Finite Group Databasebeta

← #14574385

Subgroups — #14574385

Order 2432.

520 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 121 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×#10597341C211yesmaximal, characteristic, complemented
2#121×D19C211yesmaximal, characteristic, complemented
3#11926859C212yesmaximal, complemented
4#11926857C211yesmaximal, characteristic, complemented
5#11926781C212yesmaximal, complemented
6#11926779C212yesmaximal, complemented
7#11926680C211yesmaximal, characteristic, complemented
8#11926679C212yesmaximal, complemented
9#11926677C211yesmaximal, characteristic, complemented
10C22⋊C8×D19C211yesmaximal, characteristic, complemented
11C19×#480C211yesmaximal, characteristic, complemented
12C2×D4×D19—21no—
13C2×D4×D19C2211yescharacteristic, complemented
14C22×D76—21no—
15C22×D76C2211yescharacteristic, complemented
16C22×C4×D19C2211yescharacteristic
17C19×#121C2211yescharacteristic
18C2×C4⋊C4×C19C2211yescharacteristic, complemented
19#10597385—21no—
20#10597384C2211yescharacteristic, complemented
21C2×#64525C2212yescomplemented
22#10597376C2211yescharacteristic
23C2×(C2×D19)⋊C4—21no—
24C2×D152C2212yescomplemented
25C2×C8×D19C2212yescomplemented
26#10597341—21no—
27#10597341—21no—
28#10597341C2212yes—
29#10597341C2211yescharacteristic, complemented
30#10597341C2212yescomplemented
31C4⋊C4×D19C2211yescharacteristic, complemented
32#10597330—21no—
33C22⋊C4×D19—21no—
34C19×#107C2212yescomplemented
35C19×#102C2212yescomplemented
36C19×C22⋊C8C2211yescharacteristic, complemented
37C22⋊(C19⋊C8)C2211yescharacteristic, complemented
38#10597278C2212yescomplemented
39(C2×D19)⋊C8C2212yescomplemented
40#10597266C2212yescomplemented
41#10597266C2212yescomplemented
42#10597264C2212yescomplemented
43C23×D19—21no—
44C23×D19—21no—
45C23×D19D411yescharacteristic
46C2×D4×C19—21no—
47C2×D4×C19C2311yescharacteristic
48C22×C4×C19—21no—
49C22×C4×C19C2311yescharacteristic
50C2×C22⋊D19—21no—
51C2×C22⋊D19—21no—
52C2×C22⋊D19—21no—
53C22×Dic19D411yescharacteristic
54D4×D19—42no—
55D4×D19—44no—
56C2×D76—22no—
57C2×D76—22no—
58C2×D76—21no—
59C2×D76—21no—
60C2×D76—42no—
61C2×D76—44no—
62C2×D76C2311yescharacteristic
63C2×D76C2312yes—
64C2×C4×D19—21no—
65C2×C4×D19—42no—
66C2×C4×D19D411yescharacteristic
67C2×C4×D19D411yescharacteristic
68C2×C4×D19C2311yescharacteristic
69C2×C4×D19C2311yescharacteristic
70C2×C8×C19C2312yes—
71C4⋊C4×C19—21no—
72C4⋊C4×C19C2312yes—
73C4⋊C4×C19C2311yescharacteristic
74C22⋊C4×C19—21no—
75C22⋊Dic19—21no—
76#64525—42no—
77(C2×D19)⋊C4—21no—
78(C2×D19)⋊C4—21no—
79(C2×D19)⋊C4—22no—
80(C2×D19)⋊C4—22no—
81C4⋊Dic19C2311yescharacteristic
82Dic19⋊C4—21no—
83C2×C19⋊C8C2312yes—
84D152—42no—
85C8×D19—42no—
86C23×C19—21no—
87C23×C19C2×D411yescharacteristic
88C22×D19—22no—
89C22×D19—21no—
90C22×D19—41no—
91C22×D19—41no—
92C22×D19—42no—
93C22×D19—42no—
94C22×D19—42no—
