Finite Group Databasebeta

← #22590504

Subgroups — #22590504

Order 9088.

124 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 124 conjugacy classes of subgroups — too many to draw. Only its 53 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
2#17985826C211yesmaximal, characteristic
3#17985824C211yesmaximal, characteristic
4C4⋊(C71⋊C16)C211yesmaximal, characteristic
5#17985803C211yesmaximal, characteristic
6#17985803C211yesmaximal, characteristic
7C4×Q16×C71C211yesmaximal, characteristic
8#14556120—21no—
9C2×C71⋊C16C2211yescharacteristic
10C2×C71⋊C16C2211yescharacteristic
11#14556062C2211yescharacteristic
12#14556062C2211yescharacteristic
13#14556060—21no—
14C2×Q16×C71C2211yescharacteristic
15C4×Q8×C71—21no—
16#107×C71C2211yescharacteristic
17#103×C71—21no—
18C4×C8×C71C2211yescharacteristic
19C4⋊Dic71—21no—
20C4⋊Dic71—21no—
21Dic71⋊C4—41no—
22Dic71⋊C4—41no—
23C71⋊C16—21no—
24C71⋊C16—21no—
25C2×Q8×C71—21no—
26Q16×C71—21no—
27Q16×C71Q812yes—
28C2×C8×C71D411yescharacteristic
29C2×C8×C71C2311yescharacteristic
30C4⋊C4×C71—21no—
31C4⋊C4×C71—41no—
32C42×C71—41no—
33C42×C71D411yescharacteristic
34Q8×C71—22no—
35Q8×C71—41no—
36C2×C4×C71—41no—
37C2×C4×C71—41no—
38C2×C4×C71D811yescharacteristic
39C2×C4×C71D811yescharacteristic
40C2×C4×C71C2×D411yescharacteristic
41C2×Dic71—41no—
42C2×Dic71—41no—
43C8×C71—21no—
44C8×C71C2×Q811yescharacteristic
45C8×C71#4111yescharacteristic
46C22×C71C2×D811yescharacteristic
47C4×C71—21no—
48C4×C71—21no—
49C4×C71—42no—
50C4×C71—81no—
51C4×C71C22⋊Q811yescharacteristic
52C4×C71#13711yescharacteristic
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×Q16D7111yescharacteristic
62#367—711no—
63#366—711no—
64C4⋊C16—711no—
65#358—711no—
66#358—711no—
67C2×Q16C2×D7111yescharacteristic
68#125—1421no—
69C4×Q8—21no—
70C2×C16—711no—
71C2×C16—711no—
72#107—711no—
73#107—711no—
74#107C2×D7111yescharacteristic
75#106—1421no—
76#103—21no—
77C4×C8C2×D7111yescharacteristic
78C2×Q8—21no—
79Q16—21no—
80Q16Dic14212yes—
81C2×C8C22⋊D7111yescharacteristic
82C2×C8C22×D7111yescharacteristic
83C4⋊C4—21no—
84C4⋊C4—41no—
85C4⋊C4—2841no—
86C4⋊C4—2841no—
87C4⋊C4—1421no—
88C4⋊C4—1421no—
89C42—41no—
90C42C22⋊D7111yescharacteristic
91C16—1421no—
92C16—1421no—
93Q8—22no—
94Q8—41no—
95C2×C4—41no—
96C2×C4—41no—
97C2×C4—2841no—
98C2×C4—2841no—
99C2×C4#1176585011yescharacteristic
100C2×C4#1176585011yescharacteristic
101C2×C4C2×C22⋊D7111yescharacteristic
102C8—21no—
103C8C2×Dic14211yescharacteristic
104C8#1176586511yescharacteristic
105C22C2×#1176585011yescharacteristic
106C4—21no—
107C4—21no—
108C4—42no—
109C4—81no—
110C4—5681no—
111C4—5681no—
112C4#1455610711yescharacteristic
113C4#1455615811yescharacteristic
114C2#1798627911yescharacteristic
115C2#1798642911yescharacteristic
116C2#1798644011yescharacteristic
subgroupG/H
centerC22C2×#11765850
commutatorC2×C8×C71C23
FrattiniC2×C8C22×D71
FittingC4×Q16×C71C2
socleC22×C71C2×D8
hypercenterC4×Q16D71
hypocenterC71#2229
LCSG ▷ C2×C8×C71 ▷ C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ C4×Q16

Complements

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

NH ≅ G/Ntype
59. C71#2229semidirect