Finite Group Databasebeta

← #43252940

Subgroups — #43252940

Order 28544.

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#28383757C211yesmaximal, characteristic
2#28383320C211yesmaximal, characteristic, complemented
3#355×C223C211yesmaximal, characteristic, complemented
4#20297349C411yescharacteristic
5#20297335—21no—
6#20297232—21no—
7#20297221C411yescharacteristic
8#20297215—21no—
9#124×C223C2211yescharacteristic
10#101×C223—21no—
11#16813170—21no—
12#16813169—41no—
13C2×C22⋊D223—41no—
14D4×D223—41no—
15#16813160—41no—
16#16813157—41no—
17#16813154—21no—
18C2×C223⋊C8—41no—
19C2×Q8×C223D411yescharacteristic
20C2×D4×C223C2×C411yescharacteristic
21M16×C223—41no—
22C22⋊C4×C223—41no—
23C42×C223D411yescharacteristic
24C22×D223—41no—
25Dic446—21no—
26D892—21no—
27C22⋊D223—42no—
28C22⋊D223—41no—
29C2×Dic223—41no—
30C4×D223—41no—
31C223⋊C8—41no—
32C223⋊C8—42no—
33C23×C223—21no—
34Q8×C223—41no—
35D4×C223—41no—
36C2×C4×C223—21no—
37C2×C4×C223—21no—
38C2×C4×C223C22⋊C411yescharacteristic
39C8×C223—81no—
40C22×C223—41no—
41C22×C223—81no—
42C22×C223#9911yescharacteristic
43C2×D223—41no—
44C2×D223—161no—
45C4×C223—21no—
46C4×C223—41no—
47C4×C223—41no—
48Dic223—41no—
49C2×C223—21no—
50C2×C223—81no—
51C2×C223AΣL(1,𝔽16)11yescharacteristic
52D223—81no—
53C223#140311yescharacteristic, complemented, Sylow
54#1403—2231nomaximal, Sylow
55#455—2231no—
56#355D22311yescharacteristic, complemented
57#329—2231no—
58H(5,𝔽2)—2231no—
59#137—4461no—
60#124C2×D22311yescharacteristic
61#104—4461no—
62#101—21no—
63#100—2231no—
64#97—4461no—
65#41—8921no—
66#41—4461no—
67C2×Q8C22⋊D22311yescharacteristic
68C2×D4—8921no—
69C2×D4—8921no—
70C2×D4C4×D22311yescharacteristic
71Q16—8921no—
72SD16—8921no—
73M16—41no—
74M16—4461no—
75C2×C8—8921no—
76C22⋊C4—41no—
77C42D89211yescharacteristic
78C23—21no—
79C23—8921no—
80Q8—41no—
81Q8—4461no—
82D4—41no—
83D4—8922no—
84D4—8921no—
85D4—4461no—
86C2×C4—21no—
87C2×C4—21no—
88C2×C4—8921no—
89C2×C4—8921no—
90C2×C4(C2×D223)⋊C411yescharacteristic
91C8—81no—
92C8—8921no—
93C8—8922no—
94C22—41no—
95C22—81no—
96C22—8921no—
97C22—35681no—
98C22#2029721811yescharacteristic
99C4—21no—
100C4—41no—
101C4—41no—
102C4—8921no—
103C2—21no—
104C2—81no—
105C2—17841no—
106C2#2838336611yescharacteristic
subgroupG/H
centerC2#28383366
commutatorC2×D4×C223C2×C4
Frattini#124C2×D223
Fitting#355×C223C2
socleC2×C223AΣL(1,𝔽16)
prime radical#20297349C4
cosocle#124×C223C22
hypercenter#355D223
hypocenterC223#1403
LCSG ▷ C2×D4×C223 ▷ C2×C4×C223 ▷ C22×C223 ▷ C2×C223 ▷ C223
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #124 ◁ #355

Complements

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

NH ≅ G/Ntype
2. #28383320C2semidirect
3. #355×C223C2semidirect
53. C223#1403semidirect
56. #355D223semidirect

Maximal subgroups

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

subgroupindex
#283837572
#283833202
#355×C2232
#1403223