Finite Group Databasebeta

← #14573110

Subgroups — #14573110

Order 2432.

584 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 133 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
1C2×#10597357C212yesmaximal, complemented
2#127×D19C211yesmaximal, characteristic, complemented
3C4×#64543C211yesmaximal, characteristic, complemented
4#11926745C211yesmaximal, characteristic, complemented
5#11926743C212yesmaximal, complemented
6#11926741C211yesmaximal, characteristic, complemented
7#11926739C211yesmaximal, characteristic, complemented
8#11926737C212yesmaximal, complemented
9#11926566C211yesmaximal, characteristic, complemented
10#11926547C212yesmaximal, complemented
11C19×#459C211yesmaximal, characteristic, complemented
12C2×#64543C2211yescharacteristic
13C2×D4×D19—21no—
14C2×D4×D19—21no—
15C2×D4×D19C2212yes—
16C2×D8×C19C2212yescomplemented
17C19×#127C2211yescharacteristic
18C4×D4×C19C2211yescharacteristic, complemented
19#10597386—21no—
20#10597386—21no—
21#10597386C2212yes—
22D4×Dic19C2211yescharacteristic, complemented
23C2×#64526C2212yescomplemented
24C2×#64525C2212yescomplemented
25C4×C22⋊D19—21no—
26C2×C4×Dic19—21no—
27#10597357—28no—
28C2×#64516C2212yescomplemented
29C2×#64515C2212yes—
30#10597338C2211yescharacteristic
31#10597333C2211yescharacteristic, complemented
32(C22⋊D19)⋊C4—21no—
33#10597323—21no—
34#10597320C2211yescharacteristic
35C42×D19C2211yescharacteristic
36C4×Dic38C2211yescharacteristic, complemented
37C19×C4⋊C8C2211yescharacteristic, complemented
38C19×#102C2212yescomplemented
39#10597289C2212yescomplemented
40#10597278C2212yescomplemented
41Dic19⋊C8C2212yescomplemented
42#10597266C2212yescomplemented
43C4⋊(C19⋊C8)C2211yescharacteristic, complemented
44C23×D19—22no—
45C2×D4×C19—21no—
46C2×D4×C19—21no—
47C2×D4×C19C2312yes—
48C2×D4×C19C2311yescharacteristic
49C22×C4×C19—21no—
50C2×C22⋊D19—21no—
51C2×C22⋊D19—22no—
52C2×C22⋊D19—22no—
53C2×C22⋊D19—22no—
54C22×Dic19—21no—
55C22×Dic19—21no—
56#64543—22no—
57#64543D414yescomplemented
58D4×D19—24no—
59D4×D19—24no—
60D4×D19—44no—
61D4×D19—44no—
62C2×D76—21no—
63C2×D76—21no—
64C2×D76C2312yes—
65C2×C4×D19D411yescharacteristic
66C2×C4×D19D411yescharacteristic
67C2×C4×D19C2311yescharacteristic
68C2×Dic38C2311yescharacteristic
69D8×C19—24no—
70C2×C8×C19C2312yes—
71C4⋊C4×C19C2311yescharacteristic
72C22⋊C4×C19—21no—
73C42×C19C2311yescharacteristic
74C22⋊Dic19—21no—
75#64526—24no—
76#64525—24no—
77(C2×D19)⋊C4—21no—
78C4⋊Dic19C2311yescharacteristic
79Dic19⋊C4—21no—
80Dic19⋊C4—21no—
81C4×Dic19—21no—
82C4×Dic19—21no—
83C4×Dic19—21no—
84C4×Dic19D411yescharacteristic
85C4×Dic19D411yescharacteristic
86C4×Dic19C2311yescharacteristic
87C2×C19⋊C8C2312yes—
88#64516—24no—
89#64515—24no—
90C23×C19—21no—
91C23×C19—22no—
92C22×D19—22no—
93C22×D19—44no—
94C22×D19—44no—
95C22×D19—44no—
96C22×D19C2×D411yescharacteristic
97D4×C19—22no—
