Finite Group Databasebeta

← #18076861

Subgroups — #18076861

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#14572303C211yesmaximal, characteristic
2#14563656C211yesmaximal, characteristic
3#14562410C211yesmaximal, characteristic, complemented
4#14562390C211yesmaximal, characteristic, complemented
5#14562015C211yesmaximal, characteristic
6#14561476C211yesmaximal, characteristic, complemented
7C19×#1303C211yesmaximal, characteristic, complemented
8C4×#64541C2211yescharacteristic
9#11926604—22no—
10#11926600—21no—
11#11926596—21no—
12#11926568C2211yescharacteristic
13C2×C4⋊(C19⋊C8)C2211yescharacteristic
14C2×#10597262—21no—
15#11926512—21no—
16#11926502—21no—
17C2×C4×C19⋊C8C2211yescharacteristic
18#11926304—21no—
19#11926297—21no—
20#11926297—21no—
21#11926294—22no—
22#11926274C411yescharacteristic, complemented
23#11926274C411yescharacteristic, complemented
24#11926271C411yescharacteristic, complemented
25#11926271C411yescharacteristic, complemented
26C19×#431C2211yescharacteristic
27C19×#423C2211yescharacteristic
28C4×C4⋊C4×C19C2211yescharacteristic
29C2×#64541D411yescharacteristic
30C2×M16×C19—21no—
31C2×C4⋊C4×C19—21no—
32C2×C42×C19—21no—
33C2×C42×C19C2311yescharacteristic
34C4×C22⋊D19—21no—
35C4×C22⋊D19—21no—
36#10597372D411yescharacteristic
37C2×#64520—21no—
38C22×C19⋊C8—21no—
39C22×C19⋊C8—21no—
40C4×D76C2×C411yescharacteristic
41C4×D76Q811yescharacteristic
42#10597318—21no—
43C42×D19—21no—
44C4×Dic38C2×C411yescharacteristic
45C4×Dic38Q811yescharacteristic
46C19×C4⋊C8—21no—
47C19×C4⋊C8C2×C411yescharacteristic
48C19×C4⋊C8C2×C411yescharacteristic
49C19×C4⋊C8D412yes—
50C19×C22⋊C8—21no—
51C4×C8×C19—21no—
52C19×#95—21no—
53(C2×D19)⋊C8—22no—
54(C2×D19)⋊C8—22no—
55#10597272—22no—
56C8×Dic19—22no—
57#10597262—42no—
58C4⋊(C19⋊C8)—21no—
59C4⋊(C19⋊C8)—21no—
60C4⋊(C19⋊C8)—21no—
61C4⋊(C19⋊C8)D411yescharacteristic
62C4⋊(C19⋊C8)D411yescharacteristic
63C4×C19⋊C8—21no—
64C4×C19⋊C8C2×C411yescharacteristic
65C4×C19⋊C8C2×C411yescharacteristic
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
80M16×C19—41no—
81M16×C19—41no—
82C2×C8×C19—21no—
83C2×C8×C19—21no—
84C2×C8×C19—22no—
85C4⋊C4×C19—22no—
86C4⋊C4×C19—41no—
87C42×C19—41no—
88C42×C19—41no—
89C42×C19C22×C411yescharacteristic
90C42×C19C2×D411yescharacteristic
91C42×C19C2×D411yescharacteristic
92C42×C19C2×Q811yescharacteristic
93C22⋊Dic19—21no—
94(C2×D19)⋊C4—21no—
95(C2×D19)⋊C4—21no—
96C4⋊Dic19C4⋊C411yescharacteristic
97C4⋊Dic19C4⋊C411yescharacteristic
98Dic19⋊C4—21no—
99Dic19⋊C4—21no—
100C4×Dic19—21no—
101C4×Dic19—21no—
102C4×Dic19—21no—
103#64520—41no—
104#64520—41no—
105C2×C19⋊C8—21no—
106C2×C19⋊C8—21no—
107C2×C19⋊C8—21no—
108C2×C19⋊C8—21no—
109C2×C19⋊C8—42no—
110C2×C19⋊C8—41no—
111C2×C19⋊C8—41no—
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—41no—
147C8×C19—41no—
148C8×C19—42no—
149C19⋊C8—22no—
150C19⋊C8—41no—
151C19⋊C8—41no—
152C19⋊C8—41no—
153C19⋊C8—81no—
154#2925—191no—
155#1806—191no—
156#1571—191no—
157#1566—191no—
158#1476—191no—
159#1303D1911yescharacteristic, complemented
160#1279—191no—
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—381no—
186#431C2×D1911yescharacteristic
187#423—191no—
188#423C2×D1911yescharacteristic
189C2×C4⋊C8—191no—
190C2×#104—381no—
191#408—381no—
192#405—381no—
193C2×C4×C8—191no—
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—21no—
211C2×M16—381no—
212C22×C8—381no—
213C22×C8—381no—
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—381no—
230C4⋊C8—381no—
231C4⋊C8—381no—
232C4⋊C8C4×D1911yescharacteristic
233C4⋊C8C4×D1911yescharacteristic
234C4⋊C8D7612yes—
235#104—762no—
236C22⋊C8—21no—
237C22⋊C8—382no—
238C22⋊C8—382no—
239#97—382no—
240C4×C8—21no—
241C4×C8—191no—
242C4×C8—191no—
243C4×C8—382no—
244C4×C8—381no—
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—41no—
262M16—41no—
263M16—761no—
264M16—761no—
265C2×C8—21no—
266C2×C8—21no—
267C2×C8—22no—
268C2×C8—381no—
269C2×C8—381no—
270C2×C8—381no—
271C2×C8—381no—
272C2×C8—762no—
273C2×C8—761no—
274C2×C8—761no—
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#1059735811yescharacteristic
323C2×C4#1059736011yescharacteristic
324C2×C4#1059736111yescharacteristic
325C2×C4#1059736511yescharacteristic
326C8—41no—
327C8—41no—
328C8—42no—
329C8—382no—
330C8—761no—
331C8—761no—
332C8—761no—
333C8—1521no—
334C22—21no—
335C22—21no—
336C22—761no—
337C22—761no—
338C22—761no—
339C22#1192641811yescharacteristic
340C22#1192686611yescharacteristic
341C22#1192688411yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—82no—
346C4—761no—
347C4—761no—
348C4—761no—
349C4#1192658111yescharacteristic
350C4#1192658311yescharacteristic
351C4#1192665811yescharacteristic
352C4#1192666311yescharacteristic
353C4#1192669211yescharacteristic
354C4#1192670711yescharacteristic
355C2—21no—
356C2—21no—
357C2—1521no—
358C2#1456383711yescharacteristic
359C2#1456387811yescharacteristic
360C2#1456391111yescharacteristic
subgroupG/H
centerC2×C4#10597328
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1303C2
socleC22×C19#385
prime radicalC2×#64541D4
cosocleC2×C42×C19C23
hypercenter#1303D19
hypocenterC19#8905
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1303

Complements

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

NH ≅ G/Ntype
3. #14562410C2semidirect
4. #14562390C2semidirect
6. #14561476C2semidirect
7. C19×#1303C2semidirect
22. #11926274C4semidirect
23. #11926274C4semidirect
24. #11926271C4semidirect
25. #11926271C4semidirect
159. #1303D19semidirect
246. C19#8905semidirect

Maximal subgroups

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

subgroupindex
#145723032
#145636562
#145624102
#145623902
#145620152
#145614762
C19×#13032
#890519