Finite Group Databasebeta

← #18080229

Subgroups — #18080229

Order 4864.

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

normal subgroups only

This group has 498 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#14572664C211yesmaximal, characteristic
2#14562352C212yesmaximal, complemented
3#14561976C211yesmaximal, characteristic
4#14561491C212yesmaximal, complemented
5C19×#2563C211yesmaximal, characteristic
6#11926616—24no—
7#11926601C2212yes—
8#11926601C2212yes—
9#11926508—21no—
10C2×C22⋊(C19⋊C8)—21no—
11#11926290—24no—
12#11926268—21no—
13#11926268—21no—
14C2×C19×C4⋊Q8C2211yescharacteristic
15C2×C4×D4×C19C2211yescharacteristic
16C19×#393—21no—
17C19×#393—21no—
18C19×#390C412yes—
19C19×#382C412yes—
20C19×#380—21no—
21C19×#380—21no—
22C4×C4⋊C4×C19C2211yescharacteristic
23C22×Q8×C19—21no—
24C22×D4×C19C2×C411yescharacteristic
25C23×C4×C19D411yescharacteristic
26C23×C4×C19D411yescharacteristic
27C19×C4⋊Q8—22no—
28C19×C4⋊Q8—22no—
29C4×D4×C19—22no—
30C4×D4×C19—22no—
31C2×C4⋊C4×C19—21no—
32C2×C4⋊C4×C19—21no—
33C2×C4⋊C4×C19C2×C412yes—
34C2×C4⋊C4×C19C2×C411yescharacteristic
35C2×C22⋊C4×C19—22no—
36C2×C22⋊C4×C19—22no—
37C2×C22⋊C4×C19D411yescharacteristic
38C2×C22⋊C4×C19D411yescharacteristic
39C2×C42×C19C2×C412yes—
40C2×C42×C19C2311yescharacteristic
41C2×#64520—22no—
42C22×C19⋊C8—22no—
43C19×#95—22no—
44C19×#95—22no—
45C19×#95—21no—
46C22⋊(C19⋊C8)—22no—
47C22⋊(C19⋊C8)—22no—
48C22⋊(C19⋊C8)—22no—
49C22⋊(C19⋊C8)—22no—
50C4⋊(C19⋊C8)—22no—
51C4⋊(C19⋊C8)D414yes—
52#10597260—22no—
53#10597260—22no—
54C24×C19C22⋊C411yescharacteristic
55C24×C19C22⋊C411yescharacteristic
56C2×Q8×C19—42no—
57C2×Q8×C19—82no—
58C2×D4×C19—22no—
59C2×D4×C19—22no—
60C2×D4×C19—41no—
61C22×C4×C19—21no—
62C22×C4×C19—21no—
63C22×C4×C19—21no—
64C22×C4×C19—21no—
65C22×C4×C19—22no—
66C22×C4×C19—22no—
67C22×C4×C19—42no—
68C22×C4×C19—42no—
69C22×C4×C19C22⋊C411yescharacteristic
70C22×C4×C19C22⋊C411yescharacteristic
71C22×C4×C19C22×C411yescharacteristic
72C22×C4×C19C2×D411yescharacteristic
73C22×C4×C19C2×D411yescharacteristic
74C4⋊C4×C19—22no—
75C4⋊C4×C19—24no—
76C4⋊C4×C19—42no—
77C4⋊C4×C19—41no—
78C4⋊C4×C19—41no—
79C22⋊C4×C19—22no—
80C22⋊C4×C19—22no—
81C22⋊C4×C19—82no—
82C22⋊C4×C19—82no—
83C42×C19—42no—
84C42×C19C2×D412yes—
85C42×C19#4112yes—
86#64520—82no—
87C2×C19⋊C8—24no—
88C2×C19⋊C8—42no—
89C2×C19⋊C8—82no—
90#9453—191nomaximal, Sylow
91C23×C19—21no—
92C23×C19—21no—
93C23×C19—21no—
94C23×C19—21no—
95C23×C19—21no—
96C23×C19—41no—
97C23×C19—41no—
98C23×C19—41no—
99C23×C19—41no—
100C23×C19#10112yes—
101C23×C19C2×C22⋊C411yescharacteristic
102Q8×C19—84no—
103D4×C19—44no—
104C2×C4×C19—21no—
105C2×C4×C19—21no—
106C2×C4×C19—22no—
107C2×C4×C19—21no—
108C2×C4×C19—21no—
109C2×C4×C19—41no—
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—42no—
120C2×C4×C19—81no—
121C2×C4×C19—81no—
122C2×C4×C19C4×D412yes—
123C2×C4×C19#12011yescharacteristic
124C2×C4×C19#12112yes—
125C2×C4×C19#12311yescharacteristic
126C19⋊C8—44no—
127C19⋊C8—82no—
128#2973—191no—
129#2563D1911yescharacteristic
130#1556—192no—
131#1466—191no—
132#1285—192no—
133C22×C19—21no—
134C22×C19—21no—
135C22×C19—22no—
136C22×C19—42no—
137C22×C19—42no—
138C22×C19—41no—
139C22×C19—41no—
140C22×C19—41no—
141C22×C19—41no—
142C22×C19—41no—
143C22×C19—81no—
144C22×C19—81no—
145C22×C19#38611yescharacteristic
146C22×C19C2×#10111yescharacteristic
147C22×C19#41311yescharacteristic
148C4×C19—21no—
149C4×C19—22no—
150C4×C19—22no—
151C4×C19—41no—
152C4×C19—41no—
153C4×C19—82no—
154C4×C19—82no—
155C4×C19#45512yes—
156C2×C4⋊Q8C2×D1911yescharacteristic
157C2×C4×D4C2×D1911yescharacteristic
158#435—384no—
