Finite Group Databasebeta

← #49120554

Subgroups — #49120554

Order 36224.

230 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 49 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#31826855C212yesmaximal, complemented
2#31826831C211yesmaximal, characteristic, complemented
3#31826207C211yesmaximal, characteristic, complemented
4#31826205C212yesmaximal, complemented
5#562×C283C211yesmaximal, characteristic, complemented
6C2×#17985379—22no—
7C2×#17985377—22no—
8#22583607C2211yescharacteristic
9#22583530—22no—
10#22583521C2211yescharacteristic
11#22583521C2212yes—
12#125×C283C2211yescharacteristic
13#124×C283C2212yes—
14#123×C283—22no—
15C22⋊Q8×C283—22no—
16#121×C283—22no—
17C2×D1132—22no—
18C2×D1132—21no—
19#17985379—44no—
20#17985377—44no—
21C2×C283⋊C8—22no—
22C2×C283⋊C8—21no—
23C2×Q8×C283D412yes—
24C2×D4×C283—22no—
25C2×D4×C283D412yes—
26C22×C4×C283—22no—
27C4⋊C4×C283—22no—
28C4⋊C4×C283—22no—
29C4⋊C4×C283D412yes—
30C22⋊C4×C283—22no—
31C22⋊C4×C283—22no—
32C22⋊C4×C283—22no—
33C42×C283C2311yescharacteristic
34C22×D283—41no—
35D1132—42no—
36D1132—42no—
37D1132—42no—
38C283⋊C8—24no—
39C283⋊C8—41no—
40C23×C283—22no—
41Q8×C283—42no—
42D4×C283—42no—
43D4×C283—82no—
44C2×C4×C283—22no—
45C2×C4×C283—22no—
46C2×C4×C283—82no—
47C2×C4×C283C2×D411yescharacteristic
48C2×C4×C283C2×D412yes—
49C22×C283—42no—
50C22×C283—42no—
51C22×C283—42no—
52C22×C283#12011yescharacteristic
53C2×D283—82no—
54C2×D283—81no—
55C4×C283—22no—
56C4×C283—21no—
57C4×C283—42no—
58C4×C283—42no—
59C2×C283—82no—
60C2×C283#45312yes—
61C2×C283#45411yescharacteristic
62D283—161no—
63C283#165611yescharacteristic, complemented, Sylow
64#1656—2831nomaximal, Sylow
65#562D28311yescharacteristic, complemented
66#496—2832no—
67#490—2831no—
68#330—2831no—
69#329—2832no—
70C2×SD16—5662no—
71C2×D8—5662no—
72#127—2831no—
73#125C2×D28311yescharacteristic
74#124C2×D28312yes—
75#123—22no—
76C22⋊Q8—22no—
77#121—22no—
78#102—5662no—
79#97—2831no—
80#97—2832no—
81C2×Q8C22⋊D28312yes—
82C2×D4—22no—
83C2×D4—5661no—
84C2×D4—5662no—
85C2×D4C22⋊D28312yes—
86C22×C4—22no—
87SD16—11324no—
88D8—11324no—
89C2×C8—5662no—
90C2×C8—5661no—
91C4⋊C4—22no—
92C4⋊C4—22no—
93C4⋊C4C22⋊D28312yes—
94C22⋊C4—22no—
95C22⋊C4—22no—
96C22⋊C4—22no—
97C42C22×D28311yescharacteristic
98C23—22no—
99C23—11321no—
100Q8—42no—
101D4—42no—
102D4—82no—
103D4—11322no—
104D4—11322no—
105D4—11322no—
106C2×C4—22no—
107C2×C4—22no—
108C2×C4—82no—
109C2×C4C2×C22⋊D28311yescharacteristic
110C2×C4C2×C22⋊D28312yes—
111C8—5664no—
112C8—11321no—
113C22—42no—
114C22—42no—
115C22—42no—
116C22—22642no—
117C22—22641no—
118C22#2258357911yescharacteristic
119C4—22no—
120C4—21no—
121C4—42no—
122C4—42no—
123C2—82no—
124C2—45281no—
125C2#3182663312yes—
126C2#3182663811yescharacteristic
subgroupG/H
centerC22#22583579
commutator, cosocleC42×C283C23
FrattiniC42C22×D283
Fitting#562×C283C2
socleC22×C283#120
hypercenter#562D283
hypocenterC283#1656
LCSG ▷ C42×C283 ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #562

Complements

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

NH ≅ G/Ntype
1. #31826855C2semidirect
2. #31826831C2semidirect
3. #31826207C2semidirect
4. #31826205C2semidirect
5. #562×C283C2semidirect
63. C283#1656semidirect
65. #562D283semidirect

Maximal subgroups

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

subgroupindex
#318268552
#318268312
#318262072
#318262052
#562×C2832
#1656283