Finite Group Databasebeta

← #18079984

Subgroups — #18079984

Order 4864.

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

normal subgroups only

This group has 840 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#14568566C211yesmaximal, characteristic
2#14562150C212yesmaximal, complemented
3#14561962C211yesmaximal, characteristic, complemented
4#14561521C212yesmaximal, complemented
5C19×#2273C211yesmaximal, 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×C19—21no—
17C22×C22⋊C4×C19C2211yescharacteristic
18C4×C22⋊C4×C19—24no—
19C4×C22⋊C4×C19—21no—
20C4×C22⋊C4×C19C2212yes—
21C25×C19D411yescharacteristic
22C23×C4×C19—22no—
23C23×C4×C19D411yescharacteristic
24C23×C4×C19C2311yescharacteristic
25C22×C22⋊D19—21no—
26C22×C22⋊D19—22no—
27C22×D76C2×C411yescharacteristic, complemented
28C2×C22⋊C4×C19—22no—
29C2×C22⋊C4×C19—28no—
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—
36C2×C42×C19—22no—
37#10597399—44no—
38C2×C22⋊Dic19—21no—
39C2×C22⋊Dic19—22no—
40#10597376—22no—
41#10597376—22no—
42#10597375—44no—
43C2×(C2×D19)⋊C4—22no—
44C2×(C2×D19)⋊C4—21no—
45C2×C4⋊Dic19C2×C411yescharacteristic, complemented
46C2×Dic19⋊C4—22no—
47C2×C4×Dic19—21no—
48C2×#64520—22no—
49C19×#95—22no—
50C19×#95D414yescomplemented
51C19⋊#95C2×C412yescomplemented
52C22⋊(C19⋊C8)—22no—
53C22⋊(C19⋊C8)—22no—
54C24×C19—21no—
55C24×C19—24no—
56C24×C19—21no—
57C24×C19—42no—
58C24×C19—81no—
59C24×C19C22⋊C412yes—
60C24×C19C2×D411yescharacteristic
61C23×D19—21no—
62C22×C4×C19—24no—
63C22×C4×C19—21no—
64C22×C4×C19—28no—
65C22×C4×C19—21no—
66C22×C4×C19—42no—
67C22×C4×C19—81no—
68C22×C4×C19—82no—
69C22×C4×C19—82no—
70C22×C4×C19C22⋊C412yes—
71C22×C4×C19C22×C411yescharacteristic
72C22×C4×C19C2×D411yescharacteristic
73C22×C4×C19C2×D412yes—
74C22×C4×C19#4112yes—
75C2×C22⋊D19—44no—
76C2×C22⋊D19—42no—
77C2×C22⋊D19—42no—
78C2×C22⋊D19—44no—
79C2×C22⋊D19—41no—
80C2×C22⋊D19—41no—
81C2×C22⋊D19—82no—
82C22×Dic19—22no—
83C22×Dic19—21no—
84C2×D76—22no—
85C2×D76—81no—
86C22⋊C4×C19—28no—
87C22⋊C4×C19—28no—
88C22⋊C4×C19—24no—
89C22⋊C4×C19—24no—
90C42×C19—82no—
91C42×C19—82no—
92C22⋊Dic19—24no—
93C22⋊Dic19—44no—
94(C2×D19)⋊C4—44no—
95(C2×D19)⋊C4—42no—
96C4⋊Dic19—22no—
97Dic19⋊C4—44no—
98C4×Dic19—81no—
99#64520—82no—
100C2×C19⋊C8—42no—
101#9409—191nomaximal, Sylow
102C23×C19—22no—
103C23×C19—22no—
104C23×C19—24no—
105C23×C19—22no—
106C23×C19—22no—
107C23×C19—22no—
108C23×C19—22no—
109C23×C19—41no—
110C23×C19—42no—
111C23×C19—42no—
112C23×C19—42no—
113C23×C19—42no—
114C23×C19—81no—
115C23×C19—81no—
116C23×C19—88no—
117C23×C19#10414yes—
118C23×C19C2×C22⋊C411yescharacteristic
119C23×C19#12011yescharacteristic
120C23×C19#12311yescharacteristic
