Finite Group Databasebeta

← #18071246

Subgroups — #18071246

Order 4864.

560 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 560 conjugacy classes of subgroups — too many to draw. Only its 83 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#14570565C211yesmaximal, characteristic, complemented
2#14564866C212yesmaximal, complemented
3#14561459C212yesmaximal, complemented
4#14561456C211yesmaximal, characteristic, complemented
5C19×#2011C211yesmaximal, characteristic
6C2×#10597381—21no—
7C2×#10597289—22no—
8C2×#10597289—22no—
9#11926474—21no—
10#11926469—22no—
11#11926442C2212yes—
12#11926419—22no—
13#11926299C2212yes—
14C22×D8×C19—21no—
15C2×C19×#127C2211yescharacteristic
16C2×C19×#102—21no—
17C19×#390C2211yescharacteristic
18C19×#336C2211yescharacteristic
19C22×D4×C19—22no—
20C22×D4×C19—21no—
21C22×D4×C19D411yescharacteristic
22C23×Dic19—21no—
23C2×D8×C19—42no—
24C2×D8×C19—42no—
25C2×D8×C19—42no—
26C22×C8×C19—21no—
27C19×#127—42no—
28C2×C4⋊C4×C19D411yescharacteristic
29C2×C22⋊C4×C19—22no—
30C2×C42×C19C2311yescharacteristic
31C2×C22⋊Dic19—22no—
32C2×C22⋊Dic19—21no—
33#10597381—42no—
34#10597381—42no—
35C2×C4⋊Dic19—21no—
36C2×C4⋊Dic19D412yes—
37C2×C4⋊Dic19D412yes—
38C2×Dic19⋊C4—22no—
39C22×C19⋊C8—22no—
40C19×#102—42no—
41#10597289—44no—
42#10597289—44no—
43C19⋊#95—22no—
44C19⋊#95—21no—
45C19⋊#95—22no—
46C24×C19—21no—
47C24×C19—41no—
48C2×D4×C19—22no—
49C2×D4×C19—24no—
50C2×D4×C19—21no—
51C2×D4×C19—41no—
52C2×D4×C19—41no—
53C2×D4×C19—41no—
54C2×D4×C19—42no—
55C2×D4×C19—42no—
56C2×D4×C19—41no—
57C2×D4×C19—42no—
58C2×D4×C19—41no—
59C2×D4×C19—41no—
60C2×D4×C19—42no—
61C2×D4×C19—41no—
62C2×D4×C19—42no—
63C2×D4×C19D812yes—
64C22×C4×C19—21no—
65C22×C4×C19C2×D412yes—
66C22×C4×C19C2×D411yescharacteristic
67C22×Dic19—22no—
68C22×Dic19—22no—
69C22×Dic19—42no—
70C22×Dic19—81no—
71C22×Dic19—81no—
72D8×C19—48no—
73C2×C8×C19—22no—
74C2×C8×C19—41no—
75C2×C8×C19—41no—
76C4⋊C4×C19—41no—
77C22⋊C4×C19—42no—
78C22⋊C4×C19—42no—
79C42×C19—41no—
80C22⋊Dic19—42no—
81C22⋊Dic19—44no—
82C4⋊Dic19—22no—
83C4⋊Dic19—22no—
84C4⋊Dic19—42no—
85C4⋊Dic19—81no—
86Dic19⋊C4—42no—
87Dic19⋊C4—42no—
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—42no—
98C23×C19—81no—
99C23×C19—82no—
100C23×C19—81no—
101C23×C19—82no—
102C23×C19#12011yescharacteristic
103D4×C19—42no—
104D4×C19—42no—
105D4×C19—42no—
106D4×C19—44no—
107D4×C19—44no—
108D4×C19—81no—
109D4×C19—81no—
110D4×C19—81no—
111D4×C19—82no—
112D4×C19—82no—
113C2×C4×C19—21no—
114C2×C4×C19—22no—
115C2×C4×C19—22no—
116C2×C4×C19—21no—
117C2×C4×C19—42no—
118C2×C4×C19—41no—
119C2×C4×C19C2×D811yescharacteristic
120C2×C4×C19#13512yes—
121C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
122C2×C4×C19AGL(1,ℤ/8)12yes—
123C2×Dic19—42no—
124C2×Dic19—42no—
125C2×Dic19—42no—
126C2×Dic19—42no—
127C2×Dic19—42no—
128C2×Dic19—42no—
129C2×Dic19—84no—
130C8×C19—42no—
131C19⋊C8—82no—
132#2724—191no—
133#2041—192no—
134#2011D1911yescharacteristic
135#1271—192no—
136#1270—191no—
137C22×C19—42no—
138C22×C19—44no—
139C22×C19—82no—
140C22×C19—81no—
141C22×C19—81no—
142C22×C19—82no—
143C22×C19—84no—
144C22×C19—161no—
145C22×C19—162no—
146C22×C19—161no—
147C22×C19#44711yescharacteristic
148C22×C19#44912yes—
149C22×C19#45311yescharacteristic
150C22×C19#45412yes—
151C22×C19B(4,𝔽2)11yescharacteristic
152C4×C19—21no—
153C4×C19—21no—
154C4×C19—22no—
155C4×C19—22no—
156C4×C19—81no—
157Dic19—82no—
158Dic19—82no—
159C22×D8—21no—
160C2×#127C2×D1911yescharacteristic
161C2×#123—381no—
