Finite Group Databasebeta

← #49123157

Subgroups — #49123157

Order 36224.

154 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 154 conjugacy classes of subgroups — too many to draw. Only its 53 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#31826901C211yesmaximal, characteristic
2#31826588C211yesmaximal, characteristic, complemented
3#31826287C211yesmaximal, characteristic, complemented
4#31826278C211yesmaximal, characteristic, complemented
5#31826274C211yesmaximal, characteristic, complemented
6#31826243C211yesmaximal, characteristic, complemented
7#442×C283C211yesmaximal, characteristic, complemented
8#22583632C2211yescharacteristic
9#22583616—21no—
10#22583554C412yescomplemented
11#22583551C412yescomplemented
12#22583550C2211yescharacteristic
13#22583550C2211yescharacteristic
14#22583546C2211yescharacteristic
15#22583538—21no—
16C2×D8×C283C2211yescharacteristic
17C4×D4×C283—21no—
18#106×C283C2211yescharacteristic
19#102×C283—21no—
20#97×C283C2211yescharacteristic
21#17985392—21no—
22Dic1132C2×C411yescharacteristic, complemented
23#17985381—21no—
24D2264C2×C411yescharacteristic, complemented
25#17985376—21no—
26#17985375—41no—
27C8×D283—41no—
28C283⋊C16—21no—
29C283⋊C16C2×C412yescomplemented
30C2×D4×C283—21no—
31C22×C4×C283—41no—
32D8×C283—21no—
33D8×C283C2×C412yes—
34C2×C8×C283D411yescharacteristic
35C2×C8×C283C2311yescharacteristic
36C4⋊C4×C283—21no—
37C22⋊C4×C283—41no—
38C42×C283D411yescharacteristic
39Dic566—21no—
40D1132—21no—
41C22⋊D283—41no—
42C4×D283—41no—
43C283⋊C8—41no—
44C23×C283—41no—
45D4×C283—22no—
46D4×C283—41no—
47C2×C4×C283—21no—
48C2×C4×C283—41no—
49C2×C4×C283—82no—
50C2×C4×C283C2×D411yescharacteristic
51C8×C283—21no—
52C8×C283C22×C411yescharacteristic
53C8×C283#4111yescharacteristic
54C22×C283—42no—
55C22×C283—81no—
56C22×C283—81no—
57C22×C283AGL(1,ℤ/8)11yescharacteristic
58C2×D283—41no—
59C4×C283—41no—
60C4×C283—81no—
61C4×C283C4×D411yescharacteristic
62C4×C283AGL(1,ℤ/8)11yescharacteristic
63Dic283—41no—
64C2×C283—21no—
65C2×C283—82no—
66C2×C283#44211yescharacteristic
67D283—81no—
68C283AGL(1,ℤ/16)11yescharacteristic, complemented, Sylow
69AGL(1,ℤ/16)—2831nomaximal, Sylow
70#509—2831no—
71#444—2831no—
72#442D28311yescharacteristic, complemented
73#365—2831no—
74#361—2831no—
75#360—2831no—
76#347—2831no—
77#135—2831no—
78C2×D8C2×D28311yescharacteristic
79#131—5661no—
80C4×D4—21no—
81SD32—2832no—
82D16—2832no—
83M32—2831no—
84M32—2831no—
85#108—2831no—
86#106C2×D28311yescharacteristic
87#104—5661no—
88#102—21no—
89#97C2×D28311yescharacteristic
90#41—5661no—
91C2×D4—21no—
92C22×C4—41no—
93Q16—2831no—
94SD16—5661no—
95D8—21no—
96D8—2831no—
97D8C4×D28312yes—
98M16—5661no—
99M16—11321no—
100C2×C8—11321no—
101C2×C8C22⋊D28311yescharacteristic
102C2×C8C22×D28311yescharacteristic
103C4⋊C4—21no—
104C22⋊C4—41no—
105C42C22⋊D28311yescharacteristic
106C16—2832no—
107C16—5661no—
108C23—41no—
109Q8—5661no—
110D4—22no—
111D4—41no—
112D4—5661no—
113D4—11321no—
114C2×C4—21no—
115C2×C4—41no—
116C2×C4—82no—
117C2×C4—11321no—
118C2×C4C2×C22⋊D28311yescharacteristic
119C8—21no—
120C8—11321no—
121C8C2×C4×D28311yescharacteristic
122C8#1798539211yescharacteristic
123C22—42no—
124C22—81no—
125C22—81no—
126C22—11321no—
127C22#2258363611yescharacteristic
128C4—41no—
129C4—81no—
130C4—11321no—
131C4C4×C22⋊D28311yescharacteristic
132C4#2258363511yescharacteristic
133C2—21no—
134C2—82no—
135C2—22641no—
136C2#3182657511yescharacteristic
subgroupG/H
centerC2#31826575
commutatorC8×C283C22×C4
FrattiniC2×C8C22×D283
Fitting#442×C283C2
socleC2×C283#442
prime radical#31826901C2
cosocleC2×C8×C283C23
hypercenter#442D283
hypocenterC283AGL(1,ℤ/16)
LCSG ▷ C8×C283 ▷ C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2 ◁ C2×C4 ◁ #97 ◁ #442

Complements

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

NH ≅ G/Ntype
2. #31826588C2semidirect
3. #31826287C2semidirect
4. #31826278C2semidirect
5. #31826274C2semidirect
6. #31826243C2semidirect
7. #442×C283C2semidirect
10. #22583554C4semidirect
11. #22583551C4semidirect
22. Dic1132C2×C4semidirect
24. D2264C2×C4semidirect
29. C283⋊C16C2×C4semidirect
68. C283AGL(1,ℤ/16)semidirect
72. #442D283semidirect

Maximal subgroups

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

subgroupindex
#318269012
#318265882
#318262872
#318262782
#318262742
#318262432
#442×C2832
AGL(1,ℤ/16)283