Finite Group Databasebeta

← #18080274

Subgroups — #18080274

Order 4864.

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

normal subgroups only

This group has 700 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
2#14563559C211yesmaximal, characteristic
3#14562168C212yesmaximal
4#14561488C212yesmaximal
5C19×#2434C211yesmaximal, characteristic
6C2×#10597372—21no—
7C2×#10597293—22no—
8#11926508C2212yes—
9#11926451—24no—
10#11926407—21no—
11#11926407C2212yes—
12#11926281—24no—
13C23×Q8×C19C2211yescharacteristic
14C2×C19×C4⋊Q8C412yescomplemented
15C2×C19×C22⋊Q8C2211yescharacteristic
16C19×#395—22no—
17C19×#391C412yescomplemented
18C19×#385—21no—
19C19×#385—21no—
20C4×C22⋊C4×C19C2211yescharacteristic
21C22×Q8×C19—22no—
22C22×Q8×C19—22no—
23C22×Q8×C19—44no—
24C22×Q8×C19C2×C411yescharacteristic
25C22×Q8×C19C2×C412yes—
26C22×Q8×C19D412yes—
27C23×C4×C19D411yescharacteristic
28C23×C4×C19D411yescharacteristic
29C23×C4×C19C2311yescharacteristic
30C19×C4⋊Q8—44no—
31C19×C22⋊Q8—22no—
32C19×C22⋊Q8—22no—
33C2×C4⋊C4×C19—22no—
34C2×C4⋊C4×C19—22no—
35C2×C4⋊C4×C19—21no—
36C2×C4⋊C4×C19C2×C411yescharacteristic
37C2×C22⋊C4×C19—21no—
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×C19C2×D411yescharacteristic
55C2×Q8×C19—24no—
56C2×Q8×C19—24no—
57C2×Q8×C19—24no—
58C2×Q8×C19—24no—
59C2×Q8×C19—22no—
60C2×Q8×C19—42no—
61C2×Q8×C19—42no—
62C2×Q8×C19—44no—
63C2×Q8×C19—44no—
64C2×Q8×C19—48no—
65C2×Q8×C19—42no—
66C22×C4×C19—21no—
67C22×C4×C19—21no—
68C22×C4×C19—24no—
69C22×C4×C19—22no—
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⋊C412yes—
77C22×C4×C19C22⋊C412yes—
78C22×C4×C19C22×C411yescharacteristic
79C22×C4×C19C2×D412yes—
80C22×C4×C19C2×D411yescharacteristic
81C22×C4×C19#4112yes—
82C22×Dic19—24no—
83C4⋊C4×C19—22no—
84C4⋊C4×C19—44no—
85C4⋊C4×C19—44no—
86C4⋊C4×C19—42no—
87C22⋊C4×C19—24no—
88C22⋊C4×C19—41no—
89C22⋊C4×C19—41no—
90C42×C19—42no—
91C22⋊Dic19—44no—
92C4⋊Dic19—44no—
93C4×Dic19—44no—
94#64520—44no—
95C2×C19⋊C8—42no—
96#9462—191nomaximal, Sylow
97C23×C19—22no—
98C23×C19—22no—
99C23×C19—41no—
100C23×C19C2×C22⋊C411yescharacteristic
101C23×C19#12011yescharacteristic
102C23×C19#12311yescharacteristic
103Q8×C19—48no—
104Q8×C19—48no—
105Q8×C19—82no—
106C2×C4×C19—22no—
107C2×C4×C19—22no—
108C2×C4×C19—24no—
109C2×C4×C19—22no—
110C2×C4×C19—22no—
111C2×C4×C19—22no—
112C2×C4×C19—22no—
113C2×C4×C19—24no—
114C2×C4×C19—22no—
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#9914yes—
128C2×C4×C19C4×D412yes—
129C2×C4×C19#12112yes—
130C2×Dic19—44no—
131C2×Dic19—44no—
132C2×Dic19—44no—
133C19⋊C8—82no—
134#2434D1911yescharacteristic
135#2310—191no—
136#1784—191no—
137#1511—192no—
138#1284—192no—
139C22×C19—21no—
140C22×C19—21no—
141C22×C19—21no—
142C22×C19—21no—
143C22×C19—21no—
144C22×C19—21no—
145C22×C19—21no—
146C22×C19—44no—
147C22×C19#38611yescharacteristic
148C22×C19C2×#9912yes—
149C22×C19#45612yes—
150C4×C19—22no—
151C4×C19—24no—
152C4×C19—22no—
153C4×C19—44no—
154C4×C19—42no—
155C4×C19—81no—
156C4×C19—81no—
157Dic19—84no—
158C23×Q8C2×D1911yescharacteristic
159C2×C4⋊Q8Dic1912yescomplemented
160C2×C22⋊Q8C2×D1911yescharacteristic
161C2×#117—381no—
162C2×#101—382no—
163#407—192no—
164#395—22no—
165#391—384no—
166#391Dic1912yescomplemented
167#385—21no—
168#385—21no—
169#381—192no—
170#381—381no—
