Finite Group Databasebeta

← #14569796

Subgroups — #14569796

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×#10597322C211yesmaximal, characteristic
2#11926482C211yesmaximal, characteristic, complemented
3#11926479C211yesmaximal, characteristic
4#11926477C212yesmaximal, complemented
5#11926475C211yesmaximal, characteristic, complemented
6#11926470C211yesmaximal, characteristic
7#11926466C212yesmaximal
8#11926439C212yesmaximal, complemented
9#11926434C212yesmaximal
10C4×C4⋊Dic19C211yesmaximal, characteristic, complemented
11C2×C19×#125C211yesmaximal, characteristic, complemented
12C19×#125—24no—
13C2×C4⋊C4×C19C2212yes—
14C2×C4⋊C4×C19C2212yes—
15C2×C4⋊C4×C19C2211yescharacteristic
16C2×C4⋊C4×C19C2211yescharacteristic
17C2×C42×C19C2211yescharacteristic
18C2×(C2×D19)⋊C4C2211yescharacteristic
19C2×(C2×D19)⋊C4C2211yescharacteristic
20C2×(C2×D19)⋊C4C2211yescharacteristic
21C2×(C2×D19)⋊C4C2212yes—
22C2×(C2×D19)⋊C4C2212yes—
23C2×C4⋊Dic19C2212yes—
24C2×Dic19⋊C4C2211yescharacteristic
25C2×Dic19⋊C4C2211yescharacteristic
26C2×Dic19⋊C4C2211yescharacteristic
27C2×Dic19⋊C4C2212yes—
28C2×Dic19⋊C4C2212yes—
29C2×C4×Dic19C2212yes—
30#10597322—24no—
31C19⋊#95C2211yescharacteristic
32C19⋊#95C2211yescharacteristic
33C19⋊#95C2212yes—
34C19⋊#95C2212yes—
35C19⋊#95C2212yes—
36C19⋊#95C2212yes—
37C23×D19C2311yescharacteristic
38C22×C4×C19C2312yes—
39C22×C4×C19C2312yes—
40C22×C4×C19C2311yescharacteristic
41C22×C4×C19C2311yescharacteristic
42C22×C4×C19C2311yescharacteristic
43C22×Dic19C2312yes—
44C22×Dic19C2311yescharacteristic
45C22×Dic19C2311yescharacteristic
46C22×Dic19C2311yescharacteristic
47C22×Dic19C2312yes—
48C4⋊C4×C19—24no—
49C4⋊C4×C19—24no—
50C4⋊C4×C19—22no—
51C4⋊C4×C19—22no—
52C42×C19D414yes—
53(C2×D19)⋊C4—22no—
54(C2×D19)⋊C4—22no—
55(C2×D19)⋊C4—22no—
56(C2×D19)⋊C4—24no—
57(C2×D19)⋊C4—42no—
58C4⋊Dic19—24no—
59Dic19⋊C4—22no—
60Dic19⋊C4—22no—
61Dic19⋊C4—22no—
62Dic19⋊C4—24no—
63Dic19⋊C4—42no—
64C4×Dic19—42no—
65C23×C19C2411yescharacteristic
66C22×D19—21no—
67C22×D19—22no—
68C22×D19—21no—
69C22×D19—22no—
70C22×D19—21no—
71C2×C4×C19—22no—
72C2×C4×C19—21no—
73C2×C4×C19—22no—
74C2×C4×C19—21no—
75C2×C4×C19—22no—
76C2×C4×C19—22no—
77C2×C4×C19—22no—
78C2×C4×C19—22no—
79C2×C4×C19—22no—
80C2×C4×C19—22no—
81C2×C4×C19C2×D412yes—
82C2×C4×C19C2×D412yes—
83C2×C4×C19C2×D412yes—
84C2×Dic19—22no—
85C2×Dic19—22no—
86C2×Dic19—21no—
87C2×Dic19—21no—
88C2×Dic19—21no—
89C2×Dic19—22no—
90C2×Dic19—22no—
91C2×Dic19—22no—
92C2×Dic19—21no—
93C2×Dic19—22no—
94C2×Dic19—22no—
95C2×Dic19—21no—
96C2×Dic19#4114yes—
97#2664—191nomaximal, Sylow
98C22×C19C22×D411yescharacteristic
99C22×C19C2×#4112yes—
100C22×C19H(5,𝔽2)11yescharacteristic
101C22×C192−1+412yes—
102C22×C192−1+411yescharacteristic
103C2×D19—41no—
104C2×D19—41no—
105C2×D19—41no—
106C2×D19—42no—
107C2×D19—42no—
108C4×C19—22no—
109C4×C19—22no—
110C4×C19—22no—
111C4×C19—42no—
