Finite Group Databasebeta

← #18080251

Subgroups — #18080251

Order 4864.

536 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 536 conjugacy classes of subgroups — too many to draw. Only its 103 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#14572720C211yesmaximal, characteristic, complemented
2#14568634C211yesmaximal, characteristic
3#14562348C212yesmaximal
4#14561490C212yesmaximal, complemented
5C19×#1467C211yesmaximal, characteristic, complemented
6C2×#10597320C2211yescharacteristic
7C2×#10597393C412yes—
8#11926675—24no—
9#11926601—21no—
10#11926601C2212yes—
11#11926597—21no—
12#11926461—21no—
13#11926461—21no—
14#11926446—21no—
15#11926446—21no—
16#11926445C412yes—
17C4×C4⋊Dic19C2211yescharacteristic
18#11926287—24no—
19C2×C4×Q8×C19C2211yescharacteristic
20C19×#432C2212yes—
21C19×#324—21no—
22C19×#324—21no—
23C22×Q8×C19C2×C411yescharacteristic
24C22×D76—21no—
25C22×D76—21no—
26C22×D76C2×C412yes—
27C4×Q8×C19—22no—
28C4×Q8×C19—22no—
29C2×C4⋊C4×C19C2×C411yescharacteristic
30C2×C4⋊C4×C19D411yescharacteristic
31C2×C4⋊C4×C19D411yescharacteristic
32C2×C42×C19D411yescharacteristic
33C2×C42×C19D411yescharacteristic
34C2×C42×C19C2311yescharacteristic
35#10597393—44no—
36C2×(C2×D19)⋊C4—22no—
37C2×(C2×D19)⋊C4—22no—
38C2×(C2×D19)⋊C4—22no—
39C2×(C2×D19)⋊C4—22no—
40C2×C4⋊Dic19—21no—
41C2×C4×Dic19C2×C412yes—
42#10597320—22no—
43#10597320—22no—
44C19×C4⋊C8—22no—
45C19×C22⋊C8—22no—
46C19×#97—22no—
47C19⋊#95—21no—
48C22⋊(C19⋊C8)—22no—
49C4⋊(C19⋊C8)—22no—
50C4⋊(C19⋊C8)—22no—
51C4⋊(C19⋊C8)D414yes—
52#10597260—22no—
53#10597260—22no—
54C4×C19⋊C8—22no—
55C23×D19—22no—
56C2×Q8×C19—22no—
57C2×Q8×C19—22no—
58C2×Q8×C19—41no—
59C22×C4×C19C22⋊C411yescharacteristic
60C22×C4×C19C22⋊C411yescharacteristic
61C22×C4×C19C22⋊C411yescharacteristic
62C22×C4×C19C22⋊C411yescharacteristic
63C22×C4×C19C22×C411yescharacteristic
64C22×C4×C19C2×D411yescharacteristic
65C22×C4×C19C2×D411yescharacteristic
66C22×Dic19—22no—
67C2×D76—24no—
68C2×D76—42no—
69C2×D76—42no—
70C2×D76—42no—
71C2×D76—42no—
72C2×D76—41no—
73C2×D76—42no—
74C2×D76—41no—
75C2×D76—82no—
76C2×C8×C19—42no—
77C4⋊C4×C19—22no—
78C4⋊C4×C19—22no—
79C4⋊C4×C19—22no—
80C42×C19—21no—
81C42×C19—21no—
82C42×C19—21no—
83C42×C19—21no—
84C42×C19C2×D412yes—
85C42×C19#4112yes—
86(C2×D19)⋊C4—44no—
87(C2×D19)⋊C4—44no—
88(C2×D19)⋊C4—82no—
89(C2×D19)⋊C4—82no—
90C4⋊Dic19—42no—
91C4×Dic19—42no—
92C2×C19⋊C8—24no—
93#9458—191nomaximal, Sylow
94C23×C19C2×C22⋊C411yescharacteristic
95C22×D19—42no—
96C22×D19—42no—
97C22×D19—42no—
98C22×D19—42no—
99C22×D19—42no—
100C22×D19—42no—
101C22×D19—42no—
102Q8×C19—44no—
103C2×C4×C19—21no—
104C2×C4×C19—21no—
105C2×C4×C19—21no—
106C2×C4×C19—21no—
107C2×C4×C19—22no—
108C2×C4×C19—21no—
109C2×C4×C19—21no—
110C2×C4×C19—21no—
111C2×C4×C19—21no—
112C2×C4×C19—21no—
113C2×C4×C19—41no—
114C2×C4×C19—41no—
115C2×C4×C19—41no—
116C2×C4×C19#10012yes—
117C2×C4×C19C4×D412yes—
118C2×C4×C19#12011yescharacteristic
119C2×C4×C19#12112yes—
120C2×C4×C19#12311yescharacteristic
121C2×Dic19—42no—
122C2×Dic19—42no—
123C2×Dic19—42no—
124D76—84no—
125D76—82no—
126D76—84no—
127D76—82no—
128C8×C19—82no—
129C19⋊C8—44no—
130#2983—191no—
131#2548—191no—
132#1555—192no—
133#1467D1911yescharacteristic, complemented
134#1285—192no—
135C22×C19—21no—
136C22×C19—21no—
137C22×C19#38611yescharacteristic
138C22×C19C2×#10011yescharacteristic
139C22×C19#41311yescharacteristic
140C2×D19—82no—
141C2×D19—82no—
142C2×D19—82no—
143C2×D19—82no—
144C2×D19—82no—
145C2×D19—82no—
146C2×D19—82no—
147C4×C19—21no—
148C4×C19—22no—
149C4×C19—22no—
150C4×C19—22no—
151C4×C19—41no—
152C4×C19—41no—
153C4×C19—41no—
