Finite Group Databasebeta

← #18071332

Subgroups — #18071332

Order 4864.

492 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 83 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#14570565C211yesmaximal, characteristic
2#14564964C212yesmaximal, complemented
3#14564717C211yesmaximal, characteristic
4#14561457C212yesmaximal, complemented
5C19×#1270C211yesmaximal, characteristic
6C22×#64526—21no—
7C2×#10597315C2211yescharacteristic
8C2×#10597381—21no—
9C2×#10597275—22no—
10C2×#10597267—21no—
11#11926474—21no—
12#11926469—22no—
13#11926442C2212yes—
14#11926419—22no—
15#11926307—22no—
16#11926299C2211yescharacteristic
17C19×#390C2211yescharacteristic
18C19×#336C2212yes—
19C22×D4×C19D411yescharacteristic
20C23×Dic19—21no—
21C22×Dic38—21no—
22C22×C8×C19—22no—
23C2×C4⋊C4×C19D411yescharacteristic
24C2×C22⋊C4×C19—22no—
25C2×C42×C19C2311yescharacteristic
26C2×C22⋊Dic19—22no—
27C2×C22⋊Dic19—21no—
28#10597381—42no—
29#10597381—42no—
30C2×#64526—42no—
31C2×#64526—42no—
32C2×#64526—42no—
33C2×C4⋊Dic19—22no—
34C2×C4⋊Dic19—21no—
35C2×C4⋊Dic19D412yes—
36C2×C4⋊Dic19D412yes—
37C2×Dic19⋊C4—22no—
38C22×C19⋊C8—21no—
39#10597315—42no—
40C19⋊#95—22no—
41C19⋊#95—21no—
42C19⋊#95—22no—
43#10597275—44no—
44#10597267—42no—
45C24×C19—21no—
46C2×D4×C19—21no—
47C2×D4×C19—41no—
48C2×D4×C19—41no—
49C2×D4×C19D812yes—
50C22×C4×C19—21no—
51C22×C4×C19C2×D411yescharacteristic
52C22×C4×C19C2×D412yes—
53C22×Dic19—22no—
54C22×Dic19—22no—
55C22×Dic19—42no—
56C22×Dic19—41no—
57C22×Dic19—81no—
58C22×Dic19—81no—
59C2×Dic38—22no—
60C2×Dic38—41no—
61C2×Dic38—41no—
62C2×Dic38—41no—
63C2×Dic38—41no—
64C2×Dic38—41no—
65C2×C8×C19—24no—
66C2×C8×C19—42no—
67C2×C8×C19—42no—
68C4⋊C4×C19—41no—
69C22⋊C4×C19—42no—
70C22⋊C4×C19—42no—
71C42×C19—41no—
72C22⋊Dic19—42no—
73C22⋊Dic19—44no—
74#64526—48no—
75C4⋊Dic19—24no—
76C4⋊Dic19—22no—
77C4⋊Dic19—22no—
78C4⋊Dic19—42no—
79C4⋊Dic19—42no—
80C4⋊Dic19—81no—
81Dic19⋊C4—42no—
82Dic19⋊C4—42no—
83C2×C19⋊C8—22no—
84C2×C19⋊C8—41no—
85C2×C19⋊C8—41no—
86#7751—191nomaximal, Sylow
87C23×C19—22no—
88C23×C19—42no—
89C23×C19—41no—
90C23×C19—42no—
91C23×C19—41no—
92C23×C19#12011yescharacteristic
93D4×C19—42no—
94D4×C19—81no—
95C2×C4×C19—21no—
96C2×C4×C19—22no—
97C2×C4×C19—21no—
98C2×C4×C19—22no—
99C2×C4×C19—42no—
100C2×C4×C19—41no—
101C2×C4×C19C2×D811yescharacteristic
102C2×C4×C19#13512yes—
103C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
104C2×C4×C19#13712yes—
105C2×Dic19—42no—
106C2×Dic19—42no—
107C2×Dic19—42no—
108C2×Dic19—42no—
109C2×Dic19—42no—
110C2×Dic19—42no—
111C2×Dic19—42no—
112C2×Dic19—84no—
113C2×Dic19—81no—
114C2×Dic19—81no—
115Dic38—42no—
116Dic38—42no—
117Dic38—81no—
118Dic38—81no—
119C8×C19—44no—
120C19⋊C8—42no—
121#2724—191no—
122#2057—192no—
123#2013—191no—
124#1271—192no—
125#1270D1911yescharacteristic
126C22×C19—42no—
127C22×C19—44no—
128C22×C19—82no—
129C22×C19—81no—
130C22×C19—81no—
131C22×C19#44711yescharacteristic
132C22×C19#45212yes—
133C22×C19#45311yescharacteristic
134C22×C19#45612yes—
135C22×C19B(4,𝔽2)11yescharacteristic
136C4×C19—21no—
137C4×C19—21no—
138C4×C19—22no—
139C4×C19—22no—
140C4×C19—81no—
141Dic19—82no—
142Dic19—82no—
143Dic19—82no—
