Finite Group Databasebeta

← #18080513

Subgroups — #18080513

Order 4864.

522 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 522 conjugacy classes of subgroups — too many to draw. Only its 107 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#14567952C211yesmaximal, characteristic
2#14563713C212yesmaximal, complemented
3#14561973C211yesmaximal, characteristic
4#14561540C212yesmaximal, complemented
5C19×#2975C211yesmaximal, characteristic
6C22×C4⋊Dic19C2211yescharacteristic
7#11926508C2212yes—
8#11926483—21no—
9#11926480—21no—
10#11926442—21no—
11#11926424C412yes—
12#11926416C412yes—
13#11926404—21no—
14#11926404C2211yescharacteristic
15#11926312—24no—
16#11926270—21no—
17#11926268—21no—
18C2×C4×D4×C19C2211yescharacteristic
19C19×#436—24no—
20C19×#431—21no—
21C19×#407—21no—
22C19×#407C2212yes—
23C22×D4×C19C2×C411yescharacteristic
24C23×C4×C19D411yescharacteristic
25C23×C4×C19C2311yescharacteristic
26C23×Dic19C2×C412yes—
27C2×M16×C19—22no—
28C2×M16×C19D414yes—
29C4×D4×C19—22no—
30C4×D4×C19—22no—
31C2×C4⋊C4×C19D411yescharacteristic
32C2×C22⋊C4×C19C2×C411yescharacteristic
33C2×C22⋊C4×C19D411yescharacteristic
34C2×C42×C19D411yescharacteristic
35C2×C22⋊Dic19—22no—
36C2×C22⋊Dic19C2×C412yes—
37C2×C4⋊Dic19—22no—
38C2×C4⋊Dic19—21no—
39C2×C4⋊Dic19—21no—
40C2×C4⋊Dic19—21no—
41C2×C4⋊Dic19—22no—
42C2×Dic19⋊C4—22no—
43C2×#64520—22no—
44C19×C4⋊C8—22no—
45C19×C22⋊C8—22no—
46C19×C22⋊C8—22no—
47C19×C22⋊C8—22no—
48C4×C8×C19—22no—
49C19⋊#95—22no—
50C19⋊#95—22no—
51C19⋊#95—21no—
52C22⋊(C19⋊C8)—22no—
53C22⋊(C19⋊C8)—22no—
54C24×C19C22⋊C411yescharacteristic
55C24×C19C22×C411yescharacteristic
56C2×D4×C19—22no—
57C2×D4×C19—22no—
58C2×D4×C19—41no—
59C22×C4×C19—21no—
60C22×C4×C19—21no—
61C22×C4×C19—42no—
62C22×C4×C19—42no—
63C22×C4×C19C22⋊C411yescharacteristic
64C22×C4×C19C22⋊C411yescharacteristic
65C22×C4×C19C22⋊C411yescharacteristic
66C22×C4×C19C2×D411yescharacteristic
67C22×C4×C19C2×D412yes—
68C22×C4×C19C2×D411yescharacteristic
69C22×C4×C19#4112yes—
70C22×Dic19—22no—
71C22×Dic19—22no—
72C22×Dic19—24no—
73C22×Dic19—82no—
74M16×C19—44no—
75M16×C19—82no—
76C2×C8×C19—24no—
77C4⋊C4×C19—22no—
78C22⋊C4×C19—22no—
79C22⋊C4×C19—22no—
80C42×C19—21no—
81C42×C19—21no—
82C22⋊Dic19—42no—
83C22⋊Dic19—82no—
84C4⋊Dic19—42no—
85C4⋊Dic19—41no—
86C4⋊Dic19—42no—
87C4⋊Dic19—41no—
88Dic19⋊C4—82no—
89#64520—44no—
90C2×C19⋊C8—42no—
91#9510—191nomaximal, Sylow
92C23×C19—21no—
93C23×C19—21no—
94C23×C19—21no—
95C23×C19—21no—
96C23×C19—21no—
97C23×C19—41no—
98C23×C19—41no—
99C23×C19—41no—
100C23×C19—41no—
101C23×C19C2×C22⋊C411yescharacteristic
102C23×C19C4×D412yes—
103D4×C19—44no—
104C2×C4×C19—21no—
105C2×C4×C19—21no—
106C2×C4×C19—24no—
107C2×C4×C19—22no—
108C2×C4×C19—21no—
109C2×C4×C19—21no—
110C2×C4×C19—41no—
111C2×C4×C19—42no—
112C2×C4×C19—42no—
113C2×C4×C19—41no—
114C2×C4×C19—41no—
115C2×C4×C19—81no—
116C2×C4×C19#10112yes—
117C2×C4×C19#12011yescharacteristic
118C2×C4×C19#12112yes—
119C2×C4×C19#12311yescharacteristic
120C2×Dic19—42no—
121C2×Dic19—42no—
122C2×Dic19—42no—
123C2×Dic19—42no—
124C2×Dic19—42no—
125C2×Dic19—42no—
126C2×Dic19—84no—
127C8×C19—44no—
128C19⋊C8—82no—
129#2975D1911yescharacteristic
130#2487—191no—
131#1821—192no—
132#1465—191no—
133#1305—192no—
134C22×C19—21no—
135C22×C19—21no—
136C22×C19—22no—
137C22×C19—22no—
138C22×C19—22no—
139C22×C19—42no—
140C22×C19—42no—
141C22×C19—42no—
142C22×C19—41no—
143C22×C19—41no—
144C22×C19—41no—
145C22×C19—81no—
146C22×C19#38611yescharacteristic
147C22×C19C2×#10111yescharacteristic
148C22×C19#41311yescharacteristic
149C4×C19—22no—
150C4×C19—21no—
151C4×C19—22no—
152C4×C19—41no—
153C4×C19—41no—
154C4×C19#45812yes—
155Dic19—82no—
156Dic19—82no—
157C2×C4×D4C2×D1911yescharacteristic
