Finite Group Databasebeta

← #18077524

Subgroups — #18077524

Order 4864.

558 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 558 conjugacy classes of subgroups — too many to draw. Only its 111 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#14572676C211yesmaximal, characteristic
2#14563734C212yesmaximal, complemented
3C4×#10597291C211yesmaximal, characteristic
4#14561521C212yesmaximal, complemented
5C19×#2395C211yesmaximal, characteristic
6#11926622—24no—
7#11926597—21no—
8C2×#10597291—21no—
9#11926508—21no—
10#11926508C2212yes—
11C4×C22⋊Dic19C2212yes—
12#11926311—21no—
13#11926303—24no—
14C2×C4×D4×C19C2211yescharacteristic
15C2×C19×#117C2211yescharacteristic
16C19×#400C411yescharacteristic, complemented
17C19×#399C411yescharacteristic, complemented
18C19×#398C411yescharacteristic, complemented
19C19×#397—21no—
20C19×#397C411yescharacteristic, complemented
21C19×#394—21no—
22C4×C4⋊C4×C19—21no—
23C4×C22⋊C4×C19—21no—
24C4×C22⋊C4×C19C2211yescharacteristic
25C22×D4×C19D411yescharacteristic
26C23×C4×C19D411yescharacteristic
27C23×C4×C19C2311yescharacteristic
28C4×D4×C19—22no—
29C4×D4×C19—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×C19C2×C411yescharacteristic
42C2×C22⋊C4×C19D411yescharacteristic
43C2×C42×C19—21no—
44C2×C42×C19—21no—
45C2×C42×C19D411yescharacteristic
46C2×C22⋊Dic19—22no—
47C2×C4×Dic19—22no—
48C2×#64520—22no—
49C2×#64520D414yes—
50C19×#95—21no—
51C19×#95—21no—
52C19×#95—21no—
53C19×#95—21no—
54C19×#95C2×C411yescharacteristic
55C19×#95C2×C411yescharacteristic
56#10597291—24no—
57C19⋊#95—22no—
58C22⋊(C19⋊C8)—22no—
59C22⋊(C19⋊C8)—22no—
60C22⋊(C19⋊C8)—22no—
61C4⋊(C19⋊C8)—22no—
62C4×C19⋊C8—22no—
63C24×C19C22⋊C411yescharacteristic
64C24×C19C2×D411yescharacteristic
65C2×D4×C19—22no—
66C2×D4×C19—22no—
67C2×D4×C19—41no—
68C22×C4×C19—21no—
69C22×C4×C19—21no—
70C22×C4×C19—21no—
71C22×C4×C19—21no—
72C22×C4×C19—21no—
73C22×C4×C19—21no—
74C22×C4×C19—42no—
75C22×C4×C19—42no—
76C22×C4×C19C22⋊C411yescharacteristic
77C22×C4×C19C22⋊C411yescharacteristic
78C22×C4×C19C22⋊C411yescharacteristic
79C22×C4×C19C22×C411yescharacteristic
80C22×C4×C19C2×D412yes—
81C22×C4×C19C2×D411yescharacteristic
82C22×C4×C19#4112yes—
83C22×Dic19—42no—
84C4⋊C4×C19—22no—
85C4⋊C4×C19—22no—
86C4⋊C4×C19—22no—
87C4⋊C4×C19—42no—
88C4⋊C4×C19—42no—
89C22⋊C4×C19—22no—
90C22⋊C4×C19—22no—
91C22⋊C4×C19—42no—
92C22⋊C4×C19—42no—
93C22⋊C4×C19—42no—
94C22⋊C4×C19—42no—
95C42×C19—21no—
96C42×C19—21no—
97C42×C19—42no—
98C42×C19—41no—
99C42×C19—41no—
100C22⋊Dic19—24no—
101C22⋊Dic19—42no—
102C4×Dic19—44no—
103#64520—44no—
104#64520—82no—
105C2×C19⋊C8—24no—
106#9012—191nomaximal, Sylow
107C23×C19—21no—
108C23×C19—21no—
109C23×C19—21no—
110C23×C19—21no—
111C23×C19—21no—
112C23×C19—41no—
113C23×C19—41no—
114C23×C19—41no—
115C23×C19—41no—