95C22×D19—42no—
96C22×D19—42no—
97C22×D19—42no—
98C22×D19D814yescomplemented
99C22×D19C2×D411yescharacteristic
100C22×D19C2×D411yescharacteristic
101D4×C19—22no—
102D4×C19—42no—
103C2×C4×C19—22no—
104C2×C4×C19—21no—
105C2×C4×C19—22no—
106C2×C4×C19—42no—
107C2×C4×C19C2×D411yescharacteristic
108C2×C4×C19C2411yescharacteristic
109C22⋊D19—42no—
110C22⋊D19—42no—
111C22⋊D19—42no—
112C2×Dic19—21no—
113C2×Dic19—41no—
114C2×Dic19C2×D411yescharacteristic
115C2×Dic19C2×D411yescharacteristic
116D76—22no—
117D76—22no—
118D76—22no—
119D76—42no—
120D76—44no—
121D76—44no—
122D76—42no—
123C4×D19—22no—
124C4×D19—22no—
125C4×D19—41no—
126C4×D19—41no—
127C4×D19—42no—
128C8×C19—22no—
129C19⋊C8—22no—
130#3186—191nomaximal, Sylow
131C22×C19—21no—
132C22×C19—21no—
133C22×C19—41no—
134C22×C19—41no—
135C22×C19—41no—
136C22×C19C2×D812yes—
137C22×C19C22×D411yescharacteristic
138C2×D19—21no—
139C2×D19—21no—
140C2×D19—21no—
141C2×D19—21no—
142C2×D19—44no—
143C2×D19—42no—
144C2×D19—41no—
145C2×D19—42no—
146C2×D19—41no—
147C2×D19—42no—
148C2×D19—41no—
149C2×D19—84no—
150C2×D19—84no—
151C2×D19C2×D812yes—
152C2×D19C2×D812yes—
153C4×C19—21no—
154C4×C19—41no—
155C4×C19—42no—
156C4×C19H(5,𝔽2)12yes—
157Dic19—21no—
158Dic19—21no—
159Dic19—41no—
160C2×#121—191no—
161C2×#121—191no—
162#480—191no—
163#480—192no—
164#480D1911yescharacteristic, complemented
165#466—192no—
166#466—192no—
167#447—191no—
168#447—192no—
169#447—191no—
170C2×C22⋊C8—191no—
171C2×C19—22no—
172C2×C19—81no—
173C2×C19#53411yescharacteristic
174C2×C19C22×D811yescharacteristic
175C2×C19#57511yescharacteristic
176D19—22no—
177D19—22no—
178D19—82no—
179D19—81no—
180C22×D4—191no—
181C22×D4—191no—
182C22×D4—381no—
183C22×D4—381no—
184C23×C4—191no—
185C2×D8—192no—
186C2×D8—192no—
187C22×C8—192no—
188#121—191no—
189#121—191no—
190#121—192no—
191#121—191no—
192#121—192no—
193#121—381no—
194#121—381no—
195#121—381no—
196#121—381no—
197#121C2×D1911yescharacteristic
198C2×C4⋊C4—191no—
199C2×C4⋊C4C2×D1911yescharacteristic, complemented
200C2×C22⋊C4—381no—
201C2×C22⋊C4—381no—
202#107—192no—
203#107C2×D1912yescomplemented
204#102—192no—
205#102—192no—
206#102—192no—
207#102C2×D1912yescomplemented
208C22⋊C8—191no—
209C22⋊C8—192no—
210C22⋊C8C2×D1911yescharacteristic, complemented
211C19#318611yescharacteristic, complemented, Sylow
212C24—191no—
213C24—381no—
214C24—381no—
215C2×D4—21no—
216C2×D4—191no—
217C2×D4—192no—
218C2×D4—381no—
219C2×D4—382no—
220C2×D4—382no—
221C2×D4—381no—
222C2×D4—381no—
223C2×D4—381no—
224C2×D4—381no—
225C2×D4—762no—
226C2×D4—764no—
227C2×D4—762no—
228C2×D4—764no—
229C2×D4C22×D1911yescharacteristic
230C22×C4—21no—
231C22×C4—191no—
232C22×C4—191no—
233C22×C4—191no—
234C22×C4—191no—
235C22×C4—191no—
236C22×C4—381no—
237C22×C4—762no—
238C22×C4C22×D1911yescharacteristic
239D8—762no—
240D8—762no—
241C2×C8—192no—
242C2×C8—762no—
243C2×C8C22×D1912yes—
