Finite Group Databasebeta

← #18078598

Subgroups — #18078598

Order 4864.

516 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 119 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#14566238C211yesmaximal, characteristic
2#14562207C212yesmaximal
3C2×#11926270C211yesmaximal, characteristic
4#14561502C212yesmaximal
5C19×#2627C211yesmaximal, characteristic
6C2×C22⋊(C19⋊C8)C2212yes—
7#11926430—24no—
8#11926407—21no—
9#11926404C2212yes—
10C4×C22⋊Dic19—21no—
11#11926281—24no—
12#11926270—22no—
13C2×C19×C22⋊Q8C2211yescharacteristic
14C22×C4⋊C4×C19C2211yescharacteristic
15C19×#400C412yescomplemented
16C19×#398—22no—
17C19×#395C412yescomplemented
18C19×#385—21no—
19C19×#381—21no—
20C19×#380C2211yescharacteristic
21C22×Q8×C19C2×C411yescharacteristic
22C23×C4×C19D411yescharacteristic
23C23×C4×C19D411yescharacteristic
24C23×C4×C19C2311yescharacteristic
25C19×C22⋊Q8—22no—
26C19×C22⋊Q8—22no—
27C2×C4⋊C4×C19—22no—
28C2×C4⋊C4×C19—22no—
29C2×C4⋊C4×C19—21no—
30C2×C4⋊C4×C19—22no—
31C2×C4⋊C4×C19—21no—
32C2×C4⋊C4×C19C2×C411yescharacteristic
33C2×C4⋊C4×C19C2×C412yes—
34C2×C4⋊C4×C19D412yes—
35C2×C22⋊C4×C19—21no—
36C2×C22⋊C4×C19—21no—
37C2×C22⋊Dic19—22no—
38C2×C4⋊Dic19—22no—
39C2×C4×Dic19—22no—
40C22×C19⋊C8—22no—
41C19×#95—22no—
42C19×#95—22no—
43C19×#95—22no—
44C19×#95C2×C412yes—
45C19⋊#95—22no—
46C19⋊#95—24no—
47C19⋊#95D414yes—
48C22⋊(C19⋊C8)—22no—
49C22⋊(C19⋊C8)—22no—
50C24×C19C2×D411yescharacteristic
51C2×Q8×C19—22no—
52C2×Q8×C19—81no—
53C22×C4×C19—21no—
54C22×C4×C19—21no—
55C22×C4×C19—21no—
56C22×C4×C19—22no—
57C22×C4×C19—22no—
58C22×C4×C19—21no—
59C22×C4×C19—21no—
60C22×C4×C19—22no—
61C22×C4×C19—21no—
62C22×C4×C19—81no—
63C22×C4×C19—81no—
64C22×C4×C19C22⋊C412yes—
65C22×C4×C19C22⋊C412yes—
66C22×C4×C19C22×C411yescharacteristic
67C22×C4×C19C2×D412yes—
68C22×C4×C19C2×D411yescharacteristic
69C22×C4×C19#4112yes—
70C22×Dic19—24no—
71C4⋊C4×C19—24no—
72C4⋊C4×C19—24no—
73C4⋊C4×C19—22no—
74C4⋊C4×C19—42no—
75C4⋊C4×C19—81no—
76C4⋊C4×C19—82no—
77C22⋊C4×C19—41no—
78C22⋊C4×C19—41no—
79C22⋊C4×C19—42no—
80C22⋊Dic19—42no—
81C22⋊Dic19—42no—
82C4⋊Dic19—82no—
83C4×Dic19—82no—
84C2×C19⋊C8—42no—
85C2×C19⋊C8—82no—
86#9202—191nomaximal, Sylow
87C23×C19—41no—
88C23×C19—41no—
89C23×C19C2×C22⋊C411yescharacteristic
90C23×C19#12011yescharacteristic
91C23×C19#12311yescharacteristic
92C23×C19#13512yes—
93C23×C19#13712yes—
94Q8×C19—82no—
95C2×C4×C19—22no—
96C2×C4×C19—22no—
97C2×C4×C19—22no—
98C2×C4×C19—22no—
99C2×C4×C19—42no—
100C2×C4×C19—42no—
101C2×C4×C19—41no—
102C2×C4×C19—41no—
103C2×C4×C19—42no—
104C2×C4×C19—42no—
105C2×C4×C19—42no—
106C2×C4×C19—42no—
107C2×C4×C19—42no—
108C2×C4×C19—42no—
109C2×C4×C19—42no—
110C2×C4×C19—42no—
111C2×C4×C19—41no—
112C2×C4×C19—41no—
113C2×C4×C19—42no—
114C2×C4×C19—81no—
115C2×C4×C19C4×D412yes—
116C2×C4×C19#12112yes—
117C2×Dic19—44no—
118C2×Dic19—44no—
119C2×Dic19—44no—
120C19⋊C8—82no—
121#2627D1911yescharacteristic
122#2313—191no—
123#1520—192no—
124C2×#324—191no—
125#1289—192no—
126C22×C19—21no—
127C22×C19—21no—
128C22×C19—21no—
129C22×C19—21no—
130C22×C19—21no—
131C22×C19—21no—
132C22×C19—42no—
133C22×C19—42no—
134C22×C19#38611yescharacteristic
135C22×C19#41611yescharacteristic
136C22×C19#41911yescharacteristic
137C22×C19#45212yes—
138C22×C19#48512yes—
139C4×C19—22no—
140C4×C19—22no—
141C4×C19—42no—
142C4×C19—42no—
143C4×C19—82no—
144C4×C19—81no—
145C4×C19—81no—
146Dic19—84no—
147C2×C22⋊Q8C2×D1911yescharacteristic
148C22×C4⋊C4C2×D1911yescharacteristic
