Finite Group Databasebeta

← #18087004

Subgroups — #18087004

Order 4864.

390 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14568874C211yesmaximal, characteristic
2#14564399C211yesmaximal, characteristic
3#14564393C211yesmaximal, characteristic
4#14563763C211yesmaximal, characteristic
5#14561519C211yesmaximal, characteristic
6#14561475C211yesmaximal, characteristic
7C19×#1279C211yesmaximal, characteristic
8C2×#10597264—21no—
9C2×#10597274—21no—
10C2×C4⋊(C19⋊C8)C2211yescharacteristic
11#11926486—22no—
12#11926442—21no—
13#11926440—21no—
14#11926414C2211yescharacteristic
15#11926414C2211yescharacteristic
16#11926410—21no—
17#11926409—21no—
18C4×C4⋊Dic19C2211yescharacteristic
19#11926307—21no—
20#11926307—22no—
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×C4×Dic19—21no—
41C22×C19⋊C8—21no—
42C19×C4⋊C8—21no—
43C19×C4⋊C8Q812yes—
44C4×C8×C19—21no—
45C4×C8×C19Q812yes—
46C19×#95—21no—
47C19⋊#95—22no—
48C19⋊#95—22no—
49C19⋊#95—22no—
50C19⋊#95—21no—
51#10597274—42no—
52#10597264—42no—
53C4⋊(C19⋊C8)—21no—
54C4⋊(C19⋊C8)Q812yes—
55C22×C4×C19—21no—
56C22×C4×C19—21no—
57C22×C4×C19C2×D411yescharacteristic
58C22×C4×C19C2×D411yescharacteristic
59C22×C4×C19C2×D411yescharacteristic
60C22×Dic19—21no—
61C22×Dic19—21no—
62C22×Dic19—22no—
63C22×Dic19—41no—
64C2×C8×C19—22no—
65C2×C8×C19—22no—
66C2×C8×C19—41no—
67C2×C8×C19—41no—
68C2×C8×C19—41no—
69C2×C8×C19—41no—
70C4⋊C4×C19—21no—
71C4⋊C4×C19—21no—
72C4⋊C4×C19—21no—
73C4⋊C4×C19—21no—
74C42×C19—41no—
75C42×C19—41no—
76C42×C19C2×Q811yescharacteristic
77C42×C19C2×Q811yescharacteristic
78C42×C19C2×Q811yescharacteristic
79C42×C19#4111yescharacteristic
80C4⋊Dic19—21no—
81C4⋊Dic19—21no—
82C4⋊Dic19—21no—
83C4⋊Dic19—21no—
84C4⋊Dic19—41no—
85C4⋊Dic19—41no—
86C4⋊Dic19—41no—
87C4⋊Dic19—41no—
88C4⋊Dic19—42no—
89C4⋊Dic19—42no—
90C4⋊Dic19—41no—
91C4⋊Dic19—41no—
92C4⋊Dic19—41no—
93C4⋊Dic19—41no—
94Dic19⋊C4—82no—
95C4×Dic19—41no—
96C4×Dic19—41no—
97C2×C19⋊C8—22no—
98C2×C19⋊C8—41no—
99C2×C19⋊C8—41no—
100#10578—191nomaximal, Sylow
101C23×C19#12011yescharacteristic
102C2×C4×C19—21no—
103C2×C4×C19—21no—
104C2×C4×C19—41no—
105C2×C4×C19—41no—
106C2×C4×C19—41no—
107C2×C4×C19—41no—
108C2×C4×C19—41no—
109C2×C4×C19—41no—
110C2×C4×C19C22⋊Q811yescharacteristic
111C2×C4×C19C22⋊Q811yescharacteristic
112C2×C4×C19C22⋊Q811yescharacteristic
113C2×C4×C19C4⋊Q811yescharacteristic
114C2×C4×C19C4⋊Q811yescharacteristic
115C2×C4×C19C4⋊Q811yescharacteristic
116C2×C4×C19#13511yescharacteristic
117C2×C4×C19#13511yescharacteristic
118C2×C4×C19#13511yescharacteristic
119C2×C4×C19#13511yescharacteristic
120C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
121C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
122C2×C4×C19#13711yescharacteristic
123C2×C4×C19#13711yescharacteristic
124C2×Dic19—41no—
125C2×Dic19—42no—
126C2×Dic19—41no—
127C2×Dic19—41no—
128C2×Dic19—41no—
129C2×Dic19—42no—
130C2×Dic19—41no—
131C2×Dic19—41no—
132C2×Dic19—42no—
133C2×Dic19—81no—
134C2×Dic19—81no—
135C2×Dic19—81no—
136C8×C19—42no—
137C8×C19—42no—
138C19⋊C8—42no—
139#2571—191no—
140#1948—191no—
141#1947—191no—
142#1834—191no—
143#1296—191no—
144#1279—191no—
145#1279D1911yescharacteristic
146C22×C19#39511yescharacteristic
147C22×C19#44911yescharacteristic
148C22×C19#44911yescharacteristic
149C22×C19#45211yescharacteristic
150C22×C19#45211yescharacteristic
151C22×C19#45411yescharacteristic
152C22×C19#45511yescharacteristic
153C4×C19—21no—
154C4×C19—21no—
155C4×C19—81no—
156C4×C19—81no—
157C4×C19#47811yescharacteristic
158C4×C19#47811yescharacteristic
159C4×C19#47911yescharacteristic
160C4×C19#47911yescharacteristic
161C4×C19#49911yescharacteristic
162C4×C19#49911yescharacteristic
163C4×C19#50111yescharacteristic
164C4×C19#50111yescharacteristic
165Dic19—81no—
166Dic19—82no—
167Dic19—81no—
168Dic19—161no—
169C2×#107—381no—
170C2×#106—381no—
171C2×C4⋊C8—191no—
172C2×C4⋊C8C2×D1911yescharacteristic
173C2×C4×C8C2×D1911yescharacteristic
174#400—382no—
175#389—381no—
176#389—381no—
177#384—191no—
