Finite Group Databasebeta

← #44482701

Subgroups — #44482701

Order 30592.

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

normal subgroups only

This group has 106 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#29504954C211yesmaximal, characteristic
2#29504521C211yesmaximal, characteristic, complemented
3#356×C239C211yesmaximal, characteristic, complemented
4#21440008C411yescharacteristic
5#21439991—21no—
6C4⋊(C239⋊C8)—21no—
7#21439888—21no—
8#21439879C411yescharacteristic
9C4⋊Q8×C239C2211yescharacteristic
10#101×C239—21no—
11#16838549—41no—
12#16838548—21no—
13#16838548—41no—
14Q8×D239—41no—
15#16838538—41no—
16#16838535—41no—
17#16838532—21no—
18C2×C239⋊C8—41no—
19C2×Q8×C239C2×C411yescharacteristic
20C2×Q8×C239D411yescharacteristic
21M16×C239—41no—
22C4⋊C4×C239—41no—
23C42×C239D411yescharacteristic
24Dic478—21no—
25Dic478—41no—
26D956—21no—
27D956—41no—
28C22⋊D239—41no—
29C4×D239—41no—
30C4×D239—42no—
31C239⋊C8—41no—
32C239⋊C8—81no—
33Q8×C239—41no—
34Q8×C239—41no—
35C2×C4×C239—21no—
36C2×C4×C239—21no—
37C2×C4×C239—21no—
38C2×C4×C239C22⋊C411yescharacteristic
39C8×C239—81no—
40C22×C239#9911yescharacteristic
41C2×D239—41no—
42C4×C239—21no—
43C4×C239—21no—
44C4×C239—21no—
45C4×C239—41no—
46C4×C239—41no—
47Dic239—41no—
48C2×C239—21no—
49C2×C239AΣL(1,𝔽16)11yescharacteristic
50D239—81no—
51C239#140511yescharacteristic, complemented, Sylow
52#1405—2391nomaximal, Sylow
53#456—2391no—
54#356D23911yescharacteristic, complemented
55#333—2391no—
562−1+4—2391no—
57#137—4781no—
58C4⋊Q8C2×D23911yescharacteristic
59C4⋊C8—4781no—
60#104—4781no—
61#101—21no—
62#101—2391no—
63#41—9561no—
64#41—9561no—
65#41—4781no—
66C2×Q8—9561no—
67C2×Q8C4×D23911yescharacteristic
68C2×Q8C22⋊D23911yescharacteristic
69Q16—9561no—
70SD16—9561no—
71M16—41no—
72M16—4781no—
73C2×C8—9561no—
74C4⋊C4—41no—
75C42D95611yescharacteristic
76Q8—41no—
77Q8—41no—
78Q8—9561no—
79Q8—4781no—
80D4—9561no—
81D4—9561no—
82D4—4781no—
83C2×C4—21no—
84C2×C4—21no—
85C2×C4—21no—
86C2×C4—9561no—
87C2×C4—9562no—
88C2×C4(C2×D239)⋊C411yescharacteristic
89C8—81no—
90C8—19121no—
91C8—9561no—
92C22—9561no—
93C22#2143987411yescharacteristic
94C4—21no—
95C4—21no—
96C4—21no—
97C4—41no—
98C4—41no—
99C4—9561no—
100C2—21no—
101C2—19121no—
102C2#2950455811yescharacteristic
subgroupG/H
centerC2#29504558
commutatorC2×Q8×C239C2×C4
FrattiniC4⋊Q8C2×D239
Fitting#356×C239C2
socleC2×C239AΣL(1,𝔽16)
prime radical#21440008C4
cosocleC4⋊Q8×C239C22
hypercenter#356D239
hypocenterC239#1405
LCSG ▷ C2×Q8×C239 ▷ C2×C4×C239 ▷ C22×C239 ▷ C2×C239 ▷ C239
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C4⋊Q8 ◁ #356

Complements

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

NH ≅ G/Ntype
2. #29504521C2semidirect
3. #356×C239C2semidirect
51. C239#1405semidirect
54. #356D239semidirect

Maximal subgroups

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

subgroupindex
#295049542
#295045212
#356×C2392
#1405239