Finite Group Databasebeta

← #14575321

Subgroups — #14575321

Order 2432.

526 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 131 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×#10597358C211yesmaximal, characteristic, complemented
2C2×D8×D19C211yesmaximal, characteristic, complemented
3#11927189C212yesmaximal, complemented
4#11926928C211yesmaximal, characteristic, complemented
5#11926786C211yesmaximal, characteristic, complemented
6#11926781C211yesmaximal, characteristic, complemented
7#11926759C212yesmaximal, complemented
8#11926696C212yesmaximal, complemented
9#11926690C212yesmaximal, complemented
10C8×D76C211yesmaximal, characteristic, complemented
11C4×D8×C19C211yesmaximal, characteristic, complemented
12C2×#64543C2212yescomplemented
13C2×D4×D19C2212yes—
14C2×D8×C19C2211yescharacteristic
15C4×D4×C19C2212yescomplemented
16C2×#64526C2212yescomplemented
17C2×#64525C2212yes—
18#10597376—22no—
19C2×(C2×D19)⋊C4—22no—
20#10597358—24no—
21D8×D19—24no—
22C2×Dic76C2211yescharacteristic, complemented
23C2×D152C2211yescharacteristic
24C2×#64516C2212yescomplemented
25C2×C8×D19C2211yescharacteristic
26C2×C8×D19C2211yescharacteristic, complemented
27#10597343C2212yes—
28#10597341C2212yescomplemented
29#10597332—22no—
30#10597328—22no—
31#10597321C2212yescomplemented
32C4×D76C2211yescharacteristic
33C19×#107C2211yescharacteristic, complemented
34C19×#102C2212yescomplemented
35C4×C8×C19C2211yescharacteristic, complemented
36(C2×D19)⋊C8C2211yescharacteristic
37(C2×D19)⋊C8C2211yescharacteristic, complemented
38#10597267C2212yescomplemented
39#10597266C2212yescomplemented
40C4⋊(C19⋊C8)C2211yescharacteristic, complemented
41C23×D19—22no—
42C2×D4×C19C2312yes—
43C22×C4×C19—22no—
44C2×C22⋊D19—22no—
45C2×C22⋊D19—22no—
46C22×Dic19—22no—
47#64543—24no—
48#64543—42no—
49D4×D19—24no—
50D4×D19—42no—
51C2×D76—22no—
52C2×D76D411yescharacteristic
53C2×D76C2312yes—
54C2×C4×D19C2311yescharacteristic
55C2×C4×D19C2311yescharacteristic
56C2×Dic38C2312yes—
57D8×C19D414yescomplemented
58C2×C8×C19C2311yescharacteristic
59C2×C8×C19C2311yescharacteristic
60C4⋊C4×C19C2312yes—
61C22⋊C4×C19—22no—
62C42×C19C2311yescharacteristic
63#64526—24no—
64#64525—24no—
65(C2×D19)⋊C4—22no—
66(C2×D19)⋊C4—22no—
67(C2×D19)⋊C4—22no—
68(C2×D19)⋊C4—22no—
69(C2×D19)⋊C4D411yescharacteristic
70(C2×D19)⋊C4D411yescharacteristic
71C4⋊Dic19—22no—
72C4⋊Dic19D411yescharacteristic
73C2×C19⋊C8C2311yescharacteristic
74C2×C19⋊C8C2311yescharacteristic
75Dic76—22no—
76D152—22no—
77#64516—42no—
78C8×D19—22no—
79C8×D19—22no—
80C23×C19—22no—
81C22×D19—22no—
82C22×D19—44no—
83C22×D19—44no—
84C22×D19—82no—
85C22×D19C2×D411yescharacteristic
86C22×D19C2×D411yescharacteristic
87D4×C19—22no—
88D4×C19C2×D414yes—
89C2×C4×C19—22no—
90C2×C4×C19—82no—
91C2×C4×C19C2×D411yescharacteristic
92C2×C4×C19C2×D411yescharacteristic
93C2×C4×C19C2411yescharacteristic
94C22⋊D19—44no—
95C22⋊D19—44no—
96C2×Dic19—22no—
97C2×Dic19—44no—
98C2×Dic19C2×D411yescharacteristic
99C2×Dic19C2×D411yescharacteristic
100D76—22no—
101D76—22no—
102D76—22no—
103D76—82no—
104C4×D19—21no—
105C4×D19—21no—
106C4×D19—21no—
107C4×D19—21no—
108Dic38—22no—
109Dic38—22no—
110C8×C19—21no—
111C8×C19C2×D412yes—
112C19⋊C8—21no—
113C19⋊C8—21no—
114#3280—191nomaximal, Sylow
115C22×C19—24no—
116C22×C19—42no—
117C22×C19—42no—
118C22×C19C22×D411yescharacteristic
119C2×D19—21no—
120C2×D19—21no—
121C2×D19—21no—
122C2×D19—21no—
123C2×D19—21no—
124C2×D19—42no—
125C2×D19—42no—
126C2×D19—42no—
127C2×D19—88no—
128C2×D19#13512yescomplemented
129C4×C19—21no—
130C4×C19—21no—
131C4×C19—42no—
132C4×C19C22×D411yescharacteristic
133C4×C19H(5,𝔽2)11yescharacteristic
134Dic19—21no—
135Dic19—21no—
136Dic19—42no—
137C2×#135—191no—
138C22×D8—191no—
139#546—192no—
140#495—191no—
141#467—191no—
142#466—191no—
143#463—192no—
144#450—192no—
145#449—192no—
146C4×D8D1911yescharacteristic, complemented
