Finite Group Databasebeta

← #18080960

Subgroups — #18080960

Order 4864.

370 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14564597C211yesmaximal, characteristic
2#14564393C211yesmaximal, characteristic
3#14563504C211yesmaximal, characteristic
4C2×#11926293C211yesmaximal, characteristic
5#14561519C211yesmaximal, characteristic
6#14561469C211yesmaximal, characteristic
7C19×#1987C211yesmaximal, characteristic
8C2×#10597264—21no—
9C2×C4⋊(C19⋊C8)C2211yescharacteristic
10C2×C4⋊(C19⋊C8)C2211yescharacteristic
11C2×#10597260—21no—
12C2×C4×C19⋊C8C2211yescharacteristic
13#11926414C2211yescharacteristic
14#11926306—21no—
15#11926306—21no—
16#11926306—21no—
17#11926299—21no—
18#11926293C414yescomplemented
19C2×C19×C4⋊Q8C2211yescharacteristic
20C2×C19×C4⋊C8C2211yescharacteristic
21C4×C4⋊C4×C19C2211yescharacteristic
22C19×#340—21no—
23C19×#340—21no—
24C22×Q8×C19—21no—
25C22×C8×C19—21no—
26C19×C4⋊Q8—21no—
27C19×C4⋊Q8—21no—
28C19×C4⋊Q8—21no—
29C19×C4⋊Q8C2×C412yes—
30C2×C4⋊C4×C19—21no—
31C2×C4⋊C4×C19—21no—
32C2×C4⋊C4×C19D411yescharacteristic
33C2×C4⋊C4×C19D411yescharacteristic
34C2×C42×C19—21no—
35C2×C42×C19C2311yescharacteristic
36C2×C4⋊Dic19—21no—
37C2×C4⋊Dic19—21no—
38C2×C4⋊Dic19—21no—
39C22×C19⋊C8—21no—
40C22×C19⋊C8—21no—
41C22×C19⋊C8D411yescharacteristic
42C22×C19⋊C8D411yescharacteristic
43C19×C4⋊C8—21no—
44C19×C4⋊C8—21no—
45C19×#95—21no—
46#10597264—42no—
47C4⋊(C19⋊C8)—21no—
48C4⋊(C19⋊C8)—21no—
49C4⋊(C19⋊C8)C2×C412yes—
50C4⋊(C19⋊C8)C2×C412yes—
51#10597260—42no—
52C4×C19⋊C8—21no—
53C4×C19⋊C8—21no—
54C2×Q8×C19—22no—
55C2×Q8×C19—41no—
56C2×Q8×C19—81no—
57C2×Q8×C19—81no—
58C22×C4×C19—21no—
59C22×C4×C19—21no—
60C22×C4×C19—41no—
61C22×C4×C19C2×D411yescharacteristic
62C22×C4×C19C2×D411yescharacteristic
63C22×C4×C19#4111yescharacteristic
64C22×Dic19—41no—
65C2×C8×C19—41no—
66C2×C8×C19—41no—
67C2×C8×C19—41no—
68C4⋊C4×C19—22no—
69C4⋊C4×C19—22no—
70C4⋊C4×C19—21no—
71C4⋊C4×C19—21no—
72C4⋊C4×C19—21no—
73C4⋊C4×C19—21no—
74C4⋊C4×C19—41no—
75C4⋊C4×C19—41no—
76C42×C19—41no—
77C42×C19—41no—
78C42×C19C22×C411yescharacteristic
79C42×C19#4111yescharacteristic
80C42×C19#4111yescharacteristic
81C42×C19#4111yescharacteristic
82C4⋊Dic19—41no—
83C4⋊Dic19—41no—
84C4⋊Dic19—41no—
85C4⋊Dic19—41no—
86C4⋊Dic19—81no—
87C2×C19⋊C8—21no—
88C2×C19⋊C8—21no—
89C2×C19⋊C8—22no—
90C2×C19⋊C8—22no—
91C2×C19⋊C8—21no—
92C2×C19⋊C8—21no—
93C2×C19⋊C8—21no—
94C2×C19⋊C8—41no—
95C2×C19⋊C8—41no—
96C2×C19⋊C8—41no—
97C2×C19⋊C8—41no—
98C2×C19⋊C8Q1612yes—
99#9576—191nomaximal, Sylow
100C23×C19#12111yescharacteristic
101Q8×C19—82no—
102Q8×C19—82no—
103C2×C4×C19—21no—
104C2×C4×C19—21no—
105C2×C4×C19—42no—
106C2×C4×C19—41no—
107C2×C4×C19—41no—
108C2×C4×C19—41no—
109C2×C4×C19—41no—
110C2×C4×C19—41no—
111C2×C4×C19—41no—
112C2×C4×C19—81no—
113C2×C4×C19—81no—
114C2×C4×C19#11711yescharacteristic