98D4×C19—21no—
99D4×C19—22no—
100D4×C19—42no—
101D4×C19—42no—
102D4×C19C2×D412yescomplemented
103C2×C4×C19—21no—
104C2×C4×C19—42no—
105C2×C4×C19C2×D411yescharacteristic
106C2×C4×C19C2×D411yescharacteristic
107C2×C4×C19C2411yescharacteristic
108C22⋊D19—24no—
109C22⋊D19—44no—
110C22⋊D19—44no—
111C22⋊D19—44no—
112C2×Dic19—21no—
113C2×Dic19—24no—
114C2×Dic19—21no—
115C2×Dic19—42no—
116C2×Dic19C2×D411yescharacteristic
117C2×Dic19C2×D411yescharacteristic
118C2×Dic19C2×D411yescharacteristic
119D76—22no—
120D76—22no—
121D76—42no—
122D76—42no—
123C4×D19—22no—
124C4×D19—22no—
125C4×D19C2×D412yes—
126C4×D19#4112yes—
127Dic38—21no—
128Dic38C2×D412yescomplemented
129C8×C19—22no—
130C19⋊C8—22no—
131#3038—191nomaximal, Sylow
132C22×C19—22no—
133C22×C19—41no—
134C22×C19—41no—
135C22×C19—42no—
136C22×C19—42no—
137C22×C19—42no—
138C22×C19C22×D411yescharacteristic
139C2×D19—21no—
140C2×D19—21no—
141C2×D19—42no—
142C2×D19—42no—
143C2×D19—42no—
144C2×D19—88no—
145C2×D19#12112yes—
146C4×C19—21no—
147C4×C19—41no—
148C4×C19AGL(1,ℤ/8)12yescomplemented
149C4×C19C22×D411yescharacteristic
150C4×C19C2×#4111yescharacteristic
151Dic19—22no—
152Dic19—21no—
153Dic19—41no—
154Dic19#12112yes—
155Dic19AGL(1,ℤ/8)12yescomplemented
156C2×AGL(1,ℤ/8)—192no—
157C2×#127—191no—
158C4×#41—191no—
159#460—191no—
160#460—191no—
161#460—192no—
162#459—192no—
163#459—191no—
164#459D1911yescharacteristic, complemented
165#423—191no—
166#418—192no—
167C2×C19—42no—
168C2×C19—82no—
169C2×C19C2×#12111yescharacteristic
170C2×C19C2×AGL(1,ℤ/8)11yescharacteristic
171C2×C19C2×AGL(1,ℤ/8)11yescharacteristic
172D19—22no—
173D19—82no—
174C2×#41—191no—
175C22×D4—192no—
176C22×D4—381no—
177C22×D4—381no—
178AGL(1,ℤ/8)—388no—
179C2×SD16—192no—
180C2×SD16—192no—
181C2×D8—192no—
182C2×D8C2×D1912yescomplemented
183C2×M16—192no—
184#127—192no—
185#127—191no—
186#127—381no—
187#127—381no—
188#127C2×D1911yescharacteristic
189C4×Q8—191no—
190C4×Q8—191no—
191C4×D4—191no—
192C4×D4—381no—
193C4×D4—381no—
194C4×D4C2×D1911yescharacteristic, complemented
195#117—191no—
196#117—381no—
197C2×C42—191no—
198C2×C42—381no—
199C4⋊C8—192no—
200C4⋊C8—191no—
201C4⋊C8C2×D1911yescharacteristic, complemented
202#102—192no—
203#102—192no—
204#102—192no—
205#102C2×D1912yescomplemented
206C19#303811yescharacteristic, complemented, Sylow
207C24—382no—
208#41—194no—
209#41—382no—
210C2×Q8—191no—
211C2×D4—21no—
212C2×D4—21no—
213C2×D4—192no—
214C2×D4—384no—
215C2×D4—384no—
216C2×D4—382no—
217C2×D4—382no—
218C2×D4—382no—
219C2×D4—381no—
220C2×D4—381no—
221C2×D4—381no—
222C2×D4—764no—
223C2×D4—764no—
224C2×D4C22×D1912yes—
225C2×D4C22×D1911yescharacteristic
226C22×C4—21no—
227C22×C4—191no—
228C22×C4—191no—
229C22×C4—191no—
230C22×C4—381no—
231C22×C4—381no—
232SD16—384no—
233SD16—384no—
234D8—24no—
235D8—384no—
236M16—384no—
237C2×C8—192no—
238C2×C8C22×D1912yes—
239C4⋊C4—191no—
