Finite Group Databasebeta

← #18070853

Subgroups — #18070853

Order 4864.

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

normal subgroups only

This group has 468 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#14566178C211yesmaximal, characteristic
2#14563777C212yesmaximal, complemented
3#14561461C211yesmaximal, characteristic, complemented
4#14561455C212yesmaximal
5C19×#1272C211yesmaximal, characteristic, complemented
6C2×#10597393C411yescharacteristic
7C2×Q8×Dic19C411yescharacteristic
8C2×#10597339C411yescharacteristic
9#11926446C2211yescharacteristic
10#11926436—22no—
11#11926409C411yescharacteristic
12#11926391—22no—
13C42×Dic19C2211yescharacteristic
14#11926299C2212yes—
15#11926298—22no—
16#11926298—22no—
17C19×#391C2211yescharacteristic
18C19×#336C2212yes—
19C22×Q8×C19C2×C411yescharacteristic
20C22×D76C2×C411yescharacteristic
21C22×C4×D19—21no—
22C22×C8×C19—22no—
23C2×C4⋊C4×C19C2×C411yescharacteristic
24C2×C42×C19C2311yescharacteristic
25#10597393—22no—
26#10597393—22no—
27Q8×Dic19—42no—
28C2×(C2×D19)⋊C4—22no—
29C2×(C2×D19)⋊C4—22no—
30C2×(C2×D19)⋊C4—21no—
31C2×C4⋊Dic19—21no—
32C2×C4⋊Dic19C2×C411yescharacteristic
33C2×C4×Dic19—21no—
34C2×C4×Dic19C2×C411yescharacteristic
35C2×C4×Dic19C2×C411yescharacteristic
36C2×C4×Dic19D412yes—
37C2×C4×Dic19D412yes—
38C22×C19⋊C8—22no—
39#10597339—42no—
40C19×#95—22no—
41C19⋊#95—22no—
42C23×D19—21no—
43C2×Q8×C19—21no—
44C2×Q8×C19—41no—
45C2×Q8×C19—41no—
46C2×Q8×C19M1612yes—
47C22×C4×C19—21no—
48C22×C4×C19—21no—
49C22×C4×C19C22×C411yescharacteristic
50C22×C4×C19C2×D412yes—
51C22×Dic19—21no—
52C22×Dic19C22⋊C412yes—
53C22×Dic19C22⋊C411yescharacteristic
54C22×Dic19C22⋊C411yescharacteristic
55C2×D76—21no—
56C2×D76—41no—
57C2×D76—41no—
58C2×D76M1612yes—
59C2×C4×D19—44no—
60C2×C4×D19—42no—
61C2×C8×C19—42no—
62C2×C8×C19—42no—
63C2×C8×C19—42no—
64C4⋊C4×C19—41no—
65C42×C19—41no—
66(C2×D19)⋊C4—28no—
67(C2×D19)⋊C4—42no—
68(C2×D19)⋊C4—42no—
69(C2×D19)⋊C4—42no—
70C4⋊Dic19—42no—
71C4⋊Dic19—41no—
72C4×Dic19—21no—
73C4×Dic19—21no—
74C4×Dic19—22no—
75C4×Dic19—22no—
76C4×Dic19—22no—
77C4×Dic19—42no—
78C4×Dic19—42no—
79C2×C19⋊C8—42no—
80C2×C19⋊C8—42no—
81C2×C19⋊C8—42no—
82#7649—191nomaximal, Sylow
83C23×C19C2×C22⋊C411yescharacteristic
84C22×D19—22no—
85C22×D19—41no—
86C22×D19—41no—
87C22×D19—42no—
88C22×D19—42no—
89Q8×C19—42no—
90Q8×C19—42no—
91C2×C4×C19—22no—
92C2×C4×C19—21no—
93C2×C4×C19—21no—
94C2×C4×C19—22no—
95C2×C4×C19—22no—
96C2×C4×C19—41no—
97C2×C4×C19—41no—
98C2×C4×C19—41no—
99C2×C4×C19—42no—
100C2×C4×C19C2×M1611yescharacteristic
101C2×C4×C19C2×M1611yescharacteristic
102C2×C4×C19#13512yes—
103C2×C4×C19#13512yes—
104C2×Dic19—22no—
105C2×Dic19—22no—
106C2×Dic19—21no—
107C2×Dic19—22no—
108C2×Dic19—22no—
109C2×Dic19—22no—
110C2×Dic19—41no—
111C2×Dic19—42no—
112C2×Dic19#10012yes—
113D76—42no—
114D76—42no—
115C4×D19—84no—
116C8×C19—82no—
117C19⋊C8—82no—
118C4×#124—191no—
119#1839—192no—
120#1272—191no—
121#1272D1911yescharacteristic, complemented
122#1270—192no—
123C22×C19#40711yescharacteristic
124C22×C19#41011yescharacteristic
125C22×C19C2×#10011yescharacteristic
126C22×C19#41612yes—
127C22×C19#42112yes—
128C2×D19—42no—
129C2×D19—44no—
130C2×D19—81no—
131C2×D19—82no—
132C2×D19—81no—
133C4×C19—21no—
134C4×C19—21no—
135C4×C19—22no—
136C4×C19—22no—
137C4×C19—42no—
138C4×C19—81no—
139Dic19—22no—
