Finite Group Databasebeta

← #18085540

Subgroups — #18085540

Order 4864.

500 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 105 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#14569605C211yesmaximal, characteristic
2#14563722C212yesmaximal
3#14561902C211yesmaximal, characteristic
4#14561515C212yesmaximal
5C19×#1280C211yesmaximal, characteristic
6C22×C4⋊Dic19C2211yescharacteristic
7#11926486—22no—
8#11926478—22no—
9#11926417—22no—
10#11926404C2212yes—
11C2×C19⋊#95—22no—
12C2×C19⋊#95C2211yescharacteristic
13#11926307—22no—
14#11926307—22no—
15C2×C19×C22⋊C8C2212yes—
16C2×C19×#95C2211yescharacteristic
17C23×C4×C19D412yes—
18C23×C4×C19C2311yescharacteristic
19C23×Dic19—21no—
20C23×Dic19—21no—
21C22×C8×C19—22no—
22C2×C22⋊Dic19—22no—
23C2×C4⋊Dic19—22no—
24C2×C4⋊Dic19—22no—
25C2×C4⋊Dic19—21no—
26C2×C4⋊Dic19D412yes—
27C2×C4⋊Dic19D412yes—
28C2×C4⋊Dic19Q812yes—
29C2×Dic19⋊C4—22no—
30C2×Dic19⋊C4—22no—
31C19×C22⋊C8—22no—
32C19×C22⋊C8—22no—
33C19×#95—22no—
34C19⋊#95—22no—
35C19⋊#95—22no—
36C19⋊#95—22no—
37C19⋊#95—22no—
38C19⋊#95—44no—
39C24×C19C2×D411yescharacteristic
40C22×C4×C19—22no—
41C22×C4×C19—22no—
42C22×C4×C19—22no—
43C22×C4×C19—42no—
44C22×C4×C19—42no—
45C22×C4×C19—42no—
46C22×C4×C19C2×D412yes—
47C22×C4×C19C2×Q811yescharacteristic
48C22×C4×C19#4112yes—
49C22×C4×C19#4111yescharacteristic
50C22×Dic19—22no—
51C22×Dic19—22no—
52C22×Dic19—22no—
53C22×Dic19—22no—
54C22×Dic19—41no—
55C22×Dic19—42no—
56C22×Dic19—41no—
57C22×Dic19—41no—
58C22×Dic19—41no—
59C22×Dic19—42no—
60C22×Dic19—42no—
61C22×Dic19—42no—
62C2×C8×C19—42no—
63C2×C8×C19—42no—
64C2×C8×C19—42no—
65C22⋊Dic19—42no—
66C22⋊Dic19—42no—
67C4⋊Dic19—24no—
68C4⋊Dic19—42no—
69C4⋊Dic19—42no—
70C4⋊Dic19—42no—
71Dic19⋊C4—82no—
72Dic19⋊C4—82no—
73#10346—191nomaximal, Sylow
74C23×C19—21no—
75C23×C19—21no—
76C23×C19—22no—
77C23×C19#12011yescharacteristic
78C23×C19C22⋊Q811yescharacteristic
79C23×C19#12411yescharacteristic
80C23×C19#13512yes—
81C23×C19AGL(1,ℤ/8)12yes—
82C2×C4×C19—22no—
83C2×C4×C19—22no—
84C2×C4×C19—41no—
85C2×C4×C19—42no—
86C2×C4×C19—41no—
87C2×C4×C19—44no—
88C2×C4×C19—42no—
89C2×C4×C19—42no—
90C2×C4×C19—42no—
91C2×C4×C19—82no—
92C2×C4×C19C22⋊Q812yes—
93C2×C4×C19#12412yes—
94C2×Dic19—44no—
95C2×Dic19—42no—
96C2×Dic19—42no—
97C2×Dic19—42no—
98C2×Dic19—42no—
99C2×Dic19—42no—
100C2×Dic19—42no—
101C2×Dic19—42no—
102C2×Dic19—42no—
103C2×Dic19—44no—
104C2×Dic19—82no—
105C2×Dic19—81no—
106C2×Dic19—82no—
107C2×Dic19—81no—
108C2×Dic19—81no—
109C2×Dic19—81no—
110C8×C19—82no—
111#2646—191no—
112#1823—192no—
113#1445—191no—
114#1294—192no—
115#1280D1911yescharacteristic
116C22×C19—22no—
117C22×C19—22no—
118C22×C19—22no—
119C22×C19—22no—
120C22×C19—21no—
121C22×C19—21no—
122C22×C19—21no—
123C22×C19—21no—
124C22×C19#39311yescharacteristic
125C22×C19#44912yes—
126C22×C19#45511yescharacteristic
127C22×C19#45611yescharacteristic
128C22×C19#45812yes—
129C22×C19#47812yes—
130C22×C19#48811yescharacteristic
131C22×C19#49011yescharacteristic
132C4×C19—22no—
133C4×C19—22no—
134C4×C19—82no—
135Dic19—82no—
136Dic19—82no—
137Dic19—82no—
138Dic19—82no—
139C22×C4⋊C4—191no—
140C2×C22⋊C8C2×D1912yes—
141#400—382no—
142#398—382no—
143#385—382no—
144#380—192no—
145C2×#95—191no—
