Finite Group Databasebeta

← #18080194

Subgroups — #18080194

Order 4864.

516 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 103 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#14572273C211yesmaximal, characteristic, complemented
2#14563712C211yesmaximal, characteristic, complemented
3#14562164C212yesmaximal
4#14561488C212yesmaximal, complemented
5C19×#2500C211yesmaximal, characteristic
6#11926605—24no—
7#11926568—21no—
8#11926508C2212yes—
9C4×#64520—21no—
10#11926407C2212yes—
11#11926311—21no—
12#11926311—21no—
13#11926278—24no—
14C2×C19×#121C2211yescharacteristic
15C2×C19×#117C2211yescharacteristic
16C19×#394—21no—
17C19×#394—21no—
18C19×#390C411yescharacteristic, complemented
19C19×#390C411yescharacteristic, complemented
20C19×#388—21no—
21C19×#388—21no—
22C19×#384C411yescharacteristic, complemented
23C19×#382C411yescharacteristic, complemented
24C4×C22⋊C4×C19C2211yescharacteristic
25C22×D4×C19—21no—
26C22×D4×C19C2×C411yescharacteristic
27C23×C4×C19C2311yescharacteristic
28C19×#121—22no—
29C19×#121—22no—
30C19×#117—22no—
31C19×#117—22no—
32C2×C4⋊C4×C19—21no—
33C2×C4⋊C4×C19—21no—
34C2×C4⋊C4×C19C2×C411yescharacteristic
35C2×C4⋊C4×C19C2×C411yescharacteristic
36C2×C4⋊C4×C19C2×C411yescharacteristic
37C2×C22⋊C4×C19—21no—
38C2×C22⋊C4×C19—21no—
39C2×C22⋊C4×C19—21no—
40C2×C22⋊C4×C19—21no—
41C2×C22⋊C4×C19—21no—
42C2×C22⋊C4×C19—21no—
43C2×C22⋊C4×C19D411yescharacteristic
44C2×C22⋊C4×C19D411yescharacteristic
45C2×C42×C19C2×C411yescharacteristic
46C2×C42×C19C2×C411yescharacteristic
47C2×C42×C19D411yescharacteristic
48C2×C42×C19D411yescharacteristic
49C2×C22⋊Dic19—22no—
50C2×#64520—22no—
51C19×#95—21no—
52C19×#95—21no—
53C19×#95—21no—
54C19⋊#95—22no—
55C19⋊#95—22no—
56C22⋊(C19⋊C8)—22no—
57C22⋊(C19⋊C8)D414yes—
58C4⋊(C19⋊C8)—24no—
59#10597260—22no—
60C4×C19⋊C8—22no—
61C24×C19—21no—
62C24×C19C2×D411yescharacteristic
63C2×D4×C19—22no—
64C2×D4×C19—41no—
65C2×D4×C19—41no—
66C2×D4×C19—42no—
67C2×D4×C19—81no—
68C2×D4×C19—81no—
69C22×C4×C19—21no—
70C22×C4×C19—21no—
71C22×C4×C19—21no—
72C22×C4×C19—41no—
73C22×C4×C19—41no—
74C22×C4×C19C22⋊C411yescharacteristic
75C22×C4×C19C22⋊C411yescharacteristic
76C22×C4×C19C22⋊C411yescharacteristic
77C22×C4×C19C22⋊C411yescharacteristic
78C22×C4×C19C22×C411yescharacteristic
79C22×C4×C19C2×D412yes—
80C22×C4×C19C2×D411yescharacteristic
81C22×C4×C19#4112yes—
82C22×Dic19—42no—
83C4⋊C4×C19—22no—
84C4⋊C4×C19—22no—
85C4⋊C4×C19—22no—
86C4⋊C4×C19—81no—
87C4⋊C4×C19—81no—
88C22⋊C4×C19—22no—
89C22⋊C4×C19—22no—
90C22⋊C4×C19—42no—
91C22⋊C4×C19—42no—
92C22⋊C4×C19—42no—
93C22⋊C4×C19—41no—
94C22⋊C4×C19—41no—
95C22⋊C4×C19—81no—
96C22⋊C4×C19—81no—
97C42×C19—21no—
98C42×C19—21no—
99C42×C19—21no—
100C42×C19—21no—
101C42×C19—41no—
102C42×C19—41no—
103C22⋊Dic19—42no—
104C22⋊Dic19—42no—
105#64520—42no—
106#64520—42no—
107C2×C19⋊C8—24no—
108#9446—191nomaximal, Sylow
