Finite Group Databasebeta

← #49170585

Subgroups — #49170585

Order 37504.

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#34036934C212yesmaximal, complemented
2#34036931C212yesmaximal, complemented
3#34036506C211yesmaximal, characteristic, complemented
4#34036400C212yesmaximal, complemented
5#34036399C212yesmaximal, complemented
6#34036298C214yesmaximal, complemented
7#34036247C211yesmaximal, characteristic, complemented
8#443×C293C211yesmaximal, characteristic, complemented
9#22627670C2214yescomplemented
10#22627652—24no—
11#22627652C2214yescomplemented
12#22627651—24no—
13#22627649C2214yescomplemented
14#22627647—22no—
15#22627646—22no—
16#22627646C2211yescharacteristic
17C2×D2344—22no—
18C2×D2344C2212yescomplemented
19C2×D2344C2212yescomplemented
20D8×D293—22no—
21#22627630C2212yescomplemented
22#22627621C2212yescomplemented
23#22627560C2211yescharacteristic, complemented
24#22627552C2212yescomplemented
25#22627540C2214yescomplemented
26#135×C293C2211yescharacteristic
27#131×C293C2212yescomplemented
28#108×C293C2211yescharacteristic, complemented
29#104×C293C2212yescomplemented
30C4×C8×C293C2211yescharacteristic, complemented
31#17989803—24no—
32#17989802—24no—
33#17989802C2312yes—
34C2×D1172—24no—
35C2×D1172—42no—
36C2×D1172C2314yes—
37D4×D293—24no—
38D4×D293—44no—
39Dic1172D411yescharacteristic, complemented
40#17989791—24no—
41#17989791D412yescomplemented
42#17989789—24no—
43D2344—24no—
44D2344—22no—
45D2344—22no—
46D2344—22no—
47D2344—22no—
48D2344D411yescharacteristic, complemented
49#17989787—24no—
50#17989786C2312yes—
51#17989785—22no—
52C8×D293—22no—
53#41×C293C2312yes—
54Q16×C293D411yescharacteristic, complemented
55SD16×C293D412yescomplemented
56D8×C293D411yescharacteristic, complemented
57M16×C293—22no—
58M16×C293C2312yes—
59C2×C8×C293—22no—
60C2×C8×C293C2311yescharacteristic
61C2×C8×C293C2311yescharacteristic
62C42×C293C2311yescharacteristic
63C22×D293—24no—
64C22×D293—44no—
65Dic586C2×D412yes—
66D1172—24no—
67D1172—24no—
68D1172—44no—
69D1172—84no—
70D1172C2×D412yes—
71C22⋊D293—22no—
72C22⋊D293—44no—
73C4×D293—22no—
74C4×D293—44no—
75#14556873—22no—
76Q8×C293C2×D412yes—
77D4×C293—22no—
78D4×C293C2×D412yes—
79C2×C4×C293—21no—
80C2×C4×C293—22no—
81C2×C4×C293C2411yescharacteristic
82C8×C293—22no—
83C8×C293C2×D411yescharacteristic
84C8×C293C2×D411yescharacteristic
85C8×C293C2×D411yescharacteristic
86C8×C293C2×D411yescharacteristic
87C22×C293—22no—
88C22×C293H(5,𝔽2)11yescharacteristic
89C2×D293—22no—
90C2×D293—44no—
91C2×D293—84no—
92C2×D293—164no—
93C4×C293—22no—
94C4×C293—22no—
95C4×C293C22×D411yescharacteristic
96C4×C293C22×D411yescharacteristic
97Dic293—22no—
98C2×C293—21no—
99C2×C293—42no—
100C2×C293D4211yescharacteristic
101D293—42no—
102D293—84no—
103C293#329211yescharacteristic, complemented, Sylow
104#3292—2931nomaximal, Sylow
105#576—2932no—
106#576—2932no—
107#493—2931no—
108#472—2932no—
109#472—2932no—
110#453—2934no—
111#443—2931no—
112#443D29311yescharacteristic, complemented
113H(5,𝔽2)—2934no—
114AGL(1,ℤ/8)—2934no—
115AGL(1,ℤ/8)—2934no—
116AGL(1,ℤ/8)—5864no—
117AGL(1,ℤ/8)—5864no—
118#135—2931no—
119#135—5862no—
120#135—5862no—
121#135C2×D29311yescharacteristic
122C2×D8—2932no—
123C2×D8—2932no—
124C2×D8—5862no—
125C2×D8—5862no—
126#131—2932no—
127#131C2×D29312yescomplemented
128#127—2932no—
129#108—2931no—
130#108C2×D29311yescharacteristic, complemented
131#104—2932no—
132#104C2×D29312yescomplemented
133#100—2934no—
134C4×C8C2×D29311yescharacteristic, complemented
135#41—2932no—
136#41—5864no—
137#41—5864no—
138#41C22×D29312yes—
139C2×D4—2934no—
140C2×D4—5864no—
141C2×D4—5864no—
142C2×D4—11722no—
143C2×D4—11724no—
144Q16—2931no—
145Q16D117211yescharacteristic, complemented
146SD16—2932no—
147SD16—5864no—
148SD16—5864no—
149SD16D117212yescomplemented
150D8—2931no—
151D8—5864no—
152D8—5864no—
153D8—5862no—
154D8—5862no—
155D8—5862no—
156D8—5862no—
157D8D117211yescharacteristic, complemented
158M16—22no—
159M16—2932no—
160M16—5862no—
161M16C22×D29312yes—
162C2×C8—22no—
163C2×C8—5862no—
164C2×C8C22×D29311yescharacteristic
165C2×C8C22×D29311yescharacteristic
166C42C22×D29311yescharacteristic
167C23—5864no—
168C23—11724no—
169Q8—2932no—
170Q8C2×D117212yes—
171D4—22no—
172D4—2932no—
173D4—23444no—
174D4—5862no—
175D4—5864no—
176D4—5864no—
177D4—11724no—
178D4—11724no—
179D4C2×D117212yes—
180C2×C4—21no—
181C2×C4—22no—
182C2×C4—5862no—
183C2×C4—11724no—
184C2×C4C23×D29311yescharacteristic
185C8—22no—
186C8—5862no—
187C8D4×D29311yescharacteristic
188C8D4×D29311yescharacteristic
189C8C2×D117211yescharacteristic
190C8C2×D117211yescharacteristic
191C22—22no—
192C22—23444no—
193C22—5862no—
194C22—46884no—
195C22—11724no—
196C22#2262767011yescharacteristic
197C4—22no—
198C4—22no—
199C4—5862no—
200C4C2×D4×D29311yescharacteristic
201C4C22×D117211yescharacteristic
202C2—21no—
203C2—42no—
204C2—23444no—
205C2—11722no—
206C2D4×D117211yescharacteristic
subgroupG/H
centerC2D4×D1172
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#443×C293C2
socleC2×C293D42
hypercenter#443D293
hypocenterC293#3292
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C2 ◁ C2×C4 ◁ #443

