Finite Group Databasebeta

← #18075922

Subgroups — #18075922

Order 4864.

544 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14566033C211yesmaximal, characteristic
2#14561862C211yesmaximal, characteristic
3#14561515C212yesmaximal
4#14561515C212yesmaximal
5C19×#1817C211yesmaximal, characteristic
6#11926412—21no—
7#11926410C411yescharacteristic, complemented
8#11926410C411yescharacteristic, complemented
9#11926407—21no—
10#11926404C2211yescharacteristic
11#11926404C2211yescharacteristic
12C4×C4⋊Dic19C411yescharacteristic, complemented
13C4×C4⋊Dic19C411yescharacteristic, complemented
14C4×C22⋊Dic19—21no—
15#11926390—21no—
16C2×C19⋊#95—21no—
17C2×C19⋊#95—21no—
18C2×C19⋊#95C2212yes—
19C22×C42×C19C2211yescharacteristic
20C2×C19×C22⋊C8C2212yes—
21C19×#336—21no—
22C19×#336—21no—
23C23×C4×C19D411yescharacteristic
24C23×C4×C19D411yescharacteristic
25C23×C4×C19C2311yescharacteristic
26C23×Dic19—22no—
27C22×C8×C19—22no—
28C2×C42×C19—24no—
29C2×C42×C19C2×C411yescharacteristic
30C2×C42×C19C2×C411yescharacteristic
31C2×C42×C19D411yescharacteristic
32C2×C42×C19D411yescharacteristic
33C2×C22⋊Dic19—21no—
34C2×C22⋊Dic19—21no—
35C2×C4⋊Dic19C2×C411yescharacteristic
36C2×C4⋊Dic19C2×C411yescharacteristic
37C2×C4⋊Dic19C2×C411yescharacteristic
38C2×C4⋊Dic19C2×C411yescharacteristic
39C2×C4×Dic19—21no—
40C2×C4×Dic19—21no—
41C19×C22⋊C8—24no—
42C19⋊#95—24no—
43C19⋊#95—21no—
44C19⋊#95—21no—
45C19⋊#95—21no—
46C19⋊#95—21no—
47C19⋊#95—21no—
48C19⋊#95—21no—
49C19⋊#95—21no—
50C19⋊#95—21no—
51C19⋊#95—24no—
52C19⋊#95—42no—
53C24×C19C2×D411yescharacteristic
54C22×C4×C19—22no—
55C22×C4×C19—22no—
56C22×C4×C19—22no—
57C22×C4×C19—21no—
58C22×C4×C19—21no—
59C22×C4×C19—22no—
60C22×C4×C19—41no—
61C22×C4×C19—41no—
62C22×C4×C19—41no—
63C22×C4×C19C22⋊C411yescharacteristic
64C22×C4×C19C22⋊C411yescharacteristic
65C22×C4×C19C22⋊C411yescharacteristic
66C22×C4×C19C22⋊C411yescharacteristic
67C22×C4×C19C22×C411yescharacteristic
68C22×C4×C19C2×D411yescharacteristic
69C22×C4×C19#4114yes—
70C22×Dic19—24no—
71C22×Dic19—21no—
72C22×Dic19—21no—
73C22×Dic19—21no—
74C22×Dic19—21no—
75C22×Dic19—42no—
76C22×Dic19—42no—
77C22×Dic19—42no—
78C22×Dic19—42no—
79C22×Dic19—42no—
80C22×Dic19—42no—
81C2×C8×C19—42no—
82C2×C8×C19—42no—
83C2×C8×C19—42no—
84C42×C19—22no—
85C42×C19—22no—
86C42×C19—22no—
87C42×C19—22no—
88C22⋊Dic19—42no—
89C22⋊Dic19—41no—
90C22⋊Dic19—41no—
91C4⋊Dic19—41no—
92C4⋊Dic19—41no—
93C4⋊Dic19—41no—
94C4⋊Dic19—41no—
95C4×Dic19—42no—
96C4×Dic19—42no—
97#8714—191nomaximal, Sylow
98C23×C19—21no—
99C23×C19—21no—
100C23×C19—21no—
101C23×C19—21no—
102C23×C19C2×C22⋊C411yescharacteristic
103C23×C19#12312yes—
104C23×C19#13512yes—
105C23×C19AGL(1,ℤ/8)11yescharacteristic
106C23×C19#13711yescharacteristic
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—21no—
