Finite Group Databasebeta

← #18089250

Subgroups — #18089250

Order 4864.

2118 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10597289C214yesmaximal, complemented
2C2×#11926299C211yesmaximal, characteristic, complemented
3#14561865C211yesmaximal, characteristic, complemented
4C22×C19×#127C211yesmaximal, characteristic
5C23×C19⋊C8C2212yes—
6C22×C4⋊Dic19C2212yes—
7C2×#10597289—28no—
8C2×#10597289—28no—
9C2×#10597289—28no—
10C2×C19⋊#95—22no—
11#11926299—22no—
12C23×D4×C19—22no—
13C23×D4×C19C2212yes—
14C2×C19×#127—28no—
15C2×C19×#127—22no—
16C2×C19×#127C414yescomplemented
17C22×C42×C19C2211yescharacteristic
18C25×C19—22no—
19C22×D4×C19—216no—
20C22×D4×C19—28no—
21C22×D4×C19—24no—
22C22×D4×C19—24no—
23C22×D4×C19—24no—
24C22×D4×C19—22no—
25C22×D4×C19—24no—
26C22×D4×C19—24no—
27C22×D4×C19—48no—
28C22×D4×C19—44no—
29C22×D4×C19—44no—
30C22×D4×C19C2×C414yes—
31C22×D4×C19D418yes—
32C23×C4×C19D412yes—
33C23×C4×C19C2311yescharacteristic
34C23×Dic19—22no—
35C19×#127—216no—
36C19×#127—216no—
37C2×C42×C19—24no—
38C2×C42×C19C2×C412yes—
39C2×C42×C19D412yes—
40C2×C4⋊Dic19—24no—
41C2×C4⋊Dic19—24no—
42C2×C4⋊Dic19—22no—
43C2×C4⋊Dic19D414yescomplemented
44C22×C19⋊C8—24no—
45C22×C19⋊C8—24no—
46C22×C19⋊C8—22no—
47C22×C19⋊C8—22no—
48C22×C19⋊C8D414yescomplemented
49#10597289—232no—
50C19⋊#95—44no—
51C24×C19—24no—
52C24×C19—28no—
53C24×C19—44no—
54C24×C19—42no—
55C24×C19—42no—
56C24×C19—44no—
57C24×C19—44no—
58C24×C19—48no—
59C24×C19C2×D411yescharacteristic
60C2×D4×C19—232no—
61C2×D4×C19—24no—
62C2×D4×C19—28no—
63C2×D4×C19—28no—
64C2×D4×C19—28no—
65C2×D4×C19—28no—
66C2×D4×C19—28no—
67C2×D4×C19—28no—
68C2×D4×C19—28no—
69C2×D4×C19—416no—
70C2×D4×C19—432no—
71C2×D4×C19—432no—
72C2×D4×C19—416no—
73C2×D4×C19—44no—
74C2×D4×C19—44no—
75C2×D4×C19—44no—
76C2×D4×C19—44no—
77C2×D4×C19—44no—
78C2×D4×C19—42no—
79C2×D4×C19—42no—
80C2×D4×C19C22⋊C418yes—
81C22×C4×C19—24no—
82C22×C4×C19—24no—
83C22×C4×C19C22⋊C414yes—
84C22×C4×C19D814yes—
85C22×C4×C19SD1614yes—
86C22×C4×C19C22×C411yescharacteristic
87C22×C4×C19C2×D412yes—
88C22×C4×C19C2×D412yes—
89C22×C4×C19C2×D414yes—
90C22×C4×C19C2×D411yescharacteristic
91C22×C4×C19#4112yes—
92C22×C4×C19#4112yes—
93C22×Dic19—24no—
94C22×Dic19—42no—
95C22×Dic19—42no—
96C22×Dic19—44no—
97C22×Dic19—44no—
98C42×C19—24no—
99C42×C19—24no—
100C4⋊Dic19—28no—
101C4⋊Dic19—44no—
102C2×C19⋊C8—28no—
103C2×C19⋊C8—24no—
104C2×C19⋊C8—42no—
105C2×C19⋊C8—44no—
106C2×C19⋊C8—42no—
107#11008—191nomaximal, Sylow
108C23×C19—28no—
109C23×C19—44no—
110C23×C19—44no—
111C23×C19—48no—
112C23×C19—48no—
113C23×C19—48no—
114C23×C19—48no—
115C23×C19—416no—
116C23×C19—416no—
117C23×C19—88no—
118C23×C19—88no—
119C23×C19—84no—
120C23×C19—84no—
121C23×C19—82no—
122C23×C19—82no—
123C23×C19—84no—
124C23×C19C2×C22⋊C411yescharacteristic
125C23×C19#12012yes—
126C23×C19#12112yes—
127C23×C19#12411yescharacteristic
128C23×C19#12711yescharacteristic
129C23×C19C2×D812yes—
130C23×C19C2×SD1612yes—
131C23×C19AGL(1,ℤ/8)14yes—
132D4×C19—216no—
133D4×C19—464no—
134D4×C19—48no—
135D4×C19—48no—
