Finite Group Databasebeta

← #18080464

Subgroups — #18080464

Order 4864.

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

normal subgroups only

This group has 660 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
2#14563709C211yesmaximal, characteristic
3#14563709C212yesmaximal
4C19⋊#1304C212yesmaximal
5C19×#2483C211yesmaximal, characteristic
6#11926437—24no—
7#11926404—21no—
8#11926400C2212yes—
9#11926400C2212yes—
10C4×C22⋊Dic19—21no—
11#11926311—22no—
12#11926311—24no—
13C22×C22⋊C4×C19C2211yescharacteristic
14C22×C22⋊C4×C19C2211yescharacteristic
15C19×#397—22no—
16C19×#385—21no—
17C19×#385C412yescomplemented
18C19×#381—21no—
19C19×#381C412yescomplemented
20C19×#379C2211yescharacteristic
21C25×C19C2311yescharacteristic
22C23×C4×C19C2×C411yescharacteristic
23C23×C4×C19C2×C411yescharacteristic
24C23×C4×C19D411yescharacteristic
25C23×C4×C19D411yescharacteristic
26C2×C4⋊C4×C19—22no—
27C2×C22⋊C4×C19—22no—
28C2×C22⋊C4×C19—22no—
29C2×C22⋊C4×C19—21no—
30C2×C22⋊C4×C19—22no—
31C2×C22⋊C4×C19—21no—
32C2×C22⋊C4×C19—21no—
33C2×C22⋊C4×C19—22no—
34C2×C22⋊C4×C19—21no—
35C2×C22⋊C4×C19C2×C412yes—
36C2×C22⋊C4×C19C2×C412yes—
37C2×C22⋊C4×C19D412yes—
38C2×C22⋊Dic19—22no—
39C2×C22⋊Dic19—22no—
40C2×C22⋊Dic19—22no—
41C2×C22⋊Dic19—22no—
42C2×C22⋊Dic19—22no—
43C2×C22⋊Dic19D414yes—
44C2×C4⋊Dic19—22no—
45C2×C4×Dic19—22no—
46C19×#95—22no—
47C19×#95—22no—
48C19×#95—22no—
49C19⋊#95—22no—
50C19⋊#95—22no—
51C24×C19—42no—
52C24×C19—42no—
53C24×C19—81no—
54C24×C19C22×C411yescharacteristic
55C24×C19C2×D412yes—
56C24×C19C2×D411yescharacteristic
57C24×C19C2×D411yescharacteristic
58C24×C19#4112yes—
59C22×C4×C19—21no—
60C22×C4×C19—21no—
61C22×C4×C19—21no—
62C22×C4×C19—21no—
63C22×C4×C19—22no—
64C22×C4×C19—21no—
65C22×C4×C19—21no—
66C22×C4×C19—22no—
67C22×C4×C19—22no—
68C22×C4×C19—42no—
69C22×C4×C19—42no—
70C22×C4×C19—81no—
71C22×C4×C19—81no—
72C22×C4×C19C22⋊C412yes—
73C22×C4×C19C22⋊C412yes—
74C22×Dic19—24no—
75C22×Dic19—42no—
76C4⋊C4×C19—82no—
77C22⋊C4×C19—24no—
78C22⋊C4×C19—24no—
79C22⋊C4×C19—42no—
80C22⋊C4×C19—41no—
81C22⋊C4×C19—42no—
82C22⋊C4×C19—41no—
83C22⋊C4×C19—42no—
84C22⋊C4×C19—81no—
85C22⋊Dic19—44no—
86C22⋊Dic19—44no—
87C22⋊Dic19—44no—
88C22⋊Dic19—44no—
89C22⋊Dic19—82no—
90C22⋊Dic19—82no—
91C4⋊Dic19—82no—
92C4×Dic19—82no—
93#9500—191nomaximal, Sylow
94C23×C19—22no—
95C23×C19—22no—
96C23×C19—22no—
97C23×C19—22no—
98C23×C19—24no—
99C23×C19—41no—
100C23×C19—41no—
101C23×C19—41no—
102C23×C19—42no—
103C23×C19—42no—
104C23×C19—41no—
105C23×C19—42no—
106C23×C19—41no—
107C23×C19—42no—
