Finite Group Databasebeta

← #18080318

Subgroups — #18080318

Order 4864.

716 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 716 conjugacy classes of subgroups — too many to draw. Only its 119 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#14567000C211yesmaximal, characteristic
2#14563623C211yesmaximal, characteristic
3#14563571C212yesmaximal, complemented
4#14561503C212yesmaximal, complemented
5C19×#2973C211yesmaximal, characteristic
6C23×Dic38C2211yescharacteristic
7C2×#10597370—21no—
8C2×#10597273—24no—
9C2×#10597291—21no—
10#11926464C412yescomplemented
11#11926456C412yescomplemented
12#11926450—21no—
13#11926424—21no—
14#11926416—21no—
15#11926404C2212yes—
16#11926404C2211yescharacteristic
17#11926311—21no—
18C2×C4×D4×C19C2211yescharacteristic
19C19×#435—24no—
20C19×#432—21no—
21C19×#407—21no—
22C2×C19×C22⋊C8C2212yes—
23C22×D4×C19D411yescharacteristic
24C23×C4×C19D411yescharacteristic
25C23×C4×C19C2311yescharacteristic
26C23×Dic19—21no—
27C22×Dic38—22no—
28C22×Dic38—21no—
29C22×Dic38—22no—
30C22×Dic38—44no—
31C22×Dic38C2×C412yes—
32C2×M16×C19—22no—
33C22×C8×C19D414yes—
34C4×D4×C19—22no—
35C4×D4×C19—22no—
36C2×C4⋊C4×C19C2×C411yescharacteristic
37C2×C22⋊C4×C19C2×C411yescharacteristic
38C2×C22⋊C4×C19D411yescharacteristic
39C2×C42×C19D411yescharacteristic
40C2×C22⋊Dic19—22no—
41C2×C22⋊Dic19—21no—
42C2×C22⋊Dic19—22no—
43C2×C4⋊Dic19—21no—
44C2×C4⋊Dic19—22no—
45#10597370—44no—
46C2×Dic19⋊C4—22no—
47C19×C4⋊C8—22no—
48C19×C22⋊C8—22no—
49C19×C22⋊C8—22no—
50C19×C22⋊C8—22no—
51C19×#97—22no—
52#10597291—42no—
53C19⋊#95—22no—
54C19⋊#95—22no—
55C19⋊#95—22no—
56C19⋊#95C2×C412yes—
57#10597273—48no—
58C24×C19C22⋊C411yescharacteristic
59C24×C19C2×D411yescharacteristic
60C2×D4×C19—22no—
61C2×D4×C19—21no—
62C2×D4×C19—21no—
63C2×D4×C19—22no—
64C22×C4×C19—21no—
65C22×C4×C19—21no—
66C22×C4×C19—42no—
67C22×C4×C19—42no—
68C22×C4×C19C22⋊C411yescharacteristic
69C22×C4×C19C22⋊C411yescharacteristic
70C22×C4×C19C22⋊C411yescharacteristic
71C22×C4×C19C22×C411yescharacteristic
72C22×C4×C19C2×D412yes—
73C22×C4×C19C2×D411yescharacteristic
74C22×C4×C19#4112yes—
75C22×Dic19—22no—
76C22×Dic19—22no—
77C22×Dic19—44no—
78C22×Dic19—42no—
79C22×Dic19—42no—
80C2×Dic38—28no—
81C2×Dic38—24no—
82C2×Dic38—24no—
83C2×Dic38—44no—
84C2×Dic38—48no—
85C2×Dic38—44no—
86C2×Dic38—42no—
87C2×Dic38—41no—
88C2×Dic38—41no—
89M16×C19—82no—
90C2×C8×C19—24no—
91C2×C8×C19—44no—
92C4⋊C4×C19—22no—
93C22⋊C4×C19—22no—
94C22⋊C4×C19—22no—
95C42×C19—21no—
96C42×C19—21no—
97C22⋊Dic19—44no—
98C22⋊Dic19—41no—
99C22⋊Dic19—41no—
100C22⋊Dic19—42no—
101C22⋊Dic19—42no—
102C4⋊Dic19—42no—
103C4⋊Dic19—44no—
104Dic19⋊C4—44no—
105#9471—191nomaximal, Sylow
106C23×C19—21no—
107C23×C19—21no—
108C23×C19—21no—
109C23×C19—41no—
110C23×C19—41no—
111C23×C19—41no—
112C23×C19—41no—
