Finite Group Databasebeta

← #18087030

Subgroups — #18087030

Order 4864.

426 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14568671C211yesmaximal, characteristic
2#14564399C211yesmaximal, characteristic
3#14564399C211yesmaximal, characteristic
4#14563762C211yesmaximal, characteristic
5#14561474C211yesmaximal, characteristic
6#14561474C211yesmaximal, characteristic
7C19×#1296C211yesmaximal, characteristic
8C2×#10597336—21no—
9C2×#10597274—21no—
10C2×#10597274—21no—
11C2×C4×C19⋊C8C2211yescharacteristic
12#11926477—22no—
13#11926443—21no—
14#11926440—21no—
15#11926414C2211yescharacteristic
16#11926413—21no—
17C4×C4⋊Dic19C2211yescharacteristic
18C4×C4⋊Dic19C2211yescharacteristic
19#11926307—21no—
20#11926307—21no—
21#11926306—22no—
22C2×C19×C4⋊C8C2211yescharacteristic
23C2×C19×C4⋊C8C2211yescharacteristic
24C19×#384C2211yescharacteristic
25C22×C8×C19—21no—
26C22×C8×C19—21no—
27C2×C4⋊C4×C19—21no—
28C2×C4⋊C4×C19—21no—
29C2×C4⋊C4×C19D412yes—
30C2×C42×C19C2311yescharacteristic
31C2×C4⋊Dic19—22no—
32C2×C4⋊Dic19—21no—
33C2×C4⋊Dic19—21no—
34C2×C4⋊Dic19—21no—
35C2×C4⋊Dic19D411yescharacteristic
36C2×C4⋊Dic19D411yescharacteristic
37C2×C4⋊Dic19D411yescharacteristic
38C2×C4⋊Dic19D411yescharacteristic
39C2×Dic19⋊C4—22no—
40C2×Dic19⋊C4—22no—
41C2×C4×Dic19—21no—
42C2×C4×Dic19—21no—
43C22×C19⋊C8—21no—
44#10597336—42no—
45#10597336—42no—
46C19×C4⋊C8—21no—
47C19×C4⋊C8—21no—
48C19×C4⋊C8Q812yes—
49C19×C4⋊C8Q812yes—
50C19⋊#95—22no—
51C19⋊#95—21no—
52C19⋊#95—21no—
53#10597274—42no—
54#10597274—42no—
55C4×C19⋊C8—21no—
56C4×C19⋊C8Q812yes—
57C22×C4×C19—22no—
58C22×C4×C19C2×D411yescharacteristic
59C22×C4×C19C2×D411yescharacteristic
60C22×C4×C19C2×D411yescharacteristic
61C22×Dic19—21no—
62C22×Dic19—21no—
63C22×Dic19—21no—
64C22×Dic19—21no—
65C22×Dic19—41no—
66C2×C8×C19—22no—
67C2×C8×C19—22no—
68C2×C8×C19—41no—
69C2×C8×C19—41no—
70C2×C8×C19—41no—
71C2×C8×C19—41no—
72C4⋊C4×C19—42no—
73C4⋊C4×C19—41no—
74C4⋊C4×C19—41no—
75C4⋊C4×C19—41no—
76C4⋊C4×C19—41no—
77C42×C19C2×Q811yescharacteristic
78C42×C19C2×Q811yescharacteristic
79C42×C19C2×Q811yescharacteristic
80C42×C19#4111yescharacteristic
81C4⋊Dic19—21no—
82C4⋊Dic19—21no—
83C4⋊Dic19—21no—
84C4⋊Dic19—21no—
85C4⋊Dic19—21no—
86C4⋊Dic19—21no—
87C4⋊Dic19—44no—
88C4⋊Dic19—42no—
89C4⋊Dic19—41no—
90C4⋊Dic19—41no—
91C4⋊Dic19—41no—
92C4⋊Dic19—41no—
93C4⋊Dic19SD1612yes—
94C4⋊Dic19SD1612yes—
95Dic19⋊C4—44no—
96Dic19⋊C4—82no—
97C4×Dic19—41no—
98C4×Dic19—41no—
99C4×Dic19—41no—
100C4×Dic19—41no—
101C2×C19⋊C8—22no—
102C2×C19⋊C8—41no—
103C2×C19⋊C8—41no—
104#10582—191nomaximal, Sylow
105C23×C19#12011yescharacteristic
106C2×C4×C19—21no—
107C2×C4×C19—21no—
108C2×C4×C19—42no—
109C2×C4×C19—42no—
110C2×C4×C19—42no—
111C2×C4×C19C22⋊Q811yescharacteristic
112C2×C4×C19C22⋊Q811yescharacteristic
113C2×C4×C19C22⋊Q811yescharacteristic