244C4⋊C4—21no—
245C4⋊C4—191no—
246C4⋊C4—381no—
247C4⋊C4C22×D1911yescharacteristic
248C4⋊C4C22×D1912yes—
249C22⋊C4—21no—
250C22⋊C4—381no—
251C22⋊C4—382no—
252C22⋊C4—382no—
253C22⋊C4—381no—
254C22⋊C4—381no—
255C23—21no—
256C23—191no—
257C23—191no—
258C23—194no—
259C23—382no—
260C23—381no—
261C23—761no—
262C23—761no—
263C23—762no—
264C23—762no—
265C23—762no—
266C23—762no—
267C23—762no—
268C23—762no—
269C23D4×D1911yescharacteristic
270D4—22no—
271D4—42no—
272D4—382no—
273D4—382no—
274D4—382no—
275D4—762no—
276D4—764no—
277D4—764no—
278D4—762no—
279D4—762no—
280D4—762no—
281D4—762no—
282C2×C4—22no—
283C2×C4—21no—
284C2×C4—22no—
285C2×C4—42no—
286C2×C4—191no—
287C2×C4—191no—
288C2×C4—382no—
289C2×C4—382no—
290C2×C4—381no—
291C2×C4—761no—
292C2×C4—761no—
293C2×C4—762no—
294C2×C4—761no—
295C2×C4D4×D1911yescharacteristic
296C2×C4C23×D1911yescharacteristic
297C8—22no—
298C8—382no—
299C22—21no—
300C22—21no—
301C22—41no—
302C22—41no—
303C22—41no—
304C22—192no—
305C22—192no—
306C22—381no—
307C22—381no—
308C22—381no—
309C22—381no—
310C22—764no—
311C22—762no—
312C22—761no—
313C22—762no—
314C22—761no—
315C22—762no—
316C22—761no—
317C22—1524no—
318C22—1524no—
319C22D8×D1912yes—
320C22C2×D4×D1911yescharacteristic
321C4—21no—
322C4—42no—
323C4—41no—
324C4—381no—
325C4—381no—
326C4—761no—
327C4#1059743512yes—
328C2—22no—
329C2—81no—
330C2—382no—
331C2—382no—
332C2—1522no—
333C2—1521no—
334C2#1192710511yescharacteristic
335C2C2×D8×D1911yescharacteristic
336C2#1192734311yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#480C2
socleC22×C19C22×D4
hypercenter#480D19
hypocenterC19#3186
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
1. C2×#10597341C2semidirect
2. #121×D19C2semidirect
3. #11926859C2semidirect
4. #11926857C2semidirect
5. #11926781C2semidirect
6. #11926779C2semidirect
7. #11926680C2semidirect
8. #11926679C2semidirect
9. #11926677C2semidirect
10. C22⋊C8×D19C2semidirect
11. C19×#480C2semidirect
13. C2×D4×D19C22semidirect
15. C22×D76C22semidirect
18. C2×C4⋊C4×C19C22semidirect
20. #10597384C22semidirect
21. C2×#64525C22semidirect
24. C2×D152C22semidirect
25. C2×C8×D19C22semidirect
29. #10597341C22semidirect
30. #10597341C22semidirect
31. C4⋊C4×D19C22semidirect
34. C19×#107C22semidirect
35. C19×#102C22semidirect
36. C19×C22⋊C8C22semidirect
37. C22⋊(C19⋊C8)C22semidirect
38. #10597278C22semidirect
39. (C2×D19)⋊C8C22semidirect
40. #10597266C22semidirect
41. #10597266C22semidirect
42. #10597264C22semidirect
98. C22×D19D8semidirect
164. #480D19semidirect
199. C2×C4⋊C4C2×D19semidirect
203. #107C2×D19semidirect
207. #102C2×D19semidirect
210. C22⋊C8C2×D19semidirect
211. C19#3186semidirect

Maximal subgroups

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

subgroupindex
C2×#105973412
#121×D192
#119268592
#119268572
#119267812
#119267792
#119266802
#119266792
#119266772
C22⋊C8×D192
C19×#4802
#318619