240C4⋊C4—381no—
241C4⋊C4—381no—
242C4⋊C4C22×D1911yescharacteristic
243C22⋊C4—21no—
244C22⋊C4—381no—
245C22⋊C4—381no—
246C42—191no—
247C42—191no—
248C42—191no—
249C42—381no—
250C42—381no—
251C42—381no—
252C42C22×D1911yescharacteristic
253C23—21no—
254C23—22no—
255C23—191no—
256C23—382no—
257C23—764no—
258C23—764no—
259C23—764no—
260Q8—192no—
261Q8—381no—
262D4—22no—
263D4—21no—
264D4—22no—
265D4—42no—
266D4—42no—
267D4—384no—
268D4—382no—
269D4—382no—
270D4—762no—
271D4—764no—
272D4—764no—
273D4—764no—
274D4—762no—
275D4D4×D1912yescomplemented
276C2×C4—21no—
277C2×C4—42no—
278C2×C4—191no—
279C2×C4—191no—
280C2×C4—192no—
281C2×C4—192no—
282C2×C4—191no—
283C2×C4—382no—
284C2×C4—384no—
285C2×C4—381no—
286C2×C4—382no—
287C2×C4—381no—
288C2×C4—762no—
289C2×C4D4×D1911yescharacteristic
290C2×C4D4×D1911yescharacteristic
291C2×C4C23×D1911yescharacteristic
292C8—22no—
293C8—382no—
294C22—22no—
295C22—41no—
296C22—41no—
297C22—42no—
298C22—42no—
299C22—42no—
300C22—192no—
301C22—381no—
302C22—381no—
303C22—762no—
304C22—762no—
305C22—762no—
306C22—1528no—
307C22C2×D4×D1911yescharacteristic
308C4—21no—
309C4—41no—
310C4—192no—
311C4—192no—
312C4—381no—
313C4—382no—
314C4—761no—
315C4#1059735712yescomplemented
316C4C2×D4×D1911yescharacteristic
317C4#41×D1911yescharacteristic
318C2—42no—
319C2—82no—
320C2—382no—
321C2—1522no—
322C2#121×D1911yescharacteristic
323C2AGL(1,ℤ/8)×D1911yescharacteristic
324C2C2×#1059735711yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#459C2
socleC22×C19C22×D4
hypercenter#459D19
hypocenterC19#3038
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. C2×#10597357C2semidirect
2. #127×D19C2semidirect
3. C4×#64543C2semidirect
4. #11926745C2semidirect
5. #11926743C2semidirect
6. #11926741C2semidirect
7. #11926739C2semidirect
8. #11926737C2semidirect
9. #11926566C2semidirect
10. #11926547C2semidirect
11. C19×#459C2semidirect
16. C2×D8×C19C22semidirect
18. C4×D4×C19C22semidirect
22. D4×Dic19C22semidirect
23. C2×#64526C22semidirect
24. C2×#64525C22semidirect
28. C2×#64516C22semidirect
31. #10597333C22semidirect
36. C4×Dic38C22semidirect
37. C19×C4⋊C8C22semidirect
38. C19×#102C22semidirect
39. #10597289C22semidirect
40. #10597278C22semidirect
41. Dic19⋊C8C22semidirect
42. #10597266C22semidirect
43. C4⋊(C19⋊C8)C22semidirect
57. #64543D4semidirect
102. D4×C19C2×D4semidirect
128. Dic38C2×D4semidirect
148. C4×C19AGL(1,ℤ/8)semidirect
155. Dic19AGL(1,ℤ/8)semidirect
164. #459D19semidirect
182. C2×D8C2×D19semidirect
194. C4×D4C2×D19semidirect
201. C4⋊C8C2×D19semidirect
205. #102C2×D19semidirect
206. C19#3038semidirect
275. D4D4×D19semidirect
315. C4#10597357semidirect

Maximal subgroups

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

subgroupindex
C2×#105973572
#127×D192
C4×#645432
#119267452
#119267432
#119267412
#119267392
#119267372
#119265662
#119265472
C19×#4592
#303819