Finite Group Databasebeta

← #18071046

Subgroups — #18071046

Order 4864.

444 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 107 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#14572002C211yesmaximal, characteristic
2#14563381C211yesmaximal, characteristic, complemented
3#14561457C212yesmaximal, complemented
4#14561455C212yesmaximal
5C19×#1745C211yesmaximal, characteristic, complemented
6C2×#10597322—21no—
7C2×C4×C19⋊C8—21no—
8#11926446C411yescharacteristic
9#11926446C411yescharacteristic
10#11926446C2211yescharacteristic
11#11926442C411yescharacteristic
12#11926442C411yescharacteristic
13#11926442C2211yescharacteristic
14#11926435—21no—
15#11926435—21no—
16#11926435—21no—
17#11926299—21no—
18#11926299C2212yes—
19C2×C19×#97—21no—
20C43×C19C2211yescharacteristic
21C19×#336—21no—
22C19×#336C2212yes—
23C22×D76C2×C411yescharacteristic
24C22×C8×C19—22no—
25C2×C42×C19C2×C411yescharacteristic
26C2×C42×C19C2×C411yescharacteristic
27C2×C42×C19D411yescharacteristic
28C2×C42×C19D411yescharacteristic
29C2×C42×C19D411yescharacteristic
30C2×C42×C19D411yescharacteristic
31C2×C42×C19C2311yescharacteristic
32C2×(C2×D19)⋊C4—21no—
33C2×(C2×D19)⋊C4—21no—
34C2×(C2×D19)⋊C4—21no—
35C2×(C2×D19)⋊C4—21no—
36C2×(C2×D19)⋊C4—21no—
37C2×(C2×D19)⋊C4—21no—
38C2×C4⋊Dic19C2×C411yescharacteristic
39C2×C4⋊Dic19C2×C411yescharacteristic
40C2×C4⋊Dic19C2×C411yescharacteristic
41C2×Dic19⋊C4—21no—
42C2×Dic19⋊C4—21no—
43C2×Dic19⋊C4—21no—
44C22×C19⋊C8—22no—
45#10597322—44no—
46C19×#97—24no—
47C19⋊#95—21no—
48C19⋊#95—21no—
49C19⋊#95—21no—
50C4×C19⋊C8—24no—
51C23×D19—21no—
52C22×C4×C19C22⋊C411yescharacteristic
53C22×C4×C19C22⋊C411yescharacteristic
54C22×C4×C19C22⋊C411yescharacteristic
55C22×C4×C19C22⋊C411yescharacteristic
56C22×C4×C19C22×C411yescharacteristic
57C22×C4×C19C2×D411yescharacteristic
58C22×C4×C19C2×D411yescharacteristic
59C22×Dic19—21no—
60C22×Dic19—21no—
61C22×Dic19—21no—
62C2×D76—22no—
63C2×D76—41no—
64C2×D76—41no—
65C2×C8×C19—24no—
66C2×C8×C19—42no—
67C2×C8×C19—42no—
68C42×C19—22no—
69C42×C19—22no—
70C42×C19—22no—
71C42×C19—22no—
72C42×C19—22no—
73C42×C19—41no—
74C42×C19—41no—
75(C2×D19)⋊C4—42no—
76(C2×D19)⋊C4—42no—
77(C2×D19)⋊C4—42no—
78(C2×D19)⋊C4—42no—
79(C2×D19)⋊C4—42no—
80(C2×D19)⋊C4—42no—
81C4⋊Dic19—22no—
82C4⋊Dic19—41no—
83C4⋊Dic19—41no—
84Dic19⋊C4—42no—
85Dic19⋊C4—42no—
86Dic19⋊C4—42no—
87C2×C19⋊C8—24no—
88C2×C19⋊C8—42no—
89C2×C19⋊C8—42no—
90#7692—191nomaximal, Sylow
91C23×C19C2×C22⋊C411yescharacteristic
92C22×D19—41no—
93C22×D19—41no—
94C22×D19—41no—
95C22×D19—41no—
96C22×D19—41no—
97C22×D19—41no—
