Finite Group Databasebeta

← #18076863

Subgroups — #18076863

Order 4864.

392 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14572300C211yesmaximal, characteristic
2#14563656C211yesmaximal, characteristic
3#14562409C211yesmaximal, characteristic, complemented
4#14562391C211yesmaximal, characteristic, complemented
5#14562018C211yesmaximal, characteristic
6#14561538C211yesmaximal, characteristic, complemented
7C19×#1279C211yesmaximal, characteristic, complemented
8C4×#64541C2211yescharacteristic
9#11926604—22no—
10#11926600—21no—
11#11926597C2211yescharacteristic
12#11926596—21no—
13#11926568C2211yescharacteristic
14#11926568C2211yescharacteristic
15C2×#10597262—21no—
16#11926510—21no—
17#11926499—21no—
18#11926304—21no—
19#11926296—21no—
20#11926296—21no—
21#11926295—22no—
22#11926276C411yescharacteristic, complemented
23#11926276C411yescharacteristic, complemented
24#11926273C411yescharacteristic, complemented
25#11926273C411yescharacteristic, complemented
26C2×C19×C4⋊C8C2211yescharacteristic
27C2×C4×C8×C19C2211yescharacteristic
28C4×C4⋊C4×C19C2211yescharacteristic
29C2×#64541D411yescharacteristic
30C22×C8×C19—21no—
31C22×C8×C19—21no—
32C2×C4⋊C4×C19—21no—
33C2×C42×C19—21no—
34C2×C42×C19C2311yescharacteristic
35C4×C22⋊D19—21no—
36C4×C22⋊D19—21no—
37#10597372D411yescharacteristic
38C2×#64520—21no—
39C2×#64520—21no—
40C4×D76C2×C411yescharacteristic
41C4×D76Q811yescharacteristic
42#10597318—21no—
43C42×D19—21no—
44C4×Dic38C2×C411yescharacteristic
45C4×Dic38Q811yescharacteristic
46C19×C4⋊C8—21no—
47C19×C4⋊C8D411yescharacteristic
48C19×C4⋊C8D411yescharacteristic
49C4×C8×C19—21no—
50C4×C8×C19C2×C411yescharacteristic
51C4×C8×C19C2×C411yescharacteristic
52C19×#95—21no—
53C22⋊(C19⋊C8)—21no—
54(C2×D19)⋊C8—22no—
55(C2×D19)⋊C8—22no—
56#10597272—22no—
57C8×Dic19—22no—
58#10597262—42no—
59C4⋊(C19⋊C8)—21no—
60C4⋊(C19⋊C8)—21no—
61C4⋊(C19⋊C8)—21no—
62C4⋊(C19⋊C8)C2×C411yescharacteristic
63C4⋊(C19⋊C8)C2×C411yescharacteristic
64C4⋊(C19⋊C8)D412yes—
65C4×C19⋊C8—21no—
66C22×C4×C19—41no—
67C22×C4×C19C2×D411yescharacteristic
68C22×C4×C19#4111yescharacteristic
69C22×C4×C19#4111yescharacteristic
70C2×C22⋊D19—21no—
71#64541—21no—
72#64541—21no—
73#64541—21no—
74#64541—21no—
75C2×D76C4⋊C411yescharacteristic
76C2×C4×D19—21no—
77C2×C4×D19—21no—
78C2×C4×D19—21no—
79C2×Dic38C4⋊C411yescharacteristic
80C2×C8×C19—21no—
81C2×C8×C19—21no—
82C2×C8×C19—21no—
83C2×C8×C19—21no—
84C2×C8×C19—42no—
85C2×C8×C19—41no—
86C2×C8×C19—41no—
87C4⋊C4×C19—22no—
88C4⋊C4×C19—41no—
89C42×C19—41no—
90C42×C19—41no—
91C42×C19C22×C411yescharacteristic
92C42×C19C2×D411yescharacteristic
93C42×C19C2×D411yescharacteristic
94C42×C19C2×Q811yescharacteristic
95C22⋊Dic19—21no—
96(C2×D19)⋊C4—21no—
97(C2×D19)⋊C4—21no—
98C4⋊Dic19C4⋊C411yescharacteristic
99C4⋊Dic19C4⋊C411yescharacteristic
100Dic19⋊C4—21no—
101Dic19⋊C4—21no—
102C4×Dic19—21no—
103C4×Dic19—21no—
104C4×Dic19—21no—
105#64520—41no—
106#64520—41no—
107#64520—41no—
108#64520—41no—
109C2×C19⋊C8—21no—
110C2×C19⋊C8—21no—
