Finite Group Databasebeta

← #26018294

Subgroups — #26018294

Order 11392.

102 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 102 conjugacy classes of subgroups — too many to draw. Only its 39 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#19151982C211yesmaximal, characteristic
2C4⋊#13083549C211yesmaximal, characteristic, complemented
3#334×C89C211yesmaximal, characteristic, complemented
4C2×Dic356C411yescharacteristic
5C2×#13083563—21no—
6C2×D712C411yescharacteristic
7#15668000—21no—
8C2×#13083549—21no—
9C4⋊C8×C89—21no—
10C4×C8×C89C2211yescharacteristic
11C2×Dic178—21no—
12C2×D356—21no—
13Dic356—41no—
14#13083563—41no—
15#13083563—41no—
16D712—41no—
17#13083551—41no—
18#13083551—41no—
19#13083549—41no—
20C2×C8×C89—41no—
21C2×C8×C89C2×C411yescharacteristic
22C2×C8×C89D411yescharacteristic
23C42×C89D411yescharacteristic
24C22×D89—41no—
25C2×C4×C89C22⋊C411yescharacteristic
26C2×C4×C89D811yescharacteristic
27C2×C4×C89SD1611yescharacteristic
28C2×Dic89—41no—
29D356—41no—
30D356—41no—
31Dic178—41no—
32Dic178—41no—
33C8×C89—21no—
34C8×C89—81no—
35C8×C89D811yescharacteristic
36C8×C89SD1611yescharacteristic
37C22×C89#10211yescharacteristic
38C2×D89—81no—
39C2×D89—81no—
40C2×D89—81no—
41C4×C89—21no—
42C4×C89—21no—
43C4×C89#10011yescharacteristic
44C4×C89#10211yescharacteristic
45Dic89—81no—
46C2×C89#33111yescharacteristic
47C2×C89#35911yescharacteristic
48C2×C89#36011yescharacteristic
49D89—161no—
50#1360—891nomaximal, Sylow
51C89#136011yescharacteristic, complemented, Sylow
52#495—891no—
53C4⋊C16—891no—
54#334D8911yescharacteristic, complemented
55C2×Q16—891no—
56C2×SD16—1781no—
57C2×D8—891no—
58#124—1781no—
59C2×C16—1781no—
60C4⋊C8—21no—
61C4×C8C2×D8911yescharacteristic
62C2×Q8—1781no—
63C2×D4—1781no—
64Q16—3561no—
65SD16—3561no—
66SD16—3561no—
67D8—3561no—
68C2×C8—41no—
69C2×C8C4×D8911yescharacteristic
70C2×C8D35611yescharacteristic
71C22⋊C4—3561no—
72C22⋊C4—3561no—
73C42C22⋊D8911yescharacteristic
74C16—3561no—
75C23—3561no—
76Q8—3561no—
77Q8—3561no—
78D4—3561no—
79D4—3561no—
80C2×C4—3561no—
81C2×C4#1308355111yescharacteristic
82C2×C4#1308355911yescharacteristic
83C2×C4#1308356111yescharacteristic
84C8—21no—
85C8—81no—
86C8D71211yescharacteristic
87C8#1308356311yescharacteristic
88C22—7121no—
89C22—7121no—
90C22—7121no—
91C22#1566793211yescharacteristic
92C4—21no—
93C4—21no—
94C4—7121no—
95C4#1566792811yescharacteristic
96C4#1566793411yescharacteristic
97C2—14241no—
98C2#1915134111yescharacteristic
99C2#1915140411yescharacteristic
100C2#1915140711yescharacteristic
subgroupG/H
centerC22#15667932
commutatorC2×C8×C89C2×C4
FrattiniC4×C8C2×D89
Fitting#334×C89C2
socleC22×C89#102
prime radicalC2×D712C4
cosocleC4×C8×C89C22
hypercenter#334D89
hypocenterC89#1360
LCSG ▷ C2×C8×C89 ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #334

Complements

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

NH ≅ G/Ntype
2. C4⋊#13083549C2semidirect
3. #334×C89C2semidirect
51. C89#1360semidirect
54. #334D89semidirect

Maximal subgroups

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

subgroupindex
#191519822
C4⋊#130835492
#334×C892
#136089