Finite Group Databasebeta

← #18069846

Subgroups — #18069846

Order 4864.

342 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 71 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#14563933C211yesmaximal, characteristic
2#14563623C211yesmaximal, characteristic
3C19×#1466C211yesmaximal, characteristic
4C22×#64520C411yescharacteristic, complemented
5C2×#10597291C412yes—
6C2×C22⋊(C19⋊C8)—21no—
7C2×C22⋊(C19⋊C8)C411yescharacteristic, complemented
8#11926404—21no—
9#11926311—21no—
10#11926299—21no—
11C2×C4×D4×C19C2211yescharacteristic
12C19×#432—21no—
13C19×#323—21no—
14C19×#323C412yescomplemented
15C22×D4×C19C2×C411yescharacteristic
16C23×C4×C19C2×C411yescharacteristic
17C23×C4×C19D411yescharacteristic
18C4×D4×C19—41no—
19C4×D4×C19—41no—
20C2×C4⋊C4×C19Q811yescharacteristic
21C2×C22⋊C4×C19C2×C411yescharacteristic
22C2×C22⋊C4×C19D411yescharacteristic
23C2×C42×C19D411yescharacteristic
24C2×C22⋊Dic19—22no—
25C2×C4⋊Dic19—41no—
26C2×#64520—42no—
27C2×#64520—41no—
28C22×C19⋊C8—21no—
29C22×C19⋊C8—21no—
30C19×C4⋊C8—41no—
31C19×C22⋊C8—22no—
32C19×#97—41no—
33#10597291—42no—
34C19⋊#95—41no—
35C22⋊(C19⋊C8)—42no—
36C22⋊(C19⋊C8)—41no—
37C24×C19C4211yescharacteristic
38C24×C19C22⋊C411yescharacteristic
39C2×D4×C19—21no—
40C2×D4×C19—21no—
41C2×D4×C19—41no—
42C2×D4×C19—41no—
43C22×C4×C19—21no—
44C22×C4×C19—21no—
45C22×C4×C19—21no—
46C22×C4×C19—21no—
47C22×C4×C19—41no—
48C22×C4×C19—41no—
49C22×C4×C19—41no—
50C22×C4×C19—41no—
51C22×C4×C19C22⋊C411yescharacteristic
52C22×C4×C19C22⋊C411yescharacteristic
53C22×C4×C19C4⋊C411yescharacteristic
54C22×C4×C19C4⋊C411yescharacteristic
55C22×C4×C19C4⋊C411yescharacteristic
56C22×Dic19—42no—
57C2×C8×C19—42no—
58C4⋊C4×C19—41no—
59C22⋊C4×C19—41no—
60C22⋊C4×C19—41no—
61C42×C19—21no—
62C42×C19—21no—
63C22⋊Dic19—42no—
64C22⋊Dic19—42no—
65C4⋊Dic19—81no—
66C4⋊Dic19—81no—
67#64520—42no—
68#64520—42no—
69C2×C19⋊C8—22no—
70C2×C19⋊C8—41no—
71C2×C19⋊C8—41no—
72C2×C19⋊C8—41no—
73C2×C19⋊C8—41no—
74C2×C19⋊C8—41no—
75#7320—191nomaximal, Sylow
76C23×C19—21no—
77C23×C19—21no—
78C23×C19—21no—
79C23×C19—21no—
80C23×C19—21no—
81C23×C19—41no—
82C23×C19—41no—
83C23×C19—41no—
84C23×C19—41no—
85C23×C19#9511yescharacteristic
86C23×C19#10011yescharacteristic
87C23×C19#10111yescharacteristic
88D4×C19—42no—
89D4×C19—42no—
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—42no—
99C2×C4×C19—41no—
100C2×C4×C19—41no—
101C2×C4×C19—41no—
102C2×C4×C19—41no—
103C2×C4×C19—41no—
104C2×C4×C19—41no—
105C2×C4×C19—41no—
106C2×C4×C19—81no—
107C2×C4×C19#9911yescharacteristic
108C2×C4×C19#9911yescharacteristic
109C2×Dic19—82no—
110C2×Dic19—82no—
111C2×Dic19—82no—
112C8×C19—82no—
113C19⋊C8—42no—
114C19⋊C8—81no—
115#1870—191no—
116#1799—191no—
117#1466D1911yescharacteristic
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—41no—
127C22×C19—41no—
128C22×C19—41no—
129C22×C19—81no—
130C22×C19—81no—
131C22×C19—81no—
132C22×C19#34211yescharacteristic
133C22×C19#34311yescharacteristic
134C22×C19#34411yescharacteristic
135C4×C19—21no—
136C4×C19—41no—
137C4×C19—41no—
138C4×C19—41no—
139C4×C19—41no—
140C4×C19AΣL(1,𝔽16)11yescharacteristic
141C4×C19#35211yescharacteristic
142Dic19—162no—
143C22×M16—191no—
144C2×C4×D4C2×D1911yescharacteristic
145#432—21no—
146C2×#99—192no—
147C2×C22⋊C8—191no—
148C2×C22⋊C8—381no—
149#380—381no—
150#342—381no—
