Finite Group Databasebeta

← #49120407

Subgroups — #49120407

Order 36224.

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

normal subgroups only

This group has 218 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#31827181C211yesmaximal, characteristic
2#31826844C211yesmaximal, characteristic, complemented
3#31826756C212yesmaximal, complemented
4#31826192C212yesmaximal, complemented
5#333×C283C211yesmaximal, characteristic, complemented
6C2×#17985382—22no—
7#22583610C2211yescharacteristic
8#22583599—22no—
9#22583585—22no—
10C4×D1132C2212yes—
11#22583568—22no—
12#22583542—22no—
13#22583532—22no—
14C4×C283⋊C8C2211yescharacteristic
15C4⋊Q8×C283C2211yescharacteristic
16C4⋊C8×C283C2212yes—
17C2×Dic566—21no—
18C2×D1132—22no—
19C2×D1132D412yes—
20C2×C4×D283—22no—
21#17985382—44no—
22C2×C283⋊C8—21no—
23C4⋊Dic283—22no—
24C4⋊Dic283D412yes—
25(C2×D283)⋊C4—24no—
26(C2×D283)⋊C4—22no—
27C4×Dic283—22no—
28C2×Q8×C283D412yes—
29C2×C8×C283—22no—
30C4⋊C4×C283—22no—
31C42×C283C2311yescharacteristic
32C22×D283—22no—
33Dic566—42no—
34D1132—22no—
35D1132—22no—
36D1132—82no—
37C2×Dic283—22no—
38C2×Dic283—41no—
39C4×D283—42no—
40C4×D283—42no—
41C283⋊C8—22no—
42Q8×C283—42no—
43C2×C4×C283—22no—
44C2×C4×C283C2×D412yes—
45C2×C4×C283C2×D411yescharacteristic
46C8×C283—42no—
47C22×C283#12011yescharacteristic
48C2×D283—42no—
49C2×D283—42no—
50C2×D283—42no—
51C4×C283—21no—
52C4×C283—42no—
53C4×C283#13512yes—
54C4×C283#13712yes—
55Dic283—42no—
56Dic283—81no—
57C2×C283#45212yes—
58C2×C283#45311yescharacteristic
59D283—82no—
60C283#163411yescharacteristic, complemented, Sylow
61#1634—2831nomaximal, Sylow
62#555—2831no—
63#494—2831no—
64#476—2832no—
65#333D28311yescharacteristic, complemented
66D4⋊C8—2832no—
67C2×Q16—5662no—
68C4⋊Q8—2831no—
69C4⋊Q8C2×D28311yescharacteristic
70#124—5662no—
71#121—5662no—
72C4×D4—2832no—
73#117—5662no—
74#106—5662no—
75C4⋊C8C2×D28312yes—
76#102—5662no—
77C4×C8—2831no—
78C2×Q8—5661no—
79C2×Q8D113212yes—
80C2×D4—2832no—
81C2×D4—5662no—
82C22×C4—5662no—
83Q16—11324no—
84C2×C8—22no—
85C2×C8—5661no—
86C4⋊C4—22no—
87C4⋊C4—2832no—
88C4⋊C4—5662no—
89C22⋊C4—5664no—
90C22⋊C4—5662no—
91C42—5662no—
92C42C22×D28311yescharacteristic
93C23—5662no—
94Q8—42no—
95Q8—11322no—
96D4—5662no—
97D4—5662no—
98D4—22642no—
99C2×C4—22no—
100C2×C4—5662no—
101C2×C4—11322no—
102C2×C4—11322no—
103C2×C4—11321no—
104C2×C4D4×D28312yes—
105C2×C4C2×D113211yescharacteristic
106C8—42no—
107C8—5662no—
108C22—11322no—
109C22—11322no—
110C22—11322no—
111C22#2258358011yescharacteristic
112C4—21no—
113C4—42no—
114C4—11322no—
115C4—22641no—
116C4#2258363112yes—
117C4#2258364212yes—
118C2—22642no—
119C2#3182663012yes—
120C2#3182663511yescharacteristic
subgroupG/H
centerC22#22583580
commutator, cosocleC42×C283C23
FrattiniC42C22×D283
Fitting#333×C283C2
socleC22×C283#120
prime radical#31827181C2
hypercenter#333D283
hypocenterC283#1634
LCSG ▷ C42×C283 ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
2. #31826844C2semidirect
3. #31826756C2semidirect
4. #31826192C2semidirect
5. #333×C283C2semidirect
60. C283#1634semidirect
65. #333D283semidirect

Maximal subgroups

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

subgroupindex
#318271812
#318268442
#318267562
#318261922
#333×C2832
#1634283