Finite Group Databasebeta

← #22590558

Subgroups — #22590558

Order 9088.

124 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 124 conjugacy classes of subgroups — too many to draw. Only its 41 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#17986254C211yesmaximal, characteristic
2#17986046C211yesmaximal, characteristic
3#17985823C211yesmaximal, characteristic, complemented
4#17985822C211yesmaximal, characteristic, complemented
5#17985815C211yesmaximal, characteristic, complemented
6#17985780C211yesmaximal, characteristic
7#362×C71C211yesmaximal, characteristic, complemented
8C2×#11765848C2211yescharacteristic
9M16×D71—21no—
10#14556104—21no—
11#14556068C2211yescharacteristic
12#14556064C2211yescharacteristic
13#14556063—21no—
14#14556060C2211yescharacteristic
15#14556052—21no—
16C2×Q16×C71C2211yescharacteristic
17M32×C71C2211yescharacteristic
18#108×C71C2211yescharacteristic
19C2×C4×D71D411yescharacteristic
20#11765849—21no—
21#11765848—21no—
22#11765848—21no—
23#11765848—41no—
24C2×C71⋊C8D411yescharacteristic
25C8×D71—41no—
26C4⋊Dic71—21no—
27Dic71⋊C4—41no—
28(C2×D71)⋊C4—41no—
29C71⋊C16—21no—
30C2×Q8×C71—21no—
31Q16×C71—21no—
32Q16×C71—21no—
33M16×C71—21no—
34C2×C8×C71C2311yescharacteristic
35C16×C71—21no—
36C22×D71SD1611yescharacteristic
37Q8×C71—41no—
38Q8×C71—41no—
39C2×C4×C71—41no—
40C2×C4×C71C2×D411yescharacteristic
41C2×Dic71—41no—
42C2×Dic71SD1611yescharacteristic
43C4×D71—21no—
44C4×D71—21no—
45C8×C71—41no—
46C8×C71#4111yescharacteristic
47C8×C71#4111yescharacteristic
48C71⋊C8—21no—
49C71⋊C8—41no—
50C22×C71C2×SD1611yescharacteristic
51C2×D71—21no—
52C2×D71—41no—
53C4×C71—81no—
54C4×C71#12311yescharacteristic
55C4×C71AGL(1,ℤ/8)11yescharacteristic
56Dic71—21no—
57Dic71—81no—
58C2×C71—21no—
59C2×C71#48111yescharacteristic
60D71—41no—
61#2239—711nomaximal, Sylow
62C71#223911yescharacteristic, complemented, Sylow
63#470—711no—
64#430—711no—
65#365—711no—
66#365—711no—
67#362—711no—
68#362D7111yescharacteristic, complemented
69#349—711no—
70C2×Q16C2×D7111yescharacteristic
71C2×M16—711no—
72C2×M16—1421no—
73C22⋊Q8—1421no—
74M32—711no—
75M32C2×D7111yescharacteristic
76#108—711no—
77#108—1421no—
78#108C2×D7111yescharacteristic
79#106—711no—
80#103—1421no—
81C2×Q8—21no—
82C22×C4—711no—
83Q16—21no—
84Q16—21no—
85M16—21no—
86M16—2841no—
87M16—1421no—
88M16—1421no—
89M16—1421no—
90C2×C8—2841no—
91C2×C8—711no—
92C2×C8C22×D7111yescharacteristic
93C4⋊C4—2841no—
94C4⋊C4—1421no—
95C22⋊C4—2841no—
96C16—21no—
97C16—1421no—
98C23—711no—
99Q8—41no—
100Q8—41no—
101C2×C4—41no—
102C2×C4—2841no—
103C2×C4—711no—
104C2×C4—1421no—
105C2×C4—1421no—
106C2×C4D4×D7111yescharacteristic
107C8—41no—
108C8—2841no—
109C8—1421no—
110C8#1176586411yescharacteristic
111C8#1176586511yescharacteristic
112C22—2841no—
113C22—1421no—
114C22SD16×D7111yescharacteristic
115C4—81no—
116C4—5681no—
117C4—1421no—
118C4#1455611011yescharacteristic
119C4#1455615211yescharacteristic
120C2—21no—
121C2—2841no—
122C2#1798631611yescharacteristic
subgroupG/H
centerC2#17986316
commutatorC2×C8×C71C23
FrattiniC2×C8C22×D71
Fitting#362×C71C2
socleC2×C71#481
hypercenter#362D71
hypocenterC71#2239
LCSG ▷ C2×C8×C71 ▷ C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #362

Complements

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

NH ≅ G/Ntype
3. #17985823C2semidirect
4. #17985822C2semidirect
5. #17985815C2semidirect
7. #362×C71C2semidirect
62. C71#2239semidirect
68. #362D71semidirect