Finite Group Databasebeta

← #18071356

Subgroups — #18071356

Order 4864.

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

normal subgroups only

This group has 480 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#14571581C211yesmaximal, characteristic
2#14564777C212yesmaximal, complemented
3#14564717C211yesmaximal, characteristic
4#14561460C212yesmaximal, complemented
5C19×#1270C211yesmaximal, characteristic
6C22×#64526—21no—
7C2×#10597315C2211yescharacteristic
8C2×#10597273—22no—
9C2×#10597267—21no—
10#11926483—21no—
11#11926456—22no—
12#11926450C2212yes—
13#11926424—21no—
14#11926419—22no—
15#11926307—22no—
16#11926299C2211yescharacteristic
17C19×#390C2211yescharacteristic
18C19×#336C2212yes—
19C22×D4×C19D411yescharacteristic
20C23×Dic19—21no—
21C22×Dic38—21no—
22C22×Dic38D412yes—
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⋊Dic19—21no—
34C2×C4⋊Dic19D412yes—
35C22×C19⋊C8—21no—
36#10597315—42no—
37C19⋊#95—22no—
38C19⋊#95—21no—
39C19⋊#95—22no—
40C19⋊#95—22no—
41#10597273—44no—
42#10597267—42no—
43C24×C19—21no—
44C2×D4×C19—21no—
45C2×D4×C19—41no—
46C2×D4×C19—41no—
47C2×D4×C19SD1612yes—
48C22×C4×C19—21no—
49C22×C4×C19C2×D411yescharacteristic
50C22×C4×C19C2×D412yes—
51C22×Dic19—22no—
52C22×Dic19—22no—
53C22×Dic19—41no—
54C22×Dic19—81no—
55C22×Dic19—82no—
56C2×Dic38—22no—
57C2×Dic38—22no—
58C2×Dic38—22no—
59C2×Dic38—42no—
60C2×Dic38—42no—
61C2×Dic38—41no—
62C2×Dic38—41no—
63C2×Dic38—41no—
64C2×Dic38—41no—
65C2×Dic38—41no—
66C2×C8×C19—42no—
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—82no—
74C22⋊Dic19—81no—
75#64526—48no—
76C4⋊Dic19—24no—
77C4⋊Dic19—42no—
78C4⋊Dic19—42no—
79C4⋊Dic19—81no—
80C2×C19⋊C8—22no—
81C2×C19⋊C8—41no—
82C2×C19⋊C8—41no—
83#7755—191nomaximal, Sylow
84C23×C19—22no—
85C23×C19—42no—
86C23×C19—41no—
87C23×C19—42no—
88C23×C19—41no—
89C23×C19#12011yescharacteristic
90D4×C19—42no—
91D4×C19—81no—
92C2×C4×C19—21no—
93C2×C4×C19—22no—
94C2×C4×C19—21no—
95C2×C4×C19—22no—
96C2×C4×C19—42no—
97C2×C4×C19—41no—
98C2×C4×C19C2×SD1611yescharacteristic
99C2×C4×C19#13512yes—
100C2×C4×C19#13711yescharacteristic
101C2×C4×C19#13712yes—
102C2×Dic19—42no—
103C2×Dic19—42no—
104C2×Dic19—42no—
105C2×Dic19—42no—
106C2×Dic19—42no—
107C2×Dic19—42no—
108C2×Dic19—42no—
109C2×Dic19—84no—
110C2×Dic19—81no—
111C2×Dic19—81no—
112Dic38—42no—
113Dic38—42no—
114Dic38—44no—
115Dic38—81no—
116Dic38—81no—
117Dic38—82no—
118C8×C19—82no—
119C19⋊C8—42no—
120#2804—191no—
121#2024—192no—
122#2013—191no—
123#1272—192no—
124#1270D1911yescharacteristic
125C22×C19—42no—
126C22×C19—44no—
127C22×C19—82no—
128C22×C19—81no—
129C22×C19—81no—
130C22×C19#44811yescharacteristic
131C22×C19#45212yes—
132C22×C19#45311yescharacteristic
133C22×C19#45512yes—
134C22×C19B(4,𝔽2)11yescharacteristic
135C4×C19—21no—
136C4×C19—21no—
137C4×C19—22no—
138C4×C19—22no—
139C4×C19—81no—
140Dic19—82no—
141Dic19—82no—
142Dic19—82no—
143C22×SD16—381no—
144C2×C4⋊Q8—191no—
145C2×#103—382no—
146C2×#103—381no—
