Finite Group Databasebeta

← #18080454

Subgroups — #18080454

Order 4864.

900 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 900 conjugacy classes of subgroups — too many to draw. Only its 107 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#14566233C211yesmaximal, characteristic, complemented
2#14563709C211yesmaximal, characteristic, complemented
3#14563550C212yesmaximal
4C19⋊#1304C212yesmaximal, complemented
5C19×#2405C211yesmaximal, characteristic
6C2×#10597291—24no—
7#11926437—24no—
8#11926404—21no—
9#11926400C2212yes—
10#11926400C2212yes—
11C4×C22⋊Dic19—21no—
12#11926311—22no—
13C23×D4×C19C2211yescharacteristic
14C2×C19×#123—21no—
15C22×C22⋊C4×C19C2211yescharacteristic
16C19×#394—22no—
17C19×#386—21no—
18C19×#385C412yescomplemented
19C19×#379C412yescomplemented
20C19×#379C2211yescharacteristic
21C25×C19C2×C411yescharacteristic
22C25×C19C2311yescharacteristic
23C22×D4×C19—21no—
24C22×D4×C19—22no—
25C22×D4×C19—21no—
26C22×D4×C19—22no—
27C22×D4×C19—44no—
28C23×C4×C19C2×C411yescharacteristic
29C23×C4×C19D411yescharacteristic
30C23×C4×C19D411yescharacteristic
31C19×#123—44no—
32C2×C4⋊C4×C19—22no—
33C2×C22⋊C4×C19—22no—
34C2×C22⋊C4×C19—22no—
35C2×C22⋊C4×C19—21no—
36C2×C22⋊C4×C19—22no—
37C2×C22⋊C4×C19—21no—
38C2×C22⋊C4×C19—22no—
39C2×C22⋊C4×C19C2×C412yes—
40C2×C22⋊C4×C19C2×C412yes—
41C2×C22⋊C4×C19D412yes—
42C2×C22⋊Dic19—22no—
43C2×C22⋊Dic19—22no—
44C2×C22⋊Dic19—22no—
45C2×C22⋊Dic19—22no—
46C2×C22⋊Dic19—22no—
47C2×C22⋊Dic19D414yes—
48C2×C4⋊Dic19—22no—
49C2×C4×Dic19—22no—
50C19×#95—22no—
51#10597291—48no—
52C19⋊#95—22no—
53C19⋊#95—22no—
54C24×C19—21no—
55C24×C19—22no—
56C24×C19—42no—
57C24×C19—42no—
58C24×C19—42no—
59C24×C19—42no—
60C24×C19—81no—
61C24×C19—81no—
62C24×C19C22×C411yescharacteristic
63C24×C19C2×D412yes—
64C24×C19C2×D411yescharacteristic
65C24×C19C2×D411yescharacteristic
66C24×C19#4112yes—
67C2×D4×C19—24no—
68C2×D4×C19—28no—
69C2×D4×C19—42no—
70C2×D4×C19—44no—
71C2×D4×C19—42no—
72C2×D4×C19—44no—
73C2×D4×C19—42no—
74C2×D4×C19—44no—
75C2×D4×C19—41no—
76C2×D4×C19—42no—
77C2×D4×C19—41no—
78C22×C4×C19—21no—
79C22×C4×C19—22no—
80C22×C4×C19—21no—
81C22×C4×C19—21no—
82C22×C4×C19—21no—
83C22×C4×C19—21no—
84C22×C4×C19—22no—
85C22×C4×C19—42no—
86C22×C4×C19—42no—
87C22×C4×C19—81no—
88C22×C4×C19C22⋊C412yes—
89C22×C4×C19C22⋊C412yes—
90C22×Dic19—24no—
91C22×Dic19—42no—
92C4⋊C4×C19—44no—
93C22⋊C4×C19—24no—
94C22⋊C4×C19—24no—
95C22⋊C4×C19—44no—
96C22⋊C4×C19—42no—
97C22⋊C4×C19—42no—
98C22⋊C4×C19—82no—
99C22⋊C4×C19—81no—
100C22⋊Dic19—44no—
101C22⋊Dic19—44no—
102C22⋊Dic19—44no—
103C22⋊Dic19—44no—
104C22⋊Dic19—82no—
105C22⋊Dic19—82no—
106C4⋊Dic19—82no—
107C4×Dic19—82no—
108#9498—191nomaximal, Sylow
109C23×C19—22no—
110C23×C19—22no—
111C23×C19—22no—
112C23×C19—22no—
113C23×C19—24no—
114C23×C19—22no—
115C23×C19—24no—
116C23×C19—41no—
117C23×C19—41no—
118C23×C19—41no—
119C23×C19—42no—
120C23×C19—42no—
121C23×C19—41no—
122C23×C19—41no—
123C23×C19—42no—
124C23×C19—42no—
