Finite Group Databasebeta

← #18070836

Subgroups — #18070836

Order 4864.

630 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 630 conjugacy classes of subgroups — too many to draw. Only its 101 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#14566124C211yesmaximal, characteristic
2#14563702C212yesmaximal, complemented
3#14561461C211yesmaximal, characteristic, complemented
4#14561455C212yesmaximal, complemented
5C19×#1272C211yesmaximal, characteristic, complemented
6C22×#64545C411yescharacteristic
7C2×#10597338C411yescharacteristic
8C2×C42×D19C2211yescharacteristic
9C2×(C2×D19)⋊C8—22no—
10#11926451C411yescharacteristic
11#11926446C2211yescharacteristic
12#11926445C411yescharacteristic
13#11926422—22no—
14#11926391—22no—
15#11926299C2212yes—
16#11926298—22no—
17C19×#391C2211yescharacteristic
18C19×#336C2212yes—
19C22×Q8×C19C2×C411yescharacteristic
20C2×#64545—22no—
21C2×#64545—22no—
22C2×#64545—42no—
23C2×#64545—42no—
24C22×D76—21no—
25C22×D76C2×C411yescharacteristic
26C22×C4×D19—21no—
27C22×C4×D19C2×C411yescharacteristic
28C22×C4×D19D412yes—
29C22×C8×C19—22no—
30C2×C4⋊C4×C19C2×C411yescharacteristic
31C2×C42×C19C2311yescharacteristic
32C2×(C2×D19)⋊C4—21no—
33C2×(C2×D19)⋊C4—22no—
34C2×(C2×D19)⋊C4—22no—
35C2×C4⋊Dic19C2×C411yescharacteristic
36C2×C4×Dic19—21no—
37C2×C4×Dic19C2×C411yescharacteristic
38C2×C4×Dic19D412yes—
39C22×C19⋊C8—22no—
40#10597338—42no—
41C42×D19—42no—
42C19×#95—22no—
43C19⋊#95—22no—
44(C2×D19)⋊C8—44no—
45C23×D19—21no—
46C23×D19C22⋊C411yescharacteristic
47C2×Q8×C19—21no—
48C2×Q8×C19—41no—
49C2×Q8×C19—41no—
50C2×Q8×C19M1612yes—
51C22×C4×C19—21no—
52C22×C4×C19—21no—
53C22×C4×C19C22×C411yescharacteristic
54C22×C4×C19C2×D412yes—
55C22×Dic19—21no—
56C22×Dic19C22⋊C412yes—
57C22×Dic19C22⋊C411yescharacteristic
58#64545—48no—
59#64545—48no—
60C2×D76—24no—
61C2×D76—21no—
62C2×D76—41no—
63C2×D76—41no—
64C2×D76—42no—
65C2×D76—42no—
66C2×D76M1612yes—
67C2×C4×D19—22no—
68C2×C4×D19—21no—
69C2×C4×D19—21no—
70C2×C4×D19—22no—
71C2×C4×D19—24no—
72C2×C4×D19—24no—
73C2×C4×D19—22no—
74C2×C4×D19—22no—
75C2×C4×D19—42no—
76C2×C4×D19—42no—
77C2×C4×D19—42no—
78C2×C8×C19—42no—
79C2×C8×C19—42no—
80C2×C8×C19—42no—
81C4⋊C4×C19—41no—
82C42×C19—41no—
83(C2×D19)⋊C4—44no—
84(C2×D19)⋊C4—42no—
85(C2×D19)⋊C4—42no—
86(C2×D19)⋊C4—42no—
87C4⋊Dic19—41no—
88C4×Dic19—41no—
89C4×Dic19—42no—
90C4×Dic19—42no—
91C2×C19⋊C8—42no—
92C2×C19⋊C8—42no—
93C2×C19⋊C8—42no—
94#7645—191nomaximal, Sylow
95C23×C19C2×C22⋊C411yescharacteristic
96C22×D19—21no—
97C22×D19—21no—
98C22×D19—22no—
99C22×D19—22no—
100C22×D19—22no—
101C22×D19—41no—
102C22×D19—41no—
103C22×D19—42no—
104C22×D19—42no—
105C22×D19#9912yes—
106Q8×C19—42no—
107Q8×C19—42no—
108C2×C4×C19—22no—
109C2×C4×C19—21no—
110C2×C4×C19—21no—
111C2×C4×C19—22no—
112C2×C4×C19—22no—
113C2×C4×C19—41no—
114C2×C4×C19—41no—
115C2×C4×C19—41no—
116C2×C4×C19—42no—
117C2×C4×C19C2×M1611yescharacteristic
118C2×C4×C19C2×M1611yescharacteristic
119C2×C4×C19#13512yes—
120C2×C4×C19#13512yes—
121C2×Dic19—21no—
122C2×Dic19—21no—
123C2×Dic19—22no—
124C2×Dic19—22no—
125C2×Dic19—22no—
126C2×Dic19—41no—
127C2×Dic19—42no—
128C2×Dic19#10012yes—
129D76—42no—
130D76—42no—
131D76—48no—
132C4×D19—24no—
133C4×D19—24no—
134C4×D19—48no—
135C4×D19—44no—
136C4×D19—44no—
137C8×C19—82no—
138C19⋊C8—82no—
139#2297—191no—
140#1817—192no—
141#1272—191no—
142#1272D1911yescharacteristic, complemented
143#1270—192no—
144C22×C19#40711yescharacteristic
145C22×C19C2×#9911yescharacteristic
146C22×C19C2×#10011yescharacteristic
147C22×C19#41612yes—
148C22×C19#42112yes—
149C2×D19—22no—
150C2×D19—24no—
151C2×D19—41no—
152C2×D19—41no—
153C2×D19—42no—
154C2×D19—42no—
155C2×D19—44no—
156C2×D19—81no—
157C2×D19—81no—
158C2×D19—82no—
159C4×C19—21no—
160C4×C19—21no—
161C4×C19—22no—
