Finite Group Databasebeta

← #14569335

Subgroups — #14569335

Order 2432.

476 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 141 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×#10597318C211yesmaximal, characteristic
2#11926482C211yesmaximal, characteristic, complemented
3#11926479C211yesmaximal, characteristic
4#11926475C211yesmaximal, characteristic, complemented
5#11926470C211yesmaximal, characteristic
6#11926439C212yesmaximal, complemented
7#11926434C212yesmaximal
8#11926425C212yesmaximal, complemented
9#11926415C212yesmaximal
10#11926390C211yesmaximal, characteristic, complemented
11C2×C19×#125C211yesmaximal, characteristic, complemented
12C22×C4×D19C2211yescharacteristic
13C19×#125—24no—
14C2×C4⋊C4×C19C2212yes—
15C2×C4⋊C4×C19C2212yes—
16C2×C4⋊C4×C19C2211yescharacteristic
17C2×C4⋊C4×C19C2211yescharacteristic
18C2×C42×C19C2211yescharacteristic
19C2×(C2×D19)⋊C4C2212yes—
20C2×(C2×D19)⋊C4C2212yes—
21C2×(C2×D19)⋊C4C2211yescharacteristic
22C2×(C2×D19)⋊C4C2211yescharacteristic
23C2×Dic19⋊C4C2212yes—
24C2×Dic19⋊C4C2212yes—
25C2×Dic19⋊C4C2211yescharacteristic
26C2×Dic19⋊C4C2211yescharacteristic
27C2×C4×Dic19C2212yes—
28C2×C4×Dic19C2211yescharacteristic
29#10597318—24no—
30C19⋊#95C2212yes—
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—
48C2×C4×D19—22no—
49C2×C4×D19—22no—
50C2×C4×D19—22no—
51C4⋊C4×C19—24no—
52C4⋊C4×C19—24no—
53C4⋊C4×C19—22no—
54C4⋊C4×C19—22no—
55C42×C19D414yes—
56(C2×D19)⋊C4—24no—
57(C2×D19)⋊C4—22no—
58(C2×D19)⋊C4—22no—
59(C2×D19)⋊C4—24no—
60Dic19⋊C4—22no—
61Dic19⋊C4—22no—
62Dic19⋊C4—24no—
63Dic19⋊C4—24no—
64C4×Dic19—22no—
65C4×Dic19—24no—
66C23×C19C2411yescharacteristic
67C22×D19—21no—
68C22×D19—22no—
69C22×D19—21no—
70C22×D19—22no—
71C22×D19#4112yes—
72C2×C4×C19—22no—
73C2×C4×C19—21no—
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×C19—22no—
82C2×C4×C19C2×D412yes—
83C2×C4×C19C2×D412yes—
84C2×C4×C19C2×D412yes—
85C2×Dic19—21no—
86C2×Dic19—22no—
87C2×Dic19—21no—
88C2×Dic19—22no—
89C2×Dic19—21no—
90C2×Dic19—21no—
91C2×Dic19—22no—
92C2×Dic19—22no—
93C2×Dic19—22no—
94C2×Dic19—22no—
95C2×Dic19—22no—
96C2×Dic19#4114yes—
97C2×Dic19#4112yes—
98C4×D19—28no—
99#2611—191nomaximal, Sylow
100C22×C19C22×D411yescharacteristic
101C22×C19C2×#4111yescharacteristic
102C22×C19C2×#4111yescharacteristic
103C22×C19C2×#4112yes—
104C22×C192−1+412yes—
105C2×D19—22no—
106C2×D19—24no—
107C2×D19—41no—
108C2×D19—41no—
109C2×D19—42no—
110C4×C19—22no—
111C4×C19—22no—
112C4×C19—22no—
113C4×C19—42no—
114C4×C19—42no—
115Dic19—22no—
116Dic19—24no—
117Dic19—41no—
118Dic19—41no—
119Dic19—42no—
120C2×#125D1911yescharacteristic, complemented
121C2×#117—191no—
122#400—191no—
123#399—191no—
124#398—191no—
125#397—191no—
126#389—192no—
127#388—192no—
128#387—192no—
129#385—192no—
130#376—191no—
