Finite Group Databasebeta

← #18085773

Subgroups — #18085773

Order 4864.

414 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 77 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#14563735C212yesmaximal
2#14563710C211yesmaximal, characteristic
3#14561543C211yesmaximal, characteristic
4#14561488C212yesmaximal
5C19×#2607C211yesmaximal, characteristic
6C2×#10597372C2211yescharacteristic
7#11926508C2212yes—
8#11926407C2211yescharacteristic
9#11926310—21no—
10#11926310—21no—
11#11926304—22no—
12#11926304—22no—
13C19×#399—21no—
14C19×#393—21no—
15C19×#391—22no—
16C19×#387—22no—
17C19×#381C2211yescharacteristic
18C4×C22⋊C4×C19C2212yes—
19C22×Q8×C19—21no—
20C23×C4×C19C2311yescharacteristic
21C2×C4⋊C4×C19—22no—
22C2×C4⋊C4×C19—21no—
23C2×C22⋊C4×C19—22no—
24C2×C22⋊C4×C19D411yescharacteristic
25C2×C22⋊C4×C19D411yescharacteristic
26C2×C42×C19D412yes—
27C2×C42×C19D412yes—
28C2×C22⋊Dic19—21no—
29C2×C22⋊Dic19—21no—
30#10597372—22no—
31#10597372—22no—
32C2×C4⋊Dic19Q812yescomplemented
33C2×C4×Dic19—21no—
34C2×#64520—22no—
35C19×#95—21no—
36C19×#95—22no—
37C19×#95—21no—
38C19×#95—22no—
39C19×#95—22no—
40C19⋊#95—22no—
41C22⋊(C19⋊C8)—22no—
42C22⋊(C19⋊C8)—22no—
43C24×C19C2×D411yescharacteristic
44C2×Q8×C19—44no—
45C2×Q8×C19—81no—
46C22×C4×C19—22no—
47C22×C4×C19—22no—
48C22×C4×C19—21no—
49C22×C4×C19—21no—
50C22×C4×C19—41no—
51C22×C4×C19—41no—
52C22×C4×C19C2×D412yes—
53C22×C4×C19C2×Q811yescharacteristic
54C22×C4×C19#4112yes—
55C22×C4×C19#4111yescharacteristic
56C22×Dic19—22no—
57C22×Dic19—41no—
58C4⋊C4×C19—44no—
59C4⋊C4×C19—81no—
60C22⋊C4×C19—44no—
61C22⋊C4×C19—41no—
62C22⋊C4×C19—41no—
63C42×C19—42no—
64C42×C19—42no—
65C22⋊Dic19—41no—
66C22⋊Dic19—41no—
67C22⋊Dic19—41no—
68C22⋊Dic19—41no—
69C4⋊Dic19—24no—
70C4×Dic19—42no—
71#64520—42no—
72#64520—42no—
73C2×C19⋊C8—42no—
74#10387—191nomaximal, Sylow
75C23×C19—21no—
76C23×C19—21no—
77C23×C19—42no—
78C23×C19#12011yescharacteristic
79C23×C19C22⋊Q811yescharacteristic
80C23×C19#12411yescharacteristic
81Q8×C19—84no—
82C2×C4×C19—22no—
83C2×C4×C19—22no—
84C2×C4×C19—24no—
85C2×C4×C19—41no—
86C2×C4×C19—41no—
87C2×C4×C19—42no—
88C2×C4×C19—42no—
89C2×C4×C19—42no—
90C2×C4×C19—42no—
91C2×C4×C19—42no—
92C2×C4×C19—42no—
93C2×C4×C19—42no—
94C2×C4×C19—42no—
95C2×C4×C19—41no—
96C2×C4×C19—41no—
97C2×C4×C19C22⋊Q812yes—
98C2×C4×C19#12412yes—
99C2×Dic19—42no—
100C2×Dic19—82no—
101C2×Dic19—81no—
102C2×Dic19—82no—
103C19⋊C8—82no—
104#2607D1911yescharacteristic
105#1826—192no—
106#1820—191no—
107#1306—191no—
108#1284—192no—
109C22×C19—22no—
110C22×C19—21no—
111C22×C19—21no—
112C22×C19—22no—
113C22×C19—22no—
114C22×C19—81no—
115C22×C19—81no—
116C22×C19#39311yescharacteristic
117C22×C19#45811yescharacteristic
118C22×C19#45811yescharacteristic
119C4×C19—22no—
120C4×C19—22no—
121C4×C19—44no—
122C4×C19—82no—
123C4×C19—81no—
124C4×C19—81no—
125Dic19—82no—
126Dic19—161no—
127C2×#117—191no—
128#407—192no—
