Finite Group Databasebeta

← #18083188

Subgroups — #18083188

Order 4864.

602 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 602 conjugacy classes of subgroups — too many to draw. Only its 81 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#14573571C212yesmaximal, complemented
2#14563710C211yesmaximal, characteristic, complemented
3#14562164C212yesmaximal, complemented
4#14561543C211yesmaximal, characteristic, complemented
5C19×#2815C211yesmaximal, characteristic
6C2×#10597372C2211yescharacteristic
7#11926865—24no—
8#11926860—22no—
9#11926855—22no—
10#11926584—22no—
11#11926549—22no—
12#11926508C2212yes—
13#11926407C2211yescharacteristic
14#11926310—22no—
15#11926278—24no—
16C2×C19×#121C2212yes—
17C19×#397—22no—
18C19×#392—22no—
19C19×#392—22no—
20C19×#381C2211yescharacteristic
21C22×D4×C19—22no—
22C22×D4×C19—22no—
23C22×D4×C19D412yes—
24C23×C4×C19C2311yescharacteristic
25C19×#121—22no—
26C19×#121—22no—
27C19×#121—22no—
28C19×#121—22no—
29C2×C4⋊C4×C19D412yes—
30C2×C22⋊C4×C19—22no—
31C2×C22⋊C4×C19—24no—
32C2×C22⋊C4×C19D412yes—
33C2×C22⋊Dic19—21no—
34C2×C22⋊Dic19—21no—
35#10597372—22no—
36#10597372—22no—
37C2×C4⋊Dic19D412yescomplemented
38C2×C4×Dic19—21no—
39C2×#64520—22no—
40C19×#95—22no—
41C19×#95—22no—
42#10597289—24no—
43#10597289—24no—
44C19⋊#95—22no—
45C22⋊(C19⋊C8)—22no—
46C22⋊(C19⋊C8)D414yescomplemented
47#10597265—24no—
48#10597264—24no—
49C24×C19—22no—
50C24×C19C2×D411yescharacteristic
51C2×D4×C19—22no—
52C2×D4×C19—22no—
53C2×D4×C19—44no—
54C2×D4×C19—42no—
55C2×D4×C19—42no—
56C2×D4×C19—84no—
57C2×D4×C19—84no—
58C2×D4×C19—82no—
59C22×C4×C19—22no—
60C22×C4×C19—22no—
61C22×C4×C19—42no—
62C22×C4×C19C2×D411yescharacteristic
63C22×C4×C19C2×D412yes—
64C22×C4×C19C2×D412yes—
65C22×C4×C19#4111yescharacteristic
66C22×Dic19—22no—
67C22×Dic19—41no—
68C4⋊C4×C19—22no—
69C4⋊C4×C19—22no—
70C22⋊C4×C19—42no—
71C22⋊C4×C19—42no—
72C22⋊C4×C19—42no—
73C22⋊C4×C19—84no—
74C22⋊Dic19—41no—
75C22⋊Dic19—41no—
76C22⋊Dic19—42no—
77C4⋊Dic19—22no—
78C4⋊Dic19—22no—
79C4×Dic19—42no—
80#64520—44no—
81C2×C19⋊C8—24no—
82#9983—191nomaximal, Sylow
83C23×C19—22no—
84C23×C19—42no—
85C23×C19—42no—
86C23×C19—42no—
87C23×C19—44no—
88C23×C19—42no—
89C23×C19—44no—
90C23×C19#12011yescharacteristic
91C23×C19#12111yescharacteristic
92C23×C19#12711yescharacteristic
93D4×C19—44no—
94D4×C19—82no—
95D4×C19—84no—
96D4×C19—84no—
97D4×C19—88no—
98C2×C4×C19—24no—
99C2×C4×C19—41no—
100C2×C4×C19—42no—
101C2×C4×C19—41no—
102C2×C4×C19—44no—
103C2×C4×C19—44no—
104C2×C4×C19—42no—
105C2×C4×C19—42no—
106C2×C4×C19#12012yes—
107C2×C4×C19#12112yes—
108C2×Dic19—42no—
109C2×Dic19—82no—
110C2×Dic19—81no—
111C2×Dic19—82no—
112C19⋊C8—44no—
113#3094—192no—
114#2815D1911yescharacteristic
115#1820—191no—
116#1510—192no—
117#1306—191no—
118C22×C19—22no—
119C22×C19—22no—
120C22×C19—22no—
121C22×C19—21no—
122C22×C19—21no—
123C22×C19—82no—
124C22×C19—84no—
125C22×C19—84no—
126C22×C19—82no—
127C22×C19—82no—
128C22×C19—82no—
129C22×C19#39211yescharacteristic
130C22×C19#45812yes—
131C4×C19—22no—
132C4×C19—22no—
133C4×C19—82no—
134C4×C19—82no—
135Dic19—82no—