131C2×C19#52511yescharacteristic
132C2×C19#53211yescharacteristic
133C2×C19#53611yescharacteristic
134C2×C19#55212yes—
135C2×C19#55212yes—
136D19—42no—
137C23×C4—191no—
138#125—24no—
139#117—384no—
140C2×C4⋊C4—191no—
141C2×C4⋊C4—191no—
142C2×C4⋊C4—192no—
143C2×C4⋊C4—192no—
144C2×C4⋊C4C2×D1912yes—
145C2×C4⋊C4C2×D1912yes—
146C2×C4⋊C4C2×D1911yescharacteristic
147C2×C4⋊C4C2×D1911yescharacteristic
148C2×C22⋊C4—191no—
149C2×C22⋊C4—191no—
150C2×C22⋊C4—192no—
151C2×C22⋊C4—192no—
152C2×C42—191no—
153C2×C42—192no—
154C2×C42C2×D1911yescharacteristic
155#95—192no—
156#95—191no—
157#95—191no—
158#95—192no—
159#95—192no—
160#95—192no—
161#95—192no—
162C19#261111yescharacteristic, complemented, Sylow
163C24—191no—
164C22×C4—192no—
165C22×C4—191no—
166C22×C4—192no—
167C22×C4—191no—
168C22×C4—191no—
169C22×C4—382no—
170C22×C4—382no—
171C22×C4—382no—
172C22×C4C22×D1912yes—
173C22×C4C22×D1912yes—
174C22×C4C22×D1911yescharacteristic
175C22×C4C22×D1911yescharacteristic
176C22×C4C22×D1911yescharacteristic
177C4⋊C4—24no—
178C4⋊C4—24no—
179C4⋊C4—22no—
180C4⋊C4—22no—
181C4⋊C4—384no—
182C4⋊C4—384no—
183C4⋊C4—382no—
184C4⋊C4—382no—
185C22⋊C4—384no—
186C22⋊C4—384no—
187C22⋊C4—382no—
188C22⋊C4—382no—
189C42—384no—
190C42—382no—
191C42C22⋊D1914yes—
192C23—192no—
193C23—382no—
194C23—382no—
195C23—381no—
196C23—381no—
197C23C23×D1911yescharacteristic
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—194no—
209C2×C4—192no—
210C2×C4—388no—
211C2×C4—382no—
212C2×C4—382no—
213C2×C4—381no—
214C2×C4—381no—
215C2×C4—382no—
216C2×C4—382no—
217C2×C4—382no—
218C2×C4—382no—
219C2×C4—382no—
220C2×C4—381no—
221C2×C4—381no—
222C2×C4C2×C22⋊D1912yes—
223C2×C4C2×C22⋊D1912yes—
224C2×C4C2×C22⋊D1912yes—
225C22—382no—
226C22—384no—
227C22—761no—
228C22—761no—
229C22—762no—
230C22#1059743312yes—
231C22#41×D1911yescharacteristic
232C22#41×D1911yescharacteristic
233C22#41×D1912yes—
234C22C22×C22⋊D1911yescharacteristic
235C4—22no—
236C4—22no—
237C4—22no—
238C4—42no—
239C4—42no—
240C4—382no—
241C4—384no—
242C4—761no—
243C4—761no—
244C4—762no—
245C2—762no—
246C2#1192705111yescharacteristic
247C2#1192709011yescharacteristic
248C2#1192711811yescharacteristic
249C2#1192722612yes—
250C2#1192722612yes—
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC2×C19×#125C2
prime radicalC23×D19C23
hypercenterC2×#125D19
hypocenterC19#2611
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. #11926475C2semidirect
6. #11926439C2semidirect
8. #11926425C2semidirect
10. #11926390C2semidirect
11. C2×C19×#125C2semidirect
120. C2×#125D19semidirect
162. C19#2611semidirect

Maximal subgroups

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

subgroupindex
C2×#105973182
#119264822
#119264792
#119264752
#119264702
#119264392
#119264342
#119264252
#119264152
#119263902
C2×C19×#1252
#261119