Finite Group Databasebeta

← #18071248

Subgroups — #18071248

Order 4864.

560 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 560 conjugacy classes of subgroups — too many to draw. Only its 87 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#14564869C212yesmaximal, complemented
2#14564705C211yesmaximal, characteristic
3#14561458C212yesmaximal, complemented
4#14561456C211yesmaximal, characteristic, complemented
5C19×#2724C211yesmaximal, characteristic, complemented
6C22×#64525—21no—
7C2×#10597320C2211yescharacteristic
8C2×#10597266—22no—
9C2×#10597266—22no—
10C2×#10597266—21no—
11#11926299C2212yes—
12#11926299C2211yescharacteristic
13C2×C19×#123—21no—
14C19×#398—21no—
15C19×#397—22no—
16C19×#390C2211yescharacteristic
17C19×#389C2212yes—
18C19×#385—22no—
19C22×D4×C19D411yescharacteristic
20C23×C4×C19—21no—
21C22×D76—22no—
22C22×D76—21no—
23C19×#123—42no—
24C19×#123—42no—
25C2×C4⋊C4×C19—22no—
26C2×C4⋊C4×C19—21no—
27C2×C4⋊C4×C19D412yes—
28C2×C4⋊C4×C19D412yes—
29C2×C4⋊C4×C19D411yescharacteristic
30C2×C22⋊C4×C19—22no—
31C2×C22⋊C4×C19—21no—
32C2×C22⋊C4×C19—22no—
33C2×C42×C19C2311yescharacteristic
34C2×#64525—42no—
35C2×#64525—42no—
36C2×#64525—42no—
37C22×C19⋊C8—21no—
38C22×C19⋊C8—22no—
39#10597320—42no—
40C19×#95—22no—
41C19×#95—21no—
42C19×#95—22no—
43#10597266—42no—
44#10597266—44no—
45#10597266—44no—
46C24×C19—21no—
47C23×D19—41no—
48C2×D4×C19—21no—
49C2×D4×C19—41no—
50C2×D4×C19—41no—
51C2×D4×C19D812yes—
52C22×C4×C19—22no—
53C22×C4×C19—21no—
54C22×C4×C19—22no—
55C22×C4×C19—42no—
56C22×C4×C19—81no—
57C22×C4×C19—81no—
58C22×C4×C19C2×D411yescharacteristic
59C22×C4×C19C2×D412yes—
60C2×D76—22no—
61C2×D76—24no—
62C2×D76—41no—
63C2×D76—42no—
64C2×D76—42no—
65C2×D76—41no—
66C2×D76—41no—
67C2×D76—42no—
68C2×D76—41no—
69C2×D76—42no—
70C2×D76—42no—
71C2×D76—41no—
72C4⋊C4×C19—22no—
73C4⋊C4×C19—22no—
74C4⋊C4×C19—41no—
75C4⋊C4×C19—42no—
76C4⋊C4×C19—42no—
77C4⋊C4×C19—42no—
78C4⋊C4×C19—81no—
79C22⋊C4×C19—42no—
80C22⋊C4×C19—44no—
81C22⋊C4×C19—42no—
82C22⋊C4×C19—42no—
83C42×C19—41no—
84#64525—48no—
85C2×C19⋊C8—22no—
86C2×C19⋊C8—41no—
87C2×C19⋊C8—41no—
88C2×C19⋊C8—42no—
89C2×C19⋊C8—42no—
90C2×C19⋊C8—42no—
91#7736—191nomaximal, Sylow
92C23×C19—22no—
93C23×C19—42no—
94C23×C19—41no—
95C23×C19—42no—
96C23×C19—41no—
97C23×C19#12011yescharacteristic
98C22×D19—42no—
99C22×D19—81no—
100C22×D19—82no—
101C22×D19—81no—
102C22×D19—82no—
103D4×C19—42no—
104D4×C19—81no—
105C2×C4×C19—21no—
106C2×C4×C19—22no—
107C2×C4×C19—22no—
108C2×C4×C19—21no—
109C2×C4×C19—42no—
110C2×C4×C19—42no—
111C2×C4×C19—42no—
112C2×C4×C19—42no—
113C2×C4×C19—41no—
114C2×C4×C19—42no—
115C2×C4×C19—42no—
116C2×C4×C19—42no—
117C2×C4×C19—84no—
118C2×C4×C19C2×D811yescharacteristic
119C2×C4×C19#13512yes—
120C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
121C2×C4×C19AGL(1,ℤ/8)12yes—
122D76—42no—
123D76—42no—
124D76—44no—
125D76—44no—
126D76—81no—
127D76—81no—
128D76—82no—
129D76—82no—
130C19⋊C8—42no—
131C19⋊C8—82no—
132#2724D1911yescharacteristic, complemented
133#2041—192no—
134#2011—191no—
135#1271—192no—
136#1270—191no—
137C22×C19—42no—
138C22×C19—44no—
139C22×C19—82no—
140C22×C19—81no—
141C22×C19—81no—
142C22×C19#44711yescharacteristic
143C22×C19#44912yes—
144C22×C19#45311yescharacteristic
145C22×C19#45412yes—
146C22×C19B(4,𝔽2)11yescharacteristic
147C2×D19—82no—
148C2×D19—84no—
149C2×D19—161no—
150C2×D19—162no—
151C2×D19—161no—
152C4×C19—21no—
153C4×C19—21no—
154C4×C19—22no—
155C4×C19—22no—
156C4×C19—82no—
157C4×C19—81no—
158C4×C19—82no—
159C22×D8—381no—
160C2×#127—191no—
161C2×#123—21no—