115C2×C4×C19C4×D411yescharacteristic
116C2×C4×C19C4×D411yescharacteristic
117C2×C4×C19#12311yescharacteristic
118C2×C4×C19#12411yescharacteristic
119C2×C4×C19#12611yescharacteristic
120C2×C4×C19C2×Q1611yescharacteristic
121C2×C4×C19#13511yescharacteristic
122C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
123C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
124C2×C4×C19#13711yescharacteristic
125C2×C4×C19#13711yescharacteristic
126C2×C4×C19#13711yescharacteristic
127C2×C4×C19#13711yescharacteristic
128C2×Dic19—81no—
129C2×Dic19—81no—
130C2×Dic19—81no—
131C8×C19—81no—
132C19⋊C8—22no—
133C19⋊C8—42no—
134C19⋊C8—42no—
135C19⋊C8—41no—
136#1990—191no—
137#1987D1911yescharacteristic
138#1947—191no—
139#1770—191no—
140C2×#333—191no—
141#1296—191no—
142#1277—191no—
143C22×C19#38811yescharacteristic
144C22×C19#46211yescharacteristic
145C22×C19#46311yescharacteristic
146C22×C19#46811yescharacteristic
147C22×C19#47011yescharacteristic
148C22×C19#47111yescharacteristic
149C22×C19#47211yescharacteristic
150C4×C19—21no—
151C4×C19—21no—
152C4×C19—82no—
153C4×C19—81no—
154C4×C19—81no—
155C4×C19C4×Q1611yescharacteristic
156C4×C19#44011yescharacteristic
157C4×C19#44011yescharacteristic
158C4×C19#44111yescharacteristic
159C4×C19#48411yescharacteristic
160C4×C19#48511yescharacteristic
161C4×C19#48911yescharacteristic
162C4×C19#49111yescharacteristic
163Dic19—161no—
164C2×C4⋊Q8C2×D1911yescharacteristic
165C2×#107—381no—
166C2×C4⋊C8—191no—
167C2×C4⋊C8—191no—
168C2×C4⋊C8C2×D1911yescharacteristic
169C2×#97—381no—
170C2×C4×C8—191no—
171#384—191no—
172C4×C4⋊C4C2×D1911yescharacteristic
173#340—21no—
174#340—21no—
175#340—381no—
176#340—381no—
177#340—381no—
178#336—381no—
179#333—194no—
180C2×C19#169211yescharacteristic
181C2×C19#169611yescharacteristic
182C2×C19#169711yescharacteristic
183C2×C19#170311yescharacteristic
184C2×C19#192811yescharacteristic
185C2×C19#193111yescharacteristic
186C2×C19#193511yescharacteristic
187C22×Q8—21no—
188C22×C8—21no—
189C22×C8—191no—
190C22×C8—191no—
191C22×C8—381no—
192C22×C8—381no—
193C4⋊Q8—21no—
194C4⋊Q8—21no—
195C4⋊Q8—21no—
196C4⋊Q8C4×D1912yes—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—381no—
200C2×C4⋊C4—381no—
201C2×C4⋊C4—381no—
202C2×C4⋊C4C22⋊D1911yescharacteristic
203C2×C4⋊C4C22⋊D1911yescharacteristic
204C2×C42—21no—
205C2×C42C22×D1911yescharacteristic
206#107—762no—
207C4⋊C8—21no—
208C4⋊C8—21no—
209C4⋊C8—192no—
210C4⋊C8—192no—
211C4⋊C8—381no—
212C4⋊C8—381no—
213#97—762no—
214C4×C8—381no—
215C4×C8—381no—
216#95—21no—
217C19#957611yescharacteristic, complemented, Sylow
218C2×Q8—22no—
219C2×Q8—41no—
220C2×Q8—81no—
221C2×Q8—81no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—41no—
225C22×C4—761no—
226C22×C4D4×D1911yescharacteristic
227C22×C4#6454311yescharacteristic
228C22×C4C2×C22⋊D1911yescharacteristic
