Finite Group Databasebeta

← #18080006

Subgroups — #18080006

Order 4864.

552 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 93 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#14569116C211yesmaximal, characteristic
2#14566235C211yesmaximal, characteristic, complemented
3#14562151C211yesmaximal, characteristic
4#14561964C211yesmaximal, characteristic, complemented
5#14561521C211yesmaximal, characteristic, complemented
6#14561520C211yesmaximal, characteristic, complemented
7C19×#1507C211yesmaximal, characteristic
8C22×Dic19⋊C4C2211yescharacteristic
9#11926508C2211yescharacteristic
10#11926482C412yescomplemented
11#11926458C412yescomplemented
12#11926438—22no—
13#11926428—22no—
14#11926426—22no—
15#11926424—21no—
16#11926424—21no—
17#11926405—21no—
18#11926402—21no—
19C4×C22⋊Dic19C2211yescharacteristic
20C4×C22⋊Dic19C2211yescharacteristic
21#11926278—22no—
22#11926269—22no—
23C2×C19×#121C2211yescharacteristic
24C19×#407C2211yescharacteristic
25C4×C22⋊C4×C19C2211yescharacteristic
26C19×#327—22no—
27C22×D4×C19—21no—
28C22×D4×C19C2×C411yescharacteristic
29C23×C4×C19C2311yescharacteristic
30C23×Dic19D411yescharacteristic
31C23×Dic19D411yescharacteristic
32C2×M16×C19—21no—
33C19×#121—21no—
34C19×#121—21no—
35C19×#121—21no—
36C19×#121—21no—
37C2×C4⋊C4×C19C2×C411yescharacteristic
38C2×C22⋊C4×C19—21no—
39C2×C22⋊C4×C19—21no—
40C2×C42×C19—21no—
41C2×C22⋊Dic19—21no—
42C2×C22⋊Dic19—21no—
43C2×C22⋊Dic19—22no—
44C2×C22⋊Dic19—22no—
45C2×Dic19⋊C4—21no—
46C2×Dic19⋊C4—21no—
47C2×Dic19⋊C4—21no—
48C2×Dic19⋊C4—21no—
49C2×Dic19⋊C4—22no—
50C2×Dic19⋊C4C2×C412yes—
51C2×Dic19⋊C4D412yes—
52C2×C4×Dic19—21no—
53C2×C4×Dic19—21no—
54C2×#64520—21no—
55C19×C22⋊C8—21no—
56C19×C22⋊C8—21no—
57C19×#95D412yes—
58C19⋊#95—22no—
59C19⋊#95—24no—
60C19⋊#95—22no—
61C19⋊#95—22no—
62C19⋊#95C2×C412yes—
63C19⋊#95D412yes—
64C22⋊(C19⋊C8)—21no—
65C22⋊(C19⋊C8)—21no—
66C24×C19—21no—
67C24×C19C2×D411yescharacteristic
68C2×D4×C19—21no—
69C2×D4×C19—21no—
70C2×D4×C19—44no—
71C2×D4×C19—41no—
72C2×D4×C19—41no—
73C2×D4×C19—81no—
74C22×C4×C19—21no—
75C22×C4×C19—22no—
76C22×C4×C19—81no—
77C22×C4×C19C22×C411yescharacteristic
78C22×C4×C19C2×D411yescharacteristic
79C22×C4×C19C2×D411yescharacteristic
80C22×C4×C19C2×D411yescharacteristic
81C22×C4×C19#4111yescharacteristic
82C22×C4×C19#4111yescharacteristic
83C22×Dic19—21no—
84C22×Dic19—21no—
85C22×Dic19—21no—
86C22×Dic19—21no—
87C22×Dic19—22no—
88C22×Dic19—22no—
89C22×Dic19—42no—
90C22×Dic19—81no—
91C22×Dic19C22⋊C412yes—
92C22×Dic19C22⋊C412yes—
93M16×C19—81no—
94C2×C8×C19—41no—
95C4⋊C4×C19—21no—
96C4⋊C4×C19—21no—
97C22⋊C4×C19—42no—
98C22⋊C4×C19—41no—
99C22⋊C4×C19—41no—
100C42×C19—81no—
101C22⋊Dic19—44no—
102C22⋊Dic19—42no—
103C22⋊Dic19—42no—
104C22⋊Dic19—82no—
105Dic19⋊C4—22no—
106Dic19⋊C4—22no—
107Dic19⋊C4—22no—
108Dic19⋊C4—22no—
109Dic19⋊C4—82no—
110C4×Dic19—81no—
111C4×Dic19—81no—