116C2×C4×C19—21no—
117C2×C4×C19—21no—
118C2×C4×C19—21no—
119C2×C4×C19—21no—
120C2×C4×C19—21no—
121C2×C4×C19—21no—
122C2×C4×C19—44no—
123C2×C4×C19—44no—
124C2×C4×C19—42no—
125C2×C4×C19—42no—
126C2×C4×C19#10412yes—
127C2×C4×C19#11712yes—
128C2×C4×C19#12312yes—
129C2×Dic19—44no—
130C2×Dic19—44no—
131C2×Dic19—44no—
132C2×Dic19—41no—
133C2×Dic19—41no—
134C2×Dic19—41no—
135C2×Dic19—41no—
136C2×Dic19—41no—
137C2×Dic19—41no—
138C2×Dic19—41no—
139C2×Dic19—41no—
140C2×Dic19—41no—
141C2×Dic19—41no—
142C2×Dic19—41no—
143C2×Dic19—41no—
144C2×Dic19—82no—
145C2×Dic19—82no—
146C2×Dic19—82no—
147C2×Dic19—82no—
148C8×C19—82no—
149#2283—191no—
150#1817D1911yescharacteristic
151#1434—191no—
152#1294—192no—
153#1294—192no—
154C22×C19—22no—
155C22×C19—22no—
156C22×C19—22no—
157C22×C19—21no—
158C22×C19—21no—
159C22×C19—21no—
160C22×C19—21no—
161C22×C19—22no—
162C22×C19#38111yescharacteristic
163C22×C19#41011yescharacteristic
164C22×C19#41011yescharacteristic
165C22×C19#41611yescharacteristic
166C22×C19#41711yescharacteristic
167C22×C19C2×#10411yescharacteristic
168C22×C19#42111yescharacteristic
169C22×C19#48212yes—
170C22×C19#48512yes—
171C4×C19—22no—
172C4×C19—22no—
173C4×C19—22no—
174C4×C19—41no—
175C4×C19—41no—
176C4×C19—41no—
177Dic19—84no—
178Dic19—81no—
179Dic19—81no—
180Dic19—81no—
181Dic19—81no—
182C22×C42C2×D1911yescharacteristic
183C2×C22⋊C8C2×D1912yes—
184#383—381no—
185#382—191no—
186#382—191no—
187#381—381no—
188#380—191no—
189#380—191no—
190C4×C4⋊C4—191no—
191C4×C4⋊C4—191no—
192C4×C22⋊C4—381no—
193#376—381no—
194C2×#95—192no—
195C2×#95—381no—
196C2×#95—381no—
197#336—21no—
198#336—21no—
199C2×C19—22no—
200C2×C19—22no—
201C2×C19#150011yescharacteristic
202C2×C19#150911yescharacteristic
203C2×C19#151211yescharacteristic
204C2×C19#152111yescharacteristic
205C2×C19#182011yescharacteristic
206C2×C19#182511yescharacteristic
207C2×C19#182611yescharacteristic
208C23×C4—382no—
209C23×C4D7611yescharacteristic
210C23×C4D7611yescharacteristic
211C23×C4C22×D1911yescharacteristic
212C22×C8—22no—
213C2×C4⋊C4—191no—
214C2×C4⋊C4—191no—
215C2×C4⋊C4—191no—
216C2×C4⋊C4—191no—
217C2×C22⋊C4—381no—
218C2×C22⋊C4—381no—
219C2×C42—24no—
220C2×C42—381no—
221C2×C42—381no—
222C2×C42C4×D1911yescharacteristic
223C2×C42C4×D1911yescharacteristic
224C2×C42C22⋊D1911yescharacteristic
225C2×C42C22⋊D1911yescharacteristic
226C22⋊C8—24no—
227#95—384no—
228#95—381no—
229#95—381no—
230#95—381no—
231#95—381no—
232#95—381no—
233#95—381no—
234#95—381no—
235#95—381no—
236#95—384no—
237#95—762no—
238C19#871411yescharacteristic, complemented, Sylow
239C24C2×D7611yescharacteristic
240C22×C4—22no—
241C22×C4—22no—
242C22×C4—22no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—22no—
246C22×C4—41no—
247C22×C4—41no—
248C22×C4—41no—
249C22×C4—384no—
250C22×C4—381no—
251C22×C4—381no—
