Finite Group Databasebeta

← #18069669

Subgroups — #18069669

Order 4864.

328 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 328 conjugacy classes of subgroups — too many to draw. Only its 95 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#14563619C211yesmaximal, characteristic
2#14563374C211yesmaximal, characteristic
3C19×#1458C211yesmaximal, characteristic
4C22×#64520—21no—
5C2×C4⋊(C19⋊C8)C411yescharacteristic
6C2×C4⋊(C19⋊C8)C411yescharacteristic
7C2×C22⋊(C19⋊C8)—21no—
8#11926313—21no—
9#11926313C412yes—
10#11926299—21no—
11C2×C19×#117C2211yescharacteristic
12C19×#431—21no—
13C19×#324—21no—
14C19×#323C412yes—
15C23×C4×C19D411yescharacteristic
16C19×#117—41no—
17C19×#117—41no—
18C2×C4⋊C4×C19C2×C411yescharacteristic
19C2×C4⋊C4×C19D411yescharacteristic
20C2×C22⋊C4×C19C2×C411yescharacteristic
21C2×C22⋊C4×C19Q811yescharacteristic
22C2×C42×C19C2×C411yescharacteristic
23C2×C42×C19D411yescharacteristic
24C2×#64520—22no—
25C2×#64520—22no—
26C2×#64520—22no—
27C2×#64520—41no—
28C2×#64520—41no—
29C2×#64520—41no—
30C22×C19⋊C8—21no—
31C22×C19⋊C8—21no—
32C22×C19⋊C8—41no—
33C19×C4⋊C8—41no—
34C19×C22⋊C8—22no—
35C4×C8×C19—41no—
36C22⋊(C19⋊C8)—41no—
37C22⋊(C19⋊C8)—41no—
38C4⋊(C19⋊C8)—41no—
39C4⋊(C19⋊C8)—41no—
40C24×C19C4⋊C411yescharacteristic
41C22×C4×C19—21no—
42C22×C4×C19—21no—
43C22×C4×C19—21no—
44C22×C4×C19—21no—
45C22×C4×C19C4211yescharacteristic
46C22×C4×C19C22⋊C411yescharacteristic
47C22×C4×C19C22⋊C411yescharacteristic
48C22×C4×C19C22⋊C411yescharacteristic
49C22×C4×C19C4⋊C411yescharacteristic
50C22×C4×C19C4⋊C411yescharacteristic
51C22×C4×C19D811yescharacteristic
52C22×C4×C19SD1611yescharacteristic
53C22×C4×C19SD1611yescharacteristic
54C22×C4×C19Q1611yescharacteristic
55C2×C8×C19—42no—
56C4⋊C4×C19—41no—
57C4⋊C4×C19—41no—
58C22⋊C4×C19—41no—
59C22⋊C4×C19—41no—
60C42×C19—21no—
61C42×C19—21no—
62C42×C19—21no—
63C42×C19—21no—
64#64520—24no—
65#64520—42no—
66#64520—42no—
67#64520—42no—
68C2×C19⋊C8—42no—
69C2×C19⋊C8—42no—
70C2×C19⋊C8—42no—
71C2×C19⋊C8—41no—
72C2×C19⋊C8—41no—
73C2×C19⋊C8—41no—
74C2×C19⋊C8—41no—
75C2×C19⋊C8—41no—
76C2×C19⋊C8—41no—
77#7253—191nomaximal, Sylow
78C23×C19—21no—
79C23×C19—21no—
80C23×C19—41no—
81C23×C19—41no—
82C23×C19#9511yescharacteristic
83C23×C19#10611yescharacteristic
84C23×C19#10711yescharacteristic
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—21no—
93C2×C4×C19—21no—
94C2×C4×C19—21no—
95C2×C4×C19—21no—
96C2×C4×C19—21no—
97C2×C4×C19—21no—
98C2×C4×C19—21no—
99C2×C4×C19—41no—
100C2×C4×C19—41no—
101C2×C4×C19—41no—
102C2×C4×C19—41no—
103C2×C4×C19#9911yescharacteristic
104C2×C4×C19#9911yescharacteristic
105C2×C4×C19#10211yescharacteristic
106C2×C4×C19#10211yescharacteristic
107C2×C4×C19#10311yescharacteristic
108C2×C4×C19#10311yescharacteristic
109C2×C4×C19#10411yescharacteristic
110C2×C4×C19#10411yescharacteristic
111C8×C19—82no—
112C19⋊C8—44no—
113C19⋊C8—81no—
114C19⋊C8—81no—
115#1798—191no—
116#1742—191no—
117#1458D1911yescharacteristic
118C22×C19—21no—
119C22×C19—21no—
120C22×C19—21no—
121C22×C19—21no—
122C22×C19—41no—
123C22×C19—41no—
124C22×C19—41no—
125C22×C19—41no—
126C22×C19—81no—
127C22×C19#33911yescharacteristic
128C22×C19#34011yescharacteristic
129C22×C19#34211yescharacteristic
130C4×C19—21no—
131C4×C19—21no—
132C4×C19—41no—
133C4×C19—41no—
134C4×C19—41no—
135C4×C19—41no—
136C4×C19#32711yescharacteristic
137C4×C19#32711yescharacteristic
138C4×C19#32811yescharacteristic
139C4×C19#32811yescharacteristic