136D4×C19—48no—
137C2×C4×C19—24no—
138C2×C4×C19—24no—
139C2×C4×C19—28no—
140C2×C4×C19—28no—
141C2×C4×C19#10218yescomplemented
142C2×C4×C19C2×C22⋊C412yes—
143C2×C4×C19C4×D412yes—
144C2×C4×C19C4×D412yes—
145C2×C4×C19#12014yes—
146C2×C4×C19#12012yes—
147C2×C4×C19#12112yes—
148C2×C4×C19#12114yes—
149C2×C4×C19#12114yes—
150C2×C4×C19#12314yes—
151C2×C4×C19#12411yescharacteristic
152C2×C4×C19#12711yescharacteristic
153C2×Dic19—44no—
154C2×Dic19—48no—
155C2×Dic19—84no—
156C2×Dic19—82no—
157C2×Dic19—82no—
158C19⋊C8—44no—
159C22×#127D1911yescharacteristic
160C22×#102—194no—
161C2×#336—191no—
162C4⋊#95—191no—
163C22×C19—48no—
164C22×C19—416no—
165C22×C19—84no—
166C22×C19—84no—
167C22×C19—88no—
168C22×C19—88no—
169C22×C19—88no—
170C22×C19—816no—
171C22×C19#37911yescharacteristic
172C22×C19#39011yescharacteristic
173C22×C19#39011yescharacteristic
174C22×C19#39212yes—
175C22×C19#39412yes—
176C22×C19C2×#10212yes—
177C22×C19#41812yes—
178C22×C19#44714yes—
179C22×C19#45014yes—
180C22×C19#45914yes—
181C22×C19#46014yes—
182C22×C19#48612yes—
183C22×C19#49012yes—
184C22×C19#49211yescharacteristic
185C22×C19#49311yescharacteristic
186C22×C19#49612yes—
187C4×C19—28no—
188C4×C19#38614yes—
189C4×C19#39212yes—
190C4×C19#39412yes—
191Dic19—84no—
192C23×D4—22no—
193C23×D4C2×D1912yes—
194C23×C8—192no—
195C2×#127—28no—
196C2×#127—22no—
197C2×#127Dic1914yescomplemented
198C22×C4⋊C4—192no—
199C22×C42C2×D1911yescharacteristic
200C2×#102—388no—
201C2×#102—388no—
202C2×#102—388no—
203C2×#95—382no—
204#336—382no—
205C2×C19—88no—
206C2×C19#143811yescharacteristic
207C2×C19#178612yes—
208C2×C19#195711yescharacteristic
209C2×C19#196111yescharacteristic
210C2×C19#198212yes—
211C2×C19#201112yes—
212C2×C19#201412yes—
213C2×C19#204114yes—
214C25—22no—
215C22×D4—216no—
216C22×D4—28no—
217C22×D4—24no—
218C22×D4—24no—
219C22×D4—24no—
220C22×D4—24no—
221C22×D4—24no—
222C22×D4—22no—
223C22×D4—48no—
224C22×D4—44no—
225C22×D4—44no—
226C22×D4C2×Dic1914yes—
227C22×D4C22⋊D1918yes—
228C23×C4—382no—
229C23×C4C22⋊D1912yes—
230C23×C4C22×D1911yescharacteristic
231C22×C8—194no—
232C22×C8—384no—
233C22×C8—382no—
234C22×C8—382no—
235C22×C8—384no—
236#127—216no—
237#127—216no—
238C2×C4⋊C4—194no—
239C2×C4⋊C4—384no—
240C2×C4⋊C4—384no—
241C2×C4⋊C4—382no—
242C2×C42—24no—
243C2×C42C2×Dic1912yes—
244C2×C42C22⋊D1912yes—
245#102—3832no—
246#95—764no—
247C19#1100811yescharacteristic, complemented, Sylow
248C24—24no—
249C24—28no—
250C24—44no—
251C24—48no—
252C24—44no—
253C24—42no—
254C24—44no—
255C24—42no—
256C24C2×C22⋊D1911yescharacteristic
257C2×D4—232no—
258C2×D4—28no—
259C2×D4—28no—
260C2×D4—28no—
261C2×D4—28no—
262C2×D4—28no—
263C2×D4—28no—
264C2×D4—24no—
265C2×D4—28no—
266C2×D4—416no—
267C2×D4—432no—
268C2×D4—432no—
269C2×D4—44no—
270C2×D4—42no—
271C2×D4—44no—
272C2×D4—44no—
273C2×D4—44no—
274C2×D4—44no—
275C2×D4—42no—
276C2×D4—416no—
277C2×D4C22⋊Dic1918yes—
278C22×C4—24no—
279C22×C4—24no—
280C22×C4—384no—
281C22×C4—764no—
282C22×C4—764no—
283C22×C4—762no—
284C22×C4—762no—
285C22×C4#6452514yes—
