Finite Group Databasebeta

← #18087020

Subgroups — #18087020

Order 4864.

442 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14568670C211yesmaximal, characteristic
2#14564398C211yesmaximal, characteristic
3#14564394C211yesmaximal, characteristic
4#14563792C211yesmaximal, characteristic
5#14561519C211yesmaximal, characteristic
6#14561475C211yesmaximal, characteristic
7C19×#1279C211yesmaximal, characteristic
8C2×#10597316—21no—
9C2×#10597275—21no—
10C2×#10597274—22no—
11C2×#10597265—21no—
12C2×C4⋊(C19⋊C8)C2211yescharacteristic
13#11926478—22no—
14#11926442—21no—
15#11926440—21no—
16#11926414C2211yescharacteristic
17#11926414C2211yescharacteristic
18#11926413—21no—
19C4×C4⋊Dic19C2211yescharacteristic
20#11926307—21no—
21#11926306—21no—
22C2×C19×C4⋊C8C2211yescharacteristic
23C2×C4×C8×C19C2211yescharacteristic
24C4×C4⋊C4×C19C2211yescharacteristic
25C22×C8×C19—21no—
26C22×C8×C19—21no—
27C2×C4⋊C4×C19D411yescharacteristic
28C2×C4⋊C4×C19D411yescharacteristic
29C2×C42×C19—21no—
30C2×C42×C19C2311yescharacteristic
31C2×C4⋊Dic19—21no—
32C2×C4⋊Dic19—21no—
33C2×C4⋊Dic19—21no—
34C2×C4⋊Dic19—21no—
35C2×C4⋊Dic19—21no—
36C2×C4⋊Dic19D411yescharacteristic
37C2×C4⋊Dic19D411yescharacteristic
38C2×C4⋊Dic19D412yes—
39C2×Dic19⋊C4—22no—
40C2×Dic19⋊C4—22no—
41C2×Dic19⋊C4—22no—
42C2×C4×Dic19—21no—
43C22×C19⋊C8—21no—
44#10597316—42no—
45#10597316—42no—
46C19×C4⋊C8—21no—
47C19×C4⋊C8Q812yes—
48C4×C8×C19—21no—
49C4×C8×C19Q812yes—
50C19×#95—21no—
51C19⋊#95—22no—
52C19⋊#95—21no—
53#10597275—42no—
54#10597274—44no—
55#10597265—42no—
56C4⋊(C19⋊C8)—21no—
57C4⋊(C19⋊C8)Q812yes—
58C22×C4×C19—21no—
59C22×C4×C19—21no—
60C22×C4×C19C2×D411yescharacteristic
61C22×C4×C19C2×D411yescharacteristic
62C22×C4×C19C2×D411yescharacteristic
63C22×Dic19—21no—
64C22×Dic19—21no—
65C22×Dic19—22no—
66C22×Dic19—41no—
67C2×C8×C19—22no—
68C2×C8×C19—22no—
69C2×C8×C19—22no—
70C2×C8×C19—22no—
71C2×C8×C19—41no—
72C2×C8×C19—41no—
73C4⋊C4×C19—21no—
74C4⋊C4×C19—21no—
75C4⋊C4×C19—21no—
76C4⋊C4×C19—21no—
77C42×C19—41no—
78C42×C19—41no—
79C42×C19C2×Q811yescharacteristic
80C42×C19C2×Q811yescharacteristic
81C42×C19C2×Q811yescharacteristic
82C42×C19#4111yescharacteristic
83C4⋊Dic19—21no—
84C4⋊Dic19—21no—
85C4⋊Dic19—41no—
86C4⋊Dic19—41no—
87C4⋊Dic19—41no—
88C4⋊Dic19—41no—
89C4⋊Dic19—42no—
90C4⋊Dic19—42no—
91C4⋊Dic19—41no—
92C4⋊Dic19—41no—
93C4⋊Dic19—41no—
94C4⋊Dic19—41no—
95C4⋊Dic19SD1612yes—
96C4⋊Dic19SD1612yes—
97Dic19⋊C4—44no—
98Dic19⋊C4—44no—
99Dic19⋊C4—82no—
100C4×Dic19—41no—
101C4×Dic19—41no—
102C2×C19⋊C8—22no—
103C2×C19⋊C8—41no—
104C2×C19⋊C8—41no—
105#10580—191nomaximal, Sylow
106C23×C19#12011yescharacteristic
107C2×C4×C19—21no—
108C2×C4×C19—21no—
109C2×C4×C19—41no—
110C2×C4×C19—41no—
111C2×C4×C19—41no—
112C2×C4×C19—41no—
113C2×C4×C19—41no—
114C2×C4×C19—41no—
115C2×C4×C19C22⋊Q811yescharacteristic
116C2×C4×C19C22⋊Q811yescharacteristic
117C2×C4×C19C22⋊Q811yescharacteristic
118C2×C4×C19C4⋊Q811yescharacteristic
