Finite Group Databasebeta

← #14575307

Subgroups — #14575307

Order 2432.

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

normal subgroups only

This group has 620 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×D8×D19C212yesmaximal, complemented
2D4×D76C211yesmaximal, characteristic, complemented
3#11927179C211yesmaximal, characteristic, complemented
4#11926920C211yesmaximal, characteristic, complemented
5#11926779C212yesmaximal, complemented
6#11926740C211yesmaximal, characteristic, complemented
7#11926679C212yesmaximal, complemented
8#11926676C212yesmaximal, complemented
9C4×#64525C211yesmaximal, characteristic, complemented
10#11926609C211yesmaximal, characteristic, complemented
11C19×#459C211yesmaximal, characteristic, complemented
12C2×D4×D19—21no—
13C2×D4×D19C2212yescomplemented
14C2×D4×D19C2212yescomplemented
15C22×D76—21no—
16C2×D8×C19C2212yescomplemented
17C19×#127C2211yescharacteristic, complemented
18C4×D4×C19C2211yescharacteristic, complemented
19#10597384—21no—
20#10597384C2212yescomplemented
21#10597383—22no—
22C2×#64525C2211yescharacteristic
23C2×#64525C2212yescomplemented
24C2×#64525C2212yescomplemented
25#10597376—21no—
26D8×D19—28no—
27C2×D152C2212yescomplemented
28C2×C8×D19C2212yescomplemented
29#10597341C2212yescomplemented
30#10597328—22no—
31#10597320C2211yescharacteristic, complemented
32C4×D76C2211yescharacteristic
33C4×D76C2211yescharacteristic, complemented
34C19×C4⋊C8C2211yescharacteristic, complemented
35C19×#102C2212yescomplemented
36#10597289C2211yescharacteristic, complemented
37#10597278C2212yescomplemented
38(C2×D19)⋊C8C2212yescomplemented
39#10597266C2211yescharacteristic, complemented
40#10597264C2211yescharacteristic, complemented
41C4×C19⋊C8C2211yescharacteristic, complemented
42C23×D19—22no—
43C23×D19—22no—
44C2×D4×C19—21no—
45C2×D4×C19—21no—
46C2×D4×C19C2312yes—
47C2×D4×C19C2311yescharacteristic
48C22×C4×C19—21no—
49C2×C22⋊D19—22no—
50C2×C22⋊D19—22no—
51C2×C22⋊D19—22no—
52D4×D19—24no—
53D4×D19—24no—
54D4×D19—42no—
55D4×D19—42no—
56D4×D19—44no—
57C2×D76—22no—
58C2×D76—21no—
59C2×D76—21no—
60C2×D76—44no—
61C2×D76D411yescharacteristic
62C2×D76C2312yes—
63C2×D76C2311yescharacteristic
64C2×C4×D19—21no—
65C2×C4×D19C2312yes—
66D8×C19—24no—
67C2×C8×C19C2312yes—
68C4⋊C4×C19C2311yescharacteristic
69C22⋊C4×C19—21no—
70C42×C19C2311yescharacteristic
71C22⋊Dic19—22no—
72#64525—24no—
73#64525—42no—
74#64525D414yescomplemented
75(C2×D19)⋊C4—21no—
76(C2×D19)⋊C4—22no—
77(C2×D19)⋊C4D412yes—
78C4⋊Dic19D411yescharacteristic
79C4⋊Dic19C2311yescharacteristic
80C2×C19⋊C8C2311yescharacteristic
81C2×C19⋊C8C2311yescharacteristic
82D152—24no—
83C8×D19—24no—
84C23×C19—21no—
85C23×C19—22no—
86C22×D19—21no—
87C22×D19—22no—
88C22×D19—44no—
89C22×D19—44no—
90C22×D19—44no—
91C22×D19—44no—
92C22×D19—82no—
93C22×D19—82no—
94C22×D19C2×D412yes—
95D4×C19—22no—
