Finite Group Databasebeta

← #14574384

Subgroups — #14574384

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×#10597384C211yesmaximal, characteristic, complemented
2#121×D19C211yesmaximal, characteristic, complemented
3#11926858C211yesmaximal, characteristic, complemented
4#11926856C212yesmaximal, complemented
5#11926855C211yesmaximal, characteristic, complemented
6#11926779C212yesmaximal, complemented
7#11926777C212yesmaximal, complemented
8#11926678C211yesmaximal, characteristic, complemented
9#11926676C212yesmaximal, complemented
10C22⋊C8×D19C211yesmaximal, characteristic, complemented
11C19×#447C211yesmaximal, characteristic, complemented
12C22×D4×C19C2211yescharacteristic, complemented
13C22×C22⋊D19—21no—
14C2×D4×D19—21no—
15C2×D4×D19C2211yescharacteristic, complemented
16C22×C4×D19C2211yescharacteristic
17C2×D8×C19C2212yescomplemented
18C19×#121C2211yescharacteristic
19C2×C22⋊Dic19—21no—
20#10597385—21no—
21#10597384—21no—
22#10597384—21no—
23#10597384C2212yes—
24#10597384C2211yescharacteristic, complemented
25#10597384C2212yescomplemented
26C2×#64525C2212yescomplemented
27#10597376C2211yescharacteristic
28C2×C4⋊Dic19C2211yescharacteristic, complemented
29C2×C8×D19C2212yescomplemented
30#10597341C2211yescharacteristic, complemented
31C4⋊C4×D19C2211yescharacteristic, complemented
32#10597330—21no—
33C22⋊C4×D19—21no—
34C19×#102C2212yescomplemented
35C19×C22⋊C8C2211yescharacteristic, complemented
36#10597289C2212yescomplemented
37#10597289C2212yescomplemented
38C22⋊(C19⋊C8)C2211yescharacteristic, complemented
39#10597278C2212yescomplemented
40(C2×D19)⋊C8C2212yescomplemented
41#10597275C2212yescomplemented
42#10597264C2212yescomplemented
43C24×C19—21no—
44C23×D19—21no—
45C23×D19D411yescharacteristic
46C2×D4×C19—21no—
47C2×D4×C19—21no—
48C2×D4×C19—42no—
49C2×D4×C19C2312yes—
50C2×D4×C19C2311yescharacteristic
51C22×C4×C19C2311yescharacteristic
52C2×C22⋊D19—21no—
53C2×C22⋊D19—22no—
54C2×C22⋊D19—22no—
55C2×C22⋊D19—21no—
56C2×C22⋊D19—21no—
57C2×C22⋊D19—44no—
58C22×Dic19—21no—
59C22×Dic19D411yescharacteristic
60D4×D19—42no—
61D4×D19—44no—
62C2×D76—21no—
63C2×D76C2311yescharacteristic
64C2×C4×D19—21no—
65C2×C4×D19—42no—
66C2×C4×D19D411yescharacteristic
67C2×C4×D19D411yescharacteristic
68C2×C4×D19C2311yescharacteristic
69C2×C4×D19C2311yescharacteristic
70D8×C19—42no—
71C2×C8×C19C2312yes—
72C4⋊C4×C19C2311yescharacteristic
73C22⋊C4×C19—21no—
74C22⋊Dic19—22no—
75C22⋊Dic19—22no—
76C22⋊Dic19—21no—
77#64525—42no—
78(C2×D19)⋊C4—21no—
79(C2×D19)⋊C4—21no—
80C4⋊Dic19—21no—
81C4⋊Dic19C2311yescharacteristic
82C4⋊Dic19C2312yes—
83Dic19⋊C4—21no—
84C2×C19⋊C8C2312yes—
85C8×D19—42no—
86C23×C19—22no—
87C23×C19—21no—
88C23×C19—42no—
