Finite Group Databasebeta

← #22590418

Subgroups — #22590418

Order 9088.

150 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 150 conjugacy classes of subgroups — too many to draw. Only its 47 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#17986440C212yesmaximal
2#17986117C211yesmaximal, characteristic
3#17985820C211yesmaximal, characteristic, complemented
4#17985815C212yesmaximal, complemented
5#494×C71C211yesmaximal, characteristic, complemented
6#14556150C2211yescharacteristic
7#14556134—21no—
8#14556074—22no—
9#14556071—22no—
10#14556068C2212yes—
11#14556064C2211yescharacteristic
12#14556056—21no—
13C2×Q16×C71—21no—
14C2×Q16×C71C2212yes—
15C4⋊Q8×C71—21no—
16C4×C8×C71C2211yescharacteristic
17#11765865—21no—
18Dic284D411yescharacteristic
19#11765854—21no—
20D568D411yescharacteristic
21#11765849—21no—
22#11765848—41no—
23C8×D71—41no—
24C71⋊C16—22no—
25C2×Q8×C71—22no—
26Q16×C71—22no—
27Q16×C71—22no—
28Q16×C71—41no—
29Q16×C71—41no—
30C2×C8×C71D411yescharacteristic
31C2×C8×C71C2311yescharacteristic
32C4⋊C4×C71—42no—
33C42×C71D411yescharacteristic
34Q8×C71—42no—
35Q8×C71—42no—
36C2×C4×C71—21no—
37C2×C4×C71—42no—
38C2×C4×C71C2×D411yescharacteristic
39C22⋊D71—41no—
40D284—21no—
41C4×D71—41no—
42Dic142—21no—
43C8×C71D811yescharacteristic
44C8×C71D811yescharacteristic
45C8×C71C2×D411yescharacteristic
46C8×C71#4111yescharacteristic
47C71⋊C8—41no—
48C22×C71AGL(1,ℤ/8)11yescharacteristic
49C2×D71—41no—
50C4×C71—22no—
51C4×C71—82no—
52C4×C71#12111yescharacteristic
53C4×C71C2×D811yescharacteristic
54Dic71—41no—
55C2×C71—21no—
56C2×C71#45911yescharacteristic
57D71—81no—
58#2214—711nomaximal, Sylow
59C71#221411yescharacteristic, complemented, Sylow
60#510—712no—
61#494D7111yescharacteristic, complemented
62#443—711no—
63#364—711no—
64#362—712no—
65#135—711no—
66C2×Q16—21no—
67C2×Q16C2×D7112yes—
68#131—1421no—
69C4⋊Q8—21no—
70Q32—1422no—
71SD32—1422no—
72M32—712no—
73#108—711no—
74#104—1421no—
75C4×C8C2×D7111yescharacteristic
76#41—1421no—
77C2×Q8—22no—
78Q16—22no—
79Q16—22no—
80Q16—41no—
81Q16—41no—
82Q16—711no—
83SD16—1421no—
84D8—711no—
85M16—2841no—
86M16—1421no—
87C2×C8—2841no—
88C2×C8C22⋊D7111yescharacteristic
89C2×C8C22×D7111yescharacteristic
90C4⋊C4—42no—
91C42C22⋊D7111yescharacteristic
92C16—1422no—
93Q8—42no—
94Q8—42no—
95Q8—1421no—
96D4—2841no—
97D4—1421no—
98C2×C4—21no—
99C2×C4—42no—
100C2×C4—2841no—
101C2×C4C2×C22⋊D7111yescharacteristic
102C8—2841no—
103C8#1176585011yescharacteristic
104C8#1176585011yescharacteristic
105C8D4×D7111yescharacteristic
106C8#1176586411yescharacteristic
107C22—2841no—
108C22#1455615411yescharacteristic
109C4—22no—
110C4—82no—
111C4—2841no—
112C4#1455609911yescharacteristic
113C4C2×#1176585011yescharacteristic
114C2—21no—
115C2—5681no—
116C2#1798619111yescharacteristic
subgroupG/H
centerC2#17986191
commutatorC2×C8×C71C23
FrattiniC2×C8C22×D71
Fitting#494×C71C2
socleC2×C71#459
hypercenter#494D71
hypocenterC71#2214
LCSG ▷ C2×C8×C71 ▷ C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #494

Complements

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

NH ≅ G/Ntype
3. #17985820C2semidirect
4. #17985815C2semidirect
5. #494×C71C2semidirect
59. C71#2214semidirect
61. #494D71semidirect