Complements

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

NH ≅ G/Ntype
1. #34036934C2semidirect
2. #34036931C2semidirect
3. #34036506C2semidirect
4. #34036400C2semidirect
5. #34036399C2semidirect
6. #34036298C2semidirect
7. #34036247C2semidirect
8. #443×C293C2semidirect
9. #22627670C22semidirect
11. #22627652C22semidirect
13. #22627649C22semidirect
18. C2×D2344C22semidirect
19. C2×D2344C22semidirect
21. #22627630C22semidirect
22. #22627621C22semidirect
23. #22627560C22semidirect
24. #22627552C22semidirect
25. #22627540C22semidirect
27. #131×C293C22semidirect
28. #108×C293C22semidirect
29. #104×C293C22semidirect
30. C4×C8×C293C22semidirect
39. Dic1172D4semidirect
41. #17989791D4semidirect
48. D2344D4semidirect
54. Q16×C293D4semidirect
55. SD16×C293D4semidirect
56. D8×C293D4semidirect
103. C293#3292semidirect
112. #443D293semidirect
127. #131C2×D293semidirect
130. #108C2×D293semidirect
132. #104C2×D293semidirect
134. C4×C8C2×D293semidirect
145. Q16D1172semidirect
149. SD16D1172semidirect
157. D8D1172semidirect

Maximal subgroups

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

subgroupindex
#340369342
#340369312
#340365062
#340364002
#340363992
#340362982
#340362472
#443×C2932
#3292293