121C22×D19—41no—
122C22×D19—42no—
123C22×D19—41no—
124C22×D19—41no—
125C22×D19—42no—
126C2×C4×C19—28no—
127C2×C4×C19—22no—
128C2×C4×C19—42no—
129C2×C4×C19—41no—
130C2×C4×C19—42no—
131C2×C4×C19—41no—
132C2×C4×C19—44no—
133C2×C4×C19—42no—
134C2×C4×C19—44no—
135C2×C4×C19—42no—
136C2×C4×C19—81no—
137C2×C4×C19—88no—
138C2×C4×C19C4×D412yes—
139C2×C4×C19#12112yes—
140C22⋊D19—88no—
141C22⋊D19—82no—
142C22⋊D19—82no—
143C2×Dic19—24no—
144C2×Dic19—42no—
145C2×Dic19—42no—
146C2×Dic19—41no—
147C2×Dic19—41no—
148C2×Dic19—41no—
149D76—82no—
150C19⋊C8—82no—
151#2539—191no—
152#2273D1911yescharacteristic, complemented
153#1507—192no—
154#1462—191no—
155#1297—192no—
156C22×C19—21no—
157C22×C19—21no—
158C22×C19—21no—
159C22×C19—21no—
160C22×C19—21no—
161C22×C19—24no—
162C22×C19—21no—
163C22×C19—21no—
164C22×C19—44no—
165C22×C19—44no—
166C22×C19—44no—
167C22×C19—44no—
168C22×C19—42no—
169C22×C19—42no—
170C22×C19—82no—
171C22×C19—84no—
172C22×C19#38611yescharacteristic
173C22×C19C2×#10412yes—
174C22×C19#45312yes—
175C2×D19—82no—
176C2×D19—82no—
177C2×D19—81no—
178C2×D19—81no—
179C2×D19—81no—
180C4×C19—22no—
181C4×C19—22no—
182C4×C19—48no—
183C4×C19—42no—
184Dic19—44no—
185Dic19—81no—
186C2×#123—381no—
187C2×#121—191no—
188C2×#120—381no—
189C22×C22⋊C4—21no—
190C22×C22⋊C4C2×D1911yescharacteristic
191#407—192no—
192#399—192no—
193#392—192no—
194#390—382no—
195C4×C22⋊C4—21no—
196C4×C22⋊C4—24no—
197C4×C22⋊C4—191no—
198C4×C22⋊C4C2×D1912yes—
199#327—384no—
200#323—382no—
201C2×C19—22no—
202C2×C19—22no—
203C2×C19—41no—
204C2×C19—44no—
205C2×C19#188711yescharacteristic
206C2×C19#189611yescharacteristic
207C2×C19#191311yescharacteristic
208D19—161no—
209C25C22⋊D1911yescharacteristic
210C22×D4—191no—
211C22×D4—381no—
212C22×D4—382no—
213C23×C4—22no—
214C23×C4C22⋊D1911yescharacteristic
215C23×C4C22×D1911yescharacteristic
216C2×M16—382no—
217#123—764no—
218#121—382no—
219#121—382no—
220#120—764no—
221C2×C4⋊C4—191no—
222C2×C4⋊C4—382no—
223C2×C22⋊C4—28no—
224C2×C22⋊C4—22no—
225C2×C22⋊C4—22no—
226C2×C22⋊C4—22no—
227C2×C22⋊C4—22no—
228C2×C22⋊C4—381no—
229C2×C22⋊C4—382no—
230C2×C22⋊C4—382no—
231C2×C22⋊C4—381no—
232C2×C22⋊C4C4×D1912yes—
233C2×C22⋊C4D7612yes—
234C2×C42—22no—
235C2×C42—22no—
236C2×C42—381no—
237C22⋊C8—382no—
238C22⋊C8—382no—
239#95—22no—
240#95—192no—
241#95C22⋊D1914yescomplemented
242C19#940911yescharacteristic, complemented, Sylow
243C24—21no—
244C24—24no—
245C24—21no—
246C24—42no—
247C24—81no—
248C24—381no—
249C24(C2×D19)⋊C412yes—
250C24C2×C22⋊D1911yescharacteristic
251C2×D4—382no—
252C2×D4—764no—
253C2×D4—762no—
254C2×D4—762no—
255C2×D4—761no—
256C2×D4—764no—
257C2×D4—761no—
258C2×D4—1521no—
259C2×D4—1522no—
