Finite Group Databasebeta

← #18069120

Subgroups — #18069120

Order 4864.

458 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 103 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#14563397C211yesmaximal, characteristic
2#14561862C211yesmaximal, characteristic
3C19×#1749C211yesmaximal, characteristic
4C2×C22⋊(C19⋊C8)—21no—
5C2×#10597260C412yescomplemented
6C2×C19⋊#95—21no—
7C2×C19⋊#95—21no—
8C2×C19⋊#95C412yes—
9#11926299—21no—
10C22×C42×C19C2211yescharacteristic
11C2×C19×C22⋊C8—21no—
12C2×C19×#97—21no—
13C19×#336C412yescomplemented
14C23×C4×C19C2×C411yescharacteristic
15C23×C4×C19D411yescharacteristic
16C23×C4×C19D411yescharacteristic
17C23×Dic19—22no—
18C22×C8×C19—22no—
19C2×C42×C19—42no—
20C2×C42×C19C2×C411yescharacteristic
21C2×C42×C19C2×C411yescharacteristic
22C2×C42×C19D411yescharacteristic
23C2×C42×C19Q811yescharacteristic
24C22×C19⋊C8—22no—
25C19×C22⋊C8—24no—
26C19×#97—42no—
27C19⋊#95—24no—
28C19⋊#95—42no—
29C19⋊#95—42no—
30C22⋊(C19⋊C8)—24no—
31#10597260—42no—
32C24×C19C22⋊C411yescharacteristic
33C22×C4×C19—21no—
34C22×C4×C19—21no—
35C22×C4×C19—22no—
36C22×C4×C19—22no—
37C22×C4×C19—22no—
38C22×C4×C19—22no—
39C22×C4×C19—41no—
40C22×C4×C19—41no—
41C22×C4×C19—41no—
42C22×C4×C19—41no—
43C22×C4×C19C4211yescharacteristic
44C22×C4×C19C22⋊C411yescharacteristic
45C22×C4×C19C22⋊C411yescharacteristic
46C22×C4×C19C4⋊C411yescharacteristic
47C22×C4×C19C4⋊C411yescharacteristic
48C22×C4×C19C4⋊C411yescharacteristic
49C22×Dic19—24no—
50C22×Dic19—42no—
51C22×Dic19—42no—
52C22×Dic19—42no—
53C22×Dic19—42no—
54C22×Dic19—42no—
55C22×Dic19—42no—
56C2×C8×C19—24no—
57C2×C8×C19—42no—
58C2×C8×C19—42no—
59C42×C19—22no—
60C42×C19—22no—
61C42×C19—41no—
62C42×C19—41no—
63C2×C19⋊C8—24no—
64C2×C19⋊C8—42no—
65C2×C19⋊C8—42no—
66#7036—191nomaximal, Sylow
67C23×C19—21no—
68C23×C19—21no—
69C23×C19—21no—
70C23×C19—21no—
71C23×C19#9511yescharacteristic
72C23×C19#10011yescharacteristic
73C23×C19#10111yescharacteristic
74C23×C19#10412yes—
75C23×C19#10412yes—
76C2×C4×C19—21no—
77C2×C4×C19—21no—
78C2×C4×C19—21no—
79C2×C4×C19—21no—
80C2×C4×C19—21no—
81C2×C4×C19—21no—
82C2×C4×C19—21no—
83C2×C4×C19—21no—
84C2×C4×C19—21no—
85C2×C4×C19—21no—
86C2×C4×C19—21no—
87C2×C4×C19—21no—
88C2×C4×C19—21no—
89C2×C4×C19—21no—
90C2×C4×C19—21no—
91C2×C4×C19—21no—
92C2×C4×C19—44no—
93C2×C4×C19—44no—
94C2×C4×C19—42no—
95C2×C4×C19—42no—
96C2×C4×C19#9912yes—
97C2×C4×C19#10412yes—
98C2×Dic19—44no—
99C2×Dic19—44no—
100C2×Dic19—44no—
101C2×Dic19—82no—
102C2×Dic19—82no—
103C2×Dic19—82no—
104C2×Dic19—82no—
105C8×C19—44no—
106C19⋊C8—44no—
107#1749—191no—
108#1749D1911yescharacteristic
109#1434—191no—
110C22×C19—22no—
111C22×C19—21no—
112C22×C19—21no—
113C22×C19—22no—
114C22×C19—22no—
115C22×C19—22no—
116C22×C19—21no—
117C22×C19—21no—
118C22×C19#32912yes—
119C22×C19#33012yes—
120C22×C19H(3,ℤ/4)11yescharacteristic
121C22×C19#33911yescharacteristic
122C22×C19#33911yescharacteristic
123C22×C19#33911yescharacteristic
124C22×C19#34211yescharacteristic
125C22×C19#34311yescharacteristic
126C22×C19#34411yescharacteristic
127C4×C19—22no—
128C4×C19—22no—
129C4×C19—41no—
130C4×C19—41no—
131C4×C19—41no—
132C4×C19—41no—
133Dic19—84no—
134C22×C42C2×D1911yescharacteristic
135C2×C22⋊C8—21no—
136C2×C22⋊C8—381no—
137C2×#97—21no—
138C2×#97—192no—
139C2×#95—192no—
140C2×#95—381no—
141C2×#95—381no—
