Finite Group Databasebeta

← #18078612

Subgroups — #18078612

Order 4864.

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

normal subgroups only

This group has 690 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#14569369C211yesmaximal, characteristic
2#14562202C212yesmaximal, complemented
3C2×#11926268C211yesmaximal, characteristic, complemented
4#14561502C212yesmaximal, complemented
5C19×#2312C211yesmaximal, characteristic, complemented
6C2×#10597376C2211yescharacteristic
7C2×#10597399—21no—
8C2×C22⋊(C19⋊C8)C2212yes—
9#11926469C412yescomplemented
10#11926460—22no—
11#11926453C412yescomplemented
12#11926423—21no—
13#11926404C2211yescharacteristic
14#11926277—24no—
15#11926268—22no—
16C22×C22⋊C4×C19C2211yescharacteristic
17C19×#388—24no—
18C19×#380C2212yes—
19C19×#379—21no—
20C4×C22⋊C4×C19—21no—
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—22no—
38C2×C22⋊Dic19—21no—
39#10597376—22no—
40#10597376—22no—
41C2×(C2×D19)⋊C4—21no—
42C2×(C2×D19)⋊C4—22no—
43C2×C4⋊Dic19—21no—
44C2×C4⋊Dic19C2×C411yescharacteristic
45C22×C19⋊C8—22no—
46C19×#95—22no—
47C19×#95D414yescomplemented
48C19⋊#95—22no—
49C19⋊#95C2×C412yes—
50C22⋊(C19⋊C8)—22no—
51C22⋊(C19⋊C8)—22no—
52C24×C19—21no—
53C24×C19—21no—
54C24×C19—22no—
55C24×C19—22no—
56C24×C19—81no—
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—81no—
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—41no—
73C2×C22⋊D19—41no—
74C2×C22⋊D19—42no—
75C2×C22⋊D19—42no—
76C2×C22⋊D19—82no—
77C2×C22⋊D19—82no—
78C22×Dic19—21no—
79C22×Dic19—22no—
80C2×D76—22no—
81C2×D76—81no—
82C4⋊C4×C19—82no—
83C22⋊C4×C19—24no—
84C22⋊C4×C19—24no—
85C22⋊C4×C19—42no—
86C22⋊C4×C19—42no—
87C22⋊C4×C19—82no—
88C22⋊C4×C19—82no—
89C42×C19—82no—
90C22⋊Dic19—44no—
91C22⋊Dic19—42no—
92(C2×D19)⋊C4—42no—
93(C2×D19)⋊C4—82no—
94C4⋊Dic19—22no—
95C4⋊Dic19—81no—
96C2×C19⋊C8—42no—
97C2×C19⋊C8—82no—
98#9205—191nomaximal, Sylow
99C23×C19—22no—
100C23×C19—22no—
101C23×C19—22no—
102C23×C19—41no—
103C23×C19—41no—
104C23×C19—42no—
105C23×C19—42no—
106C23×C19—42no—
107C23×C19—42no—
108C23×C19—42no—
109C23×C19—42no—
110C23×C19—81no—
111C23×C19—81no—
112C23×C19—84no—
113C23×C19—84no—
114C23×C19C2×C22⋊C411yescharacteristic
115C23×C19#12011yescharacteristic
116C23×C19#12311yescharacteristic
117C23×C19#13512yes—
118C23×C19AGL(1,ℤ/8)12yes—
119C22×D19—42no—
120C22×D19—42no—
121C22×D19—41no—
122C22×D19—41no—
123C22×D19—41no—
124C2×C4×C19—22no—
125C2×C4×C19—42no—
126C2×C4×C19—41no—
127C2×C4×C19—42no—
128C2×C4×C19—41no—
129C2×C4×C19—42no—
130C2×C4×C19—42no—
131C2×C4×C19—44no—
132C2×C4×C19—44no—
133C2×C4×C19—44no—
134C2×C4×C19—81no—
135C2×C4×C19C4×D412yes—
136C2×C4×C19#12112yes—
137C22⋊D19—88no—
138C22⋊D19—82no—
139C22⋊D19—82no—
140C2×Dic19—42no—
141C2×Dic19—42no—
142C2×Dic19—41no—
143C2×Dic19—41no—
144C2×Dic19—42no—
145C2×Dic19—41no—
146D76—82no—
147C19⋊C8—82no—
148#2617—191no—
149#2312D1911yescharacteristic, complemented
150#1519—192no—
151C2×#323—191no—
152#1289—192no—
153C22×C19—21no—
154C22×C19—21no—
155C22×C19—21no—
156C22×C19—21no—
157C22×C19—21no—
158C22×C19—21no—
159C22×C19—42no—
160C22×C19—42no—
161C22×C19—44no—
162C22×C19—42no—
163C22×C19—42no—
164C22×C19—42no—
165C22×C19—82no—
166C22×C19—84no—
167C22×C19—84no—
168C22×C19#38611yescharacteristic
169C22×C19#41611yescharacteristic
170C22×C19#41811yescharacteristic
171C22×C19#44912yes—
172C22×C19#48212yes—
173C2×D19—82no—
174C2×D19—82no—
175C2×D19—81no—
176C2×D19—81no—
177C2×D19—81no—
178C4×C19—22no—
179C4×C19—22no—
180C4×C19—42no—
181C4×C19—84no—
182Dic19—82no—
183Dic19—81no—
184C2×#121—191no—
185C2×#120—381no—
186C22×C22⋊C4C2×D1911yescharacteristic
187C2×C22⋊C8—192no—
188#397—192no—
189#394—382no—
190#392—192no—
191#388—24no—
192#386—381no—
193#380—191no—
194#380C2×D1912yes—
195#379—21no—
196C4×C22⋊C4—21no—
197#327—384no—
198#323—382no—
199C2×C19—21no—
200C2×C19—22no—
