Finite Group Databasebeta

← #22581167

Subgroups — #22581167

Order 8896.

124 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 124 conjugacy classes of subgroups — too many to draw. Only its 39 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
1C2×#14555774C211yesmaximal, characteristic, complemented
2C2×#14555770C211yesmaximal, characteristic
3#17984829C211yesmaximal, characteristic, complemented
4#17984804C211yesmaximal, characteristic, complemented
5Dic139⋊C8C211yesmaximal, characteristic, complemented
6#17984765C211yesmaximal, characteristic, complemented
7#102×C139C211yesmaximal, characteristic, complemented
8C2×Dic278C2211yescharacteristic
9C2×D556C2211yescharacteristic
10C2×C4×D139—21no—
11#14555774—22no—
12#14555770—22no—
13C2×C139⋊C8C2211yescharacteristic
14C22⋊Dic139—21no—
15C22⋊Dic139—21no—
16(C2×D139)⋊C4—21no—
17C4×Dic139C2211yescharacteristic
18C2×D4×C139C2211yescharacteristic
19C2×C8×C139C2211yescharacteristic
20C4⋊C4×C139C2211yescharacteristic
21C22×D139—21no—
22Dic278—21no—
23Dic278—21no—
24D556—21no—
25D556D412yes—
26C2×Dic139—21no—
27C2×Dic139D411yescharacteristic
28C2×Dic139D411yescharacteristic
29C4×D139—42no—
30C139⋊C8—21no—
31C23×C139—21no—
32D4×C139—21no—
33D4×C139—21no—
34C2×C4×C139—21no—
35C2×C4×C139C2311yescharacteristic
36C8×C139—21no—
37C22×C139—41no—
38C22×C139—41no—
39C22×C139—41no—
40C22×C139C2×D411yescharacteristic
41C2×D139—22no—
42C2×D139—41no—
43C2×D139—41no—
44C4×C139—41no—
45C4×C139C2×D411yescharacteristic
46C4×C139#4111yescharacteristic
47Dic139—21no—
48Dic139—21no—
49Dic139—41no—
50C2×C139—81no—
51C2×C139#12111yescharacteristic
52C2×C139#13511yescharacteristic
53C2×C139AGL(1,ℤ/8)11yescharacteristic
54D139—42no—
55C139#46311yescharacteristic, complemented, Sylow
56#463—1391nomaximal, Sylow
57C2×SD16—1391no—
58C2×D8—1391no—
59#124—1391no—
60C4×D4—1391no—
61C4⋊C8—1391no—
62#103—1391no—
63#102D13911yescharacteristic, complemented
64C2×Q8—1391no—
65C2×D4—1391no—
66C2×D4C2×D13911yescharacteristic
67C22×C4—2781no—
68SD16—2782no—
69D8—2782no—
70C2×C8—1391no—
71C2×C8C2×D13911yescharacteristic
72C4⋊C4C2×D13911yescharacteristic
73C22⋊C4—2781no—
74C22⋊C4—2781no—
75C22⋊C4—2781no—
76C42—1391no—
77C23—21no—
78C23—2781no—
79Q8—2781no—
80Q8—2781no—
81D4—21no—
82D4—21no—
83D4—2781no—
84D4—1392no—
85C2×C4—21no—
86C2×C4—2781no—
87C2×C4—5562no—
88C2×C4—1391no—
89C2×C4—1391no—
90C2×C4C22×D13911yescharacteristic
91C8—21no—
92C8—2781no—
93C22—41no—
94C22—41no—
95C22—41no—
96C22—2782no—
97C22—5561no—
98C22—5561no—
99C22D4×D13911yescharacteristic
100C4—41no—
101C4—2781no—
102C4—2781no—
103C4—5561no—
104C4D4×D13911yescharacteristic
105C4#1455578511yescharacteristic
106C2—81no—
107C2—5562no—
108C2#1798481511yescharacteristic
109C2#1798486311yescharacteristic
110C2#1798486611yescharacteristic
subgroupG/H
centerC22D4×D139
commutatorC2×C4×C139C23
FrattiniC2×C4C22×D139
Fitting#102×C139C2
socleC22×C139C2×D4
hypercenter#102D139
hypocenterC139#463
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
1. C2×#14555774C2semidirect
3. #17984829C2semidirect
4. #17984804C2semidirect
5. Dic139⋊C8C2semidirect
6. #17984765C2semidirect
7. #102×C139C2semidirect
55. C139#463semidirect
63. #102D139semidirect