Finite Group Databasebeta

← #18083493

Subgroups — #18083493

Order 4864.

520 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 85 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#14573730C212yesmaximal
2#14564432C211yesmaximal, characteristic
3#14562250C212yesmaximal, complemented
4#14561505C211yesmaximal, characteristic, complemented
5C19×#3249C211yesmaximal, characteristic, complemented
6C2×C4×D76C2211yescharacteristic
7#11926877—22no—
8#11926821—22no—
9#11926746—22no—
10#11926694—22no—
11#11926642—24no—
12#11926601C2212yes—
13C2×(C2×D19)⋊C8—22no—
14C2×#10597260C2211yescharacteristic
15#11926286—24no—
16C19×#533C2212yes—
17C19×#477—22no—
18C19×#467—22no—
19C19×#462—22no—
20C2×C19×C4⋊C8C2211yescharacteristic
21C22×D76D411yescharacteristic
22C22×C4×D19—21no—
23C2×Q16×C19—22no—
24C22×C8×C19D412yes—
25C19×C4⋊Q8D412yes—
26C19×C4⋊Q8D412yes—
27C19×#125—22no—
28C19×C22⋊Q8—22no—
29C19×C22⋊Q8—22no—
30C4×Q8×C19—22no—
31C4×Q8×C19—22no—
32C19×#117—22no—
33C2×C42×C19C2311yescharacteristic
34C2×#64527—24no—
35C2×(C2×D19)⋊C4—21no—
36C2×C4⋊Dic19D411yescharacteristic
37C22×C19⋊C8—21no—
38C4×D76—22no—
39C4×D76—22no—
40C19×#107—22no—
41C19×C4⋊C8—22no—
42C19×#103—24no—
43#10597292—24no—
44C22⋊(C19⋊C8)—22no—
45(C2×D19)⋊C8—44no—
46#10597266—24no—
47#10597264—24no—
48C4⋊(C19⋊C8)—22no—
49#10597260—22no—
50#10597260D414yes—
51C23×D19—21no—
52C2×Q8×C19—22no—
53C2×Q8×C19—22no—
54C22×C4×C19C2×D411yescharacteristic
55C22×C4×C19C2×D411yescharacteristic
56C22×C4×C19#4111yescharacteristic
57C22×Dic19—21no—
58C2×D76—22no—
59C2×D76—42no—
60C2×C4×D19—42no—
61C2×C4×D19—42no—
62C2×C4×D19—41no—
63C2×C4×D19—41no—
64Q16×C19—82no—
65C2×C8×C19—22no—
66C2×C8×C19—42no—
67C4⋊C4×C19—22no—
68C4⋊C4×C19—22no—
69C4⋊C4×C19—22no—
70C4⋊C4×C19—22no—
71C4⋊C4×C19—42no—
72C4⋊C4×C19—42no—
73C22⋊C4×C19—42no—
74C42×C19—42no—
75C42×C19C2×D412yes—
76C42×C19C2×D412yes—
77#64527—48no—
78(C2×D19)⋊C4—42no—
79C4⋊Dic19—22no—
80C2×C19⋊C8—22no—
81C2×C19⋊C8—24no—
82C2×C19⋊C8—41no—
83C2×C19⋊C8—41no—
84#10030—191nomaximal, Sylow
85C23×C19#12111yescharacteristic
86C22×D19—22no—
87C22×D19—42no—
88C22×D19—41no—
89C22×D19—41no—
90C22×D19—42no—
91Q8×C19—44no—
92Q8×C19—42no—
93Q8×C19—42no—
94C2×C4×C19—22no—
95C2×C4×C19—21no—
96C2×C4×C19—21no—
97C2×C4×C19—41no—
98C2×C4×C19—42no—
99C2×C4×C19—42no—
100C2×C4×C19#12012yes—
101C2×C4×C19#12011yescharacteristic
102C2×C4×C19#12112yes—
103C2×C4×C19#12711yescharacteristic
104C2×Dic19—42no—
105C2×Dic19—41no—
106D76—24no—
107D76—42no—
108C4×D19—82no—
109C4×D19—81no—
110C4×D19—81no—
111C8×C19—42no—
112C19⋊C8—42no—
113C19⋊C8—44no—
114#3249D1911yescharacteristic, complemented
115#3110—192no—
116#1955—191no—
117#1531—192no—
118#1290—191no—
119C22×C19—21no—
120C22×C19—21no—
121C22×C19#39211yescharacteristic
122C22×C19#47312yes—
123C2×D19—44no—
124C2×D19—42no—
125C2×D19—82no—
126C2×D19—81no—
127C2×D19—81no—
128C4×C19—21no—
129C4×C19—22no—
130C4×C19—22no—
131C4×C19—82no—
132C4×C19—82no—
133C4×C19#45311yescharacteristic
134C4×C19#45411yescharacteristic
135Dic19—81no—
136#533C2×D1912yes—
137C2×C4×D4—191no—
138#484—382no—
