Finite Group Databasebeta

← #11763836

Subgroups — #11763836

Order 1088.

134 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 134 conjugacy classes of subgroups — too many to draw. Only its 56 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
1C22×#3624C211yesmaximal, characteristic, complemented
2C2×#63242C211yesmaximal, characteristic, complemented
3#10587567C211yesmaximal, characteristic
4C22⋊#3624C211yesmaximal, characteristic, complemented
5#10587544C211yesmaximal, characteristic, complemented
6#10587543C211yesmaximal, characteristic, complemented
7C4×#3624C211yesmaximal, characteristic, complemented
8C2×C22⋊D17C411yescharacteristic
9C22×Dic17C2211yescharacteristic
10C2×C4×D17C2211yescharacteristic
11C2×#3624—22no—
12C2×#3624C2211yescharacteristic
13C2×#3624C2211yescharacteristic
14C2×#3624C2211yescharacteristic
15C2×#3624C2211yescharacteristic
16#63242—22no—
17C22⋊C4×C17C411yescharacteristic
18#63227C411yescharacteristic
19#63225C411yescharacteristic
20C4×Dic17C2211yescharacteristic
21C23×C17C2×C411yescharacteristic
22C22×D17C2×C411yescharacteristic
23C2×C4×C17C2×C411yescharacteristic
24C2×C4×C17C2×C411yescharacteristic
25C22⋊D17C814yescomplemented
26C2×Dic17—21no—
27C2×Dic17—21no—
28C2×Dic17C2×C411yescharacteristic
29C2×Dic17C2×C411yescharacteristic
30C2×Dic17C2311yescharacteristic
31C4×D17—21no—
32C4×D17—21no—
33#3624—21no—
34#3624—21no—
35#3624—21no—
36#3624D412yescomplemented
37C22×C17—21no—
38C22×C17—21no—
39C22×C17C2×C812yescomplemented
40C22×C17C22×C411yescharacteristic
41C2×D17—21no—
42C2×D17—21no—
43C2×D17C2×C812yescomplemented
44C4×C17—21no—
45C4×C17—21no—
46Dic17—21no—
47Dic17C2×C812yescomplemented
48Dic17C2×D411yescharacteristic
49Dic17#4111yescharacteristic
50C8×D4—171nomaximal, Sylow
51C2×C17—22no—
52C2×C17C4×D411yescharacteristic
53C2×C17C22×C811yescharacteristic
54C2×C17#13111yescharacteristic
55D17—22no—
56C22×C8—171no—
57C22×C8—171no—
58C4×D4—171no—
59C4⋊C8—171no—
60C22⋊C8—171no—
61C22⋊C8—171no—
62C4×C8—171no—
63C17C8×D411yescharacteristic, complemented, Sylow
64C2×D4—171no—
65C22×C4—171no—
66C22×C4—171no—
67C2×C8—171no—
68C2×C8—171no—
69C2×C8—171no—
70C2×C8—171no—
71C2×C8—342no—
72C2×C8—342no—
73C4⋊C4—171no—
74C22⋊C4—171no—
75C22⋊C4#59511yescharacteristic
76C42—171no—
77C23—171no—
78C23C2×#59511yescharacteristic
79D4—174no—
80C2×C4—171no—
81C2×C4—171no—
82C2×C4—171no—
83C2×C4—341no—
84C2×C4—341no—
85C2×C4—341no—
86C2×C4—341no—
87C2×C4C2×#59511yescharacteristic
88C2×C4C2×#59511yescharacteristic
89C8—172no—
90C8—341no—
91C8—341no—
92C8—341no—
93C22—21no—
94C22—21no—
95C22—172no—
96C22—341no—
97C22—341no—
98C22#6324212yescomplemented
99C22C22×#59511yescharacteristic
100C4—21no—
101C4—21no—
102C4—172no—
103C4—171no—
104C4—171no—
105C4—341no—
106C2—22no—
107C2—342no—
108C2C2×#6324211yescharacteristic
109C2#1058767811yescharacteristic
110C2D4×#59511yescharacteristic
subgroupG/H
center, FrattiniC22C22×#595
commutatorC2×C17C22×C8
FittingC22⋊C4×C17C4
socleC22×C17C22×C4
prime radicalC2×C22⋊D17C4
cosocleC2×Dic17C23
hypercenterC22⋊C4#595
hypocenterC17C8×D4
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#3624C2semidirect
2. C2×#63242C2semidirect
4. C22⋊#3624C2semidirect
5. #10587544C2semidirect
6. #10587543C2semidirect
7. C4×#3624C2semidirect
25. C22⋊D17C8semidirect
36. #3624D4semidirect
39. C22×C17C2×C8semidirect
43. C2×D17C2×C8semidirect
47. Dic17C2×C8semidirect
63. C17C8×D4semidirect
98. C22#63242semidirect

Maximal subgroups

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

subgroupindex
C22×#36242
C2×#632422
#105875672
C22⋊#36242
#105875442
#105875432
C4×#36242
C8×D417