162C2×#102—21no—
163C2×#102—382no—
164C2×#102—382no—
165#398—381no—
166#397—382no—
167#390C2×D1911yescharacteristic
168#389—192no—
169#385—382no—
170#336—192no—
171#336C2×D1911yescharacteristic
172C2×C19—82no—
173C2×C19—162no—
174C2×C19#159511yescharacteristic
175C2×C19#159712yes—
176C2×C19#162011yescharacteristic
177C2×C19#162512yes—
178C2×C19#165711yescharacteristic
179C22×D4—22no—
180C22×D4—21no—
181C22×D4C22⋊D1911yescharacteristic
182C23×C4—381no—
183C2×D8—42no—
184C2×D8—42no—
185C2×D8—42no—
186C22×C8—21no—
187C22×C8—382no—
188#127—42no—
189#123—762no—
190#123—762no—
191C2×C4⋊C4—192no—
192C2×C4⋊C4—192no—
193C2×C4⋊C4—382no—
194C2×C4⋊C4—381no—
195C2×C4⋊C4C22⋊D1911yescharacteristic
196C2×C22⋊C4—22no—
197C2×C22⋊C4—382no—
198C2×C22⋊C4—381no—
199C2×C42C22×D1911yescharacteristic
200#102—42no—
201#102—764no—
202#102—764no—
203#95—382no—
204#95—381no—
205#95—382no—
206C19#773611yescharacteristic, complemented, Sylow
207C24—21no—
208C24—41no—
209C2×D4—24no—
210C2×D4—22no—
211C2×D4—21no—
212C2×D4—41no—
213C2×D4—41no—
214C2×D4—41no—
215C2×D4—41no—
216C2×D4—42no—
217C2×D4—42no—
218C2×D4—42no—
219C2×D4—41no—
220C2×D4—41no—
221C2×D4—41no—
222C2×D4—42no—
223C2×D4—42no—
224C2×D4#6452512yes—
225C22×C4—21no—
226C22×C4—382no—
227C22×C4—382no—
228C22×C4—762no—
229C22×C4—1521no—
230C22×C4—1521no—
231C22×C4D4×D1912yes—
232C22×C4C2×C22⋊D1911yescharacteristic
233D8—48no—
234C2×C8—22no—
235C2×C8—41no—
236C2×C8—41no—
237C2×C8—762no—
238C2×C8—762no—
239C2×C8—762no—
240C4⋊C4—41no—
241C4⋊C4—382no—
242C4⋊C4—382no—
243C4⋊C4—762no—
244C4⋊C4—762no—
245C4⋊C4—762no—
246C4⋊C4—1521no—
247C22⋊C4—42no—
248C22⋊C4—42no—
249C22⋊C4—762no—
250C22⋊C4—764no—
251C42—41no—
252C23—22no—
253C23—42no—
254C23—41no—
255C23—42no—
256C23—41no—
257C23—42no—
258C23—81no—
259C23—82no—
260C23—81no—
261C23—82no—
262C23#1059738311yescharacteristic
263D4—42no—
264D4—42no—
265D4—44no—
266D4—44no—
267D4—42no—
268D4—81no—
269D4—82no—
270D4—82no—
271D4—81no—
272D4—81no—
273C2×C4—21no—
274C2×C4—22no—
275C2×C4—22no—
276C2×C4—21no—
277C2×C4—42no—
278C2×C4—41no—
279C2×C4—762no—
280C2×C4—762no—
281C2×C4—762no—
282C2×C4—762no—
283C2×C4—762no—
284C2×C4—762no—
285C2×C4—1524no—
286C2×C4#1059735712yes—
287C2×C4#1059735812yes—
288C2×C4C2×#6452511yescharacteristic
289C2×C4#1059739511yescharacteristic
290C8—42no—
291C8—1522no—
292C22—44no—
293C22—42no—
294C22—82no—
295C22—81no—
296C22—81no—
297C22—84no—
298C22—82no—
299C22—161no—
300C22—161no—
301C22—162no—
302C22#1192667711yescharacteristic
303C22#1192668612yes—
304C22#1192671111yescharacteristic
305C22#1192671512yes—
306C22#1192673011yescharacteristic
307C4—22no—
308C4—22no—
309C4—21no—
310C4—21no—
311C4—81no—
312C4—1522no—
313C4—1522no—
314C2—82no—
315C2—162no—
316C2#1456255211yescharacteristic
317C2#1456256112yes—
318C2#1456269211yescharacteristic
319C2#1456272212yes—
320C2#1456293111yescharacteristic
subgroupG/H
centerC23#10597383
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
Fitting, prime radicalC19×#2011C2
socleC23×C19#120
hypercenter#2011D19
hypocenterC19#7736
LCSG ▷ C2×C42×C19 ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2011

Complements

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

NH ≅ G/Ntype
1. #14570565C2semidirect
2. #14564866C2semidirect
3. #14561459C2semidirect
4. #14561456C2semidirect
206. C19#7736semidirect

Maximal subgroups

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

subgroupindex
#145705652
#145648662
#145614592
#145614562
C19×#20112
#773619