Finite Group Databasebeta

← #11763878

Subgroups — #11763878

Order 1088.

294 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 294 conjugacy classes of subgroups — too many to draw. Only its 138 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#41×D17C211yesmaximal, characteristic
2Q8×#595C212yesmaximal, complemented
3D4×#595C216yesmaximal, complemented
4#10587677C213yesmaximal, complemented
5C2×C4⋊#595C213yesmaximal, complemented
6C22×#595C2216yes—
7#41×C17C411yescharacteristic, complemented
8#63256C411yescharacteristic, complemented
9Q8×D17C2211yescharacteristic
10#63254C413yescomplemented
11D4×D17C2213yes—
12#63252C413yescomplemented
13C2×C4×D17C2213yes—
14C22⋊#595C2216yes—
15C4⋊#595C2213yes—
16C4⋊#595C2216yes—
17C4⋊#595C2211yescharacteristic
18C4×#595C2216yes—
19C22×D17C2313yes—
20C2×#595—46no—
21C2×#595C2312yes—
22C2×#595C2316yes—
23Q8×C17C2×C411yescharacteristic, complemented
24D4×C17C2×C413yescomplemented
25C2×C4×C17C2×C413yescomplemented
26C22⋊D17C2×C416yescomplemented
27C2×Dic17C2×C413yescomplemented
28D68C2×C413yescomplemented
29C4×D17C2×C413yescomplemented
30C4×D17C2×C413yescomplemented
31C4×D17C2313yes—
32C4×D17C2311yescharacteristic
33Dic34C2×C413yescomplemented
34C22×C17C22×C413yes—
35C2×D17—23no—
36C2×D17—23no—
37C2×D17C22×C413yes—
38C2×D17C2411yescharacteristic
39#595—26no—
40#595—22no—
41C4×C17C22×C413yes—
42C4×C17C22×C411yescharacteristic
43Dic17C22×C413yes—
44Dic17C22×C411yescharacteristic
45#520—171nomaximal, Sylow
46C2×C17—23no—
47C2×C17C23×C411yescharacteristic
48D17—23no—
49D17H(5,𝔽2)11yescharacteristic
50D172−1+411yescharacteristic
51C2×#41—171no—
52C4×Q8—172no—
53C4×D4—176no—
54#117—173no—
55C2×C4⋊C4—173no—
56C17#52011yescharacteristic, complemented, Sylow
57#41—171no—
58#41—173no—
59#41—173no—
60#41#59511yescharacteristic, complemented
61C2×Q8—171no—
62C2×D4—173no—
63C22×C4—173no—
64C22×C4—176no—
65C4⋊C4—173no—
66C4⋊C4—176no—
67C4⋊C4—171no—
68C22⋊C4—176no—
69C42—176no—
70C23—173no—
71Q8—173no—
72Q8C2×#59511yescharacteristic, complemented
73D4—176no—
74D4—173no—
75D4C2×#59513yescomplemented
76C2×C4—173no—
77C2×C4—173no—
78C2×C4—171no—
79C2×C4—173no—
80C2×C4—173no—
81C2×C4—172no—
82C2×C4—176no—
83C2×C4—686no—
84C2×C4C2×#59513yescomplemented
85C22—171no—
86C22—173no—
87C22—343no—
88C22—343no—
89C22C22×#59513yes—
90C4—171no—
91C4—173no—
92C4—346no—
93C4—342no—
94C4C22×#59511yescharacteristic
95C4C22×#59513yes—
96C2—23no—
97C2—171no—
98C2—171no—
99C2—343no—
100C2C23×#59511yescharacteristic
subgroupG/H
center, FrattiniC2C23×#595
commutator, socleC2×C17C23×C4
Fitting#41×C17C4
prime radical#41×D17C2
cosocleC2×D17C24
hypercenter#41#595
hypocenterC17#520
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C2 ◁ #41

Complements

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

NH ≅ G/Ntype
2. Q8×#595C2semidirect
3. D4×#595C2semidirect
4. #10587677C2semidirect
5. C2×C4⋊#595C2semidirect
7. #41×C17C4semidirect
8. #63256C4semidirect
10. #63254C4semidirect
12. #63252C4semidirect
23. Q8×C17C2×C4semidirect
24. D4×C17C2×C4semidirect
25. C2×C4×C17C2×C4semidirect
26. C22⋊D17C2×C4semidirect
27. C2×Dic17C2×C4semidirect
28. D68C2×C4semidirect
29. C4×D17C2×C4semidirect
30. C4×D17C2×C4semidirect
33. Dic34C2×C4semidirect
56. C17#520semidirect
60. #41#595semidirect
72. Q8C2×#595semidirect
75. D4C2×#595semidirect
84. C2×C4C2×#595semidirect

Maximal subgroups

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

subgroupindex
#41×D172
Q8×#5952
D4×#5952
#105876772
C2×C4⋊#5952
#52017