125C23×C19—42no—
126C23×C19—42no—
127C23×C19—41no—
128C23×C19—42no—
129C23×C19—41no—
130C23×C19—42no—
131C23×C19—82no—
132C23×C19—82no—
133C23×C19—88no—
134C23×C19—88no—
135C23×C19C2×C22⋊C411yescharacteristic
136C23×C19C4×D412yes—
137C23×C19#12011yescharacteristic
138C23×C19#12112yes—
139C23×C19#12311yescharacteristic
140D4×C19—48no—
141D4×C19—44no—
142D4×C19—44no—
143C2×C4×C19—22no—
144C2×C4×C19—24no—
145C2×C4×C19—22no—
146C2×C4×C19—22no—
147C2×C4×C19—42no—
148C2×C4×C19—41no—
149C2×C4×C19—42no—
150C2×C4×C19—41no—
151C2×C4×C19—42no—
152C2×C4×C19—42no—
153C2×C4×C19—42no—
154C2×C4×C19—42no—
155C2×C4×C19—42no—
156C2×C4×C19—42no—
157C2×C4×C19—81no—
158C2×C4×C19—81no—
159C2×Dic19—44no—
160C2×Dic19—44no—
161C2×Dic19—44no—
162C2×Dic19—82no—
163C2×Dic19—82no—
164C2×Dic19—82no—
165#2405D1911yescharacteristic
166#2312—191no—
167#1819—191no—
168#1781—192no—
169#1304—192no—
170C22×C19—21no—
171C22×C19—21no—
172C22×C19—21no—
173C22×C19—21no—
174C22×C19—22no—
175C22×C19—22no—
176C22×C19—21no—
177C22×C19—22no—
178C22×C19—22no—
179C22×C19—21no—
180C22×C19—22no—
181C22×C19—21no—
182C22×C19—22no—
183C22×C19—44no—
184C22×C19—44no—
185C22×C19—44no—
186C22×C19—42no—
187C22×C19—84no—
188C22×C19—82no—
189C22×C19—82no—
190C22×C19—84no—
191C22×C19—84no—
192C22×C19—84no—
193C22×C19—81no—
194C22×C19—81no—
195C22×C19#38611yescharacteristic
196C22×C19#41012yes—
197C22×C19B(4,𝔽2)12yes—
198C4×C19—42no—
199C4×C19—42no—
200C4×C19—42no—
201C4×C19—82no—
202Dic19—84no—
203Dic19—162no—
204C23×D4C2×D1911yescharacteristic
205C2×#123—21no—
206C22×C22⋊C4C2×D1911yescharacteristic
207C2×#99—384no—
208#394—22no—
209#388—384no—
210#386—21no—
211#385Dic1912yescomplemented
212#380—381no—
213#379—192no—
214#379—192no—
215#379Dic1912yescomplemented
216#379C2×D1911yescharacteristic
217C4×C22⋊C4—381no—
218#342—382no—
219C2×C19—22no—
220C2×C19—22no—
221C2×C19—42no—
222C2×C19—41no—
223C2×C19—42no—
224C2×C19—82no—
225C2×C19#188911yescharacteristic
226C2×C19#189911yescharacteristic
227C2×C19#191311yescharacteristic
228C25C2×Dic1911yescharacteristic
229C25C22×D1911yescharacteristic
230C22×D4—22no—
231C22×D4—21no—
232C22×D4—22no—
233C22×D4—21no—
234C22×D4—44no—
235C23×C4C2×Dic1911yescharacteristic
236C23×C4C22⋊D1911yescharacteristic
237C23×C4C22⋊D1911yescharacteristic
238#123—44no—
239C2×C4⋊C4—22no—
240C2×C4⋊C4—382no—
241C2×C22⋊C4—22no—
242C2×C22⋊C4—22no—
243C2×C22⋊C4—21no—
244C2×C22⋊C4—22no—
245C2×C22⋊C4—21no—
246C2×C22⋊C4—22no—
247C2×C22⋊C4—194no—
248C2×C22⋊C4—382no—
249C2×C22⋊C4—382no—
250C2×C22⋊C4—382no—
251C2×C22⋊C4—382no—
252C2×C22⋊C4—382no—
253C2×C22⋊C4C2×Dic1912yes—
254C2×C22⋊C4C2×Dic1912yes—
255C2×C22⋊C4C22⋊D1912yes—
256C2×C42—382no—
257#99—768no—
258#95—22no—
259#95—382no—
260#95—382no—
261C19#949811yescharacteristic, complemented, Sylow
262C24—21no—
263C24—22no—
264C24—42no—
265C24—42no—
266C24—42no—
267C24—42no—
268C24—81no—
269C24—81no—
270C24D4×D1912yes—
271C24#6454312yes—
272C24C22×Dic1911yescharacteristic