114C2×C4×C19C4⋊Q811yescharacteristic
115C2×C4×C19C4⋊Q811yescharacteristic
116C2×C4×C19C4⋊Q811yescharacteristic
117C2×C4×C19C2×SD1611yescharacteristic
118C2×C4×C19C2×SD1611yescharacteristic
119C2×C4×C19#13511yescharacteristic
120C2×C4×C19#13511yescharacteristic
121C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
122C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
123C2×C4×C19#13711yescharacteristic
124C2×C4×C19#13711yescharacteristic
125C2×Dic19—22no—
126C2×Dic19—22no—
127C2×Dic19—41no—
128C2×Dic19—41no—
129C2×Dic19—41no—
130C2×Dic19—41no—
131C2×Dic19—41no—
132C2×Dic19—41no—
133C2×Dic19—41no—
134C2×Dic19—41no—
135C2×Dic19—41no—
136C2×Dic19—41no—
137C2×Dic19—81no—
138C2×Dic19—81no—
139C2×Dic19—81no—
140C8×C19—42no—
141C8×C19—42no—
142C19⋊C8—42no—
143#2552—191no—
144#1948—191no—
145#1948—191no—
146#1834—191no—
147#1296D1911yescharacteristic
148#1279—191no—
149#1279—191no—
150C22×C19#39511yescharacteristic
151C22×C19#44811yescharacteristic
152C22×C19#44911yescharacteristic
153C22×C19#45011yescharacteristic
154C22×C19#45211yescharacteristic
155C22×C19#45411yescharacteristic
156C22×C19#45511yescharacteristic
157C4×C19—21no—
158C4×C19—21no—
159C4×C19—82no—
160C4×C19#47511yescharacteristic
161C4×C19#47611yescharacteristic
162C4×C19#47811yescharacteristic
163C4×C19#47911yescharacteristic
164C4×C19#49811yescharacteristic
165C4×C19#49911yescharacteristic
166C4×C19#50111yescharacteristic
167C4×C19#50111yescharacteristic
168Dic19—42no—
169Dic19—42no—
170Dic19—81no—
171Dic19—81no—
172Dic19—161no—
173C2×#125—381no—
174C2×#106—381no—
175C2×#106—381no—
176C2×C4⋊C8C2×D1911yescharacteristic
177C2×C4⋊C8C2×D1911yescharacteristic
178C2×C4×C8—191no—
179#398—382no—
180#389—381no—
181#389—381no—
182#384—191no—
183#384—381no—
184#384C2×D1911yescharacteristic
185C4×C4⋊C4—191no—
186C4×C4⋊C4—191no—
187#340—381no—
188#340—381no—
189#340—382no—
190C2×C19#162611yescharacteristic
191C2×C19#163511yescharacteristic
192C2×C19#164211yescharacteristic
193C2×C19#164311yescharacteristic
194C2×C19#205811yescharacteristic
195C2×C19#205911yescharacteristic
196C2×C19#206111yescharacteristic
197C22×C8—21no—
198C22×C8—21no—
199C22×C8—381no—
200#125—762no—
201#125—762no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—191no—
205C2×C4⋊C4—191no—
206C2×C4⋊C4—191no—
207C2×C4⋊C4—191no—
208C2×C4⋊C4—382no—
209C2×C4⋊C4—382no—
210C2×C4⋊C4—381no—
211C2×C4⋊C4—381no—
212C2×C4⋊C4—381no—
213C2×C4⋊C4—382no—
214C2×C4⋊C4D7612yes—
215C2×C42—381no—
216C2×C42—381no—
217C2×C42C22×D1911yescharacteristic
218#106—762no—
219#106—762no—
220C4⋊C8—21no—
221C4⋊C8—21no—
222C4⋊C8Dic3812yes—
223C4⋊C8Dic3812yes—
224C4×C8—192no—
225C4×C8—381no—
226#95—382no—
227#95—381no—
228#95—381no—
229C19#1058211yescharacteristic, complemented, Sylow
230C22×C4—22no—
231C22×C4—381no—
232C22×C4—381no—
233C22×C4—381no—
234C22×C4—381no—
