Finite Group Databasebeta

← #18071859

Subgroups — #18071859

Order 4864.

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

normal subgroups only

This group has 438 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#14565172C212yesmaximal, complemented
3#14565168C211yesmaximal, characteristic
4#14561460C212yesmaximal, complemented
5C19×#1270C211yesmaximal, characteristic
6C2×#10597275—22no—
7C2×#10597265—21no—
8C2×#10597273—22no—
9C2×#10597289—21no—
10#11926483—21no—
11#11926456—22no—
12#11926450C2212yes—
13#11926424—21no—
14#11926419—22no—
15#11926414C2211yescharacteristic
16#11926299C2211yescharacteristic
17C19×#390C2211yescharacteristic
18C19×#336C2212yes—
19C22×D4×C19D411yescharacteristic
20C23×Dic19—21no—
21C22×Dic38D412yes—
22C22×C8×C19—22no—
23C2×C4⋊C4×C19D411yescharacteristic
24C2×C22⋊C4×C19—22no—
25C2×C42×C19C2311yescharacteristic
26C2×C22⋊Dic19—22no—
27C2×C22⋊Dic19—21no—
28C2×C4⋊Dic19—21no—
29C2×C4⋊Dic19—22no—
30C2×C4⋊Dic19—21no—
31C2×C4⋊Dic19D412yes—
32C22×C19⋊C8—21no—
33#10597289—42no—
34C19⋊#95—22no—
35C19⋊#95—21no—
36C19⋊#95—22no—
37C19⋊#95—22no—
38#10597275—44no—
39#10597273—44no—
40#10597265—42no—
41C24×C19—21no—
42C2×D4×C19—21no—
43C2×D4×C19—41no—
44C2×D4×C19—41no—
45C2×D4×C19Q1612yes—
46C22×C4×C19—21no—
47C22×C4×C19C2×D411yescharacteristic
48C22×C4×C19C2×D412yes—
49C22×Dic19—22no—
50C22×Dic19—22no—
51C22×Dic19—41no—
52C22×Dic19—82no—
53C22×Dic19—81no—
54C2×Dic38—22no—
55C2×Dic38—22no—
56C2×Dic38—42no—
57C2×Dic38—42no—
58C2×C8×C19—24no—
59C2×C8×C19—42no—
60C2×C8×C19—42no—
61C4⋊C4×C19—41no—
62C22⋊C4×C19—42no—
63C22⋊C4×C19—42no—
64C42×C19—41no—
65C22⋊Dic19—82no—
66C22⋊Dic19—81no—
67C4⋊Dic19—42no—
68C4⋊Dic19—41no—
69C4⋊Dic19—42no—
70C4⋊Dic19—42no—
71C4⋊Dic19—41no—
72C4⋊Dic19—81no—
73C2×C19⋊C8—22no—
74C2×C19⋊C8—41no—
75C2×C19⋊C8—41no—
76#7833—191nomaximal, Sylow
77C23×C19—22no—
78C23×C19—42no—
79C23×C19—42no—
80C23×C19—41no—
81C23×C19—41no—
82C23×C19#12011yescharacteristic
83D4×C19—42no—
84D4×C19—81no—
85C2×C4×C19—21no—
86C2×C4×C19—22no—
87C2×C4×C19—21no—
88C2×C4×C19—22no—
89C2×C4×C19—42no—
90C2×C4×C19—41no—
91C2×C4×C19C2×Q1611yescharacteristic
92C2×C4×C19#13512yes—
93C2×C4×C19#13711yescharacteristic
94C2×C4×C19#13712yes—
95C2×Dic19—42no—
96C2×Dic19—42no—
97C2×Dic19—42no—
98C2×Dic19—42no—
99C2×Dic19—42no—
100C2×Dic19—42no—
101C2×Dic19—84no—
102C2×Dic19—82no—
103C2×Dic19—81no—
104Dic38—44no—
105Dic38—82no—
106C8×C19—44no—
107C19⋊C8—42no—
108#2804—191no—
109#2095—192no—
110#2094—191no—
111#1272—192no—
112#1270D1911yescharacteristic
113C22×C19—42no—
114C22×C19—44no—
115C22×C19—82no—
116C22×C19—81no—
117C22×C19—81no—
118C22×C19#45111yescharacteristic
119C22×C19#45212yes—
120C22×C19#45312yes—
121C22×C19#45311yescharacteristic
122C22×C19#45811yescharacteristic
123C4×C19—21no—
124C4×C19—21no—
125C4×C19—22no—
126C4×C19—22no—
127C4×C19—81no—
128Dic19—82no—
129Dic19—82no—
130Dic19—161no—
131C2×#107—382no—
132C2×#106—381no—