142#336—381no—
143#336Dic1912yescomplemented
144C2×C19—22no—
145C2×C19—22no—
146C2×C19#128411yescharacteristic
147C2×C19#128511yescharacteristic
148C2×C19#128811yescharacteristic
149C2×C19#129511yescharacteristic
150C2×C19#129711yescharacteristic
151C2×C19#130011yescharacteristic
152C2×C19#130511yescharacteristic
153C23×C4—382no—
154C23×C4C4×D1911yescharacteristic
155C23×C4D7611yescharacteristic
156C23×C4C22⋊D1911yescharacteristic
157C22×C8—22no—
158C22×C8—382no—
159C2×C42—42no—
160C2×C42Dic3811yescharacteristic
161C2×C42C4×D1911yescharacteristic
162C2×C42C2×Dic1911yescharacteristic
163C2×C42C22⋊D1911yescharacteristic
164C22⋊C8—24no—
165C22⋊C8—384no—
166#97—42no—
167#97—762no—
168#95—384no—
169#95—762no—
170#95—762no—
171C19#703611yescharacteristic, complemented, Sylow
172C24(C2×D19)⋊C411yescharacteristic
173C22×C4—22no—
174C22×C4—21no—
175C22×C4—21no—
176C22×C4—22no—
177C22×C4—22no—
178C22×C4—22no—
179C22×C4—41no—
180C22×C4—41no—
181C22×C4—41no—
182C22×C4—41no—
183C22×C4—384no—
184C22×C4—762no—
185C22×C4—762no—
186C22×C4—762no—
187C22×C4—762no—
188C22×C4—762no—
189C22×C4—762no—
190C22×C4C4×Dic1911yescharacteristic
191C22×C4Dic19⋊C411yescharacteristic
192C22×C4Dic19⋊C411yescharacteristic
193C22×C4C4⋊Dic1911yescharacteristic
194C22×C4(C2×D19)⋊C411yescharacteristic
195C22×C4C22⋊Dic1911yescharacteristic
196C2×C8—24no—
197C2×C8—42no—
198C2×C8—42no—
199C2×C8—384no—
200C2×C8—762no—
201C2×C8—762no—
202C42—22no—
203C42—22no—
204C42—41no—
205C42—41no—
206C23—21no—
207C23—21no—
208C23—21no—
209C23—21no—
210C23#1059726212yes—
211C23#1059728011yescharacteristic
212C23#1059728111yescharacteristic
213C23#1059728212yes—
214C23C19⋊#9511yescharacteristic
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—44no—
232C2×C4—44no—
233C2×C4—42no—
234C2×C4—42no—
235C2×C4—764no—
236C2×C4—764no—
237C2×C4—764no—
238C2×C4—1522no—
239C2×C4—1522no—
240C2×C4—1522no—
241C2×C4—1522no—
242C2×C4#1059726312yes—
243C2×C4#1059729412yes—
244C8—44no—
245C8—764no—
246C22—21no—
247C22—21no—
248C22—22no—
249C22—21no—
250C22—21no—
251C22—22no—
252C22—22no—
253C22—22no—
254C22#1192628312yes—
255C22#1192628512yes—
256C22#1192630111yescharacteristic
257C22#1192630311yescharacteristic
258C22#1192630411yescharacteristic
259C22#1192630511yescharacteristic
260C22#1192631011yescharacteristic
261C22#1192631211yescharacteristic
262C22#1192631511yescharacteristic
263C4—22no—
264C4—22no—
265C4—41no—
266C4—41no—
267C4—41no—
268C4—41no—
269C4—1524no—
270C2—22no—
271C2—22no—
272C2#1456148911yescharacteristic
273C2#1456149211yescharacteristic
274C2#1456150011yescharacteristic
275C2#1456151711yescharacteristic
276C2#1456152111yescharacteristic
277C2#1456152711yescharacteristic
278C2#1456154211yescharacteristic
subgroupG/H
centerC23C19⋊#95
commutatorC22×C4×C19C42
FrattiniC22×C42C2×D19
FittingC19×#1749C2
socleC23×C19#95
prime radicalC24×C19C22⋊C4
cosocleC22×C42×C19C22
hypercenter#1749D19
hypocenterC19#7036
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1749

Complements

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

NH ≅ G/Ntype
5. C2×#10597260C4semidirect
13. C19×#336C4semidirect
143. #336Dic19semidirect
171. C19#7036semidirect

Maximal subgroups

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

subgroupindex
#145633972
#145618622
C19×#17492
#703619