235C22×C4—761no—
236C22×C4C2×D7611yescharacteristic
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—382no—
246C2×C8—761no—
247C2×C8—761no—
248C4⋊C4—42no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—192no—
254C4⋊C4—192no—
255C4⋊C4—381no—
256C4⋊C4—381no—
257C4⋊C4—381no—
258C4⋊C4—381no—
259C4⋊C4—381no—
260C4⋊C4—381no—
261C4⋊C4—762no—
262C4⋊C4—764no—
263C4⋊C4—764no—
264C4⋊C4—761no—
265C4⋊C4—761no—
266C4⋊C4—761no—
267C4⋊C4—761no—
268C4⋊C4—1522no—
269C42—761no—
270C42—761no—
271C42—761no—
272C42—761no—
273C42C2×Dic3811yescharacteristic
274C42C2×Dic3811yescharacteristic
275C42#6454311yescharacteristic
276C42Q8×D1911yescharacteristic
277C23#1059732811yescharacteristic
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—382no—
284C2×C4—382no—
285C2×C4—761no—
286C2×C4—761no—
287C2×C4—761no—
288C2×C4—761no—
289C2×C4—761no—
290C2×C4—761no—
291C2×C4—761no—
292C2×C4—761no—
293C2×C4—761no—
294C2×C4—761no—
295C2×C4—1521no—
296C2×C4—1521no—
297C2×C4—1521no—
298C2×C4#1059731511yescharacteristic
299C2×C4#1059732411yescharacteristic
300C2×C4#1059732411yescharacteristic
301C2×C4#1059733411yescharacteristic
302C2×C4#1059733411yescharacteristic
303C2×C4#1059734311yescharacteristic
304C2×C4#1059735711yescharacteristic
305C2×C4#1059735711yescharacteristic
306C2×C4SD16×D1911yescharacteristic
307C2×C4SD16×D1911yescharacteristic
308C2×C4#1059736211yescharacteristic
309C2×C4#1059736211yescharacteristic
310C2×C4#1059736411yescharacteristic
311C2×C4#1059736411yescharacteristic
312C8—42no—
313C8—42no—
314C8—762no—
315C22#1192646511yescharacteristic
316C22#1192668411yescharacteristic
317C22#1192669011yescharacteristic
318C22#1192669611yescharacteristic
319C22#1192670911yescharacteristic
320C22#1192671911yescharacteristic
321C22#1192672411yescharacteristic
322C4—21no—
323C4—21no—
324C4—82no—
325C4—3041no—
326C4—762no—
327C4—762no—
328C4—1521no—
329C4—1521no—
330C4#1192682711yescharacteristic
331C4#1192683211yescharacteristic
332C4#1192684611yescharacteristic
333C4#1192684911yescharacteristic
334C4#1192694111yescharacteristic
335C4#1192694411yescharacteristic
336C4#1192695211yescharacteristic
337C4#1192695211yescharacteristic
338C2#1456273211yescharacteristic
339C2#1456278711yescharacteristic
340C2#1456283611yescharacteristic
341C2#1456284311yescharacteristic
342C2#1456496711yescharacteristic
343C2#1456497211yescharacteristic
344C2#1456498611yescharacteristic
subgroupG/H
centerC23#10597328
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#1296C2
socle, prime radicalC23×C19#120
hypercenter#1296D19
hypocenterC19#10582
LCSG ▷ C2×C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
229. C19#10582semidirect

Maximal subgroups

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

subgroupindex
#145686712
#145643992
#145637622
#145614742
C19×#12962
#1058219