98C22×D19—41no—
99C2×C4×C19—21no—
100C2×C4×C19—21no—
101C2×C4×C19—21no—
102C2×C4×C19—21no—
103C2×C4×C19—21no—
104C2×C4×C19—21no—
105C2×C4×C19—21no—
106C2×C4×C19—21no—
107C2×C4×C19—21no—
108C2×C4×C19—21no—
109C2×C4×C19—21no—
110C2×C4×C19—21no—
111C2×C4×C19—21no—
112C2×C4×C19—21no—
113C2×C4×C19—21no—
114C2×C4×C19—21no—
115C2×C4×C19#10412yes—
116C2×C4×C19#10412yes—
117C2×C4×C19#13112yes—
118C2×C4×C19#13512yes—
119C2×C4×C19AGL(1,ℤ/8)12yes—
120C2×Dic19—41no—
121C2×Dic19—41no—
122C2×Dic19—41no—
123C2×Dic19—41no—
124C2×Dic19—41no—
125C2×Dic19—41no—
126C2×Dic19—41no—
127C2×Dic19—41no—
128C2×Dic19—41no—
129D76—82no—
130C8×C19—44no—
131C19⋊C8—44no—
132#2860—191no—
133#1745D1911yescharacteristic, complemented
134#1744—191no—
135#1271—192no—
136#1270—192no—
137C22×C19#40811yescharacteristic
138C22×C19#41011yescharacteristic
139C22×C19#41311yescharacteristic
140C22×C19#41611yescharacteristic
141C22×C19#41811yescharacteristic
142C22×C19C2×#10411yescharacteristic
143C22×C19C2×#10411yescharacteristic
144C2×D19—81no—
145C2×D19—81no—
146C2×D19—81no—
147C2×D19—81no—
148C2×D19—81no—
149C2×D19—81no—
150C2×D19—81no—
151C4×C19—22no—
152C4×C19—22no—
153C4×C19—22no—
154C4×C19—22no—
155C4×C19—22no—
156C4×C19—41no—
157C4×C19—41no—
158Dic19—81no—
159Dic19—81no—
160Dic19—81no—
161C2×#126—381no—
162C2×#97—21no—
163C2×C4×C8—381no—
164#390—191no—
165#390—191no—
166#390—191no—
167#389—191no—
168#389—191no—
169#389—191no—
170#388—381no—
171#388—381no—
172#388—381no—
173C43C2×D1911yescharacteristic
174#336—21no—
175#336—192no—
176#336—381no—
177#336C2×D1912yes—
178C2×C19#147311yescharacteristic
179C2×C19#148411yescharacteristic
180C2×C19#149411yescharacteristic
181C2×C19#150011yescharacteristic
182C2×C19#150511yescharacteristic
183C2×C19#152411yescharacteristic
184C2×C19#155311yescharacteristic
185D19—161no—
186C22×D4—191no—
187C22×C8—22no—
188C22×C8—382no—
189#126—764no—
190C2×C4⋊C4—191no—
191C2×C4⋊C4—191no—
192C2×C4⋊C4—191no—
193C2×C4⋊C4—381no—
194C2×C4⋊C4—381no—
195C2×C4⋊C4—381no—
196C2×C22⋊C4—381no—
197C2×C22⋊C4—381no—
198C2×C22⋊C4—381no—
199C2×C22⋊C4—381no—
200C2×C22⋊C4—381no—
201C2×C22⋊C4—381no—
202C2×C42C4×D1911yescharacteristic
203C2×C42C4×D1911yescharacteristic
204C2×C42D7611yescharacteristic
205C2×C42D7611yescharacteristic
206C2×C42C22⋊D1911yescharacteristic
207C2×C42C22⋊D1911yescharacteristic
208C2×C42C22×D1911yescharacteristic
209#97—24no—
210C4×C8—384no—
211#95—381no—
212#95—381no—
213#95—381no—
214C19#769211yescharacteristic, complemented, Sylow
215C24—381no—
216C2×D4—382no—
217C2×D4—761no—
218C2×D4—761no—
219C22×C4—381no—
