Finite Group Databasebeta

← #18080459

Subgroups — #18080459

Order 4864.

956 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 956 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14566213C211yesmaximal, characteristic
2#14563709C212yesmaximal, complemented
3#14563550C211yesmaximal, characteristic
4C19⋊#1304C212yesmaximal, complemented
5C19×#2405C211yesmaximal, characteristic
6C22×C22⋊Dic19—21no—
7C2×#10597291—22no—
8#11926424—24no—
9#11926407—21no—
10#11926400C2212yes—
11#11926400C2212yes—
12#11926311—24no—
13C23×D4×C19C2211yescharacteristic
14C2×C19×#123C412yescomplemented
15C22×C22⋊C4×C19C2211yescharacteristic
16C19×#394—22no—
17C19×#386C412yescomplemented
18C19×#385—21no—
19C19×#379—21no—
20C19×#379C2211yescharacteristic
21C25×C19D411yescharacteristic
22C25×C19C2311yescharacteristic
23C22×D4×C19—22no—
24C22×D4×C19—22no—
25C22×D4×C19—44no—
26C22×D4×C19C2×C412yes—
27C22×D4×C19D412yes—
28C23×C4×C19C2×C411yescharacteristic, complemented
29C23×C4×C19C2×C411yescharacteristic, complemented
30C23×C4×C19D411yescharacteristic
31C23×Dic19—22no—
32C19×#123—44no—
33C2×C4⋊C4×C19—22no—
34C2×C22⋊C4×C19—22no—
35C2×C22⋊C4×C19—21no—
36C2×C22⋊C4×C19—21no—
37C2×C22⋊C4×C19—22no—
38C2×C22⋊C4×C19—21no—
39C2×C22⋊C4×C19—22no—
40C2×C22⋊C4×C19—22no—
41C2×C22⋊C4×C19—21no—
42C2×C22⋊C4×C19C2×C412yescomplemented
43C2×C22⋊Dic19—22no—
44C2×C22⋊Dic19—22no—
45C2×C22⋊Dic19—22no—
46C2×C22⋊Dic19—22no—
47C2×C22⋊Dic19—22no—
48C2×C22⋊Dic19—22no—
49C2×C22⋊Dic19—44no—
50C2×C22⋊Dic19D414yes—
51C19×#95—22no—
52#10597291—44no—
53C19⋊#95—24no—
54C24×C19—21no—
55C24×C19—24no—
56C24×C19—21no—
57C24×C19—42no—
58C24×C19—42no—
59C24×C19—42no—
60C24×C19—81no—
61C24×C19—81no—
62C24×C19C22⋊C412yes—
63C24×C19C22×C411yescharacteristic
64C24×C19C2×D412yes—
65C24×C19C2×D411yescharacteristic
66C24×C19C2×D411yescharacteristic
67C24×C19#4112yes—
68C2×D4×C19—24no—
69C2×D4×C19—24no—
70C2×D4×C19—24no—
71C2×D4×C19—24no—
72C2×D4×C19—42no—
73C2×D4×C19—42no—
74C2×D4×C19—44no—
75C2×D4×C19—44no—
76C2×D4×C19—48no—
77C22×C4×C19—21no—
78C22×C4×C19—21no—
79C22×C4×C19—22no—
80C22×C4×C19—21no—
81C22×C4×C19—21no—
82C22×C4×C19—22no—
83C22×C4×C19—22no—
84C22×C4×C19—42no—
85C22×C4×C19—42no—
86C22×C4×C19—81no—
87C22×C4×C19C22⋊C412yes—
88C22×Dic19—24no—
89C22×Dic19—44no—
90C22×Dic19—42no—
91C22×Dic19—82no—
92C22×Dic19—82no—
93C4⋊C4×C19—44no—
94C22⋊C4×C19—42no—
95C22⋊C4×C19—44no—
96C22⋊C4×C19—41no—
97C22⋊C4×C19—42no—
98C22⋊C4×C19—41no—
99C22⋊C4×C19—42no—
100C22⋊C4×C19—81no—
101C22⋊C4×C19—82no—
102C22⋊Dic19—44no—
103C22⋊Dic19—44no—
104C22⋊Dic19—44no—
105C22⋊Dic19—44no—
106C22⋊Dic19—44no—
107C22⋊Dic19—82no—
108C22⋊Dic19—82no—
109#9499—191nomaximal, Sylow
110C23×C19—22no—
111C23×C19—22no—
112C23×C19—24no—
113C23×C19—22no—
114C23×C19—22no—
115C23×C19—22no—
116C23×C19—22no—
117C23×C19—22no—
118C23×C19—22no—
119C23×C19—24no—
120C23×C19—41no—
121C23×C19—41no—
122C23×C19—41no—
123C23×C19—42no—
124C23×C19—42no—
125C23×C19—41no—
126C23×C19—42no—
127C23×C19—42no—
128C23×C19—41no—
129C23×C19—42no—
130C23×C19—42no—
131C23×C19—42no—
132C23×C19—42no—
133C23×C19—42no—
