Finite Group Databasebeta

← #14571734

Subgroups — #14571734

Order 2432.

464 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 117 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#11926485C212yesmaximal, complemented
2#11926480C211yesmaximal, characteristic, complemented
3#11926472C212yesmaximal, complemented
4#11926467C212yesmaximal, complemented
5#11926458C212yesmaximal, complemented
6#11926458C212yesmaximal, complemented
7#11926424C212yesmaximal, complemented
8#11926416C211yesmaximal, characteristic, complemented
9C19×#392C211yesmaximal, characteristic
10C22×D4×C19C2212yes—
11C22×D4×C19C2211yescharacteristic
12C23×Dic19C2211yescharacteristic
13C2×C22⋊C4×C19C2211yescharacteristic
14C2×C22⋊C4×C19C2212yes—
15C2×C22⋊Dic19C2211yescharacteristic
16C2×C22⋊Dic19C2212yes—
17C2×C22⋊Dic19C2212yes—
18C2×C22⋊Dic19C2212yes—
19C2×C22⋊Dic19C2212yes—
20C2×C22⋊Dic19C2212yes—
21C2×C4⋊Dic19C2211yescharacteristic
22C2×Dic19⋊C4C2212yes—
23C2×Dic19⋊C4C2212yes—
24C2×Dic19⋊C4C2212yes—
25C19×#95C2211yescharacteristic
26C19⋊#95C2212yes—
27C19⋊#95C2212yes—
28C19⋊#95C2212yes—
29C19⋊#95C2212yes—
30C19⋊#95C2211yescharacteristic
31C24×C19C2312yes—
32C24×C19C2311yescharacteristic
33C2×D4×C19—24no—
34C2×D4×C19—42no—
35C2×D4×C19—42no—
36C2×D4×C19—42no—
37C2×D4×C19—41no—
38C22×C4×C19C2311yescharacteristic
39C22×C4×C19C2312yes—
40C22×C4×C19C2311yescharacteristic
41C22×Dic19—42no—
42C22×Dic19—41no—
43C22×Dic19C2312yes—
44C22×Dic19C2312yes—
45C22×Dic19C2312yes—
46C22×Dic19C2312yes—
47C22⋊C4×C19—42no—
48C22⋊C4×C19—41no—
49C22⋊Dic19—22no—
50C22⋊Dic19—42no—
51C22⋊Dic19—42no—
52C22⋊Dic19—42no—
53C22⋊Dic19—42no—
54C22⋊Dic19—42no—
55C4⋊Dic19—41no—
56Dic19⋊C4—42no—
57Dic19⋊C4—42no—
58Dic19⋊C4—42no—
59C23×C19—22no—
60C23×C19—21no—
61C23×C19—22no—
62C23×C19—21no—
63C23×C19—22no—
64C23×C19—22no—
65C23×C19—22no—
66C23×C19—22no—
67C23×C19—22no—
68C23×C19—22no—
69C23×C19—22no—
70C23×C19#4112yes—
71C23×C19C2411yescharacteristic
72D4×C19—48no—
73D4×C19—44no—
74C2×C4×C19—22no—
75C2×C4×C19—22no—
76C2×C4×C19—22no—
77C2×C4×C19—22no—
78C2×C4×C19—21no—
79C2×C4×C19—22no—
80C2×C4×C19—21no—
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×Dic19—22no—
90C2×Dic19—22no—
91C2×Dic19—22no—
92C2×Dic19—22no—
93C2×Dic19—44no—
94#2826—191nomaximal, Sylow
95C22×C19—24no—
96C22×C19—22no—
97C22×C19—41no—
98C22×C19—41no—
99C22×C19—42no—
100C22×C19—42no—
101C22×C19—42no—
102C22×C19—42no—
103C22×C19—42no—
104C22×C19—42no—
105C22×C19—42no—
106C22×C19—42no—
107C22×C19C2×#4111yescharacteristic
108C22×C19H(5,𝔽2)12yes—
109C22×C19H(5,𝔽2)12yes—
110C22×C19H(5,𝔽2)11yescharacteristic
111C22×C192−1+411yescharacteristic
112C4×C19—42no—
113C4×C19—41no—
114C4×C19—41no—
115Dic19—42no—
116Dic19—42no—
117Dic19—42no—
118Dic19—42no—
119#400—192no—
120#399—191no—
121#397—192no—
122#396—192no—
123#394—192no—
124#394—192no—
125#392D1911yescharacteristic
126#386—192no—
127#385—191no—
128C2×C19—42no—