147C8×D4—191no—
148C2×C19—44no—
149C2×C19D4211yescharacteristic
150C2×C19C2×#13511yescharacteristic
151C2×C19#57611yescharacteristic
152D19—22no—
153D19—41no—
154D19—82no—
155C2×#41—192no—
156C22×D4—192no—
157#135—384no—
158C2×Q16—191no—
159C2×SD16—192no—
160C2×SD16—192no—
161C2×D8—192no—
162C2×D8—191no—
163C2×D8—384no—
164C2×D8C2×D1911yescharacteristic
165C22×C8—191no—
166C22×C8—191no—
167#124—192no—
168#123—382no—
169C22⋊Q8—192no—
170#121—192no—
171#121—382no—
172#120—382no—
173C4×D4—191no—
174C4×D4C2×D1912yescomplemented
175C2×C22⋊C4—382no—
176#107C2×D1911yescharacteristic, complemented
177C4⋊C8—191no—
178#103—192no—
179#102—192no—
180#102C2×D1912yescomplemented
181C22⋊C8—191no—
182C22⋊C8—191no—
183C4×C8C2×D1911yescharacteristic, complemented
184C19#328011yescharacteristic, complemented, Sylow
185C24—382no—
186#41—384no—
187#41—762no—
188C2×Q8—192no—
189C2×D4—191no—
190C2×D4—192no—
191C2×D4—382no—
192C2×D4—382no—
193C2×D4—384no—
194C2×D4—382no—
195C2×D4—762no—
196C2×D4C22×D1912yes—
197C22×C4—22no—
198C22×C4—191no—
199C22×C4—191no—
200C22×C4—382no—
201Q16—382no—
202SD16—384no—
203SD16—762no—
204D8—384no—
205D8—382no—
206D8D7614yescomplemented
207C2×C8—191no—
208C2×C8—191no—
209C2×C8—382no—
210C2×C8—382no—
211C2×C8C22×D1911yescharacteristic
212C2×C8C22×D1911yescharacteristic
213C4⋊C4—191no—
214C4⋊C4—382no—
215C4⋊C4C22×D1912yes—
216C22⋊C4—22no—
217C22⋊C4—191no—
218C22⋊C4—191no—
219C22⋊C4—382no—
220C22⋊C4—382no—
221C22⋊C4—382no—
222C22⋊C4—382no—
223C42C22×D1911yescharacteristic
224C23—22no—
225C23—191no—
226C23—191no—
227C23—382no—
228C23—764no—
229C23—764no—
230C23—1522no—
231Q8—382no—
232Q8—382no—
233D4—22no—
234D4—382no—
235D4—382no—
236D4—382no—
237D4—764no—
238D4—764no—
239D4—1522no—
240D4C2×D7614yes—
241C2×C4—22no—
242C2×C4—82no—
243C2×C4—191no—
244C2×C4—191no—
245C2×C4—381no—
246C2×C4—381no—
247C2×C4—381no—
248C2×C4—381no—
249C2×C4—382no—
250C2×C4—764no—
251C2×C4D4×D1911yescharacteristic
252C2×C4D4×D1911yescharacteristic
253C2×C4C23×D1911yescharacteristic
254C8—21no—
255C8—381no—
256C8—381no—
257C8C2×D7612yes—
258C22—24no—
259C22—42no—
260C22—42no—
261C22—192no—
262C22—381no—
263C22—381no—
264C22—381no—
265C22—381no—
266C22—381no—
267C22—762no—
268C22—762no—
269C22—762no—
270C22—1528no—
271C22C2×D4×D1911yescharacteristic
272C4—21no—
273C4—21no—
274C4—42no—
275C4—381no—
276C4—381no—
277C4—762no—
278C4C22×D7611yescharacteristic
279C4#1059743511yescharacteristic
280C2—44no—
281C2—382no—
282C2—761no—
283C2—1522no—
284C2D4×D7611yescharacteristic
285C2#135×D1911yescharacteristic
286C2#1192734511yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC4×D8×C19C2
socleC22×C19C22×D4
hypercenterC4×D8D19
hypocenterC19#3280
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. C2×#10597358C2semidirect
2. C2×D8×D19C2semidirect
3. #11927189C2semidirect
4. #11926928C2semidirect
5. #11926786C2semidirect
6. #11926781C2semidirect
7. #11926759C2semidirect
8. #11926696C2semidirect
9. #11926690C2semidirect
10. C8×D76C2semidirect
11. C4×D8×C19C2semidirect
12. C2×#64543C22semidirect
15. C4×D4×C19C22semidirect
16. C2×#64526C22semidirect
22. C2×Dic76C22semidirect
24. C2×#64516C22semidirect
26. C2×C8×D19C22semidirect
28. #10597341C22semidirect
31. #10597321C22semidirect
33. C19×#107C22semidirect
34. C19×#102C22semidirect
35. C4×C8×C19C22semidirect
37. (C2×D19)⋊C8C22semidirect
38. #10597267C22semidirect
39. #10597266C22semidirect
40. C4⋊(C19⋊C8)C22semidirect
57. D8×C19D4semidirect
128. C2×D19#135semidirect
146. C4×D8D19semidirect
174. C4×D4C2×D19semidirect
176. #107C2×D19semidirect
180. #102C2×D19semidirect
183. C4×C8C2×D19semidirect
184. C19#3280semidirect
206. D8D76semidirect

Maximal subgroups

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

subgroupindex
C2×#105973582
C2×D8×D192
#119271892
#119269282
#119267862
#119267812
#119267592
#119266962
#119266902
C8×D762
C4×D8×C192
#328019