146C2×#95—382no—
147C2×#95C2×D1911yescharacteristic
148#340—382no—
149#340—382no—
150C2×C19—21no—
151C2×C19—22no—
152C2×C19—21no—
153C2×C19#160912yes—
154C2×C19#161212yes—
155C2×C19#202511yescharacteristic
156C2×C19#202811yescharacteristic
157C2×C19#203011yescharacteristic
158C23×C4—381no—
159C23×C4—381no—
160C23×C4D7612yes—
161C23×C4C22×D1911yescharacteristic
162C22×C8—22no—
163C2×C4⋊C4—192no—
164C2×C4⋊C4—192no—
165C2×C4⋊C4—192no—
166C2×C4⋊C4—382no—
167C2×C4⋊C4—382no—
168C2×C4⋊C4—381no—
169C2×C4⋊C4—382no—
170C2×C4⋊C4—382no—
171C2×C22⋊C4—382no—
172C22⋊C8—22no—
173C22⋊C8—22no—
174#95—22no—
175#95—382no—
176#95—382no—
177#95—382no—
178#95—382no—
179#95—764no—
180C19#1034611yescharacteristic, complemented, Sylow
181C24C2×D7611yescharacteristic
182C22×C4—22no—
183C22×C4—22no—
184C22×C4—22no—
185C22×C4—42no—
186C22×C4—42no—
187C22×C4—42no—
188C22×C4—382no—
189C22×C4—382no—
190C22×C4—382no—
191C22×C4—382no—
192C22×C4—761no—
193C22×C4—762no—
194C22×C4—761no—
195C22×C4—761no—
196C22×C4—761no—
197C22×C4—762no—
198C22×C4—762no—
199C22×C4—762no—
200C22×C4#6454112yes—
201C22×C4D4×D1912yes—
202C22×C4#6454311yescharacteristic
203C22×C4Q8×D1911yescharacteristic
204C2×C8—42no—
205C2×C8—42no—
206C2×C8—42no—
207C4⋊C4—384no—
208C4⋊C4—762no—
209C4⋊C4—762no—
210C4⋊C4—762no—
211C4⋊C4—1522no—
212C4⋊C4—1522no—
213C22⋊C4—762no—
214C22⋊C4—762no—
215C23—21no—
216C23—21no—
217C23—22no—
218C23#1059732111yescharacteristic
219C23#1059732811yescharacteristic
220C23#1059734311yescharacteristic
221C23#1059735012yes—
222C23#1059735412yes—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—42no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—44no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—42no—
232C2×C4—82no—
233C2×C4—764no—
234C2×C4—762no—
235C2×C4—764no—
236C2×C4—762no—
237C2×C4—762no—
238C2×C4—762no—
239C2×C4—762no—
240C2×C4—762no—
241C2×C4—762no—
242C2×C4—762no—
243C2×C4—1522no—
244C2×C4—1521no—
245C2×C4—1521no—
246C2×C4—1521no—
247C2×C4—1521no—
248C2×C4—1522no—
249C2×C4#1059733112yes—
250C2×C4#1059734212yes—
251C8—82no—
252C22—22no—
253C22—22no—
254C22—22no—
255C22—22no—
256C22—21no—
257C22—21no—
258C22—21no—
259C22—21no—
260C22#1192645711yescharacteristic
261C22#1192669112yes—
262C22#1192672411yescharacteristic
263C22#1192672911yescharacteristic
264C22#1192673512yes—
265C22#1192684512yes—
266C22#1192689911yescharacteristic
267C22#1192690911yescharacteristic
268C4—22no—
269C4—22no—
270C4—82no—
271C4—1522no—
272C4—1522no—
273C4—1522no—
274C4—1522no—
275C2—21no—
276C2—22no—
277C2—21no—
278C2#1456263412yes—
279C2#1456265112yes—
280C2#1456478211yescharacteristic
281C2#1456479711yescharacteristic
282C2#1456480311yescharacteristic
subgroupG/H
centerC23#10597328
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
FittingC19×#1280C2
socleC23×C19#120
prime radicalC24×C19C2×D4
hypercenter#1280D19
hypocenterC19#10346
LCSG ▷ C23×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1280

Complements

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

NH ≅ G/Ntype
180. C19#10346semidirect

Maximal subgroups

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

subgroupindex
#145696052
#145637222
#145619022
#145615152
C19×#12802
#1034619