151#336—381no—
152#323—21no—
153#323Dic1912yescomplemented
154C2×C19—21no—
155C2×C19—21no—
156C2×C19—41no—
157C2×C19—41no—
158C2×C19—81no—
159C2×C19#130511yescharacteristic
160C2×C19#139011yescharacteristic
161C2×C19#139111yescharacteristic
162C22×D4C4×D1911yescharacteristic
163C23×C4C4×D1911yescharacteristic
164C23×C4D7611yescharacteristic
165C2×M16—762no—
166C2×M16—761no—
167C22×C8—381no—
168C22×C8—381no—
169C4×D4—41no—
170C4×D4—41no—
171C2×C4⋊C4—761no—
172C2×C4⋊C4Dic3811yescharacteristic
173C2×C22⋊C4—382no—
174C2×C22⋊C4C2×Dic1911yescharacteristic
175C2×C22⋊C4C22⋊D1911yescharacteristic
176C2×C42C22⋊D1911yescharacteristic
177C4⋊C8—41no—
178#99—762no—
179C22⋊C8—22no—
180C22⋊C8—762no—
181C22⋊C8—761no—
182#97—41no—
183#95—761no—
184C19#732011yescharacteristic, complemented, Sylow
185C24C4×Dic1911yescharacteristic
186C24(C2×D19)⋊C411yescharacteristic
187C2×D4—21no—
188C2×D4—21no—
189C2×D4—41no—
190C2×D4—41no—
191C22×C4—21no—
192C22×C4—21no—
193C22×C4—21no—
194C22×C4—21no—
195C22×C4—41no—
196C22×C4—41no—
197C22×C4—41no—
198C22×C4—41no—
199C22×C4—762no—
200C22×C4Dic19⋊C411yescharacteristic
201C22×C4Dic19⋊C411yescharacteristic
202C22×C4C4⋊Dic1911yescharacteristic
203C22×C4(C2×D19)⋊C411yescharacteristic
204C22×C4C22⋊Dic1911yescharacteristic
205M16—762no—
206M16—762no—
207C2×C8—42no—
208C2×C8—382no—
209C2×C8—761no—
210C2×C8—761no—
211C2×C8—761no—
212C2×C8—761no—
213C2×C8—761no—
214C4⋊C4—41no—
215C4⋊C4—1521no—
216C4⋊C4—1521no—
217C22⋊C4—41no—
218C22⋊C4—41no—
219C22⋊C4—762no—
220C22⋊C4—762no—
221C42—21no—
222C42—21no—
223C23—21no—
224C23—21no—
225C23—21no—
226C23—21no—
227C23—21no—
228C23—41no—
229C23—41no—
230C23—41no—
231C23—41no—
232C23#1059728011yescharacteristic
233C23#1059728111yescharacteristic
234C23C19⋊#9511yescharacteristic
235D4—42no—
236D4—42no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—42no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—81no—
254C2×C4—1522no—
255C2×C4—1522no—
256C2×C4—1522no—
257C2×C4#1059726311yescharacteristic
258C2×C4#1059726311yescharacteristic
259C8—82no—
260C8—762no—
261C8—1521no—
262C22—21no—
263C22—21no—
264C22—21no—
265C22—21no—
266C22—41no—
267C22—41no—
268C22—41no—
269C22—41no—
270C22—41no—
271C22—41no—
272C22—41no—
273C22—81no—
274C22—81no—
275C22—81no—
276C22#1192631011yescharacteristic
277C22#1192631211yescharacteristic
278C22#1192631511yescharacteristic
279C4—21no—
280C4—41no—
281C4—41no—
282C4—41no—
283C4—41no—
284C4—3042no—
285C4#1192633211yescharacteristic
286C4#1192633511yescharacteristic
287C2—21no—
288C2—21no—
289C2—41no—
290C2—41no—
291C2—81no—
292C2#1456154211yescharacteristic
293C2#1456175411yescharacteristic
294C2#1456175511yescharacteristic
subgroupG/H
centerC22#11926310
commutatorC24×C19C42
FrattiniC2×C4×D4C2×D19
FittingC19×#1466C2
socleC22×C19#342
prime radicalC22×D4×C19C2×C4
cosocleC2×C4×D4×C19C22
hypercenter#1466D19
hypocenterC19#7320
LCSG ▷ C24×C19 ▷ C23×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1466

Complements

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

NH ≅ G/Ntype
4. C22×#64520C4semidirect
7. C2×C22⋊(C19⋊C8)C4semidirect
14. C19×#323C4semidirect
153. #323Dic19semidirect
184. C19#7320semidirect

Maximal subgroups

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

subgroupindex
#145639332
#145636232
C19×#14662
#732019