Finite Group Databasebeta

← #18078547

Subgroups — #18078547

Order 4864.

458 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 115 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#14569456C211yesmaximal, characteristic
2#14562317C212yesmaximal, complemented
3#14561949C211yesmaximal, characteristic
4#14561495C212yesmaximal, complemented
5C19×#2921C211yesmaximal, characteristic
6C2×#10597315C2211yescharacteristic
7#11926597C2212yes—
8#11926483—21no—
9#11926480—21no—
10#11926464C412yes—
11#11926456C412yes—
12#11926442—21no—
13#11926410C2211yescharacteristic
14#11926404—21no—
15#11926292—24no—
16#11926270—21no—
17#11926268—21no—
18C2×C19×#117C2211yescharacteristic
19C19×#433—24no—
20C19×#423C2212yes—
21C19×#407—21no—
22C4×M16×C19—21no—
23C23×C4×C19D411yescharacteristic
24C22×Dic38C2×C412yes—
25C2×M16×C19—22no—
26C19×#117—22no—
27C19×#117—22no—
28C2×C4⋊C4×C19C2×C411yescharacteristic
29C2×C4⋊C4×C19D411yescharacteristic
30C2×C22⋊C4×C19C2×C411yescharacteristic
31C2×C22⋊C4×C19D411yescharacteristic
32C2×C42×C19D411yescharacteristic
33C2×C42×C19C2311yescharacteristic
34C2×C22⋊Dic19—22no—
35C2×C4⋊Dic19—21no—
36C2×C4⋊Dic19—21no—
37C2×C4⋊Dic19—21no—
38C2×Dic19⋊C4—22no—
39#10597315—22no—
40#10597315—22no—
41C19×C4⋊C8—22no—
42C19×C4⋊C8D414yes—
43C19×C22⋊C8—24no—
44C19×#97—22no—
45C4×C8×C19—22no—
46C19⋊#95—22no—
47C19⋊#95—22no—
48C19⋊#95—21no—
49C19⋊#95C2×C412yes—
50C22⋊(C19⋊C8)—22no—
51C4⋊(C19⋊C8)—22no—
52C4×C19⋊C8—22no—
53C24×C19C22⋊C411yescharacteristic
54C22×C4×C19—21no—
55C22×C4×C19—21no—
56C22×C4×C19—22no—
57C22×C4×C19—22no—
58C22×C4×C19C22⋊C411yescharacteristic
59C22×C4×C19C22⋊C411yescharacteristic
60C22×C4×C19C22⋊C411yescharacteristic
61C22×C4×C19C22×C411yescharacteristic
62C22×C4×C19C2×D411yescharacteristic
63C22×C4×C19C2×D411yescharacteristic
64C22×Dic19—22no—
65C22×Dic19—22no—
66C2×Dic38—24no—
67C2×Dic38—82no—
68M16×C19—42no—
69M16×C19—42no—
70C2×C8×C19—24no—
71C4⋊C4×C19—22no—
72C4⋊C4×C19—22no—
73C22⋊C4×C19—22no—
74C22⋊C4×C19—22no—
75C42×C19—21no—
76C42×C19—21no—
77C42×C19C2×D412yes—
78C42×C19#4112yes—
79C22⋊Dic19—82no—
80C4⋊Dic19—41no—
81C4⋊Dic19—42no—
82C4⋊Dic19—41no—
83C4⋊Dic19—42no—
84Dic19⋊C4—82no—
85C2×C19⋊C8—42no—
86#9192—191nomaximal, Sylow
87C23×C19—21no—
88C23×C19—21no—
89C23×C19—21no—
90C23×C19—41no—
91C23×C19—41no—
92C23×C19C2×C22⋊C411yescharacteristic
93C2×C4×C19—21no—
94C2×C4×C19—21no—
95C2×C4×C19—21no—
96C2×C4×C19—21no—
97C2×C4×C19—21no—
98C2×C4×C19—41no—
99C2×C4×C19—41no—
100C2×C4×C19—42no—
101C2×C4×C19—42no—
102C2×C4×C19—41no—
103C2×C4×C19—41no—
104C2×C4×C19C4×D412yes—
105C2×C4×C19#12011yescharacteristic
106C2×C4×C19#12112yes—
107C2×C4×C19#12311yescharacteristic
108C2×C4×C19#13512yes—
109C2×C4×C19#13712yes—
110C2×Dic19—42no—
111C2×Dic19—42no—
112C2×Dic19—42no—
113C2×Dic19—42no—
114C2×Dic19—42no—
115C2×Dic19—42no—
116Dic38—84no—
117C8×C19—44no—
118C19⋊C8—82no—
119#2921D1911yescharacteristic
120#2628—191no—
121#1548—192no—
122#1458—191no—
123#1286—192no—
124C22×C19—21no—
125C22×C19—21no—
126C22×C19—42no—
127C22×C19—41no—
128C22×C19—41no—
129C22×C19—41no—
130C22×C19—81no—
131C22×C19#38611yescharacteristic
132C22×C19#41611yescharacteristic
133C22×C19#41911yescharacteristic
134C4×C19—22no—
135C4×C19—22no—
136C4×C19—41no—
137C4×C19—41no—
138C4×C19—41no—
139C4×C19#45212yes—
140C4×C19#48512yes—
141Dic19—82no—
142Dic19—82no—
143C2×C4⋊Q8—191no—
