Finite Group Databasebeta

← #31804551

Subgroups — #31804551

Order 17792.

112 conjugacy classes of subgroups; only the 23 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 23 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#22581130C211yesmaximal, characteristic
2#22580693C211yesmaximal, characteristic, complemented
3#355×C139C211yesmaximal, characteristic, complemented
4#17984887C411yescharacteristic
5#17984873—21no—
6#17984770—21no—
7#17984759C411yescharacteristic
8#17984753—21no—
9#124×C139C2211yescharacteristic
10#101×C139—21no—
11#14555785—21no—
12#14555784—41no—
13C2×C22⋊D139—41no—
14D4×D139—41no—
15#14555775—41no—
16#14555772—41no—
17#14555769—21no—
18C2×C139⋊C8—41no—
19C2×Q8×C139D411yescharacteristic
20C2×D4×C139C2×C411yescharacteristic
21M16×C139—41no—
22C22⋊C4×C139—41no—
23C42×C139D411yescharacteristic
24C22×D139—41no—
25Dic278—21no—
26D556—21no—
27C22⋊D139—42no—
28C22⋊D139—41no—
29C2×Dic139—41no—
30C4×D139—41no—
31C139⋊C8—41no—
32C139⋊C8—42no—
33C23×C139—21no—
34Q8×C139—41no—
35D4×C139—41no—
36C2×C4×C139—21no—
37C2×C4×C139—21no—
38C2×C4×C139C22⋊C411yescharacteristic
39C8×C139—81no—
40C22×C139—41no—
41C22×C139—81no—
42C22×C139#9911yescharacteristic
43C2×D139—41no—
44C2×D139—161no—
45C4×C139—21no—
46C4×C139—41no—
47C4×C139—41no—
48Dic139—41no—
49C2×C139—21no—
50C2×C139—81no—
51C2×C139AΣL(1,𝔽16)11yescharacteristic
52D139—81no—
53C139#140311yescharacteristic, complemented, Sylow
54#1403—1391nomaximal, Sylow
55#455—1391no—
56#355D13911yescharacteristic, complemented
57#329—1391no—
58H(5,𝔽2)—1391no—
59#137—2781no—
60#124C2×D13911yescharacteristic
61#104—2781no—
62#101—21no—
63#100—1391no—
64#97—2781no—
65#41—2781no—
66#41—5561no—
67C2×Q8C22⋊D13911yescharacteristic
68C2×D4—5561no—
69C2×D4—5561no—
70C2×D4C4×D13911yescharacteristic
71Q16—5561no—
72SD16—5561no—
73M16—41no—
74M16—2781no—
75C2×C8—5561no—
76C22⋊C4—41no—
77C42D55611yescharacteristic
78C23—21no—
79C23—5561no—
80Q8—41no—
81Q8—2781no—
82D4—41no—
83D4—2781no—
84D4—5562no—
85D4—5561no—
86C2×C4—21no—
87C2×C4—21no—
88C2×C4—5561no—
89C2×C4—5561no—
90C2×C4(C2×D139)⋊C411yescharacteristic
91C8—81no—
92C8—5561no—
93C8—5562no—
94C22—41no—
95C22—81no—
96C22—5561no—
97C22—22241no—
98C22#1798475611yescharacteristic
99C4—21no—
100C4—41no—
101C4—41no—
102C4—5561no—
103C2—21no—
104C2—81no—
105C2—11121no—
106C2#2258073911yescharacteristic
subgroupG/H
centerC2#22580739
commutatorC2×D4×C139C2×C4
Frattini#124C2×D139
Fitting#355×C139C2
socleC2×C139AΣL(1,𝔽16)
prime radical#17984887C4
cosocle#124×C139C22
hypercenter#355D139
hypocenterC139#1403
LCSG ▷ C2×D4×C139 ▷ C2×C4×C139 ▷ C22×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #124 ◁ #355

Complements

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

NH ≅ G/Ntype
2. #22580693C2semidirect
3. #355×C139C2semidirect
53. C139#1403semidirect
56. #355D139semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#225811302
#225806932
#355×C1392
#1403139