Finite Group Databasebeta

← #14572998

Subgroups — #14572998

Order 2432.

698 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 698 conjugacy classes of subgroups — too many to draw. Only its 145 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×#10597433C211yesmaximal, characteristic, complemented
2#11927342C212yesmaximal, complemented
3#11926726C214yesmaximal, complemented
4#11926716C214yesmaximal, complemented
5#11926562C212yesmaximal, complemented
6C2×#10597293C211yesmaximal, characteristic, complemented
7C19×#536C211yesmaximal, characteristic, complemented
8C2×#41×C19C2211yescharacteristic
9C22×Q8×C19C2211yescharacteristic
10#10597433—22no—
11#10597433—24no—
12#10597433C2214yes—
13C2×#64545—22no—
14C2×Q8×D19—22no—
15C2×#64541—22no—
16C2×#64541C2212yes—
17C19×C4⋊Q8C2212yescomplemented
18C19×#124C2212yescomplemented
19C19×#123—22no—
20C19×C22⋊Q8—22no—
21C19×#117C2211yescharacteristic
22#10597397—22no—
23#10597396—24no—
24#10597395—22no—
25#10597388C2214yescomplemented
26#10597378C2214yescomplemented
27C2×#64520C2212yes—
28#10597293C2214yescomplemented
29#10597262C2218yescomplemented
30#41×C19—22no—
31#41×C19—22no—
32C2×Q8×C19—22no—
33C2×Q8×C19—22no—
34C2×Q8×C19D412yes—
35C2×Q8×C19C2311yescharacteristic
36C2×Q8×C19C2312yes—
37C2×D4×C19—21no—
38C2×D4×C19C2311yescharacteristic
39C22×C4×C19—21no—
40C22×C4×C19D412yes—
41C22×C4×C19C2311yescharacteristic
42C2×C22⋊D19—22no—
43#64545—28no—
44#64545—28no—
45Q8×D19—28no—
46Q8×D19—28no—
47#64541—28no—
48#64541—28no—
49#64541—22no—
50#64541—22no—
51#64541D414yes—
52#64541C2314yes—
53C2×D76—22no—
54C2×D76D412yes—
55C2×C4×D19—24no—
56C2×C4×D19—22no—
57C2×Dic38—22no—
58C2×Dic38D412yes—
59C4⋊C4×C19—21no—
60C4⋊C4×C19—24no—
61C22⋊C4×C19—21no—
62C22⋊C4×C19—24no—
63C42×C19C2312yes—
64#64528—24no—
65#64527—24no—
66#64526—24no—
67#64525—24no—
68#64520—22no—
69#64520C2314yes—
70C2×C19⋊C8—22no—
71C23×C19—21no—
72C23×C19C2×D411yescharacteristic
73C22×D19—22no—
74Q8×C19—24no—
75Q8×C19—24no—
76Q8×C19—22no—
77D4×C19—22no—
78D4×C19—41no—
79D4×C19—41no—
80C2×C4×C19—22no—
81C2×C4×C19—22no—
82C2×C4×C19—22no—
83C2×C4×C19—21no—
84C2×C4×C19—42no—
85C2×C4×C19C2×D412yes—
86C2×C4×C19C2×D412yes—
87C2×C4×C19C2×D414yes—
88C2×C4×C19C2×D411yescharacteristic
89C2×C4×C19C2411yescharacteristic
90C22⋊D19—24no—
91C22⋊D19—24no—
92C2×Dic19—22no—
93D76—28no—
94D76—22no—
95D76C2×D414yes—
96C4×D19—216no—
97C4×D19—24no—
98C4×D19—24no—
99Dic38—28no—
100Dic38—22no—
101Dic38C2×D414yes—
102C19⋊C8—24no—
103#3020—191nomaximal, Sylow
104C22×C19—41no—
105C22×C19—42no—
106C22×C19—41no—
107C22×C19#12011yescharacteristic
108C22×C19#12011yescharacteristic
109C22×C19C22×D411yescharacteristic
110C2×D19—24no—
111C2×D19—44no—
112C4×C19—24no—
113C4×C19—42no—
114C4×C19—41no—
115C4×C19#12012yes—
116C4×C19C22×D412yes—
117Dic19—24no—
118C2×2−1+4—191no—
119#575—192no—
120#536D1911yescharacteristic, complemented
121#456—194no—
122#454—194no—
123#421—192no—
124C2×#101—191no—
125C2×C19—21no—
126C2×C19—21no—
127C2×C19—21no—
128C2×C19—81no—
129C2×C19C2×#12011yescharacteristic
130D19—44no—