113C23×C19C2×C22⋊C411yescharacteristic
114C23×C19#12112yes—
115C23×C19AGL(1,ℤ/8)11yescharacteristic
116C23×C19#13711yescharacteristic
117C23×C19#13712yes—
118D4×C19—42no—
119D4×C19—42no—
120C2×C4×C19—24no—
121C2×C4×C19—22no—
122C2×C4×C19—21no—
123C2×C4×C19—21no—
124C2×C4×C19—21no—
125C2×C4×C19—21no—
126C2×C4×C19—21no—
127C2×C4×C19—41no—
128C2×C4×C19—42no—
129C2×C4×C19—42no—
130C2×C4×C19—41no—
131C2×C4×C19—41no—
132C2×C4×C19—81no—
133C2×C4×C19C4×D412yes—
134C2×C4×C19#12011yescharacteristic
135C2×C4×C19#12311yescharacteristic
136C2×Dic19—24no—
137C2×Dic19—48no—
138C2×Dic19—42no—
139C2×Dic19—42no—
140C2×Dic19—42no—
141C2×Dic19—42no—
142C2×Dic19—42no—
143C2×Dic19—82no—
144C2×Dic19—82no—
145C2×Dic19—82no—
146Dic38—28no—
147Dic38—44no—
148Dic38—44no—
149Dic38—44no—
150C8×C19—44no—
151#2973D1911yescharacteristic
152#2409—191no—
153#1799—191no—
154#1787—192no—
155#1289—192no—
156C22×C19—21no—
157C22×C19—22no—
158C22×C19—21no—
159C22×C19—22no—
160C22×C19—41no—
161C22×C19—41no—
162C22×C19—42no—
163C22×C19—42no—
164C22×C19—41no—
165C22×C19—41no—
166C22×C19—41no—
167C22×C19—81no—
168C22×C19#38611yescharacteristic
169C22×C19#41711yescharacteristic
170C22×C19#41911yescharacteristic
171C22×C19#46812yes—
172C22×C19#47012yes—
173C4×C19—22no—
174C4×C19—21no—
175C4×C19—41no—
176C4×C19—41no—
177C4×C19—41no—
178C4×C19B(4,𝔽2)12yes—
179Dic19—44no—
180Dic19—82no—
181Dic19—162no—
182C23×Q8—191no—
183C2×C22⋊Q8—381no—
184C2×C4×D4C2×D1911yescharacteristic
185#435—24no—
186#432—21no—
187C2×#103—384no—
188C2×#99—381no—
189#407—21no—
190C2×C22⋊C8C2×D1912yes—
191#395—192no—
192#393—192no—
193#391—381no—
194#386—381no—
195#385—381no—
196#380—191no—
197#380—192no—
198#342—381no—
199C2×C19—21no—
200C2×C19—22no—
201C2×C19—21no—
202C2×C19—22no—
203C2×C19—81no—
204C2×C19#188911yescharacteristic
205C2×C19#189411yescharacteristic
206C2×C19#190911yescharacteristic
207C22×Q8—192no—
208C22×Q8—381no—
209C22×Q8—382no—
210C22×Q8—382no—
211C22×Q8—764no—
212C22×D4D7611yescharacteristic
213C23×C4—381no—
214C23×C4C22⋊D1911yescharacteristic
215C23×C4C22×D1911yescharacteristic
216C2×M16—22no—
217C22×C8C22⋊D1914yes—
218C22⋊Q8—764no—
219C4×D4—22no—
220C4×D4—22no—
221C2×C4⋊C4—382no—
222C2×C4⋊C4—381no—
223C2×C4⋊C4—382no—
224C2×C4⋊C4C4×D1911yescharacteristic
225C2×C22⋊C4—382no—
226C2×C22⋊C4—381no—
227C2×C22⋊C4—382no—
228C2×C22⋊C4C4×D1911yescharacteristic
229C2×C22⋊C4D7611yescharacteristic
230C2×C42C22⋊D1911yescharacteristic
231C4⋊C8—22no—
232#103—768no—
233#99—762no—
234C22⋊C8—22no—
235C22⋊C8—22no—
236C22⋊C8—22no—
237#97—22no—
238#95—192no—
239#95—382no—
240#95—382no—
241#95—382no—
242C19#947111yescharacteristic, complemented, Sylow
243C24(C2×D19)⋊C411yescharacteristic
244C24C2×D7611yescharacteristic
245C2×Q8—384no—
246C2×Q8—388no—
247C2×Q8—384no—
248C2×Q8—764no—
