Finite Group Databasebeta

← #18080158

Subgroups — #18080158

Order 4864.

490 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 99 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#14574021C211yesmaximal, characteristic
2#14562259C211yesmaximal, characteristic
3#14562146C212yesmaximal, complemented
4#14561528C212yesmaximal, complemented
5C19×#2372C211yesmaximal, characteristic
6#11927101C2211yescharacteristic
7#11926903C414yescomplemented
8#11926898—22no—
9#11926601C2212yes—
10#11926553—21no—
11#11926549—21no—
12C4×#64520C2211yescharacteristic
13#11926284—22no—
14#11926280—22no—
15#11926280—22no—
16C2×C19×#124C2211yescharacteristic
17C19×#391—21no—
18C19×#388—22no—
19C19×#386—21no—
20C4×C22⋊C4×C19—22no—
21C19×#376C2212yes—
22C22×Q8×C19D411yescharacteristic
23C22×D4×C19D411yescharacteristic
24C23×C4×C19—21no—
25C19×#124—22no—
26C19×#124C2×C412yes—
27C19×#124D412yes—
28C2×C4⋊C4×C19—21no—
29C2×C22⋊C4×C19—22no—
30C2×C22⋊C4×C19—22no—
31C2×C22⋊C4×C19—21no—
32C2×C42×C19—22no—
33C2×C42×C19—21no—
34C2×C42×C19C2311yescharacteristic
35#10597372—21no—
36#10597370—22no—
37C2×#64520—21no—
38#10597316—21no—
39#10597315C2×C412yescomplemented
40C4×Dic38—22no—
41C19×#95—22no—
42C19×#95—22no—
43C19×#95D412yes—
44C19×#95D412yes—
45#10597292—24no—
46#10597289—24no—
47C22⋊(C19⋊C8)—22no—
48C4⋊(C19⋊C8)—22no—
49#10597260—22no—
50#10597260C2×C412yescomplemented
51C4×C19⋊C8—21no—
52C24×C19—21no—
53C2×Q8×C19—21no—
54C2×Q8×C19—41no—
55C2×Q8×C19—41no—
56C2×Q8×C19C22⋊C412yes—
57C2×D4×C19—21no—
58C2×D4×C19—41no—
59C2×D4×C19—41no—
60C2×D4×C19C22⋊C412yes—
61C22×C4×C19—22no—
62C22×C4×C19—21no—
63C22×C4×C19—22no—
64C22×C4×C19—44no—
65C22×C4×C19—81no—
66C22×C4×C19C2×D411yescharacteristic
67C22×C4×C19C2×D412yes—
68C2×Dic38—22no—
69C4⋊C4×C19—81no—
70C22⋊C4×C19—24no—
71C22⋊C4×C19—24no—
72C22⋊C4×C19—44no—
73C22⋊C4×C19—81no—
74C42×C19—44no—
75C42×C19—81no—
76C42×C19C22×C411yescharacteristic
77C42×C19C2×D411yescharacteristic
78C42×C19#4112yes—
79C22⋊Dic19—41no—
80C4⋊Dic19—22no—
81C4⋊Dic19—22no—
82Dic19⋊C4—42no—
83C4×Dic19—41no—
84#64520—41no—
85#64520—41no—
86C2×C19⋊C8—22no—
87C2×C19⋊C8—42no—
88#9439—191nomaximal, Sylow
89C23×C19—22no—
90C23×C19—42no—
91C23×C19—42no—
92C23×C19—41no—
93C23×C19—41no—
94C23×C19#12011yescharacteristic
95Q8×C19—42no—
96Q8×C19—81no—
97D4×C19—42no—
98D4×C19—81no—
99C2×C4×C19—21no—
100C2×C4×C19—21no—
101C2×C4×C19—24no—
102C2×C4×C19—22no—
103C2×C4×C19—42no—
104C2×C4×C19—42no—
105C2×C4×C19—42no—
106C2×C4×C19—41no—
107C2×C4×C19—41no—
108C2×C4×C19—42no—
109C2×C4×C19—42no—
110C2×C4×C19—42no—
111C2×C4×C19—84no—
112C2×C4×C19C2×C22⋊C411yescharacteristic
113C2×C4×C19C4×D412yes—
114C2×C4×C19#12112yes—
115C2×C4×C19#12311yescharacteristic
116C2×Dic19—42no—
117Dic38—82no—
118C19⋊C8—42no—
119C19⋊C8—82no—
120#3140—191no—
121#2372D1911yescharacteristic
122#1533—191no—
123#1506—192no—
124#1300—192no—
125C22×C19—22no—
126C22×C19—42no—
127C22×C19—44no—
128C22×C19—81no—
129C22×C19—81no—
130C22×C19—82no—
131C22×C19#38611yescharacteristic
132C22×C19#45511yescharacteristic
133C22×C19#45511yescharacteristic
134C4×C19—21no—
135C4×C19—21no—
136C4×C19—22no—
137C4×C19—22no—
138C4×C19—44no—
139C4×C19—42no—
140C4×C19—82no—
141Dic19—82no—
142#533—191no—