111C2×C19⋊C8—22no—
112C2×C19⋊C8—41no—
113#8905—191nomaximal, Sylow
114C23×C19#12311yescharacteristic
115C22×D19—21no—
116C2×C4×C19—21no—
117C2×C4×C19—21no—
118C2×C4×C19—41no—
119C2×C4×C19—42no—
120C2×C4×C19—81no—
121C2×C4×C19—81no—
122C2×C4×C19C2×C4⋊C411yescharacteristic
123C2×C4×C19C4×D411yescharacteristic
124C2×C4×C19C4×D411yescharacteristic
125C2×C4×C19#12011yescharacteristic
126C2×C4×C19C22⋊Q811yescharacteristic
127C2×C4×C19C22⋊Q811yescharacteristic
128C2×C4×C19#13511yescharacteristic
129C2×C4×C19#13511yescharacteristic
130C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
131C2×C4×C19#13711yescharacteristic
132C22⋊D19—41no—
133C22⋊D19—41no—
134C2×Dic19—21no—
135C2×Dic19—21no—
136C2×Dic19—21no—
137D76—21no—
138D76—21no—
139C4×D19—41no—
140C4×D19—41no—
141C4×D19—41no—
142C4×D19—41no—
143C4×D19—81no—
144Dic38—21no—
145Dic38—21no—
146C8×C19—22no—
147C8×C19—41no—
148C8×C19—41no—
149C8×C19—41no—
150C19⋊C8—41no—
151C19⋊C8—41no—
152C19⋊C8—42no—
153C19⋊C8—81no—
154#2925—191no—
155#1806—191no—
156#1571—191no—
157#1566—191no—
158#1476—191no—
159#1303—191no—
160#1279D1911yescharacteristic, complemented
161C22×C19—21no—
162C22×C19—21no—
163C22×C19#38511yescharacteristic
164C22×C19#48211yescharacteristic
165C22×C19#48511yescharacteristic
166C2×D19—41no—
167C2×D19—41no—
168C2×D19—41no—
169C4×C19—21no—
170C4×C19—21no—
171C4×C19—21no—
172C4×C19—82no—
173C4×C19#42711yescharacteristic
174C4×C19#42811yescharacteristic
175C4×C19#44311yescharacteristic
176C4×C19#44411yescharacteristic
177C4×C19#44911yescharacteristic
178C4×C19#45211yescharacteristic
179Dic19—41no—
180Dic19—41no—
181Dic19—41no—
182C4×#41—191no—
183#433—382no—
184#432—381no—
185#431—191no—
186#431—381no—
187#423—191no—
188#423—191no—
189C2×C4⋊C8C2×D1911yescharacteristic
190C2×#104—381no—
191#408—381no—
192#405—381no—
193C2×C4×C8C2×D1911yescharacteristic
194C4×C4⋊C4C2×D1911yescharacteristic
195#339—381no—
196#335—381no—
197#335—381no—
198#334—382no—
199Q8⋊C8—191no—
200Q8⋊C8—191no—
201D4⋊C8—191no—
202D4⋊C8—191no—
203C2×C19—21no—
204C2×C19—21no—
205C2×C19#185411yescharacteristic
206C2×C19#186111yescharacteristic
207C2×C19#186611yescharacteristic
208D19—81no—
209C2×#41—191no—
210C2×M16—381no—
211C2×M16—381no—
212C22×C8—21no—
213C22×C8—21no—
214C4×Q8—191no—
215C4×Q8—191no—
216C4×D4—191no—
217C4×D4—191no—
218C4×D4—381no—
219C4×D4—381no—
220#117—191no—
221#117—381no—
222C2×C4⋊C4—21no—
223C2×C42—21no—
224C2×C42—381no—
225C2×C42C22×D1911yescharacteristic
226C4⋊C8—21no—
227C4⋊C8—191no—
228C4⋊C8—191no—
229C4⋊C8—192no—
230C4⋊C8—381no—
231C4⋊C8—381no—
232C4⋊C8—381no—
233C4⋊C8D7611yescharacteristic
234C4⋊C8D7611yescharacteristic
235#104—762no—
236C22⋊C8—382no—
237C22⋊C8—382no—
238C22⋊C8—381no—
239#97—382no—
240C4×C8—21no—
241C4×C8—382no—
242C4×C8—381no—
243C4×C8C4×D1911yescharacteristic
244C4×C8C4×D1911yescharacteristic
245#95—21no—
246C19#890511yescharacteristic, complemented, Sylow
247#41—381no—
248#41—381no—
249#41—381no—
250#41—381no—
251C2×Q8—191no—