133C2×#103—382no—
134C2×#102—381no—
135#400—381no—
136#393—382no—
137#391—192no—
138#390C2×D1911yescharacteristic
139#386—381no—
140#385—382no—
141#384—191no—
142#336—191no—
143#336C2×D1912yes—
144C2×C19—82no—
145C2×C19#161411yescharacteristic
146C2×C19#161812yes—
147C2×C19#163011yescharacteristic
148C2×C19#163212yes—
149C2×C19#165511yescharacteristic
150C22×Q8—192no—
151C22×D4D7611yescharacteristic
152C23×C4—381no—
153C22×C8—22no—
154C22×C8—381no—
155C2×C4⋊C4—192no—
156C2×C4⋊C4—381no—
157C2×C4⋊C4—382no—
158C2×C4⋊C4—381no—
159C2×C4⋊C4D7611yescharacteristic
160C2×C22⋊C4—22no—
161C2×C22⋊C4—382no—
162C2×C22⋊C4—381no—
163C2×C42C22×D1911yescharacteristic
164#107—764no—
165#106—762no—
166#103—764no—
167#102—762no—
168#95—382no—
169#95—381no—
170#95—382no—
171#95—382no—
172C19#783311yescharacteristic, complemented, Sylow
173C24—21no—
174C2×Q8—382no—
175C2×Q8—382no—
176C2×Q8—762no—
177C2×Q8—762no—
178C2×D4—21no—
179C2×D4—41no—
180C2×D4—41no—
181C2×D4Dic7612yes—
182C22×C4—21no—
183C22×C4—382no—
184C22×C4—382no—
185C22×C4—761no—
186C22×C4—1522no—
187C22×C4—1521no—
188C22×C4C2×D7611yescharacteristic
189C22×C4D4×D1912yes—
190C2×C8—24no—
191C2×C8—42no—
192C2×C8—42no—
193C2×C8—382no—
194C2×C8—761no—
195C2×C8—761no—
196C4⋊C4—41no—
197C4⋊C4—762no—
198C4⋊C4—761no—
199C4⋊C4—762no—
200C4⋊C4—761no—
201C4⋊C4—762no—
202C4⋊C4—1521no—
203C22⋊C4—42no—
204C22⋊C4—42no—
205C22⋊C4—1522no—
206C22⋊C4—1521no—
207C42—41no—
208C23—22no—
209C23—42no—
210C23—42no—
211C23—41no—
212C23—41no—
213C23#1059732811yescharacteristic
214Q8—764no—
215Q8—1522no—
216D4—42no—
217D4—81no—
218C2×C4—22no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—21no—
222C2×C4—42no—
223C2×C4—41no—
224C2×C4—762no—
225C2×C4—762no—
226C2×C4—762no—
227C2×C4—762no—
228C2×C4—762no—
229C2×C4—762no—
230C2×C4—1522no—
231C2×C4—1521no—
232C2×C4—1524no—
233C2×C4C2×Dic7611yescharacteristic
234C2×C4#1059735511yescharacteristic
235C2×C4#1059735812yes—
236C2×C4#1059736112yes—
237C8—44no—
238C8—762no—
239C22—42no—
240C22—44no—
241C22—81no—
242C22—82no—
243C22—81no—
244C22#1192670211yescharacteristic
245C22#1192670712yes—
246C22#1192671312yes—
247C22#1192671411yescharacteristic
248C22#1192673511yescharacteristic
249C4—21no—
250C4—21no—
251C4—22no—
252C4—22no—
253C4—81no—
254C4—3041no—
255C4—1522no—
256C4—1522no—
257C2—82no—
258C2#1456266211yescharacteristic
259C2#1456268412yes—
260C2#1456275711yescharacteristic
261C2#1456277112yes—
262C2#1456292511yescharacteristic
subgroupG/H
centerC23#10597328
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#1270C2
socleC23×C19#120
prime radicalC22×D4×C19D4
hypercenter#1270D19
hypocenterC19#7833
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. #14565172C2semidirect
4. #14561460C2semidirect
172. C19#7833semidirect

Maximal subgroups

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

subgroupindex
#145715812
#145651722
#145651682
#145614602
C19×#12702
#783319