Finite Group Databasebeta

← #18079247

Subgroups — #18079247

Order 4864.

470 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14566355C211yesmaximal, characteristic
2#14564617C211yesmaximal, characteristic
3#14562307C211yesmaximal, characteristic
4#14562199C211yesmaximal, characteristic
5#14561494C211yesmaximal, characteristic
6#14561463C211yesmaximal, characteristic
7C19×#3229C211yesmaximal, characteristic
8C2×Q8×Dic19—21no—
9#11926597C2211yescharacteristic
10#11926568C2211yescharacteristic
11#11926451—21no—
12#11926430—22no—
13#11926430—22no—
14#11926410C2211yescharacteristic
15#11926390C2211yescharacteristic
16#11926303—21no—
17#11926303—21no—
18#11926290—22no—
19#11926281—22no—
20C19×#533C2211yescharacteristic
21C2×C19×C4⋊Q8C2211yescharacteristic
22C19×#498C412yescomplemented
23C19×#487C412yescomplemented
24C19×#483—22no—
25C19×#475—22no—
26C19×#431C2211yescharacteristic
27C22×Q8×C19—21no—
28C19×C4⋊Q8—21no—
29C19×C4⋊Q8—21no—
30C19×C4⋊Q8C2×C411yescharacteristic
31C19×C4⋊Q8C2×C411yescharacteristic
32C19×C4⋊Q8C2×C412yes—
33C19×C4⋊Q8D412yes—
34C19×#125—21no—
35C19×C22⋊Q8—21no—
36C19×C22⋊Q8—21no—
37C4×Q8×C19—21no—
38C4×Q8×C19—21no—
39C19×#117—21no—
40C2×C4⋊C4×C19—21no—
41C2×C4⋊C4×C19D412yes—
42C2×C42×C19C2311yescharacteristic
43Q8×Dic19—42no—
44Q8×Dic19—42no—
45C2×C4⋊Dic19—22no—
46C2×C4⋊Dic19—21no—
47C2×C4×Dic19—22no—
48C2×C4×Dic19D411yescharacteristic
49C2×C4×Dic19D411yescharacteristic
50C2×#64520—21no—
51C19×#106—24no—
52C19×C4⋊C8—21no—
53C19×#103—24no—
54C19×C22⋊C8—21no—
55C4×C8×C19C2×C412yes—
56C19⋊#95—24no—
57C19⋊#95—21no—
58C19⋊#95—21no—
59C19⋊#95—21no—
60C19⋊#95D412yes—
61C22⋊(C19⋊C8)—21no—
62C4⋊(C19⋊C8)—21no—
63C4⋊(C19⋊C8)—21no—
64C4⋊(C19⋊C8)—21no—
65C4×C19⋊C8—21no—
66C2×Q8×C19—22no—
67C2×Q8×C19—22no—
68C2×Q8×C19—21no—
69C2×Q8×C19—21no—
70C2×Q8×C19—41no—
71C2×Q8×C19—41no—
72C2×Q8×C19—41no—
73C2×Q8×C19—41no—
74C22×C4×C19—22no—
75C22×C4×C19C2×D411yescharacteristic
76C22×C4×C19C2×D411yescharacteristic
77C22×C4×C19C2×D411yescharacteristic
78C22×Dic19—21no—
79C22×Dic19—21no—
80C22×Dic19—22no—
81C2×C8×C19—22no—
82C4⋊C4×C19—22no—
83C4⋊C4×C19—22no—
84C4⋊C4×C19—22no—
85C4⋊C4×C19—21no—
86C4⋊C4×C19—21no—
87C4⋊C4×C19—21no—
88C4⋊C4×C19—21no—
89C4⋊C4×C19—41no—
90C4⋊C4×C19—41no—
91C4⋊C4×C19C22⋊C414yes—
92C22⋊C4×C19—41no—
93C42×C19—41no—
94C42×C19C22×C411yescharacteristic
95C42×C19C2×D411yescharacteristic
96C42×C19#4111yescharacteristic
97C42×C19#4111yescharacteristic
98C4⋊Dic19—44no—
99C4⋊Dic19—41no—
100C4⋊Dic19—41no—
101C4×Dic19—21no—
102C4×Dic19—21no—
103C4×Dic19—21no—
104C4×Dic19—44no—
105C4×Dic19SD1612yes—
106#64520—41no—
107#64520—41no—
108C2×C19⋊C8—41no—
109C2×C19⋊C8—41no—
110#9296—191nomaximal, Sylow