220C22×C4—381no—
221C22×C4—381no—
222C22×C4(C2×D19)⋊C411yescharacteristic
223C22×C4(C2×D19)⋊C411yescharacteristic
224C22×C4(C2×D19)⋊C411yescharacteristic
225C22×C4(C2×D19)⋊C411yescharacteristic
226C22×C4C2×C4×D1911yescharacteristic
227C22×C4C2×D7611yescharacteristic
228C22×C4C2×C22⋊D1911yescharacteristic
229C2×C8—24no—
230C2×C8—42no—
231C2×C8—42no—
232C2×C8—384no—
233C2×C8—762no—
234C2×C8—762no—
235C4⋊C4—382no—
236C4⋊C4—761no—
237C4⋊C4—761no—
238C4⋊C4—762no—
239C4⋊C4—762no—
240C4⋊C4—762no—
241C22⋊C4—762no—
242C22⋊C4—762no—
243C22⋊C4—762no—
244C22⋊C4—762no—
245C22⋊C4—762no—
246C22⋊C4—762no—
247C42—22no—
248C42—22no—
249C42—22no—
250C42—22no—
251C42—22no—
252C42—41no—
253C42—41no—
254C23—761no—
255C23—761no—
256C23—761no—
257C23—761no—
258C23—761no—
259C23—761no—
260C23—761no—
261C23C2×(C2×D19)⋊C411yescharacteristic
262D4—1522no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—761no—
280C2×C4—761no—
281C2×C4—761no—
282C2×C4—761no—
283C2×C4—761no—
284C2×C4—761no—
285C2×C4—761no—
286C2×C4—761no—
287C2×C4—761no—
288C2×C4#1059726212yes—
289C2×C4#1059728212yes—
290C2×C4#1059735312yes—
291C2×C4#1059735412yes—
292C2×C4#1059739612yes—
293C8—44no—
294C8—764no—
295C22—1521no—
296C22—1521no—
297C22—1521no—
298C22—1521no—
299C22—1521no—
300C22—1521no—
301C22—1521no—
302C22#1192651211yescharacteristic
303C22#1192651711yescharacteristic
304C22#1192652611yescharacteristic
305C22#1192653811yescharacteristic
306C22#1192655011yescharacteristic
307C22C2×#1059728211yescharacteristic
308C22C2×#1059726211yescharacteristic
309C4—22no—
310C4—22no—
311C4—22no—
312C4—22no—
313C4—22no—
314C4—41no—
315C4—41no—
316C4—1521no—
317C4—1521no—
318C4—1521no—
319C2—3041no—
320C2#1456200511yescharacteristic
321C2#1456205311yescharacteristic
322C2#1456209311yescharacteristic
323C2#1456211911yescharacteristic
324C2#1456214411yescharacteristic
325C2#1456222411yescharacteristic
326C2#1456234111yescharacteristic
subgroupG/H
centerC23C2×(C2×D19)⋊C4
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1745C2
socleC23×C19C2×C22⋊C4
prime radicalC22×D76C2×C4
cosocleC2×C42×C19C23
hypercenter#1745D19
hypocenterC19#7692
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C43 ◁ #1745

Complements

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

NH ≅ G/Ntype
2. #14563381C2semidirect
3. #14561457C2semidirect
5. C19×#1745C2semidirect
133. #1745D19semidirect
214. C19#7692semidirect

Maximal subgroups

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

subgroupindex
#145720022
#145633812
#145614572
#145614552
C19×#17452
#769219