109C23×C19—21no—
110C23×C19—21no—
111C23×C19—41no—
112C23×C19—41no—
113C23×C19—41no—
114C23×C19—41no—
115C23×C19—41no—
116C23×C19—41no—
117C23×C19—41no—
118C23×C19—41no—
119C23×C19—41no—
120C23×C19C2×C22⋊C411yescharacteristic
121C23×C19#12112yes—
122D4×C19—82no—
123D4×C19—84no—
124C2×C4×C19—21no—
125C2×C4×C19—21no—
126C2×C4×C19—21no—
127C2×C4×C19—21no—
128C2×C4×C19—22no—
129C2×C4×C19—21no—
130C2×C4×C19—21no—
131C2×C4×C19—21no—
132C2×C4×C19—21no—
133C2×C4×C19—42no—
134C2×C4×C19—42no—
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—41no—
146C2×C4×C19—41no—
147C2×C4×C19C4×D412yes—
148C2×C4×C19#12011yescharacteristic
149C2×C4×C19#12311yescharacteristic
150C2×Dic19—82no—
151C2×Dic19—82no—
152C2×Dic19—82no—
153C19⋊C8—44no—
154#2921—191no—
155#2500D1911yescharacteristic
156#1820—191no—
157#1510—192no—
158#1284—192no—
159C22×C19—21no—
160C22×C19—21no—
161C22×C19—22no—
162C22×C19—22no—
163C22×C19—22no—
164C22×C19—81no—
165C22×C19—81no—
166C22×C19—81no—
167C22×C19—81no—
168C22×C19—81no—
169C22×C19—81no—
170C22×C19—81no—
171C22×C19—81no—
172C22×C19—81no—
173C22×C19#38611yescharacteristic
174C22×C19#41011yescharacteristic
175C22×C19#41011yescharacteristic
176C4×C19—21no—
177C4×C19—22no—
178C4×C19—21no—
179C4×C19—42no—
180C4×C19—41no—
181C4×C19—41no—
182C4×C19—41no—
183C4×C19—41no—
184C4×C19—81no—
185C4×C19—81no—
186Dic19—162no—
187C2×#121C2×D1911yescharacteristic
188C2×#117C2×D1911yescharacteristic
189#433—384no—
190#423—381no—
191#407—192no—
192C4×M16—381no—
193#394—21no—
194#394—21no—
195#390Dic1911yescharacteristic, complemented
196#390Dic1911yescharacteristic, complemented
197#388—21no—
198#388—21no—
199#384Dic1911yescharacteristic, complemented
200#382Dic1911yescharacteristic, complemented
201#381—192no—
202C4×C22⋊C4C2×D1911yescharacteristic
203#342—381no—
204#342—381no—
205#327—384no—
206C2×C19—21no—
207C2×C19—21no—
208C2×C19—42no—
209C2×C19—161no—
210C2×C19#188411yescharacteristic
211C2×C19#189911yescharacteristic
212C2×C19#191011yescharacteristic
213C22×D4—21no—
214C22×D4C2×Dic1911yescharacteristic
215C23×C4C22×D1911yescharacteristic
216C2×M16—382no—
217#121—22no—
218#121—22no—
219#117—22no—
220#117—22no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4C2×Dic1911yescharacteristic
224C2×C4⋊C4C2×Dic1911yescharacteristic
225C2×C4⋊C4C2×Dic1911yescharacteristic
226C2×C22⋊C4—21no—
227C2×C22⋊C4—21no—
228C2×C22⋊C4—21no—
229C2×C22⋊C4—21no—
230C2×C22⋊C4—21no—
231C2×C22⋊C4—21no—
232C2×C22⋊C4—382no—
233C2×C22⋊C4C22⋊D1911yescharacteristic
234C2×C22⋊C4C22⋊D1911yescharacteristic
235C2×C42C2×Dic1911yescharacteristic
236C2×C42C2×Dic1911yescharacteristic
237C2×C42C22⋊D1911yescharacteristic
238C2×C42C22⋊D1911yescharacteristic
239C4⋊C8—384no—
240C22⋊C8—194no—
241C22⋊C8—382no—
242#97—382no—
243C4×C8—382no—
244#95—21no—
245#95—21no—
246#95—21no—
247#95—382no—
248#95—382no—