111C23×C19#12011yescharacteristic
112Q8×C19—42no—
113Q8×C19—42no—
114Q8×C19—42no—
115Q8×C19—42no—
116Q8×C19—42no—
117Q8×C19—81no—
118C2×C4×C19—24no—
119C2×C4×C19—41no—
120C2×C4×C19—41no—
121C2×C4×C19—42no—
122C2×C4×C19—42no—
123C2×C4×C19—41no—
124C2×C4×C19—41no—
125C2×C4×C19C2×C22⋊C411yescharacteristic
126C2×C4×C19C4×D411yescharacteristic
127C2×C4×C19C4×D411yescharacteristic
128C2×C4×C19#12111yescharacteristic
129C2×C4×C19#12111yescharacteristic
130C2×C4×C19#12311yescharacteristic
131C2×C4×C19C2×SD1611yescharacteristic
132C2×C4×C19#13511yescharacteristic
133C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
134C2×C4×C19#13711yescharacteristic
135C2×Dic19—22no—
136C2×Dic19—41no—
137C2×Dic19—41no—
138C2×Dic19—41no—
139C2×Dic19—42no—
140C2×Dic19—41no—
141C2×Dic19—42no—
142C2×Dic19—42no—
143C2×Dic19—41no—
144C8×C19—42no—
145C19⋊C8—81no—
146C19⋊C8—81no—
147#3229D1911yescharacteristic
148#2327—191no—
149#1995—191no—
150#1546—191no—
151#1518—191no—
152#1286—191no—
153#1274—191no—
154C22×C19—21no—
155C22×C19—21no—
156C22×C19#38611yescharacteristic
157C22×C19#45011yescharacteristic
158C22×C19#45211yescharacteristic
159C4×C19—21no—
160C4×C19—21no—
161C4×C19—21no—
162C4×C19—21no—
163C4×C19—44no—
164C4×C19—81no—
165C4×C19—81no—
166C4×C19C4×SD1611yescharacteristic
167C4×C19#44011yescharacteristic
168C4×C19#46111yescharacteristic
169C4×C19#46311yescharacteristic
170Dic19—42no—
171Dic19—82no—
172Dic19—81no—
173#533C2×D1911yescharacteristic
174C2×C4⋊Q8C2×D1911yescharacteristic
175C2×C4×Q8—381no—
176#498Dic1912yescomplemented
177#487Dic1912yescomplemented
178#483—22no—
179#475—22no—
180#431—191no—
181#431C2×D1911yescharacteristic
182#423—191no—
183#391—381no—
184#387—382no—
185#387—382no—
186#382—191no—
187#376—191no—
188#339—381no—
189#339—381no—
190#332—382no—
191#328—382no—
192C2×C19—21no—
193C2×C19—21no—
194C2×C19#187711yescharacteristic
195C2×C19#190511yescharacteristic
196C2×C19#191211yescharacteristic
197C22×Q8—21no—
198C2×M16—381no—
199C4⋊Q8—21no—
200C4⋊Q8—21no—
201C4⋊Q8C2×Dic1911yescharacteristic
202C4⋊Q8C2×Dic1911yescharacteristic
203C4⋊Q8C2×Dic1912yes—
204C4⋊Q8C22⋊D1912yes—
205#125—21no—
206C22⋊Q8—21no—
207C22⋊Q8—21no—
208C4×Q8—21no—
209C4×Q8—21no—
210C4×Q8—762no—
211C4×Q8—762no—
212#117—21no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—382no—
215C2×C4⋊C4—381no—
216C2×C4⋊C4C22⋊D1912yes—
217C2×C42—191no—
218C2×C42—191no—
219C2×C42—382no—
220C2×C42C22×D1911yescharacteristic
221#106—24no—
222C4⋊C8—21no—
223C4⋊C8—381no—
224C4⋊C8—381no—
225C4⋊C8—381no—
226#103—24no—
227C22⋊C8—21no—
228C22⋊C8—381no—
229C4×C8—381no—
230C4×C8C2×Dic1912yes—
231#95—192no—
232#95—384no—
233#95—381no—
234#95—381no—
235#95—381no—
236C19#929611yescharacteristic, complemented, Sylow
