Finite Group Databasebeta

← #18080239

Subgroups — #18080239

Order 4864.

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

normal subgroups only

This group has 554 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×#2542C211yesmaximal, 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×C19×C22⋊Q8—21no—
16C2×C19×C22⋊Q8—21no—
17C2×C4×D4×C19C2211yescharacteristic
18C19×#399—21no—
19C19×#399—21no—
20C19×#390C412yes—
21C19×#384C412yes—
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—
29C19×C22⋊Q8—44no—
30C19×C22⋊Q8—44no—
31C4×D4×C19—22no—
32C4×D4×C19—22no—
33C2×C4⋊C4×C19—21no—
34C2×C4⋊C4×C19—22no—
35C2×C4⋊C4×C19—22no—
36C2×C4⋊C4×C19—21no—
37C2×C4⋊C4×C19C2×C412yes—
38C2×C4⋊C4×C19C2×C411yescharacteristic
39C2×C22⋊C4×C19—22no—
40C2×C22⋊C4×C19—22no—
41C2×C22⋊C4×C19D411yescharacteristic
42C2×C22⋊C4×C19D411yescharacteristic
43C2×C42×C19C2×C412yes—
44C2×C42×C19C2311yescharacteristic
45C2×#64520—22no—
46C22×C19⋊C8—22no—
47C19×#95—21no—
48C22⋊(C19⋊C8)—22no—
49C22⋊(C19⋊C8)—22no—
50C22⋊(C19⋊C8)—22no—
51C22⋊(C19⋊C8)—22no—
52C4⋊(C19⋊C8)—22no—
53C4⋊(C19⋊C8)D414yes—
54#10597260—22no—
55#10597260—22no—
56C24×C19C22⋊C411yescharacteristic
57C24×C19C22⋊C411yescharacteristic
58C2×Q8×C19—42no—
59C2×Q8×C19—42no—
60C2×Q8×C19—41no—
61C2×Q8×C19—41no—
62C2×D4×C19—22no—
63C2×D4×C19—22no—
64C2×D4×C19—41no—
65C22×C4×C19—22no—
66C22×C4×C19—21no—
67C22×C4×C19—21no—
68C22×C4×C19—21no—
69C22×C4×C19—21no—
70C22×C4×C19—22no—
71C22×C4×C19—42no—
72C22×C4×C19—42no—
73C22×C4×C19C22⋊C411yescharacteristic
74C22×C4×C19C22⋊C411yescharacteristic
75C22×C4×C19C22×C411yescharacteristic
76C22×C4×C19C2×D411yescharacteristic
77C22×C4×C19C2×D411yescharacteristic
78C4⋊C4×C19—24no—
79C4⋊C4×C19—22no—
80C4⋊C4×C19—24no—
81C4⋊C4×C19—44no—
82C4⋊C4×C19—44no—
83C4⋊C4×C19—42no—
84C22⋊C4×C19—22no—
85C22⋊C4×C19—22no—
86C22⋊C4×C19—44no—
87C22⋊C4×C19—44no—
88C42×C19—42no—
89C42×C19C2×D412yes—
90C42×C19#4112yes—
91#64520—82no—
92C2×C19⋊C8—24no—
93C2×C19⋊C8—42no—
94C2×C19⋊C8—82no—
95#9455—191nomaximal, Sylow
96C23×C19—21no—
97C23×C19—21no—
98C23×C19—21no—
99C23×C19—21no—
100C23×C19—21no—
101C23×C19—41no—
102C23×C19—41no—
103C23×C19—41no—
104C23×C19—41no—
105C23×C19#10112yes—
106C23×C19C2×C22⋊C411yescharacteristic
107Q8×C19—82no—
108Q8×C19—82no—
109D4×C19—44no—
110C2×C4×C19—21no—
111C2×C4×C19—21no—
112C2×C4×C19—22no—
113C2×C4×C19—24no—
114C2×C4×C19—21no—
115C2×C4×C19—21no—
116C2×C4×C19—41no—
117C2×C4×C19—42no—
118C2×C4×C19—42no—
119C2×C4×C19—42no—
120C2×C4×C19—42no—
121C2×C4×C19—41no—
122C2×C4×C19—41no—
123C2×C4×C19—42no—
124C2×C4×C19—42no—
125C2×C4×C19—42no—
126C2×C4×C19—81no—
127C2×C4×C19—81no—
128C2×C4×C19C4×D412yes—
129C2×C4×C19#12011yescharacteristic
130C2×C4×C19#12112yes—
131C2×C4×C19#12311yescharacteristic
132C19⋊C8—44no—
133C19⋊C8—82no—
134#2973—191no—
135#2542D1911yescharacteristic
136#1556—192no—
137#1466—191no—
138#1285—192no—
139C22×C19—21no—
140C22×C19—21no—
141C22×C19—22no—
142C22×C19—42no—
143C22×C19—42no—
144C22×C19—41no—
145C22×C19—41no—
146C22×C19—41no—
147C22×C19—41no—
148C22×C19—41no—
149C22×C19—81no—
150C22×C19—81no—
151C22×C19#38611yescharacteristic
152C22×C19C2×#10111yescharacteristic
153C22×C19#41311yescharacteristic
154C4×C19—21no—
155C4×C19—22no—
156C4×C19—22no—
157C4×C19—44no—
158C4×C19—41no—
159C4×C19—41no—
160C4×C19—82no—
161C4×C19#45312yes—
162C2×C4⋊Q8C2×D1911yescharacteristic
163C2×C22⋊Q8—21no—
164C2×C22⋊Q8—21no—
165C2×C4×D4C2×D1911yescharacteristic
166#435—384no—
167#432—192no—
168#432—192no—
169#407—381no—