89C23×C19—42no—
90C23×C19—42no—
91C23×C19C2×D411yescharacteristic
92C22×D19—21no—
93C22×D19—41no—
94C22×D19—41no—
95C22×D19—42no—
96C22×D19—42no—
97C22×D19—42no—
98C22×D19D814yescomplemented
99C22×D19C2×D411yescharacteristic
100C22×D19C2×D411yescharacteristic
101D4×C19—22no—
102D4×C19—22no—
103D4×C19—22no—
104D4×C19—42no—
105D4×C19—42no—
106C2×C4×C19—22no—
107C2×C4×C19—21no—
108C2×C4×C19C2×D411yescharacteristic
109C2×C4×C19C2411yescharacteristic
110C22⋊D19—42no—
111C22⋊D19—42no—
112C22⋊D19—42no—
113C22⋊D19—44no—
114C22⋊D19—44no—
115C2×Dic19—21no—
116C2×Dic19—22no—
117C2×Dic19—41no—
118C2×Dic19—42no—
119C2×Dic19C2×D411yescharacteristic
120C2×Dic19C2×D411yescharacteristic
121D76—22no—
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—42no—
135C22×C19—42no—
136C22×C19—41no—
137C22×C19—41no—
138C22×C19—42no—
139C22×C19—84no—
140C22×C19C2×D812yes—
141C22×C19C22×D411yescharacteristic
142C2×D19—21no—
143C2×D19—21no—
144C2×D19—21no—
145C2×D19—21no—
146C2×D19—44no—
147C2×D19—41no—
148C2×D19—41no—
149C2×D19—41no—
150C2×D19—84no—
151C2×D19C2×D812yes—
152C2×D19C2×D812yes—
153C4×C19—21no—
154C4×C19—41no—
155C4×C19H(5,𝔽2)12yes—
156Dic19—21no—
157Dic19—21no—
158Dic19—41no—
159Dic19—42no—
160C2×#121—191no—
161C2×#121—191no—
162#480—191no—
163#480—192no—
164#480—191no—
165#466—192no—
166#466—192no—
167#447—191no—
168#447—192no—
169#447D1911yescharacteristic, complemented
170C2×C22⋊C8—191no—
171C2×C19—22no—
172C2×C19—81no—
173C2×C19—82no—
174C2×C19#53411yescharacteristic
175C2×C19C22×D811yescharacteristic
176C2×C19#57511yescharacteristic
177D19—22no—
178D19—22no—
179D19—81no—
180C22×D4—191no—
181C22×D4—381no—
182C22×D4—381no—
183C22×D4C2×D1911yescharacteristic, complemented
184C23×C4—191no—
185C2×D8—192no—
186C2×D8C2×D1912yescomplemented
187C22×C8—192no—
188#121—192no—
189#121—191no—
190#121—192no—
191#121—191no—
192#121—191no—
193#121—381no—
194#121—381no—
195#121—381no—
196#121—381no—
197#121C2×D1911yescharacteristic
198C2×C4⋊C4—191no—
199C2×C4⋊C4—191no—
200C2×C22⋊C4—381no—
201C2×C22⋊C4—381no—
202#107—192no—
203#107—192no—
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—21no—
213C24—191no—
214C24—381no—
215C2×D4—21no—
216C2×D4—21no—
217C2×D4—42no—
218C2×D4—191no—
219C2×D4—381no—
220C2×D4—381no—
221C2×D4—381no—
222C2×D4—382no—
223C2×D4—382no—
224C2×D4—381no—
225C2×D4—762no—
226C2×D4—764no—
227C2×D4—764no—
228C2×D4C22×D1911yescharacteristic
229C2×D4C22×D1912yes—
230C22×C4—191no—
231C22×C4—191no—
232C22×C4—191no—
233C22×C4—191no—
234C22×C4—191no—
235C22×C4—381no—
236C22×C4—381no—
237C22×C4—762no—
238C22×C4C22×D1911yescharacteristic
239D8—42no—
240D8—762no—
241C2×C8—192no—
242C2×C8—762no—
243C2×C8C22×D1912yes—
244C4⋊C4—191no—
245C4⋊C4—192no—
