Finite Group Databasebeta

← #34080910

Subgroups — #34080910

Order 19328.

476 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 125 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#23753017C212yesmaximal, complemented
2#23753014C212yesmaximal, complemented
3#23752589C211yesmaximal, characteristic, complemented
4#23752483C212yesmaximal, complemented
5#23752482C212yesmaximal, complemented
6#23752381C214yesmaximal, complemented
7#23752330C211yesmaximal, characteristic, complemented
8#443×C151C211yesmaximal, characteristic, complemented
9#18012785C2214yescomplemented
10#18012767—24no—
11#18012767C2214yescomplemented
12#18012766—24no—
13#18012764C2214yescomplemented
14#18012762—22no—
15#18012761—22no—
16#18012761C2211yescharacteristic
17C2×D1208—22no—
18C2×D1208C2212yescomplemented
19C2×D1208C2212yescomplemented
20D8×D151—22no—
21#18012745C2212yescomplemented
22#18012736C2212yescomplemented
23#18012675C2211yescharacteristic, complemented
24#18012667C2212yescomplemented
25#18012655C2214yescomplemented
26#135×C151C2211yescharacteristic
27#131×C151C2212yescomplemented
28#108×C151C2211yescharacteristic, complemented
29#104×C151C2212yescomplemented
30C4×C8×C151C2211yescharacteristic, complemented
31#14559005—24no—
32#14559004—24no—
33#14559004C2312yes—
34C2×D604—24no—
35C2×D604—42no—
36C2×D604C2314yes—
37D4×D151—24no—
38D4×D151—44no—
39Dic604D411yescharacteristic, complemented
40#14558993—24no—
41#14558993D412yescomplemented
42#14558991—24no—
43D1208—24no—
44D1208—22no—
45D1208—22no—
46D1208—22no—
47D1208—22no—
48D1208D411yescharacteristic, complemented
49#14558989—24no—
50#14558988C2312yes—
51#14558987—22no—
52C8×D151—22no—
53#41×C151C2312yes—
54Q16×C151D411yescharacteristic, complemented
55SD16×C151D412yescomplemented
56D8×C151D411yescharacteristic, complemented
57M16×C151—22no—
58M16×C151C2312yes—
59C2×C8×C151—22no—
60C2×C8×C151C2311yescharacteristic
61C2×C8×C151C2311yescharacteristic
62C42×C151C2311yescharacteristic
63C22×D151—24no—
64C22×D151—44no—
65Dic302C2×D412yes—
66D604—24no—
67D604—24no—
68D604—44no—
69D604—84no—
70D604C2×D412yes—
71C22⋊D151—22no—
72C22⋊D151—44no—
73C4×D151—22no—
74C4×D151—44no—
75C151⋊C8—22no—
76Q8×C151C2×D412yes—
77D4×C151—22no—
78D4×C151C2×D412yes—
79C2×C4×C151—21no—
80C2×C4×C151—22no—
81C2×C4×C151C2411yescharacteristic
82C8×C151—22no—
83C8×C151C2×D411yescharacteristic
84C8×C151C2×D411yescharacteristic
85C8×C151C2×D411yescharacteristic
86C8×C151C2×D411yescharacteristic
87C22×C151—22no—
88C22×C151H(5,𝔽2)11yescharacteristic
89C2×D151—22no—
90C2×D151—44no—
91C2×D151—84no—
92C2×D151—164no—
93C4×C151—22no—
94C4×C151—22no—
95C4×C151C22×D411yescharacteristic
96C4×C151C22×D411yescharacteristic
97Dic151—22no—
98C2×C151—21no—
99C2×C151—42no—
100C2×C151D4211yescharacteristic
101D151—42no—
102D151—84no—
103C151#329211yescharacteristic, complemented, Sylow
104#3292—1511nomaximal, Sylow
105#576—1512no—
106#576—1512no—
107#493—1511no—
108#472—1512no—
109#472—1512no—
110#453—1514no—
111#443—1511no—
112#443D15111yescharacteristic, complemented
113H(5,𝔽2)—1514no—
114AGL(1,ℤ/8)—3024no—
115AGL(1,ℤ/8)—3024no—
116AGL(1,ℤ/8)—1514no—
117AGL(1,ℤ/8)—1514no—
118#135—3022no—
119#135—3022no—
120#135—1511no—
121#135C2×D15111yescharacteristic
122C2×D8—3022no—
123C2×D8—3022no—
124C2×D8—1512no—
125C2×D8—1512no—
126#131—1512no—
127#131C2×D15112yescomplemented
128#127—1512no—
129#108—1511no—
130#108C2×D15111yescharacteristic, complemented
131#104—1512no—
132#104C2×D15112yescomplemented
133#100—1514no—
134C4×C8C2×D15111yescharacteristic, complemented
135#41—3024no—
136#41—3024no—
137#41—1512no—
138#41C22×D15112yes—
139C2×D4—3024no—
140C2×D4—3024no—
141C2×D4—6042no—
142C2×D4—6044no—
143C2×D4—1514no—
144Q16—1511no—
145Q16D60411yescharacteristic, complemented
146SD16—3024no—
147SD16—3024no—
148SD16—1512no—
149SD16D60412yescomplemented
150D8—3024no—
151D8—3024no—
152D8—3022no—
153D8—3022no—
154D8—3022no—
155D8—3022no—
156D8—1511no—
157D8D60411yescharacteristic, complemented
158M16—22no—
159M16—3022no—
160M16—1512no—
161M16C22×D15112yes—
162C2×C8—22no—
163C2×C8—3022no—
164C2×C8C22×D15111yescharacteristic
165C2×C8C22×D15111yescharacteristic
166C42C22×D15111yescharacteristic
167C23—3024no—
168C23—6044no—
169Q8—1512no—
170Q8C2×D60412yes—
171D4—22no—
172D4—3022no—
173D4—3024no—
174D4—3024no—
175D4—6044no—
176D4—6044no—
177D4—1512no—
178D4—12084no—
179D4C2×D60412yes—
180C2×C4—21no—
181C2×C4—22no—
182C2×C4—3022no—
183C2×C4—6044no—
184C2×C4C23×D15111yescharacteristic
185C8—22no—
186C8—3022no—
187C8D4×D15111yescharacteristic
188C8D4×D15111yescharacteristic
189C8C2×D60411yescharacteristic
190C8C2×D60411yescharacteristic
191C22—22no—
192C22—3022no—
193C22—6044no—
194C22—24164no—
195C22—12084no—
196C22#1801278511yescharacteristic
197C4—22no—
198C4—22no—
199C4—3022no—
200C4C2×D4×D15111yescharacteristic
201C4C22×D60411yescharacteristic
202C2—21no—
203C2—42no—
204C2—6042no—
205C2—12084no—
206C2D4×D60411yescharacteristic
subgroupG/H
centerC2D4×D604
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#443×C151C2
socleC2×C151D42
hypercenter#443D151
hypocenterC151#3292
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2 ◁ C2×C4 ◁ #443

