Finite Group Databasebeta

← #34056491

Subgroups — #34056491

Order 19072.

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#23750430C212yesmaximal, complemented
2#23750427C212yesmaximal, complemented
3#23750002C211yesmaximal, characteristic, complemented
4#23749896C212yesmaximal, complemented
5#23749895C212yesmaximal, complemented
6#23749794C214yesmaximal, complemented
7#23749743C211yesmaximal, characteristic, complemented
8#443×C149C211yesmaximal, characteristic, complemented
9#18011957C2214yescomplemented
10#18011939—24no—
11#18011939C2214yescomplemented
12#18011938—24no—
13#18011936C2214yescomplemented
14#18011934—22no—
15#18011933—22no—
16#18011933C2211yescharacteristic
17C2×D1192—22no—
18C2×D1192C2212yescomplemented
19C2×D1192C2212yescomplemented
20D8×D149—22no—
21#18011917C2212yescomplemented
22#18011908C2212yescomplemented
23#18011847C2211yescharacteristic, complemented
24#18011839C2212yescomplemented
25#18011827C2214yescomplemented
26#135×C149C2211yescharacteristic
27#131×C149C2212yescomplemented
28#108×C149C2211yescharacteristic, complemented
29#104×C149C2212yescomplemented
30C4×C8×C149C2211yescharacteristic, complemented
31#14558737—24no—
32#14558736—24no—
33#14558736C2312yes—
34C2×D596—24no—
35C2×D596—42no—
36C2×D596C2314yes—
37D4×D149—24no—
38D4×D149—44no—
39Dic596D411yescharacteristic, complemented
40#14558725—24no—
41#14558725D412yescomplemented
42#14558723—24no—
43D1192—24no—
44D1192—22no—
45D1192—22no—
46D1192—22no—
47D1192—22no—
48D1192D411yescharacteristic, complemented
49#14558721—24no—
50#14558720C2312yes—
51#14558719—22no—
52C8×D149—22no—
53#41×C149C2312yes—
54Q16×C149D411yescharacteristic, complemented
55SD16×C149D412yescomplemented
56D8×C149D411yescharacteristic, complemented
57M16×C149—22no—
58M16×C149C2312yes—
59C2×C8×C149—22no—
60C2×C8×C149C2311yescharacteristic
61C2×C8×C149C2311yescharacteristic
62C42×C149C2311yescharacteristic
63C22×D149—24no—
64C22×D149—44no—
65Dic298C2×D412yes—
66D596—24no—
67D596—24no—
68D596—44no—
69D596—84no—
70D596C2×D412yes—
71C22⋊D149—22no—
72C22⋊D149—44no—
73C4×D149—22no—
74C4×D149—44no—
75#11924746—22no—
76Q8×C149C2×D412yes—
77D4×C149—22no—
78D4×C149C2×D412yes—
79C2×C4×C149—21no—
80C2×C4×C149—22no—
81C2×C4×C149C2411yescharacteristic
82C8×C149—22no—
83C8×C149C2×D411yescharacteristic
84C8×C149C2×D411yescharacteristic
85C8×C149C2×D411yescharacteristic
86C8×C149C2×D411yescharacteristic
87C22×C149—22no—
88C22×C149H(5,𝔽2)11yescharacteristic
89C2×D149—22no—
90C2×D149—44no—
91C2×D149—84no—
92C2×D149—164no—
93C4×C149—22no—
94C4×C149—22no—
95C4×C149C22×D411yescharacteristic
96C4×C149C22×D411yescharacteristic
97Dic149—22no—
98C2×C149—21no—
99C2×C149—42no—
100C2×C149D4211yescharacteristic
101D149—42no—
102D149—84no—
103C149#329211yescharacteristic, complemented, Sylow
104#3292—1491nomaximal, Sylow
105#576—1492no—
106#576—1492no—
107#493—1491no—
108#472—1492no—
109#472—1492no—
110#453—1494no—
111#443—1491no—
112#443D14911yescharacteristic, complemented
113H(5,𝔽2)—1494no—
114AGL(1,ℤ/8)—2984no—
115AGL(1,ℤ/8)—2984no—
116AGL(1,ℤ/8)—1494no—
117AGL(1,ℤ/8)—1494no—
118#135—2982no—
119#135—2982no—
120#135—1491no—
121#135C2×D14911yescharacteristic
122C2×D8—2982no—
123C2×D8—2982no—
124C2×D8—1492no—
125C2×D8—1492no—
126#131—1492no—
127#131C2×D14912yescomplemented
128#127—1492no—
129#108—1491no—
130#108C2×D14911yescharacteristic, complemented
131#104—1492no—
132#104C2×D14912yescomplemented
133#100—1494no—
134C4×C8C2×D14911yescharacteristic, complemented
135#41—2984no—
136#41—2984no—
137#41—1492no—
138#41C22×D14912yes—
139C2×D4—2984no—
140C2×D4—2984no—
141C2×D4—5962no—
142C2×D4—5964no—
143C2×D4—1494no—
144Q16—1491no—
145Q16D59611yescharacteristic, complemented
146SD16—2984no—
147SD16—2984no—
148SD16—1492no—
149SD16D59612yescomplemented
150D8—2984no—
151D8—2984no—
152D8—2982no—
153D8—2982no—
154D8—2982no—
155D8—2982no—
156D8—1491no—
157D8D59611yescharacteristic, complemented
158M16—22no—
159M16—2982no—
160M16—1492no—
161M16C22×D14912yes—
162C2×C8—22no—
163C2×C8—2982no—
164C2×C8C22×D14911yescharacteristic
165C2×C8C22×D14911yescharacteristic
166C42C22×D14911yescharacteristic
167C23—2984no—
168C23—5964no—
169Q8—1492no—
170Q8C2×D59612yes—
171D4—22no—
172D4—2982no—
173D4—2984no—
174D4—2984no—
175D4—5964no—
176D4—5964no—
177D4—1492no—
178D4—11924no—
179D4C2×D59612yes—
180C2×C4—21no—
181C2×C4—22no—
182C2×C4—2982no—
183C2×C4—5964no—
184C2×C4C23×D14911yescharacteristic
185C8—22no—
186C8—2982no—
187C8D4×D14911yescharacteristic
188C8D4×D14911yescharacteristic
189C8C2×D59611yescharacteristic
190C8C2×D59611yescharacteristic
191C22—22no—
192C22—2982no—
193C22—23844no—
194C22—5964no—
195C22—11924no—
196C22#1801195711yescharacteristic
197C4—22no—
198C4—22no—
199C4—2982no—
200C4C2×D4×D14911yescharacteristic
201C4C22×D59611yescharacteristic
202C2—21no—
203C2—42no—
204C2—5962no—
205C2—11924no—
206C2D4×D59611yescharacteristic
subgroupG/H
centerC2D4×D596
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#443×C149C2
socleC2×C149D42
hypercenter#443D149
hypocenterC149#3292
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C2×C4 ◁ #443