159#432—192no—
160#432—192no—
161#407—381no—
162C2×C22⋊C8—381no—
163#393—21no—
164#393—21no—
165#390Dic1912yes—
166#382Dic1912yes—
167#380—21no—
168#380—21no—
169C4×C4⋊C4C2×D1911yescharacteristic
170#332—384no—
171#323—381no—
172#323—381no—
173C2×C19—21no—
174C2×C19—21no—
175C2×C19—42no—
176C2×C19—81no—
177C2×C19#188511yescharacteristic
178C2×C19#190111yescharacteristic
179C2×C19#191011yescharacteristic
180C22×Q8—21no—
181C22×D4C2×Dic1911yescharacteristic
182C23×C4C22⋊D1911yescharacteristic
183C23×C4C22⋊D1911yescharacteristic
184C2×M16—382no—
185C22×C8—382no—
186C4⋊Q8—22no—
187C4⋊Q8—22no—
188C4×D4—22no—
189C4×D4—22no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4C2×Dic1912yes—
193C2×C4⋊C4C2×Dic1911yescharacteristic
194C2×C22⋊C4—22no—
195C2×C22⋊C4—22no—
196C2×C22⋊C4C22⋊D1911yescharacteristic
197C2×C22⋊C4C22⋊D1911yescharacteristic
198C2×C42C2×Dic1912yes—
199C2×C42C22×D1911yescharacteristic
200C4⋊C8—194no—
201C4⋊C8—382no—
202C22⋊C8—382no—
203C22⋊C8—382no—
204C22⋊C8—382no—
205C22⋊C8—382no—
206#97—382no—
207#97—382no—
208#95—22no—
209#95—22no—
210#95—21no—
211C19#945311yescharacteristic, complemented, Sylow
212C24C22⋊Dic1911yescharacteristic
213C24C22⋊Dic1911yescharacteristic
214C2×Q8—42no—
215C2×Q8—82no—
216C2×D4—22no—
217C2×D4—22no—
218C2×D4—41no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—22no—
224C22×C4—22no—
225C22×C4—42no—
226C22×C4—42no—
227C22×C4C22⋊Dic1911yescharacteristic
228C22×C4C22⋊Dic1911yescharacteristic
229C22×C4C22×Dic1911yescharacteristic
230C22×C4C2×C22⋊D1911yescharacteristic
231C22×C4C2×C22⋊D1911yescharacteristic
232M16—1522no—
233C2×C8—384no—
234C2×C8—762no—
235C2×C8—1522no—
236C4⋊C4—22no—
237C4⋊C4—24no—
238C4⋊C4—42no—
239C4⋊C4—41no—
240C4⋊C4—41no—
241C22⋊C4—22no—
242C22⋊C4—22no—
243C22⋊C4—82no—
244C22⋊C4—82no—
245C42—42no—
246C42D4×D1912yes—
247C42#6454312yes—
248C23—21no—
249C23—21no—
250C23—21no—
251C23—21no—
252C23—21no—
253C23—41no—
254C23—41no—
255C23—41no—
256C23—41no—
257C23#1059729312yes—
258C23C2×C22⋊Dic1911yescharacteristic
259Q8—84no—
260D4—44no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—22no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—41no—
267C2×C4—42no—
268C2×C4—42no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—42no—
272C2×C4—42no—
273C2×C4—42no—
274C2×C4—42no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—81no—
278C2×C4—81no—
279C2×C4D4×Dic1912yes—
280C2×C4#1059738111yescharacteristic
281C2×C4#1059738311yescharacteristic
282C2×C4#1059738512yes—
283C8—764no—
284C8—1522no—
285C22—21no—
286C22—21no—
287C22—22no—
288C22—42no—
289C22—42no—
290C22—41no—
291C22—41no—
292C22—41no—
293C22—41no—
294C22—41no—
295C22—81no—
296C22—81no—
297C22#1192642411yescharacteristic
298C22C2×#1059729311yescharacteristic
299C22#1192652811yescharacteristic
300C4—22no—
301C4—22no—
302C4—21no—
303C4—41no—
304C4—41no—
305C4—82no—
306C4—82no—
307C4#1192672112yes—
308C2—21no—
309C2—21no—
310C2—42no—
311C2—81no—
312C2#1456402411yescharacteristic
313C2#1456410411yescharacteristic
314C2#1456416311yescharacteristic
subgroupG/H
centerC22#11926424
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#2563C2
socleC22×C19#386
prime radicalC22×D4×C19C2×C4
cosocleC2×C42×C19C23
hypercenter#2563D19
hypocenterC19#9453
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2563

Complements

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

NH ≅ G/Ntype
2. #14562352C2semidirect
4. #14561491C2semidirect
211. C19#9453semidirect

Maximal subgroups

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

subgroupindex
#145726642
#145623522
#145619762
#145614912
C19×#25632
#945319