Finite Group Databasebeta

← #18080004

Subgroups — #18080004

Order 4864.

720 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 720 conjugacy classes of subgroups — too many to draw. Only its 103 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#14568566C211yesmaximal, characteristic
2#14562150C212yesmaximal, complemented
3#14561962C211yesmaximal, characteristic, complemented
4#14561521C212yesmaximal, complemented
5C19×#2312C211yesmaximal, characteristic, complemented
6C2×#10597375—21no—
7C2×#10597376C2211yescharacteristic
8C2×#10597399—21no—
9#11926508C2212yes—
10#11926480C412yescomplemented
11#11926453C412yescomplemented
12#11926444—22no—
13C4×C22⋊Dic19C2211yescharacteristic
14#11926277—24no—
15#11926268—22no—
16C22×C22⋊C4×C19C2211yescharacteristic
17C19×#388—24no—
18C19×#380—21no—
19C19×#379—21no—
20C4×C22⋊C4×C19C2212yes—
21C25×C19D411yescharacteristic
22C23×C4×C19D411yescharacteristic
23C23×C4×C19C2311yescharacteristic
24C22×C22⋊D19—21no—
25C22×C22⋊D19—22no—
26C22×D76C2×C411yescharacteristic
27C2×C4⋊C4×C19—22no—
28C2×C22⋊C4×C19—22no—
29C2×C22⋊C4×C19—22no—
30C2×C22⋊C4×C19—22no—
31C2×C22⋊C4×C19—22no—
32C2×C22⋊C4×C19—22no—
33C2×C22⋊C4×C19C2×C412yes—
34C2×C22⋊C4×C19D412yes—
35C2×C42×C19—22no—
36#10597399—44no—
37C2×C22⋊Dic19—21no—
38C2×C22⋊Dic19—22no—
39#10597376—22no—
40#10597376—22no—
41#10597375—44no—
42C2×(C2×D19)⋊C4—22no—
43C2×(C2×D19)⋊C4—21no—
44C2×C4⋊Dic19C2×C411yescharacteristic
45C2×Dic19⋊C4—22no—
46C2×C4×Dic19—21no—
47C2×#64520—22no—
48C19×#95—22no—
49C19×#95D414yescomplemented
50C19⋊#95C2×C412yes—
51C22⋊(C19⋊C8)—22no—
52C22⋊(C19⋊C8)—22no—
53C24×C19—21no—
54C24×C19—21no—
55C24×C19—42no—
56C24×C19—42no—
57C24×C19—81no—
58C24×C19C22⋊C412yes—
59C24×C19C2×D411yescharacteristic
60C23×D19—21no—
61C22×C4×C19—21no—
62C22×C4×C19—21no—
63C22×C4×C19—24no—
64C22×C4×C19—42no—
65C22×C4×C19—81no—
66C22×C4×C19C22⋊C412yes—
67C22×C4×C19C22×C411yescharacteristic
68C22×C4×C19C2×D411yescharacteristic
69C22×C4×C19C2×D412yes—
70C22×C4×C19#4112yes—
71C2×C22⋊D19—44no—
72C2×C22⋊D19—42no—
73C2×C22⋊D19—44no—
74C2×C22⋊D19—42no—
75C2×C22⋊D19—41no—
76C2×C22⋊D19—41no—
77C2×C22⋊D19—82no—
78C22×Dic19—22no—
79C22×Dic19—21no—
80C2×D76—22no—
81C2×D76—81no—
82C4⋊C4×C19—82no—
83C22⋊C4×C19—24no—
84C22⋊C4×C19—24no—
85C22⋊C4×C19—44no—
86C22⋊C4×C19—82no—
87C22⋊C4×C19—82no—
88C42×C19—82no—
89C22⋊Dic19—24no—
90C22⋊Dic19—44no—
91(C2×D19)⋊C4—44no—
92(C2×D19)⋊C4—42no—
93C4⋊Dic19—22no—
94Dic19⋊C4—44no—
95C4×Dic19—81no—
96#64520—82no—
97C2×C19⋊C8—42no—
98#9413—191nomaximal, Sylow
99C23×C19—22no—
100C23×C19—22no—
101C23×C19—22no—
102C23×C19—22no—
103C23×C19—22no—
104C23×C19—41no—
105C23×C19—42no—
106C23×C19—42no—
107C23×C19—42no—
108C23×C19—42no—