139#477—22no—
140#474—382no—
141#467—22no—
142#462—22no—
143#461—382no—
144#450—382no—
145#440—384no—
146#432—192no—
147C2×C4⋊C8C2×D1911yescharacteristic
148C2×C22⋊C8—382no—
149C2×#97—191no—
150#330—384no—
151C2×C19—22no—
152C2×C19#200611yescharacteristic
153C2×C19#201011yescharacteristic
154C2×C19#202011yescharacteristic
155D19—82no—
156C22×D4—191no—
157C23×C4—381no—
158C2×Q16—22no—
159C2×SD16—384no—
160C22×C8—381no—
161C22×C8C22⋊D1912yes—
162C4⋊Q8C22⋊D1912yes—
163C4⋊Q8C22⋊D1912yes—
164#125—22no—
165C22⋊Q8—22no—
166C22⋊Q8—22no—
167C4×Q8—22no—
168C4×Q8—22no—
169C4×D4—382no—
170C4×D4—382no—
171#117—22no—
172C2×C4⋊C4—191no—
173C2×C22⋊C4—381no—
174C2×C42C22×D1911yescharacteristic
175#107—22no—
176#107—384no—
177C4⋊C8—22no—
178C4⋊C8—382no—
179#103—24no—
180#103—384no—
181#102—384no—
182C22⋊C8—382no—
183C22⋊C8—764no—
184#97—194no—
185#97—382no—
186C19#1003011yescharacteristic, complemented, Sylow
187C24—381no—
188C2×Q8—22no—
189C2×Q8—22no—
190C2×D4—382no—
191C2×D4—762no—
192C22×C4—381no—
193C22×C4—762no—
194C22×C4—762no—
195C22×C4—761no—
196C22×C4—761no—
197C22×C4D4×D1911yescharacteristic
198C22×C4#6454311yescharacteristic
199C22×C4C2×C22⋊D1911yescharacteristic
200Q16—82no—
201SD16—768no—
202C2×C8—22no—
203C2×C8—42no—
204C2×C8—382no—
205C2×C8—384no—
206C2×C8—761no—
207C2×C8—761no—
208C4⋊C4—22no—
209C4⋊C4—22no—
210C4⋊C4—22no—
211C4⋊C4—22no—
212C4⋊C4—42no—
213C4⋊C4—42no—
214C4⋊C4—382no—
215C22⋊C4—42no—
216C22⋊C4—762no—
217C42—42no—
218C42D4×D1912yes—
219C42C2×C22⋊D1912yes—
220C23—382no—
221C23—762no—
222C23—761no—
223C23—762no—
224C23—761no—
225C23#1059738411yescharacteristic
226Q8—44no—
227Q8—42no—
228Q8—42no—
229D4—384no—
230D4—762no—
231C2×C4—22no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—41no—
235C2×C4—42no—
236C2×C4—42no—
237C2×C4—762no—
238C2×C4—761no—
239C2×C4—1522no—
240C2×C4—1521no—
241C2×C4—1521no—
242C2×C4#1059738312yes—
243C2×C4#1059738512yes—
244C2×C4#1059738611yescharacteristic
245C2×C4#1059739911yescharacteristic
246C8—42no—
247C8—762no—
248C8—764no—
249C22—21no—
250C22—21no—
251C22—764no—
252C22—762no—
253C22—1522no—
254C22—1521no—
255C22—1521no—
256C22#1192645211yescharacteristic
257C22#1192681612yes—
258C4—21no—
259C4—22no—
260C4—22no—
261C4—82no—
262C4—82no—
263C4—1521no—
264C4#1192671211yescharacteristic
265C4#1192671711yescharacteristic
266C2—22no—
267C2—1522no—
268C2#1456467711yescharacteristic
269C2#1456469911yescharacteristic
270C2#1456475411yescharacteristic
subgroupG/H
centerC22#11926452
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#3249C2
socleC22×C19#392
prime radicalC22×D76D4
hypercenter#3249D19
hypocenterC19#10030
LCSG ▷ C2×C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3249

Complements

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

NH ≅ G/Ntype
3. #14562250C2semidirect
4. #14561505C2semidirect
5. C19×#3249C2semidirect
114. #3249D19semidirect
186. C19#10030semidirect

Maximal subgroups

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

subgroupindex
#145737302
#145644322
#145622502
#145615052
C19×#32492
#1003019