Finite Group Databasebeta

← #18069157

Subgroups — #18069157

Order 4864.

476 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 53 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#14563544C211yesmaximal, characteristic
2#14561559C211yesmaximal, characteristic, complemented
3C19×#1314C211yesmaximal, characteristic, complemented
4C23×C4×D19C411yescharacteristic
5C2×C22⋊(C19⋊C8)C411yescharacteristic
6C2×(C2×D19)⋊C8—21no—
7C2×(C2×D19)⋊C8—21no—
8C22⋊(C19⋊C16)—21no—
9C2×C19×C22⋊C8C2211yescharacteristic
10C19×C22⋊C16—21no—
11C24×D19C811yescharacteristic
12C23×C4×C19C2×C411yescharacteristic
13C23×Dic19C811yescharacteristic
14C22×C4×D19—21no—
15C22×C4×D19—21no—
16C22×C4×D19—42no—
17C22×C4×D19—42no—
18C22×C4×D19—41no—
19C22×C4×D19—41no—
20C22×C8×C19D411yescharacteristic
21C22×C8×C19D411yescharacteristic
22C22×C19⋊C8—21no—
23C2×C16×C19—41no—
24C19×C22⋊C8—41no—
25C22⋊(C19⋊C8)—41no—
26(C2×D19)⋊C8—42no—
27(C2×D19)⋊C8—42no—
28C2×C19⋊C16—41no—
29C24×C19C2×C811yescharacteristic
30C23×D19—21no—
31C23×D19—21no—
32C23×D19—42no—
33C23×D19—42no—
34C23×D19—41no—
35C23×D19—41no—
36C23×D19C1612yescomplemented
37C22×C4×C19—21no—
38C22×C4×C19—21no—
39C22×C4×C19—41no—
40C22×C4×C19—41no—
41C22×C4×C19C22⋊C411yescharacteristic
42C22×C4×C19M1611yescharacteristic
43C22×Dic19—21no—
44C22×Dic19—42no—
45C22×Dic19—41no—
46C2×C4×D19—22no—
47C2×C4×D19—22no—
48C2×C4×D19—42no—
49C2×C4×D19—41no—
50C2×C4×D19—41no—
51C2×C4×D19—42no—
52C2×C4×D19—42no—
53C2×C4×D19—44no—
54C2×C4×D19—44no—
55C2×C4×D19—42no—
56C2×C4×D19—42no—
57C2×C4×D19—41no—
58C2×C4×D19—41no—
59C2×C4×D19—42no—
60C2×C4×D19—42no—
61C2×C8×C19—21no—
62C2×C8×C19—21no—
63C2×C8×C19—41no—
64C2×C8×C19—41no—
65C2×C19⋊C8—41no—
66C2×C19⋊C8—41no—
67C2×C19⋊C8—41no—
68C16×C19—81no—
69C19⋊C16—81no—
70#7054—191nomaximal, Sylow
71C23×C19—21no—
72C23×C19—21no—
73C23×C19—41no—
74C23×C19—41no—
75C23×C19C22⋊C811yescharacteristic
76C23×C19C2×C1611yescharacteristic
77C23×C19M3211yescharacteristic
78C22×D19—22no—
79C22×D19—22no—
80C22×D19—22no—
81C22×D19—44no—
82C22×D19—44no—
83C22×D19—41no—
84C22×D19—41no—
85C22×D19—42no—
86C22×D19—42no—
87C22×D19—48no—
88C22×D19—42no—
89C22×D19—41no—
90C22×D19—41no—
91C22×D19—42no—
92C22×D19—42no—
93C22×D19—42no—
94C2×C4×C19—21no—
95C2×C4×C19—21no—
96C2×C4×C19—21no—
97C2×C4×C19—42no—
98C2×C4×C19—41no—
99C2×C4×C19—41no—
100C2×C4×C19—41no—
101C2×C4×C19#9911yescharacteristic
102C2×C4×C19#10011yescharacteristic
103C2×Dic19—22no—
104C2×Dic19—41no—
105C2×Dic19—42no—
106C2×Dic19—41no—
107C2×Dic19—42no—
108C4×D19—42no—
109C4×D19—42no—
110C4×D19—44no—
111C4×D19—44no—
112C4×D19—42no—
113C4×D19—42no—
114C8×C19—41no—
115C8×C19—41no—
116C19⋊C8—81no—
117#1779—191no—
118#1314—191no—
119#1314D1911yescharacteristic, complemented
120C22×C19—21no—
121C22×C19—21no—
122C22×C19—21no—
123C22×C19—21no—
124C22×C19—41no—
125C22×C19—41no—
126C22×C19—42no—
127C22×C19—41no—
128C22×C19—41no—
129C22×C19#32311yescharacteristic
130C22×C19C22⋊C1611yescharacteristic
131C22×C19#34911yescharacteristic
132C2×D19—24no—
133C2×D19—42no—
134C2×D19—42no—
135C2×D19—42no—
136C2×D19—44no—
137C2×D19—44no—
138C2×D19—44no—
139C2×D19—42no—
140C2×D19—42no—
141C2×D19—42no—
142C2×D19—44no—
143C4×C19—21no—
144C4×C19—41no—
145C4×C19AΣL(1,𝔽16)11yescharacteristic
146C4×C19AΣL(1,𝔽16)11yescharacteristic
147Dic19—42no—
148C24×C4—191no—
149C2×C22⋊C8—191no—
150C2×C22⋊C8—381no—
151C2×C22⋊C8—381no—
152C2×C22⋊C8C2×D1911yescharacteristic