249C2×Q8—762no—
250C2×Q8—764no—
251C2×Q8—768no—
252C2×Q8—761no—
253C2×Q8—761no—
254C2×D4—22no—
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—22no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—42no—
261C22×C4—42no—
262C22×C4—382no—
263C22×C4—382no—
264C22×C4—764no—
265C22×C4—762no—
266C22×C4—762no—
267C22×C4(C2×D19)⋊C411yescharacteristic
268C22×C4(C2×D19)⋊C411yescharacteristic
269C22×C4(C2×D19)⋊C411yescharacteristic
270C22×C4C2×C4×D1911yescharacteristic
271C22×C4#6454112yes—
272C22×C4C2×C22⋊D1912yes—
273C22×C4C2×C22⋊D1911yescharacteristic
274M16—82no—
275C2×C8—24no—
276C2×C8—44no—
277C4⋊C4—22no—
278C4⋊C4—762no—
279C4⋊C4—764no—
280C4⋊C4—764no—
281C22⋊C4—22no—
282C22⋊C4—22no—
283C22⋊C4—764no—
284C22⋊C4—761no—
285C22⋊C4—761no—
286C22⋊C4—762no—
287C22⋊C4—762no—
288C42—21no—
289C42—21no—
290C23—21no—
291C23—21no—
292C23—21no—
293C23—41no—
294C23—41no—
295C23—41no—
296C23—41no—
297C23#1059735411yescharacteristic
298C23#1059735512yes—
299C23#1059735511yescharacteristic
300C23C2×(C2×D19)⋊C411yescharacteristic
301C23#1059737612yes—
302Q8—388no—
303Q8—764no—
304Q8—764no—
305Q8—764no—
306D4—42no—
307D4—42no—
308C2×C4—24no—
309C2×C4—22no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—41no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—81no—
321C2×C4—384no—
322C2×C4—762no—
323C2×C4—768no—
324C2×C4—762no—
325C2×C4—762no—
326C2×C4—762no—
327C2×C4—762no—
328C2×C4—1522no—
329C2×C4—1522no—
330C2×C4—1522no—
331C2×C4C4×C22⋊D1912yes—
332C2×C4#1059737511yescharacteristic
333C2×C4#1059739911yescharacteristic
334C8—44no—
335C22—21no—
336C22—22no—
337C22—21no—
338C22—22no—
339C22—41no—
340C22—42no—
341C22—41no—
342C22—42no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—81no—
347C22#1192642311yescharacteristic
348C22#1192654611yescharacteristic
349C22#1192655411yescharacteristic
350C22#1192679012yes—
351C22#1192680212yes—
352C4—21no—
353C4—22no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—3042no—
358C4—764no—
359C4—1522no—
360C4#1192673112yes—
361C2—22no—
362C2—21no—
363C2—21no—
364C2—22no—
365C2—81no—
366C2#1456404311yescharacteristic
367C2#1456406811yescharacteristic
368C2#1456415711yescharacteristic
subgroupG/H
centerC22#11926423
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#2973C2
socleC22×C19#386
prime radicalC22×D4×C19D4
cosocleC23×C4×C19C23
hypercenter#2973D19
hypocenterC19#9471
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2973

Complements

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

NH ≅ G/Ntype
3. #14563571C2semidirect
4. #14561503C2semidirect
10. #11926464C4semidirect
11. #11926456C4semidirect
242. C19#9471semidirect

Maximal subgroups

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

subgroupindex
#145670002
#145636232
#145635712
#145615032
C19×#29732
#947119