286C22×C4#6452614yes—
287C22×C4C22⋊Dic1914yes—
288C22×C4D4×D1912yes—
289C22×C4D4×D1912yes—
290C22×C4#6454312yes—
291C22×C4#6454312yes—
292C22×C4C22×Dic1911yescharacteristic
293C22×C4C2×C22⋊D1914yes—
294C22×C4C2×C22⋊D1911yescharacteristic
295C2×C8—388no—
296C2×C8—384no—
297C2×C8—764no—
298C2×C8—762no—
299C2×C8—762no—
300C4⋊C4—388no—
301C4⋊C4—764no—
302C42—24no—
303C42—24no—
304C23—28no—
305C23—48no—
306C23—48no—
307C23—416no—
308C23—416no—
309C23—44no—
310C23—44no—
311C23—48no—
312C23—48no—
313C23—84no—
314C23—84no—
315C23—82no—
316C23—82no—
317C23—84no—
318C23—88no—
319C23—88no—
320C23C2×#6452512yes—
321C23#1059737814yes—
322C23C2×#6452612yes—
323C23#1059738211yescharacteristic
324C23#1059738412yes—
325C23#1059738611yescharacteristic
326C23C2×C22⋊Dic1911yescharacteristic
327C23#1059739912yes—
328D4—216no—
329D4—464no—
330D4—48no—
331D4—48no—
332D4—48no—
333C2×C4—24no—
334C2×C4—24no—
335C2×C4—28no—
336C2×C4—28no—
337C2×C4—764no—
338C2×C4—768no—
339C2×C4—1522no—
340C2×C4—1522no—
341C2×C4—1524no—
342C2×C4#1059728918yescomplemented
343C2×C4D4×Dic1912yes—
344C2×C4D4×Dic1912yes—
345C2×C4#1059738114yes—
346C2×C4#1059738211yescharacteristic
347C2×C4#1059738314yes—
348C2×C4#1059738412yes—
349C2×C4#1059738514yes—
350C2×C4#1059738514yes—
351C2×C4#1059738611yescharacteristic
352C2×C4C2×C22⋊Dic1912yes—
353C2×C4#1059739912yes—
354C8—764no—
355C22—48no—
356C22—416no—
357C22—816no—
358C22—84no—
359C22—88no—
360C22—84no—
361C22—88no—
362C22—88no—
363C22#1192640011yescharacteristic
364C22#1192644711yescharacteristic
365C22#1192644711yescharacteristic
366C22#1192645212yes—
367C22#1192645812yes—
368C22C2×#1059728912yes—
369C22#1192654912yes—
370C22#1192667814yes—
371C22#1192669514yes—
372C22#1192673614yes—
373C22#1192674114yes—
374C22#1192689012yes—
375C22#1192690812yes—
376C22#1192691611yescharacteristic
377C22#1192692011yescharacteristic
378C22#1192693112yes—
379C4—28no—
380C4—1524no—
381C4#1192642414yes—
382C4#1192645212yes—
383C4#1192645812yes—
384C2—88no—
385C2#1456187611yescharacteristic
386C2#1456356612yes—
387C2#1456444211yescharacteristic
388C2#1456446011yescharacteristic
389C2#1456456312yes—
390C2#1456470612yes—
391C2#1456472312yes—
392C2#1456486614yes—
subgroupG/H
centerC24C2×C22⋊D19
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
Fitting, prime radicalC22×C19×#127C2
socleC24×C19C2×D4
cosocleC23×C4×C19C23
hypercenterC22×#127D19
hypocenterC19#11008
LCSG ▷ C22×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C24 ◁ C22×C42 ◁ C22×#127

Complements

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

NH ≅ G/Ntype
1. C22×#10597289C2semidirect
2. C2×#11926299C2semidirect
3. #14561865C2semidirect
16. C2×C19×#127C4semidirect
43. C2×C4⋊Dic19D4semidirect
48. C22×C19⋊C8D4semidirect
141. C2×C4×C19#102semidirect
197. C2×#127Dic19semidirect
247. C19#11008semidirect
342. C2×C4#10597289semidirect

Maximal subgroups

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

subgroupindex
C22×#105972892
C2×#119262992
#145618652
C22×C19×#1272
#1100819