Finite Group Databasebeta

← #18080008

Subgroups — #18080008

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#14569110C211yesmaximal, characteristic
2#14566235C211yesmaximal, characteristic, complemented
3#14562152C211yesmaximal, characteristic
4#14562150C211yesmaximal, characteristic
5#14561964C211yesmaximal, characteristic, complemented
6#14561521C211yesmaximal, characteristic, complemented
7C19×#1297C211yesmaximal, characteristic, complemented
8C2×#10597376C2211yescharacteristic
9C22×Dic19⋊C4C2211yescharacteristic
10#11926508C2211yescharacteristic
11#11926484C412yescomplemented
12#11926462C412yescomplemented
13#11926435—22no—
14#11926428—22no—
15#11926426—22no—
16#11926421—21no—
17#11926421—21no—
18#11926405—21no—
19#11926402—21no—
20C4×C22⋊Dic19C2211yescharacteristic
21#11926279—22no—
22#11926277—22no—
23#11926269—22no—
24C19×#407C2211yescharacteristic
25C4×C22⋊C4×C19C2211yescharacteristic
26C4×C22⋊C4×C19C2211yescharacteristic
27C23×C4×C19C2311yescharacteristic
28C22×C22⋊D19—21no—
29C23×Dic19D411yescharacteristic
30C23×Dic19D411yescharacteristic
31C22×D76C2×C411yescharacteristic
32C2×M16×C19—21no—
33C2×C22⋊C4×C19—21no—
34C2×C22⋊C4×C19—21no—
35C2×C42×C19—21no—
36C2×C42×C19—21no—
37C2×C22⋊Dic19—21no—
38#10597376—21no—
39#10597376—21no—
40#10597376—21no—
41#10597376—21no—
42C2×(C2×D19)⋊C4—21no—
43C2×(C2×D19)⋊C4—22no—
44C2×(C2×D19)⋊C4—22no—
45C2×C4⋊Dic19C2×C411yescharacteristic
46C2×Dic19⋊C4—21no—
47C2×Dic19⋊C4—21no—
48C2×Dic19⋊C4—21no—
49C2×Dic19⋊C4—21no—
50C2×Dic19⋊C4—22no—
51C2×Dic19⋊C4C2×C412yes—
52C2×Dic19⋊C4D412yes—
53C2×C4×Dic19—21no—
54C2×#64520—21no—
55C19×C22⋊C8—21no—
56C19×C22⋊C8—21no—
57C19×#95C2×C412yes—
58C19×#95D412yes—
59C19⋊#95—22no—
60C19⋊#95—24no—
61C19⋊#95—22no—
62C19⋊#95—22no—
63C19⋊#95D412yes—
64C22⋊(C19⋊C8)—21no—
65C22⋊(C19⋊C8)—21no—
66C24×C19C2×D411yescharacteristic
67C23×D19—21no—
68C22×C4×C19—22no—
69C22×C4×C19—22no—
70C22×C4×C19—81no—
71C22×C4×C19C22×C411yescharacteristic
72C22×C4×C19C2×D411yescharacteristic
73C22×C4×C19C2×D411yescharacteristic
74C22×C4×C19C2×D411yescharacteristic
75C22×C4×C19#4111yescharacteristic
76C22×C4×C19#4111yescharacteristic
77C2×C22⋊D19—44no—
78C2×C22⋊D19—41no—
79C2×C22⋊D19—41no—
80C22×Dic19—21no—
81C22×Dic19—21no—
82C22×Dic19—21no—
83C22×Dic19—21no—
84C22×Dic19—21no—
85C22×Dic19—22no—
86C22×Dic19—42no—
87C22×Dic19—81no—
88C22×Dic19C22⋊C412yes—
89C22×Dic19C22⋊C412yes—
90C2×D76—21no—
91C2×D76—21no—
92C2×D76—81no—
93M16×C19—81no—
94C2×C8×C19—41no—
95C22⋊C4×C19—42no—
96C22⋊C4×C19—42no—
97C42×C19—81no—
98C42×C19—81no—
99C22⋊Dic19—42no—
100(C2×D19)⋊C4—44no—
101(C2×D19)⋊C4—41no—
102(C2×D19)⋊C4—41no—
103(C2×D19)⋊C4—82no—
104C4⋊Dic19—21no—
105C4⋊Dic19—21no—
106Dic19⋊C4—22no—
107Dic19⋊C4—22no—
