Finite Group Databasebeta

← D19×#508 #14576749

Subgroups — D19×#508 #14576749

Order 2432.

368 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 115 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
1#135×D19C212yesmaximal, complemented
2#11926977C211yesmaximal, characteristic, complemented
3#11926976C211yesmaximal, characteristic, complemented
4#11926975C212yesmaximal, complemented
5#11926974C212yesmaximal, complemented
6#11926973C211yesmaximal, characteristic, complemented
7Q32×D19C211yesmaximal, characteristic, complemented
8SD32×D19C212yesmaximal, complemented
9D16×D19C211yesmaximal, characteristic, complemented
10C2×C16×D19C211yesmaximal, characteristic, complemented
11C19×#508C211yesmaximal, characteristic, complemented
12#41×D19—22no—
13C19×#135C2212yescomplemented
14#10597396—22no—
15#10597365C2212yescomplemented
16Q16×D19C2212yes—
17#10597362—22no—
18SD16×D19—22no—
19#10597358C2212yescomplemented
20D8×D19C2212yes—
21#10597350C2212yescomplemented
22C2×C8×D19C2211yescharacteristic
23C19×Q32C2211yescharacteristic, complemented
24C19×SD32C2212yescomplemented
25C19×D16C2211yescharacteristic, complemented
26C2×C16×C19C2211yescharacteristic, complemented
27#10597286C2212yescomplemented
28#10597285C2212yescomplemented
29#10597284C2212yescomplemented
30#10597283C2212yescomplemented
31C2×C19⋊C16C2211yescharacteristic, complemented
32Dic152C2211yescharacteristic, complemented
33#10597257C2212yescomplemented
34D304C2211yescharacteristic, complemented
35C16×D19C2211yescharacteristic
36C16×D19C2211yescharacteristic
37C16×D19C2211yescharacteristic, complemented
38C16×D19C2211yescharacteristic, complemented
39#41×C19—22no—
40#64545—22no—
41Q8×D19—22no—
42#64543—22no—
43#64543—42no—
44D4×D19—22no—
45D4×D19—42no—
46#64541—22no—
47#64541—42no—
48C2×C4×D19—42no—
49C2×C4×D19D411yescharacteristic
50Q16×C19C2312yes—
51SD16×C19—22no—
52D8×C19C2312yes—
53C2×C8×C19C2311yescharacteristic
54#64528—22no—
55#64527—22no—
56#64526—22no—
57#64525—22no—
58C2×C19⋊C8D411yescharacteristic
59Dic76C2312yes—
60D152C2312yes—
61#64516—22no—
62C8×D19D411yescharacteristic
63C8×D19D411yescharacteristic
64C8×D19C2311yescharacteristic
65C8×D19C2311yescharacteristic
66C16×C19C2311yescharacteristic
67C16×C19C2311yescharacteristic
68C19⋊C16C2311yescharacteristic
69C19⋊C16C2311yescharacteristic
70C22×D19—42no—
71C22×D19D811yescharacteristic
72Q8×C19—22no—
73D4×C19—22no—
74D4×C19—42no—
75C2×C4×C19—42no—
76C2×C4×C19C2×D411yescharacteristic
77C22⋊D19—42no—
78C22⋊D19—42no—
79C22⋊D19—42no—
80C2×Dic19—42no—
81C2×Dic19D811yescharacteristic
82D76—22no—
83D76—42no—
84C4×D19—42no—
85C4×D19—42no—
86C4×D19—42no—
87C4×D19D811yescharacteristic
88C4×D19D811yescharacteristic
89C4×D19C2×D411yescharacteristic
90C4×D19C2×D411yescharacteristic
91Dic38—22no—
92Dic38—42no—
93C8×C19C2×D411yescharacteristic
94C8×C19C2411yescharacteristic
95C19⋊C8C2×D411yescharacteristic
96C19⋊C8C2×D411yescharacteristic
97C2×#508—191nomaximal, Sylow
98C22×C19—42no—
99C22×C19C2×D811yescharacteristic
100C2×D19—22no—
101C2×D19—42no—
102C2×D19—84no—
103C2×D19C2×D811yescharacteristic
104C2×D19C2×D811yescharacteristic
105C4×C19—42no—
106C4×C19C2×D811yescharacteristic
107C4×C19C22×D411yescharacteristic
108Dic19—42no—
109Dic19C2×D811yescharacteristic
110Dic19C2×D811yescharacteristic
111C2×#135—192no—
112#508—192no—
113#508—191no—
114#508—192no—
115#508—191no—
116#508—191no—
117#508D1911yescharacteristic, direct product factor
118C2×Q32—191no—
119C2×SD32—192no—
120C2×D16—191no—
121C22×C16—191no—
122C2×C19—21no—
123C2×C19—82no—
124C2×C19C22×D811yescharacteristic
125D19—21no—
126D19—82no—
127D19#50812yesdirect product factor
128C2×#41—382no—
129#135—192no—
130#135—192no—
131#135—192no—
132#135—382no—
133#135—382no—
134#135C2×D1912yescomplemented
135C2×Q16—192no—
136C2×SD16—382no—
137C2×D8—192no—
138C22×C8—191no—
139Q32—192no—
140Q32—191no—
141Q32C2×D1911yescharacteristic, complemented
142SD32—192no—
143SD32—192no—
144SD32—192no—
145SD32C2×D1912yescomplemented
146D16—192no—
147D16—191no—
148D16C2×D1911yescharacteristic, complemented
149C2×C16—191no—
150C2×C16—191no—
151C2×C16—191no—
152C2×C16—191no—
153C2×C16—191no—
154C2×C16C2×D1911yescharacteristic, complemented
155C19C2×#50811yescharacteristic, complemented, Sylow
156#41—22no—
157#41—382no—
158#41—382no—
159#41—382no—
160#41—762no—
161#41—762no—
162C2×Q8—382no—
163C2×D4—382no—
164C2×D4—762no—
165C22×C4—191no—
166C22×C4—762no—
167Q16—192no—
168Q16—382no—
169Q16C22×D1912yes—
170SD16—22no—
171SD16—382no—
172SD16—382no—
173SD16—382no—
174D8—192no—
175D8—382no—
176D8C22×D1912yes—
177C2×C8—191no—
178C2×C8—191no—
179C2×C8—191no—
180C2×C8—191no—
181C2×C8—191no—
182C2×C8C22×D1911yescharacteristic
183C16—191no—
184C16—191no—
185C16C22×D1911yescharacteristic
186C16C22×D1911yescharacteristic
187C23—191no—
188C23—762no—
189Q8—22no—
190Q8—382no—
191Q8—762no—
192D4—22no—
193D4—42no—
194D4—382no—
195D4—762no—
196D4—762no—
197D4—762no—
198D4—762no—
199C2×C4—42no—
200C2×C4—191no—
201C2×C4—191no—
202C2×C4—191no—
203C2×C4—191no—
204C2×C4—191no—
205C2×C4—762no—
206C2×C4—762no—
207C2×C4—762no—
208C2×C4—762no—
209C2×C4D4×D1911yescharacteristic
210C8—191no—
211C8—191no—
212C8D4×D1911yescharacteristic
213C8C23×D1911yescharacteristic
214C22—42no—
215C22—191no—
216C22—191no—
217C22—382no—
218C22—762no—
219C22—1524no—
220C22D8×D1911yescharacteristic
221C4—42no—
222C4—191no—
223C4—191no—
224C4—762no—
225C4D8×D1911yescharacteristic
226C4C2×D4×D1911yescharacteristic
227C2—21no—
228C2—82no—
229C2—192no—
230C2—381no—
231C2—1522no—
232C2C2×D8×D1911yescharacteristic
subgroupG/H
centerC4D8×D19
commutator, cosocleC8×C19C24
FrattiniC8C23×D19
FittingC19×#508C2
socleC2×C19C22×D8
hypercenter#508D19
hypocenterC19C2×#508
LCSG ▷ C8×C19 ▷ C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×C8 ◁ #508