119C2×C4×C19C4⋊Q811yescharacteristic
120C2×C4×C19C4⋊Q811yescharacteristic
121C2×C4×C19C2×SD1611yescharacteristic
122C2×C4×C19C2×SD1611yescharacteristic
123C2×C4×C19#13511yescharacteristic
124C2×C4×C19#13511yescharacteristic
125C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
126C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
127C2×C4×C19#13711yescharacteristic
128C2×C4×C19#13711yescharacteristic
129C2×Dic19—22no—
130C2×Dic19—22no—
131C2×Dic19—41no—
132C2×Dic19—41no—
133C2×Dic19—41no—
134C2×Dic19—41no—
135C2×Dic19—42no—
136C2×Dic19—42no—
137C2×Dic19—42no—
138C2×Dic19—81no—
139C2×Dic19—81no—
140C2×Dic19—81no—
141C8×C19—24no—
142C8×C19—42no—
143C19⋊C8—42no—
144#2552—191no—
145#1948—191no—
146#1947—191no—
147#1844—191no—
148#1296—191no—
149#1279—191no—
150#1279D1911yescharacteristic
151C22×C19#39511yescharacteristic
152C22×C19#44811yescharacteristic
153C22×C19#44911yescharacteristic
154C22×C19#45011yescharacteristic
155C22×C19#45211yescharacteristic
156C22×C19#45311yescharacteristic
157C22×C19#45611yescharacteristic
158C4×C19—21no—
159C4×C19—21no—
160C4×C19—81no—
161C4×C19—81no—
162C4×C19#47511yescharacteristic
163C4×C19#47611yescharacteristic
164C4×C19#47811yescharacteristic
165C4×C19#47911yescharacteristic
166C4×C19#49811yescharacteristic
167C4×C19#49911yescharacteristic
168C4×C19#50111yescharacteristic
169C4×C19#50111yescharacteristic
170Dic19—42no—
171Dic19—42no—
172Dic19—82no—
173Dic19—161no—
174C2×#125—381no—
175C2×#107—381no—
176C2×#106—382no—
177C2×#106—381no—
178C2×C4⋊C8—191no—
179C2×C4⋊C8C2×D1911yescharacteristic
180C2×C4×C8C2×D1911yescharacteristic
181#398—382no—
182#389—381no—
183#389—381no—
184#384—191no—
185#384—191no—
186#384—381no—
187C4×C4⋊C4—191no—
188C4×C4⋊C4C2×D1911yescharacteristic
189#340—381no—
190#340—381no—
191C2×C19#162211yescharacteristic
192C2×C19#163111yescharacteristic
193C2×C19#165311yescharacteristic
194C2×C19#165411yescharacteristic
195C2×C19#205811yescharacteristic
196C2×C19#205911yescharacteristic
197C2×C19#206011yescharacteristic
198C22×C8—21no—
199C22×C8—21no—
200C22×C8—381no—
201#125—762no—
202#125—762no—
203C2×C4⋊C4—191no—
204C2×C4⋊C4—191no—
205C2×C4⋊C4—192no—
206C2×C4⋊C4—382no—
207C2×C4⋊C4—382no—
208C2×C4⋊C4—381no—
209C2×C4⋊C4—381no—
210C2×C4⋊C4—381no—
211C2×C4⋊C4—381no—
212C2×C4⋊C4—381no—
213C2×C4⋊C4—382no—
214C2×C4⋊C4D7611yescharacteristic
215C2×C4⋊C4D7611yescharacteristic
216C2×C42—21no—
217C2×C42—381no—
218C2×C42C22×D1911yescharacteristic
219#107—762no—
220#106—762no—
221#106—764no—
222C4⋊C8—21no—
223C4⋊C8—192no—
224C4⋊C8—381no—
225C4⋊C8Dic3812yes—
226C4×C8—21no—
227C4×C8Dic3812yes—
228#95—21no—
229#95—382no—
230#95—381no—
231C19#1058011yescharacteristic, complemented, Sylow
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—381no—
235C22×C4—381no—
236C22×C4—382no—
237C22×C4—761no—
238C22×C4C2×D7611yescharacteristic
239C22×C4D4×D1911yescharacteristic
240C22×C4D4×D1911yescharacteristic