108Dic19⋊C4—22no—
109Dic19⋊C4—22no—
110Dic19⋊C4—82no—
111C4×Dic19—81no—
112#64520—81no—
113C2×C19⋊C8—41no—
114#9414—191nomaximal, Sylow
115C23×C19—22no—
116C23×C19—22no—
117C23×C19—41no—
118C23×C19C2×C22⋊C411yescharacteristic
119C23×C19#12011yescharacteristic
120C23×C19#12311yescharacteristic
121C22×D19—42no—
122C22×D19—42no—
123C22×D19—41no—
124C22×D19—42no—
125C2×C4×C19—41no—
126C2×C4×C19—41no—
127C2×C4×C19—41no—
128C2×C4×C19—41no—
129C2×C4×C19—41no—
130C2×C4×C19—41no—
131C2×C4×C19—42no—
132C2×C4×C19—42no—
133C2×C4×C19—42no—
134C2×C4×C19—42no—
135C2×C4×C19—42no—
136C2×C4×C19—42no—
137C2×C4×C19C4×D411yescharacteristic
138C2×C4×C19C4×D411yescharacteristic
139C2×C4×C19#12111yescharacteristic
140C2×C4×C19#12111yescharacteristic
141C22⋊D19—82no—
142C22⋊D19—82no—
143C2×Dic19—22no—
144C2×Dic19—22no—
145C2×Dic19—22no—
146C2×Dic19—22no—
147C2×Dic19—42no—
148C2×Dic19—42no—
149C2×Dic19—42no—
150C2×Dic19—42no—
151C2×Dic19—42no—
152C2×Dic19—42no—
153C2×Dic19—42no—
154C2×Dic19—41no—
155C2×Dic19—42no—
156C2×Dic19—81no—
157D76—81no—
158D76—81no—
159C8×C19—81no—
160C19⋊C8—81no—
161#2591—191no—
162#2313—191no—
163#1507—191no—
164#1507—191no—
165#1463—191no—
166#1297—191no—
167#1297D1911yescharacteristic, complemented
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#38611yescharacteristic
177C22×C19#42112yes—
178C22×C19#45412yes—
179C2×D19—84no—
180C2×D19—81no—
181C2×D19—81no—
182C2×D19—81no—
183C4×C19—21no—
184C4×C19—21no—
185C4×C19—21no—
186C4×C19—21no—
187C4×C19—82no—
188C4×C19—82no—
189Dic19—42no—
190Dic19—42no—
191Dic19—82no—
192Dic19—81no—
193C2×#121—191no—
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⋊C4C2×D1911yescharacteristic
208C4×C22⋊C4C2×D1911yescharacteristic
209#327—382no—
210#327—382no—
211#324—382no—
212C2×C19—22no—
213C2×C19—22no—
214C2×C19—41no—
215C2×C19#188811yescharacteristic
216C2×C19#189711yescharacteristic
217C2×C19#191311yescharacteristic
218D19—161no—
219C22×D4—191no—
220C22×D4—381no—
221C23×C4—191no—
222C23×C4—191no—
223C23×C4C22×D1911yescharacteristic
224C2×M16—21no—
225C2×M16—381no—
226#121—381no—
227#121—381no—
228#121—381no—
229#121—381no—
230C2×C4⋊C4—192no—
231C2×C4⋊C4—192no—
232C2×C4⋊C4—191no—
233C2×C4⋊C4—381no—
234C2×C4⋊C4—381no—
235C2×C4⋊C4—381no—
236C2×C4⋊C4—381no—
237C2×C4⋊C4—382no—
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—21no—
246C2×C42—381no—
247C22⋊C8—21no—
248C22⋊C8—21no—
249C22⋊C8—381no—
250C22⋊C8—381no—
251#95—192no—
252#95—382no—
253#95—382no—
254#95—382no—
255#95—384no—
256#95C4×D1912yes—
257#95D7612yes—
258C19#941411yescharacteristic, complemented, Sylow
259C24—381no—
260C24D4×D1911yescharacteristic
261C2×D4—381no—
262C2×D4—381no—
263C2×D4—764no—
264C2×D4—761no—
265C2×D4—761no—
266C2×D4—1521no—
