Finite Group Databasebeta

← #22590516

Subgroups — #22590516

Order 9088.

120 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 49 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, complemented
2#17985823C212yesmaximal, complemented
3#17985820C211yesmaximal, characteristic, complemented
4#17985809C212yesmaximal
5#443×C71C211yesmaximal, characteristic
6#14556120—21no—
7#14556068C2212yes—
8#14556062—21no—
9#14556060C2212yes—
10#135×C71C2211yescharacteristic
11#131×C71—21no—
12#108×C71C2211yescharacteristic
13#104×C71—21no—
14C4×C8×C71C2211yescharacteristic
15C4⋊Dic71—22no—
16Dic71⋊C4—42no—
17C71⋊C16—22no—
18#41×C71—21no—
19Q16×C71Q811yescharacteristic
20SD16×C71—21no—
21D8×C71Q811yescharacteristic
22M16×C71—21no—
23M16×C71—41no—
24C2×C8×C71—41no—
25C2×C8×C71D411yescharacteristic
26C2×C8×C71C2311yescharacteristic
27C42×C71D411yescharacteristic
28Q8×C71—21no—
29D4×C71—21no—
30D4×C71—41no—
31C2×C4×C71—21no—
32C2×C4×C71—41no—
33C2×C4×C71C2×D411yescharacteristic
34C2×Dic71—42no—
35C8×C71—41no—
36C8×C71SD1611yescharacteristic
37C8×C71SD1611yescharacteristic
38C8×C71C2×Q811yescharacteristic
39C8×C71#4111yescharacteristic
40C22×C71—41no—
41C22×C71AGL(1,ℤ/8)11yescharacteristic
42C4×C71—41no—
43C4×C71—41no—
44C4×C71C22⋊Q811yescharacteristic
45C4×C71C2×SD1611yescharacteristic
46Dic71—82no—
47C2×C71—21no—
48C2×C71—81no—
49C2×C71#47611yescharacteristic
50#2231—711nomaximal, Sylow
51C71#223111yescharacteristic, complemented, Sylow
52#499—711no—
53#443D7111yescharacteristic
54#365—712no—
55#364—711no—
56#360—712no—
57#135C2×D7111yescharacteristic
58#131—21no—
59#125—1421no—
60M32—712no—
61#108C2×D7111yescharacteristic
62#107—1421no—
63#106—712no—
64#104—21no—
65C4×C8C2×D7111yescharacteristic
66#41—21no—
67Q16Dic14211yescharacteristic
68SD16—21no—
69D8Dic14211yescharacteristic
70M16—21no—
71M16—41no—
72C2×C8—41no—
73C2×C8C22⋊D7111yescharacteristic
74C2×C8C22×D7111yescharacteristic
75C4⋊C4—2842no—
76C4⋊C4—1422no—
77C42C22⋊D7111yescharacteristic
78C16—1422no—
79Q8—21no—
80D4—21no—
81D4—41no—
82C2×C4—21no—
83C2×C4—41no—
84C2×C4—2842no—
85C2×C4C2×C22⋊D7111yescharacteristic
86C8—41no—
87C8#1176585311yescharacteristic
88C8#1176585311yescharacteristic
89C8C2×Dic14211yescharacteristic
90C8#1176586511yescharacteristic
91C22—41no—
92C22#1455615311yescharacteristic
93C4—41no—
94C4—41no—
95C4—5682no—
96C4#1455610711yescharacteristic
97C4C2×#1176585311yescharacteristic
98C2—21no—
99C2—81no—
100C2#1798628911yescharacteristic
subgroupG/H
centerC2#17986289
commutatorC2×C8×C71C23
FrattiniC2×C8C22×D71
Fitting#443×C71C2
socleC2×C71#476
hypercenter#443D71
hypocenterC71#2231
LCSG ▷ C2×C8×C71 ▷ C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #443

Complements

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

NH ≅ G/Ntype
1. #17986401C2semidirect
2. #17985823C2semidirect
3. #17985820C2semidirect
51. C71#2231semidirect