116C23×C19C2×C22⋊C411yescharacteristic
117C23×C19#12112yes—
118D4×C19—44no—
119C2×C4×C19—21no—
120C2×C4×C19—21no—
121C2×C4×C19—24no—
122C2×C4×C19—22no—
123C2×C4×C19—22no—
124C2×C4×C19—21no—
125C2×C4×C19—21no—
126C2×C4×C19—41no—
127C2×C4×C19—42no—
128C2×C4×C19—41no—
129C2×C4×C19—41no—
130C2×C4×C19—42no—
131C2×C4×C19—41no—
132C2×C4×C19—41no—
133C2×C4×C19—41no—
134C2×C4×C19—41no—
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—81no—
143C2×C4×C19#10412yes—
144C2×C4×C19C4×D412yes—
145C2×C4×C19#12011yescharacteristic
146C2×C4×C19#12311yescharacteristic
147C2×Dic19—44no—
148C2×Dic19—82no—
149C2×Dic19—82no—
150C19⋊C8—44no—
151#2975—191no—
152#2395D1911yescharacteristic
153#1826—192no—
154C4×#99—191no—
155#1297—192no—
156C22×C19—21no—
157C22×C19—21no—
158C22×C19—22no—
159C22×C19—22no—
160C22×C19—22no—
161C22×C19—42no—
162C22×C19—41no—
163C22×C19—41no—
164C22×C19—41no—
165C22×C19—81no—
166C22×C19—81no—
167C22×C19—81no—
168C22×C19#38611yescharacteristic
169C22×C19C2×#10411yescharacteristic
170C22×C19#42111yescharacteristic
171C4×C19—22no—
172C4×C19—21no—
173C4×C19—22no—
174C4×C19—42no—
175C4×C19—41no—
176C4×C19—41no—
177C4×C19—81no—
178C4×C19—81no—
179C4×C19—81no—
180C4×C19#45812yes—
181Dic19—84no—
182C2×C4×D4C2×D1911yescharacteristic
183C2×#117C2×D1911yescharacteristic
184#436—384no—
185#431—381no—
186C2×#99—381no—
187#407—192no—
188#407—381no—
189#400Dic1911yescharacteristic, complemented
190#399Dic1911yescharacteristic, complemented
191#398Dic1911yescharacteristic, complemented
192#397—21no—
193#397Dic1911yescharacteristic, complemented
194#394—21no—
195C4×C4⋊C4—21no—
196C4×C22⋊C4—21no—
197C4×C22⋊C4—192no—
198C4×C22⋊C4C2×D1911yescharacteristic
199#342—381no—
200#339—384no—
201C2×C19—21no—
202C2×C19—21no—
203C2×C19—42no—
204C2×C19—81no—
205C2×C19#187111yescharacteristic
206C2×C19#188411yescharacteristic
207C2×C19#189011yescharacteristic
208C22×D4C22⋊D1911yescharacteristic
209C23×C4C22⋊D1911yescharacteristic
210C23×C4C22×D1911yescharacteristic
211C2×M16—194no—
212C2×M16—382no—
213C4×D4—22no—
214C4×D4—22no—
215#117—22no—
216#117—22no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4C2×Dic1911yescharacteristic
220C2×C4⋊C4C2×Dic1911yescharacteristic
221C2×C4⋊C4C2×Dic1911yescharacteristic
222C2×C22⋊C4—21no—
223C2×C22⋊C4—21no—
224C2×C22⋊C4—21no—
225C2×C22⋊C4—21no—
226C2×C22⋊C4—382no—
227C2×C22⋊C4C2×Dic1911yescharacteristic
228C2×C22⋊C4C22⋊D1911yescharacteristic
229C2×C42—21no—
230C2×C42—21no—
231C2×C42—382no—
232C2×C42C22⋊D1911yescharacteristic
233C4⋊C8—382no—
234#99—384no—
235C22⋊C8—382no—
236C22⋊C8—382no—
237C22⋊C8—382no—
238C4×C8—382no—
239#95—21no—
240#95—21no—
241#95—21no—
242#95—21no—
243#95—382no—
244#95C2×Dic1911yescharacteristic
245#95C2×Dic1911yescharacteristic
246C19#901211yescharacteristic, complemented, Sylow