140C22×M16—381no—
141C2×#117C2×D1911yescharacteristic
142#431—21no—
143C2×C4⋊C8—191no—
144C2×C4⋊C8—191no—
145C2×C22⋊C8—381no—
146#343—192no—
147#343—381no—
148#336—381no—
149#324—21no—
150#323Dic1912yes—
151C2×C19—21no—
152C2×C19—21no—
153C2×C19—41no—
154C2×C19—41no—
155C2×C19#129411yescharacteristic
156C2×C19#139211yescharacteristic
157C2×C19#139511yescharacteristic
158C23×C4D7611yescharacteristic
159C2×M16—382no—
160C2×M16—382no—
161C2×M16—382no—
162C2×M16—761no—
163C2×M16—761no—
164C2×M16—761no—
165C22×C8—381no—
166C22×C8—381no—
167C22×C8—761no—
168#117—41no—
169#117—41no—
170C2×C4⋊C4C4×D1911yescharacteristic
171C2×C4⋊C4C22⋊D1911yescharacteristic
172C2×C22⋊C4Dic3811yescharacteristic
173C2×C22⋊C4C2×Dic1911yescharacteristic
174C2×C42C4×D1911yescharacteristic
175C2×C42C22⋊D1911yescharacteristic
176C4⋊C8—41no—
177C4⋊C8—761no—
178C4⋊C8—761no—
179C22⋊C8—22no—
180C22⋊C8—761no—
181C22⋊C8—761no—
182C4×C8—41no—
183C19#725311yescharacteristic, complemented, Sylow
184C24C4⋊Dic1911yescharacteristic
185C22×C4—21no—
186C22×C4—21no—
187C22×C4—21no—
188C22×C4—21no—
189C22×C4#6451611yescharacteristic
190C22×C4#6451611yescharacteristic
191C22×C4D15211yescharacteristic
192C22×C4Dic7611yescharacteristic
193C22×C4C4×Dic1911yescharacteristic
194C22×C4Dic19⋊C411yescharacteristic
195C22×C4Dic19⋊C411yescharacteristic
196C22×C4(C2×D19)⋊C411yescharacteristic
197C22×C4(C2×D19)⋊C411yescharacteristic
198C22×C4C22⋊Dic1911yescharacteristic
199M16—384no—
200M16—762no—
201M16—762no—
202M16—762no—
203C2×C8—42no—
204C2×C8—762no—
205C2×C8—762no—
206C2×C8—762no—
207C2×C8—761no—
208C2×C8—761no—
209C2×C8—761no—
210C2×C8—761no—
211C2×C8—761no—
212C2×C8—761no—
213C4⋊C4—41no—
214C4⋊C4—41no—
215C22⋊C4—41no—
216C22⋊C4—41no—
217C42—21no—
218C42—21no—
219C42—21no—
220C42—21no—
221C23—21no—
222C23—21no—
223C23—41no—
224C23—41no—
225C23#1059727411yescharacteristic
226C23#1059727511yescharacteristic
227C23C19⋊#9511yescharacteristic
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4#1059726311yescharacteristic
247C2×C4#1059726311yescharacteristic
248C2×C4#1059727311yescharacteristic
249C2×C4#1059727311yescharacteristic
250C2×C4#1059727811yescharacteristic
251C2×C4#1059727811yescharacteristic
252C2×C4#1059728211yescharacteristic
253C2×C4#1059728211yescharacteristic
254C8—82no—
255C8—764no—
256C8—1521no—
257C8—1521no—
258C22—21no—
259C22—21no—
260C22—21no—
261C22—21no—
262C22—41no—
263C22—41no—
264C22—41no—
265C22—41no—
266C22—81no—
267C22#1192630511yescharacteristic
268C22#1192630711yescharacteristic
269C22#1192631011yescharacteristic
270C4—21no—
271C4—21no—
272C4—41no—
273C4—41no—
274C4—41no—
275C4—41no—
276C4#1192627911yescharacteristic
277C4#1192627911yescharacteristic
278C4#1192628211yescharacteristic
279C4#1192628211yescharacteristic
280C2—21no—
281C2—21no—
282C2—41no—
283C2—41no—
284C2#1456151511yescharacteristic
285C2#1456175711yescharacteristic
286C2#1456176311yescharacteristic
subgroupG/H
centerC2×C4#10597263
commutatorC22×C4×C19C42
FrattiniC2×#117C2×D19
FittingC19×#1458C2
socleC22×C19#342
prime radicalC24×C19C4⋊C4
cosocleC2×C19×#117C22
hypercenter#1458D19
hypocenterC19#7253
LCSG ▷ C22×C4×C19 ▷ C23×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#117 ◁ #1458

Complements

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

NH ≅ G/Ntype
183. C19#7253semidirect

Maximal subgroups

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

subgroupindex
#145636192
#145633742
C19×#14582
#725319