109C23×C19—42no—
110C23×C19—42no—
111C23×C19—81no—
112C23×C19—81no—
113C23×C19—88no—
114C23×C19C2×C22⋊C411yescharacteristic
115C23×C19#12011yescharacteristic
116C23×C19#12311yescharacteristic
117C22×D19—41no—
118C22×D19—42no—
119C22×D19—41no—
120C22×D19—41no—
121C22×D19—42no—
122C2×C4×C19—22no—
123C2×C4×C19—42no—
124C2×C4×C19—41no—
125C2×C4×C19—42no—
126C2×C4×C19—41no—
127C2×C4×C19—42no—
128C2×C4×C19—42no—
129C2×C4×C19—44no—
130C2×C4×C19—44no—
131C2×C4×C19—44no—
132C2×C4×C19—81no—
133C2×C4×C19C4×D412yes—
134C2×C4×C19#12112yes—
135C22⋊D19—88no—
136C22⋊D19—82no—
137C22⋊D19—82no—
138C2×Dic19—24no—
139C2×Dic19—42no—
140C2×Dic19—42no—
141C2×Dic19—41no—
142C2×Dic19—41no—
143C2×Dic19—41no—
144D76—82no—
145C19⋊C8—82no—
146#2539—191no—
147#2312D1911yescharacteristic, complemented
148#1507—192no—
149#1462—191no—
150#1297—192no—
151C22×C19—21no—
152C22×C19—21no—
153C22×C19—21no—
154C22×C19—21no—
155C22×C19—21no—
156C22×C19—21no—
157C22×C19—21no—
158C22×C19—44no—
159C22×C19—44no—
160C22×C19—42no—
161C22×C19—42no—
162C22×C19—42no—
163C22×C19—82no—
164C22×C19—84no—
165C22×C19—84no—
166C22×C19#38611yescharacteristic
167C22×C19#42112yes—
168C22×C19#45312yes—
169C2×D19—82no—
170C2×D19—82no—
171C2×D19—81no—
172C2×D19—81no—
173C2×D19—81no—
174C4×C19—22no—
175C4×C19—22no—
176C4×C19—42no—
177C4×C19—84no—
178Dic19—44no—
179Dic19—81no—
180C2×#123—381no—
181C2×#121—191no—
182C2×#120—381no—
183C22×C22⋊C4C2×D1911yescharacteristic
184#407—192no—
185#399—192no—
186#392—192no—
187#390—382no—
188#388—24no—
189#380—21no—
190#379—21no—
191C4×C22⋊C4—191no—
192C4×C22⋊C4C2×D1912yes—
193#327—384no—
194#323—382no—
195C2×C19—22no—
196C2×C19—22no—
197C2×C19—41no—
198C2×C19—82no—
199C2×C19#188711yescharacteristic
200C2×C19#189711yescharacteristic
201C2×C19#191311yescharacteristic
202D19—161no—
203C25C22⋊D1911yescharacteristic
204C22×D4—191no—
205C22×D4—381no—
206C22×D4—382no—
207C23×C4C22⋊D1911yescharacteristic
208C23×C4C22×D1911yescharacteristic
209C2×M16—382no—
210#123—764no—
211#121—382no—
212#121—382no—
213#120—764no—
214C2×C4⋊C4—22no—
215C2×C4⋊C4—191no—
216C2×C4⋊C4—382no—
217C2×C22⋊C4—22no—
218C2×C22⋊C4—22no—
219C2×C22⋊C4—22no—
220C2×C22⋊C4—22no—
221C2×C22⋊C4—22no—
222C2×C22⋊C4—381no—
223C2×C22⋊C4—382no—
224C2×C22⋊C4—382no—
225C2×C22⋊C4—381no—
226C2×C22⋊C4C4×D1912yes—
227C2×C22⋊C4D7612yes—
228C2×C42—22no—
229C2×C42—381no—
230C22⋊C8—382no—
231C22⋊C8—382no—
232#95—22no—
233#95—192no—
234#95C22⋊D1914yescomplemented
235C19#941311yescharacteristic, complemented, Sylow
236C24—21no—
237C24—21no—
238C24—42no—
239C24—42no—
240C24—81no—
241C24—381no—
242C24(C2×D19)⋊C412yes—
243C24C2×C22⋊D1911yescharacteristic
244C2×D4—382no—
245C2×D4—764no—
246C2×D4—762no—