143C2×#124C2×D1911yescharacteristic
144#489—194no—
145#488—382no—
146#432—192no—
147#419—381no—
148#418—381no—
149C4×M16—191no—
150#391—21no—
151#388—22no—
152#386—21no—
153C4×C22⋊C4—22no—
154#376C2×D1912yes—
155#329—382no—
156#328—382no—
157#328—382no—
158C2×C19—21no—
159C2×C19—21no—
160C2×C19—82no—
161C2×C19#188511yescharacteristic
162C2×C19#190612yes—
163C22×Q8C22⋊D1911yescharacteristic
164C22×D4C22⋊D1911yescharacteristic
165C23×C4—21no—
166C2×M16—381no—
167C4⋊Q8—192no—
168#125—381no—
169#124—22no—
170#124C4×D1912yes—
171#124D7612yes—
172C22⋊Q8—382no—
173C4×Q8—382no—
174#117—381no—
175C2×C4⋊C4—21no—
176C2×C22⋊C4—22no—
177C2×C22⋊C4—22no—
178C2×C22⋊C4—21no—
179C2×C42—22no—
180C2×C42—21no—
181C2×C42C22×D1911yescharacteristic
182C4⋊C8—382no—
183#103—384no—
184#102—384no—
185C22⋊C8—382no—
186#97—192no—
187#97—382no—
188C4×C8—381no—
189#95—22no—
190#95—22no—
191#95C22⋊D1912yes—
192#95C22⋊D1912yes—
193C19#943911yescharacteristic, complemented, Sylow
194C24—21no—
195C2×Q8—21no—
196C2×Q8—41no—
197C2×Q8—41no—
198C2×Q8—382no—
199C2×Q8(C2×D19)⋊C412yes—
200C2×D4—21no—
201C2×D4—41no—
202C2×D4—41no—
203C2×D4(C2×D19)⋊C412yes—
204C22×C4—22no—
205C22×C4—21no—
206C22×C4—22no—
207C22×C4—44no—
208C22×C4—81no—
209C22×C4C2×C22⋊D1911yescharacteristic
210C22×C4C2×C22⋊D1912yes—
211M16—761no—
212M16—761no—
213C2×C8—382no—
214C2×C8—762no—
215C4⋊C4—81no—
216C4⋊C4—382no—
217C4⋊C4—382no—
218C4⋊C4—762no—
219C22⋊C4—24no—
220C22⋊C4—24no—
221C22⋊C4—44no—
222C22⋊C4—81no—
223C22⋊C4—761no—
224C42—44no—
225C42—81no—
226C42—761no—
227C42C2×C4×D1911yescharacteristic
228C42C2×D7611yescharacteristic
229C42#6454112yes—
230C23—22no—
231C23—42no—
232C23—42no—
233C23—41no—
234C23—41no—
235C23#1059739911yescharacteristic
236Q8—42no—
237Q8—81no—
238Q8—1522no—
239D4—42no—
240D4—81no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—24no—
244C2×C4—22no—
245C2×C4—42no—
246C2×C4—42no—
247C2×C4—42no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—42no—
251C2×C4—42no—
252C2×C4—42no—
253C2×C4—84no—
254C2×C4—762no—
255C2×C4C2×(C2×D19)⋊C411yescharacteristic
256C2×C4C4×C22⋊D1912yes—
257C2×C4#1059737511yescharacteristic
258C2×C4#1059737612yes—
259C8—762no—
260C8—1522no—
261C22—22no—
262C22—44no—
263C22—42no—
264C22—81no—
265C22—81no—
266C22—82no—
267C22#1192642311yescharacteristic
268C22#1192672211yescharacteristic
269C22#1192672211yescharacteristic
270C4—22no—
271C4—22no—
272C4—21no—
273C4—21no—
274C4—44no—
275C4—42no—
276C4—82no—
277C4—1522no—
278C2—21no—
279C2—21no—
280C2—82no—
281C2#1456402311yescharacteristic
282C2#1456413612yes—
subgroupG/H
centerC22#11926423
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#2372C2
socleC22×C19#386
prime radicalC22×D4×C19D4
cosocleC2×C42×C19C23
hypercenter#2372D19
hypocenterC19#9439
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2372

Complements

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

NH ≅ G/Ntype
3. #14562146C2semidirect
4. #14561528C2semidirect
7. #11926903C4semidirect
39. #10597315C2×C4semidirect
50. #10597260C2×C4semidirect
193. C19#9439semidirect

Maximal subgroups

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

subgroupindex
#145740212
#145622592
#145621462
#145615282
C19×#23722
#943919