247C24C22⋊Dic1911yescharacteristic
248C24C2×C22⋊D1911yescharacteristic
249C2×D4—22no—
250C2×D4—22no—
251C2×D4—41no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—42no—
259C22×C4—42no—
260C22×C4—762no—
261C22×C4C22⋊Dic1911yescharacteristic
262C22×C4C22⋊Dic1911yescharacteristic
263C22×C4C22⋊Dic1911yescharacteristic
264C22×C4D4×D1912yes—
265C22×C4#6454312yes—
266C22×C4C22×Dic1911yescharacteristic
267C22×C4C2×C22⋊D1911yescharacteristic
268M16—764no—
269M16—1522no—
270C2×C8—384no—
271C4⋊C4—22no—
272C4⋊C4—22no—
273C4⋊C4—22no—
274C4⋊C4—42no—
275C4⋊C4—42no—
276C22⋊C4—22no—
277C22⋊C4—22no—
278C22⋊C4—42no—
279C22⋊C4—42no—
280C22⋊C4—42no—
281C22⋊C4—42no—
282C22⋊C4—384no—
283C22⋊C4—762no—
284C42—21no—
285C42—21no—
286C42—42no—
287C42—41no—
288C42—41no—
289C42—764no—
290C23—21no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—21no—
295C23—41no—
296C23—41no—
297C23—41no—
298C23—41no—
299C23#1059738512yes—
300C23C2×C22⋊Dic1911yescharacteristic
301D4—44no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—22no—
305C2×C4—24no—
306C2×C4—22no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—42no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—42no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—81no—
326C2×C4—764no—
327C2×C4—1522no—
328C2×C4—1522no—
329C2×C4#1059729412yes—
330C2×C4D4×Dic1912yes—
331C2×C4#1059738111yescharacteristic
332C2×C4#1059738311yescharacteristic
333C8—764no—
334C22—21no—
335C22—21no—
336C22—22no—
337C22—22no—
338C22—22no—
339C22—42no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—81no—
344C22—81no—
345C22—81no—
346C22#1192642411yescharacteristic
347C22C2×#1059729411yescharacteristic
348C22#1192656111yescharacteristic
349C4—22no—
350C4—21no—
351C4—22no—
352C4—42no—
353C4—41no—
354C4—41no—
355C4—81no—
356C4—81no—
357C4—81no—
358C4—1524no—
359C4#1192673312yes—
360C2—21no—
361C2—21no—
362C2—42no—
363C2—81no—
364C2#1456393811yescharacteristic
365C2#1456401911yescharacteristic
366C2#1456404911yescharacteristic
subgroupG/H
centerC2×C4#10597383
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#2395C2
socleC22×C19#386
prime radicalC22×D4×C19D4
cosocleC23×C4×C19C23
hypercenter#2395D19
hypocenterC19#9012
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #2395

Complements

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

NH ≅ G/Ntype
2. #14563734C2semidirect
4. #14561521C2semidirect
16. C19×#400C4semidirect
17. C19×#399C4semidirect
18. C19×#398C4semidirect
20. C19×#397C4semidirect
189. #400Dic19semidirect
190. #399Dic19semidirect
191. #398Dic19semidirect
193. #397Dic19semidirect
246. C19#9012semidirect

Maximal subgroups

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

subgroupindex
#145726762
#145637342
C4×#105972912
#145615212
C19×#23952
#901219