144C22×SD16—381no—
145C2×C4⋊Q8—191no—
146C2×#123—381no—
147C2×#107—382no—
148C2×#103—381no—
149#398—381no—
150#397—382no—
151#390C2×D1911yescharacteristic
152#389—192no—
153#385—382no—
154#340—382no—
155#336—191no—
156#336C2×D1912yes—
157C2×C19—82no—
158C2×C19#159511yescharacteristic
159C2×C19#160312yes—
160C2×C19#163011yescharacteristic
161C2×C19#164712yes—
162C2×C19#166011yescharacteristic
163C22×Q8—381no—
164C22×D4D7611yescharacteristic
165C23×C4—381no—
166C2×SD16—762no—
167C2×SD16—762no—
168C2×SD16—762no—
169C22×C8—22no—
170C22×C8—381no—
171C4⋊Q8—762no—
172#123—762no—
173#123—762no—
174C2×C4⋊C4—192no—
175C2×C4⋊C4—192no—
176C2×C4⋊C4—382no—
177C2×C4⋊C4—382no—
178C2×C4⋊C4—381no—
179C2×C4⋊C4D7611yescharacteristic
180C2×C22⋊C4—22no—
181C2×C22⋊C4—382no—
182C2×C22⋊C4—381no—
183C2×C42C22×D1911yescharacteristic
184#107—764no—
185#103—762no—
186#95—382no—
187#95—381no—
188#95—382no—
189C19#775111yescharacteristic, complemented, Sylow
190C24—21no—
191C2×Q8—382no—
192C2×Q8—761no—
193C2×Q8—761no—
194C2×Q8—761no—
195C2×Q8—761no—
196C2×Q8—761no—
197C2×D4—21no—
198C2×D4—41no—
199C2×D4—41no—
200C2×D4D15212yes—
201C22×C4—21no—
202C22×C4—382no—
203C22×C4—382no—
204C22×C4—762no—
205C22×C4—761no—
206C22×C4—1521no—
207C22×C4—1521no—
208C22×C4C2×D7611yescharacteristic
209C22×C4D4×D1912yes—
210SD16—768no—
211C2×C8—24no—
212C2×C8—42no—
213C2×C8—42no—
214C2×C8—382no—
215C2×C8—761no—
216C2×C8—761no—
217C4⋊C4—41no—
218C4⋊C4—384no—
219C4⋊C4—382no—
220C4⋊C4—382no—
221C4⋊C4—762no—
222C4⋊C4—762no—
223C4⋊C4—762no—
224C4⋊C4—762no—
225C4⋊C4—1521no—
226C22⋊C4—42no—
227C22⋊C4—42no—
228C22⋊C4—762no—
229C22⋊C4—764no—
230C42—41no—
231C23—22no—
232C23—42no—
233C23—41no—
234C23—42no—
235C23—41no—
236C23#1059732811yescharacteristic
237Q8—762no—
238Q8—762no—
239Q8—1521no—
240Q8—1521no—
241D4—42no—
242D4—81no—
243C2×C4—21no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—21no—
247C2×C4—42no—
248C2×C4—41no—
249C2×C4—762no—
250C2×C4—762no—
251C2×C4—762no—
252C2×C4—762no—
253C2×C4—762no—
254C2×C4—762no—
255C2×C4—762no—
256C2×C4—1524no—
257C2×C4—1521no—
258C2×C4—1521no—
259C2×C4C2×D15211yescharacteristic
260C2×C4#1059735411yescharacteristic
261C2×C4#1059735812yes—
262C2×C4#1059736112yes—
263C8—44no—
264C8—762no—
265C22—44no—
266C22—42no—
267C22—82no—
268C22—81no—
269C22—81no—
270C22#1192668011yescharacteristic
271C22#1192670712yes—
272C22#1192671411yescharacteristic
273C22#1192672812yes—
274C22#1192673211yescharacteristic
275C4—22no—
276C4—22no—
277C4—21no—
278C4—21no—
279C4—81no—
280C4—1522no—
281C4—1522no—
282C4—1522no—
283C2—82no—
284C2#1456255511yescharacteristic
285C2#1456259912yes—
286C2#1456275711yescharacteristic
287C2#1456287212yes—
288C2#1456294711yescharacteristic
subgroupG/H
centerC23#10597328
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#1270C2
socleC23×C19#120
prime radicalC22×D4×C19D4
hypercenter#1270D19
hypocenterC19#7751
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. #14564964C2semidirect
4. #14561457C2semidirect
189. C19#7751semidirect

Maximal subgroups

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

subgroupindex
#145705652
#145649642
#145647172
#145614572
C19×#12702
#775119