Finite Group Databasebeta

← #14569797

Subgroups — #14569797

Order 2432.

434 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 137 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×#10597316C211yesmaximal, characteristic, complemented
2#11926483C211yesmaximal, characteristic, complemented
3#11926480C211yesmaximal, characteristic
4#11926477C212yesmaximal, complemented
5#11926474C211yesmaximal, characteristic, complemented
6#11926469C211yesmaximal, characteristic
7#11926467C212yesmaximal
8#11926439C212yesmaximal, complemented
9#11926438C212yesmaximal
10C4×C4⋊Dic19C211yesmaximal, characteristic, complemented
11C2×C19×#126C211yesmaximal, characteristic
12C19×#126—24no—
13C2×C4⋊C4×C19C2211yescharacteristic
14C2×C4⋊C4×C19C2211yescharacteristic
15C2×C4⋊C4×C19C2211yescharacteristic
16C2×C22⋊C4×C19C2211yescharacteristic
17C2×C22⋊C4×C19C2211yescharacteristic
18C2×C22⋊C4×C19C2211yescharacteristic
19C2×C42×C19C2211yescharacteristic
20C2×C22⋊Dic19C2212yes—
21C2×C22⋊Dic19C2212yes—
22C2×C4⋊Dic19C2211yescharacteristic
23C2×C4⋊Dic19C2211yescharacteristic
24C2×C4⋊Dic19C2212yes—
25C2×Dic19⋊C4C2212yes—
26C2×Dic19⋊C4C2212yes—
27C2×Dic19⋊C4C2212yes—
28C2×Dic19⋊C4C2212yes—
29C2×C4×Dic19C2212yes—
30#10597316—24no—
31C19⋊#95C2211yescharacteristic
32C19⋊#95C2211yescharacteristic
33C19⋊#95C2212yes—
34C19⋊#95C2212yes—
35C19⋊#95C2212yes—
36C19⋊#95C2212yes—
37C24×C19C2311yescharacteristic
38C22×C4×C19C2311yescharacteristic
39C22×C4×C19C2311yescharacteristic
40C22×C4×C19C2311yescharacteristic
41C22×C4×C19C2311yescharacteristic
42C22×C4×C19C2311yescharacteristic
43C22×C4×C19C2311yescharacteristic
44C22×Dic19C2312yes—
45C22×Dic19C2312yes—
46C22×Dic19C2312yes—
47C22×Dic19C2312yes—
48C4⋊C4×C19—22no—
49C4⋊C4×C19—22no—
50C4⋊C4×C19—22no—
51C22⋊C4×C19—22no—
52C22⋊C4×C19—22no—
53C22⋊C4×C19—22no—
54C42×C19D414yes—
55C22⋊Dic19—24no—
56C22⋊Dic19—42no—
57C4⋊Dic19—22no—
58C4⋊Dic19—22no—
59C4⋊Dic19—24no—
60Dic19⋊C4—24no—
61Dic19⋊C4—24no—
62Dic19⋊C4—24no—
63Dic19⋊C4—42no—
64C4×Dic19—42no—
65C23×C19—21no—
66C23×C19—22no—
67C23×C19—21no—
68C23×C19—22no—
69C23×C19—21no—
70C23×C19C2411yescharacteristic
71C2×C4×C19—22no—
72C2×C4×C19—21no—
73C2×C4×C19—22no—
74C2×C4×C19—21no—
75C2×C4×C19—21no—
76C2×C4×C19—21no—
77C2×C4×C19—21no—
78C2×C4×C19—22no—
79C2×C4×C19—21no—
80C2×C4×C19—22no—
81C2×C4×C19—21no—
82C2×C4×C19C2×D412yes—
83C2×C4×C19C2×D412yes—
84C2×C4×C19C2×D412yes—
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—22no—
94C2×Dic19—22no—
95C2×Dic19—22no—
96C2×Dic19#4114yes—
97#2664—191nomaximal, Sylow
98C22×C19—41no—
99C22×C19—41no—
100C22×C19—41no—
101C22×C19—42no—
102C22×C19—42no—
103C22×C19C22×D411yescharacteristic
104C22×C19C2×#4112yes—
105C22×C19H(5,𝔽2)11yescharacteristic
106C22×C192−1+412yes—
107C22×C192−1+411yescharacteristic
108C4×C19—22no—
109C4×C19—22no—
110C4×C19—22no—
111C4×C19—41no—
112C4×C19—41no—
113C4×C19—41no—
114Dic19—24no—
115Dic19—42no—
116Dic19—42no—
117Dic19—42no—
118C2×#126D1911yescharacteristic
119C2×#125—191no—
120#400—191no—
121#399—191no—