Complements

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

NH ≅ G/Ntype
1. #135×D19C2semidirect
2. #11926977C2semidirect
3. #11926976C2semidirect
4. #11926975C2semidirect
5. #11926974C2semidirect
6. #11926973C2semidirect
7. Q32×D19C2semidirect
8. SD32×D19C2semidirect
9. D16×D19C2semidirect
10. C2×C16×D19C2semidirect
11. C19×#508C2semidirect
13. C19×#135C22semidirect
15. #10597365C22semidirect
19. #10597358C22semidirect
21. #10597350C22semidirect
23. C19×Q32C22semidirect
24. C19×SD32C22semidirect
25. C19×D16C22semidirect
26. C2×C16×C19C22semidirect
27. #10597286C22semidirect
28. #10597285C22semidirect
29. #10597284C22semidirect
30. #10597283C22semidirect
31. C2×C19⋊C16C22semidirect
32. Dic152C22semidirect
33. #10597257C22semidirect
34. D304C22semidirect
37. C16×D19C22semidirect
38. C16×D19C22semidirect
117. #508D19direct (N × H)
127. D19#508direct (N × H)
134. #135C2×D19semidirect
141. Q32C2×D19semidirect
145. SD32C2×D19semidirect
148. D16C2×D19semidirect
154. C2×C16C2×D19semidirect
155. C19C2×#508semidirect

Maximal subgroups

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

subgroupindex
#135×D192
#119269772
#119269762
#119269752
#119269742
#119269732
Q32×D192
SD32×D192
D16×D192
C2×C16×D192
C19×#5082
C2×#50819