229C2×C8—41no—
230C2×C8—41no—
231C2×C8—41no—
232C2×C8—192no—
233C2×C8—381no—
234C2×C8—381no—
235C2×C8—382no—
236C2×C8—381no—
237C2×C8—381no—
238C2×C8—381no—
239C2×C8—382no—
240C2×C8—761no—
241C2×C8—761no—
242C2×C8—761no—
243C2×C8—761no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—22no—
249C4⋊C4—22no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—761no—
253C4⋊C4—761no—
254C4⋊C4—761no—
255C4⋊C4—761no—
256C4⋊C4—1521no—
257C42—41no—
258C42—41no—
259C42C2×C4×D1911yescharacteristic
260C42#6454111yescharacteristic
261C42#6454311yescharacteristic
262C42#6454311yescharacteristic
263C23#1059738511yescharacteristic
264Q8—82no—
265Q8—82no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—42no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—81no—
276C2×C4—81no—
277C2×C4—1521no—
278C2×C4—1521no—
279C2×C4—1521no—
280C2×C4#1059732311yescharacteristic
281C2×C4#1059732511yescharacteristic
282C2×C4(C22⋊D19)⋊C411yescharacteristic
283C2×C4#1059732911yescharacteristic
284C2×C4#1059736011yescharacteristic
285C2×C4#1059736211yescharacteristic
286C2×C4Q16×D1911yescharacteristic
287C2×C4#1059736411yescharacteristic
288C2×C4C4×C22⋊D1911yescharacteristic
289C2×C4#1059738211yescharacteristic
290C2×C4#1059738811yescharacteristic
291C2×C4#1059738811yescharacteristic
292C2×C4#1059739511yescharacteristic
293C2×C4#1059739711yescharacteristic
294C8—81no—
295C8—382no—
296C8—761no—
297C8—762no—
298C8—762no—
299C22#1192643811yescharacteristic
300C22#1192675211yescharacteristic
301C22#1192676111yescharacteristic
302C22#1192679211yescharacteristic
303C22#1192680011yescharacteristic
304C22#1192680511yescharacteristic
305C22#1192681211yescharacteristic
306C4—21no—
307C4—21no—
308C4—81no—
309C4—81no—
310C4—82no—
311C4—3041no—
312C4#1192663611yescharacteristic
313C4#1192664211yescharacteristic
314C4#1192664711yescharacteristic
315C4#1192664911yescharacteristic
316C4#1192687811yescharacteristic
317C4#1192688311yescharacteristic
318C4#1192690311yescharacteristic
319C4#1192691211yescharacteristic
320C2#1456314311yescharacteristic
321C2#1456316111yescharacteristic
322C2#1456317011yescharacteristic
323C2#1456321211yescharacteristic
324C2#1456427911yescharacteristic
325C2#1456430011yescharacteristic
326C2#1456432811yescharacteristic
subgroupG/H
centerC23#10597385
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1987C2
socle, prime radicalC23×C19#121
cosocleC2×C42×C19C23
hypercenter#1987D19
hypocenterC19#9576
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1987

Complements

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

NH ≅ G/Ntype
18. #11926293C4semidirect
217. C19#9576semidirect

Maximal subgroups

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

subgroupindex
#145645972
#145643932
#145635042
C2×#119262932
#145615192
#145614692
C19×#19872
#957619