134C23×C19—81no—
135C23×C19—81no—
136C23×C19—88no—
137C23×C19—88no—
138C23×C19#9914yes—
139C23×C19C2×C22⋊C411yescharacteristic
140C23×C19C4×D412yes—
141C23×C19#12011yescharacteristic
142C23×C19#12112yes—
143C23×C19#12311yescharacteristic
144D4×C19—48no—
145D4×C19—48no—
146C2×C4×C19—22no—
147C2×C4×C19—22no—
148C2×C4×C19—22no—
149C2×C4×C19—42no—
150C2×C4×C19—42no—
151C2×C4×C19—42no—
152C2×C4×C19—42no—
153C2×C4×C19—42no—
154C2×C4×C19—41no—
155C2×C4×C19—41no—
156C2×C4×C19—42no—
157C2×C4×C19—42no—
158C2×C4×C19—82no—
159C2×C4×C19—82no—
160C2×Dic19—44no—
161C2×Dic19—44no—
162C2×Dic19—44no—
163C2×Dic19—88no—
164C2×Dic19—82no—
165C2×Dic19—82no—
166C2×Dic19—82no—
167#2405D1911yescharacteristic
168#2308—191no—
169#1819—192no—
170#1781—191no—
171#1304—192no—
172C22×C19—21no—
173C22×C19—21no—
174C22×C19—21no—
175C22×C19—21no—
176C22×C19—22no—
177C22×C19—21no—
178C22×C19—22no—
179C22×C19—22no—
180C22×C19—21no—
181C22×C19—22no—
182C22×C19—24no—
183C22×C19—22no—
184C22×C19—22no—
185C22×C19—21no—
186C22×C19—44no—
187C22×C19—44no—
188C22×C19—44no—
189C22×C19—44no—
190C22×C19—44no—
191C22×C19—42no—
192C22×C19—42no—
193C22×C19—84no—
194C22×C19—82no—
195C22×C19—82no—
196C22×C19—84no—
197C22×C19—84no—
198C22×C19#38611yescharacteristic
199C22×C19C2×#9912yes—
200C22×C19#45812yes—
201C4×C19—42no—
202C4×C19—82no—
203C4×C19—81no—
204C4×C19—81no—
205Dic19—84no—
206Dic19—162no—
207C23×D4C2×D1911yescharacteristic
208C2×#123Dic1912yescomplemented
209C22×C22⋊C4—381no—
210C22×C22⋊C4C2×D1911yescharacteristic
211C2×#99—382no—
212#394—22no—
213#386—384no—
214#386Dic1912yescomplemented
215#385—21no—
216#381—381no—
217#379—21no—
218#379—192no—
219#379—192no—
220#379C2×D1911yescharacteristic
221#342—384no—
222C2×C19—22no—
223C2×C19—22no—
224C2×C19—42no—
225C2×C19—42no—
226C2×C19—41no—
227C2×C19—44no—
228C2×C19#189011yescharacteristic
229C2×C19#189811yescharacteristic
230C2×C19#191311yescharacteristic
231C25C22⋊D1911yescharacteristic
232C25C22×D1911yescharacteristic
233C22×D4—22no—
234C22×D4—22no—
235C22×D4—44no—
236C22×D4C2×Dic1912yes—
237C22×D4C22⋊D1912yes—
238C23×C4—382no—
239C23×C4C2×Dic1911yescharacteristic, complemented
240C23×C4C2×Dic1911yescharacteristic, complemented
241C23×C4C22⋊D1911yescharacteristic
242#123—44no—
243C2×C4⋊C4—22no—
244C2×C22⋊C4—22no—
245C2×C22⋊C4—22no—
246C2×C22⋊C4—22no—
247C2×C22⋊C4—21no—
248C2×C22⋊C4—21no—
249C2×C22⋊C4—21no—
250C2×C22⋊C4—22no—
251C2×C22⋊C4—21no—
252C2×C22⋊C4—194no—
253C2×C22⋊C4—382no—
254C2×C22⋊C4—382no—
255C2×C22⋊C4—382no—
256C2×C22⋊C4—382no—
257C2×C22⋊C4—382no—
258C2×C22⋊C4—382no—
259C2×C22⋊C4—764no—
260C2×C22⋊C4C2×Dic1912yescomplemented
261#99—764no—
262#95—22no—
263#95—384no—
264C19#949911yescharacteristic, complemented, Sylow
265C24—21no—
266C24—21no—
267C24—24no—
268C24—42no—
269C24—42no—
270C24—42no—
271C24—81no—
272C24—81no—
273C24C22⋊Dic1912yes—
274C24D4×D1912yes—
275C24#6454312yes—
276C24C22×Dic1911yescharacteristic
277C24C2×C22⋊D1911yescharacteristic
278C24C2×C22⋊D1911yescharacteristic
279C2×D4—24no—
280C2×D4—24no—
281C2×D4—24no—
282C2×D4—24no—