247C2×D4—762no—
248C2×D4—764no—
249C2×D4—761no—
250C2×D4—761no—
251C2×D4—1521no—
252C2×D4—1522no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—24no—
256C22×C4—42no—
257C22×C4—81no—
258C22×C4—382no—
259C22×C4—381no—
260C22×C4(C2×D19)⋊C412yes—
261C22×C4C2×C4×D1911yescharacteristic
262C22×C4C2×D7611yescharacteristic
263C22×C4#6454112yes—
264C22×C4C2×C22⋊D1912yes—
265M16—1522no—
266C2×C8—762no—
267C4⋊C4—82no—
268C4⋊C4—382no—
269C4⋊C4—764no—
270C22⋊C4—24no—
271C22⋊C4—24no—
272C22⋊C4—44no—
273C22⋊C4—82no—
274C22⋊C4—82no—
275C22⋊C4—384no—
276C22⋊C4—764no—
277C22⋊C4—764no—
278C22⋊C4—762no—
279C42—82no—
280C42—1521no—
281C23—22no—
282C23—22no—
283C23—22no—
284C23—22no—
285C23—22no—
286C23—41no—
287C23—42no—
288C23—42no—
289C23—42no—
290C23—42no—
291C23—42no—
292C23—42no—
293C23—81no—
294C23—81no—
295C23—88no—
296C23—761no—
297C23—761no—
298C23—762no—
299C23—762no—
300C23—761no—
301C23C2×(C2×D19)⋊C411yescharacteristic
302C23#1059737511yescharacteristic
303C23#1059739911yescharacteristic
304D4—1522no—
305D4—1528no—
306D4—1522no—
307D4—1522no—
308C2×C4—22no—
309C2×C4—42no—
310C2×C4—41no—
311C2×C4—42no—
312C2×C4—41no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—44no—
316C2×C4—44no—
317C2×C4—44no—
318C2×C4—81no—
319C2×C4—384no—
320C2×C4—762no—
321C2×C4—762no—
322C2×C4—761no—
323C2×C4—761no—
324C2×C4—761no—
325C2×C4C4×C22⋊D1912yes—
326C2×C4#1059737612yes—
327C8—1522no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—44no—
336C22—44no—
337C22—42no—
338C22—42no—
339C22—42no—
340C22—82no—
341C22—84no—
342C22—84no—
343C22—1522no—
344C22—1522no—
345C22—1521no—
346C22—1521no—
347C22—1521no—
348C22#1192642311yescharacteristic
349C22#1192656212yes—
350C22#1192671212yes—
351C4—22no—
352C4—22no—
353C4—42no—
354C4—84no—
355C4—764no—
356C4—1521no—
357C2—22no—
358C2—22no—
359C2—41no—
360C2—82no—
361C2—3041no—
362C2#1456403311yescharacteristic
363C2#1456408311yescharacteristic
364C2#1456417711yescharacteristic
subgroupG/H
centerC22#11926423
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#2312C2
socleC22×C19#386
prime radical#14568566C2
cosocleC23×C4×C19C23
hypercenter#2312D19
hypocenterC19#9413
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2312

Complements

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

NH ≅ G/Ntype
2. #14562150C2semidirect
3. #14561962C2semidirect
4. #14561521C2semidirect
5. C19×#2312C2semidirect
10. #11926480C4semidirect
11. #11926453C4semidirect
49. C19×#95D4semidirect
147. #2312D19semidirect
234. #95C22⋊D19semidirect
235. C19#9413semidirect

Maximal subgroups

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

subgroupindex
#145685662
#145621502
#145619622
#145615212
C19×#23122
#941319