Finite Group Databasebeta

← #18078265

Subgroups — #18078265

Order 4864.

694 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 694 conjugacy classes of subgroups — too many to draw. Only its 143 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
1C2×#11926390C211yesmaximal, characteristic
2#14563703C211yesmaximal, characteristic
3C2×#11926281C212yesmaximal
4#14561513C212yesmaximal
5C19×#2855C211yesmaximal, characteristic
6C22×C4×Dic19—21no—
7C2×C22⋊(C19⋊C8)C2212yes—
8#11926390—24no—
9C2×C19⋊#95—21no—
10C2×C19⋊#95C2212yes—
11#11926299—22no—
12#11926281—24no—
13C2×C19×C22⋊Q8C2211yescharacteristic
14C22×C42×C19C2211yescharacteristic
15C19×#391C412yescomplemented
16C19×#389C412yescomplemented
17C19×#387—22no—
18C19×#385—21no—
19C19×#381—21no—
20C19×#380C2211yescharacteristic
21C22×Q8×C19C2×C411yescharacteristic
22C23×C4×C19D411yescharacteristic
23C23×C4×C19D411yescharacteristic
24C23×C4×C19C2311yescharacteristic
25C23×Dic19—22no—
26C19×C22⋊Q8—22no—
27C19×C22⋊Q8—22no—
28C2×C4⋊C4×C19—22no—
29C2×C4⋊C4×C19—21no—
30C2×C4⋊C4×C19C2×C411yescharacteristic
31C2×C4⋊C4×C19C2×C412yes—
32C2×C22⋊C4×C19—21no—
33C2×C22⋊C4×C19—21no—
34C2×C42×C19—22no—
35C2×C42×C19—22no—
36C2×C42×C19C2×C412yes—
37C2×C42×C19D412yes—
38C2×C4×Dic19—24no—
39C2×C4×Dic19—28no—
40C22×C19⋊C8—22no—
41C19×#95—22no—
42C19×#95—22no—
43C19×#95—22no—
44C19×#95—21no—
45C19⋊#95—24no—
46C19⋊#95—22no—
47C19⋊#95D414yes—
48C22⋊(C19⋊C8)—22no—
49C22⋊(C19⋊C8)—22no—
50C24×C19C2×D411yescharacteristic
51C2×Q8×C19—22no—
52C2×Q8×C19—42no—
53C22×C4×C19—21no—
54C22×C4×C19—21no—
55C22×C4×C19—24no—
56C22×C4×C19—21no—
57C22×C4×C19—21no—
58C22×C4×C19—22no—
59C22×C4×C19—22no—
60C22×C4×C19—21no—
61C22×C4×C19—22no—
62C22×C4×C19—21no—
63C22×C4×C19—42no—
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—28no—
71C22×Dic19—24no—
72C22×Dic19—44no—
73C22×Dic19—42no—
74C22×Dic19—42no—
75C4⋊C4×C19—22no—
76C4⋊C4×C19—42no—
77C4⋊C4×C19—44no—
78C4⋊C4×C19—42no—
79C22⋊C4×C19—41no—
80C22⋊C4×C19—41no—
81C22⋊C4×C19—42no—
82C42×C19—24no—
83C42×C19—24no—
84C4×Dic19—216no—
85C2×C19⋊C8—44no—
86C2×C19⋊C8—42no—
87#9145—191nomaximal, Sylow
88C23×C19—22no—
89C23×C19—22no—
90C23×C19C2×C22⋊C411yescharacteristic
91C23×C19#12011yescharacteristic
92C23×C19#12311yescharacteristic
93C23×C19#13512yes—
94C23×C19#13712yes—
95Q8×C19—82no—
96C2×C4×C19—24no—
97C2×C4×C19—24no—
98C2×C4×C19—22no—
99C2×C4×C19—22no—
100C2×C4×C19—22no—
101C2×C4×C19—22no—
102C2×C4×C19—22no—
103C2×C4×C19—22no—
104C2×C4×C19—22no—
105C2×C4×C19—42no—
106C2×C4×C19—42no—
107C2×C4×C19—42no—
108C2×C4×C19—42no—
109C2×C4×C19—41no—
110C2×C4×C19—41no—
111C2×C4×C19—42no—
112C2×C4×C19—42no—
113C2×C4×C19—42no—
114C2×C4×C19—42no—
115C2×C4×C19—42no—
116C2×C4×C19#10414yes—
117C2×C4×C19C4×D412yes—
118C2×C4×C19#12112yes—
119C2×Dic19—28no—
120C2×Dic19—44no—
121C2×Dic19—48no—
122C2×Dic19—48no—
123C2×Dic19—44no—
124C19⋊C8—82no—
125#2855D1911yescharacteristic
126C2×#376—191no—
127#1817—191no—
128C2×#328—192no—
129#1294—192no—
130C22×C19—21no—
131C22×C19—21no—
132C22×C19—21no—
133C22×C19—21no—
134C22×C19—24no—
135C22×C19—24no—
136C22×C19#38611yescharacteristic
137C22×C19#41012yes—
138C22×C19#41611yescharacteristic
139C22×C19#41911yescharacteristic
140C22×C19C2×#10412yes—
141C22×C19#45212yes—
142C22×C19#48512yes—
143C4×C19—24no—
144C4×C19—22no—
145C4×C19—22no—
146C4×C19—42no—
147C4×C19—81no—
148C4×C19—81no—
149C4×C19—82no—
150Dic19—48no—
151C2×C22⋊Q8C2×D1911yescharacteristic
152C22×C42—381no—
153C22×C42C2×D1911yescharacteristic
154C2×C22⋊C8—192no—
155#391Dic1912yescomplemented