140Dic19—41no—
141Dic19—42no—
142Dic19—81no—
143C2×#124—191no—
144C2×C4×Q8—191no—
145C2×C4×D4—191no—
146#391C2×D1911yescharacteristic
147#390—191no—
148#388—382no—
149#382—191no—
150C4×C22⋊C4—382no—
151C43—191no—
152#336—192no—
153#336—382no—
154#336—382no—
155#336C2×D1912yes—
156C2×C19#146611yescharacteristic
157C2×C19#148812yes—
158C2×C19#152112yes—
159C2×C19#153311yescharacteristic
160C2×C19#154311yescharacteristic
161D19—82no—
162C22×Q8C4×D1911yescharacteristic
163C22×D4—191no—
164C23×C4—381no—
165C22×C8—22no—
166C22×C8—382no—
167#124—382no—
168#124—382no—
169C4×Q8—762no—
170C4×D4—762no—
171C2×C4⋊C4—191no—
172C2×C4⋊C4—381no—
173C2×C4⋊C4C4×D1911yescharacteristic
174C2×C22⋊C4—382no—
175C2×C22⋊C4—381no—
176C2×C22⋊C4—382no—
177C2×C42—191no—
178C2×C42—191no—
179C2×C42—192no—
180C2×C42—192no—
181C2×C42—381no—
182C2×C42C22×D1911yescharacteristic
183#95—22no—
184#95—382no—
185C19#764911yescharacteristic, complemented, Sylow
186C24—381no—
187C2×Q8—21no—
188C2×Q8—41no—
189C2×Q8—41no—
190C2×Q8#6451512yes—
191C2×D4—192no—
192C2×D4—381no—
193C2×D4—761no—
194C2×D4—761no—
195C22×C4—21no—
196C22×C4—21no—
197C22×C4—191no—
198C22×C4—192no—
199C22×C4—191no—
200C22×C4—381no—
201C22×C4—762no—
202C22×C4—764no—
203C22×C4C2×C4×D1911yescharacteristic
204C22×C4D4×D1912yes—
205C2×C8—42no—
206C2×C8—42no—
207C2×C8—42no—
208C2×C8—762no—
209C2×C8—762no—
210C2×C8—762no—
211C4⋊C4—41no—
212C4⋊C4—761no—
213C4⋊C4—762no—
214C22⋊C4—388no—
215C22⋊C4—762no—
216C22⋊C4—762no—
217C22⋊C4—762no—
218C42—41no—
219C42—382no—
220C42—381no—
221C42—381no—
222C42—382no—
223C42—382no—
224C42—762no—
225C42—762no—
226C23—382no—
227C23—762no—
228C23—762no—
229C23—761no—
230C23—761no—
231C23C22⋊C4×D1911yescharacteristic
232Q8—42no—
233Q8—42no—
234D4—762no—
235D4—762no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—22no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—42no—
244C2×C4—41no—
245C2×C4—192no—
246C2×C4—382no—
247C2×C4—382no—
248C2×C4—382no—
249C2×C4—382no—
250C2×C4—382no—
251C2×C4—381no—
252C2×C4—762no—
253C2×C4—761no—
254C2×C4—1524no—
255C2×C4C2×#6451511yescharacteristic
256C2×C4M16×D1911yescharacteristic
257C2×C4#1059736212yes—
258C2×C4#1059736512yes—
259C8—82no—
260C8—1522no—
261C22—764no—
262C22—762no—
263C22—1522no—
264C22—1521no—
265C22—1521no—
266C22#1192650611yescharacteristic
267C22#1192651611yescharacteristic
268C22#100×D1911yescharacteristic
269C22#1192653912yes—
270C22#1192655912yes—
271C4—22no—
272C4—22no—
273C4—21no—
274C4—21no—
275C4—42no—
276C4—81no—
277C4—382no—
278C4—762no—
279C4—761no—
280C4—1521no—
281C2—1522no—
282C2#1456197411yescharacteristic
283C2#1456206812yes—
284C2#1456221112yes—
285C2#1456225711yescharacteristic
286C2#1456229611yescharacteristic
subgroupG/H
centerC23C22⋊C4×D19
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1272C2
socleC23×C19C2×C22⋊C4
prime radicalC22×D76C2×C4
cosocleC2×C42×C19C23
hypercenter#1272D19
hypocenterC19#7649
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

Complements

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

NH ≅ G/Ntype
2. #14563777C2semidirect
3. #14561461C2semidirect
5. C19×#1272C2semidirect
121. #1272D19semidirect
185. C19#7649semidirect

Maximal subgroups

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

subgroupindex
#145661782
#145637772
#145614612
#145614552
C19×#12722
#764919