144C2×#117C2×D1911yescharacteristic
145#433—24no—
146#431—192no—
147#423C2×D1912yes—
148#407—21no—
149C4×M16—21no—
150#400—381no—
151#399—381no—
152#395—192no—
153#393—192no—
154#389—381no—
155#382—191no—
156#380—381no—
157#333—384no—
158#324—381no—
159#323—381no—
160C2×C19—21no—
161C2×C19—21no—
162C2×C19—81no—
163C2×C19#187311yescharacteristic
164C2×C19#190911yescharacteristic
165C2×C19#191411yescharacteristic
166C22×Q8—192no—
167C23×C4C22⋊D1911yescharacteristic
168C2×M16—22no—
169C4⋊Q8—382no—
170C4⋊Q8—382no—
171#117—22no—
172#117—22no—
173C2×C4⋊C4—381no—
174C2×C4⋊C4—381no—
175C2×C4⋊C4—381no—
176C2×C4⋊C4—382no—
177C2×C4⋊C4C4×D1911yescharacteristic
178C2×C4⋊C4D7611yescharacteristic
179C2×C22⋊C4—382no—
180C2×C22⋊C4C4×D1911yescharacteristic
181C2×C22⋊C4D7611yescharacteristic
182C2×C42C22⋊D1911yescharacteristic
183C2×C42C22×D1911yescharacteristic
184C4⋊C8—22no—
185C4⋊C8—382no—
186C4⋊C8C22⋊D1914yes—
187C22⋊C8—24no—
188C22⋊C8—382no—
189#97—22no—
190C4×C8—22no—
191C4×C8—382no—
192#95—192no—
193#95—382no—
194#95—382no—
195#95—381no—
196C19#919211yescharacteristic, complemented, Sylow
197C24(C2×D19)⋊C411yescharacteristic
198C2×Q8—384no—
199C2×Q8—1522no—
200C22×C4—22no—
201C22×C4—22no—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—382no—
205C22×C4—382no—
206C22×C4(C2×D19)⋊C411yescharacteristic
207C22×C4(C2×D19)⋊C411yescharacteristic
208C22×C4(C2×D19)⋊C411yescharacteristic
209C22×C4C2×C4×D1911yescharacteristic
210C22×C4C2×D7611yescharacteristic
211C22×C4C2×C22⋊D1911yescharacteristic
212M16—42no—
213M16—42no—
214C2×C8—24no—
215C2×C8—762no—
216C4⋊C4—22no—
217C4⋊C4—22no—
218C4⋊C4—762no—
219C4⋊C4—762no—
220C4⋊C4—761no—
221C4⋊C4—761no—
222C4⋊C4—1522no—
223C22⋊C4—22no—
224C22⋊C4—22no—
225C22⋊C4—1522no—
226C42—21no—
227C42—21no—
228C42#6454112yes—
229C42C2×C22⋊D1912yes—
230C23—21no—
231C23—21no—
232C23—21no—
233C23—41no—
234C23—41no—
235C23C2×(C2×D19)⋊C411yescharacteristic
236Q8—1524no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—42no—
245C2×C4—42no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—762no—
249C2×C4—762no—
250C2×C4—762no—
251C2×C4—762no—
252C2×C4—762no—
253C2×C4—762no—
254C2×C4C4×C22⋊D1912yes—
255C2×C4#1059737511yescharacteristic
256C2×C4#1059737612yes—
257C2×C4#1059739612yes—
258C2×C4#1059739712yes—
259C2×C4#1059739911yescharacteristic
260C8—44no—
261C8—1522no—
262C22—21no—
263C22—21no—
264C22—42no—
265C22—41no—
266C22—41no—
267C22—41no—
268C22—81no—
269C22#1192642311yescharacteristic
270C22#1192653811yescharacteristic
271C22#1192655211yescharacteristic
272C4—22no—
273C4—22no—
274C4—41no—
275C4—41no—
276C4—41no—
277C4—1522no—
278C4—1522no—
279C4#1192670612yes—
280C4#1192688512yes—
281C2—21no—
282C2—21no—
283C2—81no—
284C2#1456394711yescharacteristic
285C2#1456415711yescharacteristic
286C2#1456418211yescharacteristic
subgroupG/H
centerC22#11926423
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#2921C2
socleC22×C19#386
prime radicalC24×C19C22⋊C4
cosocleC2×C42×C19C23
hypercenter#2921D19
hypocenterC19#9192
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2921

Complements

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

NH ≅ G/Ntype
2. #14562317C2semidirect
4. #14561495C2semidirect
196. C19#9192semidirect

Maximal subgroups

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

subgroupindex
#145694562
#145623172
#145619492
#145614952
C19×#29212
#919219