Finite Group Databasebeta

← #18080889

Subgroups — #18080889

Order 4864.

398 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14564597C211yesmaximal, characteristic
2#14564559C211yesmaximal, characteristic
3#14564394C211yesmaximal, characteristic
4#14563500C211yesmaximal, characteristic
5#14561519C211yesmaximal, characteristic
6#14561469C211yesmaximal, characteristic
7C2×C19×#332C211yesmaximal, characteristic
8C2×#10597275—21no—
9C2×C4⋊(C19⋊C8)C2211yescharacteristic
10C2×#10597292—21no—
11C2×#10597292—21no—
12C2×C4×C19⋊C8C2211yescharacteristic
13C2×C8×Dic19—21no—
14#11926414C2211yescharacteristic
15C4×C4⋊Dic19C2211yescharacteristic
16#11926307—21no—
17#11926306—21no—
18#11926306—21no—
19#11926298—21no—
20C2×C19×C4⋊Q8C2211yescharacteristic
21C2×C19×C4⋊C8C2211yescharacteristic
22C2×C19×C4⋊C8C2211yescharacteristic
23C19×#332C414yescomplemented
24C22×Q8×C19—21no—
25C22×C8×C19—21no—
26C22×C8×C19—21no—
27C19×C4⋊Q8—21no—
28C19×C4⋊Q8—21no—
29C19×C4⋊Q8—21no—
30C19×C4⋊Q8C2×C412yes—
31C2×C4⋊C4×C19—21no—
32C2×C4⋊C4×C19—21no—
33C2×C42×C19C2311yescharacteristic
34C2×C4⋊Dic19—21no—
35C2×C4⋊Dic19—21no—
36C2×C4⋊Dic19—21no—
37C2×C4⋊Dic19D411yescharacteristic
38C2×C4⋊Dic19D411yescharacteristic
39C2×C4×Dic19—21no—
40C22×C19⋊C8—21no—
41C22×C19⋊C8D411yescharacteristic
42C22×C19⋊C8D411yescharacteristic
43C19×C4⋊C8—21no—
44C19×C4⋊C8—21no—
45C19×C4⋊C8C2×C412yes—
46C19×C4⋊C8C2×C412yes—
47#10597292—42no—
48#10597292—42no—
49C19⋊#95—21no—
50#10597275—42no—
51C8×Dic19—42no—
52C4⋊(C19⋊C8)—21no—
53C4⋊(C19⋊C8)—21no—
54C4×C19⋊C8—21no—
55C4×C19⋊C8—21no—
56C2×Q8×C19—22no—
57C2×Q8×C19—41no—
58C2×Q8×C19—41no—
59C2×Q8×C19—41no—
60C2×Q8×C19—41no—
61C2×Q8×C19—41no—
62C22×C4×C19—41no—
63C22×C4×C19C2×D411yescharacteristic
64C22×C4×C19C2×D411yescharacteristic
65C22×C4×C19#4111yescharacteristic
66C22×Dic19—21no—
67C22×Dic19—21no—
68C22×Dic19—41no—
69C2×C8×C19—22no—
70C2×C8×C19—22no—
71C2×C8×C19—41no—
72C2×C8×C19—41no—
73C2×C8×C19—41no—
74C2×C8×C19—41no—
75C4⋊C4×C19—22no—
76C4⋊C4×C19—22no—
77C4⋊C4×C19—41no—
78C4⋊C4×C19—41no—
79C42×C19C22×C411yescharacteristic
80C42×C19#4111yescharacteristic
81C42×C19#4111yescharacteristic
82C42×C19#4111yescharacteristic
83C4⋊Dic19—21no—
84C4⋊Dic19—21no—
85C4⋊Dic19—41no—
86C4⋊Dic19—41no—
87C4⋊Dic19—41no—
88C4⋊Dic19—41no—
89C4⋊Dic19—81no—
90C4⋊Dic19D812yes—
91C4⋊Dic19SD1612yes—
92C4×Dic19—41no—
93C4×Dic19—41no—
94C2×C19⋊C8—21no—
95C2×C19⋊C8—21no—
96C2×C19⋊C8—21no—
97C2×C19⋊C8—21no—
98C2×C19⋊C8—21no—
99C2×C19⋊C8—41no—
100C2×C19⋊C8—41no—
101C2×C19⋊C8—41no—
102C2×C19⋊C8Q1612yes—
103#9566—191nomaximal, Sylow
104C23×C19#12111yescharacteristic
105Q8×C19—42no—
106Q8×C19—42no—
107Q8×C19—81no—
108Q8×C19—81no—
109C2×C4×C19—21no—
110C2×C4×C19—21no—
111C2×C4×C19—42no—
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×D811yescharacteristic
