Finite Group Databasebeta

← #22590505

Subgroups — #22590505

Order 9088.

124 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 124 conjugacy classes of subgroups — too many to draw. Only its 51 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#17986401C211yesmaximal, characteristic
2C4×Dic284C211yesmaximal, characteristic
3#17985827C211yesmaximal, characteristic
4#17985825C211yesmaximal, characteristic
5#17985804C211yesmaximal, characteristic
6#17985804C211yesmaximal, characteristic
7C4⋊C16×C71C211yesmaximal, characteristic
8C2×Dic284C2211yescharacteristic
9#14556120—21no—
10C4×Dic142—21no—
11#14556062C2211yescharacteristic
12#14556062C2211yescharacteristic
13#14556062C2211yescharacteristic
14#14556060—21no—
15#14556053—21no—
16C2×C16×C71C2211yescharacteristic
17C2×C16×C71C2211yescharacteristic
18C4×C8×C71C2211yescharacteristic
19C2×Dic142—21no—
20Dic284—21no—
21Dic284Q812yes—
22C4⋊Dic71—21no—
23C4⋊Dic71—21no—
24C4⋊Dic71—21no—
25Dic71⋊C4—41no—
26Dic71⋊C4—41no—
27Dic71⋊C4—41no—
28C4×Dic71—41no—
29C2×C8×C71D411yescharacteristic
30C2×C8×C71C2311yescharacteristic
31C42×C71D411yescharacteristic
32C16×C71—21no—
33C16×C71—21no—
34C2×C4×C71D811yescharacteristic
35C2×C4×C71D811yescharacteristic
36C2×C4×C71C2×D411yescharacteristic
37C2×Dic71—41no—
38C2×Dic71—41no—
39C2×Dic71—41no—
40C2×Dic71—41no—
41Dic142—22no—
42Dic142—41no—
43C8×C71—21no—
44C8×C71C2×Q811yescharacteristic
45C8×C71#4111yescharacteristic
46C22×C71C2×D811yescharacteristic
47C4×C71—21no—
48C4×C71—21no—
49C4×C71C22⋊Q811yescharacteristic
50C4×C71#13711yescharacteristic
51Dic71—42no—
52Dic71—81no—
53Dic71—81no—
54Dic71—81no—
55C2×C71#47411yescharacteristic
56C2×C71#50811yescharacteristic
57C2×C71#51011yescharacteristic
58#2229—711nomaximal, Sylow
59C71#222911yescharacteristic, complemented, Sylow
60#499—711no—
61C4×Q16—711no—
62#367—711no—
63#366—711no—
64C4⋊C16D7111yescharacteristic
65#358—711no—
66#358—711no—
67C2×Q16—711no—
68#125—1421no—
69C4×Q8—1421no—
70C2×C16C2×D7111yescharacteristic
71C2×C16C2×D7111yescharacteristic
72#107—711no—
73#107—711no—
74#107—711no—
75#106—1421no—
76#103—1421no—
77C4×C8C2×D7111yescharacteristic
78C2×Q8—1421no—
79Q16—712no—
80Q16—1421no—
81C2×C8D28411yescharacteristic
82C2×C8C22×D7111yescharacteristic
83C4⋊C4—2841no—
84C4⋊C4—2841no—
85C4⋊C4—2841no—
86C4⋊C4—1421no—
87C4⋊C4—1421no—
88C4⋊C4—1421no—
89C42—2841no—
90C42D28411yescharacteristic
91C16—21no—
92C16—21no—
93Q8—2841no—
94Q8—1422no—
95C2×C4—2841no—
96C2×C4—2841no—
97C2×C4—2841no—
98C2×C4—2841no—
99C2×C4D56811yescharacteristic
100C2×C4D56811yescharacteristic
101C2×C4C2×D28411yescharacteristic
102C8—21no—
103C8Q8×D7111yescharacteristic
104C8#1176586411yescharacteristic
105C22C2×D56811yescharacteristic
106C4—21no—
107C4—21no—
108C4—2842no—
109C4—5681no—
110C4—5681no—
111C4—5681no—
112C4#1455610811yescharacteristic
113C4#1455616111yescharacteristic
114C2#1798628011yescharacteristic
115C2#1798643111yescharacteristic
116C2#1798644211yescharacteristic
subgroupG/H
centerC22C2×D568
commutatorC2×C8×C71C23
FrattiniC2×C8C22×D71
FittingC4⋊C16×C71C2
socleC22×C71C2×D8
hypercenterC4⋊C16D71
hypocenterC71#2229
LCSG ▷ C2×C8×C71 ▷ C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ C4⋊C16

Complements

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

NH ≅ G/Ntype
59. C71#2229semidirect