108C23×C19—42no—
109C23×C19—88no—
110C23×C19C2×C22⋊C411yescharacteristic
111C23×C19C4×D412yes—
112C23×C19#12011yescharacteristic
113C23×C19#12112yes—
114C23×C19#12311yescharacteristic
115C2×C4×C19—22no—
116C2×C4×C19—22no—
117C2×C4×C19—42no—
118C2×C4×C19—42no—
119C2×C4×C19—42no—
120C2×C4×C19—42no—
121C2×C4×C19—42no—
122C2×C4×C19—42no—
123C2×C4×C19—42no—
124C2×C4×C19—41no—
125C2×C4×C19—41no—
126C2×C4×C19—42no—
127C2×C4×C19—42no—
128C2×C4×C19—81no—
129C2×C4×C19—81no—
130C2×C4×C19—82no—
131C2×C4×C19—82no—
132C2×Dic19—44no—
133C2×Dic19—44no—
134C2×Dic19—44no—
135C2×Dic19—82no—
136C2×Dic19—82no—
137C2×Dic19—82no—
138#2483D1911yescharacteristic
139#2312—191no—
140#1819—192no—
141#1819—191no—
142#1304—192no—
143C22×C19—21no—
144C22×C19—21no—
145C22×C19—21no—
146C22×C19—21no—
147C22×C19—22no—
148C22×C19—21no—
149C22×C19—22no—
150C22×C19—22no—
151C22×C19—22no—
152C22×C19—21no—
153C22×C19—22no—
154C22×C19—22no—
155C22×C19—21no—
156C22×C19—44no—
157C22×C19—44no—
158C22×C19—84no—
159C22×C19—82no—
160C22×C19—84no—
161C22×C19#38611yescharacteristic
162C22×C19#41012yes—
163C22×C19#45812yes—
164C4×C19—42no—
165C4×C19—42no—
166C4×C19—82no—
167C4×C19—81no—
168C4×C19—81no—
169Dic19—84no—
170Dic19—162no—
171C22×C22⋊C4C2×D1911yescharacteristic
172C22×C22⋊C4C2×D1911yescharacteristic
173#397—22no—
174#388—384no—
175#385—21no—
176#385Dic1912yescomplemented
177#381—21no—
178#381Dic1912yescomplemented
179#380—381no—
180#379—192no—
181#379—192no—
182#379C2×D1911yescharacteristic
183C4×C22⋊C4—381no—
184#342—384no—
185#342—382no—
186C2×C19—22no—
187C2×C19—22no—
188C2×C19—42no—
189C2×C19—41no—
190C2×C19—42no—
191C2×C19#189011yescharacteristic
192C2×C19#189911yescharacteristic
193C2×C19#191311yescharacteristic
194C25C22×D1911yescharacteristic
195C23×C4C2×Dic1911yescharacteristic
196C23×C4C2×Dic1911yescharacteristic
197C23×C4C22⋊D1911yescharacteristic
198C23×C4C22⋊D1911yescharacteristic
199C2×C4⋊C4—22no—
200C2×C4⋊C4—382no—
201C2×C22⋊C4—22no—
202C2×C22⋊C4—22no—
203C2×C22⋊C4—22no—
204C2×C22⋊C4—22no—
205C2×C22⋊C4—21no—
206C2×C22⋊C4—21no—
207C2×C22⋊C4—21no—
208C2×C22⋊C4—21no—
209C2×C22⋊C4—194no—
210C2×C22⋊C4—382no—
211C2×C22⋊C4—382no—
212C2×C22⋊C4—382no—
213C2×C22⋊C4—382no—
214C2×C22⋊C4—382no—
215C2×C22⋊C4C2×Dic1912yes—
216C2×C22⋊C4C2×Dic1912yes—
217C2×C22⋊C4C22⋊D1912yes—
218C2×C42—382no—
219#95—22no—
220#95—22no—
221#95—22no—
222#95—382no—
223#95—382no—
224C19#950011yescharacteristic, complemented, Sylow
225C24—42no—
226C24—42no—
227C24—81no—
228C24D4×D1912yes—
229C24#6454312yes—
230C24C22×Dic1911yescharacteristic
