Finite Group Databasebeta

← #18082731

Subgroups — #18082731

Order 4864.

548 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14563615C211yesmaximal, characteristic
2#14561862C211yesmaximal, characteristic
3#14561513C212yesmaximal
4#14561513C212yesmaximal
5C19×#2851C211yesmaximal, characteristic
6C2×C4⋊(C19⋊C8)—21no—
7C2×C22⋊(C19⋊C8)C2212yes—
8C2×C19⋊#95—21no—
9C2×C19⋊#95—21no—
10C2×C19⋊#95C2212yes—
11#11926299—21no—
12C2×C19×#125C411yescharacteristic, complemented
13C22×C42×C19C2211yescharacteristic
14C19×#389C411yescharacteristic, complemented
15C19×#389C411yescharacteristic, complemented
16C19×#387—21no—
17C19×#387—21no—
18C19×#385—21no—
19C19×#385—21no—
20C19×#382C411yescharacteristic, complemented
21C19×#380C2211yescharacteristic
22C19×#380C2211yescharacteristic
23C23×C4×C19D411yescharacteristic
24C23×C4×C19D411yescharacteristic
25C23×C4×C19C2311yescharacteristic
26C23×Dic19—22no—
27C19×#125—42no—
28C2×C4⋊C4×C19—21no—
29C2×C4⋊C4×C19—21no—
30C2×C4⋊C4×C19—21no—
31C2×C4⋊C4×C19—21no—
32C2×C4⋊C4×C19C2×C411yescharacteristic
33C2×C4⋊C4×C19C2×C411yescharacteristic
34C2×C4⋊C4×C19C2×C411yescharacteristic
35C2×C4⋊C4×C19C2×C411yescharacteristic
36C2×C22⋊C4×C19—21no—
37C2×C22⋊C4×C19—21no—
38C2×C42×C19—42no—
39C2×C42×C19C2×C411yescharacteristic
40C2×C42×C19C2×C411yescharacteristic
41C2×C42×C19D411yescharacteristic
42C2×C42×C19D411yescharacteristic
43C22×C19⋊C8—22no—
44C19×#95—21no—
45C19×#95—21no—
46C19×#95—21no—
47C19×#95—21no—
48C19×#95—21no—
49C19×#95—21no—
50C19⋊#95—22no—
51C19⋊#95—42no—
52C19⋊#95—42no—
53C19⋊#95Q814yes—
54C22⋊(C19⋊C8)—24no—
55C4⋊(C19⋊C8)—42no—
56C24×C19C2×D411yescharacteristic
57C22×C4×C19—22no—
58C22×C4×C19—21no—
59C22×C4×C19—21no—
60C22×C4×C19—22no—
61C22×C4×C19—21no—
62C22×C4×C19—21no—
63C22×C4×C19—21no—
64C22×C4×C19—21no—
65C22×C4×C19—41no—
66C22×C4×C19—41no—
67C22×C4×C19—41no—
68C22×C4×C19—41no—
69C22×C4×C19—41no—
70C22×C4×C19C22⋊C411yescharacteristic
71C22×C4×C19C22⋊C411yescharacteristic
72C22×C4×C19C22⋊C411yescharacteristic
73C22×C4×C19C22⋊C411yescharacteristic
74C22×C4×C19C22×C411yescharacteristic
75C22×C4×C19C2×D411yescharacteristic
76C22×C4×C19C2×Q812yes—
77C22×C4×C19#4112yes—
78C22×Dic19—24no—
79C22×Dic19—42no—
80C22×Dic19—42no—
81C22×Dic19—42no—
82C22×Dic19—42no—
83C22×Dic19—42no—
84C22×Dic19—42no—
85C4⋊C4×C19—41no—
86C4⋊C4×C19—41no—
87C4⋊C4×C19—41no—
88C4⋊C4×C19—41no—
89C4⋊C4×C19—42no—
90C4⋊C4×C19—42no—
91C4⋊C4×C19—42no—
92C4⋊C4×C19—42no—
93C22⋊C4×C19—42no—
94C22⋊C4×C19—41no—
95C22⋊C4×C19—41no—
96C42×C19—22no—
97C42×C19—22no—
98C42×C19—41no—
99C42×C19—41no—
100C2×C19⋊C8—42no—
101C2×C19⋊C8—42no—
102C2×C19⋊C8—42no—
103#9913—191nomaximal, Sylow
104C23×C19—21no—
105C23×C19—21no—
106C23×C19—21no—
107C23×C19—21no—
108C23×C19C2×C22⋊C411yescharacteristic
109C23×C19C22⋊Q812yes—
110C23×C19#13512yes—
111C23×C19AGL(1,ℤ/8)11yescharacteristic
112C23×C19#13711yescharacteristic
113C2×C4×C19—21no—
114C2×C4×C19—21no—
115C2×C4×C19—21no—
116C2×C4×C19—21no—
117C2×C4×C19—21no—
118C2×C4×C19—21no—