121C2×C4×C19C2×SD1611yescharacteristic
122C2×C4×C19C2×Q1611yescharacteristic
123C2×C4×C19#13511yescharacteristic
124C2×C4×C19#13511yescharacteristic
125C2×C4×C19#13511yescharacteristic
126C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
127C2×C4×C19#13711yescharacteristic
128C2×Dic19—22no—
129C2×Dic19—22no—
130C2×Dic19—41no—
131C2×Dic19—41no—
132C2×Dic19—41no—
133C2×Dic19—41no—
134C2×Dic19—81no—
135C2×Dic19—81no—
136C2×Dic19—81no—
137C8×C19—42no—
138C8×C19—42no—
139C19⋊C8—22no—
140C19⋊C8—41no—
141C19⋊C8—81no—
142#1990—191no—
143#1981—191no—
144#1947—191no—
145C8×C4⋊C4—191no—
146C2×#332D1911yescharacteristic
147#1296—191no—
148#1277—191no—
149C22×C19#38811yescharacteristic
150C22×C19#46211yescharacteristic
151C22×C19#46311yescharacteristic
152C22×C19#46511yescharacteristic
153C22×C19#46611yescharacteristic
154C22×C19#47111yescharacteristic
155C22×C19#47311yescharacteristic
156C4×C19—21no—
157C4×C19—21no—
158C4×C19—82no—
159C4×C19C4×D811yescharacteristic
160C4×C19C4×SD1611yescharacteristic
161C4×C19C4×Q1611yescharacteristic
162C4×C19#44011yescharacteristic
163C4×C19#48411yescharacteristic
164C4×C19#48511yescharacteristic
165C4×C19#48611yescharacteristic
166C4×C19#48811yescharacteristic
167Dic19—42no—
168Dic19—42no—
169Dic19—161no—
170C2×C4⋊Q8C2×D1911yescharacteristic
171C2×#107—381no—
172C2×C4⋊C8—191no—
173C2×C4⋊C8C2×D1911yescharacteristic
174C2×C4⋊C8C2×D1911yescharacteristic
175C2×#103—381no—
176C2×#103—381no—
177C2×C4×C8—191no—
178C2×C4×C8—381no—
179#384—191no—
180C4×C4⋊C4—191no—
181#340—381no—
182#340—381no—
183#340—381no—
184#336—381no—
185#332Dic1914yescomplemented
186C2×C19#167211yescharacteristic
187C2×C19#167411yescharacteristic
188C2×C19#167911yescharacteristic
189C2×C19#168111yescharacteristic
190C2×C19#192811yescharacteristic
191C2×C19#193011yescharacteristic
192C2×C19#193411yescharacteristic
193C22×Q8—21no—
194C22×C8—21no—
195C22×C8—21no—
196C22×C8—191no—
197C22×C8—191no—
198C22×C8—381no—
199C4⋊Q8—21no—
200C4⋊Q8—21no—
201C4⋊Q8—21no—
202C4⋊Q8C2×Dic1912yes—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—191no—
206C2×C4⋊C4—191no—
207C2×C4⋊C4—381no—
208C2×C4⋊C4—381no—
209C2×C4⋊C4—381no—
210C2×C42—381no—
211C2×C42C22×D1911yescharacteristic
212#107—762no—
213C4⋊C8—21no—
214C4⋊C8—21no—
215C4⋊C8—381no—
216C4⋊C8—381no—
217C4⋊C8C2×Dic1912yes—
218C4⋊C8C2×Dic1912yes—
219#103—762no—
220#103—762no—
221C4×C8—381no—
222C4×C8—381no—
223C4×C8—762no—
224#95—381no—
225C19#956611yescharacteristic, complemented, Sylow
226C2×Q8—22no—
227C2×Q8—41no—
228C2×Q8—41no—
229C2×Q8—41no—
230C2×Q8—41no—
231C2×Q8—41no—
232C22×C4—41no—
233C22×C4—381no—
234C22×C4—381no—
235C22×C4—761no—
236C22×C4#6454111yescharacteristic
237C22×C4D4×D1911yescharacteristic
238C22×C4D4×D1911yescharacteristic
239C2×C8—22no—
240C2×C8—22no—
241C2×C8—41no—
242C2×C8—41no—
