Finite Group Databasebeta

← #18071351

Subgroups — #18071351

Order 4864.

536 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 536 conjugacy classes of subgroups — too many to draw. Only its 87 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#14570007C211yesmaximal, characteristic
2#14564969C212yesmaximal, complemented
3#14564717C211yesmaximal, characteristic
4#14561459C212yesmaximal, complemented
5C19×#1270C211yesmaximal, characteristic
6C22×#64526—21no—
7C2×#10597315C2211yescharacteristic
8C2×#10597324—22no—
9C2×#10597274—22no—
10C2×#10597267—21no—
11#11926467—22no—
12#11926464—21no—
13#11926442C2212yes—
14#11926424—21no—
15#11926307—22no—
16#11926299C2211yescharacteristic
17C19×#390C2211yescharacteristic
18C19×#336C2212yes—
19C22×D4×C19D411yescharacteristic
20C23×Dic19—21no—
21C22×Dic38—21no—
22C22×Dic38—21no—
23C22×C8×C19—22no—
24C2×C4⋊C4×C19D411yescharacteristic
25C2×C22⋊C4×C19—22no—
26C2×C42×C19C2311yescharacteristic
27C2×C22⋊Dic19—22no—
28C2×C22⋊Dic19—21no—
29C2×#64526—42no—
30C2×#64526—42no—
31C2×#64526—42no—
32C2×C4⋊Dic19—22no—
33C2×C4⋊Dic19D412yes—
34C2×C4⋊Dic19D412yes—
35C2×Dic19⋊C4—22no—
36C2×Dic19⋊C4—22no—
37C22×C19⋊C8—21no—
38#10597324—44no—
39#10597324—44no—
40#10597315—42no—
41C19⋊#95—21no—
42C19⋊#95—22no—
43#10597274—44no—
44#10597267—42no—
45C24×C19—21no—
46C2×D4×C19—21no—
47C2×D4×C19—41no—
48C2×D4×C19—41no—
49C2×D4×C19SD1612yes—
50C22×C4×C19—21no—
51C22×C4×C19C2×D411yescharacteristic
52C22×C4×C19C2×D412yes—
53C22×Dic19—22no—
54C22×Dic19—22no—
55C22×Dic19—44no—
56C22×Dic19—41no—
57C22×Dic19—81no—
58C2×Dic38—22no—
59C2×Dic38—41no—
60C2×Dic38—41no—
61C2×Dic38—41no—
62C2×Dic38—41no—
63C2×Dic38—44no—
64C2×Dic38—41no—
65C2×Dic38—81no—
66C2×C8×C19—24no—
67C2×C8×C19—42no—
68C2×C8×C19—42no—
69C4⋊C4×C19—41no—
70C22⋊C4×C19—42no—
71C22⋊C4×C19—42no—
72C42×C19—41no—
73C22⋊Dic19—44no—
74C22⋊Dic19—81no—
75#64526—48no—
76C4⋊Dic19—22no—
77C4⋊Dic19—24no—
78C4⋊Dic19—42no—
79C4⋊Dic19—42no—
80C4⋊Dic19SD1614yescomplemented
81Dic19⋊C4—44no—
82Dic19⋊C4—42no—
83Dic19⋊C4—42no—
84C2×C19⋊C8—22no—
85C2×C19⋊C8—41no—
86C2×C19⋊C8—41no—
87#7754—191nomaximal, Sylow
88C23×C19—22no—
89C23×C19—42no—
90C23×C19—41no—
91C23×C19—42no—
92C23×C19—41no—
93C23×C19#12011yescharacteristic
94D4×C19—42no—
95D4×C19—81no—
96C2×C4×C19—21no—
97C2×C4×C19—22no—
98C2×C4×C19—21no—
99C2×C4×C19—22no—
100C2×C4×C19—42no—
101C2×C4×C19—41no—
102C2×C4×C19C2×SD1611yescharacteristic
103C2×C4×C19C2×SD1612yes—
104C2×C4×C19AGL(1,ℤ/8)12yes—
105C2×C4×C19#13711yescharacteristic
106C2×Dic19—24no—
107C2×Dic19—42no—
108C2×Dic19—42no—
109C2×Dic19—42no—
110C2×Dic19—42no—
111C2×Dic19—42no—
112C2×Dic19—42no—
113C2×Dic19—84no—
114C2×Dic19—81no—
115C2×Dic19—81no—
116Dic38—42no—
117Dic38—42no—
118Dic38—84no—
119Dic38—81no—
120Dic38—81no—
121C8×C19—44no—
122C19⋊C8—42no—
123#2683—191no—
124#2058—192no—
125#2013—191no—
126#1271—192no—
127#1270D1911yescharacteristic
128C22×C19—42no—
129C22×C19—44no—
130C22×C19—82no—
131C22×C19—81no—
132C22×C19—81no—
133C22×C19#44811yescharacteristic
134C22×C19#45012yes—
135C22×C19#45311yescharacteristic
136C22×C19#45612yes—
137C22×C19B(4,𝔽2)11yescharacteristic
138C4×C19—21no—
139C4×C19—21no—
140C4×C19—22no—
141C4×C19—22no—
142C4×C19—81no—
143Dic19—44no—
144Dic19—82no—
145Dic19—82no—
146C22×SD16—381no—
147C2×C4⋊Q8—191no—
