Finite Group Databasebeta

← #18079990

Subgroups — #18079990

Order 4864.

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

normal subgroups only

This group has 644 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#14565992C211yesmaximal, characteristic, complemented
2#14562151C212yesmaximal
3#14561965C211yesmaximal, characteristic, complemented
4#14561521C212yesmaximal, complemented
5C19×#2591C211yesmaximal, characteristic
6C2×#10597372—21no—
7#11926508C2212yes—
8C4⋊C4×Dic19—24no—
9C4×C22⋊Dic19—21no—
10C4×C22⋊Dic19C2212yes—
11#11926278—24no—
12#11926270—22no—
13C2×C19×#121C2211yescharacteristic
14C22×C4⋊C4×C19C2211yescharacteristic
15C19×#400C412yescomplemented
16C19×#394C412yescomplemented
17C19×#388—22no—
18C19×#386—21no—
19C19×#386—21no—
20C4×C22⋊C4×C19C2211yescharacteristic
21C22×D4×C19—21no—
22C22×D4×C19C2×C411yescharacteristic
23C23×C4×C19D411yescharacteristic
24C23×C4×C19D411yescharacteristic
25C23×C4×C19C2311yescharacteristic
26C19×#121—22no—
27C19×#121—22no—
28C2×C4⋊C4×C19—22no—
29C2×C4⋊C4×C19—22no—
30C2×C4⋊C4×C19C2×C411yescharacteristic
31C2×C4⋊C4×C19C2×C412yes—
32C2×C4⋊C4×C19D412yes—
33C2×C22⋊C4×C19—21no—
34C2×C22⋊C4×C19—22no—
35C2×C22⋊C4×C19—21no—
36C2×C22⋊C4×C19—22no—
37C2×C42×C19—21no—
38C2×C22⋊Dic19—22no—
39#10597372—28no—
40C2×C4⋊Dic19—22no—
41C2×C4×Dic19—22no—
42C2×C4×Dic19—22no—
43C2×C4×Dic19—22no—
44C2×#64520—22no—
45C19×#95—22no—
46C19×#95—22no—
47C19×#95C2×C412yes—
48C19⋊#95—22no—
49C19⋊#95D414yes—
50C22⋊(C19⋊C8)—22no—
51C22⋊(C19⋊C8)—22no—
52C24×C19—21no—
53C24×C19C2×D411yescharacteristic
54C2×D4×C19—22no—
55C2×D4×C19—44no—
56C2×D4×C19—41no—
57C2×D4×C19—41no—
58C2×D4×C19—81no—
59C22×C4×C19—21no—
60C22×C4×C19—21no—
61C22×C4×C19—24no—
62C22×C4×C19—21no—
63C22×C4×C19—21no—
64C22×C4×C19—22no—
65C22×C4×C19—21no—
66C22×C4×C19—81no—
67C22×C4×C19—81no—
68C22×C4×C19C22⋊C412yes—
69C22×C4×C19C22⋊C412yes—
70C22×C4×C19C22×C411yescharacteristic
71C22×C4×C19C2×D412yes—
72C22×C4×C19C2×D411yescharacteristic
73C22×C4×C19#4112yes—
74C22×Dic19—24no—
75C4⋊C4×C19—24no—
76C4⋊C4×C19—24no—
77C4⋊C4×C19—22no—
78C22⋊C4×C19—42no—
79C22⋊C4×C19—44no—
80C22⋊C4×C19—42no—
81C22⋊C4×C19—82no—
82C42×C19—81no—
83C22⋊Dic19—28no—
84C4⋊Dic19—28no—
85C4×Dic19—28no—
86C4×Dic19—82no—
87C4×Dic19—82no—
88#64520—82no—
89C2×C19⋊C8—42no—
90#9410—191nomaximal, Sylow
91C23×C19—22no—
92C23×C19—22no—
93C23×C19—41no—
94C23×C19—42no—
95C23×C19—42no—
96C23×C19—41no—
97C23×C19—42no—
98C23×C19C2×C22⋊C411yescharacteristic
99C23×C19#12011yescharacteristic
100C23×C19#12311yescharacteristic
101D4×C19—82no—
102D4×C19—82no—
103D4×C19—82no—
104C2×C4×C19—22no—
105C2×C4×C19—22no—
106C2×C4×C19—24no—
107C2×C4×C19—22no—
108C2×C4×C19—22no—
109C2×C4×C19—22no—
110C2×C4×C19—42no—
111C2×C4×C19—42no—
112C2×C4×C19—41no—
113C2×C4×C19—41no—
114C2×C4×C19—42no—
115C2×C4×C19—42no—
116C2×C4×C19—42no—
117C2×C4×C19—42no—
118C2×C4×C19—42no—
119C2×C4×C19—41no—
120C2×C4×C19—42no—
121C2×C4×C19—81no—
122C2×C4×C19#10414yes—
123C2×C4×C19C4×D412yes—
124C2×C4×C19#12112yes—
125C2×Dic19—28no—
126C2×Dic19—44no—
127C2×Dic19—44no—
128C19⋊C8—82no—
129#2591D1911yescharacteristic
130#2274—191no—
131#1507—192no—
132#1463—191no—
133#1297—192no—
134C22×C19—21no—
135C22×C19—21no—
136C22×C19—21no—
137C22×C19—21no—
138C22×C19—21no—
139C22×C19—21no—
140C22×C19—21no—
141C22×C19—44no—
142C22×C19—84no—
143C22×C19—81no—
144C22×C19—81no—
145C22×C19—81no—
146C22×C19#38611yescharacteristic
147C22×C19C2×#10412yes—
148C22×C19#45412yes—
149C4×C19—24no—
150C4×C19—22no—
151C4×C19—22no—
152C4×C19—42no—
153C4×C19—82no—
154C4×C19—81no—
155Dic19—48no—
156C2×#121C2×D1911yescharacteristic
157C2×#117—381no—
158C22×C4⋊C4C2×D1911yescharacteristic