156#389Dic1912yescomplemented
157#387—22no—
158#385—21no—
159#381—21no—
160#380C2×D1911yescharacteristic
161#376—384no—
162C2×#95—192no—
163C2×#95—381no—
164#336—382no—
165#328—384no—
166C2×C19—22no—
167C2×C19—22no—
168C2×C19#150012yes—
169C2×C19#150612yes—
170C2×C19#187311yescharacteristic
171C2×C19#189611yescharacteristic
172C2×C19#189911yescharacteristic
173C22×Q8C2×Dic1911yescharacteristic
174C23×C4—382no—
175C23×C4C22⋊D1911yescharacteristic
176C23×C4C22⋊D1911yescharacteristic
177C23×C4C22×D1911yescharacteristic
178C22×C8—382no—
179C22⋊Q8—22no—
180C22⋊Q8—22no—
181C2×C4⋊C4—22no—
182C2×C4⋊C4—21no—
183C2×C4⋊C4C2×Dic1911yescharacteristic
184C2×C4⋊C4C2×Dic1912yes—
185C2×C22⋊C4—21no—
186C2×C22⋊C4—21no—
187C2×C42—22no—
188C2×C42—22no—
189C2×C42—384no—
190C2×C42—388no—
191C2×C42C2×Dic1912yes—
192C2×C42C22⋊D1912yes—
193C22⋊C8—382no—
194C22⋊C8—382no—
195#95—22no—
196#95—22no—
197#95—22no—
198#95—21no—
199#95—194no—
200#95—384no—
201#95—382no—
202C19#914511yescharacteristic, complemented, Sylow
203C24C2×C22⋊D1911yescharacteristic
204C2×Q8—22no—
205C2×Q8—42no—
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—24no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—22no—
212C22×C4—22no—
213C22×C4—22no—
214C22×C4—21no—
215C22×C4—21no—
216C22×C4—42no—
217C22×C4—388no—
218C22×C4—384no—
219C22×C4—764no—
220C22×C4—762no—
221C22×C4—762no—
222C22×C4C22⋊Dic1912yes—
223C22×C4C22⋊Dic1912yes—
224C22×C4D4×D1912yes—
225C22×C4#6454312yes—
226C22×C4C22×Dic1911yescharacteristic
227C22×C4C2×C22⋊D1911yescharacteristic
228C2×C8—764no—
229C2×C8—762no—
230C4⋊C4—22no—
231C4⋊C4—42no—
232C4⋊C4—42no—
233C4⋊C4—44no—
234C22⋊C4—41no—
235C22⋊C4—41no—
236C22⋊C4—42no—
237C42—24no—
238C42—24no—
239C42—3816no—
240C23—22no—
241C23—22no—
242C23#1059738111yescharacteristic
243C23#1059738311yescharacteristic
244C23#1059738812yes—
245C23#1059739612yes—
246C23C2×C22⋊Dic1911yescharacteristic
247Q8—82no—
248C2×C4—24no—
249C2×C4—24no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—22no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4—42no—
261C2×C4—42no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—42no—
267C2×C4—42no—
268C2×C4—388no—
269C2×C4—768no—
270C2×C4—768no—
271C2×C4—764no—
272C2×C4—764no—
273C2×C4#1059729414yes—
274C2×C4D4×Dic1912yes—
275C2×C4#1059738512yes—
276C8—1522no—
277C22—24no—
278C22—24no—
279C22—21no—
280C22—21no—
281C22—21no—
282C22—21no—
283C22#1192642411yescharacteristic
284C22#1192651812yes—
285C22#1192654011yescharacteristic
286C22#1192655311yescharacteristic
287C22C2×#1059729412yes—
288C22#1192670412yes—
289C22#1192688212yes—
290C4—24no—
291C4—22no—
292C4—22no—
293C4—42no—
294C4—82no—
295C4—81no—
296C4—81no—
297C4—768no—
298C2—22no—
299C2—22no—
300C2#1456212112yes—
301C2#1456214712yes—
302C2#1456394811yescharacteristic
303C2#1456407911yescharacteristic
304C2#1456409411yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic19
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#2855C2
socleC23×C19C2×C22⋊C4
prime radicalC24×C19C2×D4
cosocleC23×C4×C19C23
hypercenter#2855D19
hypocenterC19#9145
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2855

Complements

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

NH ≅ G/Ntype
15. C19×#391C4semidirect
16. C19×#389C4semidirect
155. #391Dic19semidirect
156. #389Dic19semidirect
202. C19#9145semidirect

Maximal subgroups

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

subgroupindex
C2×#119263902
#145637032
C2×#119262812
#145615132
C19×#28552
#914519