Finite Group Databasebeta

← #18078568

Subgroups — #18078568

Order 4864.

478 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 119 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#14572273C211yesmaximal, characteristic
2#14562307C212yesmaximal, complemented
3#14561949C211yesmaximal, characteristic
4#14561493C212yesmaximal, complemented
5C19×#2621C211yesmaximal, characteristic
6#11926605—24no—
7#11926597C2212yes—
8#11926568C2212yes—
9#11926508—21no—
10C4×#64520—21no—
11#11926290—24no—
12#11926270—21no—
13#11926268—21no—
14C2×C19×C4⋊Q8C2211yescharacteristic
15C2×C19×C22⋊Q8—21no—
16C2×C19×#117C2211yescharacteristic
17C19×#398—21no—
18C19×#398C412yes—
19C19×#397—21no—
20C19×#397C412yes—
21C19×#391—21no—
22C19×#382C2211yescharacteristic
23C22×Q8×C19—21no—
24C23×C4×C19D411yescharacteristic
25C19×C4⋊Q8—22no—
26C19×C4⋊Q8—22no—
27C19×C22⋊Q8—44no—
28C19×#117—22no—
29C19×#117—22no—
30C2×C4⋊C4×C19—22no—
31C2×C4⋊C4×C19—21no—
32C2×C4⋊C4×C19—21no—
33C2×C4⋊C4×C19C2×C412yes—
34C2×C4⋊C4×C19C2×C411yescharacteristic
35C2×C4⋊C4×C19D411yescharacteristic
36C2×C22⋊C4×C19—22no—
37C2×C22⋊C4×C19C2×C411yescharacteristic
38C2×C22⋊C4×C19D411yescharacteristic
39C2×C42×C19D411yescharacteristic
40C2×C42×C19C2311yescharacteristic
41C2×#64520—22no—
42C19×#95—22no—
43C19×#95—22no—
44C19×#95—21no—
45C19×#95C2×C412yes—
46C22⋊(C19⋊C8)—24no—
47C22⋊(C19⋊C8)—22no—
48C4⋊(C19⋊C8)—22no—
49C4⋊(C19⋊C8)—22no—
50C4⋊(C19⋊C8)D414yes—
51#10597260—22no—
52C4×C19⋊C8—22no—
53C4×C19⋊C8—22no—
54C24×C19C22⋊C411yescharacteristic
55C2×Q8×C19—41no—
56C2×Q8×C19—41no—
57C2×Q8×C19—42no—
58C2×Q8×C19—42no—
59C22×C4×C19—21no—
60C22×C4×C19—21no—
61C22×C4×C19—22no—
62C22×C4×C19—22no—
63C22×C4×C19—22no—
64C22×C4×C19—22no—
65C22×C4×C19C22⋊C411yescharacteristic
66C22×C4×C19C22⋊C411yescharacteristic
67C22×C4×C19C22⋊C411yescharacteristic
68C22×C4×C19C22×C411yescharacteristic
69C22×C4×C19C2×D411yescharacteristic
70C22×C4×C19C2×D411yescharacteristic
71C4⋊C4×C19—22no—
72C4⋊C4×C19—22no—
73C4⋊C4×C19—24no—
74C4⋊C4×C19—44no—
75C4⋊C4×C19—42no—
76C4⋊C4×C19—42no—
77C22⋊C4×C19—22no—
78C22⋊C4×C19—22no—
79C22⋊C4×C19—44no—
80C42×C19—21no—
81C42×C19—21no—
82C42×C19C2×D412yes—
83C42×C19#4112yes—
84#64520—42no—
85#64520—42no—
86C2×C19⋊C8—24no—
87C2×C19⋊C8—42no—
88#9196—191nomaximal, Sylow
89C23×C19—21no—
90C23×C19—21no—
91C23×C19—21no—
92C23×C19—41no—
93C23×C19—41no—
94C23×C19C2×C22⋊C411yescharacteristic
95Q8×C19—82no—
96Q8×C19—82no—
97C2×C4×C19—21no—
98C2×C4×C19—21no—
99C2×C4×C19—21no—
100C2×C4×C19—21no—
101C2×C4×C19—21no—
102C2×C4×C19—41no—
103C2×C4×C19—41no—
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—42no—
112C2×C4×C19—42no—
113C2×C4×C19—42no—
114C2×C4×C19C4×D412yes—
115C2×C4×C19#12011yescharacteristic
116C2×C4×C19#12112yes—
117C2×C4×C19#12311yescharacteristic
118C2×C4×C19#13512yes—
119C2×C4×C19AGL(1,ℤ/8)12yes—
120C19⋊C8—44no—
121C19⋊C8—82no—
122#2921—191no—
123#2621D1911yescharacteristic
124#1546—192no—
125#1458—191no—
126#1286—192no—
127C22×C19—21no—
128C22×C19—21no—
129C22×C19—42no—
130C22×C19—41no—
131C22×C19—41no—
132C22×C19—41no—
133C22×C19—81no—
134C22×C19#38611yescharacteristic
135C22×C19#41611yescharacteristic
136C22×C19#41811yescharacteristic
137C4×C19—22no—
138C4×C19—22no—
139C4×C19—41no—
140C4×C19—41no—
141C4×C19—41no—
142C4×C19—82no—
143C4×C19—82no—
144C4×C19#44912yes—
145C4×C19#48212yes—
146C2×C4⋊Q8C2×D1911yescharacteristic
147C2×C22⋊Q8—21no—
