Finite Group Databasebeta

← #18075106

Subgroups — #18075106

Order 4864.

656 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 656 conjugacy classes of subgroups — too many to draw. Only its 115 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#14578130C211yesmaximal, characteristic
2#14564612C212yesmaximal
3#14562373C211yesmaximal, characteristic
4#14562372C212yesmaximal
5C19×#1994C211yesmaximal, characteristic
6C19⋊#564C414yescomplemented
7#11927273—22no—
8#11927272—22no—
9#11927269—22no—
10#11927156—22no—
11#11927154—24no—
12#11927101C2212yes—
13#11926568C2212yes—
14#11926304—24no—
15#11926291—22no—
16#11926290—22no—
17#11926289—22no—
18C19×#533C2211yescharacteristic
19C19×#423C2211yescharacteristic
20C43×C19C2211yescharacteristic
21C19×#339—22no—
22C2×M16×C19—21no—
23C19×C4⋊Q8D412yes—
24C19×#125C2×C412yes—
25C19×C22⋊Q8—22no—
26C4×Q8×C19—22no—
27C19×#117D412yes—
28C2×C42×C19—22no—
29C2×C42×C19—21no—
30C2×C42×C19C2311yescharacteristic
31Q8×Dic19—24no—
32#10597390—24no—
33#10597372D414yes—
34#10597370—22no—
35#10597370—22no—
36C2×#64520—22no—
37#10597336—24no—
38#10597336—28no—
39#10597335—28no—
40#10597335—28no—
41#10597333—24no—
42#10597325—28no—
43#10597316—22no—
44#10597316C2×C414yes—
45#10597315—22no—
46#10597315D412yes—
47#10597315D412yes—
48C4×Dic38—24no—
49C4×Dic38—22no—
50C4×Dic38—22no—
51C19×C4⋊C8—22no—
52C4⋊(C19⋊C8)—22no—
53C4⋊(C19⋊C8)—22no—
54C2×Q8×C19—22no—
55C22×C4×C19—41no—
56C22×C4×C19C2×D412yes—
57C22×C4×C19C2×D411yescharacteristic
58C2×Dic38—22no—
59C2×Dic38—22no—
60M16×C19—42no—
61C2×C8×C19—41no—
62C4⋊C4×C19—24no—
63C4⋊C4×C19—22no—
64C4⋊C4×C19C22⋊C414yes—
65C22⋊C4×C19—22no—
66C42×C19—22no—
67C42×C19—24no—
68C42×C19—22no—
69C42×C19—42no—
70C42×C19—41no—
71C42×C19C22×C411yescharacteristic
72C42×C19C2×D411yescharacteristic
73C42×C19C2×D412yes—
74C22⋊Dic19—24no—
75C4⋊Dic19—28no—
76C4⋊Dic19—22no—
77C4⋊Dic19—22no—
78C4⋊Dic19C22⋊C414yes—
79C4⋊Dic19C22⋊C414yes—
80Dic19⋊C4—28no—
81Dic19⋊C4—28no—
82Dic19⋊C4—24no—
83Dic19⋊C4—24no—
84C4×Dic19—28no—
85C4×Dic19—24no—
86#64520—44no—
87C2×C19⋊C8—42no—
88#8533—191nomaximal, Sylow
89C23×C19#12011yescharacteristic
90Q8×C19—42no—
91Q8×C19—42no—
92C2×C4×C19—22no—
93C2×C4×C19—21no—
94C2×C4×C19—21no—
95C2×C4×C19—22no—
96C2×C4×C19—24no—
97C2×C4×C19—42no—
98C2×C4×C19—44no—
99C2×C4×C19C2×C22⋊C412yes—
100C2×C4×C19C2×C22⋊C411yescharacteristic
101C2×C4×C19#12011yescharacteristic
102C2×C4×C19#12012yes—
103C2×Dic19—24no—
104C2×Dic19—24no—
105Dic38—42no—
106Dic38—42no—
107Dic38—42no—
108Dic38—42no—
109C8×C19—81no—
110C19⋊C8—82no—
111#3556—191no—
112#1994—192no—
113#1994D1911yescharacteristic
114#1561—192no—
115#1561—191no—
116C22×C19—21no—
117C22×C19—22no—
118C22×C19#37911yescharacteristic
119C4×C19—21no—
120C4×C19—22no—
121C4×C19—44no—
122C4×C19—44no—
123C4×C19#45411yescharacteristic
124C4×C19#45412yes—
125C4×C19#45611yescharacteristic