283C2×D4—42no—
284C2×D4—42no—
285C2×D4—44no—
286C2×D4—44no—
287C2×D4—48no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—22no—
292C22×C4—21no—
293C22×C4—22no—
294C22×C4—22no—
295C22×C4—42no—
296C22×C4—42no—
297C22×C4—81no—
298C22×C4—384no—
299C22×C4—764no—
300C22×C4—762no—
301C22×C4—1522no—
302C22×C4—1522no—
303C22×C4C22⋊Dic1912yes—
304C4⋊C4—44no—
305C22⋊C4—42no—
306C22⋊C4—41no—
307C22⋊C4—41no—
308C22⋊C4—42no—
309C22⋊C4—44no—
310C22⋊C4—42no—
311C22⋊C4—81no—
312C22⋊C4—82no—
313C22⋊C4—764no—
314C22⋊C4—764no—
315C22⋊C4—764no—
316C22⋊C4—764no—
317C22⋊C4—764no—
318C22⋊C4—1522no—
319C22⋊C4—1522no—
320C23—22no—
321C23—22no—
322C23—24no—
323C23—22no—
324C23—22no—
325C23—22no—
326C23—22no—
327C23—24no—
328C23—22no—
329C23—22no—
330C23—41no—
331C23—41no—
332C23—41no—
333C23—41no—
334C23—42no—
335C23—42no—
336C23—42no—
337C23—42no—
338C23—42no—
339C23—41no—
340C23—42no—
341C23—42no—
342C23—42no—
343C23—42no—
344C23—81no—
345C23—81no—
346C23—88no—
347C23—88no—
348C23#1059729114yes—
349C23D4×Dic1912yes—
350C23#1059738111yescharacteristic
351C23#1059738311yescharacteristic
352C23#1059738512yes—
353C23C2×C22⋊Dic1911yescharacteristic
354D4—48no—
355D4—48no—
356C2×C4—22no—
357C2×C4—22no—
358C2×C4—22no—
359C2×C4—42no—
360C2×C4—42no—
361C2×C4—42no—
362C2×C4—42no—
363C2×C4—42no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—42no—
367C2×C4—42no—
368C2×C4—82no—
369C2×C4—82no—
370C2×C4—764no—
371C2×C4—764no—
372C2×C4—764no—
373C2×C4—1522no—
374C2×C4—1522no—
375C2×C4—1522no—
376C2×C4—1528no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—22no—
382C22—22no—
383C22—21no—
384C22—22no—
385C22—21no—
386C22—22no—
387C22—21no—
388C22—22no—
389C22—22no—
390C22—24no—
391C22—44no—
392C22—44no—
393C22—44no—
394C22—44no—
395C22—44no—
396C22—42no—
397C22—42no—
398C22—82no—
399C22—82no—
400C22—84no—
401C22—84no—
402C22—84no—
403C22#1192642411yescharacteristic
404C22C2×#1059729112yes—
405C22#1192673312yes—
406C4—42no—
407C4—82no—
408C4—81no—
409C4—81no—
410C4—3042no—
411C4—1524no—
412C2—22no—
413C2—22no—
414C2—42no—
415C2—41no—
416C2—42no—
417C2—44no—
418C2#1456404911yescharacteristic
419C2#1456408911yescharacteristic
420C2#1456417811yescharacteristic
subgroupG/H
centerC22#11926424
commutatorC24×C19C22×C4
FrattiniC25C22×D19
FittingC19×#2405C2
socleC22×C19#386
prime radicalC23×D4×C19C22
cosocleC25×C19C23
hypercenter#2405D19
hypocenterC19#9499
LCSG ▷ C24×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C25 ◁ #2405

Complements

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

NH ≅ G/Ntype
2. #14563709C2semidirect
4. C19⋊#1304C2semidirect
14. C2×C19×#123C4semidirect
17. C19×#386C4semidirect
28. C23×C4×C19C2×C4semidirect
29. C23×C4×C19C2×C4semidirect
42. C2×C22⋊C4×C19C2×C4semidirect
208. C2×#123Dic19semidirect
214. #386Dic19semidirect
239. C23×C4C2×Dic19semidirect
240. C23×C4C2×Dic19semidirect
260. C2×C22⋊C4C2×Dic19semidirect
264. C19#9499semidirect

Maximal subgroups

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

subgroupindex
#145662132
#145637092
#145635502
C19⋊#13042
C19×#24052
#949919