170C2×C22⋊C8—381no—
171#399—21no—
172#399—21no—
173#390Dic1912yes—
174#384Dic1912yes—
175C4×C4⋊C4C2×D1911yescharacteristic
176#332—384no—
177#323—381no—
178#323—381no—
179C2×C19—21no—
180C2×C19—21no—
181C2×C19—42no—
182C2×C19—81no—
183C2×C19#188711yescharacteristic
184C2×C19#190111yescharacteristic
185C2×C19#190911yescharacteristic
186C22×Q8—21no—
187C22×D4C2×Dic1911yescharacteristic
188C23×C4C22⋊D1911yescharacteristic
189C23×C4C22⋊D1911yescharacteristic
190C2×M16—382no—
191C22×C8—382no—
192C4⋊Q8—22no—
193C4⋊Q8—22no—
194C22⋊Q8—44no—
195C22⋊Q8—44no—
196C4×D4—22no—
197C4×D4—22no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—22no—
200C2×C4⋊C4—22no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4C2×Dic1912yes—
203C2×C4⋊C4C2×Dic1911yescharacteristic
204C2×C22⋊C4—22no—
205C2×C22⋊C4—22no—
206C2×C22⋊C4C22⋊D1911yescharacteristic
207C2×C22⋊C4C22⋊D1911yescharacteristic
208C2×C42C2×Dic1912yes—
209C2×C42C22×D1911yescharacteristic
210C4⋊C8—194no—
211C4⋊C8—382no—
212C22⋊C8—382no—
213C22⋊C8—382no—
214C22⋊C8—382no—
215C22⋊C8—382no—
216#97—382no—
217#97—382no—
218#95—21no—
219C19#945511yescharacteristic, complemented, Sylow
220C24C22⋊Dic1911yescharacteristic
221C24C22⋊Dic1911yescharacteristic
222C2×Q8—42no—
223C2×Q8—42no—
224C2×Q8—41no—
225C2×Q8—41no—
226C2×D4—22no—
227C2×D4—22no—
228C2×D4—41no—
229C22×C4—22no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—22no—
235C22×C4—42no—
236C22×C4—42no—
237C22×C4C22⋊Dic1911yescharacteristic
238C22×C4C22⋊Dic1911yescharacteristic
239C22×C4C22×Dic1911yescharacteristic
240C22×C4C2×C22⋊D1911yescharacteristic
241C22×C4C2×C22⋊D1911yescharacteristic
242M16—1522no—
243C2×C8—384no—
244C2×C8—762no—
245C2×C8—1522no—
246C4⋊C4—24no—
247C4⋊C4—22no—
248C4⋊C4—24no—
249C4⋊C4—44no—
250C4⋊C4—44no—
251C4⋊C4—42no—
252C22⋊C4—22no—
253C22⋊C4—22no—
254C22⋊C4—44no—
255C22⋊C4—44no—
256C42—42no—
257C42D4×D1912yes—
258C42#6454312yes—
259C23—21no—
260C23—21no—
261C23—21no—
262C23—21no—
263C23—21no—
264C23—41no—
265C23—41no—
266C23—41no—
267C23—41no—
268C23#1059729312yes—
269C23C2×C22⋊Dic1911yescharacteristic
270Q8—82no—
271Q8—82no—
272D4—44no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—22no—
276C2×C4—24no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—41no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—81no—
290C2×C4—81no—
291C2×C4D4×Dic1912yes—
292C2×C4#1059738111yescharacteristic
293C2×C4#1059738311yescharacteristic
294C2×C4#1059738512yes—
295C8—764no—
296C8—1522no—
297C22—21no—
298C22—21no—
299C22—22no—
300C22—42no—
301C22—42no—
302C22—41no—
303C22—41no—
304C22—41no—
305C22—41no—
306C22—41no—
307C22—81no—
308C22—81no—
309C22#1192642411yescharacteristic
310C22C2×#1059729311yescharacteristic
311C22#1192652811yescharacteristic
312C4—22no—
313C4—22no—
314C4—21no—
315C4—44no—
316C4—41no—
317C4—41no—
318C4—82no—
319C4#1192671112yes—
320C2—21no—
321C2—21no—
322C2—42no—
323C2—81no—
324C2#1456403411yescharacteristic
325C2#1456410411yescharacteristic
326C2#1456415811yescharacteristic
subgroupG/H
centerC22#11926424
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#2542C2
socleC22×C19#386
prime radicalC22×D4×C19C2×C4
cosocleC2×C42×C19C23
hypercenter#2542D19
hypocenterC19#9455
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2542

Complements

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

NH ≅ G/Ntype
2. #14562352C2semidirect
4. #14561491C2semidirect
219. C19#9455semidirect

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×#25422
#945519