201C2×C19—21no—
202C2×C19—22no—
203C2×C19—82no—
204C2×C19#187511yescharacteristic
205C2×C19#191111yescharacteristic
206C2×C19#191311yescharacteristic
207D19—161no—
208C25C22⋊D1911yescharacteristic
209C22×D4—191no—
210C22×D4—381no—
211C22×D4—382no—
212C23×C4C22⋊D1911yescharacteristic
213C23×C4C22×D1911yescharacteristic
214C22×C8—382no—
215#121—382no—
216#121—382no—
217#120—764no—
218C2×C4⋊C4—22no—
219C2×C4⋊C4—191no—
220C2×C4⋊C4—381no—
221C2×C22⋊C4—22no—
222C2×C22⋊C4—22no—
223C2×C22⋊C4—22no—
224C2×C22⋊C4—22no—
225C2×C22⋊C4—22no—
226C2×C22⋊C4—382no—
227C2×C22⋊C4—381no—
228C2×C22⋊C4—381no—
229C2×C22⋊C4—382no—
230C2×C22⋊C4C4×D1912yes—
231C2×C22⋊C4D7612yes—
232C2×C42—22no—
233C22⋊C8—382no—
234C22⋊C8—382no—
235#95—22no—
236#95—192no—
237#95—382no—
238#95C22⋊D1914yescomplemented
239C19#920511yescharacteristic, complemented, Sylow
240C24—21no—
241C24—22no—
242C24—22no—
243C24—21no—
244C24—81no—
245C24—81no—
246C24—381no—
247C24(C2×D19)⋊C412yes—
248C24C2×C22⋊D1911yescharacteristic
249C2×D4—382no—
250C2×D4—764no—
251C2×D4—762no—
252C2×D4—762no—
253C2×D4—761no—
254C2×D4—761no—
255C2×D4—1521no—
256C2×D4—1522no—
257C2×D4—1522no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—24no—
261C22×C4—81no—
262C22×C4—81no—
263C22×C4—382no—
264C22×C4—381no—
265C22×C4(C2×D19)⋊C412yes—
266C22×C4C2×C4×D1911yescharacteristic
267C22×C4C2×D7611yescharacteristic
268C22×C4#6454112yes—
269C22×C4C2×C22⋊D1912yes—
270C2×C8—762no—
271C2×C8—1522no—
272C4⋊C4—82no—
273C4⋊C4—382no—
274C4⋊C4—1521no—
275C22⋊C4—24no—
276C22⋊C4—24no—
277C22⋊C4—42no—
278C22⋊C4—42no—
279C22⋊C4—82no—
280C22⋊C4—82no—
281C22⋊C4—764no—
282C22⋊C4—762no—
283C22⋊C4—762no—
284C22⋊C4—1522no—
285C42—82no—
286C23—22no—
287C23—22no—
288C23—22no—
289C23—41no—
290C23—41no—
291C23—42no—
292C23—42no—
293C23—42no—
294C23—42no—
295C23—42no—
296C23—42no—
297C23—81no—
298C23—81no—
299C23—84no—
300C23—84no—
301C23—762no—
302C23—762no—
303C23—761no—
304C23—761no—
305C23—761no—
306C23C2×(C2×D19)⋊C411yescharacteristic
307C23#1059737511yescharacteristic
308C23#1059739512yes—
309C23#1059739612yes—
310C23#1059739911yescharacteristic
311D4—1522no—
312D4—1528no—
313D4—1522no—
314D4—1522no—
315C2×C4—22no—
316C2×C4—42no—
317C2×C4—41no—
318C2×C4—42no—
319C2×C4—41no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—44no—
323C2×C4—44no—
324C2×C4—44no—
325C2×C4—81no—
326C2×C4—762no—
327C2×C4—762no—
328C2×C4—761no—
329C2×C4—762no—
330C2×C4—761no—
331C2×C4—761no—
332C2×C4C4×C22⋊D1912yes—
333C2×C4#1059737612yes—
334C8—1522no—
335C22—21no—
336C22—21no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—42no—
342C22—42no—
343C22—44no—
344C22—42no—
345C22—42no—
346C22—42no—
347C22—82no—
348C22—84no—
349C22—84no—
350C22—1522no—
351C22—1522no—
352C22—1521no—
353C22—1521no—
354C22—1521no—
355C22#1192642311yescharacteristic
356C22#1192653811yescharacteristic
357C22#1192654811yescharacteristic
358C22#1192668912yes—
359C22#1192686812yes—
360C4—22no—
361C4—22no—
362C4—42no—
363C4—84no—
364C4—1522no—
365C4—1521no—
366C2—22no—
367C2—21no—
368C2—21no—
369C2—22no—
370C2—82no—
371C2—3041no—
372C2#1456395711yescharacteristic
373C2#1456416711yescharacteristic
374C2#1456417711yescharacteristic
subgroupG/H
centerC22#11926423
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#2312C2
socleC22×C19#386
prime radical#14569369C2
cosocleC23×C4×C19C23
hypercenter#2312D19
hypocenterC19#9205
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. #14562202C2semidirect
3. C2×#11926268C2semidirect
4. #14561502C2semidirect
5. C19×#2312C2semidirect
9. #11926469C4semidirect
11. #11926453C4semidirect
47. C19×#95D4semidirect
149. #2312D19semidirect
238. #95C22⋊D19semidirect
239. C19#9205semidirect

Maximal subgroups

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

subgroupindex
#145693692
#145622022
C2×#119262682
#145615022
C19×#23122
#920519