162C2×#102—381no—
163C2×#102—382no—
164C2×#102—382no—
165#398—21no—
166#397—22no—
167#390C2×D1911yescharacteristic
168#389C2×D1912yes—
169#385—22no—
170#336—191no—
171#336—192no—
172C2×C19—82no—
173C2×C19#159511yescharacteristic
174C2×C19#159712yes—
175C2×C19#162011yescharacteristic
176C2×C19#162512yes—
177C2×C19#165711yescharacteristic
178D19—162no—
179C22×D4—381no—
180C22×D4—382no—
181C22×D4C22⋊D1911yescharacteristic
182C23×C4—21no—
183C2×D8—762no—
184C2×D8—762no—
185C2×D8—762no—
186C22×C8—381no—
187C22×C8—382no—
188#127—762no—
189#123—42no—
190#123—42no—
191C2×C4⋊C4—22no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4C22⋊D1912yes—
194C2×C4⋊C4C22⋊D1912yes—
195C2×C4⋊C4C22⋊D1911yescharacteristic
196C2×C22⋊C4—22no—
197C2×C22⋊C4—21no—
198C2×C22⋊C4—22no—
199C2×C42C22×D1911yescharacteristic
200#102—764no—
201#102—762no—
202#102—764no—
203#95—22no—
204#95—21no—
205#95—22no—
206C19#773611yescharacteristic, complemented, Sylow
207C24—21no—
208C24—761no—
209C2×D4—21no—
210C2×D4—41no—
211C2×D4—41no—
212C2×D4—384no—
213C2×D4—382no—
214C2×D4—761no—
215C2×D4—761no—
216C2×D4—762no—
217C2×D4—762no—
218C2×D4—762no—
219C2×D4—761no—
220C2×D4—761no—
221C2×D4—761no—
222C2×D4—762no—
223C2×D4—762no—
224C2×D4#6452512yes—
225C22×C4—22no—
226C22×C4—21no—
227C22×C4—22no—
228C22×C4—42no—
229C22×C4—81no—
230C22×C4—81no—
231C22×C4C2×C22⋊D1911yescharacteristic
232C22×C4C2×C22⋊D1912yes—
233D8—768no—
234C2×C8—382no—
235C2×C8—761no—
236C2×C8—761no—
237C2×C8—762no—
238C2×C8—762no—
239C2×C8—762no—
240C4⋊C4—22no—
241C4⋊C4—22no—
242C4⋊C4—41no—
243C4⋊C4—42no—
244C4⋊C4—42no—
245C4⋊C4—42no—
246C4⋊C4—81no—
247C22⋊C4—42no—
248C22⋊C4—44no—
249C22⋊C4—42no—
250C22⋊C4—42no—
251C42—41no—
252C23—22no—
253C23—42no—
254C23—41no—
255C23—42no—
256C23—41no—
257C23—762no—
258C23—1521no—
259C23—1522no—
260C23—1521no—
261C23—1522no—
262C23#1059739911yescharacteristic
263D4—42no—
264D4—81no—
265D4—762no—
266D4—764no—
267D4—764no—
268D4—762no—
269D4—1522no—
270D4—1522no—
271D4—1521no—
272D4—1521no—
273C2×C4—21no—
274C2×C4—22no—
275C2×C4—22no—
276C2×C4—21no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—41no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4—42no—
285C2×C4—84no—
286C2×C4C2×#6452511yescharacteristic
287C2×C4#1059737811yescharacteristic
288C2×C4#1059739512yes—
289C2×C4#1059739612yes—
290C8—762no—
291C8—1522no—
292C22—44no—
293C22—42no—
294C22—82no—
295C22—81no—
296C22—81no—
297C22—3041no—
298C22—3041no—
299C22—3042no—
300C22—1524no—
301C22—1522no—
302C22#1192667811yescharacteristic
303C22#1192668912yes—
304C22#1192671211yescharacteristic
305C22#1192671712yes—
306C22#1192673111yescharacteristic
307C4—22no—
308C4—22no—
309C4—21no—
310C4—21no—
311C4—81no—
312C4—82no—
313C4—82no—
314C2—82no—
315C2—3042no—
316C2#1456255311yescharacteristic
317C2#1456256412yes—
318C2#1456269411yescharacteristic
319C2#1456272412yes—
320C2#1456293311yescharacteristic
subgroupG/H
centerC23#10597399
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#2724C2
socleC23×C19#120
prime radical#14564705C2
hypercenter#2724D19
hypocenterC19#7736
LCSG ▷ C2×C42×C19 ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2724

Complements

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

NH ≅ G/Ntype
1. #14564869C2semidirect
3. #14561458C2semidirect
4. #14561456C2semidirect
5. C19×#2724C2semidirect
132. #2724D19semidirect
206. C19#7736semidirect

Maximal subgroups

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

subgroupindex
#145648692
#145647052
#145614582
#145614562
C19×#27242
#773619