158C22×C4⋊C4—191no—
159#436—24no—
160#431—21no—
161#407—21no—
162#407—192no—
163#407C2×D1912yes—
164#400—381no—
165#399—381no—
166#389—381no—
167#386—192no—
168#385—192no—
169#380—191no—
170#380—381no—
171#343—384no—
172#324—381no—
173#323—381no—
174C2×C19—21no—
175C2×C19—21no—
176C2×C19—42no—
177C2×C19—81no—
178C2×C19#189011yescharacteristic
179C2×C19#190111yescharacteristic
180C2×C19#191411yescharacteristic
181C22×D4C4×D1911yescharacteristic
182C23×C4—192no—
183C23×C4C22⋊D1911yescharacteristic
184C23×C4C22×D1911yescharacteristic
185C2×M16—22no—
186C2×M16—382no—
187C2×M16C22⋊D1914yes—
188C4×D4—22no—
189C4×D4—22no—
190C2×C4⋊C4—381no—
191C2×C4⋊C4—382no—
192C2×C4⋊C4—382no—
193C2×C4⋊C4—381no—
194C2×C4⋊C4—381no—
195C2×C4⋊C4—382no—
196C2×C4⋊C4D7611yescharacteristic
197C2×C22⋊C4—192no—
198C2×C22⋊C4—382no—
199C2×C22⋊C4C4×D1911yescharacteristic
200C2×C22⋊C4D7611yescharacteristic
201C2×C42C22⋊D1911yescharacteristic
202C4⋊C8—22no—
203C22⋊C8—22no—
204C22⋊C8—22no—
205C22⋊C8—22no—
206C22⋊C8—382no—
207C22⋊C8—382no—
208C4×C8—22no—
209#95—382no—
210#95—382no—
211#95—381no—
212C19#951011yescharacteristic, complemented, Sylow
213C24(C2×D19)⋊C411yescharacteristic
214C24C2×C4×D1911yescharacteristic
215C2×D4—22no—
216C2×D4—22no—
217C2×D4—41no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—42no—
221C22×C4—42no—
222C22×C4—382no—
223C22×C4—382no—
224C22×C4—384no—
225C22×C4—1522no—
226C22×C4(C2×D19)⋊C411yescharacteristic
227C22×C4(C2×D19)⋊C411yescharacteristic
228C22×C4(C2×D19)⋊C411yescharacteristic
229C22×C4C2×D7611yescharacteristic
230C22×C4#6454112yes—
231C22×C4C2×C22⋊D1912yes—
232C22×C4C2×C22⋊D1911yescharacteristic
233M16—44no—
234M16—82no—
235M16—764no—
236C2×C8—24no—
237C2×C8—762no—
238C4⋊C4—22no—
239C4⋊C4—762no—
240C4⋊C4—762no—
241C4⋊C4—761no—
242C4⋊C4—761no—
243C4⋊C4—1522no—
244C22⋊C4—22no—
245C22⋊C4—22no—
246C22⋊C4—762no—
247C22⋊C4—1522no—
248C42—21no—
249C42—21no—
250C23—21no—
251C23—21no—
252C23—21no—
253C23—21no—
254C23—21no—
255C23—41no—
256C23—41no—
257C23—41no—
258C23—41no—
259C23C2×(C2×D19)⋊C411yescharacteristic
260C23C4×C22⋊D1912yes—
261D4—44no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—22no—
265C2×C4—24no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—41no—
269C2×C4—42no—
270C2×C4—42no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—81no—
274C2×C4—762no—
275C2×C4—762no—
276C2×C4—762no—
277C2×C4—762no—
278C2×C4—762no—
279C2×C4—762no—
280C2×C4—1524no—
281C2×C4#1059728112yes—
282C2×C4#1059737511yescharacteristic
283C2×C4#1059737612yes—
284C2×C4#1059739911yescharacteristic
285C8—44no—
286C8—1522no—
287C22—21no—
288C22—21no—
289C22—22no—
290C22—22no—
291C22—22no—
292C22—42no—
293C22—42no—
294C22—42no—
295C22—41no—
296C22—41no—
297C22—41no—
298C22—81no—
299C22#1192642311yescharacteristic
300C22C2×#1059728111yescharacteristic
301C22#1192652611yescharacteristic
302C4—22no—
303C4—22no—
304C4—21no—
305C4—41no—
306C4—41no—
307C4—1522no—
308C4—1522no—
309C4#1192673412yes—
310C2—21no—
311C2—21no—
312C2—42no—
313C2—81no—
314C2#1456404811yescharacteristic
315C2#1456410311yescharacteristic
316C2#1456418211yescharacteristic
subgroupG/H
centerC22#11926423
commutatorC24×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#2975C2
socleC22×C19#386
prime radicalC22×D4×C19C2×C4
cosocleC23×C4×C19C23
hypercenter#2975D19
hypocenterC19#9510
LCSG ▷ C24×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2975

Complements

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

NH ≅ G/Ntype
2. #14563713C2semidirect
4. #14561540C2semidirect
212. C19#9510semidirect

Maximal subgroups

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

subgroupindex
#145679522
#145637132
#145619732
#145615402
C19×#29752
#951019