96D4×C19—21no—
97D4×C19—22no—
98D4×C19—42no—
99D4×C19—81no—
100D4×C19C2×D412yescomplemented
101C2×C4×C19—21no—
102C2×C4×C19—42no—
103C2×C4×C19C2×D411yescharacteristic
104C2×C4×C19C2×D411yescharacteristic
105C2×C4×C19C2411yescharacteristic
106C22⋊D19—44no—
107C22⋊D19—44no—
108C22⋊D19—44no—
109C2×Dic19—21no—
110C2×Dic19C2×D412yes—
111D76—22no—
112D76—21no—
113D76—22no—
114D76—44no—
115D76—42no—
116D76—81no—
117D76D814yescomplemented
118D76C2×D412yescomplemented
119C4×D19—22no—
120C4×D19—22no—
121C4×D19—42no—
122C8×C19—22no—
123C19⋊C8—21no—
124C19⋊C8C2×D412yescomplemented
125D4×D8—191nomaximal, Sylow
126C22×C19—22no—
127C22×C19—41no—
128C22×C19—41no—
129C22×C19—42no—
130C22×C19—42no—
131C22×C19—42no—
132C22×C19C22×D411yescharacteristic
133C2×D19—22no—
134C2×D19—22no—
135C2×D19—22no—
136C2×D19—41no—
137C2×D19—41no—
138C2×D19—42no—
139C2×D19—42no—
140C2×D19—42no—
141C2×D19—88no—
142C2×D19—88no—
143C2×D19C2×D814yescomplemented
144C4×C19—21no—
145C4×C19—41no—
146C4×C19C2×D812yescomplemented
147C4×C19C22×D411yescharacteristic
148C4×C19H(5,𝔽2)11yescharacteristic
149Dic19—22no—
150Dic19—41no—
151C22×D8—192no—
152D42—191no—
153D42—191no—
154#493—191no—
155#466—192no—
156#459—191no—
157#459D1911yescharacteristic, complemented
158#447—192no—
159#447—192no—
160C4×D8—191no—
161C8×D4—191no—
162C2×C19—42no—
163C2×C19—82no—
164C2×C19D4211yescharacteristic
165C2×C19C22×D811yescharacteristic
166C2×C19#57611yescharacteristic
167D19—24no—
168D19—42no—
169D19—82no—
170C22×D4—192no—
171C22×D4—192no—
172C22×D4—381no—
173C22×D4—381no—
174C2×D8—191no—
175C2×D8—192no—
176C2×D8—192no—
177C2×D8—192no—
178C2×D8—388no—
179C2×D8C2×D1912yescomplemented
180C22×C8—192no—
181#127—191no—
182#127C2×D1911yescharacteristic, complemented
183#121—192no—
184#121—192no—
185#121—381no—
186#121—381no—
187#120—382no—
188#120—382no—
189C4×D4—191no—
190C4×D4—191no—
191C4×D4C2×D1911yescharacteristic, complemented
192#107—191no—
193C4⋊C8C2×D1911yescharacteristic, complemented
194#102—191no—
195#102—192no—
196#102—191no—
197#102C2×D1912yescomplemented
198C22⋊C8—192no—
199C4×C8—191no—
200C19D4×D811yescharacteristic, complemented, Sylow
201C24—382no—
202C24—382no—
203C2×D4—21no—
204C2×D4—21no—
205C2×D4—191no—
206C2×D4—191no—
207C2×D4—192no—
208C2×D4—382no—
209C2×D4—382no—
210C2×D4—382no—
211C2×D4—384no—
212C2×D4—384no—
213C2×D4—382no—
214C2×D4—381no—
215C2×D4—381no—
216C2×D4—764no—
217C2×D4—762no—
218C2×D4—762no—
219C2×D4—764no—
220C2×D4C22×D1912yes—
221C2×D4C22×D1911yescharacteristic
222C22×C4—21no—
223C22×C4—192no—
224C22×C4—381no—
225D8—24no—
226D8—194no—
227D8—384no—
228D8—384no—
229D8—762no—
230C2×C8—191no—
231C2×C8—191no—
232C2×C8—384no—
233C2×C8C22×D1912yes—
234C4⋊C4—191no—
235C4⋊C4—191no—
236C4⋊C4C22×D1911yescharacteristic
237C22⋊C4—21no—
238C22⋊C4—192no—
239C22⋊C4—382no—
240C22⋊C4—382no—
241C22⋊C4—381no—
242C42C22×D1911yescharacteristic