162C4×C19—22no—
163C4×C19—42no—
164C4×C19—81no—
165Dic19—22no—
166Dic19—42no—
167Dic19—81no—
168C22×#41—191no—
169C2×#117—191no—
170C22×C42—191no—
171C2×C22⋊C8—382no—
172#391—191no—
173#391C2×D1911yescharacteristic
174#390—191no—
175#390—191no—
176#386—382no—
177C4×C22⋊C4—382no—
178#336—192no—
179#336—382no—
180#336C2×D1912yes—
181C2×C19#146211yescharacteristic
182C2×C19#148812yes—
183C2×C19#151612yes—
184C2×C19#153611yescharacteristic
185C2×C19#154311yescharacteristic
186D19—42no—
187D19—82no—
188C2×#41—382no—
189C2×#41—382no—
190C2×#41—762no—
191C2×#41—762no—
192C22×Q8C4×D1911yescharacteristic
193C22×D4—191no—
194C22×D4—381no—
195C23×C4—191no—
196C23×C4—192no—
197C23×C4—381no—
198C22×C8—22no—
199C22×C8—382no—
200#117—762no—
201C2×C4⋊C4—191no—
202C2×C4⋊C4C4×D1911yescharacteristic
203C2×C22⋊C4—382no—
204C2×C22⋊C4—381no—
205C2×C22⋊C4—382no—
206C2×C42—191no—
207C2×C42—192no—
208C2×C42—381no—
209C2×C42—762no—
210C2×C42C22×D1911yescharacteristic
211C22⋊C8—764no—
212#95—22no—
213#95—382no—
214C19#764511yescharacteristic, complemented, Sylow
215C24—191no—
216C24—381no—
217#41—768no—
218#41—768no—
219C2×Q8—21no—
220C2×Q8—41no—
221C2×Q8—41no—
222C2×Q8#6451512yes—
223C2×D4—192no—
224C2×D4—384no—
225C2×D4—381no—
226C2×D4—761no—
227C2×D4—761no—
228C2×D4—762no—
229C2×D4—762no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—191no—
233C22×C4—192no—
234C22×C4—382no—
235C22×C4—382no—
236C22×C4—384no—
237C22×C4—384no—
238C22×C4—381no—
239C22×C4—381no—
240C22×C4—382no—
241C22×C4—382no—
242C22×C4—381no—
243C22×C4—762no—
244C22×C4—762no—
245C22×C4—762no—
246C22×C4C2×C4×D1911yescharacteristic
247C22×C4D4×D1912yes—
248C2×C8—42no—
249C2×C8—42no—
250C2×C8—42no—
251C2×C8—762no—
252C2×C8—762no—
253C2×C8—762no—
254C4⋊C4—41no—
255C4⋊C4—761no—
256C22⋊C4—764no—
257C22⋊C4—762no—
258C22⋊C4—762no—
259C22⋊C4—762no—
260C42—41no—
261C42—762no—
262C42—761no—
263C42—762no—
264C23—192no—
265C23—382no—
266C23—382no—
267C23—381no—
268C23—381no—
269C23—382no—
270C23—762no—
271C23—762no—
272C23—761no—
273C23—761no—
274C23C22⋊C4×D1911yescharacteristic
275Q8—42no—
276Q8—42no—
277D4—762no—
278D4—762no—
279D4—768no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—22no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—42no—
288C2×C4—41no—
289C2×C4—192no—
290C2×C4—384no—
291C2×C4—384no—
292C2×C4—381no—
293C2×C4—381no—
294C2×C4—382no—
295C2×C4—382no—
296C2×C4—382no—
297C2×C4—764no—
298C2×C4—764no—
299C2×C4—768no—
300C2×C4—762no—
301C2×C4—761no—
302C2×C4C2×#6451511yescharacteristic
303C2×C4M16×D1911yescharacteristic
304C2×C4#1059736212yes—
305C2×C4#1059736512yes—
306C8—82no—
307C8—1522no—
308C22—384no—
309C22—382no—
310C22—762no—
311C22—761no—
312C22—761no—
313C22—764no—
314C22—762no—
315C22—1522no—
316C22—1521no—
317C22—1521no—
318C22#1192650611yescharacteristic
319C22#99×D1911yescharacteristic
320C22#100×D1911yescharacteristic
321C22#1192653912yes—
322C22#1192655912yes—
323C4—22no—
324C4—22no—
325C4—21no—
326C4—21no—
327C4—42no—
328C4—81no—
329C4—382no—
330C4—762no—
331C4—1521no—
332C2—762no—
333C2—1522no—
334C2#1456196011yescharacteristic
335C2#1456206812yes—
336C2#1456219012yes—
337C2#1456226811yescharacteristic
338C2#1456229611yescharacteristic
subgroupG/H
centerC23C22⋊C4×D19
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1272C2
socleC23×C19C2×C22⋊C4
prime radicalC22×#64545C4
cosocleC2×C42×C19C23
hypercenter#1272D19
hypocenterC19#7645
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. #14563702C2semidirect
3. #14561461C2semidirect
4. #14561455C2semidirect
5. C19×#1272C2semidirect
142. #1272D19semidirect
214. C19#7645semidirect

Maximal subgroups

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

subgroupindex
#145661242
#145637022
#145614612
#145614552
C19×#12722
#764519