154C4×C19#45412yes—
155Dic19—82no—
156C2×#127—191no—
157C2×#124—192no—
158C2×C4×Q8C2×D1911yescharacteristic
159#446—384no—
160#432—192no—
161#432—381no—
162#432C2×D1912yes—
163#431—381no—
164#394—381no—
165#394—381no—
166#390—192no—
167#390—381no—
168#390—381no—
169C4×C4⋊C4—191no—
170#331—384no—
171#324—21no—
172#324—21no—
173C2×C19—21no—
174C2×C19—21no—
175C2×C19#188811yescharacteristic
176C2×C19#190011yescharacteristic
177C2×C19#191011yescharacteristic
178D19—162no—
179C22×Q8C4×D1911yescharacteristic
180C22×D4—192no—
181C22×D4—381no—
182C22×D4—381no—
183#127—382no—
184#127—382no—
185#124—764no—
186C4×Q8—22no—
187C4×Q8—22no—
188C2×C4⋊C4—381no—
189C2×C4⋊C4C4×D1911yescharacteristic
190C2×C4⋊C4C22⋊D1911yescharacteristic
191C2×C4⋊C4C22⋊D1911yescharacteristic
192C2×C22⋊C4—382no—
193C2×C22⋊C4—382no—
194C2×C22⋊C4—382no—
195C2×C22⋊C4—382no—
196C2×C42—192no—
197C2×C42D7611yescharacteristic
198C2×C42D7611yescharacteristic
199C2×C42C22×D1911yescharacteristic
200C4⋊C8—22no—
201C4⋊C8—194no—
202C4⋊C8—382no—
203C4⋊C8—382no—
204C22⋊C8—22no—
205C22⋊C8—382no—
206#97—22no—
207#97—382no—
208#97—382no—
209C4×C8—382no—
210#95—381no—
211C19#945811yescharacteristic, complemented, Sylow
212C24—382no—
213C2×Q8—22no—
214C2×Q8—22no—
215C2×Q8—41no—
216C2×D4—384no—
217C2×D4—762no—
218C2×D4—762no—
219C2×D4—762no—
220C2×D4—762no—
221C2×D4—762no—
222C2×D4—761no—
223C2×D4—761no—
224C2×D4—1522no—
225C22×C4—382no—
226C22×C4(C2×D19)⋊C411yescharacteristic
227C22×C4(C2×D19)⋊C411yescharacteristic
228C22×C4(C2×D19)⋊C411yescharacteristic
229C22×C4(C2×D19)⋊C411yescharacteristic
230C22×C4C2×C4×D1911yescharacteristic
231C22×C4C2×D7611yescharacteristic
232C22×C4C2×C22⋊D1911yescharacteristic
233C2×C8—42no—
234C2×C8—384no—
235C4⋊C4—22no—
236C4⋊C4—22no—
237C4⋊C4—22no—
238C4⋊C4—762no—
239C22⋊C4—764no—
240C22⋊C4—764no—
241C22⋊C4—1522no—
242C22⋊C4—1522no—
243C42—21no—
244C42—21no—
245C42—21no—
246C42—21no—
247C42—762no—
248C42D4×D1912yes—
249C42#6454312yes—
250C23—762no—
251C23—762no—
252C23—762no—
253C23—762no—
254C23—762no—
255C23—762no—
256C23—762no—
257C23C2×(C2×D19)⋊C411yescharacteristic
258Q8—44no—
259D4—1524no—
260D4—1522no—
261D4—1524no—
262D4—1522no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—22no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—762no—
277C2×C4—762no—
278C2×C4—762no—
279C2×C4#1059728012yes—
280C2×C4(C22⋊D19)⋊C412yes—
281C2×C4#1059732811yescharacteristic
282C2×C4#1059733211yescharacteristic
283C2×C4#1059738512yes—
284C8—82no—
285C8—764no—
286C22—21no—
287C22—21no—
288C22—1522no—
289C22—1522no—
290C22—1522no—
291C22—1522no—
292C22—1522no—
293C22—1522no—
294C22—1522no—
295C22#1192642111yescharacteristic
296C22C2×#1059728011yescharacteristic
297C22#1192652611yescharacteristic
298C4—22no—
299C4—22no—
300C4—22no—
301C4—21no—
302C4—41no—
303C4—41no—
304C4—41no—
305C4—1522no—
306C4#1192671912yes—
307C2—21no—
308C2—21no—
309C2—3042no—
310C2#1456403611yescharacteristic
311C2#1456409611yescharacteristic
312C2#1456416011yescharacteristic
subgroupG/H
centerC22#11926421
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1467C2
socleC22×C19#386
prime radicalC2×#10597320C22
cosocleC2×C42×C19C23
hypercenter#1467D19
hypocenterC19#9458
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1467

Complements

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

NH ≅ G/Ntype
1. #14572720C2semidirect
4. #14561490C2semidirect
5. C19×#1467C2semidirect
133. #1467D19semidirect
211. C19#9458semidirect

Maximal subgroups

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

subgroupindex
#145727202
#145686342
#145623482
#145614902
C19×#14672
#945819