237C2×Q8—22no—
238C2×Q8—22no—
239C2×Q8—21no—
240C2×Q8—21no—
241C2×Q8—41no—
242C2×Q8—41no—
243C2×Q8—41no—
244C2×Q8—41no—
245C22×C4—22no—
246C22×C4—381no—
247C22×C4—382no—
248C22×C4—381no—
249C22×C4D4×D1911yescharacteristic
250C22×C4D4×D1911yescharacteristic
251C22×C4C2×C22⋊D1911yescharacteristic
252M16—761no—
253M16—761no—
254C2×C8—22no—
255C2×C8—761no—
256C2×C8—761no—
257C4⋊C4—22no—
258C4⋊C4—22no—
259C4⋊C4—22no—
260C4⋊C4—21no—
261C4⋊C4—21no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—764no—
267C4⋊C4—761no—
268C4⋊C4—761no—
269C4⋊C4C22⋊Dic1914yes—
270C22⋊C4—41no—
271C42—41no—
272C42—192no—
273C42—381no—
274C42—381no—
275C42—381no—
276C42—764no—
277C42#6454311yescharacteristic
278C42#6454311yescharacteristic
279C42C22×Dic1911yescharacteristic
280C42C2×C22⋊D1911yescharacteristic
281C23#1059738311yescharacteristic
282Q8—42no—
283Q8—42no—
284Q8—42no—
285Q8—42no—
286Q8—42no—
287Q8—81no—
288C2×C4—24no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—382no—
296C2×C4—761no—
297C2×C4—761no—
298C2×C4—762no—
299C2×C4—761no—
300C2×C4—762no—
301C2×C4—761no—
302C2×C4—762no—
303C2×C4—761no—
304C2×C4SD16×D1911yescharacteristic
305C2×C4#1059736011yescharacteristic
306C2×C4#1059736111yescharacteristic
307C2×C4#1059736211yescharacteristic
308C2×C4D4×Dic1911yescharacteristic
309C2×C4D4×Dic1911yescharacteristic
310C2×C4#1059738111yescharacteristic
311C2×C4#1059738511yescharacteristic
312C2×C4#1059738511yescharacteristic
313C2×C4C2×C22⋊Dic1911yescharacteristic
314C8—42no—
315C8—1521no—
316C8—1521no—
317C22—21no—
318C22—21no—
319C22#1192642411yescharacteristic
320C22#1192669311yescharacteristic
321C22#1192670311yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—44no—
327C4—81no—
328C4—81no—
329C4—762no—
330C4—1522no—
331C4—1521no—
332C4SD16×Dic1911yescharacteristic
333C4#1192664511yescharacteristic
334C4#1192674711yescharacteristic
335C4#1192676111yescharacteristic
336C2—21no—
337C2—21no—
338C2#1456397111yescharacteristic
339C2#1456413111yescharacteristic
340C2#1456417311yescharacteristic
subgroupG/H
centerC22#11926424
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#3229C2
socleC22×C19#386
prime radicalC23×C19#120
cosocleC2×C42×C19C23
hypercenter#3229D19
hypocenterC19#9296
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3229

Complements

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

NH ≅ G/Ntype
22. C19×#498C4semidirect
23. C19×#487C4semidirect
176. #498Dic19semidirect
177. #487Dic19semidirect
236. C19#9296semidirect

Maximal subgroups

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

subgroupindex
#145663552
#145646172
#145623072
#145621992
#145614942
#145614632
C19×#32292
#929619