Finite Group Databasebeta

← #22580926

Subgroups — #22580926

Order 8896.

158 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 59 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×#14555785C211yesmaximal, characteristic
2#17984801C211yesmaximal, characteristic, complemented
3#17984756C214yesmaximal, complemented
4#117×C139C211yesmaximal, characteristic, complemented
5#14555785—21no—
6#14555785—21no—
7#14555785—21no—
8#14555785—21no—
9C2×Dic278C411yescharacteristic, complemented
10C2×D556C411yescharacteristic, complemented
11C2×C22⋊D139C2212yes—
12C2×C4×D139C412yescomplemented
13C4⋊Dic139—21no—
14C22⋊Dic139C2212yes—
15C4×Dic139—21no—
16C22×C4×C139C2211yescharacteristic
17C4⋊C4×C139—21no—
18C22⋊C4×C139C2212yes—
19C42×C139—21no—
20C22×D139C2×C412yes—
21Dic278—21no—
22Dic278—21no—
23D556—21no—
24D556—21no—
25C22⋊D139—22no—
26C22⋊D139—22no—
27C2×Dic139—22no—
28C2×Dic139C2×C412yes—
29C4×D139—22no—
30C4×D139—22no—
31C23×C139C2311yescharacteristic
32C2×C4×C139—22no—
33C2×C4×C139C2×C411yescharacteristic
34C2×C4×C139C2×C411yescharacteristic
35C2×C4×C139D411yescharacteristic
36C2×C4×C139D411yescharacteristic
37C2×C4×C139D411yescharacteristic
38C2×C4×C139D411yescharacteristic
39C22×C139—41no—
40C22×C139C22×C411yescharacteristic
41C22×C139C2×D411yescharacteristic
42C22×C139C2×D411yescharacteristic
43C2×D139—22no—
44C2×D139—42no—
45C4×C139—42no—
46C4×C139C22⋊C411yescharacteristic
47C4×C139C22⋊C411yescharacteristic
48C4×C139C22⋊C411yescharacteristic
49C4×C139C22⋊C411yescharacteristic
50Dic139—22no—
51Dic139—42no—
52C2×C139—21no—
53C2×C139—21no—
54C2×C139—21no—
55C2×C139C2×C22⋊C411yescharacteristic
56D139—42no—
57C139#41011yescharacteristic, complemented, Sylow
58#410—1391nomaximal, Sylow
59C2×#41—1391no—
60#117—1391no—
61#117D13911yescharacteristic, complemented
62#99—1394no—
63#41—2781no—
64#41—2781no—
65#41—2781no—
66#41—2781no—
67C2×Q8—1391no—
68C2×D4—1392no—
69C2×D4—1391no—
70C22×C4—1392no—
71C22×C4C2×D13911yescharacteristic
72C4⋊C4—21no—
73C4⋊C4—2781no—
74C22⋊C4—1392no—
75C22⋊C4C2×D13912yes—
76C42—21no—
77C42—2781no—
78C23—1392no—
79C23C22×D13911yescharacteristic
80Q8—2781no—
81Q8—2781no—
82D4—2782no—
83D4—2782no—
84D4—2781no—
85D4—2781no—
86C2×C4—22no—
87C2×C4—2782no—
88C2×C4—2782no—
89C2×C4—2782no—
90C2×C4—1392no—
91C2×C4C4×D13911yescharacteristic
92C2×C4C4×D13911yescharacteristic
93C2×C4C22⋊D13911yescharacteristic
94C2×C4C22⋊D13911yescharacteristic
95C2×C4D55611yescharacteristic
96C2×C4D55611yescharacteristic
97C22—41no—
98C22—2782no—
99C22—5562no—
100C22C2×C4×D13911yescharacteristic
101C22C2×C22⋊D13911yescharacteristic
102C22C2×D55611yescharacteristic
103C4—42no—
104C4—2782no—
105C4—5562no—
106C4(C2×D139)⋊C411yescharacteristic
107C4(C2×D139)⋊C411yescharacteristic
108C4(C2×D139)⋊C411yescharacteristic
109C4(C2×D139)⋊C411yescharacteristic
110C2—21no—
111C2—21no—
112C2—21no—
113C2—5562no—
114C2C2×(C2×D139)⋊C411yescharacteristic
subgroupG/H
centerC4(C2×D139)⋊C4
commutatorC22×C139C22×C4
FrattiniC23C22×D139
Fitting#117×C139C2
socleC2×C139C2×C22⋊C4
hypercenter#117D139
hypocenterC139#410
LCSG ▷ C22×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. #17984801C2semidirect
3. #17984756C2semidirect
4. #117×C139C2semidirect
9. C2×Dic278C4semidirect
10. C2×D556C4semidirect
12. C2×C4×D139C4semidirect
57. C139#410semidirect
61. #117D139semidirect