267C22×C4—22no—
268C22×C4—22no—
269C22×C4—81no—
270C22×C4—192no—
271C22×C4—192no—
272C22×C4—381no—
273C22×C4—381no—
274C22×C4—381no—
275C22×C4—381no—
276C22×C4—381no—
277C22×C4—382no—
278C22×C4—762no—
279C22×C4—1521no—
280C22×C4C2×C4×D1911yescharacteristic
281C22×C4C2×D7611yescharacteristic
282C22×C4#6454111yescharacteristic
283C22×C4D4×D1911yescharacteristic
284C22×C4D4×D1911yescharacteristic
285C22×C4#6454511yescharacteristic
286M16—81no—
287M16—1521no—
288C2×C8—41no—
289C2×C8—761no—
290C4⋊C4—382no—
291C4⋊C4—382no—
292C4⋊C4—382no—
293C4⋊C4—382no—
294C4⋊C4—381no—
295C4⋊C4—381no—
296C4⋊C4—1522no—
297C22⋊C4—42no—
298C22⋊C4—42no—
299C22⋊C4—764no—
300C22⋊C4—762no—
301C22⋊C4—761no—
302C22⋊C4—761no—
303C22⋊C4—1522no—
304C42—81no—
305C42—81no—
306C42—1521no—
307C23—22no—
308C23—22no—
309C23—41no—
310C23—762no—
311C23—762no—
312C23—762no—
313C23—761no—
314C23C22⋊C4×D1911yescharacteristic
315C23#1059732811yescharacteristic
316C23#1059734011yescharacteristic
317D4—1521no—
318D4—1521no—
319D4—1522no—
320D4—1522no—
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—42no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4—382no—
334C2×C4—382no—
335C2×C4—382no—
336C2×C4—382no—
337C2×C4—762no—
338C2×C4—762no—
339C2×C4—762no—
340C2×C4—762no—
341C2×C4—762no—
342C2×C4—762no—
343C2×C4—762no—
344C2×C4—761no—
345C2×C4—762no—
346C2×C4—1521no—
347C2×C4C4×D7611yescharacteristic
348C2×C4#1059733011yescharacteristic
349C2×C4#1059733911yescharacteristic
350C2×C4#1059734111yescharacteristic
351C8—81no—
352C8—1521no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—44no—
361C22—1524no—
362C22—1521no—
363C22—1521no—
364C22—1521no—
365C22#1192642211yescharacteristic
366C22#1192655912yes—
367C22#1192671812yes—
368C4—21no—
369C4—21no—
370C4—21no—
371C4—21no—
372C4—82no—
373C4—82no—
374C4—762no—
375C4—762no—
376C4—1522no—
377C4—1521no—
378C2—22no—
379C2—22no—
380C2—41no—
381C2—3041no—
382C2#1456403711yescharacteristic
383C2#1456408211yescharacteristic
384C2#1456417611yescharacteristic
subgroupG/H
centerC22#11926422
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#1297C2
socleC22×C19#386
prime radicalC2×#10597376C22
cosocleC23×C4×C19C23
hypercenter#1297D19
hypocenterC19#9414
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1297

Complements

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

NH ≅ G/Ntype
2. #14566235C2semidirect
5. #14561964C2semidirect
6. #14561521C2semidirect
7. C19×#1297C2semidirect
11. #11926484C4semidirect
12. #11926462C4semidirect
167. #1297D19semidirect
258. C19#9414semidirect

Maximal subgroups

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

subgroupindex
#145691102
#145662352
#145621522
#145621502
#145619642
#145615212
C19×#12972
#941419