Finite Group Databasebeta

← #53385

Subgroups — #53385

Order 256.

673 conjugacy classes of subgroups; only the 389 normal subgroups are shown.

normal subgroups only

This group has 673 conjugacy classes of subgroups — too many to draw. Only its 389 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#2866C211yesmaximal, characteristic, complemented
2#2866C211yesmaximal, characteristic, complemented
3#2865C211yesmaximal, characteristic, complemented
4#2783C217yesmaximal, complemented
5#2773C217yesmaximal, complemented
6#2772C217yesmaximal, complemented
7#2735C217yesmaximal
8#400C2217yescomplemented
9#399C2217yes—
10#398C2217yescomplemented
11#397C2217yes—
12#397C2217yes—
13#397C2217yes—
14#396C2217yes—
15#396C2217yes—
16#389C2217yescomplemented
17#389C2217yescomplemented
18#388C2217yes—
19#388C2217yes—
20#388C2217yes—
21#388C2217yes—
22#388C2217yes—
23#388C2217yes—
24#387C2217yescomplemented
25#387C2217yescomplemented
26#387C2217yescomplemented
27#387C2217yescomplemented
28#382C2217yescomplemented
29#379C2217yes—
30C43C2211yescharacteristic, complemented
31C25C2311yescharacteristic
32C2×C4⋊C4C2317yes—
33C2×C4⋊C4C2317yes—
34C2×C4⋊C4C2317yes—
35C2×C4⋊C4C2317yes—
36C2×C4⋊C4C2317yes—
37C2×C4⋊C4C2317yes—
38C2×C22⋊C4C2317yes—
39C2×C22⋊C4C2317yes—
40C2×C22⋊C4C2317yes—
41C2×C22⋊C4C2317yes—
42C2×C22⋊C4C2317yes—
43C2×C22⋊C4C2317yes—
44C2×C42C2317yes—
45C2×C42C2317yes—
46#95C2317yes—
47#95C2317yes—
48#95C2317yes—
49#95C2317yes—
50#95C2317yes—
51#95C2317yes—
52#95C2317yes—
53#95C2317yes—
54C24—47no—
55C24C2411yescharacteristic
56C24C2411yescharacteristic
57C24C2411yescharacteristic
58C22×C4C2417yes—
59C22×C4C2417yes—
60C22×C4C2417yes—
61C22×C4C2417yes—
62C4⋊C4—47no—
63C4⋊C4—47no—
64C4⋊C4—47no—
65C4⋊C4—47no—
66C4⋊C4—47no—
67C4⋊C4—47no—
68C22⋊C4—47no—
69C22⋊C4—47no—
70C22⋊C4—47no—
71C22⋊C4—47no—
72C22⋊C4—47no—
73C22⋊C4—47no—
74C42—47no—
75C42—47no—
76C23—27no—
77C23—27no—
78C23—27no—
79C23—814no—
80C23C2511yescharacteristic
81C2×C4—27no—
82C2×C4—27no—
83C2×C4—27no—
84C2×C4—27no—
85C2×C4—27no—
86C2×C4—27no—
87C2×C4—27no—
88C2×C4—27no—
89C2×C4—27no—
90C2×C4—27no—
91C2×C4—27no—
92C2×C4—27no—
93C22—47no—
94C22—47no—
95C22—47no—
96C22—88no—
97C22#58517yes—
98C4—47no—
99C4—47no—
100C4—47no—
101C4—47no—
102C2—81no—
103C2—81no—
104C2—81no—
105C2#356617yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C25
prime radicalC25C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #2866C2semidirect
2. #2866C2semidirect
3. #2865C2semidirect
4. #2783C2semidirect
5. #2773C2semidirect
6. #2772C2semidirect
8. #400C22semidirect
10. #398C22semidirect
16. #389C22semidirect
17. #389C22semidirect
24. #387C22semidirect
25. #387C22semidirect
26. #387C22semidirect
27. #387C22semidirect
28. #382C22semidirect
30. C43C22semidirect

Maximal subgroups

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

subgroupindex
#28662
#28652
#27832
#27732
#27722
#27352