246C4⋊C4—381no—
247C4⋊C4—381no—
248C4⋊C4C22×D1911yescharacteristic
249C22⋊C4—21no—
250C22⋊C4—381no—
251C22⋊C4—381no—
252C22⋊C4—382no—
253C22⋊C4—382no—
254C22⋊C4—381no—
255C23—21no—
256C23—22no—
257C23—42no—
258C23—42no—
259C23—42no—
260C23—191no—
261C23—191no—
262C23—194no—
263C23—381no—
264C23—761no—
265C23—761no—
266C23—762no—
267C23—762no—
268C23—762no—
269C23D4×D1911yescharacteristic
270D4—22no—
271D4—22no—
272D4—22no—
273D4—42no—
274D4—42no—
275D4—382no—
276D4—762no—
277D4—762no—
278D4—762no—
279D4—764no—
280D4—764no—
281D4—762no—
282C2×C4—22no—
283C2×C4—21no—
284C2×C4—191no—
285C2×C4—191no—
286C2×C4—382no—
287C2×C4—382no—
288C2×C4—382no—
289C2×C4—381no—
290C2×C4—761no—
291C2×C4—761no—
292C2×C4—762no—
293C2×C4—761no—
294C2×C4—762no—
295C2×C4D4×D1911yescharacteristic
296C2×C4C23×D1911yescharacteristic
297C8—22no—
298C8—382no—
299C22—21no—
300C22—21no—
301C22—41no—
302C22—42no—
303C22—42no—
304C22—41no—
305C22—42no—
306C22—41no—
307C22—84no—
308C22—192no—
309C22—192no—
310C22—381no—
311C22—381no—
312C22—381no—
313C22—381no—
314C22—764no—
315C22—761no—
316C22—761no—
317C22—761no—
318C22—1524no—
319C22D8×D1912yes—
320C22C2×D4×D1911yescharacteristic
321C4—21no—
322C4—41no—
323C4—381no—
324C4—381no—
325C4—761no—
326C4—762no—
327C4#1059743012yes—
328C2—22no—
329C2—82no—
330C2—81no—
331C2—382no—
332C2—382no—
333C2—1521no—
334C2#1192710411yescharacteristic
335C2C2×D8×D1911yescharacteristic
336C2#1192734011yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#447C2
socleC22×C19C22×D4
hypercenter#447D19
hypocenterC19#3186
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. C2×#10597384C2semidirect
2. #121×D19C2semidirect
3. #11926858C2semidirect
4. #11926856C2semidirect
5. #11926855C2semidirect
6. #11926779C2semidirect
7. #11926777C2semidirect
8. #11926678C2semidirect
9. #11926676C2semidirect
10. C22⋊C8×D19C2semidirect
11. C19×#447C2semidirect
12. C22×D4×C19C22semidirect
15. C2×D4×D19C22semidirect
17. C2×D8×C19C22semidirect
24. #10597384C22semidirect
25. #10597384C22semidirect
26. C2×#64525C22semidirect
28. C2×C4⋊Dic19C22semidirect
29. C2×C8×D19C22semidirect
30. #10597341C22semidirect
31. C4⋊C4×D19C22semidirect
34. C19×#102C22semidirect
35. C19×C22⋊C8C22semidirect
36. #10597289C22semidirect
37. #10597289C22semidirect
38. C22⋊(C19⋊C8)C22semidirect
39. #10597278C22semidirect
40. (C2×D19)⋊C8C22semidirect
41. #10597275C22semidirect
42. #10597264C22semidirect
98. C22×D19D8semidirect
169. #447D19semidirect
183. C22×D4C2×D19semidirect
186. C2×D8C2×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×#105973842
#121×D192
#119268582
#119268562
#119268552
#119267792
#119267772
#119266782
#119266762
C22⋊C8×D192
C19×#4472
#318619