Finite Group Databasebeta

← #18078305

Subgroups — #18078305

Order 4864.

586 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 586 conjugacy classes of subgroups — too many to draw. Only its 135 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
1C2×#11926412C211yesmaximal, characteristic
2#14563703C211yesmaximal, characteristic
3C2×#11926281C212yesmaximal
4#14561513C212yesmaximal
5C19×#2855C211yesmaximal, characteristic
6C2×C22⋊(C19⋊C8)C2212yes—
7#11926412—24no—
8C2×C19⋊#95—21no—
9C2×C19⋊#95—21no—
10C2×C19⋊#95C2212yes—
11#11926299—22no—
12#11926281—24no—
13C2×C19×C22⋊Q8C2211yescharacteristic
14C22×C42×C19C2211yescharacteristic
15C19×#391C412yescomplemented
16C19×#389C412yescomplemented
17C19×#387—22no—
18C19×#385—21no—
19C19×#381—21no—
20C19×#380C2211yescharacteristic
21C22×Q8×C19C2×C411yescharacteristic
22C23×C4×C19D411yescharacteristic
23C23×C4×C19D411yescharacteristic
24C23×C4×C19C2311yescharacteristic
25C23×Dic19—22no—
26C19×C22⋊Q8—22no—
27C19×C22⋊Q8—22no—
28C2×C4⋊C4×C19—22no—
29C2×C4⋊C4×C19—21no—
30C2×C4⋊C4×C19C2×C411yescharacteristic
31C2×C4⋊C4×C19C2×C412yes—
32C2×C22⋊C4×C19—21no—
33C2×C22⋊C4×C19—21no—
34C2×C42×C19—22no—
35C2×C42×C19—22no—
36C2×C42×C19C2×C412yes—
37C2×C42×C19D412yes—
38C22×C19⋊C8—22no—
39C19×#95—22no—
40C19×#95—22no—
41C19×#95—22no—
42C19×#95—21no—
43C19⋊#95—24no—
44C19⋊#95—24no—
45C19⋊#95—22no—
46C19⋊#95D414yes—
47C22⋊(C19⋊C8)—22no—
48C22⋊(C19⋊C8)—22no—
49C24×C19C2×D411yescharacteristic
50C2×Q8×C19—22no—
51C2×Q8×C19—42no—
52C22×C4×C19—21no—
53C22×C4×C19—21no—
54C22×C4×C19—21no—
55C22×C4×C19—21no—
56C22×C4×C19—22no—
57C22×C4×C19—22no—
58C22×C4×C19—21no—
59C22×C4×C19—22no—
60C22×C4×C19—21no—
61C22×C4×C19—42no—
62C22×C4×C19—42no—
63C22×C4×C19C22⋊C412yes—
64C22×C4×C19C22⋊C412yes—
65C22×C4×C19C22×C411yescharacteristic
66C22×C4×C19C2×D412yes—
67C22×C4×C19C2×D411yescharacteristic
68C22×C4×C19#4112yes—
69C22×Dic19—24no—
70C22×Dic19—44no—
71C22×Dic19—44no—
72C22×Dic19—42no—
73C22×Dic19—42no—
74C4⋊C4×C19—22no—
75C4⋊C4×C19—42no—
76C4⋊C4×C19—44no—
77C4⋊C4×C19—42no—
78C22⋊C4×C19—41no—
79C22⋊C4×C19—41no—
80C22⋊C4×C19—42no—
81C42×C19—24no—
82C42×C19—24no—
83C2×C19⋊C8—44no—
84C2×C19⋊C8—42no—
85#9153—191nomaximal, Sylow
86C23×C19—22no—
87C23×C19—22no—
88C23×C19C2×C22⋊C411yescharacteristic
89C23×C19#12011yescharacteristic
90C23×C19#12311yescharacteristic
91C23×C19#13512yes—
92C23×C19#13712yes—
93Q8×C19—82no—
94C2×C4×C19—22no—
95C2×C4×C19—22no—
96C2×C4×C19—22no—
97C2×C4×C19—22no—
98C2×C4×C19—22no—
99C2×C4×C19—22no—
100C2×C4×C19—22no—
101C2×C4×C19—22no—
102C2×C4×C19—42no—
103C2×C4×C19—42no—
104C2×C4×C19—42no—
105C2×C4×C19—42no—
106C2×C4×C19—42no—
107C2×C4×C19—42no—
108C2×C4×C19—41no—
109C2×C4×C19—41no—
110C2×C4×C19—42no—
111C2×C4×C19—42no—
112C2×C4×C19—42no—
113C2×C4×C19—42no—
114C2×C4×C19—42no—
115C2×C4×C19C4×D412yes—
116C2×C4×C19#12112yes—
117C2×Dic19—44no—
118C2×Dic19—44no—
119C2×Dic19—44no—
120C2×Dic19—84no—
121C2×Dic19—84no—
122C19⋊C8—82no—
123#2855D1911yescharacteristic
124C2×#383—191no—
125#1817—191no—
126C2×#328—192no—
127#1294—192no—
128C22×C19—21no—
129C22×C19—21no—
130C22×C19—21no—
131C22×C19—21no—
132C22×C19—24no—
133C22×C19—24no—
134C22×C19#38611yescharacteristic
135C22×C19#41012yes—
136C22×C19#41611yescharacteristic
137C22×C19#41911yescharacteristic
138C22×C19#42112yes—
139C22×C19#45212yes—
140C22×C19#48512yes—
141C4×C19—22no—
142C4×C19—22no—
143C4×C19—42no—
144C4×C19—42no—
145C4×C19—81no—
146C4×C19—81no—
147C4×C19—82no—
148Dic19—84no—
149C2×C22⋊Q8C2×D1911yescharacteristic
150C22×C42C2×D1911yescharacteristic