119C2×C4×C19—21no—
120C2×C4×C19—21no—
121C2×C4×C19—21no—
122C2×C4×C19—21no—
123C2×C4×C19—21no—
124C2×C4×C19—21no—
125C2×C4×C19—21no—
126C2×C4×C19—21no—
127C2×C4×C19—21no—
128C2×C4×C19—42no—
129C2×C4×C19—42no—
130C2×C4×C19—44no—
131C2×C4×C19—42no—
132C2×C4×C19—42no—
133C2×C4×C19—41no—
134C2×C4×C19—41no—
135C2×C4×C19—41no—
136C2×C4×C19—41no—
137C2×C4×C19—41no—
138C2×C4×C19—41no—
139C2×C4×C19—41no—
140C2×C4×C19—41no—
141C2×C4×C19—41no—
142C2×C4×C19—41no—
143C2×C4×C19—41no—
144C2×C4×C19—41no—
145C2×C4×C19#9912yes—
146C2×C4×C19C4×Q812yes—
147C2×C4×C19#12411yescharacteristic
148C2×C4×C19C4⋊Q811yescharacteristic
149C2×Dic19—44no—
150C2×Dic19—44no—
151C2×Dic19—44no—
152C2×Dic19—82no—
153C2×Dic19—82no—
154C2×Dic19—82no—
155C2×Dic19—82no—
156C19⋊C8—82no—
157#2851D1911yescharacteristic
158#1797—191no—
159#1434—191no—
160#1294—192no—
161#1294—192no—
162C22×C19—22no—
163C22×C19—22no—
164C22×C19—21no—
165C22×C19—21no—
166C22×C19—21no—
167C22×C19—21no—
168C22×C19—22no—
169C22×C19—22no—
170C22×C19#39111yescharacteristic
171C22×C19C2×#9911yescharacteristic
172C22×C19#41011yescharacteristic
173C22×C19#41611yescharacteristic
174C22×C19#41711yescharacteristic
175C22×C19#42111yescharacteristic
176C22×C19#42111yescharacteristic
177C22×C19#47812yes—
178C22×C19#47912yes—
179C4×C19—21no—
180C4×C19—22no—
181C4×C19—21no—
182C4×C19—22no—
183C4×C19—41no—
184C4×C19—41no—
185C4×C19—41no—
186C4×C19—81no—
187C4×C19—81no—
188C4×C19—81no—
189C4×C19—81no—
190Dic19—84no—
191C2×#125Dic1911yescharacteristic, complemented
192C22×C42C2×D1911yescharacteristic
193C2×C4⋊C8—381no—
194C2×C22⋊C8—192no—
195#389Dic1911yescharacteristic, complemented
196#389Dic1911yescharacteristic, complemented
197#387—21no—
198#387—21no—
199#385—21no—
200#385—21no—
201#382Dic1911yescharacteristic, complemented
202#380C2×D1911yescharacteristic
203#380C2×D1911yescharacteristic
204C2×#95—192no—
205C2×#95—381no—
206C2×#95—381no—
207#336—381no—
208C2×C19—22no—
209C2×C19—22no—
210C2×C19#151211yescharacteristic
211C2×C19#151311yescharacteristic
212C2×C19#151611yescharacteristic
213C2×C19#152111yescharacteristic
214C2×C19#198911yescharacteristic
215C2×C19#199511yescharacteristic
216C2×C19#199611yescharacteristic
217C23×C4—382no—
218C23×C4C22⋊D1911yescharacteristic
219C23×C4C22⋊D1911yescharacteristic
220C23×C4C22×D1911yescharacteristic
221C22×C8—382no—
222#125—42no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4C2×Dic1911yescharacteristic
228C2×C4⋊C4C2×Dic1911yescharacteristic
229C2×C4⋊C4C2×Dic1911yescharacteristic
230C2×C4⋊C4C2×Dic1911yescharacteristic
231C2×C22⋊C4—21no—
232C2×C22⋊C4—21no—
233C2×C42—42no—
234C2×C42C2×Dic1911yescharacteristic
235C2×C42C2×Dic1911yescharacteristic
236C2×C42C22⋊D1911yescharacteristic
237C2×C42C22⋊D1911yescharacteristic
238C4⋊C8—762no—
239C22⋊C8—384no—
240#95—21no—
241#95—21no—
242#95—21no—
243#95—21no—
244#95—21no—
245#95—21no—
246#95—194no—
247#95—382no—
248#95—762no—
249#95—762no—
250C19#991311yescharacteristic, complemented, Sylow