153C22⋊C16—21no—
154C22⋊C16—381no—
155C2×C19—21no—
156C2×C19—21no—
157C2×C19—41no—
158C2×C19—41no—
159C2×C19#131411yescharacteristic
160C2×C19#131611yescharacteristic
161C2×C19#132011yescharacteristic
162D19—44no—
163C25—191no—
164C23×C4—191no—
165C23×C4—381no—
166C23×C4—381no—
167C23×C4—761no—
168C23×C4—761no—
169C23×C4—762no—
170C23×C4—762no—
171C23×C4C4×D1911yescharacteristic
172C22×C8—381no—
173C22×C8D7611yescharacteristic
174C22×C8C22⋊D1911yescharacteristic
175C2×C16—41no—
176C2×C16—761no—
177C22⋊C8—41no—
178C22⋊C8—762no—
179C22⋊C8—762no—
180C22⋊C8—761no—
181C19#705411yescharacteristic, complemented, Sylow
182C24—192no—
183C24—381no—
184C24—381no—
185C24—761no—
186C24—761no—
187C24—762no—
188C24—762no—
189C24C8×D1911yescharacteristic
190C22×C4—21no—
191C22×C4—21no—
192C22×C4—41no—
193C22×C4—41no—
194C22×C4—382no—
195C22×C4—382no—
196C22×C4—381no—
197C22×C4—761no—
198C22×C4—761no—
199C22×C4—762no—
200C22×C4—762no—
201C22×C4—762no—
202C22×C4—764no—
203C22×C4—764no—
204C22×C4—762no—
205C22×C4—762no—
206C22×C4—762no—
207C22×C4—762no—
208C22×C4—762no—
209C22×C4—761no—
210C22×C4—761no—
211C22×C4—761no—
212C22×C4#6451511yescharacteristic
213C22×C4(C2×D19)⋊C411yescharacteristic
214C2×C8—21no—
215C2×C8—21no—
216C2×C8—41no—
217C2×C8—41no—
218C2×C8—761no—
219C2×C8—761no—
220C2×C8—761no—
221C16—81no—
222C16—1521no—
223C23—21no—
224C23—21no—
225C23—41no—
226C23—41no—
227C23—382no—
228C23—382no—
229C23—382no—
230C23—762no—
231C23—761no—
232C23—761no—
233C23—762no—
234C23—764no—
235C23—764no—
236C23—762no—
237C23—762no—
238C23—762no—
239C23—768no—
240C23—762no—
241C23—761no—
242C23—761no—
243C23C16×D1911yescharacteristic
244C23#1059725511yescharacteristic
245C23(C2×D19)⋊C811yescharacteristic
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—42no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—382no—
254C2×C4—762no—
255C2×C4—762no—
256C2×C4—764no—
257C2×C4—764no—
258C2×C4—761no—
259C2×C4—762no—
260C2×C4—761no—
261C2×C4—762no—
262C2×C4—762no—
263C2×C4—762no—
264C2×C4#1059726311yescharacteristic
265C2×C4#1059728011yescharacteristic
266C8—41no—
267C8—41no—
268C8—1521no—
269C22—21no—
270C22—21no—
271C22—21no—
272C22—21no—
273C22—41no—
274C22—41no—
275C22—42no—
276C22—41no—
277C22—41no—
278C22—384no—
279C22—762no—
280C22—762no—
281C22—762no—
282C22—764no—
283C22—764no—
284C22—764no—
285C22—764no—
286C22—762no—
287C22—762no—
288C22—762no—
289C22#1192626711yescharacteristic
290C22(C2×D19)⋊C1611yescharacteristic
291C22#1192632511yescharacteristic
292C4—21no—
293C4—41no—
294C4—762no—
295C4#1192633011yescharacteristic
296C4#1192633211yescharacteristic
297C2—21no—
298C2—21no—
299C2—41no—
300C2—41no—
301C2—764no—
302C2#1456155811yescharacteristic
303C2#1456156211yescharacteristic
304C2#1456157011yescharacteristic
subgroupG/H
centerC2×C4#10597263
commutatorC23×C19C2×C16
FrattiniC2×C22⋊C8C2×D19
FittingC19×#1314C2
socleC22×C19#323
prime radicalC24×D19C8
cosocleC2×C19×C22⋊C8C22
hypercenter#1314D19
hypocenterC19#7054
LCSG ▷ C23×C19 ▷ C22×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C22⋊C8 ◁ #1314

Complements

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

NH ≅ G/Ntype
2. #14561559C2semidirect
3. C19×#1314C2semidirect
36. C23×D19C16semidirect
119. #1314D19semidirect
181. C19#7054semidirect

Maximal subgroups

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

subgroupindex
#145635442
#145615592
C19×#13142
#705419