273C24C2×C22⋊D1911yescharacteristic
274C24C2×C22⋊D1911yescharacteristic
275C2×D4—28no—
276C2×D4—24no—
277C2×D4—42no—
278C2×D4—44no—
279C2×D4—42no—
280C2×D4—44no—
281C2×D4—42no—
282C2×D4—44no—
283C2×D4—41no—
284C2×D4—41no—
285C2×D4—42no—
286C22×C4—22no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—22no—
293C22×C4—42no—
294C22×C4—42no—
295C22×C4—81no—
296C22×C4—384no—
297C22×C4—762no—
298C22×C4C22⋊Dic1912yes—
299C22×C4C22⋊Dic1912yes—
300C4⋊C4—44no—
301C4⋊C4—1522no—
302C22⋊C4—24no—
303C22⋊C4—24no—
304C22⋊C4—44no—
305C22⋊C4—42no—
306C22⋊C4—42no—
307C22⋊C4—82no—
308C22⋊C4—81no—
309C22⋊C4—764no—
310C22⋊C4—764no—
311C22⋊C4—764no—
312C22⋊C4—764no—
313C22⋊C4—1522no—
314C22⋊C4—1522no—
315C42—1522no—
316C23—22no—
317C23—22no—
318C23—22no—
319C23—24no—
320C23—22no—
321C23—22no—
322C23—24no—
323C23—41no—
324C23—41no—
325C23—41no—
326C23—41no—
327C23—42no—
328C23—42no—
329C23—42no—
330C23—41no—
331C23—42no—
332C23—42no—
333C23—42no—
334C23—41no—
335C23—42no—
336C23—41no—
337C23—42no—
338C23—82no—
339C23—82no—
340C23—88no—
341C23—88no—
342C23D4×Dic1912yes—
343C23#1059738111yescharacteristic
344C23#1059738311yescharacteristic
345C23#1059738512yes—
346C23C2×C22⋊Dic1911yescharacteristic
347D4—44no—
348D4—48no—
349D4—44no—
350C2×C4—22no—
351C2×C4—24no—
352C2×C4—22no—
353C2×C4—22no—
354C2×C4—42no—
355C2×C4—41no—
356C2×C4—42no—
357C2×C4—41no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—42no—
361C2×C4—42no—
362C2×C4—42no—
363C2×C4—42no—
364C2×C4—81no—
365C2×C4—81no—
366C2×C4—764no—
367C2×C4—764no—
368C2×C4—764no—
369C2×C4—1522no—
370C2×C4—1522no—
371C2×C4—1522no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—22no—
378C22—22no—
379C22—22no—
380C22—21no—
381C22—22no—
382C22—22no—
383C22—22no—
384C22—21no—
385C22—44no—
386C22—44no—
387C22—44no—
388C22—42no—
389C22—82no—
390C22—84no—
391C22—82no—
392C22—84no—
393C22—84no—
394C22—84no—
395C22—81no—
396C22—81no—
397C22#1192642411yescharacteristic
398C22#1192651812yes—
399C22#1192673012yes—
400C4—42no—
401C4—42no—
402C4—42no—
403C4—82no—
404C4—3042no—
405C4—1524no—
406C2—22no—
407C2—22no—
408C2—42no—
409C2—42no—
410C2—41no—
411C2—82no—
412C2#1456404411yescharacteristic
413C2#1456409411yescharacteristic
414C2#1456417811yescharacteristic
subgroupG/H
centerC22#11926424
commutatorC24×C19C22×C4
FrattiniC25C22×D19
FittingC19×#2405C2
socleC22×C19#386
prime radicalC23×D4×C19C22
cosocleC25×C19C23
hypercenter#2405D19
hypocenterC19#9498
LCSG ▷ C24×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C25 ◁ #2405

Complements

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

NH ≅ G/Ntype
1. #14566233C2semidirect
2. #14563709C2semidirect
4. C19⋊#1304C2semidirect
18. C19×#385C4semidirect
19. C19×#379C4semidirect
211. #385Dic19semidirect
215. #379Dic19semidirect
261. C19#9498semidirect

Maximal subgroups

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

subgroupindex
#145662332
#145637092
#145635502
C19⋊#13042
C19×#24052
#949819