159#407—192no—
160#400Dic1912yescomplemented
161#394Dic1912yescomplemented
162#388—22no—
163#386—21no—
164#386—21no—
165C4×C4⋊C4—384no—
166C4×C22⋊C4—192no—
167C4×C22⋊C4—381no—
168C4×C22⋊C4C2×D1911yescharacteristic
169#327—384no—
170#324—382no—
171C2×C19—22no—
172C2×C19—22no—
173C2×C19—41no—
174C2×C19—161no—
175C2×C19#188811yescharacteristic
176C2×C19#189611yescharacteristic
177C2×C19#191311yescharacteristic
178C22×D4—21no—
179C22×D4C2×Dic1911yescharacteristic
180C23×C4C22⋊D1911yescharacteristic
181C23×C4C22⋊D1911yescharacteristic
182C23×C4C22×D1911yescharacteristic
183C2×M16—382no—
184#121—22no—
185#121—22no—
186#117—388no—
187C2×C4⋊C4—22no—
188C2×C4⋊C4—22no—
189C2×C4⋊C4—382no—
190C2×C4⋊C4C2×Dic1911yescharacteristic
191C2×C4⋊C4C2×Dic1912yes—
192C2×C4⋊C4C22⋊D1912yes—
193C2×C22⋊C4—21no—
194C2×C22⋊C4—22no—
195C2×C22⋊C4—21no—
196C2×C22⋊C4—22no—
197C2×C22⋊C4—382no—
198C2×C42—21no—
199C2×C42—382no—
200C2×C42—382no—
201C2×C42—382no—
202C22⋊C8—382no—
203C22⋊C8—382no—
204#95—22no—
205#95—22no—
206#95—194no—
207#95—382no—
208#95C2×Dic1912yes—
209C19#941011yescharacteristic, complemented, Sylow
210C24—21no—
211C24C2×C22⋊D1911yescharacteristic
212C2×D4—22no—
213C2×D4—44no—
214C2×D4—41no—
215C2×D4—41no—
216C2×D4—81no—
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—24no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—22no—
224C22×C4—81no—
225C22×C4—81no—
226C22×C4—384no—
227C22×C4C22⋊Dic1912yes—
228C22×C4C22⋊Dic1912yes—
229C22×C4D4×D1912yes—
230C22×C4#6454312yes—
231C22×C4C22×Dic1911yescharacteristic
232C22×C4C2×C22⋊D1911yescharacteristic
233M16—1522no—
234C2×C8—762no—
235C4⋊C4—24no—
236C4⋊C4—24no—
237C4⋊C4—22no—
238C4⋊C4—388no—
239C22⋊C4—42no—
240C22⋊C4—42no—
241C22⋊C4—44no—
242C22⋊C4—82no—
243C22⋊C4—388no—
244C42—81no—
245C42—388no—
246C42—1522no—
247C42—1522no—
248C23—22no—
249C23—22no—
250C23—41no—
251C23—42no—
252C23—42no—
253C23—42no—
254C23—41no—
255C23#1059738111yescharacteristic
256C23#1059738311yescharacteristic
257C23C2×C22⋊Dic1911yescharacteristic
258D4—82no—
259D4—82no—
260D4—82no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—24no—
264C2×C4—22no—
265C2×C4—22no—
266C2×C4—22no—
267C2×C4—41no—
268C2×C4—42no—
269C2×C4—42no—
270C2×C4—41no—
271C2×C4—42no—
272C2×C4—42no—
273C2×C4—42no—
274C2×C4—42no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—41no—
278C2×C4—81no—
279C2×C4—388no—
280C2×C4—764no—
281C2×C4—764no—
282C2×C4#1059729414yes—
283C2×C4D4×Dic1912yes—
284C2×C4#1059738512yes—
285C8—1522no—
286C22—21no—
287C22—21no—
288C22—21no—
289C22—21no—
290C22—21no—
291C22—21no—
292C22—21no—
293C22—44no—
294C22—84no—
295C22—81no—
296C22—81no—
297C22—81no—
298C22#1192642411yescharacteristic
299C22C2×#1059729412yes—
300C22#1192671612yes—
301C4—22no—
302C4—22no—
303C4—24no—
304C4—42no—
305C4—82no—
306C4—81no—
307C4—768no—
308C2—22no—
309C2—22no—
310C2—41no—
311C2—161no—
312C2#1456403911yescharacteristic
313C2#1456407911yescharacteristic
314C2#1456417811yescharacteristic
subgroupG/H
centerC22#11926424
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#2591C2
socleC22×C19#386
prime radicalC2×C19×#121C22
cosocleC23×C4×C19C23
hypercenter#2591D19
hypocenterC19#9410
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2591

Complements

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

NH ≅ G/Ntype
1. #14565992C2semidirect
3. #14561965C2semidirect
4. #14561521C2semidirect
15. C19×#400C4semidirect
16. C19×#394C4semidirect
160. #400Dic19semidirect
161. #394Dic19semidirect
209. C19#9410semidirect

Maximal subgroups

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

subgroupindex
#145659922
#145621512
#145619652
#145615212
C19×#25912
#941019