147#400—381no—
148#393—382no—
149#391—192no—
150#390C2×D1911yescharacteristic
151#386—381no—
152#385—382no—
153#340—382no—
154#336—191no—
155#336C2×D1912yes—
156C2×C19—82no—
157C2×C19#159611yescharacteristic
158C2×C19#160612yes—
159C2×C19#163011yescharacteristic
160C2×C19#164312yes—
161C2×C19#165911yescharacteristic
162C22×Q8—192no—
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—
172C2×C4⋊C4—192no—
173C2×C4⋊C4—382no—
174C2×C4⋊C4—381no—
175C2×C4⋊C4D7611yescharacteristic
176C2×C22⋊C4—22no—
177C2×C22⋊C4—382no—
178C2×C22⋊C4—381no—
179C2×C42C22×D1911yescharacteristic
180#103—762no—
181#103—764no—
182#95—382no—
183#95—381no—
184#95—382no—
185#95—382no—
186C19#775511yescharacteristic, complemented, Sylow
187C24—21no—
188C2×Q8—382no—
189C2×Q8—382no—
190C2×Q8—382no—
191C2×Q8—761no—
192C2×Q8—762no—
193C2×Q8—762no—
194C2×Q8—761no—
195C2×Q8—761no—
196C2×Q8—761no—
197C2×Q8—761no—
198C2×D4—21no—
199C2×D4—41no—
200C2×D4—41no—
201C2×D4#6451612yes—
202C22×C4—21no—
203C22×C4—382no—
204C22×C4—382no—
205C22×C4—761no—
206C22×C4—1521no—
207C22×C4—1522no—
208C22×C4C2×D7611yescharacteristic
209C22×C4D4×D1912yes—
210SD16—768no—
211C2×C8—42no—
212C2×C8—42no—
213C2×C8—42no—
214C2×C8—382no—
215C2×C8—761no—
216C2×C8—761no—
217C4⋊C4—41no—
218C4⋊C4—384no—
219C4⋊C4—762no—
220C4⋊C4—762no—
221C4⋊C4—1521no—
222C22⋊C4—42no—
223C22⋊C4—42no—
224C22⋊C4—1522no—
225C22⋊C4—1521no—
226C42—41no—
227C23—22no—
228C23—42no—
229C23—41no—
230C23—42no—
231C23—41no—
232C23#1059732811yescharacteristic
233Q8—762no—
234Q8—762no—
235Q8—764no—
236Q8—1522no—
237Q8—1521no—
238Q8—1521no—
239D4—42no—
240D4—81no—
241C2×C4—21no—
242C2×C4—22no—
243C2×C4—22no—
244C2×C4—21no—
245C2×C4—42no—
246C2×C4—41no—
247C2×C4—762no—
248C2×C4—762no—
249C2×C4—762no—
250C2×C4—762no—
251C2×C4—762no—
252C2×C4—762no—
253C2×C4—762no—
254C2×C4—1524no—
255C2×C4—1521no—
256C2×C4—1521no—
257C2×C4C2×#6451611yescharacteristic
258C2×C4#1059735511yescharacteristic
259C2×C4#1059735812yes—
260C2×C4#1059736112yes—
261C8—82no—
262C8—762no—
263C22—42no—
264C22—44no—
265C22—82no—
266C22—81no—
267C22—81no—
268C22#1192668511yescharacteristic
269C22#1192670712yes—
270C22#1192671411yescharacteristic
271C22#1192672312yes—
272C22#1192673211yescharacteristic
273C4—21no—
274C4—21no—
275C4—22no—
276C4—22no—
277C4—81no—
278C4—1522no—
279C4—1522no—
280C4—1522no—
281C2—82no—
282C2#1456256011yescharacteristic
283C2#1456261612yes—
284C2#1456275711yescharacteristic
285C2#1456284412yes—
286C2#1456294211yescharacteristic
subgroupG/H
centerC23#10597328
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#1270C2
socleC23×C19#120
prime radicalC22×D4×C19D4
hypercenter#1270D19
hypocenterC19#7755
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. #14564777C2semidirect
4. #14561460C2semidirect
186. C19#7755semidirect

Maximal subgroups

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

subgroupindex
#145715812
#145647772
#145647172
#145614602
C19×#12702
#775519