129#399—21no—
130#393—21no—
131#391—22no—
132#387—22no—
133#381—191no—
134#381C2×D1911yescharacteristic
135C4×C22⋊C4C2×D1912yes—
136#342—381no—
137#342—381no—
138#339—382no—
139#339—382no—
140C2×C19—21no—
141C2×C19—21no—
142C2×C19—41no—
143C2×C19—41no—
144C2×C19#203011yescharacteristic
145C2×C19#203112yes—
146C22×Q8—21no—
147C23×C4C22×D1911yescharacteristic
148C2×M16—382no—
149#117—382no—
150#117—382no—
151C2×C4⋊C4—22no—
152C2×C4⋊C4—21no—
153C2×C4⋊C4—192no—
154C2×C22⋊C4—22no—
155C2×C22⋊C4—381no—
156C2×C22⋊C4—381no—
157C2×C22⋊C4C22⋊D1911yescharacteristic
158C2×C22⋊C4C22⋊D1911yescharacteristic
159C2×C42—381no—
160C2×C42C22⋊D1912yes—
161C2×C42C22⋊D1912yes—
162C22⋊C8—382no—
163C22⋊C8—382no—
164#95—21no—
165#95—22no—
166#95—21no—
167#95—22no—
168#95—22no—
169#95—382no—
170C19#1038711yescharacteristic, complemented, Sylow
171C24C2×C22⋊D1911yescharacteristic
172C2×Q8—44no—
173C2×Q8—81no—
174C22×C4—22no—
175C22×C4—21no—
176C22×C4—22no—
177C22×C4—21no—
178C22×C4—41no—
179C22×C4—41no—
180C22×C4—382no—
181C22×C4—761no—
182C22×C4Q8×D1911yescharacteristic
183C22×C4#6454512yes—
184C22×C4#6454511yescharacteristic
185C22×C4C2×C22⋊D1912yes—
186M16—762no—
187M16—762no—
188C2×C8—762no—
189C4⋊C4—44no—
190C4⋊C4—81no—
191C4⋊C4—384no—
192C22⋊C4—44no—
193C22⋊C4—41no—
194C22⋊C4—41no—
195C22⋊C4—761no—
196C22⋊C4—761no—
197C22⋊C4—761no—
198C22⋊C4—761no—
199C42—42no—
200C42—42no—
201C42—762no—
202C23—21no—
203C23—21no—
204C23—42no—
205C23#1059739211yescharacteristic
206C23#1059739311yescharacteristic
207C23#1059739911yescharacteristic
208Q8—84no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—24no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—42no—
215C2×C4—42no—
216C2×C4—42no—
217C2×C4—42no—
218C2×C4—42no—
219C2×C4—42no—
220C2×C4—42no—
221C2×C4—42no—
222C2×C4—41no—
223C2×C4—41no—
224C2×C4—762no—
225C2×C4—1521no—
226C2×C4—1522no—
227C2×C4—1522no—
228C2×C4#1059739212yes—
229C2×C4#1059739312yes—
230C8—1522no—
231C22—22no—
232C22—21no—
233C22—21no—
234C22—22no—
235C22—22no—
236C22—81no—
237C22—81no—
238C22#1192645511yescharacteristic
239C22#1192673411yescharacteristic
240C22#1192673411yescharacteristic
241C4—22no—
242C4—22no—
243C4—44no—
244C4—81no—
245C4—82no—
246C4—81no—
247C4—3041no—
248C4—1522no—
249C2—21no—
250C2—21no—
251C2—41no—
252C2—41no—
253C2#1456480111yescharacteristic
254C2#1456480412yes—
subgroupG/H
centerC22#11926455
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
FittingC19×#2607C2
socleC22×C19#393
prime radicalC24×C19C2×D4
hypercenter#2607D19
hypocenterC19#10387
LCSG ▷ C23×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2607

Complements

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

NH ≅ G/Ntype
32. C2×C4⋊Dic19Q8semidirect
170. C19#10387semidirect

Maximal subgroups

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

subgroupindex
#145637352
#145637102
#145615432
#145614882
C19×#26072
#1038719