Finite Group Databasebeta

← #14575245

Subgroups — #14575245

Order 2432.

520 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 129 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#11927189C212yesmaximal, complemented
3#11926928C211yesmaximal, characteristic, complemented
4#11926791C212yesmaximal, complemented
5#11926759C212yesmaximal, complemented
6#11926707C212yesmaximal, complemented
7#11926679C212yesmaximal, complemented
8#11926623C211yesmaximal, characteristic, complemented
9C4×D8×C19C211yesmaximal, characteristic, complemented
10C2×#64543C2212yes—
11C2×D4×D19C2212yescomplemented
12C2×D8×C19C2211yescharacteristic
13C4×D4×C19C2212yescomplemented
14C2×#64526C2212yescomplemented
15C2×#64525C2212yes—
16#10597376—22no—
17C2×(C2×D19)⋊C4—22no—
18#10597357—28no—
19C2×Dic76C2211yescharacteristic, complemented
20C2×D152C2211yescharacteristic
21C2×#64516C2212yescomplemented
22C2×#64515C2212yescomplemented
23#10597343C2212yescomplemented
24#10597341C2212yes—
25#10597332—22no—
26#10597328—22no—
27#10597321C2212yescomplemented
28C4×D76C2211yescharacteristic
29C19×#107C2211yescharacteristic, complemented
30C19×#102C2212yescomplemented
31C4×C8×C19C2211yescharacteristic, complemented
32(C2×D19)⋊C8C2212yescomplemented
33#10597267C2212yescomplemented
34#10597266C2212yescomplemented
35C4⋊(C19⋊C8)C2211yescharacteristic, complemented
36C23×D19—22no—
37C2×D4×C19C2312yes—
38C22×C4×C19—22no—
39C2×C22⋊D19—22no—
40C2×C22⋊D19—22no—
41C22×Dic19—22no—
42#64543—24no—
43#64543—42no—
44D4×D19—24no—
45D4×D19—42no—
46C2×D76—22no—
47C2×D76D411yescharacteristic
48C2×D76C2312yes—
49C2×C4×D19C2312yes—
50C2×Dic38C2312yes—
51D8×C19D414yescomplemented
52C2×C8×C19C2311yescharacteristic
53C2×C8×C19C2311yescharacteristic
54C4⋊C4×C19C2312yes—
55C22⋊C4×C19—22no—
56C42×C19C2311yescharacteristic
57#64526—24no—
58#64525—24no—
59(C2×D19)⋊C4—22no—
60(C2×D19)⋊C4—22no—
61(C2×D19)⋊C4—22no—
62(C2×D19)⋊C4—22no—
63(C2×D19)⋊C4D412yes—
64C4⋊Dic19—22no—
65C4⋊Dic19D411yescharacteristic
66C2×C19⋊C8C2312yes—
67Dic76—41no—
68D152—41no—
69#64516—24no—
70#64515—24no—
71C23×C19—22no—
72C22×D19—22no—
73C22×D19—44no—
74C22×D19—44no—
75C22×D19—82no—
76C22×D19C2×D412yes—
77D4×C19—22no—
78D4×C19C2×D414yes—
79C2×C4×C19—22no—
80C2×C4×C19—82no—
81C2×C4×C19C2×D411yescharacteristic
82C2×C4×C19C2×D411yescharacteristic
83C2×C4×C19C2411yescharacteristic
84C22⋊D19—44no—
85C22⋊D19—44no—
86C2×Dic19—22no—
87C2×Dic19—44no—
88C2×Dic19C2×D412yes—
89D76—22no—
90D76—22no—
91D76—41no—
92D76—82no—
93C4×D19—22no—
94C4×D19—22no—
95Dic38—22no—
96Dic38—22no—
97C8×C19—21no—
98C8×C19C2×D412yes—
99C19⋊C8—22no—
100#3273—191nomaximal, Sylow
101C22×C19—24no—
102C22×C19—42no—
103C22×C19—42no—
104C22×C19C22×D411yescharacteristic
105C2×D19—22no—
106C2×D19—22no—
107C2×D19—22no—
108C2×D19—42no—
109C2×D19—42no—
110C2×D19—42no—
111C2×D19—88no—
112C4×C19—21no—
113C4×C19—21no—
114C4×C19—42no—
115C4×C19C22×D411yescharacteristic
116C4×C19H(5,𝔽2)11yescharacteristic
117Dic19—22no—
118Dic19—42no—
119C2×AGL(1,ℤ/8)—192no—
120#546—192no—
121#495—191no—
122#468—192no—
123#463—192no—
124#452—192no—
125#447—192no—
126C4×D8D1911yescharacteristic, complemented
127#436—191no—
128C2×C19—44no—
129C2×C19D4211yescharacteristic
130C2×C19#57511yescharacteristic
131C2×C19#57611yescharacteristic
132D19—42no—
133D19—82no—
134C2×#41—192no—
