Finite Group Databasebeta

← #18080294

Subgroups — #18080294

Order 4864.

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

normal subgroups only

This group has 726 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#14566221C211yesmaximal, characteristic, complemented
2#14563559C211yesmaximal, characteristic, complemented
3#14562164C212yesmaximal
4#14561488C212yesmaximal, complemented
5C19×#2436C211yesmaximal, characteristic
6C2×#10597372—21no—
7C2×#10597293—22no—
8#11926508C2212yes—
9#11926451—24no—
10#11926407—21no—
11#11926407C2212yes—
12#11926278—24no—
13C23×Q8×C19C2211yescharacteristic
14C2×C19×#124C412yescomplemented
15C2×C19×#121C2211yescharacteristic
16C19×#393—22no—
17C19×#391C412yescomplemented
18C19×#386—21no—
19C19×#386—21no—
20C4×C22⋊C4×C19C2211yescharacteristic
21C22×Q8×C19—22no—
22C22×Q8×C19—22no—
23C22×Q8×C19—44no—
24C22×Q8×C19C2×C412yes—
25C22×Q8×C19D412yes—
26C22×D4×C19—21no—
27C22×D4×C19C2×C411yescharacteristic
28C23×C4×C19D411yescharacteristic
29C23×C4×C19D411yescharacteristic
30C23×C4×C19C2311yescharacteristic
31C19×#124—44no—
32C19×#121—22no—
33C19×#121—22no—
34C2×C4⋊C4×C19C2×C411yescharacteristic
35C2×C22⋊C4×C19—21no—
36C2×C22⋊C4×C19—22no—
37C2×C22⋊C4×C19—22no—
38C2×C22⋊C4×C19—21no—
39C2×C42×C19C2×C412yes—
40C2×C22⋊Dic19—22no—
41#10597372—44no—
42C2×C4⋊Dic19—22no—
43C2×C4×Dic19—22no—
44C2×#64520—22no—
45C19×#95—22no—
46C19×#95—22no—
47C19×#95—21no—
48#10597293—44no—
49C19⋊#95—24no—
50C19⋊#95—22no—
51C19⋊#95D414yes—
52C22⋊(C19⋊C8)—22no—
53C22⋊(C19⋊C8)—22no—
54C24×C19—21no—
55C24×C19C2×D411yescharacteristic
56C2×Q8×C19—24no—
57C2×Q8×C19—24no—
58C2×Q8×C19—24no—
59C2×Q8×C19—24no—
60C2×Q8×C19—42no—
61C2×Q8×C19—42no—
62C2×Q8×C19—44no—
63C2×Q8×C19—44no—
64C2×Q8×C19—48no—
65C2×D4×C19—22no—
66C2×D4×C19—42no—
67C2×D4×C19—44no—
68C2×D4×C19—41no—
69C2×D4×C19—41no—
70C22×C4×C19—21no—
71C22×C4×C19—21no—
72C22×C4×C19—24no—
73C22×C4×C19—21no—
74C22×C4×C19—21no—
75C22×C4×C19—22no—
76C22×C4×C19—21no—
77C22×C4×C19—42no—
78C22×C4×C19—42no—
79C22×C4×C19C22⋊C412yes—
80C22×C4×C19C22⋊C412yes—
81C22×C4×C19C22×C411yescharacteristic
82C22×C4×C19C2×D412yes—
83C22×C4×C19C2×D411yescharacteristic
84C22×C4×C19#4112yes—
85C22×Dic19—24no—
86C4⋊C4×C19—22no—
87C22⋊C4×C19—44no—
88C22⋊C4×C19—42no—
89C22⋊C4×C19—44no—
90C22⋊C4×C19—42no—
91C42×C19—42no—
92C22⋊Dic19—44no—
93C4⋊Dic19—44no—
94C4×Dic19—44no—
95#64520—44no—
96C2×C19⋊C8—42no—
97#9466—191nomaximal, Sylow
98C23×C19—22no—
99C23×C19—22no—
100C23×C19—41no—
101C23×C19—42no—
102C23×C19—42no—
103C23×C19—41no—
104C23×C19—42no—
105C23×C19C2×C22⋊C411yescharacteristic
106C23×C19#12011yescharacteristic
107C23×C19#12311yescharacteristic
108Q8×C19—48no—
109Q8×C19—48no—
110D4×C19—82no—
111D4×C19—82no—
112D4×C19—82no—
113C2×C4×C19—22no—
114C2×C4×C19—22no—
115C2×C4×C19—24no—
116C2×C4×C19—22no—
117C2×C4×C19—22no—
118C2×C4×C19—22no—
119C2×C4×C19—22no—
120C2×C4×C19—22no—
121C2×C4×C19—22no—
122C2×C4×C19—22no—
123C2×C4×C19—42no—
124C2×C4×C19—42no—
125C2×C4×C19—42no—
126C2×C4×C19—42no—
127C2×C4×C19—42no—
128C2×C4×C19—42no—
129C2×C4×C19—42no—
130C2×C4×C19—41no—
131C2×C4×C19—42no—
132C2×C4×C19#9914yes—
133C2×C4×C19C4×D412yes—
134C2×C4×C19#12112yes—
135C2×Dic19—44no—
136C2×Dic19—44no—
137C2×Dic19—44no—
138C19⋊C8—82no—
139#2436D1911yescharacteristic
140#2310—191no—
141#1784—191no—
142#1510—192no—
143#1284—192no—
144C22×C19—21no—
145C22×C19—21no—
146C22×C19—21no—
147C22×C19—21no—
148C22×C19—21no—
149C22×C19—21no—
150C22×C19—21no—
151C22×C19—44no—
152C22×C19—84no—
153C22×C19—81no—
154C22×C19—81no—
155C22×C19—81no—
156C22×C19#38611yescharacteristic
157C22×C19C2×#9912yes—
158C22×C19#45412yes—
159C4×C19—22no—
160C4×C19—24no—
161C4×C19—22no—
162C4×C19—42no—
163C4×C19—82no—
164C4×C19—81no—
165Dic19—84no—
166C23×Q8C2×D1911yescharacteristic
