Finite Group Databasebeta

← #18079985

Subgroups — #18079985

Order 4864.

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

normal subgroups only

This group has 840 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#14565988C211yesmaximal, characteristic, complemented
2#14562151C212yesmaximal, complemented
3#14561962C211yesmaximal, characteristic, complemented
4#14561521C212yesmaximal, complemented
5C19×#2539C211yesmaximal, characteristic
6C22×C22⋊Dic19—21no—
7#11926508C2212yes—
8C22⋊C4×Dic19—24no—
9C4×C22⋊Dic19—21no—
10C4×C22⋊Dic19C2212yes—
11#11926278—24no—
12#11926268—22no—
13C2×C19×#123—21no—
14C2×C19×#121C2211yescharacteristic
15C2×C19×#120—21no—
16C22×C22⋊C4×C19C2211yescharacteristic
17C19×#399C412yescomplemented
18C19×#392C412yescomplemented
19C19×#390—22no—
20C4×C22⋊C4×C19C2211yescharacteristic
21C25×C19D411yescharacteristic
22C22×D4×C19—21no—
23C22×D4×C19—22no—
24C22×D4×C19C2×C411yescharacteristic, complemented
25C23×C4×C19D411yescharacteristic
26C23×C4×C19C2311yescharacteristic
27C23×Dic19—22no—
28C19×#123—44no—
29C19×#121—22no—
30C19×#121—22no—
31C19×#120—44no—
32C2×C4⋊C4×C19—22no—
33C2×C4⋊C4×C19C2×C411yescharacteristic, complemented
34C2×C22⋊C4×C19—21no—
35C2×C22⋊C4×C19—22no—
36C2×C22⋊C4×C19—22no—
37C2×C22⋊C4×C19—22no—
38C2×C22⋊C4×C19—22no—
39C2×C22⋊C4×C19—21no—
40C2×C22⋊C4×C19C2×C412yes—
41C2×C22⋊C4×C19D412yes—
42C2×C42×C19—21no—
43C2×C22⋊Dic19—22no—
44C2×C22⋊Dic19—28no—
45C2×C22⋊Dic19—22no—
46C2×C4×Dic19—22no—
47C2×C4×Dic19—22no—
48C2×#64520—22no—
49C19×#95C2×C412yescomplemented
50C19⋊#95—22no—
51C19⋊#95D414yescomplemented
52C22⋊(C19⋊C8)—22no—
53C22⋊(C19⋊C8)—22no—
54C24×C19—21no—
55C24×C19—24no—
56C24×C19—21no—
57C24×C19—21no—
58C24×C19—42no—
59C24×C19—81no—
60C24×C19C22⋊C412yes—
61C24×C19C2×D411yescharacteristic
62C2×D4×C19—22no—
63C2×D4×C19—44no—
64C2×D4×C19—42no—
65C2×D4×C19—42no—
66C2×D4×C19—44no—
67C2×D4×C19—41no—
68C2×D4×C19—41no—
69C2×D4×C19—82no—
70C2×D4×C19—81no—
71C22×C4×C19—22no—
72C22×C4×C19—21no—
73C22×C4×C19—21no—
74C22×C4×C19—21no—
75C22×C4×C19—42no—
76C22×C4×C19—81no—
77C22×C4×C19C22⋊C412yes—
78C22×C4×C19C22×C411yescharacteristic
79C22×C4×C19C2×D412yes—
80C22×C4×C19C2×D411yescharacteristic
81C22×C4×C19#4112yes—
82C22×Dic19—24no—
83C22×Dic19—28no—
84C22×Dic19—82no—
85C22×Dic19—82no—
86C4⋊C4×C19—22no—
87C4⋊C4×C19—44no—
88C22⋊C4×C19—24no—
89C22⋊C4×C19—24no—
90C22⋊C4×C19—24no—
91C22⋊C4×C19—44no—
92C22⋊C4×C19—44no—
93C22⋊C4×C19—42no—
94C42×C19—81no—
95C22⋊Dic19—28no—
96C22⋊Dic19—28no—
97C4×Dic19—82no—
98C4×Dic19—82no—
99#64520—82no—
100C2×C19⋊C8—42no—
101#9409—191nomaximal, Sylow
102C23×C19—22no—
103C23×C19—22no—
104C23×C19—24no—
105C23×C19—22no—
106C23×C19—22no—
107C23×C19—22no—
108C23×C19—22no—
109C23×C19—41no—
110C23×C19—42no—
111C23×C19—42no—
112C23×C19—42no—
113C23×C19—41no—
114C23×C19—41no—
115C23×C19—42no—
116C23×C19—42no—