112#64520—81no—
113C2×C19⋊C8—41no—
114#9414—191nomaximal, Sylow
115C23×C19—22no—
116C23×C19—22no—
117C23×C19—41no—
118C23×C19—42no—
119C23×C19—42no—
120C23×C19—41no—
121C23×C19—42no—
122C23×C19C2×C22⋊C411yescharacteristic
123C23×C19#12011yescharacteristic
124C23×C19#12311yescharacteristic
125D4×C19—81no—
126D4×C19—81no—
127D4×C19—82no—
128D4×C19—82no—
129C2×C4×C19—41no—
130C2×C4×C19—41no—
131C2×C4×C19—41no—
132C2×C4×C19—41no—
133C2×C4×C19—41no—
134C2×C4×C19—41no—
135C2×C4×C19—42no—
136C2×C4×C19—42no—
137C2×C4×C19—42no—
138C2×C4×C19—41no—
139C2×C4×C19—42no—
140C2×C4×C19C4×D411yescharacteristic
141C2×C4×C19C4×D411yescharacteristic
142C2×C4×C19#12111yescharacteristic
143C2×C4×C19#12111yescharacteristic
144C2×Dic19—22no—
145C2×Dic19—22no—
146C2×Dic19—22no—
147C2×Dic19—22no—
148C2×Dic19—42no—
149C2×Dic19—42no—
150C2×Dic19—42no—
151C2×Dic19—42no—
152C2×Dic19—42no—
153C2×Dic19—42no—
154C2×Dic19—42no—
155C2×Dic19—42no—
156C2×Dic19—42no—
157C2×Dic19—42no—
158C2×Dic19—81no—
159C8×C19—81no—
160C19⋊C8—81no—
161#2591—191no—
162#2313—191no—
163#1507—191no—
164#1507D1911yescharacteristic
165#1463—191no—
166#1297—191no—
167#1297—191no—
168C22×C19—21no—
169C22×C19—21no—
170C22×C19—21no—
171C22×C19—21no—
172C22×C19—21no—
173C22×C19—21no—
174C22×C19—21no—
175C22×C19—44no—
176C22×C19—84no—
177C22×C19—81no—
178C22×C19—81no—
179C22×C19—81no—
180C22×C19#38611yescharacteristic
181C22×C19#42112yes—
182C22×C19#45412yes—
183C4×C19—21no—
184C4×C19—21no—
185C4×C19—21no—
186C4×C19—21no—
187C4×C19—82no—
188C4×C19—81no—
189Dic19—42no—
190Dic19—42no—
191Dic19—82no—
192Dic19—82no—
193C2×#121C2×D1911yescharacteristic
194C22×C4⋊C4—191no—
195#407—191no—
196#407C2×D1911yescharacteristic
197#400—192no—
198#394—192no—
199#388—382no—
200#387—382no—
201#387—382no—
202#386—381no—
203#386—381no—
204#381—381no—
205#380—381no—
206C4×C22⋊C4—191no—
207C4×C22⋊C4—191no—
208C4×C22⋊C4C2×D1911yescharacteristic
209#327—22no—
210#327—382no—
211#324—382no—
212C2×C19—22no—
213C2×C19—22no—
214C2×C19—41no—
215C2×C19—161no—
216C2×C19#188811yescharacteristic
217C2×C19#189711yescharacteristic
218C2×C19#191311yescharacteristic
219C22×D4—21no—
220C22×D4C4×D1911yescharacteristic
221C23×C4—191no—
222C23×C4—191no—
223C23×C4C22×D1911yescharacteristic
224C2×M16—21no—
225C2×M16—381no—
226#121—21no—
227#121—21no—
228#121—21no—
229#121—21no—
230C2×C4⋊C4—192no—
231C2×C4⋊C4—192no—
232C2×C4⋊C4—381no—
233C2×C4⋊C4—381no—
234C2×C4⋊C4—381no—
235C2×C4⋊C4—381no—
236C2×C4⋊C4—382no—
237C2×C4⋊C4C4×D1911yescharacteristic
238C2×C22⋊C4—21no—
239C2×C22⋊C4—21no—
240C2×C22⋊C4—382no—
241C2×C22⋊C4—381no—
242C2×C22⋊C4—381no—
243C2×C22⋊C4—382no—
244C2×C42—21no—
245C2×C42—381no—
246C2×C42—381no—
247C22⋊C8—21no—
248C22⋊C8—21no—
249C22⋊C8—381no—
250C22⋊C8—381no—
251#95—192no—
252#95—192no—
253#95—382no—
254#95—382no—
255#95—382no—
256#95—384no—
257#95C22⋊D1912yes—