136Dic19—161no—
137C2×#121C2×D1912yes—
138C2×#117—191no—
139#482—384no—
140#481—382no—
141#480—382no—
142#428—382no—
143#418—382no—
144#407—192no—
145#397—22no—
146#392—22no—
147#392—22no—
148#381—191no—
149#381C2×D1911yescharacteristic
150#342—382no—
151#327—384no—
152C2×C19—22no—
153C2×C19—41no—
154C2×C19—41no—
155C2×C19—162no—
156C2×C19#200812yes—
157C2×C19#202211yescharacteristic
158C22×D4—22no—
159C22×D4—22no—
160C22×D4C22⋊D1912yes—
161C23×C4C22×D1911yescharacteristic
162C2×M16—382no—
163#121—22no—
164#121—22no—
165#121—22no—
166#121—22no—
167#117—382no—
168#117—382no—
169C2×C4⋊C4—192no—
170C2×C4⋊C4C22⋊D1912yes—
171C2×C22⋊C4—22no—
172C2×C22⋊C4—24no—
173C2×C22⋊C4—381no—
174C2×C22⋊C4—381no—
175C2×C22⋊C4C22⋊D1912yes—
176C2×C42—381no—
177#107—384no—
178#106—384no—
179#102—384no—
180#102—384no—
181C22⋊C8—194no—
182C22⋊C8—382no—
183#95—22no—
184#95—22no—
185#95—382no—
186C19#998311yescharacteristic, complemented, Sylow
187C24—22no—
188C24C2×C22⋊D1911yescharacteristic
189C2×D4—22no—
190C2×D4—22no—
191C2×D4—44no—
192C2×D4—42no—
193C2×D4—42no—
194C2×D4—84no—
195C2×D4—84no—
196C2×D4—82no—
197C22×C4—22no—
198C22×C4—22no—
199C22×C4—42no—
200C22×C4—382no—
201C22×C4—761no—
202C22×C4D4×D1911yescharacteristic
203C22×C4D4×D1912yes—
204C22×C4#6454311yescharacteristic
205C22×C4C2×C22⋊D1912yes—
206M16—764no—
207C2×C8—384no—
208C4⋊C4—22no—
209C4⋊C4—22no—
210C4⋊C4—382no—
211C4⋊C4—382no—
212C22⋊C4—42no—
213C22⋊C4—42no—
214C22⋊C4—42no—
215C22⋊C4—84no—
216C22⋊C4—761no—
217C22⋊C4—761no—
218C22⋊C4—762no—
219C42—762no—
220C23—22no—
221C23—42no—
222C23—42no—
223C23—42no—
224C23—44no—
225C23—42no—
226C23—44no—
227C23#1059738411yescharacteristic
228C23#1059738611yescharacteristic
229C23#1059739911yescharacteristic
230D4—44no—
231D4—82no—
232D4—84no—
233D4—84no—
234D4—88no—
235C2×C4—24no—
236C2×C4—41no—
237C2×C4—42no—
238C2×C4—41no—
239C2×C4—44no—
240C2×C4—44no—
241C2×C4—42no—
242C2×C4—42no—
243C2×C4—762no—
244C2×C4—1521no—
245C2×C4—1522no—
246C2×C4—1522no—
247C2×C4#1059738312yes—
248C2×C4#1059738512yes—
249C8—764no—
250C22—22no—
251C22—22no—
252C22—22no—
253C22—21no—
254C22—21no—
255C22—82no—
256C22—84no—
257C22—84no—
258C22—82no—
259C22—82no—
260C22—82no—
261C22#1192645211yescharacteristic
262C22#1192673412yes—
263C4—22no—
264C4—22no—
265C4—82no—
266C4—82no—
267C4—3041no—
268C4—1522no—
269C2—22no—
270C2—41no—
271C2—41no—
272C2—162no—
273C2#1456468812yes—
274C2#1456476411yescharacteristic
subgroupG/H
centerC22#11926452
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
Fitting, prime radicalC19×#2815C2
socleC22×C19#392
hypercenter#2815D19
hypocenterC19#9983
LCSG ▷ C23×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2815

Complements

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

NH ≅ G/Ntype
1. #14573571C2semidirect
2. #14563710C2semidirect
3. #14562164C2semidirect
4. #14561543C2semidirect
37. C2×C4⋊Dic19D4semidirect
46. C22⋊(C19⋊C8)D4semidirect
186. C19#9983semidirect

Maximal subgroups

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

subgroupindex
#145735712
#145637102
#145621642
#145615432
C19×#28152
#998319