241C2×C8—22no—
242C2×C8—22no—
243C2×C8—22no—
244C2×C8—22no—
245C2×C8—41no—
246C2×C8—41no—
247C2×C8—382no—
248C2×C8—761no—
249C2×C8—761no—
250C4⋊C4—21no—
251C4⋊C4—21no—
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—192no—
255C4⋊C4—192no—
256C4⋊C4—381no—
257C4⋊C4—381no—
258C4⋊C4—762no—
259C4⋊C4—762no—
260C4⋊C4—764no—
261C4⋊C4—764no—
262C4⋊C4—761no—
263C4⋊C4—761no—
264C4⋊C4—761no—
265C4⋊C4—761no—
266C4⋊C4—761no—
267C4⋊C4—761no—
268C4⋊C4—761no—
269C4⋊C4—761no—
270C4⋊C4—1522no—
271C42—41no—
272C42—41no—
273C42—761no—
274C42—761no—
275C42C2×Dic3811yescharacteristic
276C42C2×Dic3811yescharacteristic
277C42#6454311yescharacteristic
278C42Q8×D1911yescharacteristic
279C23#1059732811yescharacteristic
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—382no—
289C2×C4—382no—
290C2×C4—761no—
291C2×C4—761no—
292C2×C4—761no—
293C2×C4—761no—
294C2×C4—762no—
295C2×C4—762no—
296C2×C4—762no—
297C2×C4—1521no—
298C2×C4—1521no—
299C2×C4—1521no—
300C2×C4#1059731511yescharacteristic
301C2×C4#1059732411yescharacteristic
302C2×C4#1059732411yescharacteristic
303C2×C4#1059733411yescharacteristic
304C2×C4#1059733411yescharacteristic
305C2×C4#1059734311yescharacteristic
306C2×C4#1059735011yescharacteristic
307C2×C4#1059735011yescharacteristic
308C2×C4#1059735411yescharacteristic
309C2×C4#1059735511yescharacteristic
310C2×C4#1059735711yescharacteristic
311C2×C4SD16×D1911yescharacteristic
312C2×C4SD16×D1911yescharacteristic
313C2×C4#1059736411yescharacteristic
314C8—24no—
315C8—42no—
316C8—762no—
317C22#1192646511yescharacteristic
318C22#1192668411yescharacteristic
319C22#1192669111yescharacteristic
320C22#1192669611yescharacteristic
321C22#1192670811yescharacteristic
322C22#1192671311yescharacteristic
323C22#1192672811yescharacteristic
324C4—21no—
325C4—21no—
326C4—81no—
327C4—81no—
328C4—3041no—
329C4—762no—
330C4—762no—
331C4—1522no—
332C4#1192682711yescharacteristic
333C4#1192683211yescharacteristic
334C4#1192684511yescharacteristic
335C4#1192685211yescharacteristic
336C4#1192694111yescharacteristic
337C4#1192694611yescharacteristic
338C4#1192695211yescharacteristic
339C4#1192695311yescharacteristic
340C2#1456271011yescharacteristic
341C2#1456276511yescharacteristic
342C2#1456291511yescharacteristic
343C2#1456292111yescharacteristic
344C2#1456496711yescharacteristic
345C2#1456497411yescharacteristic
346C2#1456497911yescharacteristic
subgroupG/H
centerC23#10597328
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#1279C2
socle, prime radicalC23×C19#120
hypercenter#1279D19
hypocenterC19#10580
LCSG ▷ C2×C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1279

Complements

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

NH ≅ G/Ntype
231. C19#10580semidirect

Maximal subgroups

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

subgroupindex
#145686702
#145643982
#145643942
#145637922
#145615192
#145614752
C19×#12792
#1058019