149C2×C22⋊C8—192no—
150#400Dic1912yescomplemented
151#398—22no—
152#395Dic1912yescomplemented
153#387—384no—
154#385—21no—
155#381—21no—
156#381—381no—
157#380—192no—
158#380C2×D1911yescharacteristic
159C4×C22⋊C4—381no—
160#328—384no—
161#324—382no—
162C2×C19—22no—
163C2×C19—21no—
164C2×C19—21no—
165C2×C19—22no—
166C2×C19#187311yescharacteristic
167C2×C19#191211yescharacteristic
168C2×C19#191311yescharacteristic
169C22×Q8C2×Dic1911yescharacteristic
170C23×C4C22⋊D1911yescharacteristic
171C23×C4C22⋊D1911yescharacteristic
172C23×C4C22×D1911yescharacteristic
173C22×C8—382no—
174C22⋊Q8—22no—
175C22⋊Q8—22no—
176C2×C4⋊C4—22no—
177C2×C4⋊C4—22no—
178C2×C4⋊C4—21no—
179C2×C4⋊C4—22no—
180C2×C4⋊C4—21no—
181C2×C4⋊C4—382no—
182C2×C4⋊C4C2×Dic1911yescharacteristic
183C2×C4⋊C4C2×Dic1912yes—
184C2×C4⋊C4C22⋊D1912yes—
185C2×C22⋊C4—21no—
186C2×C22⋊C4—21no—
187C2×C22⋊C4—382no—
188C2×C42—382no—
189C22⋊C8—382no—
190C22⋊C8—382no—
191#95—22no—
192#95—22no—
193#95—22no—
194#95—194no—
195#95—382no—
196#95—384no—
197#95C2×Dic1912yes—
198C19#920211yescharacteristic, complemented, Sylow
199C24C2×C22⋊D1911yescharacteristic
200C2×Q8—22no—
201C2×Q8—81no—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—21no—
205C22×C4—22no—
206C22×C4—22no—
207C22×C4—21no—
208C22×C4—21no—
209C22×C4—22no—
210C22×C4—21no—
211C22×C4—81no—
212C22×C4—81no—
213C22×C4—384no—
214C22×C4C22⋊Dic1912yes—
215C22×C4C22⋊Dic1912yes—
216C22×C4D4×D1912yes—
217C22×C4#6454312yes—
218C22×C4C22×Dic1911yescharacteristic
219C22×C4C2×C22⋊D1911yescharacteristic
220C2×C8—762no—
221C2×C8—1522no—
222C4⋊C4—24no—
223C4⋊C4—24no—
224C4⋊C4—22no—
225C4⋊C4—42no—
226C4⋊C4—81no—
227C4⋊C4—82no—
228C4⋊C4—1522no—
229C22⋊C4—41no—
230C22⋊C4—41no—
231C22⋊C4—42no—
232C22⋊C4—762no—
233C22⋊C4—762no—
234C42—1522no—
235C23—41no—
236C23—41no—
237C23#1059738111yescharacteristic
238C23#1059738311yescharacteristic
239C23#1059738812yes—
240C23#1059739612yes—
241C23C2×C22⋊Dic1911yescharacteristic
242Q8—82no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—41no—
248C2×C4—42no—
249C2×C4—42no—
250C2×C4—41no—
251C2×C4—42no—
252C2×C4—42no—
253C2×C4—42no—
254C2×C4—42no—
255C2×C4—42no—
256C2×C4—42no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—81no—
263C2×C4—764no—
264C2×C4—764no—
265C2×C4—764no—
266C2×C4D4×Dic1912yes—
267C2×C4#1059738512yes—
268C8—1522no—
269C22—21no—
270C22—21no—
271C22—21no—
272C22—21no—
273C22—21no—
274C22—21no—
275C22—42no—
276C22—42no—
277C22#1192642411yescharacteristic
278C22#1192654011yescharacteristic
279C22#1192655311yescharacteristic
280C22#1192670412yes—
281C22#1192688212yes—
282C4—22no—
283C4—22no—
284C4—42no—
285C4—42no—
286C4—82no—
287C4—81no—
288C4—81no—
289C4—1524no—
290C2—21no—
291C2—22no—
292C2—21no—
293C2—22no—
294C2#1456394811yescharacteristic
295C2#1456417311yescharacteristic
296C2#1456417811yescharacteristic
subgroupG/H
centerC22#11926424
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#2627C2
socleC22×C19#386
prime radicalC24×C19C2×D4
cosocleC23×C4×C19C23
hypercenter#2627D19
hypocenterC19#9202
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2627

Complements

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

NH ≅ G/Ntype
15. C19×#400C4semidirect
17. C19×#395C4semidirect
150. #400Dic19semidirect
152. #395Dic19semidirect
198. C19#9202semidirect

Maximal subgroups

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

subgroupindex
#145662382
#145622072
C2×#119262702
#145615022
C19×#26272
#920219