1312−1+4—194no—
1322−1+4—384no—
1332−1+4—382no—
134C2×#41—192no—
135C2×#41—382no—
136C2×#41—382no—
137C2×#41C2×D1911yescharacteristic
138C22×Q8—382no—
139C22×Q8C2×D1911yescharacteristic
140#137—194no—
141#137—382no—
142AGL(1,ℤ/8)—194no—
143AGL(1,ℤ/8)—382no—
144#135—384no—
145C2×M16—192no—
146C4⋊Q8C2×D1912yescomplemented
147#124C2×D1912yescomplemented
148#123—22no—
149C22⋊Q8—22no—
150#117C2×D1911yescharacteristic
151#104—198no—
152#101—194no—
153C19#302011yescharacteristic, complemented, Sylow
154#41—22no—
155#41—22no—
156#41—194no—
157#41—194no—
158#41—388no—
159#41—388no—
160#41—388no—
161#41—382no—
162#41—382no—
163#41—388no—
164C2×Q8—22no—
165C2×Q8—22no—
166C2×Q8—192no—
167C2×Q8—382no—
168C2×Q8—388no—
169C2×Q8—388no—
170C2×Q8C22⋊D1912yes—
171C2×Q8C22×D1911yescharacteristic
172C2×Q8C22×D1912yes—
173C2×D4—21no—
174C2×D4—192no—
175C2×D4—382no—
176C2×D4—382no—
177C2×D4C22×D1911yescharacteristic
178C22×C4—21no—
179C22×C4—384no—
180C22×C4—382no—
181C22×C4C22⋊D1912yes—
182C22×C4C22×D1911yescharacteristic
183Q16—384no—
184SD16—384no—
185SD16—384no—
186D8—384no—
187M16—194no—
188M16—382no—
189C2×C8—382no—
190C4⋊C4—21no—
191C4⋊C4—24no—
192C22⋊C4—21no—
193C22⋊C4—24no—
194C42C22×D1912yes—
195C23—21no—
196C23—382no—
197C23C2×C22⋊D1911yescharacteristic
198Q8—24no—
199Q8—24no—
200Q8—22no—
201Q8—194no—
202Q8—388no—
203Q8—382no—
204D4—22no—
205D4—41no—
206D4—41no—
207D4—194no—
208D4—388no—
209D4—384no—
210D4—384no—
211D4—382no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—21no—
216C2×C4—42no—
217C2×C4—3816no—
218C2×C4—382no—
219C2×C4—384no—
220C2×C4—384no—
221C2×C4D4×D1912yes—
222C2×C4D4×D1912yes—
223C2×C4C2×C22⋊D1914yes—
224C2×C4C2×C22⋊D1911yescharacteristic
225C2×C4C23×D1911yescharacteristic
226C8—384no—
227C22—41no—
228C22—42no—
229C22—41no—
230C22—384no—
231C22—764no—
232C22#1059738311yescharacteristic
233C22#1059738311yescharacteristic
234C22C22×C22⋊D1911yescharacteristic
235C4—24no—
236C4—42no—
237C4—41no—
238C4—384no—
239C4#1059738312yes—
240C4C2×D4×D1912yes—
241C2—21no—
242C2—21no—
243C2—21no—
244C2—81no—
245C2—764no—
246C2C2×#1059738311yescharacteristic
subgroupG/H
centerC2C2×#10597383
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#536C2
socleC2×C19C2×#120
hypercenter#536D19
hypocenterC19#3020
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C2 ◁ C22×C4 ◁ #536

Complements

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

NH ≅ G/Ntype
1. C2×#10597433C2semidirect
2. #11927342C2semidirect
3. #11926726C2semidirect
4. #11926716C2semidirect
5. #11926562C2semidirect
6. C2×#10597293C2semidirect
7. C19×#536C2semidirect
17. C19×C4⋊Q8C22semidirect
18. C19×#124C22semidirect
25. #10597388C22semidirect
26. #10597378C22semidirect
28. #10597293C22semidirect
29. #10597262C22semidirect
120. #536D19semidirect
146. C4⋊Q8C2×D19semidirect
147. #124C2×D19semidirect
153. C19#3020semidirect

Maximal subgroups

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

subgroupindex
C2×#105974332
#119273422
#119267262
#119267162
#119265622
C2×#105972932
C19×#5362
#302019