251C24C2×C22⋊D1911yescharacteristic
252C22×C4—21no—
253C22×C4—22no—
254C22×C4—21no—
255C22×C4—22no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—41no—
261C22×C4—41no—
262C22×C4—41no—
263C22×C4—41no—
264C22×C4—41no—
265C22×C4—384no—
266C22×C4—762no—
267C22×C4—762no—
268C22×C4—762no—
269C22×C4—762no—
270C22×C4—762no—
271C22×C4—762no—
272C22×C4C22⋊Dic1911yescharacteristic
273C22×C4C22⋊Dic1911yescharacteristic
274C22×C4C22⋊Dic1911yescharacteristic
275C22×C4C22⋊Dic1911yescharacteristic
276C22×C4Q8×D1912yes—
277C22×C4#6454512yes—
278C22×C4C22×Dic1911yescharacteristic
279C22×C4C2×C22⋊D1911yescharacteristic
280C2×C8—762no—
281C2×C8—762no—
282C2×C8—762no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C4⋊C4—42no—
288C4⋊C4—42no—
289C4⋊C4—42no—
290C4⋊C4—42no—
291C22⋊C4—41no—
292C22⋊C4—42no—
293C22⋊C4—41no—
294C42—22no—
295C42—22no—
296C42—41no—
297C42—41no—
298C23—21no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23#1059739212yes—
303C23#1059739511yescharacteristic
304C23#1059739612yes—
305C23#1059739711yescharacteristic
306C23C2×C22⋊Dic1911yescharacteristic
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—44no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—764no—
340C2×C4—764no—
341C2×C4—764no—
342C2×C4—1522no—
343C2×C4—1522no—
344C2×C4—1522no—
345C2×C4—1522no—
346C2×C4#1059729112yes—
347C2×C4#1059739011yescharacteristic
348C2×C4Q8×Dic1912yes—
349C2×C4#1059739311yescharacteristic
350C8—1522no—
351C22—22no—
352C22—22no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—22no—
358C22—22no—
359C22#1192645111yescharacteristic
360C22C2×#1059729111yescharacteristic
361C22#1192651811yescharacteristic
362C22#1192654011yescharacteristic
363C22#1192654511yescharacteristic
364C22#1192656111yescharacteristic
365C22#1192656111yescharacteristic
366C22#1192684112yes—
367C22#1192684812yes—
368C4—21no—
369C4—21no—
370C4—22no—
371C4—22no—
372C4—41no—
373C4—41no—
374C4—41no—
375C4—81no—
376C4—81no—
377C4—81no—
378C4—81no—
379C4—1524no—
380C2—22no—
381C2—22no—
382C2#1456217311yescharacteristic
383C2#1456217811yescharacteristic
384C2#1456219111yescharacteristic
385C2#1456221211yescharacteristic
386C2#1456459311yescharacteristic
387C2#1456461711yescharacteristic
388C2#1456462111yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic19
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#2851C2
socleC23×C19C2×C22⋊C4
prime radicalC24×C19C2×D4
cosocleC23×C4×C19C23
hypercenter#2851D19
hypocenterC19#9913
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2851

Complements

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

NH ≅ G/Ntype
12. C2×C19×#125C4semidirect
14. C19×#389C4semidirect
15. C19×#389C4semidirect
20. C19×#382C4semidirect
191. C2×#125Dic19semidirect
195. #389Dic19semidirect
196. #389Dic19semidirect
201. #382Dic19semidirect
250. C19#9913semidirect

Maximal subgroups

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

subgroupindex
#145636152
#145618622
#145615132
C19×#28512
#991319