231C24C2×C22⋊D1911yescharacteristic
232C24C2×C22⋊D1911yescharacteristic
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—22no—
239C22×C4—21no—
240C22×C4—22no—
241C22×C4—22no—
242C22×C4—42no—
243C22×C4—42no—
244C22×C4—81no—
245C22×C4—81no—
246C22×C4—384no—
247C22×C4—762no—
248C22×C4C22⋊Dic1912yes—
249C22×C4C22⋊Dic1912yes—
250C4⋊C4—82no—
251C4⋊C4—1522no—
252C22⋊C4—24no—
253C22⋊C4—24no—
254C22⋊C4—42no—
255C22⋊C4—41no—
256C22⋊C4—41no—
257C22⋊C4—42no—
258C22⋊C4—42no—
259C22⋊C4—81no—
260C22⋊C4—764no—
261C22⋊C4—764no—
262C22⋊C4—764no—
263C22⋊C4—764no—
264C22⋊C4—1522no—
265C22⋊C4—1522no—
266C42—1522no—
267C23—22no—
268C23—22no—
269C23—22no—
270C23—24no—
271C23—22no—
272C23—41no—
273C23—41no—
274C23—41no—
275C23—41no—
276C23—42no—
277C23—42no—
278C23—42no—
279C23—42no—
280C23—42no—
281C23—41no—
282C23—88no—
283C23D4×Dic1912yes—
284C23#1059738111yescharacteristic
285C23#1059738311yescharacteristic
286C23#1059738512yes—
287C23C2×C22⋊Dic1911yescharacteristic
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—42no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4—42no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—42no—
300C2×C4—42no—
301C2×C4—81no—
302C2×C4—81no—
303C2×C4—82no—
304C2×C4—82no—
305C2×C4—764no—
306C2×C4—764no—
307C2×C4—764no—
308C2×C4—1522no—
309C2×C4—1522no—
310C2×C4—1522no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—21no—
315C22—22no—
316C22—21no—
317C22—22no—
318C22—21no—
319C22—22no—
320C22—22no—
321C22—22no—
322C22—22no—
323C22—21no—
324C22—44no—
325C22—44no—
326C22—82no—
327C22—84no—
328C22—84no—
329C22#1192642411yescharacteristic
330C22#1192651812yes—
331C22#1192673312yes—
332C4—42no—
333C4—42no—
334C4—82no—
335C4—81no—
336C4—81no—
337C4—3042no—
338C4—1524no—
339C2—22no—
340C2—22no—
341C2—42no—
342C2—42no—
343C2—41no—
344C2#1456404911yescharacteristic
345C2#1456409411yescharacteristic
346C2#1456417811yescharacteristic
subgroupG/H
centerC22#11926424
commutatorC24×C19C22×C4
FrattiniC25C22×D19
FittingC19×#2483C2
socleC22×C19#386
prime radical, cosocleC25×C19C23
hypercenter#2483D19
hypocenterC19#9500
LCSG ▷ C24×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C25 ◁ #2483

Complements

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

NH ≅ G/Ntype
17. C19×#385C4semidirect
19. C19×#381C4semidirect
176. #385Dic19semidirect
178. #381Dic19semidirect
224. C19#9500semidirect

Maximal subgroups

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

subgroupindex
#145662332
#145637092
C19⋊#13042
C19×#24832
#950019