Finite Group Databasebeta

← #43252939

Subgroups — #43252939

Order 28544.

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

normal subgroups only

This group has 122 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#28383747C211yesmaximal, characteristic
2#28383373C211yesmaximal, characteristic, complemented
3#331×C223C211yesmaximal, characteristic, complemented
4#20297349C411yescharacteristic, complemented
5#20297330—21no—
6#20297232—21no—
7#20297221C411yescharacteristic, complemented
8#20297219—21no—
9#127×C223C2211yescharacteristic
10C4⋊C8×C223—21no—
11#16813170—21no—
12#16813169—41no—
13C2×C22⋊D223—41no—
14D4×D223—41no—
15#16813158—41no—
16#16813155—41no—
17#16813154—21no—
18C22⋊Dic223—41no—
19C2×D4×C223—41no—
20C2×D4×C223C2×C411yescharacteristic
21C2×D4×C223D411yescharacteristic
22C2×C8×C223—41no—
23C42×C223D411yescharacteristic
24C22×D223—41no—
25Dic446—21no—
26D892—21no—
27C22⋊D223—42no—
28C22⋊D223—41no—
29C2×Dic223—41no—
30C2×Dic223—81no—
31C4×D223—41no—
32C223⋊C8—41no—
33C23×C223—21no—
34C23×C223—21no—
35D4×C223—41no—
36D4×C223—41no—
37D4×C223—81no—
38D4×C223—81no—
39C2×C4×C223—21no—
40C2×C4×C223C22⋊C411yescharacteristic
41C8×C223—81no—
42C22×C223—41no—
43C22×C223—41no—
44C22×C223—81no—
45C22×C223—81no—
46C22×C223#9911yescharacteristic
47C2×D223—41no—
48C2×D223—161no—
49C4×C223—21no—
50C4×C223—21no—
51C4×C223—21no—
52Dic223—41no—
53Dic223—161no—
54C2×C223—21no—
55C2×C223—81no—
56C2×C223—81no—
57C2×C223AΣL(1,𝔽16)11yescharacteristic
58D223—81no—
59C223#140211yescharacteristic, complemented, Sylow
60#1402—2231nomaximal, Sylow
61#453—2231no—
62#353—2231no—
63#331D22311yescharacteristic, complemented
64H(5,𝔽2)—2231no—
65AGL(1,ℤ/8)—4461no—
66#127C2×D22311yescharacteristic
67C4⋊C8—21no—
68#104—4461no—
69#100—2231no—
70#99—4461no—
71#41—8921no—
72#41—4461no—
73C2×D4—41no—
74C2×D4—8921no—
75C2×D4—8921no—
76C2×D4C4×D22311yescharacteristic
77C2×D4D89211yescharacteristic
78SD16—8921no—
79D8—8921no—
80M16—4461no—
81C2×C8—41no—
82C22⋊C4—8921no—
83C42C22⋊D22311yescharacteristic
84C23—21no—
85C23—21no—
86C23—8921no—
87Q8—4461no—
88D4—41no—
89D4—41no—
90D4—81no—
91D4—81no—
92D4—8922no—
93D4—8921no—
94D4—4461no—
95C2×C4—21no—
96C2×C4—8921no—
97C2×C4—8921no—
98C2×C4—17841no—
99C2×C4(C2×D223)⋊C411yescharacteristic
100C8—81no—
101C8—8921no—
102C22—41no—
103C22—41no—
104C22—81no—
105C22—81no—
106C22—8921no—
107C22—35681no—
108C22#2029721811yescharacteristic
109C4—21no—
110C4—21no—
111C4—21no—
112C4—8921no—
113C4—35681no—
114C2—21no—
115C2—81no—
116C2—81no—
117C2—17841no—
118C2#2838336811yescharacteristic
subgroupG/H
centerC2#28383368
commutatorC2×D4×C223C2×C4
Frattini#127C2×D223
Fitting#331×C223C2
socleC2×C223AΣL(1,𝔽16)
prime radical#28383747C2
cosocle#127×C223C22
hypercenter#331D223
hypocenterC223#1402
LCSG ▷ C2×D4×C223 ▷ C2×C4×C223 ▷ C22×C223 ▷ C2×C223 ▷ C223
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #127 ◁ #331

Complements

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

NH ≅ G/Ntype
2. #28383373C2semidirect
3. #331×C223C2semidirect
4. #20297349C4semidirect
7. #20297221C4semidirect
59. C223#1402semidirect
63. #331D223semidirect

Maximal subgroups

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

subgroupindex
#283837472
#283833732
#331×C2232
#1402223