252C22×C4—381no—
253C22×C4—381no—
254C22×C4—762no—
255C22×C4—762no—
256C22×C4—762no—
257C22×C4—762no—
258C22×C4—762no—
259C22×C4—762no—
260C22×C4(C2×D19)⋊C411yescharacteristic
261C22×C4(C2×D19)⋊C411yescharacteristic
262C22×C4(C2×D19)⋊C411yescharacteristic
263C22×C4(C2×D19)⋊C411yescharacteristic
264C22×C4C2×C4×D1911yescharacteristic
265C22×C4#6454314yes—
266C22×C4C2×C22⋊D1911yescharacteristic
267C2×C8—42no—
268C2×C8—42no—
269C2×C8—42no—
270C4⋊C4—761no—
271C4⋊C4—761no—
272C4⋊C4—761no—
273C4⋊C4—761no—
274C22⋊C4—762no—
275C22⋊C4—761no—
276C22⋊C4—761no—
277C42—22no—
278C42—22no—
279C42—22no—
280C42—22no—
281C42—762no—
282C42—762no—
283C23—21no—
284C23—21no—
285C23—21no—
286C23—21no—
287C23#1059733212yes—
288C23#1059735012yes—
289C23#1059735411yescharacteristic
290C23#1059735511yescharacteristic
291C23C2×(C2×D19)⋊C411yescharacteristic
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—44no—
308C2×C4—44no—
309C2×C4—42no—
310C2×C4—42no—
311C2×C4—764no—
312C2×C4—764no—
313C2×C4—764no—
314C2×C4—761no—
315C2×C4—761no—
316C2×C4—761no—
317C2×C4—761no—
318C2×C4—761no—
319C2×C4—761no—
320C2×C4—761no—
321C2×C4—761no—
322C2×C4—761no—
323C2×C4—761no—
324C2×C4—761no—
325C2×C4—761no—
326C2×C4—1522no—
327C2×C4—1522no—
328C2×C4—1522no—
329C2×C4—1522no—
330C2×C4#1059728212yes—
331C2×C4#1059732312yes—
332C2×C4#1059738112yes—
333C8—82no—
334C22—22no—
335C22—21no—
336C22—21no—
337C22—21no—
338C22—21no—
339C22—22no—
340C22—22no—
341C22—22no—
342C22#1192640511yescharacteristic
343C22#1192651711yescharacteristic
344C22#1192651711yescharacteristic
345C22#1192654111yescharacteristic
346C22#1192654611yescharacteristic
347C22C2×#1059728211yescharacteristic
348C22#1192656011yescharacteristic
349C22#1192686912yes—
350C22#1192688612yes—
351C4—22no—
352C4—22no—
353C4—22no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—1524no—
358C4—1521no—
359C4—1521no—
360C4—1521no—
361C4—1521no—
362C2—22no—
363C2—22no—
364C2#1456212211yescharacteristic
365C2#1456216111yescharacteristic
366C2#1456217411yescharacteristic
367C2#1456221311yescharacteristic
368C2#1456371011yescharacteristic
369C2#1456373111yescharacteristic
370C2#1456373211yescharacteristic
subgroupG/H
centerC23C2×(C2×D19)⋊C4
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#1817C2
socleC23×C19C2×C22⋊C4
prime radicalC24×C19C2×D4
cosocleC23×C4×C19C23
hypercenter#1817D19
hypocenterC19#8714
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1817

Complements

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

NH ≅ G/Ntype
7. #11926410C4semidirect
8. #11926410C4semidirect
12. C4×C4⋊Dic19C4semidirect
13. C4×C4⋊Dic19C4semidirect
238. C19#8714semidirect

Maximal subgroups

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

subgroupindex
#145660332
#145618622
#145615152
C19×#18172
#871419