Complements

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

NH ≅ G/Ntype
1. #23750430C2semidirect
2. #23750427C2semidirect
3. #23750002C2semidirect
4. #23749896C2semidirect
5. #23749895C2semidirect
6. #23749794C2semidirect
7. #23749743C2semidirect
8. #443×C149C2semidirect
9. #18011957C22semidirect
11. #18011939C22semidirect
13. #18011936C22semidirect
18. C2×D1192C22semidirect
19. C2×D1192C22semidirect
21. #18011917C22semidirect
22. #18011908C22semidirect
23. #18011847C22semidirect
24. #18011839C22semidirect
25. #18011827C22semidirect
27. #131×C149C22semidirect
28. #108×C149C22semidirect
29. #104×C149C22semidirect
30. C4×C8×C149C22semidirect
39. Dic596D4semidirect
41. #14558725D4semidirect
48. D1192D4semidirect
54. Q16×C149D4semidirect
55. SD16×C149D4semidirect
56. D8×C149D4semidirect
103. C149#3292semidirect
112. #443D149semidirect
127. #131C2×D149semidirect
130. #108C2×D149semidirect
132. #104C2×D149semidirect
134. C4×C8C2×D149semidirect
145. Q16D596semidirect
149. SD16D596semidirect
157. D8D596semidirect

Maximal subgroups

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

subgroupindex
#237504302
#237504272
#237500022
#237498962
#237498952
#237497942
#237497432
#443×C1492
#3292149