178#384—191no—
179#382—381no—
180#382—381no—
181C4×C4⋊C4—191no—
182C4×C4⋊C4C2×D1911yescharacteristic
183#340—382no—
184#340—381no—
185#340—381no—
186C2×C19#162811yescharacteristic
187C2×C19#163811yescharacteristic
188C2×C19#164011yescharacteristic
189C2×C19#164611yescharacteristic
190C2×C19#205911yescharacteristic
191C2×C19#205911yescharacteristic
192C2×C19#206111yescharacteristic
193C22×C8—21no—
194C22×C8—21no—
195C22×C8—381no—
196C2×C4⋊C4—191no—
197C2×C4⋊C4—191no—
198C2×C4⋊C4—192no—
199C2×C4⋊C4—381no—
200C2×C4⋊C4—381no—
201C2×C4⋊C4—381no—
202C2×C4⋊C4—381no—
203C2×C4⋊C4—381no—
204C2×C4⋊C4—382no—
205C2×C4⋊C4D7611yescharacteristic
206C2×C4⋊C4D7611yescharacteristic
207C2×C42—21no—
208C2×C42—381no—
209C2×C42C22×D1911yescharacteristic
210#107—762no—
211#106—762no—
212C4⋊C8—21no—
213C4⋊C8—192no—
214C4⋊C8—381no—
215C4⋊C8Dic3812yes—
216C4×C8—21no—
217C4×C8Dic3812yes—
218#95—21no—
219#95—382no—
220#95—382no—
221#95—382no—
222#95—381no—
223C19#1057811yescharacteristic, complemented, Sylow
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—381no—
227C22×C4—381no—
228C22×C4—382no—
229C22×C4—761no—
230C22×C4C2×D7611yescharacteristic
231C22×C4D4×D1911yescharacteristic
232C22×C4D4×D1911yescharacteristic
233C2×C8—22no—
234C2×C8—22no—
235C2×C8—41no—
236C2×C8—41no—
237C2×C8—41no—
238C2×C8—41no—
239C2×C8—382no—
240C2×C8—761no—
241C2×C8—761no—
242C4⋊C4—21no—
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—381no—
247C4⋊C4—381no—
248C4⋊C4—381no—
249C4⋊C4—381no—
250C4⋊C4—762no—
251C4⋊C4—762no—
252C4⋊C4—761no—
253C4⋊C4—761no—
254C4⋊C4—761no—
255C4⋊C4—761no—
256C4⋊C4—761no—
257C4⋊C4—761no—
258C4⋊C4—761no—
259C4⋊C4—761no—
260C4⋊C4—1522no—
261C42—41no—
262C42—41no—
263C42—761no—
264C42—761no—
265C42C2×Dic3811yescharacteristic
266C42C2×Dic3811yescharacteristic
267C42#6454311yescharacteristic
268C42Q8×D1911yescharacteristic
269C23#1059732811yescharacteristic
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—761no—
279C2×C4—762no—
280C2×C4—761no—
281C2×C4—761no—
282C2×C4—761no—
283C2×C4—762no—
284C2×C4—761no—
285C2×C4—762no—
286C2×C4—761no—
287C2×C4—1521no—
288C2×C4—1521no—
289C2×C4—1521no—
290C2×C4#1059731511yescharacteristic
291C2×C4#1059732411yescharacteristic
292C2×C4#1059732411yescharacteristic
293C2×C4#1059733411yescharacteristic
294C2×C4#1059733411yescharacteristic
295C2×C4#1059734311yescharacteristic
296C2×C4#1059735011yescharacteristic
297C2×C4#1059735011yescharacteristic
298C2×C4#1059735411yescharacteristic
299C2×C4#1059735511yescharacteristic
300C2×C4#1059735711yescharacteristic
301C2×C4#1059736211yescharacteristic
302C2×C4#1059736211yescharacteristic
303C2×C4#1059736411yescharacteristic
304C8—42no—
305C8—42no—
306C8—762no—
307C22#1192646511yescharacteristic
308C22#1192669011yescharacteristic
309C22#1192669111yescharacteristic
310C22#1192670811yescharacteristic
311C22#1192670911yescharacteristic
312C22#1192671811yescharacteristic
313C22#1192672311yescharacteristic
314C4—21no—
315C4—21no—
316C4—81no—
317C4—81no—
318C4—3041no—
319C4—1522no—
320C4—1521no—
321C4—1521no—
322C4#1192684511yescharacteristic
323C4#1192684611yescharacteristic
324C4#1192684911yescharacteristic
325C4#1192685211yescharacteristic
326C4#1192694411yescharacteristic
327C4#1192694611yescharacteristic
328C4#1192695211yescharacteristic
329C4#1192695311yescharacteristic
330C2#1456274711yescharacteristic
331C2#1456281011yescharacteristic
332C2#1456282311yescharacteristic
333C2#1456286611yescharacteristic
334C2#1456497211yescharacteristic
335C2#1456497411yescharacteristic
336C2#1456498411yescharacteristic
subgroupG/H
centerC23#10597328
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#1279C2
socle, prime radicalC23×C19#120
hypercenter#1279D19
hypocenterC19#10578
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
223. C19#10578semidirect

Maximal subgroups

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

subgroupindex
#145688742
#145643992
#145643932
#145637632
#145615192
#145614752
C19×#12792
#1057819