126C4×C19#45612yes—
127Dic19—44no—
128Dic19—44no—
129#564—194no—
130#557—382no—
131#557—382no—
132#557—382no—
133#541—384no—
134#541—382no—
135#533—192no—
136#533C2×D1911yescharacteristic
137#423—192no—
138#423C2×D1911yescharacteristic
139C43C2×D1911yescharacteristic
140#339—22no—
141#339—384no—
142#332—382no—
143#332—382no—
144#332—382no—
145C2×C19—41no—
146C2×C19#179311yescharacteristic
147C2×C19#179312yes—
148C2×M16—21no—
149C2×M16—382no—
150C4⋊Q8—192no—
151C4⋊Q8—192no—
152C4⋊Q8—382no—
153C4⋊Q8—384no—
154C4⋊Q8D7612yes—
155#126—388no—
156#125—194no—
157#125—382no—
158#125—388no—
159#125—388no—
160#125—384no—
161#125—388no—
162#125C4×D1912yes—
163C22⋊Q8—22no—
164C22⋊Q8—382no—
165C22⋊Q8—382no—
166C4×Q8—22no—
167C4×Q8—384no—
168C4×Q8—384no—
169C4×Q8—384no—
170C4×Q8—382no—
171C4×Q8—382no—
172#117—194no—
173#117C22⋊D1912yes—
174C2×C42—22no—
175C2×C42—21no—
176C2×C42C22×D1911yescharacteristic
177C4⋊C8—22no—
178C4⋊C8—382no—
179C4⋊C8—382no—
180C19#853311yescharacteristic, complemented, Sylow
181C2×Q8—22no—
182C2×Q8—382no—
183C2×Q8—382no—
184C22×C4—41no—
185C22×C4D4×D1912yes—
186C22×C4C2×C22⋊D1911yescharacteristic
187M16—42no—
188M16—764no—
189C2×C8—41no—
190C2×C8—762no—
191C4⋊C4—24no—
192C4⋊C4—22no—
193C4⋊C4—194no—
194C4⋊C4—194no—
195C4⋊C4—388no—
196C4⋊C4—388no—
197C4⋊C4—388no—
198C4⋊C4—382no—
199C4⋊C4—384no—
200C4⋊C4—382no—
201C4⋊C4—384no—
202C4⋊C4(C2×D19)⋊C414yes—
203C22⋊C4—22no—
204C22⋊C4—384no—
205C42—22no—
206C42—22no—
207C42—24no—
208C42—41no—
209C42—42no—
210C42—388no—
211C42—384no—
212C42C2×C4×D1911yescharacteristic
213C42C2×D7611yescharacteristic
214C42D4×D1912yes—
215C23#1059738311yescharacteristic
216Q8—42no—
217Q8—42no—
218Q8—762no—
219Q8—762no—
220Q8—762no—
221Q8—762no—
222C2×C4—21no—
223C2×C4—22no—
224C2×C4—21no—
225C2×C4—22no—
226C2×C4—24no—
227C2×C4—42no—
228C2×C4—44no—
229C2×C4—384no—
230C2×C4—384no—
231C2×C4C22⋊C4×D1912yes—
232C2×C4#1059732812yes—
233C2×C4C2×(C2×D19)⋊C411yescharacteristic
234C2×C4#1059738311yescharacteristic
235C8—81no—
236C8—1522no—
237C22—21no—
238C22—22no—
239C22#1192639911yescharacteristic
240C4—21no—
241C4—22no—
242C4—44no—
243C4—44no—
244C4—764no—
245C4—764no—
246C4#1192671611yescharacteristic
247C4#1192671812yes—
248C4#1192672611yescharacteristic
249C4#1192672812yes—
250C2—41no—
251C2#1456359311yescharacteristic
252C2#1456359512yes—
subgroupG/H
centerC22#11926399
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1994C2
socleC22×C19#379
prime radicalC23×C19#120
cosocleC2×C42×C19C23
hypercenter#1994D19
hypocenterC19#8533
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1994

Complements

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

NH ≅ G/Ntype
6. C19⋊#564C4semidirect
180. C19#8533semidirect

Maximal subgroups

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

subgroupindex
#145781302
#145646122
#145623732
#145623722
C19×#19942
#853319