243C23—21no—
244C23—22no—
245C23—192no—
246C23—381no—
247C23—382no—
248C23—764no—
249C23—764no—
250C23—764no—
251C23—764no—
252C23—1522no—
253C23—1522no—
254D4—22no—
255D4—21no—
256D4—22no—
257D4—42no—
258D4—81no—
259D4—192no—
260D4—194no—
261D4—382no—
262D4—381no—
263D4—382no—
264D4—764no—
265D4—764no—
266D4—764no—
267D4—764no—
268D4—762no—
269D4—1521no—
270D4D4×D1912yescomplemented
271C2×C4—21no—
272C2×C4—42no—
273C2×C4—192no—
274C2×C4—382no—
275C2×C4—382no—
276C2×C4—381no—
277C2×C4—762no—
278C2×C4D4×D1911yescharacteristic
279C2×C4D4×D1911yescharacteristic
280C2×C4C23×D1911yescharacteristic
281C8—22no—
282C8—192no—
283C8—381no—
284C22—22no—
285C22—41no—
286C22—41no—
287C22—42no—
288C22—42no—
289C22—42no—
290C22—194no—
291C22—382no—
292C22—382no—
293C22—382no—
294C22—761no—
295C22—761no—
296C22—762no—
297C22—762no—
298C22—762no—
299C22—1528no—
300C22—1528no—
301C22C2×D4×D1911yescharacteristic
302C4—21no—
303C4—41no—
304C4—382no—
305C4—761no—
306C4D8×D1912yescomplemented
307C4C2×D4×D1911yescharacteristic
308C4#1059743511yescharacteristic
309C2—42no—
310C2—82no—
311C2—384no—
312C2—762no—
313C2—1522no—
314C2#1192717811yescharacteristic
315C2C2×D8×D1911yescharacteristic
316C2#1192734811yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#459C2
socleC22×C19C22×D4
hypercenter#459D19
hypocenterC19D4×D8
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×D8×D19C2semidirect
2. D4×D76C2semidirect
3. #11927179C2semidirect
4. #11926920C2semidirect
5. #11926779C2semidirect
6. #11926740C2semidirect
7. #11926679C2semidirect
8. #11926676C2semidirect
9. C4×#64525C2semidirect
10. #11926609C2semidirect
11. C19×#459C2semidirect
13. C2×D4×D19C22semidirect
14. C2×D4×D19C22semidirect
16. C2×D8×C19C22semidirect
17. C19×#127C22semidirect
18. C4×D4×C19C22semidirect
20. #10597384C22semidirect
23. C2×#64525C22semidirect
24. C2×#64525C22semidirect
27. C2×D152C22semidirect
28. C2×C8×D19C22semidirect
29. #10597341C22semidirect
31. #10597320C22semidirect
33. C4×D76C22semidirect
34. C19×C4⋊C8C22semidirect
35. C19×#102C22semidirect
36. #10597289C22semidirect
37. #10597278C22semidirect
38. (C2×D19)⋊C8C22semidirect
39. #10597266C22semidirect
40. #10597264C22semidirect
41. C4×C19⋊C8C22semidirect
74. #64525D4semidirect
100. D4×C19C2×D4semidirect
117. D76D8semidirect
118. D76C2×D4semidirect
124. C19⋊C8C2×D4semidirect
143. C2×D19C2×D8semidirect
146. C4×C19C2×D8semidirect
157. #459D19semidirect
179. C2×D8C2×D19semidirect
182. #127C2×D19semidirect
191. C4×D4C2×D19semidirect
193. C4⋊C8C2×D19semidirect
197. #102C2×D19semidirect
200. C19D4×D8semidirect
270. D4D4×D19semidirect
306. C4D8×D19semidirect

Maximal subgroups

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

subgroupindex
C2×D8×D192
D4×D762
#119271792
#119269202
#119267792
#119267402
#119266792
#119266762
C4×#645252
#119266092
C19×#4592
D4×D819