129C2×C19—82no—
130C2×C19#53812yes—
131C2×C19#53911yescharacteristic
132C2×C19#56011yescharacteristic
133C2×C19#56011yescharacteristic
134C2×C19#56212yes—
135C22×D4C2×D1912yes—
136C22×D4C2×D1911yescharacteristic
137C23×C4—191no—
138C2×C4⋊C4—192no—
139C2×C4⋊C4—192no—
140C2×C4⋊C4—192no—
141C2×C4⋊C4—191no—
142C2×C22⋊C4—191no—
143C2×C22⋊C4—192no—
144C2×C22⋊C4—192no—
145C2×C22⋊C4—192no—
146C2×C22⋊C4—192no—
147C2×C22⋊C4—192no—
148C2×C22⋊C4C2×D1911yescharacteristic
149C2×C22⋊C4C2×D1912yes—
150#95—192no—
151#95—192no—
152#95—192no—
153#95—192no—
154#95—191no—
155#95C2×D1911yescharacteristic
156C19#282611yescharacteristic, complemented, Sylow
157C24C22×D1912yes—
158C24C22×D1911yescharacteristic
159C2×D4—24no—
160C2×D4—42no—
161C2×D4—41no—
162C2×D4—42no—
163C2×D4—42no—
164C22×C4—192no—
165C22×C4—192no—
166C22×C4—192no—
167C22×C4—192no—
168C22×C4—761no—
169C22×C4—762no—
170C22×C4C22×D1912yes—
171C22×C4C22×D1911yescharacteristic
172C22×C4C22×D1911yescharacteristic
173C4⋊C4—762no—
174C4⋊C4—762no—
175C4⋊C4—762no—
176C4⋊C4—761no—
177C22⋊C4—41no—
178C22⋊C4—42no—
179C22⋊C4—382no—
180C22⋊C4—762no—
181C22⋊C4—762no—
182C22⋊C4—762no—
183C22⋊C4—762no—
184C22⋊C4—762no—
185C23—21no—
186C23—22no—
187C23—22no—
188C23—21no—
189C23—22no—
190C23—22no—
191C23—22no—
192C23—22no—
193C23—22no—
194C23—22no—
195C23—22no—
196C23#6454312yes—
197C23C23×D1911yescharacteristic
198D4—48no—
199D4—44no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—21no—
203C2×C4—22no—
204C2×C4—21no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—382no—
208C2×C4—382no—
209C2×C4—382no—
210C2×C4—382no—
211C2×C4—382no—
212C2×C4—382no—
213C2×C4—382no—
214C2×C4—382no—
215C2×C4—382no—
216C2×C4—382no—
217C2×C4—382no—
218C2×C4—382no—
219C2×C4—764no—
220C22—24no—
221C22—22no—
222C22—41no—
223C22—41no—
224C22—42no—
225C22—42no—
226C22—42no—
227C22—42no—
228C22—42no—
229C22—42no—
230C22—42no—
231C22—42no—
232C22C2×#6454311yescharacteristic
233C22#1059743012yes—
234C22#1059743012yes—
235C22#1059743011yescharacteristic
236C22#1059743611yescharacteristic
237C4—42no—
238C4—41no—
239C4—41no—
240C4—762no—
241C4—762no—
242C4—762no—
243C4—762no—
244C2—42no—
245C2—82no—
246C2#1192712912yes—
247C2#1192713911yescharacteristic
248C2#1192728111yescharacteristic
249C2#1192728311yescharacteristic
250C2#1192728912yes—
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
Fitting, prime radicalC19×#392C2
hypercenter#392D19
hypocenterC19#2826
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. #11926485C2semidirect
2. #11926480C2semidirect
3. #11926472C2semidirect
4. #11926467C2semidirect
5. #11926458C2semidirect
6. #11926458C2semidirect
7. #11926424C2semidirect
8. #11926416C2semidirect
156. C19#2826semidirect

Maximal subgroups

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

subgroupindex
#119264852
#119264802
#119264722
#119264672
#119264582
#119264242
#119264162
C19×#3922
#282619