148C2×C22⋊Q8—382no—
149C2×#106—382no—
150C2×#103—381no—
151#396—382no—
152#395—381no—
153#390C2×D1911yescharacteristic
154#389—192no—
155#386—381no—
156#340—382no—
157#336—191no—
158#336C2×D1912yes—
159C2×C19—82no—
160C2×C19#159611yescharacteristic
161C2×C19#160412yes—
162C2×C19#162911yescharacteristic
163C2×C19#165112yes—
164C2×C19#166011yescharacteristic
165C22×Q8—381no—
166C22×Q8—381no—
167C22×D4D7611yescharacteristic
168C23×C4—381no—
169C2×SD16—762no—
170C2×SD16—762no—
171C2×SD16—762no—
172C22×C8—22no—
173C22×C8—381no—
174C4⋊Q8—762no—
175C22⋊Q8—764no—
176C22⋊Q8—764no—
177C2×C4⋊C4—192no—
178C2×C4⋊C4—192no—
179C2×C4⋊C4—382no—
180C2×C4⋊C4—382no—
181C2×C4⋊C4—382no—
182C2×C4⋊C4D7611yescharacteristic
183C2×C22⋊C4—22no—
184C2×C22⋊C4—382no—
185C2×C22⋊C4—381no—
186C2×C42C22×D1911yescharacteristic
187#106—764no—
188#103—762no—
189#95—381no—
190#95—382no—
191C19#775411yescharacteristic, complemented, Sylow
192C24—21no—
193C2×Q8—382no—
194C2×Q8—761no—
195C2×Q8—761no—
196C2×Q8—761no—
197C2×Q8—764no—
198C2×Q8—761no—
199C2×Q8—761no—
200C2×Q8—1521no—
201C2×D4—21no—
202C2×D4—41no—
203C2×D4—41no—
204C2×D4#6451612yes—
205C22×C4—21no—
206C22×C4—382no—
207C22×C4—382no—
208C22×C4—764no—
209C22×C4—761no—
210C22×C4—1521no—
211C22×C4C2×D7611yescharacteristic
212C22×C4D4×D1912yes—
213SD16—768no—
214C2×C8—24no—
215C2×C8—42no—
216C2×C8—42no—
217C2×C8—382no—
218C2×C8—761no—
219C2×C8—761no—
220C4⋊C4—41no—
221C4⋊C4—194no—
222C4⋊C4—384no—
223C4⋊C4—382no—
224C4⋊C4—762no—
225C4⋊C4—762no—
226C4⋊C4—764no—
227C4⋊C4—762no—
228C4⋊C4—762no—
229C22⋊C4—42no—
230C22⋊C4—42no—
231C22⋊C4—764no—
232C22⋊C4—1521no—
233C42—41no—
234C23—22no—
235C23—42no—
236C23—41no—
237C23—42no—
238C23—41no—
239C23#1059732811yescharacteristic
240Q8—762no—
241Q8—762no—
242Q8—1521no—
243Q8—1521no—
244Q8—1524no—
245D4—42no—
246D4—81no—
247C2×C4—21no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—21no—
251C2×C4—42no—
252C2×C4—41no—
253C2×C4—384no—
254C2×C4—762no—
255C2×C4—762no—
256C2×C4—762no—
257C2×C4—762no—
258C2×C4—762no—
259C2×C4—762no—
260C2×C4—1524no—
261C2×C4—1521no—
262C2×C4—1521no—
263C2×C4C2×#6451611yescharacteristic
264C2×C4#1059735511yescharacteristic
265C2×C4#1059735712yes—
266C2×C4SD16×D1912yes—
267C8—44no—
268C8—762no—
269C22—42no—
270C22—44no—
271C22—82no—
272C22—81no—
273C22—81no—
274C22#1192668511yescharacteristic
275C22#1192669612yes—
276C22#1192671411yescharacteristic
277C22#1192672812yes—
278C22#1192673211yescharacteristic
279C4—21no—
280C4—21no—
281C4—22no—
282C4—22no—
283C4—81no—
284C4—764no—
285C4—1522no—
286C4—1522no—
287C2—82no—
288C2#1456256011yescharacteristic
289C2#1456260512yes—
290C2#1456275211yescharacteristic
291C2#1456290012yes—
292C2#1456294711yescharacteristic
subgroupG/H
centerC23#10597328
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#1270C2
socleC23×C19#120
prime radicalC22×D4×C19D4
hypercenter#1270D19
hypocenterC19#7754
LCSG ▷ C2×C42×C19 ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1270

Complements

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

NH ≅ G/Ntype
2. #14564969C2semidirect
4. #14561459C2semidirect
80. C4⋊Dic19SD16semidirect
191. C19#7754semidirect

Maximal subgroups

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

subgroupindex
#145700072
#145649692
#145647172
#145614592
C19×#12702
#775419