—192no—
139C2×C22⋊C4—192no—
140C2×C22⋊C4—192no—
141C2×C22⋊C4—192no—
142C2×C22⋊C4—192no—
143C2×C42—191no—
144#95—191no—
145#95—192no—
146#95C2×D1912yes—
147#95C2×D1911yescharacteristic
148C19#282311yescharacteristic, complemented, Sylow
149C24—192no—
150C2×D4—761no—
151C2×D4—762no—
152C22×C4—192no—
153C22×C4—192no—
154C22×C4—192no—
155C22×C4C22×D1911yescharacteristic
156C22×C4C22×D1912yes—
157C22×C4C22×D1912yes—
158C22×C4C22×D1911yescharacteristic
159C22×C4C22×D1911yescharacteristic
160C4⋊C4—24no—
161C4⋊C4—41no—
162C4⋊C4—41no—
163C4⋊C4—384no—
164C4⋊C4—384no—
165C4⋊C4—762no—
166C4⋊C4—762no—
167C4⋊C4—762no—
168C4⋊C4—761no—
169C22⋊C4—384no—
170C22⋊C4—384no—
171C22⋊C4—384no—
172C22⋊C4—762no—
173C22⋊C4—762no—
174C22⋊C4—762no—
175C42—194no—
176C23—382no—
177C23—382no—
178C23—382no—
179C23—382no—
180C23—382no—
181C23—382no—
182C23—382no—
183C23C23×D1911yescharacteristic
184D4—764no—
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—22no—
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—194no—
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—762no—
208C22—762no—
209C22—762no—
210C22—762no—
211C22—762no—
212C22—762no—
213C22—762no—
214C22C2×D4×D1911yescharacteristic
215C22#1059743011yescharacteristic
216C22#1059743312yes—
217C22#1059743512yes—
218C22#1059743611yescharacteristic
219C4—22no—
220C4—42no—
221C4—42no—
222C4—41no—
223C4—41no—
224C4—384no—
225C4—762no—
226C4—762no—
227C2—1522no—
228C2#1192712111yescharacteristic
229C2#1192712412yes—
230C2#1192728411yescharacteristic
231C2#1192729311yescharacteristic
232C2#1192729812yes—
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC19×#398C2
prime radicalC22×D76C22
hypercenter#398D19
hypocenterC19#2823
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
1. C2×#10597344C2semidirect
2. #11926478C2semidirect
3. #11926468C2semidirect
4. #11926466C2semidirect
5. #11926466C2semidirect
8. #11926413C2semidirect
9. C19×#398C2semidirect
58. C4×Dic19D4semidirect
113. #398D19semidirect
148. C19#2823semidirect

Maximal subgroups

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

subgroupindex
C2×#105973442
#119264782
#119264682
#119264662
#119264622
#119264612
#119264132
C19×#3982
#282319