148C2×#117C2×D1911yescharacteristic
149#433—384no—
150#431—192no—
151#423—192no—
152#407—381no—
153C4×M16—381no—
154#398—21no—
155#398Dic1912yes—
156#397—21no—
157#397Dic1912yes—
158#391—21no—
159#382C2×D1911yescharacteristic
160#332—384no—
161#324—381no—
162#323—381no—
163C2×C19—21no—
164C2×C19—21no—
165C2×C19—81no—
166C2×C19#187511yescharacteristic
167C2×C19#190911yescharacteristic
168C2×C19#191511yescharacteristic
169C22×Q8—21no—
170C23×C4C22⋊D1911yescharacteristic
171C2×M16—382no—
172C4⋊Q8—22no—
173C4⋊Q8—22no—
174C22⋊Q8—44no—
175#117—22no—
176#117—22no—
177C2×C4⋊C4—22no—
178C2×C4⋊C4—21no—
179C2×C4⋊C4—21no—
180C2×C4⋊C4C2×Dic1912yes—
181C2×C4⋊C4C2×Dic1911yescharacteristic
182C2×C4⋊C4C22⋊D1911yescharacteristic
183C2×C22⋊C4—22no—
184C2×C22⋊C4C2×Dic1911yescharacteristic
185C2×C22⋊C4C22⋊D1911yescharacteristic
186C2×C42C22⋊D1911yescharacteristic
187C2×C42C22×D1911yescharacteristic
188C4⋊C8—194no—
189C4⋊C8—382no—
190C4⋊C8—382no—
191C22⋊C8—384no—
192C22⋊C8—382no—
193#97—382no—
194C4×C8—382no—
195C4×C8—382no—
196#95—22no—
197#95—22no—
198#95—21no—
199#95C2×Dic1912yes—
200C19#919611yescharacteristic, complemented, Sylow
201C24C22⋊Dic1911yescharacteristic
202C2×Q8—42no—
203C2×Q8—41no—
204C2×Q8—41no—
205C2×Q8—42no—
206C22×C4—22no—
207C22×C4—21no—
208C22×C4—21no—
209C22×C4—22no—
210C22×C4—22no—
211C22×C4—22no—
212C22×C4C22⋊Dic1911yescharacteristic
213C22×C4C22⋊Dic1911yescharacteristic
214C22×C4C22⋊Dic1911yescharacteristic
215C22×C4C22×Dic1911yescharacteristic
216C22×C4C2×C22⋊D1911yescharacteristic
217C22×C4C2×C22⋊D1911yescharacteristic
218M16—762no—
219M16—762no—
220C2×C8—384no—
221C2×C8—762no—
222C4⋊C4—22no—
223C4⋊C4—22no—
224C4⋊C4—24no—
225C4⋊C4—44no—
226C4⋊C4—42no—
227C4⋊C4—42no—
228C22⋊C4—22no—
229C22⋊C4—22no—
230C22⋊C4—44no—
231C42—21no—
232C42—21no—
233C42D4×D1912yes—
234C42#6454312yes—
235C23—21no—
236C23—21no—
237C23—21no—
238C23—41no—
239C23—41no—
240C23C2×C22⋊Dic1911yescharacteristic
241Q8—82no—
242Q8—82no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—42no—
251C2×C4—42no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—42no—
255C2×C4—42no—
256C2×C4—42no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4#1059737812yes—
261C2×C4D4×Dic1912yes—
262C2×C4#1059738111yescharacteristic
263C2×C4#1059738311yescharacteristic
264C2×C4#1059738512yes—
265C2×C4#1059739612yes—
266C8—764no—
267C8—1522no—
268C22—21no—
269C22—21no—
270C22—42no—
271C22—41no—
272C22—41no—
273C22—41no—
274C22—81no—
275C22#1192642411yescharacteristic
276C22#1192654011yescharacteristic
277C22#1192654911yescharacteristic
278C4—22no—
279C4—22no—
280C4—41no—
281C4—41no—
282C4—41no—
283C4—82no—
284C4—82no—
285C4#1192668712yes—
286C4#1192686512yes—
287C2—21no—
288C2—21no—
289C2—81no—
290C2#1456395811yescharacteristic
291C2#1456415811yescharacteristic
292C2#1456418811yescharacteristic
subgroupG/H
centerC22#11926424
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#2621C2
socleC22×C19#386
prime radicalC24×C19C22⋊C4
cosocleC2×C42×C19C23
hypercenter#2621D19
hypocenterC19#9196
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2621

Complements

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

NH ≅ G/Ntype
2. #14562307C2semidirect
4. #14561493C2semidirect
200. C19#9196semidirect

Maximal subgroups

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

subgroupindex
#145722732
#145623072
#145619492
#145614932
C19×#26212
#919619