249C19#944611yescharacteristic, complemented, Sylow
250C24—21no—
251C24C2×C22⋊D1911yescharacteristic
252C2×D4—22no—
253C2×D4—41no—
254C2×D4—41no—
255C2×D4—42no—
256C2×D4—81no—
257C2×D4—81no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—41no—
262C22×C4—41no—
263C22×C4—762no—
264C22×C4C22⋊Dic1911yescharacteristic
265C22×C4C22⋊Dic1911yescharacteristic
266C22×C4C22⋊Dic1911yescharacteristic
267C22×C4C22⋊Dic1911yescharacteristic
268C22×C4D4×D1912yes—
269C22×C4#6454312yes—
270C22×C4C22×Dic1911yescharacteristic
271C22×C4C2×C22⋊D1911yescharacteristic
272M16—762no—
273M16—762no—
274C2×C8—384no—
275C4⋊C4—22no—
276C4⋊C4—22no—
277C4⋊C4—22no—
278C4⋊C4—81no—
279C4⋊C4—81no—
280C22⋊C4—22no—
281C22⋊C4—22no—
282C22⋊C4—42no—
283C22⋊C4—42no—
284C22⋊C4—42no—
285C22⋊C4—41no—
286C22⋊C4—41no—
287C22⋊C4—81no—
288C22⋊C4—81no—
289C22⋊C4—762no—
290C22⋊C4—762no—
291C42—21no—
292C42—21no—
293C42—21no—
294C42—21no—
295C42—41no—
296C42—41no—
297C23—21no—
298C23—21no—
299C23—41no—
300C23—41no—
301C23—41no—
302C23—41no—
303C23—41no—
304C23—41no—
305C23—41no—
306C23—41no—
307C23—41no—
308C23#1059738512yes—
309C23C2×C22⋊Dic1911yescharacteristic
310D4—82no—
311D4—84no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—22no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
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—1522no—
336C2×C4—1522no—
337C2×C4—1522no—
338C2×C4D4×Dic1912yes—
339C2×C4#1059738111yescharacteristic
340C2×C4#1059738311yescharacteristic
341C8—764no—
342C22—21no—
343C22—21no—
344C22—22no—
345C22—22no—
346C22—22no—
347C22—81no—
348C22—81no—
349C22—81no—
350C22—81no—
351C22—81no—
352C22—81no—
353C22—81no—
354C22—81no—
355C22—81no—
356C22#1192642411yescharacteristic
357C22#1192651811yescharacteristic
358C22#1192651811yescharacteristic
359C4—21no—
360C4—22no—
361C4—21no—
362C4—42no—
363C4—41no—
364C4—41no—
365C4—41no—
366C4—41no—
367C4—81no—
368C4—81no—
369C4—3042no—
370C2—21no—
371C2—21no—
372C2—42no—
373C2—161no—
374C2#1456401911yescharacteristic
375C2#1456409411yescharacteristic
376C2#1456416311yescharacteristic
subgroupG/H
centerC22#11926424
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#2500C2
socleC22×C19#386
prime radicalC2×C19×#121C22
cosocleC23×C4×C19C23
hypercenter#2500D19
hypocenterC19#9446
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2500

Complements

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

NH ≅ G/Ntype
1. #14572273C2semidirect
2. #14563712C2semidirect
4. #14561488C2semidirect
18. C19×#390C4semidirect
19. C19×#390C4semidirect
22. C19×#384C4semidirect
23. C19×#382C4semidirect
195. #390Dic19semidirect
196. #390Dic19semidirect
199. #384Dic19semidirect
200. #382Dic19semidirect
249. C19#9446semidirect

Maximal subgroups

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

subgroupindex
#145722732
#145637122
#145621642
#145614882
C19×#25002
#944619