258C19#941411yescharacteristic, complemented, Sylow
259C24—21no—
260C24D4×D1911yescharacteristic
261C2×D4—21no—
262C2×D4—21no—
263C2×D4—44no—
264C2×D4—41no—
265C2×D4—41no—
266C2×D4—81no—
267C22×C4—22no—
268C22×C4—21no—
269C22×C4—81no—
270C22×C4—192no—
271C22×C4—192no—
272C22×C4—381no—
273C22×C4—381no—
274C22×C4—381no—
275C22×C4—381no—
276C22×C4—382no—
277C22×C4—382no—
278C22×C4—762no—
279C22×C4—1521no—
280C22×C4C2×C4×D1911yescharacteristic
281C22×C4#6454111yescharacteristic
282C22×C4D4×D1911yescharacteristic
283C22×C4D4×D1911yescharacteristic
284C22×C4#6454311yescharacteristic
285C22×C4C2×C22⋊D1911yescharacteristic
286M16—81no—
287M16—1521no—
288C2×C8—41no—
289C2×C8—761no—
290C4⋊C4—21no—
291C4⋊C4—21no—
292C4⋊C4—382no—
293C4⋊C4—382no—
294C4⋊C4—382no—
295C4⋊C4—382no—
296C4⋊C4—1522no—
297C22⋊C4—42no—
298C22⋊C4—41no—
299C22⋊C4—41no—
300C22⋊C4—764no—
301C22⋊C4—762no—
302C22⋊C4—762no—
303C22⋊C4—1522no—
304C42—81no—
305C42—1521no—
306C42—1521no—
307C23—22no—
308C23—22no—
309C23—41no—
310C23—42no—
311C23—42no—
312C23—42no—
313C23—41no—
314C23C22⋊C4×D1911yescharacteristic
315C23#1059732911yescharacteristic
316C23#1059738311yescharacteristic
317D4—81no—
318D4—81no—
319D4—82no—
320D4—82no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—41no—
331C2×C4—42no—
332C2×C4—382no—
333C2×C4—382no—
334C2×C4—382no—
335C2×C4—382no—
336C2×C4—762no—
337C2×C4—762no—
338C2×C4—762no—
339C2×C4—762no—
340C2×C4—762no—
341C2×C4—762no—
342C2×C4—762no—
343C2×C4—762no—
344C2×C4—762no—
345C2×C4—762no—
346C2×C4—1521no—
347C2×C4(C22⋊D19)⋊C411yescharacteristic
348C2×C4#1059733011yescharacteristic
349C2×C4C4×C22⋊D1911yescharacteristic
350C2×C4#1059738411yescharacteristic
351C8—81no—
352C8—1521no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—44no—
361C22—84no—
362C22—81no—
363C22—81no—
364C22—81no—
365C22#1192642011yescharacteristic
366C22#1192655912yes—
367C22#1192671512yes—
368C4—21no—
369C4—21no—
370C4—21no—
371C4—21no—
372C4—82no—
373C4—81no—
374C4—762no—
375C4—762no—
376C4—1522no—
377C4—1522no—
378C2—22no—
379C2—22no—
380C2—41no—
381C2—161no—
382C2#1456403511yescharacteristic
383C2#1456408011yescharacteristic
384C2#1456417411yescharacteristic
subgroupG/H
centerC22#11926420
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#1507C2
socleC22×C19#386
prime radicalC2×C19×#121C22
cosocleC23×C4×C19C23
hypercenter#1507D19
hypocenterC19#9414
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1507

Complements

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

NH ≅ G/Ntype
2. #14566235C2semidirect
4. #14561964C2semidirect
5. #14561521C2semidirect
6. #14561520C2semidirect
10. #11926482C4semidirect
11. #11926458C4semidirect
258. C19#9414semidirect

Maximal subgroups

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

subgroupindex
#145691162
#145662352
#145621512
#145619642
#145615212
#145615202
C19×#15072
#941419