117C23×C19—41no—
118C23×C19—42no—
119C23×C19—81no—
120C23×C19—81no—
121C23×C19—88no—
122C23×C19#10414yes—
123C23×C19C2×C22⋊C411yescharacteristic
124C23×C19#12011yescharacteristic
125C23×C19#12311yescharacteristic
126D4×C19—82no—
127D4×C19—88no—
128D4×C19—82no—
129D4×C19—82no—
130C2×C4×C19—24no—
131C2×C4×C19—22no—
132C2×C4×C19—42no—
133C2×C4×C19—42no—
134C2×C4×C19—41no—
135C2×C4×C19—41no—
136C2×C4×C19—42no—
137C2×C4×C19—42no—
138C2×C4×C19—42no—
139C2×C4×C19—42no—
140C2×C4×C19—41no—
141C2×C4×C19—41no—
142C2×C4×C19—41no—
143C2×C4×C19—81no—
144C2×C4×C19C4×D412yes—
145C2×C4×C19#12112yes—
146C2×Dic19—28no—
147C2×Dic19—44no—
148C2×Dic19—44no—
149C2×Dic19—88no—
150C19⋊C8—82no—
151#2539D1911yescharacteristic
152#2273—191no—
153#1507—192no—
154#1462—191no—
155#1297—192no—
156C22×C19—21no—
157C22×C19—21no—
158C22×C19—21no—
159C22×C19—21no—
160C22×C19—21no—
161C22×C19—24no—
162C22×C19—21no—
163C22×C19—21no—
164C22×C19—44no—
165C22×C19—44no—
166C22×C19—44no—
167C22×C19—44no—
168C22×C19—42no—
169C22×C19—42no—
170C22×C19—82no—
171C22×C19—82no—
172C22×C19—82no—
173C22×C19—84no—
174C22×C19—81no—
175C22×C19—81no—
176C22×C19—81no—
177C22×C19#38611yescharacteristic
178C22×C19C2×#10412yes—
179C22×C19#45312yes—
180C4×C19—22no—
181C4×C19—22no—
182C4×C19—44no—
183C4×C19—42no—
184C4×C19—81no—
185Dic19—48no—
186C2×#123—21no—
187C2×#121C2×D1911yescharacteristic
188C2×#120—21no—
189C22×C22⋊C4—381no—
190C22×C22⋊C4C2×D1911yescharacteristic
191#407—192no—
192#399Dic1912yescomplemented
193#392Dic1912yescomplemented
194#390—22no—
195C4×C22⋊C4—192no—
196C4×C22⋊C4—384no—
197C4×C22⋊C4—381no—
198C4×C22⋊C4C2×D1911yescharacteristic
199#327—384no—
200#323—382no—
201C2×C19—22no—
202C2×C19—22no—
203C2×C19—41no—
204C2×C19—44no—
205C2×C19—161no—
206C2×C19#188711yescharacteristic
207C2×C19#189611yescharacteristic
208C2×C19#191311yescharacteristic
209C25C22⋊D1911yescharacteristic
210C22×D4—21no—
211C22×D4—22no—
212C22×D4C2×Dic1911yescharacteristic, complemented
213C23×C4—382no—
214C23×C4C22⋊D1911yescharacteristic
215C23×C4C22×D1911yescharacteristic
216C2×M16—382no—
217#123—44no—
218#121—22no—
219#121—22no—
220#120—44no—
221C2×C4⋊C4—22no—
222C2×C4⋊C4C2×Dic1911yescharacteristic, complemented
223C2×C22⋊C4—21no—
224C2×C22⋊C4—22no—
225C2×C22⋊C4—22no—
226C2×C22⋊C4—22no—
227C2×C22⋊C4—22no—
228C2×C22⋊C4—21no—
229C2×C22⋊C4—388no—
230C2×C22⋊C4—382no—
231C2×C22⋊C4—382no—
232C2×C22⋊C4C2×Dic1912yes—
233C2×C22⋊C4C22⋊D1912yes—
234C2×C42—21no—
235C2×C42—382no—
236C2×C42—382no—
237C22⋊C8—382no—
238C22⋊C8—382no—
239#95—194no—
240#95—382no—
241#95C2×Dic1912yescomplemented
242C19#940911yescharacteristic, complemented, Sylow
243C24—21no—
244C24—21no—
245C24—24no—
246C24—21no—
247C24—42no—
248C24—81no—
249C24C22⋊Dic1912yes—
250C24C2×C22⋊D1911yescharacteristic
251C2×D4—22no—
252C2×D4—44no—
253C2×D4—42no—
254C2×D4—42no—