167C2×#124Dic1912yescomplemented
168C2×#121C2×D1911yescharacteristic
169C2×#117—381no—
170C2×#101—382no—
171#407—192no—
172#393—22no—
173#391—384no—
174#391Dic1912yescomplemented
175#386—21no—
176#386—21no—
177#381—192no—
178#381—381no—
179C4×C22⋊C4C2×D1911yescharacteristic
180#327—384no—
181C2×C19—22no—
182C2×C19—22no—
183C2×C19—41no—
184C2×C19—161no—
185C2×C19#188811yescharacteristic
186C2×C19#189811yescharacteristic
187C2×C19#191211yescharacteristic
188C22×Q8—22no—
189C22×Q8—22no—
190C22×Q8—44no—
191C22×Q8C2×Dic1912yes—
192C22×Q8C22⋊D1912yes—
193C22×D4—21no—
194C22×D4C2×Dic1911yescharacteristic
195C23×C4C22⋊D1911yescharacteristic
196C23×C4C22⋊D1911yescharacteristic
197C23×C4C22×D1911yescharacteristic
198C2×M16—382no—
199#124—44no—
200#121—22no—
201#121—22no—
202#117—764no—
203C2×C4⋊C4—382no—
204C2×C4⋊C4C2×Dic1911yescharacteristic
205C2×C22⋊C4—21no—
206C2×C22⋊C4—22no—
207C2×C22⋊C4—22no—
208C2×C22⋊C4—21no—
209C2×C22⋊C4—382no—
210C2×C42—382no—
211C2×C42C2×Dic1912yes—
212#101—764no—
213C22⋊C8—382no—
214C22⋊C8—382no—
215#95—22no—
216#95—22no—
217#95—21no—
218#95—194no—
219#95—384no—
220#95—382no—
221C19#946611yescharacteristic, complemented, Sylow
222C24—21no—
223C24C2×C22⋊D1911yescharacteristic
224C2×Q8—24no—
225C2×Q8—24no—
226C2×Q8—24no—
227C2×Q8—24no—
228C2×Q8—42no—
229C2×Q8—42no—
230C2×Q8—44no—
231C2×Q8—44no—
232C2×Q8—48no—
233C2×D4—22no—
234C2×D4—42no—
235C2×D4—44no—
236C2×D4—41no—
237C2×D4—41no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—24no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—22no—
245C22×C4—42no—
246C22×C4—42no—
247C22×C4—384no—
248C22×C4C22⋊Dic1912yes—
249C22×C4C22⋊Dic1912yes—
250C22×C4D4×D1912yes—
251C22×C4#6454312yes—
252C22×C4C22×Dic1911yescharacteristic
253C22×C4C2×C22⋊D1911yescharacteristic
254M16—764no—
255C2×C8—762no—
256C4⋊C4—22no—
257C4⋊C4—764no—
258C22⋊C4—44no—
259C22⋊C4—42no—
260C22⋊C4—42no—
261C22⋊C4—44no—
262C22⋊C4—764no—
263C42—42no—
264C42—764no—
265C23—22no—
266C23—22no—
267C23—41no—
268C23—42no—
269C23—42no—
270C23—41no—
271C23—42no—
272C23#1059738111yescharacteristic
273C23#1059738311yescharacteristic
274C23C2×C22⋊Dic1911yescharacteristic
275Q8—48no—
276Q8—48no—
277D4—82no—
278D4—82no—
279D4—82no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—24no—
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—22no—
286C2×C4—22no—
287C2×C4—22no—
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—42no—
299C2×C4—764no—
300C2×C4—764no—
301C2×C4—764no—
302C2×C4#1059729114yes—
303C2×C4D4×Dic1912yes—
304C2×C4#1059738512yes—
305C8—1522no—
306C22—21no—
307C22—21no—
308C22—21no—
309C22—21no—
310C22—21no—
311C22—21no—
312C22—21no—
313C22—44no—
314C22—84no—
315C22—81no—
316C22—81no—
317C22—81no—
318C22#1192642411yescharacteristic
319C22C2×#1059729112yes—
320C22#1192671612yes—
321C4—22no—
322C4—24no—
323C4—22no—
324C4—42no—
325C4—82no—
326C4—81no—
327C4—1524no—
328C2—22no—
329C2—22no—
330C2—41no—
331C2—161no—
332C2#1456403911yescharacteristic
333C2#1456408911yescharacteristic
334C2#1456417311yescharacteristic
subgroupG/H
centerC22#11926424
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#2436C2
socleC22×C19#386
prime radicalC2×C19×#121C22
cosocleC23×C4×C19C23
hypercenter#2436D19
hypocenterC19#9466
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2436

Complements

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

NH ≅ G/Ntype
1. #14566221C2semidirect
2. #14563559C2semidirect
4. #14561488C2semidirect
14. C2×C19×#124C4semidirect
17. C19×#391C4semidirect
167. C2×#124Dic19semidirect
174. #391Dic19semidirect
221. C19#9466semidirect

Maximal subgroups

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

subgroupindex
#145662212
#145635592
#145621642
#145614882
C19×#24362
#946619