135C22×D4—192no—
136AGL(1,ℤ/8)—388no—
137C2×Q16—191no—
138C2×SD16—192no—
139C2×SD16—192no—
140C2×D8—192no—
141C2×D8—191no—
142C2×D8C2×D1911yescharacteristic
143C2×M16—192no—
144#124—192no—
145#123—382no—
146C22⋊Q8—192no—
147#121—192no—
148#121—382no—
149#120—382no—
150C4×D4—191no—
151C4×D4C2×D1912yescomplemented
152C2×C22⋊C4—382no—
153#107C2×D1911yescharacteristic, complemented
154C4⋊C8—191no—
155#103—192no—
156#102—192no—
157#102C2×D1912yescomplemented
158C22⋊C8—192no—
159C4×C8C2×D1911yescharacteristic, complemented
160C19#327311yescharacteristic, complemented, Sylow
161C24—382no—
162#41—384no—
163#41—762no—
164C2×Q8—192no—
165C2×D4—191no—
166C2×D4—192no—
167C2×D4—382no—
168C2×D4—382no—
169C2×D4—384no—
170C2×D4—382no—
171C2×D4—762no—
172C2×D4C22×D1912yes—
173C22×C4—22no—
174C22×C4—192no—
175C22×C4—382no—
176Q16—761no—
177SD16—384no—
178SD16—384no—
179D8—384no—
180D8—761no—
181D8D7614yescomplemented
182M16—384no—
183C2×C8—192no—
184C2×C8C22×D1911yescharacteristic
185C2×C8C22×D1911yescharacteristic
186C4⋊C4—191no—
187C4⋊C4—382no—
188C4⋊C4C22×D1912yes—
189C22⋊C4—22no—
190C22⋊C4—192no—
191C22⋊C4—382no—
192C22⋊C4—382no—
193C22⋊C4—382no—
194C22⋊C4—382no—
195C42C22×D1911yescharacteristic
196C23—22no—
197C23—192no—
198C23—382no—
199C23—764no—
200C23—764no—
201C23—1522no—
202Q8—382no—
203Q8—382no—
204D4—22no—
205D4—382no—
206D4—382no—
207D4—761no—
208D4—764no—
209D4—764no—
210D4—1522no—
211D4C2×D7614yes—
212C2×C4—22no—
213C2×C4—82no—
214C2×C4—192no—
215C2×C4—382no—
216C2×C4—382no—
217C2×C4—382no—
218C2×C4—764no—
219C2×C4D4×D1911yescharacteristic
220C2×C4D4×D1911yescharacteristic
221C2×C4C23×D1911yescharacteristic
222C8—21no—
223C8—382no—
224C8C2×D7612yes—
225C22—24no—
226C22—42no—
227C22—42no—
228C22—382no—
229C22—382no—
230C22—382no—
231C22—762no—
232C22—762no—
233C22—762no—
234C22—1528no—
235C22C2×D4×D1911yescharacteristic
236C4—21no—
237C4—21no—
238C4—42no—
239C4—382no—
240C4—762no—
241C4C22×D7611yescharacteristic
242C4#1059743511yescharacteristic
243C2—44no—
244C2—762no—
245C2—1522no—
246C2D4×D7611yescharacteristic
247C2#1192734111yescharacteristic
248C2#1192734511yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC4×D8×C19C2
socleC22×C19C22×D4
hypercenterC4×D8D19
hypocenterC19#3273
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×#10597357C2semidirect
2. #11927189C2semidirect
3. #11926928C2semidirect
4. #11926791C2semidirect
5. #11926759C2semidirect
6. #11926707C2semidirect
7. #11926679C2semidirect
8. #11926623C2semidirect
9. C4×D8×C19C2semidirect
11. C2×D4×D19C22semidirect
13. C4×D4×C19C22semidirect
14. C2×#64526C22semidirect
19. C2×Dic76C22semidirect
21. C2×#64516C22semidirect
22. C2×#64515C22semidirect
23. #10597343C22semidirect
27. #10597321C22semidirect
29. C19×#107C22semidirect
30. C19×#102C22semidirect
31. C4×C8×C19C22semidirect
32. (C2×D19)⋊C8C22semidirect
33. #10597267C22semidirect
34. #10597266C22semidirect
35. C4⋊(C19⋊C8)C22semidirect
51. D8×C19D4semidirect
126. C4×D8D19semidirect
151. C4×D4C2×D19semidirect
153. #107C2×D19semidirect
157. #102C2×D19semidirect
159. C4×C8C2×D19semidirect
160. C19#3273semidirect
181. D8D76semidirect

Maximal subgroups

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

subgroupindex
C2×#105973572
#119271892
#119269282
#119267912
#119267592
#119267072
#119266792
#119266232
C4×D8×C192
#327319