255C2×D4—41no—
256C2×D4—41no—
257C2×D4—44no—
258C2×D4—82no—
259C2×D4—81no—
260C22×C4—21no—
261C22×C4—22no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—42no—
265C22×C4—81no—
266C22×C4—384no—
267C22×C4—388no—
268C22×C4—1522no—
269C22×C4—1522no—
270C22×C4C22⋊Dic1912yes—
271C22×C4D4×D1912yes—
272C22×C4#6454312yes—
273C22×C4C22×Dic1911yescharacteristic
274C22×C4C2×C22⋊D1911yescharacteristic
275M16—1522no—
276C2×C8—762no—
277C4⋊C4—22no—
278C4⋊C4—44no—
279C22⋊C4—24no—
280C22⋊C4—24no—
281C22⋊C4—24no—
282C22⋊C4—44no—
283C22⋊C4—44no—
284C22⋊C4—42no—
285C22⋊C4—388no—
286C22⋊C4—388no—
287C42—81no—
288C42—1522no—
289C42—1522no—
290C23—22no—
291C23—22no—
292C23—24no—
293C23—22no—
294C23—22no—
295C23—22no—
296C23—22no—
297C23—41no—
298C23—42no—
299C23—42no—
300C23—42no—
301C23—41no—
302C23—41no—
303C23—42no—
304C23—42no—
305C23—42no—
306C23—41no—
307C23—81no—
308C23—81no—
309C23—88no—
310C23#1059729414yes—
311C23#1059738111yescharacteristic
312C23#1059738311yescharacteristic
313C23C2×C22⋊Dic1911yescharacteristic
314D4—82no—
315D4—88no—
316D4—82no—
317D4—82no—
318C2×C4—24no—
319C2×C4—22no—
320C2×C4—41no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—41no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—81no—
332C2×C4—388no—
333C2×C4—764no—
334C2×C4—764no—
335C2×C4—1528no—
336C2×C4D4×Dic1912yes—
337C2×C4#1059738512yes—
338C8—1522no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—24no—
347C22—44no—
348C22—44no—
349C22—44no—
350C22—44no—
351C22—42no—
352C22—42no—
353C22—82no—
354C22—82no—
355C22—82no—
356C22—84no—
357C22—81no—
358C22—81no—
359C22—81no—
360C22#1192642411yescharacteristic
361C22C2×#1059729412yes—
362C22#1192671112yes—
363C4—22no—
364C4—22no—
365C4—44no—
366C4—42no—
367C4—81no—
368C4—768no—
369C2—22no—
370C2—22no—
371C2—41no—
372C2—44no—
373C2—161no—
374C2#1456403411yescharacteristic
375C2#1456407911yescharacteristic
376C2#1456417811yescharacteristic
subgroupG/H
centerC22#11926424
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
Fitting, prime radicalC19×#2539C2
socleC22×C19#386
cosocleC23×C4×C19C23
hypercenter#2539D19
hypocenterC19#9409
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2539

Complements

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

NH ≅ G/Ntype
1. #14565988C2semidirect
2. #14562151C2semidirect
3. #14561962C2semidirect
4. #14561521C2semidirect
17. C19×#399C4semidirect
18. C19×#392C4semidirect
24. C22×D4×C19C2×C4semidirect
33. C2×C4⋊C4×C19C2×C4semidirect
49. C19×#95C2×C4semidirect
51. C19⋊#95D4semidirect
192. #399Dic19semidirect
193. #392Dic19semidirect
212. C22×D4C2×Dic19semidirect
222. C2×C4⋊C4C2×Dic19semidirect
241. #95C2×Dic19semidirect
242. C19#9409semidirect

Maximal subgroups

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

subgroupindex
#145659882
#145621512
#145619622
#145615212
C19×#25392
#940919