252C2×D4—191no—
253C2×D4—381no—
254C22×C4—41no—
255C22×C4—381no—
256C22×C4—381no—
257C22×C4—381no—
258C22×C4#6454111yescharacteristic
259C22×C4D4×D1911yescharacteristic
260C22×C4#6454311yescharacteristic
261M16—761no—
262M16—761no—
263M16—761no—
264M16—761no—
265C2×C8—21no—
266C2×C8—21no—
267C2×C8—21no—
268C2×C8—21no—
269C2×C8—42no—
270C2×C8—41no—
271C2×C8—41no—
272C2×C8—381no—
273C2×C8—381no—
274C2×C8—382no—
275C2×C8—761no—
276C4⋊C4—22no—
277C4⋊C4—41no—
278C4⋊C4—191no—
279C4⋊C4—191no—
280C4⋊C4—381no—
281C4⋊C4—381no—
282C22⋊C4—381no—
283C22⋊C4—381no—
284C22⋊C4—381no—
285C42—41no—
286C42—41no—
287C42—381no—
288C42—381no—
289C42—381no—
290C42C2×C4×D1911yescharacteristic
291C42C2×D7611yescharacteristic
292C42D4×D1911yescharacteristic
293C42Q8×D1911yescharacteristic
294C23—381no—
295C23#1059732911yescharacteristic
296Q8—381no—
297Q8—381no—
298D4—381no—
299D4—381no—
300D4—761no—
301D4—761no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—41no—
305C2×C4—42no—
306C2×C4—81no—
307C2×C4—81no—
308C2×C4—381no—
309C2×C4—381no—
310C2×C4—381no—
311C2×C4—761no—
312C2×C4—761no—
313C2×C4—761no—
314C2×C4—761no—
315C2×C4—1521no—
316C2×C4C4×D7611yescharacteristic
317C2×C4(C22⋊D19)⋊C411yescharacteristic
318C2×C4#1059732811yescharacteristic
319C2×C4C4⋊C4×D1911yescharacteristic
320C2×C4#1059734211yescharacteristic
321C2×C4#1059734311yescharacteristic
322C2×C4#1059735711yescharacteristic
323C2×C4#1059736211yescharacteristic
324C2×C4#1059736211yescharacteristic
325C2×C4#1059736411yescharacteristic
326C8—22no—
327C8—41no—
328C8—41no—
329C8—41no—
330C8—761no—
331C8—761no—
332C8—762no—
333C8—1521no—
334C22—21no—
335C22—21no—
336C22—761no—
337C22—761no—
338C22—761no—
339C22#1192641811yescharacteristic
340C22#1192686711yescharacteristic
341C22#1192688311yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—82no—
346C4—761no—
347C4—761no—
348C4—761no—
349C4#1192657911yescharacteristic
350C4#1192658511yescharacteristic
351C4#1192666211yescharacteristic
352C4#1192666711yescharacteristic
353C4#1192669011yescharacteristic
354C4#1192670911yescharacteristic
355C2—21no—
356C2—21no—
357C2—1521no—
358C2#1456383511yescharacteristic
359C2#1456387611yescharacteristic
360C2#1456391311yescharacteristic
subgroupG/H
centerC2×C4#10597328
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1279C2
socleC22×C19#385
prime radicalC2×#64541D4
cosocleC2×C42×C19C23
hypercenter#1279D19
hypocenterC19#8905
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1279

Complements

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

NH ≅ G/Ntype
3. #14562409C2semidirect
4. #14562391C2semidirect
6. #14561538C2semidirect
7. C19×#1279C2semidirect
22. #11926276C4semidirect
23. #11926276C4semidirect
24. #11926273C4semidirect
25. #11926273C4semidirect
160. #1279D19semidirect
246. C19#8905semidirect

Maximal subgroups

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

subgroupindex
#145723002
#145636562
#145624092
#145623912
#145620182
#145615382
C19×#12792
#890519