151C2×C22⋊C8—192no—
152#391Dic1912yescomplemented
153#389Dic1912yescomplemented
154#387—22no—
155#385—21no—
156#383—384no—
157#381—21no—
158#380C2×D1911yescharacteristic
159C2×#95—192no—
160C2×#95—381no—
161C2×#95—381no—
162#336—382no—
163#328—384no—
164C2×C19—22no—
165C2×C19—22no—
166C2×C19#151512yes—
167C2×C19#152112yes—
168C2×C19#187311yescharacteristic
169C2×C19#189711yescharacteristic
170C2×C19#189911yescharacteristic
171C22×Q8C2×Dic1911yescharacteristic
172C23×C4—382no—
173C23×C4C22⋊D1911yescharacteristic
174C23×C4C22⋊D1911yescharacteristic
175C23×C4C22×D1911yescharacteristic
176C22×C8—382no—
177C22⋊Q8—22no—
178C22⋊Q8—22no—
179C2×C4⋊C4—22no—
180C2×C4⋊C4—21no—
181C2×C4⋊C4C2×Dic1911yescharacteristic
182C2×C4⋊C4C2×Dic1912yes—
183C2×C22⋊C4—21no—
184C2×C22⋊C4—21no—
185C2×C42—22no—
186C2×C42—22no—
187C2×C42C2×Dic1912yes—
188C2×C42C22⋊D1912yes—
189C22⋊C8—382no—
190C22⋊C8—382no—
191#95—22no—
192#95—22no—
193#95—22no—
194#95—21no—
195#95—194no—
196#95—384no—
197#95—384no—
198#95—382no—
199C19#915311yescharacteristic, complemented, Sylow
200C24C2×C22⋊D1911yescharacteristic
201C2×Q8—22no—
202C2×Q8—42no—
203C22×C4—21no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—22no—
208C22×C4—22no—
209C22×C4—22no—
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—42no—
213C22×C4—42no—
214C22×C4—384no—
215C22×C4—764no—
216C22×C4—764no—
217C22×C4—762no—
218C22×C4—762no—
219C22×C4C22⋊Dic1912yes—
220C22×C4C22⋊Dic1912yes—
221C22×C4D4×D1912yes—
222C22×C4#6454312yes—
223C22×C4C22×Dic1911yescharacteristic
224C22×C4C2×C22⋊D1911yescharacteristic
225C2×C8—764no—
226C2×C8—762no—
227C4⋊C4—22no—
228C4⋊C4—42no—
229C4⋊C4—44no—
230C4⋊C4—42no—
231C22⋊C4—41no—
232C22⋊C4—41no—
233C22⋊C4—42no—
234C42—24no—
235C42—24no—
236C23—22no—
237C23—22no—
238C23#1059738111yescharacteristic
239C23#1059738311yescharacteristic
240C23#1059738812yes—
241C23#1059739612yes—
242C23C2×C22⋊Dic1911yescharacteristic
243Q8—82no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—42no—
253C2×C4—42no—
254C2×C4—42no—
255C2×C4—42no—
256C2×C4—42no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4—42no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—42no—
264C2×C4—42no—
265C2×C4—764no—
266C2×C4—764no—
267C2×C4—764no—
268C2×C4—1524no—
269C2×C4—1524no—
270C2×C4D4×Dic1912yes—
271C2×C4#1059738512yes—
272C8—1522no—
273C22—24no—
274C22—24no—
275C22—21no—
276C22—21no—
277C22—21no—
278C22—21no—
279C22#1192642411yescharacteristic
280C22#1192651812yes—
281C22#1192654011yescharacteristic
282C22#1192655311yescharacteristic
283C22#1192656112yes—
284C22#1192670412yes—
285C22#1192688212yes—
286C4—22no—
287C4—22no—
288C4—42no—
289C4—42no—
290C4—82no—
291C4—81no—
292C4—81no—
293C4—1524no—
294C2—22no—
295C2—22no—
296C2#1456218612yes—
297C2#1456221212yes—
298C2#1456394811yescharacteristic
299C2#1456408411yescharacteristic
300C2#1456409411yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic19
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#2855C2
socleC23×C19C2×C22⋊C4
prime radicalC24×C19C2×D4
cosocleC23×C4×C19C23
hypercenter#2855D19
hypocenterC19#9153
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2855

Complements

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

NH ≅ G/Ntype
15. C19×#391C4semidirect
16. C19×#389C4semidirect
152. #391Dic19semidirect
153. #389Dic19semidirect
199. C19#9153semidirect

Maximal subgroups

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

subgroupindex
C2×#119264122
#145637032
C2×#119262812
#145615132
C19×#28552
#915319