171C4×C22⋊C4C2×D1911yescharacteristic
172#328—384no—
173C2×C19—22no—
174C2×C19—22no—
175C2×C19—41no—
176C2×C19#188611yescharacteristic
177C2×C19#189811yescharacteristic
178C2×C19#191211yescharacteristic
179C22×Q8—22no—
180C22×Q8—22no—
181C22×Q8—44no—
182C22×Q8C2×Dic1911yescharacteristic
183C22×Q8C2×Dic1912yes—
184C22×Q8C22⋊D1912yes—
185C23×C4C22⋊D1911yescharacteristic
186C23×C4C22⋊D1911yescharacteristic
187C23×C4C22×D1911yescharacteristic
188C2×M16—382no—
189C4⋊Q8—44no—
190C22⋊Q8—22no—
191C22⋊Q8—22no—
192#117—764no—
193C2×C4⋊C4—22no—
194C2×C4⋊C4—22no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—382no—
197C2×C4⋊C4C2×Dic1911yescharacteristic
198C2×C22⋊C4—21no—
199C2×C22⋊C4—21no—
200C2×C22⋊C4—382no—
201C2×C42—382no—
202C2×C42C2×Dic1912yes—
203#101—764no—
204C22⋊C8—382no—
205C22⋊C8—382no—
206#95—22no—
207#95—22no—
208#95—21no—
209#95—194no—
210#95—384no—
211#95—382no—
212C19#946211yescharacteristic, complemented, Sylow
213C24C2×C22⋊D1911yescharacteristic
214C2×Q8—24no—
215C2×Q8—24no—
216C2×Q8—24no—
217C2×Q8—24no—
218C2×Q8—22no—
219C2×Q8—42no—
220C2×Q8—42no—
221C2×Q8—44no—
222C2×Q8—44no—
223C2×Q8—48no—
224C2×Q8—42no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—24no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—22no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—42no—
234C22×C4—42no—
235C22×C4—384no—
236C22×C4C22⋊Dic1912yes—
237C22×C4C22⋊Dic1912yes—
238C22×C4D4×D1912yes—
239C22×C4#6454312yes—
240C22×C4C22×Dic1911yescharacteristic
241C22×C4C2×C22⋊D1911yescharacteristic
242M16—764no—
243C2×C8—762no—
244C4⋊C4—22no—
245C4⋊C4—44no—
246C4⋊C4—42no—
247C4⋊C4—44no—
248C4⋊C4—764no—
249C22⋊C4—24no—
250C22⋊C4—41no—
251C22⋊C4—41no—
252C22⋊C4—764no—
253C42—42no—
254C42—764no—
255C23—22no—
256C23—22no—
257C23—41no—
258C23#1059738111yescharacteristic
259C23#1059738311yescharacteristic
260C23C2×C22⋊Dic1911yescharacteristic
261Q8—48no—
262Q8—48no—
263Q8—82no—
264C2×C4—22no—
265C2×C4—22no—
266C2×C4—24no—
267C2×C4—22no—
268C2×C4—22no—
269C2×C4—22no—
270C2×C4—22no—
271C2×C4—24no—
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—42no—
285C2×C4—764no—
286C2×C4—764no—
287C2×C4—764no—
288C2×C4#1059729114yes—
289C2×C4D4×Dic1912yes—
290C2×C4#1059738512yes—
291C8—1522no—
292C22—21no—
293C22—21no—
294C22—21no—
295C22—21no—
296C22—21no—
297C22—21no—
298C22—21no—
299C22—44no—
300C22#1192642411yescharacteristic
301C22C2×#1059729112yes—
302C22#1192672612yes—
303C4—22no—
304C4—24no—
305C4—22no—
306C4—44no—
307C4—42no—
308C4—81no—
309C4—81no—
310C4—1524no—
311C2—22no—
312C2—22no—
313C2—41no—
314C2#1456402911yescharacteristic
315C2#1456408911yescharacteristic
316C2#1456417311yescharacteristic
subgroupG/H
centerC22#11926424
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#2434C2
socleC22×C19#386
prime radicalC24×C19C2×D4
cosocleC23×C4×C19C23
hypercenter#2434D19
hypocenterC19#9462
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2434

Complements

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

NH ≅ G/Ntype
14. C2×C19×C4⋊Q8C4semidirect
17. C19×#391C4semidirect
159. C2×C4⋊Q8Dic19semidirect
166. #391Dic19semidirect
212. C19#9462semidirect

Maximal subgroups

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

subgroupindex
#145662212
#145635592
#145621682
#145614882
C19×#24342
#946219