Complements

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

NH ≅ G/Ntype
1. #23753017C2semidirect
2. #23753014C2semidirect
3. #23752589C2semidirect
4. #23752483C2semidirect
5. #23752482C2semidirect
6. #23752381C2semidirect
7. #23752330C2semidirect
8. #443×C151C2semidirect
9. #18012785C22semidirect
11. #18012767C22semidirect
13. #18012764C22semidirect
18. C2×D1208C22semidirect
19. C2×D1208C22semidirect
21. #18012745C22semidirect
22. #18012736C22semidirect
23. #18012675C22semidirect
24. #18012667C22semidirect
25. #18012655C22semidirect
27. #131×C151C22semidirect
28. #108×C151C22semidirect
29. #104×C151C22semidirect
30. C4×C8×C151C22semidirect
39. Dic604D4semidirect
41. #14558993D4semidirect
48. D1208D4semidirect
54. Q16×C151D4semidirect
55. SD16×C151D4semidirect
56. D8×C151D4semidirect
103. C151#3292semidirect
112. #443D151semidirect
127. #131C2×D151semidirect
130. #108C2×D151semidirect
132. #104C2×D151semidirect
134. C4×C8C2×D151semidirect
145. Q16D604semidirect
149. SD16D604semidirect
157. D8D604semidirect

Maximal subgroups

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

subgroupindex
#237530172
#237530142
#237525892
#237524832
#237524822
#237523812
#237523302
#443×C1512
#3292151