112C4×C19—42no—
113Dic19—24no—
114Dic19—41no—
115Dic19—41no—
116Dic19—41no—
117Dic19—42no—
118C2×#126—191no—
119C2×#125D1911yescharacteristic, complemented
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#53211yescharacteristic
130C2×C19#53611yescharacteristic
131C2×C19#53711yescharacteristic
132C2×C19#53912yes—
133C2×C19#54112yes—
134D19—81no—
135#126—384no—
136#125—24no—
137C2×C4⋊C4—191no—
138C2×C4⋊C4—191no—
139C2×C4⋊C4—191no—
140C2×C4⋊C4—192no—
141C2×C4⋊C4—192no—
142C2×C4⋊C4—192no—
143C2×C4⋊C4C2×D1912yes—
144C2×C4⋊C4C2×D1912yes—
145C2×C4⋊C4C2×D1911yescharacteristic
146C2×C4⋊C4C2×D1911yescharacteristic
147C2×C22⋊C4—191no—
148C2×C22⋊C4—191no—
149C2×C22⋊C4—191no—
150C2×C22⋊C4—192no—
151C2×C22⋊C4—192no—
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
161C24—191no—
162C22×C4—192no—
163C22×C4—192no—
164C22×C4—191no—
165C22×C4—191no—
166C22×C4—191no—
167C22×C4C22×D1912yes—
168C22×C4C22×D1912yes—
169C22×C4C22×D1911yescharacteristic
170C22×C4C22×D1911yescharacteristic
171C22×C4C22×D1911yescharacteristic
172C4⋊C4—24no—
173C4⋊C4—24no—
174C4⋊C4—22no—
175C4⋊C4—22no—
176C4⋊C4—384no—
177C4⋊C4—384no—
178C4⋊C4—382no—
179C4⋊C4—382no—
180C4⋊C4—382no—
181C4⋊C4—762no—
182C22⋊C4—384no—
183C22⋊C4—382no—
184C22⋊C4—382no—
185C22⋊C4—382no—
186C22⋊C4—762no—
187C42—762no—
188C42C22⋊D1914yes—
189C23—382no—
190C23—382no—
191C23—381no—
192C23—381no—
193C23—381no—
194C23C23×D1911yescharacteristic
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—194no—
206C2×C4—382no—
207C2×C4—382no—
208C2×C4—382no—
209C2×C4—382no—
210C2×C4—382no—
211C2×C4—382no—
212C2×C4—382no—
213C2×C4—381no—
214C2×C4—381no—
215C2×C4—381no—
216C2×C4—381no—
217C2×C4—381no—
218C2×C4C2×C22⋊D1912yes—
219C2×C4C2×C22⋊D1912yes—
220C2×C4C2×C22⋊D1912yes—
221C22—761no—
222C22—761no—
223C22—761no—
224C22—762no—
225C22—762no—
226C22#1059743312yes—
227C22#41×D1912yes—
228C22#1059743511yescharacteristic
229C22#1059743611yescharacteristic
230C22C22×C22⋊D1911yescharacteristic
231C4—22no—
232C4—22no—
233C4—22no—
234C4—42no—
235C4—42no—
236C4—384no—
237C4—761no—
238C4—761no—
239C4—761no—
240C4—762no—
241C2—1521no—
242C2#1192709011yescharacteristic
243C2#1192711811yescharacteristic
244C2#1192712211yescharacteristic
245C2#1192714212yes—
246C2#1192715312yes—
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC2×C19×#125C2
prime radicalC23×D19C23
hypercenterC2×#125D19
hypocenterC19#2664
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
2. #11926482C2semidirect
4. #11926477C2semidirect
5. #11926475C2semidirect
8. #11926439C2semidirect
10. C4×C4⋊Dic19C2semidirect
11. C2×C19×#125C2semidirect
119. C2×#125D19semidirect
160. C19#2664semidirect

Maximal subgroups

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

subgroupindex
C2×#105973222
#119264822
#119264792
#119264772
#119264752
#119264702
#119264662
#119264392
#119264342
C4×C4⋊Dic192
C2×C19×#1252
#266419