260C22×C4—21no—
261C22×C4—24no—
262C22×C4—28no—
263C22×C4—21no—
264C22×C4—42no—
265C22×C4—81no—
266C22×C4—82no—
267C22×C4—82no—
268C22×C4—382no—
269C22×C4—381no—
270C22×C4(C2×D19)⋊C412yes—
271C22×C4C2×C4×D1911yescharacteristic
272C22×C4C2×D7611yescharacteristic
273C22×C4#6454112yes—
274C22×C4C2×C22⋊D1912yes—
275M16—1522no—
276C2×C8—762no—
277C4⋊C4—382no—
278C4⋊C4—764no—
279C22⋊C4—28no—
280C22⋊C4—28no—
281C22⋊C4—24no—
282C22⋊C4—24no—
283C22⋊C4—384no—
284C22⋊C4—764no—
285C22⋊C4—764no—
286C22⋊C4—762no—
287C42—82no—
288C42—82no—
289C42—1521no—
290C23—22no—
291C23—22no—
292C23—24no—
293C23—22no—
294C23—22no—
295C23—22no—
296C23—22no—
297C23—41no—
298C23—42no—
299C23—42no—
300C23—42no—
301C23—42no—
302C23—81no—
303C23—81no—
304C23—88no—
305C23—761no—
306C23—761no—
307C23—762no—
308C23—762no—
309C23—761no—
310C23#1059726214yes—
311C23C2×(C2×D19)⋊C411yescharacteristic
312C23#1059737511yescharacteristic
313C23#1059739911yescharacteristic
314D4—1522no—
315D4—1528no—
316D4—1522no—
317D4—1522no—
318C2×C4—28no—
319C2×C4—22no—
320C2×C4—42no—
321C2×C4—41no—
322C2×C4—42no—
323C2×C4—41no—
324C2×C4—44no—
325C2×C4—42no—
326C2×C4—44no—
327C2×C4—42no—
328C2×C4—81no—
329C2×C4—88no—
330C2×C4—384no—
331C2×C4—762no—
332C2×C4—762no—
333C2×C4—761no—
334C2×C4—761no—
335C2×C4—761no—
336C2×C4C4×C22⋊D1912yes—
337C2×C4#1059737612yes—
338C8—1522no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—24no—
346C22—21no—
347C22—44no—
348C22—44no—
349C22—44no—
350C22—44no—
351C22—42no—
352C22—42no—
353C22—82no—
354C22—84no—
355C22—1522no—
356C22—1522no—
357C22—1521no—
358C22—1521no—
359C22—1521no—
360C22#1192642311yescharacteristic
361C22C2×#1059726212yes—
362C22#1192671212yes—
363C4—22no—
364C4—22no—
365C4—48no—
366C4—42no—
367C4—764no—
368C4—1521no—
369C2—22no—
370C2—22no—
371C2—41no—
372C2—44no—
373C2—3041no—
374C2#1456403311yescharacteristic
375C2#1456407811yescharacteristic
376C2#1456417711yescharacteristic
subgroupG/H
centerC22#11926423
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#2273C2
socleC22×C19#386
prime radical#14568566C2
cosocleC23×C4×C19C23
hypercenter#2273D19
hypocenterC19#9409
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2273

Complements

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

NH ≅ G/Ntype
2. #14562150C2semidirect
3. #14561962C2semidirect
4. #14561521C2semidirect
5. C19×#2273C2semidirect
10. #11926480C4semidirect
11. #11926453C4semidirect
27. C22×D76C2×C4semidirect
45. C2×C4⋊Dic19C2×C4semidirect
50. C19×#95D4semidirect
51. C19⋊#95C2×C4semidirect
152. #2273D19semidirect
241. #95C22⋊D19semidirect
242. C19#9409semidirect

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×#22732
#940919