Finite Group Databasebeta

← #16856084

Subgroups — #16856084

Order 3968.

484 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 121 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#14521605C211yesmaximal, characteristic, complemented
2#127×D31C211yesmaximal, characteristic
3#14521415C211yesmaximal, characteristic, complemented
4#14521414C211yesmaximal, characteristic, complemented
5#14521413C211yesmaximal, characteristic, complemented
6#14521394C214yesmaximal, complemented
7#14521052C214yesmaximal, complemented
8#14521001C211yesmaximal, characteristic, complemented
9C31×#490C211yesmaximal, characteristic, complemented
10C2×D4×D31—22no—
11C2×D4×D31C2212yes—
12C31×#127C2211yescharacteristic
13C31×#125C2211yescharacteristic, complemented
14#11758517—22no—
15#11758517C2212yes—
16C2×#92469C2212yes—
17#11758473—22no—
18#11758469C2212yes—
19#11758465C2212yescomplemented
20#11758464—22no—
21#11758451C2211yescharacteristic
22C42×D31C2211yescharacteristic
23#11758447C2211yescharacteristic, complemented
24C31×#102C2214yescomplemented
25C31×#97C2211yescharacteristic, complemented
26#11758420C2214yescomplemented
27#11758409C2214yescomplemented
28C8×Dic31C2212yescomplemented
29#11758397C2214yescomplemented
30#11758391C2211yescharacteristic, complemented
31C23×D31—22no—
32C2×D4×C31—22no—
33C2×D4×C31C2312yes—
34C2×C22⋊D31—22no—
35C2×C22⋊D31—24no—
36D4×D31—28no—
37D4×D31—48no—
38C2×D124—22no—
39C2×D124C2312yes—
40C2×C4×D31D412yes—
41C2×C4×D31C2311yescharacteristic
42C2×Dic62—22no—
43C2×C8×C31C2312yes—
44C4⋊C4×C31—22no—
45C4⋊C4×C31C2312yes—
46C42×C31C2311yescharacteristic
47(C2×D31)⋊C4—22no—
48C4⋊Dic31C2312yes—
49Dic31⋊C4—22no—
50Dic31⋊C4—22no—
51C4×Dic31—22no—
52C4×Dic31D412yes—
53C4×Dic31C2311yescharacteristic
54C2×C31⋊C8C2312yes—
55#92469—24no—
56C23×C31—22no—
57C22×D31—22no—
58C22×D31—48no—
59C22×D31—44no—
60C22×D31C2×D411yescharacteristic
61D4×C31—24no—
62D4×C31—44no—
63C2×C4×C31—22no—
64C2×C4×C31C2×D412yes—
65C2×C4×C31C2411yescharacteristic
66C22⋊D31—44no—
67C22⋊D31—48no—
68C2×Dic31—22no—
69C2×Dic31C2×D411yescharacteristic
70C2×Dic31C2×D412yes—
71D124—24no—
72D124—44no—
73C4×D31—24no—
74C4×D31#4114yes—
75Dic62—44no—
76C8×C31—22no—
77C31⋊C8—22no—
78#3138—311nomaximal, Sylow
79C22×C31—42no—
80C22×C31—44no—
81C22×C31C22×D411yescharacteristic
82C2×D31—22no—
83C2×D31—42no—
84C2×D31—44no—
85C2×D31—88no—
86C2×D31#12412yes—
87C4×C31—22no—
88C4×C31—42no—
89C4×C31C2×#4112yes—
90Dic31—42no—
91Dic31#12412yes—
92Dic31AGL(1,ℤ/8)14yes—
93#533—311no—
94C2×#127—311no—
95#490—311no—
96#490—311no—
97#490—311no—
98#490D3111yescharacteristic, complemented
99#486—314no—
100#418—314no—
101C4×M16—311no—
102C2×C31—82no—
103C2×C31C2×#12411yescharacteristic
104C2×C31C2×AGL(1,ℤ/8)12yes—
105D31—22no—
106D31—82no—
107C22×D4—312no—
108C22×D4—622no—
109C2×M16—312no—
110C4⋊Q8—312no—
111#127—312no—
112#127—311no—
113#127—622no—
114#127C2×D3111yescharacteristic
115#125—311no—
116#125C2×D3111yescharacteristic, complemented
117C22⋊Q8—622no—
118C4×Q8—622no—
119#117—312no—
120C2×C42—311no—
121#102—314no—
122#102—314no—
123#102—314no—
124#102C2×D3114yescomplemented
125#97—311no—
126#97C2×D3111yescharacteristic, complemented
127C4×C8—312no—
128C31#313811yescharacteristic, complemented, Sylow
129C24—622no—
130C2×Q8—622no—
131C2×D4—22no—
132C2×D4—312no—
133C2×D4—628no—
134C2×D4—624no—
135C2×D4—622no—
136C2×D4—622no—
137C2×D4—1248no—
138C2×D4C22×D3112yes—
139C22×C4—311no—
140C22×C4—312no—
141M16—624no—
142C2×C8—312no—
143C2×C8C22×D3112yes—
144C4⋊C4—22no—
145C4⋊C4—312no—
146C4⋊C4—622no—
147C4⋊C4—622no—
148C4⋊C4C22×D3112yes—
149C22⋊C4—622no—
150C42—312no—
151C42—311no—
152C42—622no—
153C42C22×D3111yescharacteristic
154C23—22no—
155C23—311no—
156C23—622no—
157C23—1244no—
158C23—1248no—
159Q8—1244no—
160D4—24no—
161D4—44no—
162D4—624no—
163D4—1244no—
164D4—1244no—
165D4—1248no—
166C2×C4—22no—
167C2×C4—311no—
168C2×C4—312no—
169C2×C4—314no—
170C2×C4—624no—
171C2×C4—622no—
172C2×C4D4×D3112yes—
173C2×C4C23×D3111yescharacteristic
174C8—22no—
175C8—622no—
176C22—42no—
177C22—44no—
178C22—312no—
179C22—622no—
180C22—1242no—
181C22—1244no—
182C22—2488no—
183C22C2×D4×D3111yescharacteristic
184C4—22no—
185C4—42no—
186C4—312no—
187C4—314no—
188C4—1242no—
189C4#41×D3112yes—
190C2—82no—
191C2—622no—
192C2—2482no—
193C2#124×D3111yescharacteristic
194C2AGL(1,ℤ/8)×D3112yes—
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#490C2
socleC22×C31C22×D4
prime radical#127×D31C2
hypercenter#490D31
hypocenterC31#3138
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. #14521605C2semidirect
3. #14521415C2semidirect
4. #14521414C2semidirect
5. #14521413C2semidirect
6. #14521394C2semidirect
7. #14521052C2semidirect
8. #14521001C2semidirect
9. C31×#490C2semidirect
13. C31×#125C22semidirect
19. #11758465C22semidirect
23. #11758447C22semidirect
24. C31×#102C22semidirect
25. C31×#97C22semidirect
26. #11758420C22semidirect
27. #11758409C22semidirect
28. C8×Dic31C22semidirect
29. #11758397C22semidirect
30. #11758391C22semidirect
98. #490D31semidirect
116. #125C2×D31semidirect
124. #102C2×D31semidirect
126. #97C2×D31semidirect
128. C31#3138semidirect

Maximal subgroups

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

subgroupindex
#145216052
#127×D312
#145214152
#145214142
#145214132
#145213942
#145210522
#145210012
C31×#4902
#313831