243C2×C8—41no—
244C2×C8—41no—
245C2×C8—192no—
246C2×C8—381no—
247C2×C8—381no—
248C2×C8—381no—
249C2×C8—381no—
250C2×C8—381no—
251C2×C8—761no—
252C2×C8—761no—
253C2×C8—761no—
254C4⋊C4—22no—
255C4⋊C4—22no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—192no—
259C4⋊C4—192no—
260C4⋊C4—381no—
261C4⋊C4—381no—
262C4⋊C4—761no—
263C4⋊C4—761no—
264C4⋊C4—761no—
265C4⋊C4—761no—
266C4⋊C4—1521no—
267C42—761no—
268C42—761no—
269C42#6454111yescharacteristic
270C42#6454311yescharacteristic
271C42#6454311yescharacteristic
272C42C22×Dic1911yescharacteristic
273C23#1059733011yescharacteristic
274Q8—42no—
275Q8—42no—
276Q8—81no—
277Q8—81no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—42no—
281C2×C4—81no—
282C2×C4—81no—
283C2×C4—382no—
284C2×C4—382no—
285C2×C4—761no—
286C2×C4—761no—
287C2×C4—761no—
288C2×C4—761no—
289C2×C4—1521no—
290C2×C4—1521no—
291C2×C4—1521no—
292C2×C4#1059732511yescharacteristic
293C2×C4#1059732911yescharacteristic
294C2×C4#1059733111yescharacteristic
295C2×C4D8×D1911yescharacteristic
296C2×C4#1059735811yescharacteristic
297C2×C4SD16×D1911yescharacteristic
298C2×C4#1059736011yescharacteristic
299C2×C4#1059736111yescharacteristic
300C2×C4#1059736211yescharacteristic
301C2×C4Q16×D1911yescharacteristic
302C2×C4#1059736511yescharacteristic
303C2×C4#1059737211yescharacteristic
304C2×C4D4×Dic1911yescharacteristic
305C2×C4D4×Dic1911yescharacteristic
306C8—42no—
307C8—42no—
308C8—382no—
309C8—761no—
310C8—1521no—
311C22#1192643711yescharacteristic
312C22#1192675311yescharacteristic
313C22#1192676211yescharacteristic
314C22#1192677211yescharacteristic
315C22#1192677911yescharacteristic
316C22#1192681011yescharacteristic
317C22#1192681811yescharacteristic
318C4—21no—
319C4—21no—
320C4—82no—
321C4—3041no—
322C4—762no—
323C4—762no—
324C4D8×Dic1911yescharacteristic
325C4SD16×Dic1911yescharacteristic
326C4Q16×Dic1911yescharacteristic
327C4#1192664511yescharacteristic
328C4#1192687811yescharacteristic
329C4#1192688411yescharacteristic
330C4#1192688911yescharacteristic
331C4#1192689711yescharacteristic
332C2#1456301611yescharacteristic
333C2#1456302811yescharacteristic
334C2#1456306111yescharacteristic
335C2#1456307511yescharacteristic
336C2#1456427811yescharacteristic
337C2#1456429211yescharacteristic
338C2#1456432011yescharacteristic
subgroupG/H
centerC23#10597330
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC2×C19×#332C2
socle, prime radicalC23×C19#121
cosocleC2×C42×C19C23
hypercenterC2×#332D19
hypocenterC19#9566
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
23. C19×#332C4semidirect
185. #332Dic19semidirect
225. C19#9566semidirect

Maximal subgroups

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

subgroupindex
#145645972
#145645592
#145643942
#145635002
#145615192
#145614692
C2×C19×#3322
#956619