122#398—191no—
123#398—192no—
124#397—191no—
125#396—192no—
126#389—192no—
127#388—192no—
128C4×C4⋊C4—191no—
129C2×C19—81no—
130C2×C19#53211yescharacteristic
131C2×C19#53611yescharacteristic
132C2×C19#53711yescharacteristic
133C2×C19#53912yes—
134C2×C19#54112yes—
135#126—24no—
136#125—384no—
137C2×C4⋊C4—192no—
138C2×C4⋊C4—192no—
139C2×C4⋊C4—191no—
140C2×C4⋊C4—191no—
141C2×C4⋊C4—192no—
142C2×C4⋊C4—192no—
143C2×C4⋊C4—192no—
144C2×C4⋊C4C2×D1911yescharacteristic
145C2×C4⋊C4C2×D1911yescharacteristic
146C2×C4⋊C4C2×D1911yescharacteristic
147C2×C22⋊C4—192no—
148C2×C22⋊C4—192no—
149C2×C22⋊C4C2×D1911yescharacteristic
150C2×C22⋊C4C2×D1911yescharacteristic
151C2×C22⋊C4C2×D1911yescharacteristic
152C2×C42—192no—
153C2×C42C2×D1911yescharacteristic
154#95—191no—
155#95—191no—
156#95—192no—
157#95—192no—
158#95—192no—
159#95—192no—
160C19#266411yescharacteristic, complemented, Sylow
161C24C22×D1911yescharacteristic
162C22×C4—192no—
163C22×C4—192no—
164C22×C4—192no—
165C22×C4—192no—
166C22×C4C22×D1911yescharacteristic
167C22×C4C22×D1911yescharacteristic
168C22×C4C22×D1911yescharacteristic
169C22×C4C22×D1911yescharacteristic
170C22×C4C22×D1911yescharacteristic
171C22×C4C22×D1911yescharacteristic
172C4⋊C4—22no—
173C4⋊C4—22no—
174C4⋊C4—22no—
175C4⋊C4—384no—
176C4⋊C4—384no—
177C4⋊C4—384no—
178C4⋊C4—384no—
179C4⋊C4—382no—
180C4⋊C4—382no—
181C4⋊C4—762no—
182C22⋊C4—22no—
183C22⋊C4—22no—
184C22⋊C4—22no—
185C22⋊C4—384no—
186C22⋊C4—762no—
187C42—762no—
188C42C22⋊D1914yes—
189C23—22no—
190C23—21no—
191C23—22no—
192C23—21no—
193C23—21no—
194C23C23×D1911yescharacteristic
195C2×C4—22no—
196C2×C4—21no—
197C2×C4—22no—
198C2×C4—21no—
199C2×C4—22no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—194no—
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×C4C2×C22⋊D1912yes—
219C2×C4C2×C22⋊D1912yes—
220C2×C4C2×C22⋊D1912yes—
221C22—41no—
222C22—41no—
223C22—41no—
224C22—42no—
225C22—42no—
226C22#41×D1912yes—
227C22#1059743511yescharacteristic
228C22#1059743612yes—
229C22#1059743611yescharacteristic
230C22C22×C22⋊D1911yescharacteristic
231C4—22no—
232C4—22no—
233C4—22no—
234C4—41no—
235C4—41no—
236C4—41no—
237C4—384no—
238C4—762no—
239C4—762no—
240C4—762no—
241C2—81no—
242C2#1192709011yescharacteristic
243C2#1192711511yescharacteristic
244C2#1192712211yescharacteristic
245C2#1192713512yes—
246C2#1192715112yes—
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC2×C19×#126C2
prime radicalC24×C19C23
hypercenterC2×#126D19
hypocenterC19#2664
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×#126

Complements

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

NH ≅ G/Ntype
1. C2×#10597316C2semidirect
2. #11926483C2semidirect
4. #11926477C2semidirect
5. #11926474C2semidirect
8. #11926439C2semidirect
10. C4×C4⋊Dic19C2semidirect
160. C19#2664semidirect

Maximal subgroups

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

subgroupindex
C2×#105973162
#119264832
#119264802
#119264772
#119264742
#119264692
#119264672
#119264392
#119264382
C4×C4⋊Dic192
C2×C19×#1262
#266419